X-ray Rocking Curve and Ferromagnetic Re

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X-ray Rocking Curve and Ferromagnetic Resonance Investigations of Ion-Implanted Crystals
Citation
Speriosu, Virgil Simon
(1983)
X-ray Rocking Curve and Ferromagnetic Resonance Investigations of Ion-Implanted Crystals.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/BET3-1831.
Abstract
A kinematical model for general Bragg case x-ray diffraction in nonuniform films is presented. The model incorporates depth-dependent strain and structure factor. For ion-implanted crystals the change in structure factor attributed to damage is calculated using a spherically symmetric Gaussian distribution of incoherent atomic displacements. Profiles of strain and structure factor are obtained by fitting experimental rocking curves. The method is applicable to ion-implanted, diffused and multilayer crystalline structures such as heterojunctions and superlattices.
A comparison is made between profiles of strain and incoherent atomic displacements obtained from rocking curves and from Rutherford backscattering spectrometry in a Gd
Ga
12
crystal implanted with 100 keV Ne
. The ranges of sensitivity of the two techniques-overlap for about one decade in implantation dose up to the amorphous threshold. Xray diffraction was found to be most sensitive to low damage levels while backscattering was found to be most sensitive to high damage levels. The two techniques are in excellent agreement on the near-surface strain, but differ significantly at depths below ≃ 500A. The discrepancy is attributed to errors caused by steering of channelled particles in backscattering spectrometry. The profiles of number of displaced atoms agree within a factor of two.
The rocking curve method is combined with analysis of ferromagnetic resonance (FMR) spectra for characterization of crystalline and magnetic properties of [111]-oriented Gd,Tm,Ga:YIG films implanted with Ne
, He
, and H
. For each implanted species the range of doses begins with easily-analyzed effects and ends with paramagnetism or amorphousness. Profiles of normal strain, lateral strain and damage were obtained. For maximum strains up to 1.3% the behavior of the strain with annealing is nearly independent of implanted species or dose. Magnetic profiles obtained before and after annealing were compared with the strain profiles. The local change in uniaxial anisotropy field ΔH
with increasing strain shows an initially linear rise for both He
and Ne
, in quantitative agreement with the magnetostriction effect estimated from the composition. For strain values between 1% and 1.5%, ΔH
saturates and for increasing strain, ΔH
decreases to nearly zero when the material becomes paramagnetic. For peak strains greater than 1.3% for He
and 1.1% for Ne
the relation between uniaxial anisotropy and strain is not unique. Behavior of the saturation magnetization 4πM, the exchange constant A and the cubic anisotropy H
was elucidated. For H
implantation the total ΔH
consists of a magnetostrictive contribution due to strain and of a comparable excess contribution associated with the local concentration of hydrogen. The profile of excess ΔH
agrees with calculated LSS range. The presence of hydrogen results in a reduction of 4πM not attributable to strain or damage. With increasing annealing temperature the excess ΔH
diminishes and above 400°C the only component of ΔH
is magnetostrictive.
Crystalline properties of Si-implanted [100] GaAs, Si, and Ge were studied by the rocking curve method. Sharp qualitative and quantitative differences were found between the damage in GaAs on one hand and Si and Ge on the other. At a moderate damage level the GaAs crystal undergoes a transition from elastic to plastic behavior. The plastically deformed region presents a barrier to epitaxial regrowth and is consistent with the well-known high defect density in regrown GaAs.
Item Type:
Thesis (Dissertation (Ph.D.))
Subject Keywords:
(Applied Physics) ; X-ray diffraction; rocking curve; double-crystal; curve fitting; thin films; garnet; magnetic; kinematical diffraction theory; ion implantion; gadolinium gallium garnet; magnetic garnet; single crystal; strain; damage; yttrium iron garnet; annealing; liquid phase epitaxy; GaAs; Si; Ge; Ne+; He+; H+; ferromagnetic resonance; FMR; X-band; magnetostriction; uniaxial anisotropy; magnetization exchange constant; gyromagnetic ratio; paramagnetic; cubic anisotropy; plastic deformation
Degree Grantor:
California Institute of Technology
Division:
Engineering and Applied Science
Major Option:
Applied Physics
Thesis Availability:
Public (worldwide access)
Research Advisor(s):
Wilts, Charles H.
Thesis Committee:
Goddard, William A., III (chair)
Johnson, William Lewis
Vreeland, Thad
Wilts, Charles H.
Nicolet, Marc-Aurele
Defense Date:
1 January 1983
Record Number:
CaltechETD:etd-10072002-110622
Persistent URL:
DOI:
10.7907/BET3-1831
Related URLs:
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URL Type
Description
DOI
Article adapted for Chapter II.
DOI
Article adapted for Chapter III.
DOI
Article adapted for Chapter IV.
DOI
Article adapted for Chapter V.
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07 Oct 2002
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07 Aug 2025 20:24
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X-RAY ROCKING CURVE AND FERROMAGNETIC RESONANCE

INVESTIGATIONS OF ION-IMPLANTED CRYSTALS

Thesis by

Virgil S. Speriosu

In Partial Fulfillment of the Requirements
for the Degree of

Doctor of Philosophy

California Institute of Technology
Pasadena, California

1983

(Submitted January , 1983)

Considerate la vostra semenza:
Fatti non foste a viver come bruti,
Ma per seguir virtude e conoscenza.

Dante

iil

Acknowledgements

During my two and a half years of apprenticeship with
Chuck Wilts, he has taught me some things that go beyond the
details of magnetism. Simply by watching him I have learned
the usefulness of the following attitudes. First, make sure
you have done your experiment correctly. Second, have the
honesty to accept what it says, no matter how weird it may
sound at first. Third, have faith that there is an explanation

and do not easily give up looking for it.

I thank Tom Kobayashi for introducing me to ion implantation
in garnet and for trusting in me at a time when few others
were willing to go that far. Howard Glass taught me much of
what I know of x-ray diffraction. He and Lavada Moudy are
largely responsible for the easy access I have had to one of
Rockwell International's laboratories. I thank Chris Bajorek
of the International Business Machines Corporation for
cousidering me worthy of a predoctoral fellowship, and I
thank Bob Scranton for its renewal. Tim Gallagher, Kochan
Ju and H. Ben Hu of IBM supplied the samples for and encouraged
a large part of this thesis. Jim Campbell suggested the use

of and provided us with an HP 9826 computer.

I thank Professor M-A. Nicolet for his interest in the
x-ray rocking curve method, for encouraging its application

to semiconductors, and for pointing out the most promising

area for this application. The expertise of Bruce Paine and
Leszek Wielunski in ion implantation and Rutherford back-
scattering has added considerably to this thesis. Joyce
Lidell and Michell Parks have typed the papers presented

here. My wife Michelle did little typing but much encouraging.

Finally, I thank my parents. As far as I am concerned,

it all started with them.

Abstract

A kinematical model for general Bragg case x-ray diffrac-
tion in nonuniform films is presented. The model incorporates
depth-dependent strain and structure factor. For ion-
implanted crystals the change in structure factor attributed
to damage is calculated using a spherically symmetric Gaussian
distribution of incoherent atomic displacements. Profiles
of strain and structure factor are obtained by fitting
experimental rocking curves. The method is applicable to
ion-implanted, diffused and multilayer crysLalline structures

such as heterojunctions and superlattices.

A comparison is made between profiles of strain and
incoherent atomic displacements obtained from rocking curves
and from Rutherford backscattering spectrometry in a Gd..Ga,0,,
crystal implanted with 100 kev Net. The ranges of sensitivity
of the two techniques: overlap for about one decade in implanta-
tion dose up to the amorphous threshold. X-ray diffraction
was found to be most sensitive to low damage levels while
backscattering was found to be most sensitive to high damage
levels. The two techniques are in excellent agreement on
the near-surface strain, but differ significantly at depths
helow «500A. The discrepancy is attributed to errors caused
by steering of channelled particles in backscattering spec-
trometry. The profiles of number of displaced atoms. agree

within a factor of two.

The rocking curve method is combined with analysis of
ferromagnetic resonance (FMR) spectra for characterization
of crystalline and magnetic properties of [111]-oriented
Gd,Tm,Ga:YIG films implanted with Net, Het, and Ho". For
each implanted species the range of doses begins with easily-
analyzed effects and ends with paramagnetism or amorphous-
ness. Profiles of normal strain, lateral strain and damage
were obtained. For maximum strains up to 1.3% the behavior
of the strain with annealing is nearly independent of implanted
species or dose. Magnetic profiles obtained before and
after annealing were compared with the strain profiles. The
local change in uniaxial anisotropy field AH, with increasing
strain shows an initially linear rise for both He* and Ne’,
in quantitative agreement with the magnetostriction effect
estimated from the composition. For strain values between
1% and 1.5%, AH, saturates and for increasing strain, AH,
decreases to nearly zero when the material becomes paramagnetic.
For peak strains greater than 1.3% for He* and 1.1% for Ne*
the relation between uniaxial anisotropy and strain is not
unique. Behavior of the saturation magnetization 4M, the
exchange constant A and the cubic anisotropy Hy was elucidated.
For Ho* implantation the total AH, consists of a magneto-
strictive contribution due to strain and of a comparable
excess contribution associated with the local concentration
of hydrogen. The profile of excess AH, agrees with calculated
LSS range. The presence of hydrogen results in a ceduction

of 41M not attributable to strain or damage. With increasing

vii

annealing Lemperature the excess AH, diminishes and above

400°C the only component of AH, is magnetostrictive.

Crystalline properties of Si-implanted [100] GaAs, Si,
and Ge were studied by the rocking curve method. Sharp
qualitative and quantitative differences were found between
the damage in GaAs on one hand and Si and Ge on the other.

At a moderate damage level the GaAs crystal undergoes a
transition from elastic to plastic behavior. The plastically
deformed region presents a barrier to epitaxial regrowth and
is consistent with the well-known high defect density in

regrown GaAs.

Chapter

IIT:

VI:

viii

Table of Contents

Page

Introduction wcccccccccescvcserseceeesevsce 1

Kinematical x-ray diffraction in

nonuniform crystalline films ............. 10

Comparison of kinematical x-ray
diffraction and backscattering

spectrometry @eeeseeeoeesevstveseovoeeeevee eee eevee ec eee 24
X-ray rocking curve and ferromagnetic
resonance investigations of ion-implanted

MAGNETIC GaAITNEt cece sccesvevsscevvesessse Be

X-ray rocking curve study of Si-implanted

GaAs, Si and Ge eserves ereerevoenervnesaenecece ec eaneee 90

Conclusion ..ccccwcceccccccesecccecesscees G4

Chapter I

Introduction

The contents of this thesis are addressed to specialists
in x-ray diffraction and ferromagnetic resonance, especially
as the latter may be applied to the study of ion-implanted
crystals. Some of the results are of immediate interest to
manufacturers of devices using magnetic garnet as host
Material. There is no need to include an introductory
description of garnets, semiconductors, magnetism, ion
implantation, x-ray diffraction or ferromagnetic resonance
Since these are well treated in textbooks and the references
cited in the following chapters. Instead this will present
my Own modest contributions to these areas. As will be
evident in the following chapters, I am the sole author of
only one of the papers. I have the pleasure to acknowledge
again the active participation of my advisor, Professor C.H.
Wilts, and of other collaborators whose efforts made this

thesis possible.

The most important development presented here is in the
area of x-ray diffraction in monocrystals with properties
that may vary with depth. The double-crystal, Bragg case,
rocking curve method is well suited for measuring the structural
properties of such crystals. In this method a beam of x-rays
is collimated, partially polarized and rendered nearly mono-

chromatic by diffraction in a stationary first crystal. The

beam then impinges on the crystal to be studied and following
diffraction emerges at the same surface. This distinguishes
the Bragg case from the Laue case where the diffracted beam
exits through a different surface. The sample crystal is
rotated finely about the Bragg condition while the diffracted
intensity is measured. The diffracted intensity normalized
to that of the incident beam is the reflecting power; the
reflecting power vs. angle is the rocking curve. For thick,
nearly perfect crystals one must consider the multiplicity

of scattering of x-rays before they emerge from the crystal.
This has been successfully treated by the dynamical theory.

In nearly perfect crystals whose properties nevertheless

vary with depth, the dynamical calculation is rather complicated.
My contribution consists of the realization that for most
monocrystals of technological importance the agiffraction of
x-rays is described with sufficient accuracy by the kinematical
(single-scattering) theory. The mathematical simplicity of
this theory (see Chapter II) has enabled me to use the
rocking curve method more extensively than anyone else for

the study of ion-implanted crystals. The displacements of
target atoms due to interactions with the ion beam are
separable into coherent and incoherent components. The
coherent component is a deformation of the unit cell (strain),
while the incoherent component (damage) changes the value of
the structure factor. In ion-implanted crystals the strain
and damage vary with depth, producing an oscillatory rocking

curve whose angular extent is typically about one degree.

For thick perfect crystals the range of nonzero reflecting

power is measured in arcseconds. By using a computer to fit
experimental rocking curves I have obtained strain and

damage profiles for various crystals implanted with a range

of species, energies, and doses. Chapter II gives the derivation
ef the equations used in the calculation and several cxamples

of the method applied to ion-implanted garnets. The chapter

is unchanged from its published form and suffers from inadequate
treatment of the relation between damage and strain. For

the helium implantations studied in this chapter the damage

is too low for an accurale delexrminalion of its profile, and
hence the linearity between damage and strain is overstated.
This matter was treated more carefully in subsequent work
reported in Chapter IV, where the linearity between damage

and strain was established more strongly through use of more

highly damaged crystals.

In addition to ion-implanted monocrystals, the rocking
curve method and the kinematical interpretation of the
rocking curve are applicable to the characterization of
crystals modified by diffusion and to epitaxial multilayer
structures such as heterojunctions and superlattices.
Although such applications are not described in detail an
example is included in which the strain profile was determined
in order to match the published experimental rocking curve
of such a structure. The authors of that paper, being

unaware of the power of this method, did not attempt a

detailed interpretation of their data.

Until now Rutherford backscattering spectrometry has |
been the most frequently used tool for measuring damage in
ion-implanted crystals. In perfect crystals for certain
directions of incidence (channels) a well-collimated beam of
high-energy « particles or protons can penetrate to several
microns with very little deflection or backscattering. Ina
damaged crystal a fraction of the beam is backscattered.

The backscattering yield is a measure of crystalline quality.
This method has several advantages; it is nearly non-
destructive, is experimentally easy and interpretation of
experimental data is relatively straightforward. These
advantages of Rutherford backscattering are shared by the x-
ray rocking curve method, which is even more nearly non-
destructive. In addition, the apparatus needed for x-ray
measurements is much simpler than Van der Graaf or other
accelerators and it is not necessary to do diffraction in
vacuum. However, backscattering has gained wide acceptance
while the rocking curve method is relatively unknown as a
tool for measuring damage in implanted crystals. A comparison
of the two methods in terms of sensitivity and richness of

information might remedy this situation.

Such a comparison is made in Chapter III for a Gd3Ga501>
crystal implanted with neon ions with a dose range of one

decade, the highest dose being sufficient to render the

crystal amorphous. The choice of this crystal was made
because of the initial uncertainty concerning the overlap of
the ranges of sensitivity for the two methods. It is now
Clear (Chapter V) that other crystals (Si, Ge, GaAs, InP,
YIG, etc.) would have served as well, if not better. The
comparison is made of the strain and damage profiles deter-
mined by the two techniques. For strain the x-ray method is
superior in accuracy and detail; in fact the strain measured
by backscattering is accurate only at the surface. For
damage they are not easily compared because they measure
different things: backscattering probes direct space while
x-ray diffraction probes reciprocal space. Uncertainties in
the radial distribution of the channelled beam and in the
scattering potential introduce uncertainties in the number
of displaced atoms deduced from backscattering yield. In x-
vray diffraction a particular distribution of atomic displace-
ments must at first be assumed in order to calculate the
structure factor. Comparison of calculated and measured
Magnitudes of the structure factor then provides moments of
the distribution of displacements. Thus the comparison of
the numbers of displaced atoms obtained from backscattering
yield and rocking curve requires that a number of reasonable
assumptions be made. With such assumptions the two measures
of damage agree within a factor of two, which suggests that
both measures are in fact related to the real damage of the

crystal.

A major portion of my thesis (Chapter IV) is concerned
with magnetic properties of implanted garnet. These properties
are the saturation magnetization 47M, the exchange stiffness
A, the uniaxial and cubic anisotropies H, and Hj, the gyro-
magnetic ratio y, and the damping parameter a. All of these
parameters are phenomenological, with meanings derived
either directly from measurement or from their use in the
Landau-Lifshitz equation. Despite their phenomenological
nature, these parameters are essential for predicting the
behavior of implanted systems such as bubble memories,
filters or delay lines, and a comparison or correlation with
Strain and damage is significant. This provides information
about the relative importance of dopant chemistry compared

to strain and damage in the implanted lattice.

Magnetic properties of implanted garnets have been
studied by several techniques, of which ferromagnetic
resonance (FMR) is the most promising. The FMR spectra of
such crystals can be very rich, with absorption peaks of
varying amplitudes and occuring in a range of several thousand
oersteds of applied magnetic field. For a given implanted
' element with increasing dose the number of detectable absorption
peaks at first increases from one (virgin material) to a
maximum of 10 or 15, and finally decreases to 5 or less.

The amplitudes and locations of these peaks vary in a complex
fashion with dose. The FMR spectrum is interpreted in terms

of magnetic excitations called spinwaves whose local wave

equation is the linearized Landau-Lifshitz equation expanded
to include the exchange interaction. The solutions of this
eigenvalue equation provide mode amplitudes and values of
applied field for resonance. If magnetic properties vary
with depth in an arbitrary way, the equation becomes complicated
and its solutions cannot be written in terms of the known
closed-form functions. C.H. Wilts has recently developed a
numerical method for calculating the spinwave spectrum of a
material with depth-dependent properties. By matching
calculated and experimental spectra, profiles of magnetic
parameters can be obtained. Wilts has done this for low

dose cases where the profiles are unimodal and the corres-
ponding spectra are relatively easily interpreted. I have
used this method to obtain magnetic properties at high

damage levels, where the interpretation of the spectra is
difficult. The solution of this problem was greatly facilitated
by comparing the magnetic structure with the strain profiles
obtained from x-ray diffraction. The detailed behavior of
magnetic and crystalline properties with dose and annealing
for neon, helium and hydrogen implantation is presented in
Chapter IV. Without repeating this information, I can state
here that many of the basic features of implanted garnet, as
determined by combining x-ray and FMR techniques, are substan-
tially different from the picture obtained with the less

accurate methods used earlier.

It is well known that implantation and annealing conditions
for optimum recrystallization and electrical characteristics
of highly damaged ("amorphous") GaAs must be different from
those used for Si and Ge. The prevailing explanation for
the difference has been the loss of stoichiometry in GaAs
due to differences in ion energy transfer to Ga versus As.
According to this view the deep portion of the layer is Ga-
enriched while the outer portion is As-enriched. However
the difference seems too small to be the plausible source of
poor regrowth. Other features, such as the insensitivity of
the regrowth to implanted species and the initial high-
quality regrowth at the interface with unimplanted material,
have not been explained. Rutherford backscattering measure-
ments. have not shown any qualitative difference between the
damage in GaAs on one hand and Si or Ge on the other. In
Chapter V the rocking curve method is applied to Si-implanted
GaAs, Si and Ge. Although the study is very brief, it is
sufficient to show that with increasing dose the evolution
of strain and damage in GaAs is qualitatively different from
that in Si or Ge. The difference implies a different structure
of the implanted layer in GaAs vs. Si or Ge. In GaAs the
highly damaged outer region and the little damaged inner
region are separated by a layer containing extended defects.
The existence of this layer depends on the local strain
regardless of the implanted species. The layer presents a
barrier to epitaxial regrowth and is consistent with the

observation of high defect density in regrown GaAs films.

Chapter II

Kinematical x-ray diffraction in nonuniform crystalline films

An expression for the reflecting powcr of nonuniform crystals
is derived from the perfect crystal dynamical theory. Profiles
of strain and damage in ion-implanted garnets and in an
epitaxial multilayer structure are obtained by fitting

experimental rocking curves.

“Kinematical x-ray diffraction in nonuniform crystalline fi films: Strain and
damage distributions in lon-implanted garnets

V.S. Speriosu® -

California Institute of Technology, Pasadena, California 91125
' {Received 23 March 1981; accepted for publication 22 June 1981)

A kinematical model for general Bragg case x-ray diffraction in nonuniform films is presented.
The model incorporates depth-dependent strain and spherically symmetric Gaussian distribution
of randomly displaced atoms. The model is applicable to ion-implanted, diffused, and other single
erystals. Layer thickness is arbitrary, provided maximum reflecting power is less than ~ 6%.
Strain and random displacement (damage) distributions in He* -implanted Gd, Tm, Ga: YIG, and
Net-implanted Gd,Ga,O,, are obtained by fitting the model to experimental rocking curves. In
the former crystal the layer thickness was 0.89 um with strain varying between 0.09 and 0.91%. In
the latter crystal a wide range of strain and damage was obtained using successively higher doses.
In each case layer thickness was 1900 A, with 2.49% strain corresponding to 0.40-A standard
deviation of random displacements. The strain distributions were strictly linear with dose. The
same, Closely linear relationship between damage and implantation-induced strain was

determined for both crystals.
PACS numbers: 61.10. — i, 61.70. — r, 61.70.Tm

I. INTRODUCTION

Bragg case x-ray diffraction is a well-established meth-
od for characterizing crystalline properties of films obtained
by various growth techniques. The diffracted intensity pro-
files (rocking curves) are highly sensitive to depth-dependent
strain and damage distributions as well as lateral variations,
but much of the information available in the rocking curves
is generally not extracted. Part of the difficulty is due to lack
of phase detection, which precludes direct inversion of the
rocking curve. The remaining difficulty is the complexity of
the dynamical theory of diffraction in nonuniform crys-
tals.'~? At the cost of long computation time, strain profiles
in diffused** and ion-implanted’ layers were obtained by
fitting dynamical theory calculations to saperimental rock-
ing curves.

The kinematical theory for symmetric reflections,®
which involves much simpler mathematics, has offered a
considerable reduction in computation time. The applica-
tion? of the Patterson series'® to this theory yielded param-
eters such as mean strain, damage, and layer thickness. In
another approach, detailed strain and damage distributions
were obtained by fitting a kinematical theory model to rock-
ing curves of successively etched samples.'!!? However,
both approaches were limited to symmetric reflections
which provide a limited amount of information.

In this paper a general Bragg case kinematical expres-
sion for the reflecting power of nonuniform films is abtained
from the uniform single-crystal dynamical theory.'* Depth-
dependent strain distributions are represented by a set of
independently but coherently diffracting laminae oriented
parallel to the surface. Each lamina incorporates many unit
cells and has uniform strain. In addition to coherent atomic
displacements, random displacements (damage) are treated
through their effect on the mean structure factor in each

"BM predoctoral fellow.

6094 J. Appl. Phys. 52(10), October 1981

0021-8979/81/106094-10$01.10

lamina. The range of validity of the kincmatical approxima-
tion is shown to include most cases of technological impor-
tance. The relative sensitivity to strain, damage, and layer
thickness is demonstrated. Using this model. strain and
damage distributions are obtained by fitting rocking curves
of Het -implanted Gd, Tm, Ga: YIG, and Ne* -implanted
gadolinium gallium garnet (GGG). In the former crystal
three different strain and damage distributions were created
by single and multiple implantations. Rocking curves of
symmetric and asymmetric reflections were fitted. The latter
crystal was implanted with single doses resulting in a wide
range of strain and damage. Symmetric reflection rocking
curves corresponding to each dose were fitted.

Il. THE KINEMATICAL MODEL

The plane-wave dynamical theory'* predicts that for
unit electric-field amplitude incident on the surface of an
isolated, uniform, nonabsorbing, single-crystal plate, the dif-

fracted amplitude at the same surface is

Ey =e7 OM + Balt, (1)

Dy =i Fa yp
oF al

x sin [4 (¥? — 1)'/2]
(Y? — 1)"? cos [A(¥? —

1/2] 4 iY sin [4 (Y? — 1)'7]
(2)

where the following definitions apply: K§, = incident exter-
nal wavevector, |K5 | = 1/A,B,, = reciprocal lattice vector,
Fr = vector from origin (chosen on the surface), F;, = struc-
ture factor, B = ¥o/V47;YoY are direction cosines of inci-
dent and diffracted wavevectors, respectively, from the in-
ward normal to the surface;

2 AF
A= —- | | t - (3)
meV (voral)™
where e7/mc? = classical electron radius, V = volume of

"unit cell, t = plate thickness,
(1 — 6/2} + (b/2)e

(v1 |) [Yul
_ e A? Fou
You = Tne @ OK”
a= —2A@sin 26,,
40=86-6,,

@, = Bragg angle.

Equations (2){4} are valid only for 7 - polarization. For 7
polarization F,, is replaced by F;, cos 26,.

If the plate thickness and/or the structure factor are
sufficiently small, corresponding tod <1, Eq. (2) reduces to
the kinematical limit:

x =i ELV ble ar SEP. (5)
Fu
Equations (3) and (4) apply to unstrained and unda-
maged lattice. If the lattice is strained in a direction perpen-
dicular to the sample surface, the corresponding change in

Eq. (4)is .
A940 + €*[l¥nl(l— Hn)? + Yr tan Gy). (8)

Here e* is the strain and the correction includes changes in
the direction and magnitude of the reciprocal lattice vector.
Equation (6) can be easily extended to include lateral strain.
However, the requirement of lattice match between film and
substrate generally does not allow lateral strain.

In ion-implanted crystals, a significant fraction of
atoms may be displaced from lattice positions. The statistical
distribution of displacements Ar, away from lattice j is de-
scribed by a function p(4r,). Such a distribution will result in
a mean structure factor

(Fis) = vif 5p0(Ar,)e - 2rBirlt, “A, (7)

where f, is the atomic scattering factor for site j, located at r,
in undamaged crystal. If the same spherically symmetric
Gaussian form is assumed for all sites, the mean structure
factor becomes

(Fa) = exp ( - O20, 0 *\Fy =

where F%, corresponds to undamaged crystal and U is the
standard deviation of displacements. This correction to F'%,
is the well-known Debye-Waller factor.’? Its form can be
readily modified for other p(4r,) distributions, but, for sim-
plicity, in this paper a spherically symmetric Gaussian p(4r,)
is assumed.

Strain and damage distributions are represented by a set
of discrete laminae oriented parallel to the surface. Each la-
mina contains a large number of unit cells, but is sufficiently
thin so that extinction'’> and normal absorption within the
lamina are negligible. Each lamina has its own uniform
strain e' and random displacement standard deviation U.
Dynamical interactions among different laminae are ne-
glected, as is the effect of extinction on the incident wave.
The total diffracted amplitude is then the sum of coherently

e— "Fi, » (8)

6095 J. Appi. Phys., Vol. 52, No. 10, October 1981

, (4).

interfering functions of the type shown in Eq. (5), adjusted
for phase lags and normal absorption during traversal ,
through the crystal. Although usually extinction is stronger
than normal absorption, '? for depth-dependent strain distri-
butions the latter can be more important. With these consid-
erations, the total amplitude from N laminae is

=i ivi Soe anen SAE stan

Fl Y, 0)

where
a; = exp Ez Yo* lal ia uf ay =1,
oval 171
H= 24

t, = thickness of lamina /,

Jol;

$; =2 LANs ¢,=0,
and the previously defined variables Y and A are now sub-
scripted to indicate dependence on strain and damage. In
addition, since Eq. (9) will be used to determine strain rela-
tive to virgin crystal, the refraction correction [(1 — b )/2],
in the definition of Y (Eq. (4)] is neglected.

In principle the total amplitude due to laminar struc-
ture and substrate is

E, = Ey +a,e7?4.%E,, (10)

where E, is the dynamical result for a thick, aborbing, per-
fect crystal. However, the observed rocking curves of thick,
supposedly uniform crystals are frequently broader than
predicted for perfect crystals. The discrepancy is due to lat-
tice parameter variations and, to a lesser extent, Compton
and thermal diffuse scattering. For the purpose of fitting
rocking curves of thin surface layers, the discrepancy in the
substrate intensity can be removed by using a function which
matches it in the angular range of interest. In addition, the
relatively wide substrate peak implies that its amplitude does
not have a well-defined phase. Therefore, the total calculat-
ed intensity should be only the sum of layer and substrate
intensities. The total reflecting power is

R;= it - 265 Wale ee +R,,
1+ cos*260, Vo
where the first factor represents the relative abundance of o-
and 7r-polarization in double-crystal diffractometry,
lx |/7o relates intensity to power, a and R, is the substrate
reflecting power.

Because of the approximations made in arriving at
Ey.(11), it cannot be indiscriminately applicd to films of arbi-
trarily large thickness. As thickness increases, particularly if
the strain distribution is constant, dynamical effects become
dominant. It is therefore important to consider the range of
validity of the kinematical theory. For constant strain and
A & 0.25, the kinematical [Eq. (5)] and dynamical [Eq. (2)]
amplitudes are in extremely close agreement. The upper lim-
it corresponds to about 6% reflecting power. For
0.25 S 4 & 1, the kinematical expression yields a sharper

(11)

‘and more peaked curve, but the discrepancy is not more than

V. S. Speriosu 6095

13:

~ 15%. Choosing 6% reflecting power as the upper limit of
validity and considering only the strongest reflections, the
corresponding layer thickness is 2000 - 4000 A for crystals
such as Si, Ge, GaAs, and magnetic garnet. This range is for
constant strain. If the strain is depth-dependent, as is true of
ion-implanted, diffused, and other films, the range of valid-
ity for the kinematical theory can be several times larger.
Dynamical effects depend strongly on the Bragg condition,
Y= 0, being satisfied throughout the layer; this does not
happen in nonuniform films. Since the thickness for which
the kinematical model is valid varies with the strain distribu-
tion, a definite upper limit cannot be given. However, the
agreement with dynamical theory for KR; = 6% suggests
that rocking curves with maxima up to this value can be
safely interpreted kinematically. For typical distributions
this value of R, corresponds to --1-4:m total thickness.

Il. ROCKING CURVE SENSITIVITY TO STRAIN, LAYER
THICKNESS, AND DAMAGE . .

Expression (9) for the diffracted amplitude, taken to the
integral limit, is proportional to the Fourier transform of the
strain and damage distributions. However, the lack of phase
detection precludes direct inversion of the rocking curve.
The distributions can be obtained by fitting the rocking
curve with Eq. (11) evaluated for assumed distributions. A
good fit of the data is then taken to mean that the actual
distributions were found. Since the validity of this assump-
- tion cannot be mathematically proved, it is useful to examine
the rocking curve sensitivity to strain and damage. Figure
1(a) shows two strain distributions obtainable by He*-im-
plantation in garnet. The distributions are plotted versus dis-

tance from the interface with the unstrained substrate. The |

number of laminae is such that further subdivision does not
affect the calculated rocking curve. The distributions have
the samc thickness but differ by + 5% in thcir detailed
shapes, i.e., distribution 1 (dashed) is slightly sharper. It is
assumed that there is no damage, i.e., U,=0 for all laminae.
The corresponding calculated rocking curves for Cu K.
(444) are shoown in Fig. 1(b). The structure in the range
—0.24deg & AP S —0.04degis entirely due to the strain
distributions of Fig. 1(a). For |A@ | & 0.03 deg, the substrate
reflecting power, obtained from dynamical theory, is.
dominant. .

Although rocking curves 1 and 2 are qualitatively very
similar, there are large differences in the positions of their.
maxima and minima. The differences indicate a high sensi-
tivity to strain distribution and furnish the confidence that a
distribution yielding a good fit of the data is not only nnique,
but also highly accurate. The accuracy depends on the par-

ticular strain distribution, and ranges from + 5% to + 2% ©

strain for layer thicknesses between ~ 2000 A and ~ 6000 A.
Similar accuracy exists for the total strained layer
thickness. For uniform strain, Eq. (5) relates the thickness to

the period of oscillation. For depth-dependent strain, the
period is no longer constant [see Fig. 1 (b)}. For positive
strain, at a given A@ it roughly measures the thickness for
which the strain is greater than the value obtained by setting
the right side of Eq. (6) equal to zero. For example, the period

6096 J. Appi. Phys., Vol. 52, No. 10, October 1984

1.0 T T T
-----
—— 2
Zo
= ost 4
wv
0.0 i l r
(a) ° 4000 ° 8900
Distance from interface (A)
“|
—e2
1OfF :
xe
~ A
= |
« ht
} 4 it ne,
hia I vill
0.5 PA a afty 14 7]
Pyaden HI !
AMARA REIT
tha Way Ue
| vu \ q iF f f ut
if | Whedpay, H '
j TEL Hitman CICtLE Ope
APU
{7 AAV WOW Wall
j v '
0.0 | ,
=0.3 -0.2 -0.! 0.0
(b) A@ (deg)

FIG. 1. (a) Strain distribution (dashed) obtainable by He*-implantation in
garnet. The solid line isa + 5% variation. The distributions are plotted vs
distance from the interface with unstrained substrate. (b) Calculated Cu XK,
(444) rocking curves corresponding to the strain distributions of Fig. 1(a).
The angle A@ is referred to the location of the substrate peak.

between — 0.06 deg and — 0.03 deg yields the total layer
thickness in Fig. 1(a).

The theoretical sensitivity to the damage parameter Uis
considerably less than to strain and thickness. For uniform

V. S. Speriosu 6096

strain and damage, the reflecting power goes as e~ 7, where
W is proportional to U? [Egq. (8)-and (11)]. From this
AR
au~ + =*
U Rr

so that for low U the relative uncertainty is quite large. At
moderate to high damage levels the sensitivity improves, ap-
proaching that for strain.

(12)

iV. EXPERIMENT

A series of (111) Gd, Tm, Ga: YIG samples subjected
’ to three He* -implantation conditions was supplied by an
external source. '* The films were grown by LPE on 0.5-mm-
thick Czochralski-grown (111) Gd,Ga,O,, (GGG), were
about 0.9 zm thick, and had a quoted composition

{ Gdo 94 TM).17 Yas | [Fe2}(Gao 39 Fe 61 )O12. Implantation
was done at room temperature, several degrees off (111)
axis and with current densities of ~0.1 A/cm”. The im-
plantation conditions were 140 keV, 3 10'° He* /cm? (de-
noted here as FI); FI + 70 keV, 1.4 10'° Het /cm?
(==FII);FII + 30 keV, 9 x 10'* He* /cm?(=FIII). Accord-
ing to a model'® relating certain magnetic properties to nu-
clear energy loss, the three conditions should yield increas-
ingly uniform properties with depth. For each implanation
condition a series of samples was made by ion milling to
successively greater depths. In addition, several duplicates
of as-implanted samples were provided. The size of these
samples was ~44 mm’.

As will be shown, the Het doses resulted in relatively
low levels of damage. In order to explore the validity of the
kinematical diffraction model over a wider range of damage,
a series of GGG samples, provided by another source, 16 was
implanted at room temperature with 100-keV Ne* at 0, 0.5,
1.0, 2.0, and 6.0 10'* atoms/cm?. These samples will be
denoted as PI through PV. The orientation, thickness, and
growth-method of the virgin GGG were the same as for the
magnetic film subtrates. ©

Double-crystal rocking curves were obtained using the
appartus shown in Fig. 2. X-rays from a Cu target operated

st Detector

Crystal

Source

FIG. 2: Double-crystal x-ray diffraction apparatus.

6097 J. Appl. Phys., Vol. 52, No. 10, October 1981

at 40 keV, 20 mA are collimated by a ~0.5 X 1-mm’ slit and
undergo Bragg diffraction by the stationary first crystal. The
diffracted beam is partially polarized, has a lateral diver-
gence of not more than ~ 25 arc sec, and consists of the K,
line. The beam is then diffracted by the sample which is
continuously rotated at 0.2 arc sec/sec in the neighborhood
of the Bragg condition. In addition to the A@ variation, the
sample can be rotated in azimuth prior to measurement. In
symmetric reflections this rotation provides information
about sample curvature and lateral uniformity. The radi-
ation is measured by a stationary “wide-open” Na I (TI) de-
tector with pulse-height analysis electronics. Typical count-
ing rate for the beam incident on the sample was ~ 10° cps.
The measured reflections were (444), (888), and (880), the
latter with both asymmetries. The sample and the first crys-
tal (a piece of (111) GGG) were cet for the came reflection
and asymmetry.

V. RESULTS

A. He*-impianted Gd, Tm, Ga:VIG

Figure 3(a) shows the experimental (dashed) and calcu-
lated (sulid) rovking curves of sample FI, implanted with 140
keV, 3X 10 Het /cm?. Curves labeled 0 correspond to as-

. implanted material, while curves 1 and 2 are of samples

which were inn milled ta mechanically determined '* depths
of ~2500 and ~ 6800 A, respectively. It should be noted
that the curves belong to different samples cut from the same
wafer, The reported uniformity of implanation across the
wafer was about + 5%. Differences in experimental rocking
curves of as-implanted samples also indicate lateral vari-
ations of up to + 5%. Unless data are taken of the same
sample before and after milling, lateral variations will limit
the agreement of experimental and calculated curves corre-
sponding to different depths. Consequently the primary ob-
jective was to obtain strain and damage distributions which
produce the best fit to the unmilled rocking curve. The distri-
butions were built from the bottom up, using curves 2 and 1,
together with the quoted milled depth, only as guides. Even
so, the final distributions, shown in Fig. 3(b), yield rocking
curves which match all three experimental curves quite well.
The discrepancy in curves 1 can be removed by lowering the
strain by about 5%.

Since strain is defined relative to the GGG substrate,

the strain distribution [solid line in Fig. 3(b)] includes a re-

" gion, 2800 A thick, of constant strain. Its source is the lattice

parameter difference between the LPE film and substrate.
At greater distances from the interface, the total strain is the
sum of the constant value and the implantation-induced
strain. At any depth, the uncertainty in strain is not more
than + 2% of the maximum strain. The distribution
[dashed in Fig. 3(b)] for the damage parameter U is linear
with implantation-induced strain. That is, U, = 0.18 &,
with ¢; in percent and U, in A. Because of the relatively large
uncertainity (+ 15%) in U at this damage level, some devi-
ation from linearity cannot be ruled out. However, the aver-
age U is determined by closely matching the integrated ex-
perimental reflecting power {Rd (4@). In addition, the
details of the rocking curves are best simulated by similar e

V. S. Speriosu 6097

T T T
ab Sample FI
(444) 7
~--— Exp. ,
—— Calc.
2- rR
ml
Ht
3 , yi
s ‘7g, |
“A
~- ’
o Y A | | '
oY WW yy AY,
1 j |
| ml
/ \ NN j )
7 1 \ i
| 4 j \\ [) rp RN)
ra C I [
-0.3 -0.2 -0.1 0.0
(a) ; AG (deg)
T T T
to- ‘Dotted lines indicate milling steps 45>
41,05 +o. >
0:
I :
‘ 1
2: i ‘ :
+ ti L: 4 0.0
0.09 6000. 12000
(b) Distance from interface (A)

FIG. 3(a) Experimental (dashed) and calculated (solid) (444) rocking curves _

of sample FI (140 keV, 3X 10° He* /cm?}. Curve Ois from unmilled materi-
al; curves 1 and 2 correspond to progressively deeper milling. The curves are
vertically displaced for clarity. (b) Strain (solid) and damage parameter U
(dashed) distributions in sample FI. The vertical dotted lines indicate mill-
ing steps and are labeled to show correspondence with the data of (a).

goss —-J. Appl. Phys., Voi. 52, No. 10, October 1981

and U distributions. In particular, the maximum e' and the
maximum U occur at the same depth.

Rocking curves of sample FI (unmilled), obtained with
(888) and (880) reflections, are shown in Fig. 4 and 5(a). Both
curves are qualitatively similar to the (444) curve, but there
are important differences. In (888) the 4@ range is about
three times greater, the maximum reflecting power is an or-
der of magnitude less, and the number of oscillations is al-
most twice as large as in (444). In (880), with 7p > |vz\|, the
A®@ range is reduced eight-fold with respect to (888), while
the reflecting power is almost the same as for (444). Yet as
shown by the agreement with calculation, both curves corre-
spond to the strain and damage distributions of Fig. 3(b).

The more rapid oscillations of the calculated (888) and
(880) curves have larger amplitude than in the experimental
curves. The discrepancy is duc to the assumption of planar
uniformity in the sample and the neglect of incident beam
divergence. In (444) the incident beam divergence is much
less than the period of oscillation, but in (880), with
Yo > |7u|, they are comparable. The convolution of the
plane-wave solution with the incident beam, approximated
here as a Gaussian with 6-arc sec standard deviation, pro-
duces the calculated curve in Fig. 5(b). The agreement with
data is very good. For the (880) reflection with opposite
asymmetry, 7p < |7,,|, the incident beam divergence is
again negligible compared to the period of oscillation. Al-
though not shown in these figures, the plane-wave calcula-
tion, based on the strain and damage of Fig. 3(b), agrees
equaliy well with the data. .

The (444) rocking curves of samples FII (double im-

0.12 | ose
fe — —_—_—
, Sample F1
(888)
---- Exp.
—— Calc
3° o25&
70.067 c
0.00 “i J 0.00
s10 -0.5 .
A@ (deg)

FIG. 4. Experimental (dashed) and calculated (solid) (888) rocking curve of
sample FI.

V. S. Speriosu 6098

; ee
Sample FI -_—|
(880), % > 1% l
OF ' 42.0
—--- Exp. :
— Calc.
oe c
0.5 10
0.0 5.00
{a)
T T T T
Sample FI
(880), % > 1%
OF \ {2.0
Convolved ——
---- Exp.
—— Calc.
c a

-0.05 0,00
(0) A@ (deg)

FIG. 5(a) Experimental (dashed) and calculated (solid) (880), 79 > |yzl;
rocking curve of sample FI. (b) Same as (a) after the plane-wave solution was
convolved with a Gaussian of 6-arc sec standard deviation.

6099 —Ss-J. Appl. Phys., Vol. 52, No. 10, October 1981

T T
2b Sample FIL -
(444)

w--- Exp.
——~ Calc. -
Ir

* { =

, i]
re) 4,
-0.3 -0.2 -0.1 0.0.
~ A@ (deg)

FIG. &. Experimental (dashed) and calcuiated (solid) (444) racking curves of
sample FI, implanted with 140 keV, 3x 10'S He* /cm? + 70 keV,
1.4x 10'5 Het /em?.

planation) and FIII (triple implanation) are shown in Fig. 6
and 7, respectively. The two curves exhibit a continuous
change from the FI data [curve 0 in Fig. 3(a)]. The peak at
A@= — 0.24 deg is becoming sharper and more intense,
while the reflecting power in the range — 0.22 deg & AO

S&S — 0.05 deg is diminishing. The strain distributions cor-
responding to this behavior are shown in Fig. 8. For clarity,
the damage distributions have been omitted. In each case,
the relationship between damage and implanation-induced
strain is the same as in Fig. 3(b). It is evident that a given
depth strain and damage are unaffected by shallower im-
plantation. The rocking curve of another unmilled FIT sam-
ple was significantly different from the data in Fig. 7. For
that sample the strain distribution was much more uniform,
with surface value of ~ 0.8%, instead of the 0.57% shown in
Fig. 8.

B. Ne*-implanted GGG

Experimental and calculated rocking curves of 100-keV
Ne*-implanted GGG are shown in Figs. 9(a)-(e). The doses
were 0, 0.5, 1.0, 2.0, and 6.0 10'* atoms/cm’, respectively.
The angle axis is the same for all cases, but the reflecting
power varies by an order of magnitude. The experimental
rocking curve of the virgin sample [Fig. 9(a)] is well enough
represented by the dynamical result for nonabsorbing crys-
tals, but no special significance should be attached to this. If

V. S. Speriosu 6099

T T
Sample FI
(444)

--—~ Exp.
—— Cale.

~—_

Ry (%)

0.0

Aé@ (deg)

FIG. 7. Experimental (dashed) and calculated (solid) (444) rocking curves of
sample F1U, implanted with 140 keV, 3x 10"° He ' cm? + 70 keV,
1.4x 10'S He*+/cm? + 30 keV, 9x 10'* He* /em?.

absorption is taken into account, the dynamical curve is con-
siderably narrower for 40 2 —O.OldegandR; & 2%. As
described in Sec. H, the increased width of the experimental
curve is attributed mainly to lattice parameter variations.
The dynamical solution for nonabsorbing thick crystals is
used throughout this paper to represent the substrate
contribution.

The range of nonzero reflecting power in Figs. 9(b), 9(c),
and 9(d} increases linearly with dose. At the same time the
peak farthest from the origin decreases in relation to other
peaks, as does the overall reflecting power. At 6x 10'*
Ne*/cm’, Fig. 9e), the oscillations are much reduced and
the reflecting power is close to that of virgin GGG. The
calculated curves match the data quite well over the entire
range of doses. ,

The strain and damage distributions corresponding to
the calculated curve in Fig. 9(d) are shown in Fig. 10. The
layer thickness, maximum strain, and maximum damage are
1900 A, 2.49% and 0.40 A, respectively. Damage is linear
with strain, with U;(A) = 0.16 €(%). As for the He*-im-
planted films, some deviation from linearity is possible. The
relatively heavy damage level presents the opportunity to
demonstrate the importance of including damage in the cal-
culation. Figure 11 shows the same experimental data as Fig.
9(d). The theoretical curve in Fig. 11 was obtained using the
strain of Fig. 10 but assuming no damage, i.c., U,==0 at all
depths. The positions of the calculated maxima and minima

6100 J. Appl. Phys., Vol. 52, No. 10, October 1981

€+ (%)

0g 6000 ;
Distance from interface (A)

FIG. 8. Strain distributions of samples FI, FIL, and FHI.

are unchanged from those in Fig. 9(d), but the integrated

. reflecting power is now several times greater. In addition,

the relative height of the maxima no longer agrees with the
data.

The strain and damage distributions obtained for the
lower doses, 0.5 and 1.0 10'*/cm?, when multipled by 3.4
and 2.0, respectively, are practically identical to those of Fig.
10. The invariance of the shape with dose strongly suggests
that strain is linear with dose. This further implies that the
ratio 3.4 instead of 4.0 between the 2.0 and 0.5 x 10'*/cm?
distributions is either due to an error in the dose or to anneal-
ing effects. The former is considered more likely. The calcu-
lated curve in Fig. 9(e) was obtained assuming linearity of
strain and damage with dose. The peak strain and damage
are then 7.5% and 1.2 A, respectively. The latter number is

_ close to the interatomic spacing and represents amorphous-

ness. Experimentally and theoretically, most of the implant-
ed layer no longer diffracts. The undulating part of the calcu-
lated curve indicates the presence of a thin crystalline region
near the interface. The undulation is much reduced in the
experimental data, possibly because of sample curvature
which increases with strain.

VI. DISCUSSION OF THE RESULTS

The kinematical theory is able to account for the rock-
ing curves of ion-implanted garnets with a wide range of
layer thickness, strain, and damage level. Symmetric refiec-
tions are sensitive only to strains perpendicular to the sur-

V. S. Speriosu 6100

0.10: T T T
Sample PI
(444)
—~—- Exp.
Calc.
® cost Zz

l L
0.00)5 -0.5
(a) 4A@ (deg)
T T T
0.3-- 4
Somple PII
(444)
on-—- Exp.
ook Calc.
oh H
] ’
0.0 l }
“=1.0 -0.5 0.0
(c) 4@ (deg)
~ Ot + 1 1
Sompie PX
(444)
mono Exp.
Calc.
% cost ~
er -
19 -O5 0.0
(e) 48 (deg)

face, while asymmetric reflections measure both perpen-
dicular and lateral strain. The agreement between calculated
and experimental curves obtained with asymmetric reflec-
tions indicates that the lattice is indeed strained only in a
direction perpendicular to the surface. Lateral strain is zero,
as expected from the lattice match requirement.

6101 J. Appl. Phys., Vol. 52, No. 10, October 1981

04 T t T
Sample PIE
(444)
ose 7777 Exp. =
—— Calc.
a |
= _
ord 0.2 r
aw |
Ole ; 4
L | thd:
0.05 =0.5 [oXe)
(b) Aé (deg)
0.10: T T T
Sample PIZ
(444)
won Exp.

Calc. H

Ry (%)

10 -O5 6.0
(a) Aa (deg)

FIG. 9. Experimental (dashed) and calculated (solid) (444) rocking curves of
GGG implanted with 100-keV Ne* at (a}0, (b) 5 10’, (c} 1 10", (d)
2x 10", (e) 6x 10'* atoms/cm’.

The theoretical reduction in reflecting power due to
random atomic displacement is very different for (444),
(888), and (880). The good fit to these curves indicates that
the assumed spherically symmetric Gaussian p(4r,) is con-
sistent with the data. However, the validity of this assump-
tion remains unproved. Since garnets are polyatomic, the

V. S, Speriosu 6101

3 T T 0.6
——e «*
--—- U
2r ~10.4
4 bey : —
w | : >
beg
tt : 70.2
z :
H mi 0.0
() 1000 2000 3000

Distance from interface (A)

FIG. 10. Strain (solid) and U (dashed) distributions for sample P/V (2 x 10'*
Ne*/cm?). The same distributions, when scaled by approximately the dose
ratios, correspond to all other doses.

contributions of various atoms to the structure factor de-
pend on the particular reflection. It is conceivable that im-
plantation results in a rearrangement of atoms such that the
effect on the magnitude of the structure factor is the same as
for random displacement. This ambiguity can be reduced by
studying several other reflections. For (444), (888), and (880),
the relative contribution of c sites, occupied by Gd, Tm, and
Y, iS ~ 80, 60, and 60%, respectively. The remaining contri-
bution is almost entirely due to a combination of a sites (Fe)
and d sites (Fe and Ga). The most abundant element, O,
contributes very little in these reflections. Assuming random
displacement, the obtained damage distributions apply
mostly to the heavier elements in garnet. In a recent com-
parison!” of the kinematical technique and backscattering
spectrometry, the damage distributions obtained by the two
methods were in satisfactory agreement.

The remarkably large strain and the linearity of the de-
tailed distribution with dose are consistent with earlier re-
sults for the maximum strain. '*-!9 Because of the lower theo-
retical sensitivity to damage, strict linearity between damage
and strain has not been established. However, the results
suggest that both the maximum and the average damage are
linear with strain and dose. For both crystals, the propor-
tionality constant between U and et is 0.17 + 0.01 A. This
relationship shows that strain and damage are initimately
connected. A priori it might be expected that strain is due to
the incorporation of implanted atoms into the unit cell. Such

6102 J. Appl. Phys., Vol. 52, No. 10, October 1981

0.15 '
Sample PIV
(444) |
~~~ Exp,
Cale. (Uj =O)
0.10}-— i
Ke f
0.05;-
Pas
Hy
ii
0.0015 ; 05

A@ (deg)

FIG. 11. Experimental (dashed) and calculated (solid) (444) rocking curves
of sample P/V. The calculated curve was obtained from strain distribution
of Fig. 10, but with zero damage.

an affect was observed in doped Si, where the strain was
negative and the damage negligible.’ However, in garnets
the range distribution of ions is significantly different from
the strain distribution.2° It was shown in Ref. 20 that the
detailed strain distribution can be explained entirely in terms
of nuclear energy loss. In that study the same strain was
obtained with Ne* and He* doses which differed by almost
two orders of magnitude. This was shown to be due to the
difference in nuclear energy loss rates for Ne+ and He*.
The presence of pronounced oscillations even in the
moderately damaged sample P/V indicates that coherence
and uniformity are maintained over macroscopic dimen-
sions. In these garnets implantation appears to create only
point defects. If extended defects, which cause strain and
orientation variations, were present, the oscillatory struc-
ture would be smoothed out. Evidence of extended defects
accompanied by severe broadening of the rocking curve was
presented’? for garnets subjected to relatively high
( 2 10'*/cm?) He* doses. In those samples annealing result-
ed in large defect clusters probably caused by He bubble

formation.

Vil. SUMMARY

A kinematical model for general Bragg case x-ray dif-
fraction in nonuniform crystals was presented. The kinema-
tical approach has the advantage of computation speed over
the more rigorous dynamical theory. The model is valid for

V. S. Speriosu 6102

films of arbitrary thickness, provided the maximum refiect-
ing power is less than ~ 6%. This requirement & anslates to
maximum thickness of ~ I zm for typical crystals such as
ion-implanted or doped Si, Ge, GaAs, and garnet. The mod-
el incorporates depth-dependent strain and random atomic
displacements. Distributions in crystals are obtained by fit-
ting the model to experimental rocking curves. The theoreti-
cal rocking curve is shown to be highly sensitive to strain

- distributions, layer thickness, lateral uniformity, and to a
lesser extent, damage distributions. Accuracy of up to ~2%
for these parameters is achievable. .

The model was applied to He* -implanted Gd, Tm,
Ga:YIG and Ne*-implanted Gd,Ga,O,,. In the former
crystal the total strained layer thickness was 0.89 zm, with
the strain varying between 0.09 and 0.917%. The maximum
standard deviation U of random atomic displacements was
0.15 A. Using symmetric and asymmetric reflections, the
absence of lateral strain was demonstrated. In addition, the
assumption of spherically symmetric random displacements
was consistent with the data. The Gd,Ga,O,, crystal was
implanted with several doses corresponding to a wide range
of damage. In all cases the layer thickness was 1900 A; strain
values of 2.49% corresponded to 0.40-A U values. The de-
tailed strain distribution was strictly proportional to ion
dose. The damage distribution was vloscly linear with im-
plantation-induced strain, although some deviation from
strict linearity has not been ruled out. Both crystals showed
the same relationship between damage and strain. The GGG
crystal maintained single crystallinity up to the amorphous
threshold.

ACKNOWLEDGMENTS

Thanks are due to C. H. Wilts for his continued support
and for a careful reading of the manuscript. The contribu-

6103 - J. Appl. Phys., Vol. 52, No. 10, October 1961

tion of H. L. Glass in the form of helpful discussions is grate-
fully acknowledged. B. M. Paine is thanked for the ion im-
plantation of the GGG samples. Technical assistance by L.
A. Moudy is acknowledged.

'§, Takagi, Acta Crystallogr. 15, 1311 (1962).

2—. Taupin, Bull. Soc. Fr. Miner. Crist. 87, 469 (1964).

35. Takagi, J. Phys. Soc. Jpn. 26, 1239 (1969).

‘J, Burgeat and D. Taupin, Acta Crystallogr. A 24, 99 (1968).

_ 5}, Burgeat and R. Colella, J. Appl. Phys. 40, 3505 (1969).

¢a, Fukuhara and Y. Takanv, Acta Crystallogr. A 33, 137 (1977).

7B. C. Larson and J. F. Barhorst, J. Appl. Phys. 51, 3181 (1980).

*R. W. James, The Optical Principles of the Diffraction of X-rays (Cornell
University, Ithaca, New York, 1965).

°4, M. Afanasev, M.V. Kovalohuk, E. V. Kovev, and V G. Kohn, Phys.
Status Solidi A 42, 415 (1977).

"See, for example, M. Buerger, Vector Space and Its Application in Crystal-

- Structure Investigation (Wiley, New York, 1953).

''V_§. Speriosu, H. L. Glass, and T. Kobayashi, Appl. Phys. Lett. 34, 539
(1979).

"V_§, Speriosu, B. E. MacNeal, and H. L, Glass, Intermag. 1980 Conf.,
Boston, paper 22-4 (unpublished).

Ww, H. Zachariasen, Theory of X-ray diffraction in Crystals (Wiley, New
York, 1945). .

“The Gd, Tm, Ga: YIG films and the ion milling were provided by the San
Jose, California laboratory of IBM Corporation.

'5K. Ju, R. O. Schwenker, and H. L. Hu, Intermag. 1979, New York
(unpublished).

‘Virgin GGG wafers were provided by the Anaheim, California laboratory
of Rockwell International.

1B. M. Paine, V. S. Speriosu, L. S. Wieluriski, H. L. Glass, and M-A.
Nicolet, Fifth International Conf. lun Beau Analysis, Sydney, Australia,
1981; Nucl. Instr. Meth. (in press).

‘8. ©, North and R. Wolfe, “Ion-Implantation Effects in Bubble Garnets”
In on-Implantation in Semi-conductors and Other Materials, edited by B.
L. Crowder (Plenum, New York, 1973).

9X Komenou, I. Hirai, K. Asama, and M. Sakai, J. Appl. Phys. 49, 5816
(1978).

20% E. MacNeal and V. S. Speriosu, J. Appl. Phys. 52, 3935 (1981).

V. S..Speriosu 6103

Application to a Four Layer Gallium Aluminum Arsenide Laser

Structure

The kinematical interpretation is valid for nonuniform
layers with thicknesses much greater than that in the garnet
films discussed earlier. An example is a GaAlAs laser
structure considered in Ref. (21). In this study a four
layer epitaxial film gave the rocking curve shown in Fig.

12(a), which at that time the authors considered too compli-
cated for detailed interpretation. According to this reference,
the curve was taken using a [100]-oriented GaAs substrate

covered with four epitaxial layers:

2. 0.5 ym Gag gAlg_jAs
4. 0.6 um Gap gAlg 14s

Since the lattice parameter of AlAs is greater than that of
GaAs, each of the four layers has a lattice parameter
different from the substrate. According to Vegard's law,
the difference is just proportional to the amount of Al
substitution. Thus the strain profile is equivalent to the
substitution profile. The rocking curve of Figure 12(b) was
calculated using the distribution quoted in Ref. (21). This
distribution is shown in Figure 12(c). ‘rhe regions with

higher strain correspond to higher Al substitution, the

Hutpuodsez109 eTtyord utes (9)

*9AIND pazeTNoITeo sy oF

*aanjzonaqys AeseT syTwep aeAeT anos

@ OF B9AIND Huryoor (GTT) ®y nD) pezetTNoTes (q) pue [TejueuTzedx” (f) “ZT arznbTt I

CUM) SOUAMILNI NOs AONYLE Ta

lo}

Coad) HiSe NIVW Wold AB IONY

T°

st - em et
NIVYLS (Y'd °Y

<=)

STS—BIS (BLEL) bh YimorersAsD Jo feunog

NVWIIN A PUES TALYVE TM

“uopoayja: toyny Ff 51}
PisAis-a[qnog “aunjonsys Josey Jo oaino Fuyyooy “p ‘8.4

INV ie

wifer-sz

seGuysy

watt ene

ase
20 svivep-d
evived

‘28808
ate
S¥iVEpD-U

‘do
2 s

‘ayeqns s¥ FH (100) ' |

CV)

degree of strain being adjusted to match the rocking curve.
For a satisfactory fit it was necessary to include transi-
tion regions between the four layers, thus showing the high
sensitivity to the strain profile stated earlier. Note that
the maximum strain is an order of magnitude smaller than in
the implanted samples considered earlier. In addition, the
4 um thickness of the structure demonstrates the validity of

the calculation for thick but nonuniform films.

Ref. 21. W.J. Bartels and W. Nijman, J.Cryst. Growth 44,

518 (1978).

Chapter III

Comparison of kinematical x-ray diffraction and backscattering

spectrometry

Strain and damage profiles obtained by the rocking curve

method are compared to those obtained by Rutherford backscattering.

80 Nuclear Instruments and Methods 191 (1981) 80-86
North-Holland Publishing Company

COMPARISON OF KINEMATIC X-RAY DIFFRACTION AND BACKSCATTERING SPECTROMETRY —
STRAIN AND DAMAGE PROFILES IN GARNET *

B.M. PAINE !, V.S. SPERIOSU !, L.S. WIELUNSKI !:"*, H.L. GLASS ? and M.A. NICOLET !

1 California Institute of Technology, Pasadena, CA 91125, U.S.A.
* Rockwell International, Microelectronics Research and Development Center, Anaheim, CA 92803, U.S.A.

We compare the results of measurements of crystal distortions made by means of two techniques: a new kinematic X-ray
diffraction technique and backscattering spectrometry of channeled MeV ions. Samples were (111) single-crystal gadolinium
gallium garnet (GGG) that had been implanted at room temperature with 100 keV Ne* ions to various doses. For these implanta-
tion conditions, the ranges of sensitivity of the two techniques overlap for about one decade in implantation dose up to the amor-
phous threshold. X-ray diffraction was found to be most sensitive to low damage levels while backscattering was found to be most
sensitive to high damage leveis. Neither method as applied here is sensitive to light atoms in a heavy matrix. In the former tech-
nique, strain and damage profiles were obtained by fitting a model to the X-ray rocking curve. In the latter technique, the damage
profile was obtained directly from the energy spectrum of backscattered particles while strain was obtained from the implanta-
tion-induced changes in the relative orientations of channeling axes, The two techniques are in excellent agreement on the near-

surtace Strain, but difter signiticantly at depths below ~50U A. Lhe damage distributions agree to within a tactor of 2.

1. Introduction

Backscattering spectrometry (BSS) of MeV ions
has long been used to obtain damage profiles in ion-
implanted single-crystals [1]. By contrast, X-ray
diffraction has generally been used only to determine
average lattice parameters in crystalline materials [2]
or lattice parameter differences between distinct
layers in composite single-crystal samples (e.g. epi-
taxial films) [3]. For single crystals with lattice param-
eters which vary with depth, dynamical X-ray diffrac-
tion theory [4] has been used successfully [5—7] to
obtain profiles of the variations in the lattice param-
eter. but at the cost of considerable computing time.
Kinematical X-ray diffraction (KXD) theory [4],
. which is mathematically much simpler, has recently
been adapted [8,9] for characterizing thin (<1 wm)
single-crystal films. The technique is believed to be
highly sensitive to variations of lattice parameters
with depth, lateral non-uniformities, and, to a lesser

* This work was partially supported by the Defense Advance
Research Projects Agency and monitored by the Air Force
Office of Scientific Research under contract number
F49620-C-80-0101 and the U.S. Army Research Office
under the Joint Services Electronic Program [DAAG-
29-80-C-0103].

** Permanent address: Institute of Nuclear Research,
Warszawa, Hoza 69, Poland.

extent, damage distributions. Where results are availa-
ble, it is in close agreement with the dynamical
theory. Both KXD and BSS can sense changes in
atomic positions that are well below the 1 A range.
To help evaluate the techniques of KXD and BSS and
to gain insight into their capabilities and limitations,
we have conducted a comparison of the results of the.
two methods applied to implanted samples otf single-
crystal garnet. We have compared their sensitivities
for a range of implantation doses and compared strain
and damage profiles obtained with a single dose.

2. Experimental procedure

Measurement were conducted on (111) single-
crystal gadolinium gallium garnet (GGG). This mate-
tial, which is cubic and has the stoichiometry
Gd3Gas0,2 was chosen because implantation with
moderate doses causes crystal distortions that are
within the ranges of sensitivity of both KMD and
BSS. Implantations were performed at room tempera-
ture with 100 keV Ne’ ions to doses ranging from 5 X
10'? to 6 X 10'* ions cm™?. These doses gave damage
concentrations ranging from low levels up to full
amorphicity as determined by both techniques. Two
sets of samples were prepared under closely similar
conditions and analyzed by the respective techniques.

The X-ray diffraction system is shown schemati-

B.M. Paine et al. | Strain and damage profiles 81

X-ray Source | : \st Crystal
Sit
€ Variation Cu Kg
Ae

Sarnple

Detector

Fig. 1. Schematic diagram of the X-ray diffraction system.

cally in fig. 1. X-rays from a Cu target pass through a
slit and impinge on the first crystal. The latter is
adjusted for the same Bragg angle as that required for
the sample and serves to reduce the beam divergence
and select the characteristic K, line. It also has the
effect of partially polarizing the beam. Radiation
diffracted from the sample is sensed by a Nal(Tl)
detector. In these measurements, the sample and
detector were rotated about an axis at the sample sur-
face to the desired Bragg condition. The sample was

then rotated finely about the same axis and the -

reflecting power recorded as a function of angle, to
give the so-called “rocking curve”. The illuminated
area on the sample was ~2 mm?. A piece of (111)
GGG was used for the first crystal.

The experimental arrangement for the backscat-
tering measurements is shown in fig. 2. To prevent
electrical charging during BSS analysis, a 100 A layer
of Al was deposited on the sample surfaces and con-
tact made by means of a steel clip. The samples were
aligned for channeling by varying 6 and ¢.

X-ray diffraction is only sensitive to displacements
of atoms in a direction perpendicular to the diffracting
plane while backscattering of channeled ions is sensi-
tive only to displacements in a direction perpendic-

ular to the channel axis. Therefore the optimum —

@ Variation

2-0 MeV Het ' Slits

Variation
Detector

Fig. 2. Schematic diagram of the backscattering system.

arrangement for comparing the two techniques would
involve channeling along axes that are parallel to the
planes employed for X-ray diffraction. However,
because of poor definition of the channels for high
index axes a compromise was made such that only a
component of the channeling directions lay in the
diffraction planes. Syuuuctic Bragg X-ray reflections
from (444) planes were employed and the backscat-
tering measurements were made with the beam
channeled in the (110) and (100) directions.

3. Analysis and results
3.1, Sensitivity—dose dependence

The raw data obtained from KXD and BSS analyses
are shown for a range of implantation doses in fig. 3.
It is clear that the two systems are roughly comple-
mentary in terms of their régimes of maximum
sensitivity: KXD is most sensitive for doses <10!*
Ne* ions cm~? while BSS is most sensitive above that
value. At a dose of 5 X 1019 Ne* ions cm™?, for exam-
ple, the KXD curve shows very prominent structure
(part a) while the BSS spectrum is little changed from
that for an unimplanted sample (parte). This is
because X-ray rocking curves are highly sensitive to
strain, even at low magnitudes, while channeling BSS
spectra mostly reveal only crystal damage. On the
other hand, for an implantation dose of 6 X 1014 Ne*
ions cm? the KXD signal is very small (part d) while
the BSS channeling spectrum has a lot of structure
(part h). This is because at high damage concentra-
tions the probability of backscattering a channeled
ion is high while the intensity of coherently
diffracted X-rays is low.

Observation of the high energy part of .a
BSS channeling spectrum reaching the same heights as
the random spectrum is typically taken to indicate
that the corresponding layer of the sample is “amor-
phous”. Similarly, in X-ray studies a thin layer is said
to be “amorphous” when it gives rise to a rocking
curve with no oscillations and a reflecting power close
to that from unimplanted material. It has not previ-
ously been clear whether these two definitions coin-
cide. From the results in parts d and h of fig. 3, it
appears that when a sample is amorphous by one of
these definitions, it does indeed satisfy the criteria for
amorphicity that are usually adopted with the other
technique.

While the respective sensitivities of the two tech-

Ii. SEMICONDUCTOR STUDIES

82 B.M. Paine et al. / Strain and damage profiles

X-RAY ROCKING CURVES BACKSCATTERING SPECTRA

joc ee a ne a a

Tt
a 13 ack ~2 Detector e@
L™ Ist X+fot 5 x10 Ne” ions cry Terie
a3 Detector Sanipie al 2OMev He’ 16
‘ 526°

X-RAY REFLECTING POWER (%)

«£- Ge
oer Sample Random oli Go | *
Cu Kg (444) tan ignment i
Impionted
0.iF a de
Fr a ee er cee Gee fq Ee
cars “05 oT) eZ
0.3F 1x10!4 Ne* ions em? 468
Random alignment!
O2r 44 —
4 Q
rr]
ol 7
Lp da w
Zz
L ji i
0.0p SOT TO 9 | &
0.3F 2x10"4 Net ions cm * 46
Random alignment g
02 a
2 44 wy
and
Olt 42 4
° a.
. <<
ae coe x
oO
0.0 i 1 de 1 L i 4 1 L i i 1 fe] _
d 05 0, [e) 10 5 h q
O.3r 6 x10!4 Net ions cmv? 46
Random alignment
O2F 44
Olp 42
L-Unimplanted:
L 1 i L L dl i Lt ia i L | fe]
0.915 -0.5 0 10 15

« (DEGREES)

Fig. 3. X-ray rocking curves and He* backscattering spectra
from GGG samples implanted with a range of doses of
100 keV Ne* ions. The angle ¢ is referred to the orientation
of the Bragg peak from undamaged crystal (at 25.5°). The
backscattering spectra were obtained with the incident beam
channeled in the (110) direction.

niques vary with damage levels, neither technique as
applied in fig.3 was sensitive to light atoms (e.g. O)
in the heavy Gd—Ga matrix. However, it should be
noted that if the light atoms had been of particular
interest, both techniques could readily have been

modified to enhance their sensitivities to such atoms:
X-ray reflections can be found for which most of the
diffracted intensity is due to the light ions, and elastic
(a, a) resonances with cross-sections far exceeding the
Rutherford level can be employed for detecting '°O
[10].

3.2. Strain profile

Strain and damage in a crystal lattice are repre-
sented schematically in fig. 4. Strain is the fractional
change Aa/a in lattice parameter resulting from a uni-
form displacement of atoms. According to KXD mea-
surements [11] ion implantation typically only
causes strain that is perpendicular to the sample sur-
face. In addition to strain, ion implantation also
induccs damage, ic. random displacements 67 of
atoms from their lattice positions.

In the KXD model, the implanted crystal acts as a
set of independently. but coherently diffracting
laminae, each incorporating many unit cells and
oriented parallel to the surface. The strain distribu-
tion is incorporated by allowing each lamina to have
its own constant strain value. The distribution of
incoherently displaced atoms (damage) is described
by a probability function p(6r) which changes the
mean structure factor in each lamina. In this paper,
for simplicity, o(6r) was assumed to be a spherically
symmetric Gaussian function.

Experimental rocking curves can be analyzed
directly in terms of this model to yield parameters
such as strained layer thickness, mean and maximum
strain, and thickness-averaged r.m.s. values of (6r). In
addition, detailed strain and r.m.s. (67) distributions

Channeled beam

No channeling

Damage

eeeneene eee

onl be ol ke a+Aa

Fig. 4. Schematic representations of strain and damage in a
crystal lattice.

B.M. Paine et al. / Strain and damage profiles 83

i | T i Tot U yo

X-RAY ROCKING CURVE
O10 Tr

0.05;--

REFLECTING POWER (%)

Fig. 5. Continuous curve: KXD rocking curve for the GGG
sample after implantation with 100 keV Ne” ioris to dose of
2x 10!4 ions cm7?. Dashed curve: fit to the data obtained
by means of the method of Speriosu et al. [8,9].

can be obtained by fitting the entire experimental
rocking curve with a curve generated by the model
described above (see refs.8 and 9 for details). The
fitting procedure was applied to the curves shown in
fig. 3a—d, and very good fits were obtained in all
cases. An example of data and fit is shown iu fig. 5.
The presence of pronounced oscillations in the data
indicates very good lateral uniformity of the sample.

The strain profile corresponding to this fit is plotted
as a heavy line in fig. 7.

The approach adopted for BSS measurement of
strain is illustrated schematically in fig. 4. If a region
of the lattice is strained in a direction perpendicular
to the surface, then the orientations relative to the
surface of axes other than the (111) axis will be
changed relative to those in an unimplanted sample.
While absolute measurements of their orientations
would be difficult, mcasurements of angular separa-
tions between axes are straightforward. Thus, energy
windows were set in the backscattering spectra on the
Gd signal at positions corresponding to a depth of
700 A, and a measurement was made of the angular
separation of the (100) and (110) axes on opposite
sides of the (111) axis for both unimplanted GGG
and the sample that had been implanted with 2X
10'* Ne* ions cm™. At each axis the goniometer
angle @ was adjusted so that the incident beam was
channeled in the (110) plane and then @ was varied in
steps of 0.1° across the axial channeling dip. The
results are shown in fig. 6. Since the (111) axes in the
mounted samples lay within 0.2° of the normal to the
goniometer, it was not necessary to change ¢ in order
to stay in the (110) plane during a scan over an axis.
Also, for this reason the ¢ coordinates of the (100)
and (110) axes differed by only 0.4°. Nevertheless,
both the @ and @ coordinates of these axes were taken
into account in calculating their angular separation.
The precise @ cuudinates of the axcs were obtained
by fitting inverted Gaussian curves to the data of
fig.6 by the method of least squares. The difference

~™ Ay Implanted

Unimpianted

BACKSCATTERING YIELD (103 COUNTS)

P| a Oe a CW Oe OC OE

ae oes Oe

a a TT TO TT TT YC) FT
et 100) AXIS CHO> Axis 48
@~ -55° |
Sample Sample 2:0 Mev Het 7
5r : Het a
2-O.MeV He < Detector 46
‘ Detector . ~35)

FOR i

BACKSCATTERING YIELD (10° COUNTS)

-56 “35 -54 -53° 34

35 36 37

GONIOMETER ANGLE @ (DEGREES)

Fig. 6. Angular scans in @ of the yield of backscattered alpha particles from a window on the Gd signal at an energy corresponding

to a depth of 700 A.

Il. SEMICONDUCTOR STUDIES

84 B.M. Paine et al. / Strain and damage profiles

STPAIN (%)

| | i"
° 15 10 5 ie)

DEPTH (102 A)

Fig. 7. Profiles of strain in the sample implanted with 2 x
1014 Ne* ions cm”? at an energy of 100 keV.

in the angular separations in the implanted and unim-
planted samples was —0.9° + 0.1°, implying a strain
of 1.7 0.2%.

In addition to the window at 700 A, three other
windows were applied to the spectra at energies corre-
sponding tv vatiuus depths and the channeling angles
in these were measured relative to those in the 700 A
window. The resulting profile of strain to a depth of
~1700 A is shown as the dotted curve in fig. 7.

It is evident from fig.7 that the two techniques
are in good agreement for the strain near the surface,
but while the KXD curve rises to a peak strain of
25% at ~700 A and falls off to essentially zero at
1800 A, the BSS curve remains roughly horizontal.
We suggest that this discrepancy is the result of
steering of the channeled alpha particles in the
strained lattice. If the variations of crystal strain with
depth are not abrupt, then it is possible that ions that
aro channeled in the surface layers of the sample are
steered into the channels with different orientations
that exist deeper in the sample. If this occurs, then
angular scans obtained with energy windows corre-
sponding to any depth will all measure mostly the
strain at the surface. It would be of interest to test
this hypothesis by recording BSS spectra from sam-
ples that have been etched to successively greater
depths.

3.3. Damage profiles

Damage profiles were also deduced by means of
both techniques for the sample that had been im-
planted with 2 X 10'* Ne” ions cm~*. The BSS profile
was derived from a spectrum obtained with the
incident beam channeled in a (110) direction, part of
which is shown in fig.8. A dechanneling curve
beneath the direct scattering peak was calculated
iteratively [12] assuming (1) a critical angle at all
depths equal to that measured at the surface (21,2 =
1.1°); (2) a uniform flux of channeled particles
within the channels; (3) that all displaced atoms inter-
act with the channeled particles; and (4) that
dechanneled particles are not scattered back into
channels. The result is the heavy stepped curve in
tig. 8. Lhis curve appears to be an underestimate since
it should reach the data level at a point beyond the
implanted region. This difference is possibly the
result of a dccrcase in the critical channcling angle
with higher damage densities below the sample sur-
face, and extra dechanneling caused by depth-depen-
dent lattice strain. Therefore. for the purpose of ob-

i] T T
He* BACKSCATTERING
a) SPECTRUM 4
rt Calculated dechanneling
° Adopted dechanneling
O10 4
a at tN
3 | TN
[o} mt
iid
w = 4 :
Sr L| be 4
B aan
5 mL
ong 7 TB

Eq (MeV)

Fig. 8. Portion of the backscattering spectrum from a GGG
sample implanted with 2 x 10!4 Ne* ions cm? at an energy
of 100 keV. The sample was oriented so the incident beam
was channeled in the (110) direction. Solid curve: dechan-
neling calculated from a simple model (see text). Dashed
curve: finally adopted dechanneling curve.

B.M. Paine et al. / Strain and damage profiles 85
0.5 T T T 1.0 T T T 10
RMS(8r) PROFILE
KxD
O4F o.8b
ot O3F a 06F w
IN x w
a =< =
5 z
0.2 ~ o4b : oe 404 ~
ass
O.1F
o2b 40.2
15 10 5 fe) fete) 5 ro . ceo

DEPTH (107A)

Fig. 9. R.m.s. value of &r obtained from the fit to the KXD
data shown in fig. 5.

taining a realistic damage profile this calculated curve
was simply scaled up to the level indicated by the
dashed curve in fig. 8. The resulting profile of Vy/N,
the relative number of displaced atoms, is shown in
fig. 10 as a dotted curve.

The KXD fitting technique described earlier yields
the profile of r.m.s. (67) in addition to the strain
profile. For this calculation, the relative sensitivities
of the Cu K, (444) reflections to Gd, Ga and O were
taken to be the same as those tor undamaged GGG,
ie. ~80%, ~20% and 0%, respectively. This assump-
tion is valid if ment is zero. The resulting r.m.s. (6r) profile is shown
in fig. 9. For comparison with the BSS results, this
curve was converted to the profile of fractional num-
ber of atoms with planar projections of 57 that are
greater than the Thomas—Fermi radius, app, in unim-
planted material (estimated to be 0.15 A). The result
is plotted as a continuous curve in fig. 10. The
damage depths are in good agreement, but the KXD
curve is about a factor 2 higher than the BSS result.
However, in the light of the very different approaches
employed by the two techniques, we regard this as
satisfactory agreement.

Several factors may be responsible for the differ-
ences in the magnitudes of the two curves in fig. 10.
The use of the Thomas—Fermi radius for calculating

DEPTH (102 A)

Fig. 10. Profiles of damage in the sample implanted with 2 x
10!4 Ne* ions cm7? at an energy of 100 keV. The BSS curve
was obtained directly from fig. 8 while the KXD curve is the
fractional number of atoms displaced by more than arr =
0.15 A in a direction parallel to the lattice plane, deduced
from the r.m.s. (¥) profile of fig. 9, assuming spherical sym-
metry.

Naf/N from the KXD results is somewhat arbitrary.
Since damage is heavy for a dose of 2 X 10'* Ne’ ions
cm™?, the effective radius is probably larger than its
value for a perfect crystal, and in fact we find good
agreement with the BSS curve if a value of ayp=
0.35 A is assumed. Also, if peaking of the tlux den-
sity of channeled ions near the centers of the channel
were taken into account, the number of displaced
atoms deduced from the BSS results would increase —
again bringing the results of the two techniques into
closer agreement. Finally, the assumptions of a
spherically symmetric Gaussian form for p(r) and that
correct.

4, Summary

We have conducted a comparison of the results of
kinematic X-ray diffraction and backscattering spec-
trometry analyses of strain and disorder in 100 keV
Ne’-implanted gadolinium gallium garnet. Our results
can be summarized as follows:

Il. SEMICONDUCTOR STUDIES

86 BM. Paine et al. / Strain and damage profiles

1) For our implantation conditions, the two tech-
niques have a common range of sensitivity for doses
varying over about one decade up to the threshold for
amorphicity.

2) KXD is most sensitive to low lattice distortion
(dose <1 X10'* Ne* ions cm?) while BSS is most
sensitive to high lattice distortion (dose 1X
10'* Ne* ions cm~*). Neither technique, as usually
applied, can readily sense light atoms in a heavy
matrix.

3) Both techniques yield the same value for the
thickness of a damaged layer.

4) Strain profiles from the two techniques are in
good agreement at the sample surface. However, the
KXD curve has a peak at ~700 A and drops off to
zero at greater depths while the BSS results are
roughly constant with depth.

5) The KXD and BSS magnitudes of the profiles
of the relative number of displaced atoms agree to
within a factor 2.

We acknowledge technical assistance from L.A.
Moudy at Rockwell International.

References

[1] See, for example, Backscattering spectrometry, eds.,
W.K. Chu, J.W. Mayer and M-A. Nicolet (Academic
Press, New York, 1978).

[2] See, for example, B.D. Cullity, Elements of X-ray
diffraction (Addison-Wesley, Reading, Massachusetts,
1956).

[3] See, for example, M.A.G. Halliwell, R. Heckingbottom
and P.L.F. Hemment, J. Phys. D 10 (1977) L29.

[4] See, for example, W.H. Zachariasen, Theory of X-ray
diffraction in crystals (Wiley, New York, 1945).

[5] J. Burgeat and D. Taupin, Acta Crystallogr. A24 (1968)
99

(6] A. Fukuhara and Y. Takano, J. Appl. Cryst. 10 (1977)
387.

{7] B.C. Larson and J.F. Barhorst, J. Appl. Phys. 51 (1980)
3181.

[8] V.S. Speriosu, H.L. Glass and T. Kobayashi, Appl. Phys.
Lett. 34 (L979) 33Y.

{9] V.S. Speriosu, to be published.

(10) L.C. Feidman and S.T. Picraux, in Ion beam handbook
for materials analysis, eds., J.W. Mayer and E. Rimini
(Academic Press, New York, 1977/) ch. 4.

[11] V.S. Speriosu, B.E. MacNeal and H.L. Glass, Intermag
1980 Conf., Boston, paper 22-4 unpublished.

[12] F.H. Eisen, in Channeling, ed. D.V. Morgan (Wiley, New
York, 1973) cn. 14.

Chapter IV

X-ray rocking curve and ferromagnetic resonance investigations

of ion-implanted magnetic garnet

Elucidation of the behavior of crystalline and magnetic

properties versus species, dose and annealing.

X-ray rocking curve and ferromagnetic resonance
investigations of ion-implanted magnetic garnet

V.S. Speriosu and C.H. Wilts

California Institute of Technulugy
Pasadena, CA 91125

Abstract

Detailed analyses of X-ray rocking curves and ferromagnetic resonance
spectra were used to characterize properties of <111>-onriented Gd,Tm,Ga:YTG
films implanted with Ne’, He”, and Hp’ For each implanted species the
range of doses begins with easily-analyzed effects and ends with paramagnetism
or anorphousness.. Ion energies were chosen to produce implanted layer thick-
nesses of 30008 to 60008. Profiles of normal strain, lateral strain, and
damage were obtained. The normal strain increases with dose and near amor-
phousness is 2.5%, 3.4%, and 3.9% for Ne’, He’, and Hos respectively. Lateral
strain is zero for all values of normal strain, implying absence of plastic
flow. Comparison of these results with the reported decrease in lateral
stress implies either a large reduction in Young's modulus or a transition
to rhombohedral equilibrium unit cell. Damage is modelled by a spherically-
symmetric gaussian distribution of incoherent atomic displacements. Due to
the use of (444), (888), and (880) reflections the sensitivity is greatest
for the c-sites occupied by Gd, Tm, and Y. The standard deviation of dis-
placements increases linearly with strain with proportionality constant 0.25,
0.18, and 0.13 Ry for Ne’, He*, and Hy’ respectively. For maximum strains
up to 1.3% annealing in air reduces the strain without changing the shape of
the profile. The behavior of the strain with annealing is nearly independent

of implanted species or dose. After annealing at 600°C the strain is 40% of

the original value. Magnetic profiles obtained before and after annealing
were compared with the strain profiles. The Jocal change in anisotropy field
AH with increasing strain shows an initially linear rise for both He* and Ne’.
The slope is -4.1 k0e/%, in agreement with the magnetostriction effect estimated
from the composition. For strain values between 1% and 1.5%, AH) Saturates
reaching peak values of -3.6 kOe for He’ and -2.8 kOe for Ne’. At strain
values near 2.3% for He* and 1.8% for Ne*, aH, drops to nearly zero and the
material is paramagnetic. For peak strains greater than 1.3% for He” and

1.1% for Ne* the relation between uniaxial anisotropy and strain is not unique.
The saturation magnetization 4nM, the ratio of exchange stiffness to magneti-
zation (A/M) and the cubic anisotropy Hy decrease with strain reaching zero

at 2.3% and 1.8% for He* and Ne’, respectively. At these strain values the
damping coefficient a is 50% and 80% greater than bulk value for He* and Ne’,
respectively. For higher observed strains the material remains paramagnetic.
Upon annealing of samples implanted with low doses of Ne* and He* the aniso-
tropy field follows uniquely the behavior with strain for unannealed material.
At 600°C the magnetization returns to bulk value but the ratio A/M remains

20% low. For Hy” implantation the total AH. consists of a magnetostrictive
contribution due to strain and of a comparable excess contribution asso-
ciated with the local concentration of hydrogen. The profile of excess AH,
agrees with calculated LSS range. The presence of hydrogen results in a
reduction of 41M not attributable to strain or damage. For a peak strain

of 0.60% and a peak total AH, of -4.5 kOe, the magnetization is only 40%

of bulk value. After annealing up to 350°C the excess AH, diminishes and
redistributes itself to the regions neighboring the peak damage. At 400°C

the excess is nearly zero. For higher annealing temperatures the only

component of AH, is magnetostrictive. At 600°C, the magnetization, the ratio

A/M, and a return to bulk values.

I. Introduction

Since the discovery(!) that ion-implantation in magnetic garnets is useful
in the manufacture of devices, there has been an interest in the properties of
implanted garnets. These properties may be subdivided into three broad categories:
(1) the damage viewed primarily from a crystallographic point of view, (2) the
possible effects due to the presence of the dopant, and (3) the magnetic properties
arising from (1) and (2).
Damage has been studied by X-ray diffraction’'~!9)

measurements (/4-16)
(20-22)

» indirectly through stress
» enhanced etch rate measurements (17719) | Rutherford back-

s and electron diffraction(*2).
(24 ,2,4)

scattering Magnetic properties have been

studied through the capping-layer effect

(Fup) (25-33) | A.C. susceptibility’>4),, Mossbauer spectroscopy

(37)

>» ferromagnetic resonance

(35,36) | vibrating

sample magnetometry ‘9? , and Kerr rotation Although no direct measurements

of dopant distribution have been published, studies have been made of their anneal-

(8)

induced desorption.
One conclusion drawn from this work is that the strain and damage are uniquely

(138,39) Generally,

related to the energy deposited through nuclear collisions
no crystallographic effects are attributed to the presence of the dopant. Another
conclusion drawn is that the major connection between changes in magnetic and
crystalline properties is magnetostriction, (40) promoting efforts to measure the
magnetostriction constant of virgin and implanted crystals, (41-43) An apparent
lack of correlation between strain and uniaxial anisotropy Hy at high doses has

led to the hypothesis that implantation destroys the growth-induced anisotropy. (44

Other effects include changes in the saturation magnetization M. in the exchange

stiffness A, in the Curie temperature Tos in the cubic anisotropy Hy and in

(9,11,13,31 532,44) In the case of H”-implanted garnet

(45)

the damping parameter a.

the unusually large variation of uniaxial anisotropy with dose and

annealing¢®*33) has been attributed to either (1) qualitatively different

(46)

damage caused by Ht implantation, or (2) chemical effects due to

the presence of H in the lattice, (893347) Despite the relatively large number

of papers devoted to implanted garnets, many of their basic features are unresolved.
Part of this is due to difficulties of interpretation of experimental results and
frequent failure to extract the maximum of quantitative information available in
the experimental data.

In this paper we have combined X-ray diffraction and ferromagnetic resonance
measurements of Ne*, Het, and Hy" implanted <111>- oriented Gd, Tm, Ga:VIG. This
choice of implanted species and host material was made because of their (previously)
widespread use in the manufacture of devices. More important, this material has
the beneficent properties of reasonably narrow linewidth and high magnetostriction

(70 Oe and Mu ~3x107°),

The narrow linewidth permits a clear identification
of mode location and amplitude in FMR, while the large VWI ensures that a rela-
tively large number of modes are supported in the implanted layer, thereby providing
data with high information content. For each implanted species, doses were chosen
to cover a range starting with easily-analyzed effects up to amorphousness. The
incident ion energy produced implanted layer thicknesses of 3000 R to 6000 R
Selected samples were annealed up to 600°C.

We have attempted to answer the following questions: (1) Can FMR and X-ray
diffraction yield detailed and unequivocal information about magnetic and
crystalline properties for all levels of damage? (2) If so, what is the extent
of correlation between magnetic and crystalline properties? The answer to the
first question is a qualified yes. Concerning the second question, there is a

strong although not total correlation between measured magnetic and measured

crystalline properties.

II. Experiment

The garnet used was LPE-grown, <111>-oriented Gd,Tm,Ga:YIG. The substrate

material was the usual single-crystal Gd,Ga,0, 5 (GGG) wafer with a 5cm diameter

and 0.5mm thickness. Two wafers with films of identical nominal composition and
very similar bulk magnetic properties were used, one (M721) for the neon and helium
implantations, and the other (M722) for the hydrogen implantations.. Two nominally
identical, 4mmx4mm samples were made for each implanted species and dose. Implan-
tation was done at room temperature. (See Table 1 for details). These three
series of implanted samples were provided to us by an external source. (48)
In the determination of magnetic profiles for high doses, it was found useful
to chemically etch some of the neon and helium implanted samples. A 30 min pre-
anneal in air at 150°C produced no detectable changes in either FMR or X-ray

diffraction. Following this, the sample was etched in hot (110°c) H,P0,. After

cleaning with organic solvents, the sample was plunged in the acid and stirred

for 5 to 10 seconds, followed by immérsion in room temperature water, The sample
was etched and measured with FMR or FMR and X-ray techniques in successive steps,
up to the disappearance or near disappearance of the signal attributed to the
implanted layer. The longest total etch time was 1 minute. The amount of

material removed was determined with an accuracy of about +50 R from the X-ray
rocking curve by inverting the process discussed in Ref. (7). Lateral nonuni-
formities attributed to uneven etching were detected by the broadening of both

the FMR absorption spectrum and the rocking curve, The broadening increased

with successive etch steps, but did not impair the X-ray determination of layer
thickness. In the case of FMR, the broadening at the last two etch steps vitiated
a meaningful measurement of some surface mode amplitudes, reduced the sensitivity
for detection of weak modes, and increased the uncertainty in surface mode location
from the usual +5 Oe (unetched) up to +150 Oe (last etch step). Other than non-
uniform etching of the surface, we tound no evidence of etch-induced changes in
either crystalline or magnetic profiles. Selected unetched samples were annealed

in air at temperatures ranging from 150°C to 600°C. in stens of 50°C. Due to the

limited supply of samples, the same sample was annealed at progressively higher

Table 1

Some bulk properties of garnet and implantation schedule

Nominal composition { Sdy gq7™ 17%. 99 \ [Fe, ] (Gay 39F€o 61192

Nominal thickness (um). 0.95
lFagq 1074
|Fooel 974
| Feaq 4 1124
Labs (um ~) 0.117
4nM (gauss )** 510
Wafer Ion Nominal Energy Nominal Dose
+ (keV) (10! em?)
M721 Ne 190 5
10
20
30
50
M721 He* 140 300
600
1200
2000
M722 Hy 120 200
300
500
2000
4000
Implantation current density 0.25uA/em

*Structure factors and normal absorption cnefficient calculated from
the composition.

**Calculated from magnetic bubble properties.

temperature in successive steps lasting .30 min each. FMR measurements were made
every 50°C, while rocking curves were taken every 100°C.

Double crystal, Bragg case, X-ray rocking curves were taken under the
conditions described in Ref. (7). The X-ray source line was Cu Ka with an incident
beam counting rate of 10°cps. The spot size at the sample was limited to ~ Imm x
Imm by a set of slits. All as-implanted samples were measured using the (444)
reflection. In certain cases described below, the (880) Yo>l¥yl > and the (880)
Ys! Yyl » reflections were also used. For the annealed samples, especially for
annealing temperatures greater than 350°C, the (888) reflection was used because
of its sensitivity to low strain. Measurements repeated up to several months
apart produced practically identical rocking curves.

Ferromagnetic resonance measurements were made at a fixed frequency of
9.5 GHz with the usual combination of rectangular cavity, microwave bridge, and
modulated external applied field. All measurements were made at room temperature
without a temperature controller. Both perpendicular and parallel FMR configu-
rations were used for each sample. For some samples FMR spectra as a function
of polar angle were also taken. The reproducibility of mode location and amplitude
determination was +5 Oe and +2%, respectively, for measurements repeated within a
few hours. However, spectra taken several days apart at times showed systematic
differences up to 50 Oe in mode location, without appreciable changes in mode
amplitude. We attribute these variations to differences in room temperature,
since one can observe shifts of several hundred Oe by blowing warm (150°C) air
into the cavity. We do not consider the observed variations to be significant,

since the range of applied field in which the modes are excited spans several

thousand Oe.

III. Theoretical Considerations

It is perhaps inappropriate to include here a qualitative description of

the basic processes of ion implantation. The major purpose of this paper is to
present experimental results. However, the impression formed by reading the
literature on ion-implanted garnets is that different authors assign different
meanings to the same words. At the risk of belaboring the point, we wish to give
a precise description of what we think we are measuring.

During ion-implantation the incident ions undergo collisions with target
atoms. Since the ion beam is aimed in a non-channeling direction, the crystal-
lographic structure of the target plays only a minor role in determining the
scattering process. The parameters which enter the expression for this process
are the masses and nuclear charges of the ion and target atoms, the density
(number of each kind of atom per unit volume) of the target, its electronic

density, and the kinetic energy of the ion beam. 49) Since the ions continuously

lose energy as they penetrate the crystal, the energy dependence becomes at least

statistically a depth dependence. Due to the low electron mass, collisions with

(49)

electrons remove energy but do not contribute to damage. For typical implan-

tation in garnet at a few hundred keV, the number of nuclear collisions per ion

is several hundred. ‘46)

At each collision the transferred energy ranges from
zero up to a value determined’ by the kinetic energy of the ion and the jon-
target mass ratio. If the transferred energy is sufficiently large, the target
atom will be ejected from its original site and may in turn eject other atoms.
Thus for each incoming ion there is a cascade of recoil atoms (a thermal spike).

(46)

The mean free path of the ion is sufficiently short » so that even for the

2 for Ne* and 108 em? for He* and

lowest doses we are considering (~ 10!3 em
Ho”) at least one atom trom almost every unit cell has been displaced by more
than one interatomic spacing. Atoms surrounding either the vacancy or the
interstitial atom are no longer located in perfect-crystal sites. Since an
interstitial and a vacancy are not equivalent, it is plausible that in the

implantation region the atoms are no longer packed as closely as in virgin crystal.

This is the positive strain uniformly observed in ion-implanted crystals with

widely different properties, such as Si, GaAs, and aaa. (7 »59)

If the displacement of a particular atom j is AY 5 then there is a probability
distribution p(Ar.) which describes the frequency of these incoherent displacements.
For a polyatomic crystal, such aS garnet, one expects that each set of equivalent
sites, occupied by a particular atomic species, has its own p(Ar;), each contri-
buting in a different way to the total (coherent) strain. For jon doses below ©
that reyuired tu render the crystal amorphous, the unit cell is still recognizable.
The registry between the implanted layer and the underlying undamaged crystal is
maintained. It constrains the average unit cell to expand only in a direction

(7)

perpendicular to the film surface. The implanted layer is therefore in lateral
compression and the total normal strain includes a Poisson (elastic) contribution.
The compressive stress may act as a source of eneryy for the creation of extended
defects. If the stress is sufficiently large, stress-reducing dislocations may

form. (2!)

Such an occurrence is accompanied by the loss of strict registry between
highly stressed and less stressed regions of the crystal. .

Up to now we have not considered any crystallographic effects due to the
presence of the implanted dopant. Although a priori it 1s not possible to exclude
the dopant as a contributor to the total strain, experimental results strongly
suggest that only the damage is effective. For the same strain, the doses for

(1,39) conforming

neon vs. helium differ by one and a half orders of magnitude,
to the difference in nuclear stopping power. The hypothesis that damage is the
source of the strain is further confirmed in Ref. (39), where the detailed strain
distribution was found to agree closely with the calculated distribution of energy
deposited in nuclear collisions, but not with the ion range. Our present results,
discussed below, suggest that in the case of hydrogen implantation there is a
detectable strain associated with the ion range.

X-ray diffraction can detect and separate the implantation-induced damage

components : point defects, strains, and extended defects. Point defects change

the value of the structure factor. If they are incoherent, the magnitude of the
structure factor is diminished. This decrease is determined by the displacement
functions p(ar,) belonging to each site j. We make the simplifying and physically
plausible assumption that these functions are spherically symmetric. gaussians
described by their standard deviations U,. A further simplification is that, at
a given depth, Us=U is the same for all sites. For the reflections used in this
work, the c-sites, occupied by Gd, Tm, and Y¥, are the dominant contributors to
the structure factor. Thus the experimental value of U refers mostly to these
atoms. The sensitivity to a- and d-sites, occupied by Fe and Ga, is much less
(20% to 40%, depending on the reflection), and the sensitivity to h-sites, occupied
by 0, is practically zero. (7)

The definition of strain used in this work is the fractional change in
lattice parameter with respect to that of virgin GGG crystal. The strain may
have a component e* in a direction perpendicular to the film surface and a

lateral component e!!. In general, both e~ and e! change the magnitude and the

direction of a particular reciprocal lattice vector. These changes are related
(7)

lu the measurable change in the angular location of the Brayy peak. X-ray
diffraction alone gives no information on stress.

Detailed information about extended defects is much more difficult to extract
from the rocking curve. If they occupy a sufficiently small volume, they are
indistinguishable from point defects. If the extended defects involve gentle,
long-range (~ lum radius) distortion of the lattice, then they result in a
broadening of the rocking curve. In this case, the mosaic-crystal theory'°2) may
be used to obtain estimates of their size, misorientation, and lateral variation
in strain. (+50)

The relationship between point defects, strain, extended defects, and dopant
chemistry on one hand, and magnetic properties on the other, is poorly understood.

We are not aware of any "first-principles" theoretical framework which would

attempt to relate magnetism to the chemistry and geometry of implanted crystals.

At low doses there is an approximately linear relationship between the shift in
location of the FMR principal surface mode and dose, strain or stress. The propor-
tionality constant roughly corresponds to the magnetostriction constant determined
by external elastic deformation of the virgin crystal. At higher doses the mode
shift is no longer simply related to any of these. In some of the references

a correlation is attempted in which the mode shift is cquated to a change in Hy
which is then related to the dose or maximum strain. This is erroneous for

several reasons. The most important of these is that H, saturates and decreases

in regions of high damage so that the mode is localized and measures the change.

in He at a point far from the point of maximum strain. It is not clear whether
the changes in other magnetic properties, such as M, A, Hy» vy, and a are due to
strain or damage or chemistry, or a combination of all. Even worse, the magnitudes
of these changes versus ion species, dose or depth are also poorly known. Ferro-
magnetic resonance spectra, when interpreted according to the model presented in

Ref, (31), provide information about profiles of these magnetic properties.

IV. The Fitting Procedure

Crystalline profiles and magnetic profiles are obtained from the rocking
curve and the FMR spectrum, respectively. Unfortunately, neither technique as
presently .used can directly yield the desired profiles from the respective
measurement. Both techniques rely on choosing a trial distribution, calculating
the corresponding spectrum, and comparing it to the experimental data. Since
the spectra characteristic of various classes of profiles (unimodal vs. polymodal,
constant or increasing or decreasing with depth, etc.) have already been calcu-
lated, these serve as a guide in choosing the initial distributions. A trial and
error procedure is then used until a satisfactory fit is obtained. A more

sophisticated approach is the use of Jacobians to determine the changes in profile

for a better fit. However, combination of this with least-squares fitting proce-

dures has been singularly unsuccessful in converging to a satisfactory fit.

In the rocking curve, the angular range of nonzero reflecting power establishes
the maximum strain, the most rapid oscillation establishes the total layer thickness,
the area under the curve establishes the thickness-averaged structure factor; and the
degree of smoothing is related to extended defects. '”) In the kinematical regime,
the rocking curve and the strain and damage distributions are related through a
Fourier transformation. However, the lack of phase detection precludes a direct

inversion of the rocking curve.

In perpendicular FMR, the location of the highest mode yields an estimate
of the maximum field for local uniform resonance Hn? the total number of surface
modes yields an estimate of the ratio A/(MT*) , where T is the layer thickness;
the linewidth is linearly related to the damping parameter a; the relative
' amplitudes of the principal surface and body modes yield a value for surface tu

bulk magnetization ratio. (37 253)

Some of this information is repeated in a
different form for parallel FMR.

For both X-ray and FMR analyses the accuracy and uniqueness of a resulting
distribution depend on several factors: the information content (i.e. structure)
of the experimental data, the sensitivity of the experimental data to variations
of the quantity in question, the extent to which other parameters produce similar
effects and of course the accuracy or quality of the fit that is demanded. The
interpretation of the rocking curve is less ambiguous than the FMR spectrum
since the rocking curve depends very strongly on only one parameter, the strain
distribution. The damage distribution though required for a fit at high doses
and strain has a much smaller effect. As a consequence the strain profile can be
quickly obtained with an apparent high accuracy, while the damage profile is less
certain. Without a formal proof, it remains our opinion that the strain distri-

bution corresponding to a given rocking curve is unique, except for mirror refiec-

tions. Typically the strain distribution is determined everywhere to a

precision of a few percent of the maximum strain, and +2% at the peak. The

depth resolution is 50 to 200 A depending on the particular distribution.
We describe the damage distribution by U the standard deviation of an assumed
gaussian distribution of random atomic displacements. The local structure factor

kU2

has an exponential dependence |F| ~e ° , and so the parameter U becomes a

dominant factor in regions of high damage and has no effect in regions of low
(7)

damage. In a later section it will be shown that a linear relation between U
and strain gives the best fit but that the proportionality constant varies with
implant element. Thus the value of this constant is determined by the fitting
process for medium to high doses.

For the samples studied here, the number of surface modes excited by per-
pendicular FMR ranges from 1 to 11. If their locations and amplitudes are used
as inputs, there are from 2 to 22 data points. The major parameters which deter-
mine mode locations and amplitudes are the field for uniform resonance Hon and
the ratio ;. When several modes are present, the FMR spectrum appears to be
uniquely related to the distribution of Hon provided this distribution is unimodal.
In such cases the precision of the determination 1s within a few percent of the
maximum everywhere, and +3% at the peak. For unimodal distributions, the depth-
averaged A/M is also determined to +10%, but the sensitivity to the shape of this
distribution is relatively poor. The same remarks apply to the distribution of M.
Parallel FMR is used to separate the various components of Hons However the
resolution of parallel FMR is less than half that of perpendicular FMR, and the
overlap of modes vitiates accurate amplitude measurement. (3!)

If the magnetic profiles are polymodal, we are unable to determine a unique
profile from a single set of spectra. One must then resort to etching (or
preferably ion-milling, since it removes the material more uniformly) and re-

construct the profiles as described in Ref. (31). The etch - or milling-steps

must be small (100 to 200 R) since larger etch-steps leave room for multiple

interpretations of the spectra. The above discussion suggests the fitting pro-
cedure we followed.

For all samples the strain and damage profiles were first obtained. Magnetic
profiles were estimated by assuming a unique relationship to exist between Ain
and Ae” for each implanted species. For neon and helium, this relationship was
immediately shown to be linear at low doses with a clear saturation of AH in for
whal we Lerm medium doses. In this range the saturation can be represented
empirically or by some convenient mathematical form. We found it convenient and
satisfactory to assume a form

- 3
AH in = K[Aet - b(Ae*)°] (1)

The magnitudes of the linear and cubic terms were adjusted to give a best fit to
the spectra for aii iow to medium doses.

The assumption that AH in and Ac* are uniquely related was not arbitrarily
made. In previous publications, the authors have separately studied the same
low-dose He-implanted garnet with properties similar to those of some of the
present samples. The magnetic profiles were determined by one of the authors (3!)
independently of any X-ray results, and the crystalline profiles were obtained
by the other author ‘7? without FMR inputs. Upon comparison, the AH in and Ac*
profiles agreed with each other to +2% of the peak values.

Various features of the FMR spectra imply differences in surface and bulk
values of other magnetic parameters. Differences in the linewidth require a
change in a; relative mode amplitudes may dictale a change in M; comparison of 4
and {| modes may require a change in H, or y; FMR as a function of polar angle
about <110> axes places limits on the allowed changes in H,- However there
is relatively poor sensitivity to the actual profile shape of these magnetic

properties. A convenient assumption that is consistent with experimental data

is that these changes are also linearly related to Ac’. The peak value for each

distribution is then independently adjusted to fit the appropriate spectrum.

In the case of low to medium doses of neon and helium, this approach pro-
duced excellent fits to the FMR spectra. For all arbitrary deviations from this
relationship that were tested, the quality of fit rapidly deteriorated. At very
high doses the structure of the FMR spectra changed so radically, that we were
unable to use the strain data to obtain magnetic profiles. In this dose range
the bimodal profile of Hun was determined independently of strain, and with
reduced precision by etching and using the methods of Ref. (31).

For the samples implanted with hydrogen, the assumption of a unique relation-
ship between AH, , and Ac* was immediately shown to be false. Nevertheless, since
the magnetic profiles are unimodal, they could be obtained directly from the FMR

spectra, without the need to resort to etching.

V. Results and Discussion

A. Experimental and calculated spectra

Since neither rocking curves nor FMR spectra corresponding to a wide range
of doses of ion-implanted garnets have been published, we include here some of
our experimental data. In addition to showing their structural peculiarities,
the figures include calculated spectra showing the quality of fit that is
obtainable. For this quality of fit the distributions of Ae* and AH un

have the accuracy quoted earlier except for high doses where portions of
the film become: amorphous or paramagnetic.

Figures la. b, and c, respectively. show the experimental (dashed) and
calculated (solid) rocking curves for several doses of Ne’, He”, and H
implanted garnet. All three sets have several features in common: the single
sharp peak near the origin corresponding to diffraction by the deep, unimplanted,
bulk portion of the film; the oscillatory structure which extends to lower

angles and becomes less intense with increasing dose; and the envelope shape

Figure 1(a). Measured (dashed line) and calculated (solid line) Cu Ky (444)

REFLECTING POWER (%)

NEON

~ Se

palhtiad ny

-0.8

ANGLE FROM GGG PEAK (DEG)

rocking curves for 190 keV Ne* implantation. Doses are 0.5, 1.0,

2.0, 3.0 and 5.0x10!4/¢

-0.4

m for curves 7 through 5, respectively.

L] ‘ t t
HELIUM
3.07
Lil
a 2.0F
UO
Zz
ts
“I i
Lil
1.0F 2

-0.8 -0.4
ANGLE FROM GGG PEAK (DEG)

Figure 1{b). Cu K (444) rocking curves for 140 keV He* implantation. Doses
are 3.0, 6.0, 12, and 20x10! °/em? for curves 1 through 4,

respectively.

HYDROGEN

REFLECTING POKER (%)3

aw
Oo
° oS SS == TS eee

ANGLE FROM GGG PERK CDEG)

Figure 1(c). Cu Ky (444) rocking curves for 120 keV Hy implantation. Doses
are 2.0, 3.0, 5.0, 20, and 40x10 !9 fem? for curves 1} through 5,

respectively.

characteristic of unimodal distributions. For all cases shown, the calculated
plane-wave solution was convolved with the incident beam, whose angular diver-
gence distribution is approximated by a gaussian with a standard deviation of
8 arcsec.

Figures 2a, b, and c, respectively, show the perpendicular FMR spectra for
the same samples. The spectra are presented in stick-diagram form, the solid
and open rectangles corresponding to measured and calculated modes, respectively.
For clarity, the modes (experimental and calculated) are shown adjacent to each
other, without overlap. The actual field is located at their boundary. The
discrepancy between calculated and measured mode location is as a rule less
than +10 Oe, rarely becoming as large as 50 Oe for some of the high dose cases.
Mode amplitudes are indicated by the relative height of the rectangles. Experi-
mental modes with amplitudes less than 10% of the principal (or first) surface
mode, and nearly zero amplitude theoretical modes where no experimental mode is
seen, are also indicated by vertical arrows. The 50 Oe width of the rectangles
does not reflect the actual mode linewidth, which increases with dose from 70 0e
(bulk modes) up to v150 Oe (surface modes for highest doses).

Only spectra for the three lowest doses of hydrogen implantation are shown
in Fig. 2c. The higher-dose spectra were excluded because the lineshape of some
of the modes indicated that the static magnetization was not completely aligned
with the applied field. For sufficiently large surface anisotropy field, this
occurs for applied fields above but near the bulk mode. Although surface modes
exist in this situation, their characteristics cannot be calculated accurately
by the methods used in this study.

The depth-dependence of the r.f. magnetization in FMR provides a convenient
classification of modes. In the present figures, the largest mode, occurring
at ¥3750 Oe, is the main bulk mode, while modes at lower fields are predominantly

sinusoidal bulk spinwave modes. The modes found at fields above the main mode

190 KEV Ne”

xle4 NOMINAL
DOSE

11]

LJ
eisvd

1 | |
. f fh | .

30
, a th

o|
al

4 3 6 ?
APPLIED FIELD (KOE)

W-

Figure 2(a).

Measured (solid rectangles) and calculated (open rectangles) 1

FMR spectra for the Ne* samples of Figure 1(a).

140 KEV He~

Jd | | | | 6108 em")
f tt as Lal il. 1 T :
1 | 1 J | '|
al a
1 | llldldd
1 | | | |

APPLIED FIELD (KOE)

Figure 2(b). 4 FMR spectra for the He* samples of Figure 1(b).

120 KEV He
EXP. fi] CALC.
x172 NOMINAL
7 DOSE
| 108 yom*>
r T T Rive T T T t T T 1
i 7 i x17 2 7 t g qT T I
| [| °
r t i T al} — T Hh T T T 1
3 _ 4 5 § 7
APPLIED FIELD (KOE)

+ :
Figure 2(c). 42 FMR spectra of the three lower dose H, samples of Figure 1(c).

are largely confined to the implanted layer and are called surface modes . (31)

For low doses, the amplitudes of the surface modes generally follow an alternating
large-small sequence which is characteristic of certain unimodal distributions of
Hint This is seen for the lowest three neon doses, the lowest two helium
doses and all three hydrogen doses.

An important feature is observed on comparing the spectra for the lowest and
highest doses in the neon and helium series. Although the nominal doses vary hy
an order of magnitude, the separation between the principal surface and bulk modes
changes by less than 30% in both cases. However the high dose spectra have
a drastically different character. In these cases the magnetic profiles become
bimodal. The details of the bimodal profiles could only be elucidated by analysis
after progressive etching.

The bimodal character was first established for the third helium implant
with dose 1.2x10!°/em®, This case showed at least ten surface modes in a complex
spectrum unlike anything seen in earlier work. The development of this spectrum
with etching was even more bizarre as seen in Fig. 3a. Mode locations are
indicated by circular symbols (or clliptical symbols for less certain locations);
mode amplitudes are given at selected depths. Question marks indicate amplitudes
uncertain by more than a factor of two. Also shown are the cumulative etch-time
intervals, and vertical arrows which indicate depths obtained by analysis of
X-ray rocking curves. The unetched spectrum is identical to one of the spectra
in Fig. 2b. The evolution of this spectrum with etch depth is quantitatively and
qualitatively different from that of a lower dose, but identical energy, He
implantation in a similar garnet (see Figure 5 of Ref. (31) for a comparison).

Figure 3b shows the calculated spectrum for the etched sample. To obtain
this structure it was necessary to use a bimodal profile for Hon with extreme

variations in magnetic profiles to be discussed below. Although there are small

discrepancies of detail between Figures 3a and 3b, the sensitivity of the

Lf i] t t 1 t i]
Z EXPERIMENTAL MODE LOCATIONS AND AMPLITUDES 7]
+ 18 2
| 140 KEV HE NOMINAL DOSE 1.210 /em” |
X-RAY
| | | DEPTH
7T 6102006300 6235—l—sC 40 45 50 Te (SEC) |
100 o— 0-0-0106 .
rts Ox, 00-070>0~- 9 190-0---— 91002 7
“ \
‘u OO4 (20 \
oO N
x BF 7 one N ‘\ \ 7
Vw oO, \ N l
o13 Qa ‘\
Q ‘o \> “ane. w ~ | —
_] nt we \ Der y-~. >
Li 40, YY , \ 1007
onl ‘o \ Q N \
LL No \ \ \ \ i
SP 4a tor \ SS rn 7
ra \ ‘0 G \
_! 40 SS \\ \ \ |
oo = ‘oO \ Q ‘0 Ss \ \ , \ \ “
a. oO NY YN A Le |
. \ Vy
a2 XN ‘) YY vary \
= ? nd
4 PO \ \ \ \ ‘ \ \ \ \ \
22n0 ‘oo bonmno 04300 044007 ose00?-———-
3 l I if l I I 1
0 2000 4000 6000

ETCH DEPTH CAD

Figure 3(a). Experimental 1 FMR spectrum versus etch depth for the sample

implanted with 140 keV He’, 1.2x10!®/em?.

CKOE D

APPLIED FIELD

U U LI ' i { {

CALCULATED MODE LOCATIONS AND AMPLITUDES

140 KEV HE NOMINAL DOSE 1.2x10°°/om |

ETCH DEPTH CAD

Figure 3(b). Calculated 1 FMR spectrum corresponding to Figure 3(a).

calculated spectrum to the extreme variations in magnetic profiles is so large
that we accept this result as sufficiently accurate.

In addition to this case, the etching and fitting procedure was repeated for
the neon implantation with dose 3x10! 4 yen. A similar profile was required and

the quality of fit is similar to that shown in Figures 3a and 3b.

BR. Profiles of Perpendicular Strain

The strain profiles obtained from the rocking curves of Figure 1 are shown
in Figures 4a, b, and c for Ne’, He’, and Ho” implantations, respectively. In
each figure the distributions are labeled to show correspondence with the appro-
priate rocking curves. Since the (444) reflection used is symmetric about the
film normal, only the perpendicular strain is measured. The unimplanted regton
shows an aS-grown component of strain. Assuming that for any single wafer this
strain is constant and independent of location on the wafer, the small spread
observed in the measured value verifies the reproducibility of experimental
rocking curves stated earlier. The implanted regions shown on the left in these
figures have thicknesses which depend on implanted species and energy. For
computational convenience the distributions are represented in laminar form, the
number of laminae being approximately the minimum required for a good eit.)
This number increases with increasing strain, as seen in the figures.

For each species the general features of the profiles conform to expectations
based on LSS theory. Going from Ne* to He* to Ho the distributions become
sharper and increasingly asymmetric about the maximum strain. The magnitude of
the maximum strain below amorphousness is about 2.5% for Ne”, 3.4% for He” and
3.9% for Hy” « For each species the surface strain is less than half of the
maximum strain. The thicknesses of the strained layer are 3300 R, 5800 R and 4900 R,
respectively. The total thickness, including the bulk region, is 9200 h for

the Ne and He* implanted wafer, and 8400 R for the Hy implanted wafer. Both

r 190 «xeV Ne 7

3r _
re 5
NA
2 - 7
te |
in
~ 2b
C) 4
O - _
lo T ]
Lu
oo Lhe —

4000 6o0o0 8000
DEPTH

Figure 4(a). Perpendicular strain profiles of New implanted samples. The
distributions are labeled to show correspondence with the rocking

curves of Fig. 1(a), from which they were obtained.

- 140 «w.eV He a
_4

3r ~
ws
ZerR a
es
jaa
ke
'¢9) 3
_j
—t
GS oF 2 L | |
e | 1
fy
at 1 oo -

a | Lu
@} l j

O 2o00. 4000. 6000 sooo
DEPTH CAD

Figure 4(b). Perpendicular strain profiles of He* implanted samples.

‘>

PERPENDICULAR STRAIN ¢

3L 5
ar
ITT
_ 7 3
T 2

120 weV H,

Oo 4 1 1 1 ——y
0 2000 4000 56000 s0d00
DEPTH CA)

Figure 4(c). Perpendicular strain profiles of Hy” implanted samples.

values are in reasonable agreement with the approximate values determined optically
by the supplier.

For the two highest doses of Hy implantation (Figure 4c, distributions 4
and 5), our resolution is sufficient to show that the presumed bulk region is not
really uniform. A two-layer representation of the strain profile in the bulk is
shown since the resolution does not permit greater detail. The variation shown
1s required to Tit the low-angle features of the rocking curve. The differerce
in strain between the two layers increases in proportion to the
maximum strain . This behavior as well as the thickness and location of the
region of higher strain leads us to conclude that the increased strain is due to
the presence of implanted hydrogen. For 120 keV Hy according to theory most of
the stopped hydrogen atoms are located in a region about 2000 R wide at a distance

of 4500 R from the surface. (4)

The region of increased strain in the bulk

region is consistent with this calculation. For these doses, the relative atomic
concentration of hydrogen is 2% to 4%, and the presumed dopant-induced strain is

4% of the maximum strain induced by damage. This relation may hold for other
implanted species but cannot be determined by the rocking curve method. For other
dopants the implanted layer is rendered amorphous for doses corresponding to dopant
concentrations well below 1%.

For each implanted species there are two curious features involving the
relation between maximum strain and dose, and the ratio of surface strain to
maximum strain. First, the maximum implantation-induced strain Aer ax does not
behave smoothly as a function of nominal dose. For example, the values of her ax in
Figure 4a are in the ratios 1] :1.8 :2.1 :3.2 :5.4. The normalized nominal doses
form a different sequence 1,2,4,6 and 10. For hydrogen (Figure 4c), the values
of her x are in the ratios 1 :2.3 :3.9 :9.8 :18.8 while the normalized nominal

dose sequence is 1, 1.5, 2.5, 10 and 20. Data for helium are also inconsistent

but in a third way. If the nominal doses are taken at face value, there is no

discernible unique relationship between maximum strain and dose. Since implanta-
tion was done in another laboratory, we are unable to assess the accuracy of the
doses. The second feature is that the detailed shape of the strain distribution
(in particular the ratio of surface strain to peak strain) does not show a
systematic trend with increasing dose. Fortunately the existence of pairs of
nominally identical samples for each species and duse has enabled a partial
resolution of this puzzle. The rocking curves obtained from each pair of samples
are in most cases decidedly different giving rise to an inconsistency in the ratio
of surface to peak strain. While the maximum strain values for each pair do not .
differ by more than 15%, a discrepancy develops between this region and the
surface, becoming as large aS 250% at the surface. It was gratifying that this
same inconsistency was found in the FMR spectra and their corresponding Hun profiles.
The lack of systematic trend mentioned above is simply a continuation of this
inconsistency. The actual reason for these variations in strain and magnetic
profiles for nominally identical samples remains unknown. This inability to
manufacture reproducible samples has hampered our attempt to determine the dose
dependence of strain and magnetic profiles. Serious inconsistencies in the pro-
perties of implanted garnets versus dose have been reported by at least two

(55,56)

other laboratories.

C. Lateral Strain and Stress

An important characteristic of ion-implanted single crystal layers is the
compressive stress in the implanted region. Its existence implies that at least
up to a certain dose, implantation causes a tendency toward an isotropic or nearly
isotropic expansion of the unit cell. But at least initially the registry with
undamaged crystal constrains the implanted layer to expand only in a direction
perpendicular to the surface. (7) Therefore the implanted layer and the much thicker

substrate are in lateral compression and lateral tension, respectively. The

44)

to 10}? yom”,

depth-averaged compressive stress has been measured hy a heam cantilever metho
For 100 keV Ne* implantation with increasing doses ranging from 10! 3 em?
in Ref. (14) the average stress initially increases linearly with dose, then satu-
rates, and finally decreases to the limit of detection. Over this range we find
that the perpendicular strain continues to increase with dose up to amorphousness.
Three possible reasons for the decrease of stress come to mind: (1) with increasing
dose the modulus of elasticity E of the implanted layer diminishes by more than an
order of magnitude; (2) dislocations are formed to accommodate the lattice mismatch
and allow the unit cell to relax back to a cubic shape; and (3) a phase transition
occurs such that the new equilibrium shape of the unit cell is rhombohedral.

By measuring lateral strain we have attempted to determine the role played by
the second possibility in the mechanism of stress relaxation. For the Cu Ky (880)
Yor l¥yl reflection in <111> garnet the glancing angles of incidence and diffraction
are 80° and 9.5°, respectively. In the ¥5<1 Yq reflection the directions of
incidence and diffraction are reversed. For both cases the rocking curve measures
lateral in addition to perpendicular strain. In the Yosensitivity to lateral strain is even greater than to perpendicular strain. In
a helium implanted sample with a maximum perpendicular strain of 0.82%, previous
meas urement showed 7) that lateral strain was below the limit of detection (10.03%).

In the present study we selected the neon distribution #4 (Aer, 71-57%) and
the helium distribution #3 (Aer = 2.00%) because the strain is high but the
damage is below the level of amorphousness (see the next section for results on
damage). The nominal dose for neon case #4 is greater than the dose for which the
stress rapidly diminishes, as reported in Ref (14). Our present result is that
for both Ne” and He” distributions the measured lateral strain at any depth is
not greater than 0.03%. Thus, even though the stress may have relaxed, the
implanted unit cell has not returned to cubic shape. This rules out possibility

#2 as the mechanism of stress relaxation. We do not believe that the modulus of

elasticity goes to zero as the implanted layer approaches amorphousness. Crystal-
line and amorphous materials of the same composition usually have similar elastic
properties. We are thus left with the hypothesis that the equilibrium shape of
the unit cell in the implanted garnet layer becomes, at a certain dose, rhombohedral.
A possible mechanism for this transition has been suggested by W.L. Johnson. (97)
Due to the interaction of the local stress field of a Frenkel pair with the macro-
scopic (average) stress, the energy of the Frenkel pair is not invariant under
rotation. During implantation at a certain dose this energy is minimized by an
uniaxial orientation of Frenkel pairs which reduces the macroscopic stress. When
this occurs the perpendicular strain no longer has a Poisson contribution. For
this and higher doses Ae’ should show a different behavior from that at lower -
doses. We are unable to verify this since the actual doses are uncertain and for
nominally identical implantation the strain distribution is not reproducible.

The assumption that in implanted <111> garnet the equilibrium unit cel]
becomes rhombohedral is supported by a measurement of the stress distribution! '6)
in a magnetic garnet implanted with 200 keV Ne’ at a dose of 2x10 4 /em?. According
to this reference, in the implanted layer the stress distribution is bimodal.

The 1000 R thick regions near the surface and near the interface with unimplanted
material are under substantial and comparable lateral stress. In the intermediate
region, also 1000 R thick, where the perpendicular strain and the damage are
greatest, the stress is barely measurable. The existence of compressive stress

in the outer region is unexplained if relaxation occurs by a crystallographic
decoupling of highly implanted from less implanted region. But if the relaxation
is accomplished by a local transition to an equilibrium rhombohedral unit cell,
then at a given depth the stress depends on the dearee of this transition. In
this case two regions with the same sign of the stress may be separated by a

region with zero stress. Since even at high doses we have measured the lateral

strain to be zero, henceforth we shall drop the term “perpendicular” when we

speak of strain.

D. Damage Profiles

For the present range of doses, for each species the area under the rocking
curve changes by roughly one order of magnitude. Since the layer thickness does
not decrease with increasing dose, the only possible interpretation is that the
magnitude of the structure factor F decreases. Amorphousness corresponds to
|F[.0. Small strains (0.1 to 0.5%) are easily measured with good accuracy.

In this region the structure factor is essentially unchanged and no information
can be obtained about the damage profile. When the maximum strain reaches about
2.5% for neon, 3.4% for helium or 3.9% for hydrogen, the structure factor in the
region of maximum strain has decreased to nearly zero and above this strain no
measurable diffraction occurs. As the peak strain falls below this critical
value, the local structure factor rises sharply, the best fit being a negative
exponential in (ac)*. Since the structure factor is known to depend in this
Same way on U (the standard deviation of the assumed gausstan random atomic
displacements) it follows that the peak value of U is linear in Ac. Elsewhere
in the profile, the sensitivity is such that U cannot be determined with equal
precision and we can only state that when the strain is high enough to give a
determination of U, the peak value occurs in the region of maximum strain.

Since it varies linearly in this region, it is a reasonable hypothesis that

this relation holds at all depths and strains, in agreement with Ref. (7). This
is consistent with the idea that the damage is the source of the strain.

With this assumption, excellent fits have been obtained for all doses. The
proportionality constant between U and Ae has the value 0.25, 0.18 and 0.138/%
for Ne*, He” and Hy” implantation, respectively. The different effective levels
of damage for the same strain are due to the discriminating sensitivity of the
(444), (888) and (880) reflections to the c-sites occupied by the heavy elements
Y, Gd, and Tm. The implication is that for the same strain,neon ions damage the

c-sublattice more severely than helium or hydrogen ions. This is in agreement

(49)

with the ballistics of implantation in polyatomic materials.

At high doses the broadening of (880) reflections indicates the presence of
lateral nonuniformities attributable to extended defects. The resolution is not
sufficient to provide quantitative information about their density or structure.

As we have shown, these defects do not result in any measurable lateral strain.

E. Magnetic Properties versus Strain for He* and Ne? implantation

The local field for uniform resonance Hon in 1 FMR is

= 2
Hin = 7 Hy, + aM + BH (2)

where w is the microwave angular frequency, y is the gyromagnetic ratio, H) is

the uniaxial anisotropy field, 4mM is the saturation magnetization, and Hy is

the cubic anisotropy field. The change in Hon is specified by AH ny? the difference
between its value and that in the bulk region. Of all magnetic properties obtain-
able by FMR, the distribution of AH in is determined with the highest precision,
However for high doses, substantial changes in other parameters are demanded by
the resonance spectrum. Even though these changes are not known with the same
precision, their general features are incontestable. A good example is shown in
Fig. 5 for the helium implantation with dose 1.2x10!©yem?, This dose is not
sufficient to give a nonmagnetic layer but produces extreme variations in almost
all magnetic parameters and gives a very rich spectrum in 1 FMR with eleven
surface modes as shown in Figs. 2b and 3b. Fig. 5a shows the profile of AH in
(solid line) and the strain profile multiplied by 4.1 k0e/% (dashed line). This
choice of multiplicative constant is made clear below. Although the strain
profile is unimodal, the distribution of AH ny is bimodal and no longer resembles
the strain profile. The profiles of 4nM and A/M are shown in Figs. 5b and 5c.

At the location of maximum strain there is an 80% reduction in 40M and a 98%

T T T T T
“-- CDELTA STRAIN) x 4.1 «OE

ep = 6A? a, — DELTA Hiy :

wi L

' i)

nat t

€KOz)

DELTA Huy

6 L CBD |

S 4t a
= | Tot |

nan 0 * | t t

Fa}

e BF cop ;
z r -_
Ww

"o 4r .
= r 4
< ai 1 1 i Il t

0 2000 4000 6000 8000
DEPTH Figure 5 Profiles corresponding to Figure 3: (a) AH in (solid) and Ae

(dashed); (b) magnetization 4nM (c) Ratio A/M.

reduction in exchange constant, A. These extreme variations are required to
produce the FMR spectra of Fig. 3b.

The relationship between AH in and Ae may be obtained by considering their
respective values for al] doses and depths. Figure 6a shows the values of AK un

versus Ac obtained for all doses of helium implantation. A different symbol is

used to represent each set of points corresponding to a particular dose. The

nominal doses and the values of Max are also shown. Tf we limit attention to

the two lower doses for which Aenax < 1.3%, all points lie on a single curve.

In this dose range the relationship between AH in and Ac is unique and independent

of dose or depth. As mentioned in a previous section, for pairs of samples with

nominally the same implantation, the values of Mena are nearly the same, but

strain values towards the surface differ by a factor as large as 2.5. Even with
such differences in profile the relationship shown in Fig. 6a is valid.

The initial slope of the curve is 4.1 k0e/%. As we shall show, in the linear
region approximately 98% of AH in is due to the change in uniaxial anisotropy Hy.
If the change in Hy is attributed to magnetostriction using bulk values of Young's

12 2)

> Poisson's ratio (v = 0.29) and magnetization

modulus (E = 2.0x10°" dynes/cm

(4nM = 510G), one obtains a value of -3.6x10 for the magnetostriction constant
Adit This number is higher than but in reasonable agreement with the value
-3.4x107° estimated from the nominal composition and the tables given in Ref. (40).
Thus we conclude that, at least for He”, at low doses the principal source of

AH, is Ac and that the relationship is the same as for external elastic deformation

(magnetostriction). |

For AE ax 2 1.3% the dependence of AH in on Ac is much more complicated.
First, AH, saturates at a value 3.6 kOe at strain Ac = 1.5% and then decreases
to a value near zero at Ae = 2.3% where the material becomes paramagnetic. The

material remains nonferrimagnetic up to the highest observed strain Ac = 3.30%

where the material is nearly amorphous. Second, in the region where AH in is

LI ij T i T i
140 KeV He
3S F NOMINAL 7
DOSE
103 em?) 3 r 12 20
” SYMBOL e o en
MAXIMUM | | | |
STRAIN
4b
a oS _
_ INNER
tl REGION
Oo
¥ 3b A :
s &
r r e "]
Ee \
cm 2b £ LY \ |
a > outer \ \ | PARAMAGNETIC >
REGION \ | |
z ° \ \ 7
° a |
s V4
1b © \\
\\
\\
° \
l I ] i] I I
05 1 2 3

DELTA STRAIN (2%)

: +
Figure 6(a). AH in versus Ac for four He doses. Each set of points corresponding

to one dose is represented by its own symbol. Nominal doses and

Ae ax values are also indicated.

(KOE)

DELTA Hyy

J t t

190 KeV Ne~
rf NOMINAL 7
DOSE
5 10 20 30 so 610!9 vom™ >
Z ° ea a & SYMBOL 7
MAXIMUM
F [| fl | | team
INNER /
4 REGION
L e .
o \ I | PARAMAGNETIC
é Va \
. o OUTER \i 4
r REGION \\
\\
| \\ 4
é \
LA \ a
Ff {
é I l l ! Ll lt
0 1 2 3

Figure 6(b).

DELTA STRAIN (%)

Anon

versus Ae for five Net doses.

saturating and decreasing with strain, the relationship is no longer unique. The
solid and dashed lines, respectively, connect the points obtained for two different

doses where de ax is equal to 2.00% and 3.30%. In each case there are two

relations between AH on and Ac. If the implanted layer is subdivided into two
regions, one (the outer) includes all points from the surface up to the location
of the peak strain, and the other (inner) region includes points from the peak
strain down to the interface with unimplanted matcrial. These regions have a
different relation between AH in and Ae. Another intriguing feature is the lower

saturation for Ae nax < 1.5% compared to the peak value for higher strains. For

now we defer discussion of the possible reasons for this behavior.

A plot of Mn vs. Ac for all neon doses is shown in Fig. 6b. The general
features seen with neon are the same as with helium. The initial slope of the
curve is 4.1 k0e/%, again supporting the conclusion that at low doses the phenomenon
giving rise to AH, is magnetostriction. The important differences between Ne"
and He* implantation are the lower peak value of AH in (2.8 kOe versus 3.6 kOe) and
the lower strain (1.8% versus 2.3%) for which the material becomes paramagnetic.

We return to He implantation for a discussion of magnetic pruperlies ulher
than Hon’. Figure 7 shows the values of 4nM, A/M, Hy and a versus maximum Ae.
Due to poorer sensitivity, the profile shapes of 4nM, A/M, Hy and a cannot be
independently determined. In the dose range below saturation of AH in? a good fit
is obtained if the implantation-induced changes are assumed proportional to Ac.
The extreme variation then occurs at the point where the strain is a maximum.
For higher doses the variations are less certain, particularly when a part of the
surface layer becomes paramagnetic. A good fit is still obtained if the changes
are proportional to Ae. except that 41M and A/M go to zero at Ae ~ 2.3% and remain
zero for higher strain. |

The variation of Hy is less certain but it clearly decreases as the strain

increases. The bulk value, -165+5 Oe, was determined with good accuracy by

L t Lj T T T
+ NOMINAL
140 kKeV He DOSE
is 2
a 500. . 3 6 12 (10 vom)? 20
ro)
“~ ~~_O
E ~s
~ —
* 350 - cA) eo
yA
“wey a
-~ 0 =
8 A-—~_
N 6r O~ _
n 4r CB) “Ky
b= ~
— 2 = ‘\, “|
SG fs m
a AL Z
~~ ~
~ ~~\
xz 100 F Oo~ “
n ~ r)
2 sok CC) ar “
mn! ~
= ~ >
re] + LI a
a CD)
t Ise Oo -----U 7
a oT @
z “7
on 1 t i if
10, : ;
x : 3

MAXIMUM DELTA STRAIN ¢€%)

Figure 7(a)-(d). Extremum values of magnetic properties versus Aenay for the

four He doses.

their own symbol.

Values obtained for each dose are represented by

(a) Saturation magnetization 4M. (b) Ratio

(A/M) of exchange stiffness constant to saturation magnetization.

zero suppression).

t i t q t lj
+ NOMINAL,
190 KeV Ne DOSE
13 2
a soo 5 10 20 30 50 (10 vom )
re) ~N
“ ~N
E ~~
oO *e
* 250 & s CA 7
DO.
“g
~ A
a 0 t t cy Aim
5 A-—-O._
YP BF . s
2 ON
n 4r N CB) _
° |. |
ww 2k \ —
= \
re) +— f\—
150 FN -
ec NL
zr 100 + On (CC) 7
pam | ~ -
“So
0 +i Ls
a _
| 7
= eH
Isr v7 (Dd) 7
£ 7
a a”
7 \
10, Il I I L i
a 4 2 3

MAXIMUM DELTA STRAIN (%)

Figure 8(a)-(d). Extremum values of magnetic properties

: +
five Ne doses.

r'
versus be nax for the

measuring the bulk resonance mode as a function of angle. This procedure when
applied to the surface modes can only be used to estimate the minimum value of
Hy since the large uniaxial anisotropy masks the effect of Hy and since accurate
analysis is not feasible for spin-wave resonance at angles other than parallel
and perpendicular. The asymmetry of the resonance field for the principal surface
mode vs. angle suggests that H, decreases about /0% for the dose where Ae = 1.3%.
Comparison of perpendicular and parallel spectra requires a change nearly twice as
large or else requires a smal] increase (~ 4%) in the surface value of y (perpen-
dicular and parallel FMR cannot distinguish between these parameters). The bulk
value of y is 1.503 x 107 (Oe sec)7!, This is 15% lower than that of pure
YIG, a feature attributed to the presence of rare earth ions. It 1s quite
plausible that implantation damage would reduce this effect. The damping
coefficient « is another parameter which increases with strain. At Ae = 2.3%,
where most magnetic parameters go to 7era, « reaches a value 50% larger than
in the bulk. For Ae > 2.3% the material is paramagnetic and a is not defined.

As shown in Figure 8, the magnetic properties of the Ne* implanted samples
behave in a way that is similar to He* implantion. The major differences are
the higher rate of decrease with strain and consequently the lower value of Ae
for which (nM, A/M, and H, go to zero (1.8% versus 2.3%), and the large increase
of «a with Ac. As for helium implantation, the transition to paramagnetism is

accompanied by a rapid drop in AH in (Fig. 6(b)).

. : . . + +, .
F. Discussion of magnetic properties for Ne and He implantation

We have seen that for both Ne’ and He” implantation the parameters M and A
which define garnet as ferrimagnetic decrease with increasing strain (and damage)
and that for a certain strain they go to zero. The local transition to para-
magnetism occurs for damage levels roughly 30% below that required for amorphous-

ness. The information obtained so far is, of course, still insufficient to

permit an identification of the source of the changes in magnetic properties.

One is tempted to attribute the destruction of ferrimagnetism to. incoherent:
atomic displacements. There is even a correspondence between the more rapid
decrease in 4nM and A/M with strain on one hand and on the other hand the larger
increase of damage with strain for neon vs. helium implantation. However amor-
phous ferromagnetic materials do exist. It is conceivable that the large albeit
coherent strains caused by implantation also contribute to the transition to
paramagnetism. We can say very little about the increase in the damping parameter
a with strain and damage. The increase implies larger losses from magnetic
excitations to lattice vibration. In unimplanted doped YIG the losses are

(40) Their role in implanted doped

attributed to the presence of rare earth ions.
YIG is poorly understood, since in Ref. (5) a large (400 Oe) virgin linewidth
decreases while in the present case a low (70 Oe) virgin linewidth increases
with damage. |
Figs. 6, 7 and 8 show that ~AH, is the dominant component of AH in? The first
important feature of the relation between AH and Ae is the initial linearity
and value of the slope which matches the estimated magnetostrictive effect. The
| component of bulk Hy attributable to growth-induced anisotropy is about 500 Oe
whereas AH, can be as large as 3000 Ue. There is therefore no evidence that at
low doses the change in Hy is due to the suppression of growth-induced anisotropy. (44)
The second important feature is the saturation and decrease in AH, with
increasing 4c. This is similar to the reported saturation and decrease in

(14,16) A detailed correlation of these separate

stress in another garnet.
experiments is not possible, but the source of the decrease in both cases might
well be the same and is likely to be the damage. The ratio of AH, to stress could
in principle be used to define a parameter 344 44/M> but it is unlikely that this
would be the same parameter obtained by application of external stress and

deformation to this same implanted material.

We do not have an explanation for the departure from a unique relation
between AH in and Ae at high doses, but the sensitivity of the fitting procedure
and the accuracy of the spectrum give us confidence that the difference is real.

It has been observed in Figs. 2a and 2b that from medium to high doses
the separation in resonance field between principal surface and body mode is
relatively insensitive to maximum strain and dose. This is a natural consequence
of the saturation and decrease in AH, with increasing slrain. In 1 FMR the
principal surface mode is localized in the region neighboring the maximum Hon? At
increasing doses this maximum does not change, but shifts location from the point
of maximum strain towards the interface with unimplanted material, even after
large portions of the implanted layer have become paramagnetic. This also indicates
thal the shift of this mode with external elastic deformation cannot be used to

measure Ay) /M in the saturation region.

G. Magnetic Profiles for Hy” Implantation

The effects of H” implantation on AH, are known to be markedly different
from those of other ions. In.a given material, for He’, BY, cr, or, and Ne*

implantation the separation AH | between principal surface and body modes in 2

(45)

FMR saturates with increasing dose at a value not exceeding 3 kOe. In the

same material, implantation with hydrogen causes AH | to increase with dose
beyond measurement capability at 10 GHz (AH, = 10 kOe). Conversely, for hydrogen

implantation AH | decreases rapidly with annealing temperature around 350°C, while
(45)

All for other ions changes relatively little. The rapid decrease in All

correlates with annealing-induced desorption of hydrogen. (8) Upon annealing up

(33)

to 700°C AH shows a nonlinear dependence on the strain. Comparison of strain,

magnetostriction constant and AH for deuterium implantation shows an excess

contribution to AH, which is not attributable to simple magnetostriction. (20)

Even in garnets with very low Mad large values of AH | are observed. (47) These
results strongly suggest chemical effects associated with the presence of
implanted hydrogen. Our results support this view.

Figure 9(a) shows the distribution of AH in as a function of depth obtained
for 120 keV, 5x10'°/cm® Hy". This distribution corresponds to the third FMR

spectrum of Figure 2(c). The maximum OH is 4.5 kOe, a value greater than any

obtained with Ne* or let implantation. If the total AH in profile is assumed to
consist of a magnetostrictive contribution due to strain and a contribution due
to a different mechanism, then a comparison with the strain profile may yield
information about the unknown mechanism. Figure 9(b) shows the strain distribution
multiplied by 4.1 k0e/%. Since the maximum Ae for this case is only 0.602, it is
reasonable tu assume that the initial linear relation between Alin and Ae found
for Ne’ and He’ is also valid here. Figure 9(c) shows the difference between
total and magnetostrictive AH un: The excess AHun is in remarkable agreement with
the calculated LSS range (the local density of hydrogen atoms). This agreement
strongly suggests a connection between AK on and the presence of hydrogen. The
connection is further confirmed by comparing the profiles of Hun and Ae before
and after annealing at successively higher temperatures. Figures 10(a) and (b)
show such a sequence for nominal doses 5x10! °yom* and 2x10!°/em, respectively.
Before annealing the ratio of maximum AH on to maximum Ae is greater for the
sample with higher dose, indicating that the excess AH un increases more rapidly
with dose than does Ac. With annealing up to 300°C the excess aH, decreases

and shifts toward the location of maximum strain and damage. Gettering of
implanted dopants from regions with low damage to regions with higher damage

(58)

has been reported for other materials. The diminishing amount of excess AH un
is consistent with the desorption of hydrogen at these temperatures. After
annealing at 400°C, little or no hydrogen remains in the crystal ‘8 and the total

AH, coincides with the contribution due to strain. Annealing at 500°C and 600°C

Figure 9.

DELTA Hy (KOE)

t Li H l} li t i}
6 + 120 KEV Ho NOMINAL 4
DOSE
- 5 x10 3 vom 2
4 TOTAL |
DELTA Huy
a | (A) |
| en Pn
0 + + + + + + +
(DELTA STRAIN) x4.1 «OE 7
2 | (B) |
re) i { + ” t " "
— EXCESS
4 DELTA Hw 7
r 4... LSS RANGE 7
> | (Cc) |
ee anect opt Seat 1
'e) 2000 4000 6000

DEPTH (AD

Depth profiles of aH, for 120 keV, 5x10'°/cm H* implantation.
(a) FMR-determined AH in distribution. (b) Ae profile multiplied
by 4.1 kOe. (c) Difference between profiles (a) and (b). Also
shown (dashed) is calculated LSS range of 60 keV H” in garnet.

| AS-IMPLANTED CAD | as-répLaNteD (B)

DELTA Huy (KOE)
DELTA Hwy (kOe)

+ §=6§00 . “+ 600 :

cinieiafnnane Gn? oo GE coocnracent unin. Maal
°5 2000 4000. 0 2000 4000 0
DEPTH (A)

Figure 10. (a) and (b), respectively, show total OH on profiles (solid) and
Aex4.1 kOe profiles (dashed) for 5x10'°/cm* and 2x10!°/cmé
120 keV Hy implantation. Profiles are for successively higher

annealing temperature. Note the different vertical scales.

decreases AH in and Ac but maintains the magnetostrictive relation.

In addition to the unusual effect on AH in which is primarily a change in
uniaxial anisotropy, hydrogen implantation also causes unusual changes in 4nM,
A/Mand a. For the case shown in Figure 9, where the maximum Ae is only 0.60%,
there is a 60% reduction in 4nM. If the same maximum strain is obtained with
Ne* or He*, the reduction is less than 30%. For hydrogen implantation the
region with significantly lowered 4nM extends beyond the strained layer up to
the depth of excess AH int However at strain Ae = 0.60% the exchange constant
A is nearly the same for all three species: 64%, 68% and 56% of bulk value
for neon, helium and hydrogen, respectively. Since for hydrogen A decreases
more slowly than M, for the distribution of Figure 9 the average A/M is 13%
greater than bulk value. This is accompanied by an increase of a factor of
two in oa.

As in the case of Ne* and He’, we have limited understanding of what causes
the changes in magnetic properties for hydrogen implantation. The reduction in
magnetization accompanied by a smaller reduction in A suggests that incoherent
atomic displacements play a smaller role than for Ne* and He’, and the profiles
support the view that the presence of hydrogen atoms is a significant factor.
The same appears to be true of H; but the uniaxial character is intriguing.

It would be informative to do detailed X-ray and FMR analyses of deuterium
implanted garnet. Since for deuterium nuclear stopping is greater than for
hydrogen, the relative contribution of the strain compared to the contribution
attributable to chemistry would be greater. Published results already show that
for deuterium AH on is greater than expected from simple magnetostriction. (26)

The discovery of large chemical effects for hydrogen implies that other jons
may also produce effects not associated with strain or damage. But if detectable
chemical effects require dopant concentrations of at least 1%, such measurements

are difficult. For all other ions the implanted garnet is rendered paramagnetic

with doses yielding concentrations well below 1%.

Bea

H. Results of Annealing

In this paper the study of annealing behavior was limited to the two lower
doses of Ne* and He* implantation and to the three lower doses of Ho implantation.
For Ne* and He* at these doses the relationships between AH in and Ae are indepen-
dent of depth and consequently FMR spectra are easily interpreted. The maximum
strain and AH in for the lowest dose hydrogen implantation were too low after
annealing to provide significant quantitative information. The reasons for
excluding the high-dose hydrogen implantations were discussed earlier.

For all three species the strain decreases with increasing annealing tempera-
ture. However the changes in profile shane are negligible. For each species it is
thus possible to normalize the profiles to the profile obtained prior to annealing.
Figure Il shows the results. It is worth noting that before annealing and normali-
Zing the maximum values of Ae were 0.49% and 0.87% for Ne"; 0.82% and 1.30% for
He’; and 0.35% and 0.60% for Hp For Ne* and Hy the annealing behavior is
nearly independent of the magnitude of the original strain. For He* implantation
at 6x10! yom? annealing at v400°C results in severe broadening of both X-ray and
FMR spectra. At this and higher doses there is a formation of He bubbles (24»5)
which results ina deterioration of crystalline and magnetic properties. The
present measurements on the lower doses of He* implantation did not show any
broadening up to 600°C.

Although the strain for hydrogen decreases more rapidly with annealing
temperature than the strain for neon and helium, the general trend is the same
for all three species. This reinforces the idea that despite the large differences
in dose, the major source of the strain is independent of ion species. The more
rapid decrease of strain for temperatures between 300°C and 400% and again between
500°C and 600°C has been previously reported for Ne* implantation. ‘!2) The

present measurements and all other measurements known to us do not provide infor-

t i Lj | | t
100 a’ -
x \>
~ \M
\ ON
a \ \
a \
a 80 ‘ NN 7
i \ Xa
\ “A
Cc ~
F NOMINAL \ NN ‘q
a DOSE No NUS
gq 60 13, 2 Y 2 \ |
(10° 7om 3} 4 e. \
\ \
i NN VN
+0 5 NA
N NE \\
f 2 10 a
a = \ 4
= 40 ne’ 2 300 ‘“
S Ee = 600
4 +4 200.
20- 2 A 500 7
0 ! | | ! l
0 200 400 600
ANNEALING TEMPERATURE (°C)
Figure 11. Normalized strain Ae versus annealing temperature for neon,

helium and hydrogen implantation.

mation permitting speculation concerning the reasons for this behavior. For all
six cases and especially after annealing the damage is too low for meaningful
measurement. .

The behavior of magnetic properties for Ne* and He” implantation is reasonably
consistent with the strain. As the strain decreases, the profiles of AH in follow
the curves of Figures 6(a) and (b). Slight inconsistencies are observed for 4nM
and A/M. The magnetization increases with annealing, reaching its bulk value at
600°C, where the strain has relaxed only half way. For both species the ratio of
A/M also increases with annealing but at 600°C remains some 20% below bulk value.
The damping parameter o decreases with annealing, reaching the bulk value around
400°C, and for higher temperature it drops 10% below this value. The cubic
anisotropy remains 20% to 50% low after annealing up to 400°C. We have already
shown the annealing behavior of AH in for hydrogen implantation. In this case
the values of 41M, A/M and «@ also move toward and reach the respective bulk values

at 600°C.

VI. Concluding Remarks

It has been shown that a considerable amount of information can be obtained
by combining detailed analyses of X-ray and FMR spectra of ion-implanted garnet.
Several conclusions afforded by detailed analysis are substantially different
from conclusions based only on considerations of AH, the separation of principal
surface mode and bulk mode in FMR and on the maximum extent Ag of the rocking curve
in X-ray diffraction. Some of the results clarify various aspects of implanted
garnet; other results raise new and difficult questions. The major feature to be
explained is the departure at high doses from a unique relationship between AH in
and Ae. Also, a study of the annealing behavior of samples implanted at high
dose would be worthwhile.

An important question is whether or not the present results are specific to

the garnet and the implanted species used. This cannot be clearly answered due

to the lack of a theory of the properties of implanted garnet. Nevertheless it

is probable that the general features of the present results are reproduced in all
magnetic garnets implanted with a variety of jon species. Judging by published
X-ray rocking curves. the strain depends on ion species, energy, dose and annealing
but is insensitive to the composition of the garnet. Regardless of implanted
spectes, all garnets are probably rendered amorphous at strains around 3%.
Complete and detailed FMR spectra of implanted garnet have been rarely published,
but the more frequently published dependence of AH on ion species, dose, etc., is
similar to our ohservations. We infer that the entire structures of these spectra
are also Similar to the present measurements. Thus we expect that magnetic
profiles of garnets with different compositions and implanted with different ions

are similar to those of the films we have studied.

Acknowledgements

One of the authors (VSS) thanks the International Business Machines Corpo-
ration for financial support in the form of a predoctoral fellowship, We thank
Tim Gallagher, Kochan Ju, H. Ben Hu and Chris Bajorek of the San Jose laboratory
of IBM for supplying the samples and encouraging this study. We express appreci-
ation to Lavada Moudy, Howard Glass and Jack Mee of Rockwell International
(Anaheim, CA) for providing easy access to a double-crystal diffractometer. We
thank Jim Campbell of Caltech for suggesting the use of and providing us with
the HP 9826 computer. Thad Vreeland of Caltech encouraged us to accept an

unusual X-ray result.

oOo ™

10.

1.
12.
13.
14.
15.

16.
17.
18.
19.
20.

References

J.C. North and R. Wolfe, "Ion- Implantation Effects in Bubble Garnets" in Ion-
Implantation in Semiconductors and Other Materials, edited by B.L. Crowder
(Plenum, New York, 1973).

K. Komenou, I. Hirai, K. Asama, and M. Sakai, J. Appl. Phys. 49, 5816 (1978)..
V.S. Speriosu, H.L. Glass and T. Kobayashi, Appl. Phys. Lett. 34, 539 (1979).
H. Jouve, P. Gerard and A. Luc, IEEE. MAG 16, 946 (1980).

V.S. Speriosu, B.E. MacNeal and H.L. Glass, Intermag 1980 Conf., Boston,
paper 22-4.

W. de Roode and J. W. Smits, J. Appl. Phys. 52, 3969 (1981).

V.S. Speriosu, J. Appl. Phys. 52, 6094, 1981.

Y. Sugita, T. Takeuchi and N. Ohta, MMM Conf. 1981, Atlanta, Paper CA-5.

Y. Satoh, M. Okashi, T. Miyashita, and K. Komenou, Int. Conf. on Magnetic
Bubbles, Tokyo (1980), paper A-4.

G. Suran, H. Jouve and P. Gerard, MMM Conf. 1981, Atlanta, Paper BA-6

(to be published).

V.S. Speriosu and C.H. Wilts, MMM Conf. 1981, Atlanta, Paper BA~9.

W.H. de Roode and H.A. Algra. J. Appl. Phys. 53. 2507 (1982).

H.A. Agra and W.H. de Roode, J. Appl. Phys. 53, 5131 (1982).

H. Jouve, J. Appl. Phys. 50, 2246 (1979).

T.J. Nelson, R. Wolfe, S.L. Blank, and W.A. Johnson, J.App]. Phys. 50,

2261 (1979).

J.P. Kersusan, P. Gerard, J.P. Gailliard, H. Jouve, IEEE MAG 17. 2917 (1981).
W.A. Johnson, J.C. North, and R. Wolfe, J. Appl. Phys. 44, 4753 (1973).

H.A. Washburn and G. Galli, J. Appl. Phys. 50, 2267 (1979).

H. Jouve and M.T. Delaye, IEEE MAG 16, 949 (1980).

P. Gerard, M.T. Delaye, R. Danielou, Thin Solid Films , 88, 75 (1982).

21.
22.

23.
24,
25.
26.
27.
28,
29,
30.
31.
32.
33.
34.
35.
36.

37.
38.
39.
40.

References Con't

P. Gerard, P. Martin, R. Danielou, to be published.
B.M. Paine, V.S. Speriosu, L.S. Wielunski, H.L. Glass and M-A. Nicolet, Nucl.
Instr. Meth. 191, 80 (1981).
T. Omi, C.L. Bauer, M.H. Kryder, MMM Conf., Atlanta, 1981, Paper DA-6.
R. Wolfe, J.C. North, and Y.P. Lai, Appl. Phys. Lett. 22, 683 (1973).
R.F. Soohoo, J. Appl. Phys. 49, 1582 (1978).
.P. Omagio and P.E. Wigen, J. Appl. Phys. 50, 2264, (1979).
.H. Wilts, J. Zebrowski, and K. Komenou, J. Appl. Phys. 50, 5878 (1979).

K Komenou, J. Zebrowski, and C.H. Wilts, J. Appl. Phys. 50, 5442 (1979).

-A. Algra and J.M. Robertson, J.Appl. Phys. 51, 3821 (1980).
J.Mada and K. Asama, J. Appl. Phys. 50, 5914, (1979).
C.H. Wilts and S. Prasad, IEEE MAG 17, 2405 (1981),
G. Suran, R. Krishnan, P. Gerard, and H. Jouve, IEEE MAG 17, 2920 (1981).
G. Suran, H. Jouve and P. Gerard, to be published.

I. Maartense and C.W. Searle, Appl. Phys. Lett. 34, 115 (1979).

ee]

cl. Smit, H.A. Algra, and J.M. Robertson, Appl. Phys. 22, 299 (1980) .
A.H. Morrish, P.d. Picone and N. Saegusa, Int. Conf. on Magnetic Bubbles,
Tokyo 1982.

R. Krishnan, S. Visnovski, V. Prosser, and P. Gerard, to be published.

K. Ju, R.O. Schwenker, and H.L. Hu, IEEE MAG 15, 1658 (1979).

B.E. MacNeal and V.S. Speriosu, J. Appl. Phys. 52, 3935 (1981).

See for example, P. Hansen, "Magnetic anisotropy and magnetostriction in

garnets", in Physics of Magnetic Garnets edited by A. Paoletti (North-Holland,

New York, 1978).

4]. B. Hoekstra, F. Van Doveren, and J.M. Robertson, Appl. Phys. 12, 261 (1977).

42.
43.

44.

45.

46.

47.

48.
49,

50.

51.
52.

53.
54.

55.
56.

57.

G.P. Vella-Coleiro, Rev. Sci. Instr. 50, 1130 (1979).

X. Wang, C.S. Krafft, M.H. Kryder, Int'l. Conf on Magnetic Bubbles, 1982,
Tokyo.

G.P. Vella-Coleiro, R. Wolfe, S.L. Blank, R. Caruso, T.J. Nelson and V.V.S.
Rana, J. Appl. Phys. 52, 2355 (1981).

R. Hirko and K. du, IEEE MAG 16, 958 (1980).

H. Matsutera, S. Esho, and Y. Hidaka, J. Appl. Phys. 53, 2504 (1982).

H. Makino, Y. Hidaka and H. Matsutera, Int'l. Conf. on Magnetic Bubbles,
1982, Tokyo.

The San Jose, Calif., Laboratory of IBM.

See, for example, J.W. Mayer, L. Eriksson and John A. Davies, Ion Implantation

in Semiconductors, (A.P., New York, 1970).

V.S. Speriosu, B.M. Paine, M-A. Nicolet and H.L. Glass, Appl. Phys. Lett. 40,
604 (1982).
G.A. Rozgonyi, P.M. Petroff, and M.B. Panish, Appl. Phys. Lett. 24, 251 (1974).

See, for example, W.H. Zachariasen, Theory of X-ray Diffraction in Crystals,

(Wiley, New York, 1945),

C.H. Wilts, MMM Conf. 1981, Atlanta, paper CA-6.

J.F. Gibbons, W.S. Johnson, and S.W. Mylroie, Projected Range Statistics,

2nd ed. (Halstead, New York, 1975).
R.D. Pierce, R. Caruso, and C.J. Mogab, J. Appl. Phys. 53, 4480 (1982).
A.M. Guzman, C.S. Krafft, X. Wang, M.H. Kryder, to be published,

W.L. Johnson, verbal communication.

See, for example, R.G. Wilson and D.M. Jamba, Electrochemical Society Meeting,

Denver, 1981, abstract 333.

930

Chapter V

X-ray rocking curve study of Si-implanted GaAs, Si and Ge

A comparative study of the evolution of strain and damage

with ion dose.

X-ray rocking curve study of Si-implanted GaAs, Si, and Ge

V.S. Speriosu,”B.M. Paine, andM-A. Nicolet

California Institute of Technology, Pasadena, California 91125

H.L. Glass

Rockwell International, Microelectronics Research and Development Center, Anaheim, California 92803

(Received 6 November 1981; accepted for publication 8 January 1982)

Crystalline properties of Si-implanted (100) GaAs, Si, and Ge have been studied by Bragg case
double-crystal x-ray diffraction. Sharp qualitative and quantitative differences were found
between the damage in GaAs on one hand and Si and Ge on the other. In Si and Ge the number
of defects and the strain increase linearly with dose up to the amorphous threshold. In GaAs the
increase in these quantities is neither linear nor monotonic with dose. At a moderate damage
level the GaAs crystal undergoes a transition from elastic to plastic behavior. This transition is
accompanied by the creation of extended defects, which are not detected in Si or Ge.

PACS numbers: 61.10.Fr, 61.70.Tm, 62.20.Fe

The existence of different annealing behavior in ion-
implanted amorphized GaAs compared to Si and Ge has
been known for some time. In Si and Ge layer regrowth is
linear with time and there is good epitaxy.'~> In GaAs layer
regrowth is nonlinear with time* and, independently of ion
species, epitaxy is poor.” To obtain good electrical activity,
implantation in Si and Ge is done at room temperature with
doses sufficient to amorphize the material.° In GaAs the
temperature is held at a few hundred °C in urder to prevent
amorphization of the layer.’ Up to the present no substantive
evidence has been published concerning the cause of these
differences. In this letter we present an x-ray diffraction
study of Si-implanted (100) GaAs, Si, and Ge. The results
indicate that the evolution of the damage up to amorphous-
ness in GaAs is very different from that in Si and Ge.

(100)-oriented GaAs, Si, and Ge single crystals, about
5 mm X5 mm X0.5 mm in size, highly polished, were im-
planted with 300-keV Sit (in GaAs and Ge) and 230-keV
Si ‘ (in Si). Implantation was done at room temperature (RT)
with a current density of 0.125 4zA/cm? and under condi-
tions excluding channeling. Doses ranged from 1 x 10'*
atom/cm? to 1.2 10" atom/cm? for GaAs, 1 10!%
atom/cm? to 7x 10"? atom/cm? for Ge, and 7 x 10"
atom/cm’ to 7 x 10'* atom/cm? for Si. These doses pro-

duced modifications in crystal structure measurable by
Bragg case double-crystal x-ray diffraction. Well-collimat-
ed, low-divergence Fe K, x rays were obtained with sym-
metric (400) refiections from nearly perfect (100) monoch-
romators (GaAs for the GaAs and Ge samples, Si for the Si
samples). The spot size at the sample was limited to ~ 1
mm X 1 mm by a set of slits. Typical counting rate for the
beam incident on the sample was ~ 10° cps. The diffracted
intensity (reficcting power) as a function of angle was mica-
sured with a Nal(T1) detector with pulse height analysis.
Representative diffraction profiles (rocking curves) for
the three crystals are shown in Fig. 1. Only the low-angle
side of the virgin crystal’s Bragg peak is shown. The high-
angle side is little changed by implantation. The virgin peak
at zero angle, also not shown, is 10 to 100 times more intense
than the oscillatory structures shown in the figure. The be-
havior of the rocking curve with increasing dose for Si [Fig.
I{a)] is similar to that for Ge [Fig. 1(b)]. For both crystals the
angular range of nonzero reflecting power increases linearly
with dose, the peak farthest from zero angle decreases in
relation to other peaks, and the overall reflecting power di-
minishes. At the highest doses the reflecting power ap-
proaches the curve obtained with virgin crystal, indicating
that the implanted layer is nearly amorphous. Pronounced

FIG. 1. Rocking curves corresponding to several
doses for (a) Si, (b) Ge, and (c) GaAs. The angle is
referred to the location of the Bragg peak of virgin
crystal. The curves are vertically displaced for clar-
ity. For each curve zero reflecting power occurs at
the lowest angle for which the curve is plotted.

i q v qT iu u T iu T T qT T qT qT
+ (a) 4 af (bd) (c)
“| S190) Si, 230 kev Si* <100> Ge, 300 kev Si* <100> GaAs, 300 kev Si*
—~ | RT IMPLANTATION R.T. IMPLANTATION i2- RT IMPLANTATION
3 ab Fe %e (400) Fe Kg (400) Fe Ky (400) DOSE
a 6r- whrent
= DOSE
14 2
OL (0's 7em*) 4 DOSE aL
a 0.7 609 em?)
Q 4 j 4
r 2+
Ww LS.
ond ca
re a 2
ef s_ AW
= 3 BANAT
4.5 ANN 45
Z z
dL ah L i L i L L L l L
70.4 =0.2 0 70.6 0.4 =0.2 ae 0

ANGLE FROM MAIN PEAK (deg)

“IBM predoctoral fellow.

604 Appi. Phys. Lett. 40(7), 1 April 1982

0003-6951 /82/070604-03$01.00

oscillations are maintained over the entire range of doses.
The behavior of the GaAs rocking curves [Fig. I(c}] is very
different. As the dose is varied by two orders of magnitude,
the range of nonzero reflecting power changes by only a fac-
tor of 3. Between 1 x 10'? atom/cm? and 1.5 10'*
atom/cm? the principal peak becomes narrower and more
intense. Between 1.5 X 10'* atom/cm? and 3.0 10"*
atom/cm? the rocking curve broadens, but its shape is differ-
ent from any obtained in Si or Ge. For doses above 6.0 x 10"
atom/cm? the oscillations are smoothed out, although, as
indicated by the single peak for the 1.2 10'5 atom/cm’
dose, the implanted layer is not amorphous.

The rocking curves of Fig. 1 have been interpreted with
the aid of a kinematical model of x-ray diffraction in crys-
tals. The model generates rocking curves for arbitrary
depth-dependent distributions of strain, point defects and
extended defects. The category of point defects includes indi-
vidual random atomic displacements as well as highly dis-
torted regions extending over a small number (i.e., one to ten)
of unit cells. The category of extended defects covers imper-
fections that generate small lattice distortions extending
over many (i.e., hundreds of) unit cells. Detailed distribu-
tions for the strain and the two types of defects are ohtainable
by fitting experimental rocking curves. The trail-and-error
fitting procedure must be performed on a computer. Howev-
er, several useful parameters are readily found directly from
the rocking curve.® The total thickness T of the damaged
layer is obtained from the most rapid oscillation in the rock-
ing curve, and the maximum strain ¢,,,, is linearly related to
the angle where the rocking curve rises from zere reflecting
power.® The estimated accuracy for 7 and €,,,, obtained in
this manner is 5%. The number of point defects can be ob-
tained by comparing the areas under rocking curves of dam-
aged and perfect crystals of the same thickness T. Similarly,
the presence of extended defects and estimates for their size,
amount of random misorientation, and lateral variation of
strain are obtainable from the degree of smoothing of the
rocking curve.*° | ,

The thickness of the damaged layer is 5200 A for Si and
5800 A for Ge and GaAs. Figure 2 shows the maximum
strain as a function of dose for the three crystals. Also in-

’ cluded is a line of slope one. The maximum strain below the
amorphous threshold is around 1% for all three crystals. For
Si and Ge, the maximum strain and, by implication, the en-
tire strain distribution, increase nearly linearly with dose.
The data for Si and Ge indicate that the number of point
defects, describable by a Debye-Waller factor,® also in-
creases nearly linearly with dose. Extended defects, as de-
fined above, are absent up to the amorphous threshold.

In GaAs the maximum strain as a function of dose is
much more complicated. Here the strain curve can be subdi-
vided into five different regions, as indicated in the figure.
Below 10)3 atom/cm? (region Ij the strain is assumed to rise

’ Hinearly with dose. Between 10"? atom/cm? and ~ 10'*
atom/cm? (region II) pronounced saturation sets in. The
saturation occurs not only in the maximum strain, but in the
entire strain distribution. This is indicated in Fig. 1(c) by the
greater sharpness of the principal peak for 1.5 x 10'*
atom/cm? compared to that for 1 x 10'? atom/cm7?. In re-

605 Appl. Phys. Lett., Vol. 40, No. 7, 1 April 1982

T Le rT ee reriy TTT
AMORPHOUSNESS,
re) or , Z
' iZ ! A 7
5 ( 4
32 ost | |
Zz a =
C= 9
id L 4
<9)
2 5 4
= /
a 3 love =]
= Ol- / 4
L | 1; | 1
. | | | | ,
I 0 0 W { ¥
i | j; Oy ]
eee ah teal fe eet) ee L
i908 104 195

DOSE (at./cm?)

FIG. 2. Maximum strain as a function of dose for Si, Ge, and GaAs. The five
dose regions apply to the strain in GaAs.

gion ITI, between 1 x 10'4 atom/cm? and 3 x 10'* atom/cm?,
there is a sharp rise in the maximum strain. Between 3 x 10'*
atom/cm? and ~ 1.2 10! atom/cm* (region IV) the maxi-
mum as well as the entire strain distribution no longer
change with dose. For higher doses (region V} the layer ap-
proaches amorphousness. From region I through III, the
number of point effects increases with the strain. In region
IV it is not clear whether net point defects continue to be
created. Instead, extended defects become observable, their
density increasing with dose and reaching a value of

~ 1/m? at 1.2 10" atom/cm?. The rocking curve con-
tains very little information concerning the detailed struc-
ture of these extended defects. All that can be said is that
they extend throughout most of the implanted layer thick-
ness; the lateral variation in strain is not more than 0.01%,
and the variation in orientation is less than ~2 arc min. At-
tempts to observe the catended defects through a-ray topog-
raphy have not been successful, probably due to the small
variation in orientation compared to the width of the rocking
curve.

The mechanism of strain creation in ion-implanted
crystals is not very well understood. It has been shown’ that
in garnets the strain distribution is proportional to the ener-
gy deposited through nuclear collisions during implanta-
tion. It has also been shown® that in garnets the strain and
damage distributions are proportional to each other. The
implanted lattice is constrained by the underlying unda-
maged crystal to expand only in a direction perpendicular to
the surface.* This places the implanted layer in lateral com-
pression!! and gives a Poisson contribution to the strain. As
indicated in Fig. 2, for the same strain the dose in Si is about
20 times larger than in Ge. However, the rocking curves
show that in both crystals comparable strains correspond to
comparable numbers of point defects.

In GaAs pronounced annealing during implantation
occurs in region ITI of Fig. 2. In region III the average strain

Speriosu et ai. 605

reaches its yield value of 0.45%. This number is nearly equal
to that obtained’? for the tensile yield strain of undamaged,
externally stressed (110) GaAs. In virgin GaAs the onset of
plastic deformation is accompanied by the abrupt creation of
60° dislocations. '? In lattice-mismatched, epitaxially grown
layers, misfit dislocations begin to appear when it is energeti-
cally favorable to decrease the macroscopic (coherent) strain
at the expense of creating localized distortions.'? The thresh-
old (yield) strain depends, among other things, on the layer
thickness as well as on the depth distribution of the strain. '*

In region IV of Fig. 2 the strain in GaAs no longer
changes with the dose. This is perhaps due to a combination
of annihilation of point defects at sinks such as extended
defects and/or to the relaxation of strict lattice match with
the underlying crystal. The deposited energy goes into the
creation of extended defects whose density increases with the
dose.

The results presented above imply a different structure
of the damaged layer for amorphized GaAs compared to Si
and Ge. This difference can explain the observed differences
in annealing behavior. For Si and Ge, starting at the deep
end of the damage deposition curve, the elastic strain and the
number of point defects rise uniformly up to the amorphous
threshold.'* With this structure one expects that, during
post-implantation annealing, the regrowth is layer by layer
using the good seed at the deep end of the damge, thus result-
ing in relatively good epitaxy.

In GaAs the implanted layer consists of three regions.
At the deep end of the damage the strain is elastic and only
point defects are present. Between the elasticaily strained
and amorphous regions is a plastically deformed region.
This region, containing extended defects, will present a bar-
rier to epitaxial regrowth. The existence of this barrier de-
pends on whether or not the yield strain is reached, regard-
less of how it is reached. Thus the regrowth of the
amorphized layer will be independent of the implanted ion
species, as observed.* At elevated implantation tempera-
tures, the rate of self-annealing is probably sufficiently high

such that for all doses the strain will remain below the yield’

value (regions I and II of Fig. 2). Thus the plastically de-

formed region does not develop. It is probably for this reason
that elevated temperature implantations of dopants in GaAs
give best regrowth and electrical properties.’ For room-tem-
perature implantation, the elastically strained portion of the
layer will regrow epitaxially. It is in fact observed that amor-
phized GaAs layers show an initial epitaxial regrowth at the

606 Appl. Phys. Lett., Vol. 40, No. 7, 1 April 1982

buried crystal/amorphous interface.° Subsequently howev-
er, the quality of the epitaxy will be impaired by the presence
of the plastically deformed region, resulting in a highly de-
fected regrown layer.'° When implantation does not fully
amorphize the layer, good epitaxy is observed.'” We at-
tribute this to strain levels that are too small to induce plastic
deformation. If the implanted layer is thin enough, good re-
growth is observed even after full amorphization.'* We pro-
pose that this occurs because for thin layers the yield strain is
large, '* with the result that amorphization occurs before the
threshold strain for plastic deformation is reached.

We thank E. Babcock for performing the ion implanta-
tion, S. S. Lau for helpful discussions, and T.. A. Mondy for

technical assistance. This work was supported in part by the
Advanced Research Agency of the Department of Defense
and was monitored by the Air Force Office of Scientific Re-
search under Contract No. 49620-T1-C-0087.

ts Csepregi, J. W. Mayer, and T. W. Sigmon, Physics Lett. 54A, 157

1975)

*L. Csepregi, J. W. Mayer, and T. W. Sigmon, Appl. Phys. Lett. 29, 92
(1976).

3J, W. Mayer, L. Csepregi, J. Gyulai, I. Nagy, G. Mezey, P. Revesz, and E.
Kotai, Thin Solid Films 32, 303 (1976).

*K. Gamo, T. Inada, J. W. Mayer, F. H. Eisen, and C. G. Rhodes, Rad. Eff.
33, 85 (1977).

5M. G. Grimaldi, B. M. Paine, M-A. Nicolet, and D. K. Sadana, J. Appl.
Phys, 52, 4038 (1981),

"See for example, J. W. Mayer, L. Eriksson, and J. A. Davies, Jon Implanta-
tion in Semiconductors (Academic, New York, 1970), p. 198.

7J. S. Harris, F. H. Eisen, B. Welch, J. D. Haskell, R. D. Pashley, and J. W.
Mayer, Appl. Phys. Lett. 21, 601 (1972).

®V, 5. Speriosu, J. Appl. Phys. 52, 6094 (1981).

°V. S. Speriosu, B. E. MacNeal, and H. L. Glass, Intermag. 1980 Conf.,
Boston, paper 22-4 (unpublished).

‘CB, E. MacNeal and V. S. Speriosu, J. Appl. Phys. 52, 3935 (1981).

"EP. EcrNissc, Appl. Phys. Lett. 16, 581 (1971).

"'H. Booyens, J. S. Vermask, and G. R. Proto, J. Appl. Phys. 49, 5435
(1978).

'3G. A. Rozgonyi, P. M. Petroff, and M. B. Panish, Appl. Phys. Lett. 24,
281 (1974).

'C. A. Ball and C. Laird, Thin Solid Films 41, 307 (1977).

'SV_S. Speriosu, B. M. Paine, M.-A. Nicolet, and H. L. Glass (to be
published).

‘6S, S. Kular, B. J. Sealy, K. G. Stephans, D. Sadana, and G. R. Booker,
Solid-State Electron. 23, 831 (1980).

"J. §. Williams and M. W. Austin, Nucl. Instr. Meth. 168, 307 (1980).

'8M, G. Grimaldi, B. M. Paine, M. Maenpaa, M.-A. Nicolet, and D. K.
Sadana, Appl. Phys. Lett. 39, 70 (1981).

Speriosu et al. 606

Chapter VI

Conclusion

A method for determining depth profiles of lattice
parameter and damage level (or structure factor) in mono-
crystals was presented. The kinematical interpretation of
x-ray diffraction in such crystals enables rapid computer
calculation of rocking curves corresponding to arbitrary
distributions. The distributions for a particular case are
obtained by fitting the experimental rocking curve. The
sensitivity of the calculated curve to variations in the
strain distribution shows that local precision of 2% of peak
strain and depth resolution of 50 to 200A are obtainable.
The sensitivity to changes in the magnitude of the local

structure factor is 10%.

The technique was applied to ion-implanted garnets and
semiconductors and to a multilayer laser structure. In
terms of sensitivity, information content and caperimental
facility the rocking curve method compares well with Ruther-
ford backscattering, presently the major tool for studying
damage in implanted crystals. Since a variation in chemical
composition usually results in a corresponding variation in
lattice parameter, the rocking curve may be able to provide
as much information as other surface analysis techniques,
such as Secondary Ion Mass Spectroscopy (SIMS) or Auger
Electron Spectroscopy (AES), both of which are destructive.

Future work will show whether or not this is the case.

965

A drawback of the present x-ray Lechnique is its reliance
on trial-and-error fitting procedures. The rocking curve
yields directly parameters such as peak strain, total thickness
and thickness-averaged structure factor. However, due to
lack of phase detection, the curve cannot be simply inverted
to yield the corresponding distributions of strain and
structure factor. For arbitrary distributions, with some
knowledge of the processing steps involved in growing or
modifying the crystal, an experienced operator can usually
converge to an excellent fit in 20 or fewer iterations. The
distribution obtained in this manner has a higher precision
than the initial trial distribution based on external information.
If this information is not available or if the rocking curve
is particularly complex, one can resort to etehing and
reconstruct the profiles as described in Chapter II. For
unimodal distributions created by ion-implantation, the
structure of the rocking curve is sufficiently simple to
permit determination of strain and damage profiles without
external. inputs. A major improvement of the technique would
be the development of an algorithm guaranteeing convergence
to satisfactory fits of arbitrary rocking curves. Work

towards this goal is in progress.

Magnetic and crystalline profiles of ion-implanted
garnet were obtained by combination of ferromagnetic resonance
and x-ray diffraction. The method developed by Wilts was

used to analyze FMR spectra corresponding to implantation

with elements (Ne, He, and H) commonly utilized in magnetic
bubble memory devices and covering a wide range of doses.
Prior to this work, the complexity of the theory of resonance
in nonuniform films and also the complexity of experimental
FMR spectra had discouraged detailed understanding. By
demanding quantitative interpretation of every detail of
these spectra we have obtained results with a degree of
clarity and certainty never attained before. Much of what
we found is at variance with established beliefs. In neon
and helium implanted garnet the initial source of the change
in uniaxial anisotropy is the strain - not the destruction
of growth-induced anisotropy. With increasing strain the
uniaxial anisotropy saturates and decreases to zero - it
does not merely saturate. Because of this decercase in the
region of maximum strain and damage, the field for resonance
of the principal surface mode in FMR cannot be used to
measure any Magnetic property in this region. By comparing
the profile of uniaxial anisotropy with the strain profile
for hydrogen implantation, we have shown conclusively Lhat
the unusually large anisotropy is due to chemical effects -
not to qualitatively different damage caused by hydrogen

implantation.

We have accomplished these things merely by asking that

x-ray rocking curves and ferromagnetic resonance spectra

make sense ~- not by doing any new experiments.