Development of apertureless microscopy and force microscopy of GaN and CeO22 - CaltechTHESIS

imaged. Experimental evidence supports many of the theoretical aspects found from
the simulations. Much controversy exists as to whether or not one can separate in-
formation that is topographical in nature from that which is optical in any near-field
imaging technique [6]. Hence, we have simulated a set of controlled experiments with
the tip-sample dipole interaction model. This model is found to be rich in features
which indicate that much of the information in the data is indeed optical in nature
with little topographical crosstalk. The dipole interaction and all others, however, will
always be an unavoidable combination of topography and optical properties since the
two are intimately connected (Chapter 2, Section 2.1.1). The following simulations
calculate the detected far-field intensity pattern based on near-field perturbations
induced by the coupling of induced on the tip and the sample.

In our simulations we model the AFM tip as a radiating dipole, where the expres-

sion for the far-field intensity pattern produced by such a dipole is [7]

L, = —— (|: sin’ @ 3.1
(= Gea lllsin’ (3.1)

where J; is the intensity, p; is the induced dipole moment of the tip, d is the distance
to the detector, k is the wave number of the radiation, c is the speed of light, €9 is
the permitivity of free space, and @ is the angle between the vector from the tip to
the detector and the dipole moment of the tip. The term in the above equation that
contains optical information about the sample is p;, since the induced dipole moment
of the tip is given by

p= Area (Ejaser of E.) (3.2)

where a; is the polarizability of the tip. The total field incident on the tip is the sum
of the laser field Exaser and the sample’s field E,, therefore it is necessary to calculate
the very near-field of the sample in order to determine the far-field radiation pattern
produced by the tip. A schematic of the situation is shown in Figure 3.1.

For simplicity, we model the features being imaged as dielectric nanospheres with
an induced dipole moment which, to first order, is p, = Amey Os E lasers where all of the

symbols are the same as before except that they refer to the sample instead of the

Pn
ane ROE AHN

AFM Tip

Polarized Features —_-
ties *

Figure 3.1: Schematic of the dipole configuration to be simulated representing the
two spheres on a plane under illumination. The laser field polarizes all the features
which then interact in the near-field to affect the far-field radiation.

tip. The value of the polarizability, a,, is dependent on the structure of the sample

and the wavelength of the external laser, and for spheres is expressed as

€,/€9 +2

where R, is the radius and ¢, is the dielectric constant of the sphere. The dependence
of the index on wavelength is contained in €,, since n = ,/e,;. The full expression for
the near-field of the sample, accurate to first order in the external field and taking

into account the finite dimensions of the dipole, is

~ (R—cos)coswt_ _ cos(Rtcos#wt, — wRssinwt. — wRs sinwt+ é
3 Os | Etaser| ae a? cd, cd -
so : :
: 2 R3 at cos wt coswty ws sinwt_ ws sinwt4+ |
8 sin @ re a re Eg

where r is the distance between the center of the sample and the observation point, @ is
the angle between the sample’s dipole moment and the vector locating the observation

point, t is time, dk = 1+ R?+2Rcosé, tz, =t—- Rodi? /e and R = r/R,. This

near-field, E,, changes the induced dipole moment of the AFM tip and effectively

jae See SE eH pea Rg OC RPS AN AIA

25

Figure 3.2: Experimental data to be compared to the simulations. Left: AFM image is
of two adjacent 50 nm diameter polystyrene nanospheres on glass. Right: Apertureless
microscope data taken with the illuminating laser randomly polarized.

modulates the scattered intensity measured at the detector as the AFM tip scans
across the sample.

We have imaged polystyrene nanospheres of diameters ranging from 30 to 200
nm. In order to compare the simulations to the experimental data, the AFM image
in Figure 3.2 is of two adjacent 50nm diameter polystyrene beads on glass. Also
shown is apertureless microscope data taken with the illuminating laser randomly
polarized.

Figures 3.3, 3.4, 3.6, and 3.7 are simulations which show the important features
of the dipole model, notably the dependence on polarization, index and tip size.
The AFM image is used as a topographical template for the simulations since the
dipole field influencing the tip will be a function of the center-to-center separation
between tip and sample. To the topography we add the locations and other pertinent
information about the sample dipoles induced by the external laser polarization. With
this information we can determine the scattered intensity at any point to construct the
final image. Unless otherwise stated, all simulations use the parameters R;;,=10nm,
Nsample=1.6, Ataser=632.8nm. The scales in the simulations are normalized to unity for
the level of background scattering off of the AFM tip in the absence of modulation
due to the sample’s electric field. All are linear plots of the normalized intensity
with full scale from 0.70(black) to 1.8(white). Values outside this intensity range are
clipped to the minimum or maximum value accordingly. Figure 3.4 shows how the

near field of the dipole orients itself with the polarization of the external laser source.

ianbionbinomgnbnGHoaNis GORMAN SHAS RRA RADHA NASR RI

26

Figure 3.3: Simulations of the apertureless microscope image of two spheres on a plane
under different illuminating wavelengths. The results indicate that the resolution is
limited by the tip and not the illuminating wavelength. A. A = 630nm and B.
A = 543nm
The figures suggest that an enhancement in resolution could be obtained with the
proper orientation of the source polarization. Our initial experiments have shown a
definite dependence on the polarization of the external laser source as indicated in
Figure 3.5.

Figure 3.7 indicates how resolution decreases with increasing tip size. Although
a larger tip radius means a larger scattering cross section and hence more signal,
the change in signal intensity with respect to the background scattering is reduced
with a larger tip. Figure 3.6 shows how the image intensity changes for features with
different bulk indices of refraction. These images show clearly that the dipole model
can account for differences in optical properties. Experimental images of adjacent

features with different indices of refraction will be discussed in the next chapter.

3.3 Conclusions

In conclusion, we have used a dipole-dipole scattering model to demonstrate that

the apertureless technique can, in theory, provide information about a sample that

igang

es

27

Figure 3.4: Simulations of the apertureless microscope image of two spheres on plane
under different illuminating polarizations at a wavelength of A = 630nm. The angular
distribution of the dipole radiation aligned along the axis of polarization is clearly
visible.

is indeed optical in nature. The model contains no fitting parameters; all physical
constants used are well known or easily measured. A significant result from the dipole
scattering model that agrees with experiments is a strong polarization dependence
in the images as well as destructive interference lowering the signal intensity when

the tip is above the sample. Both of these important observations shed light on the

physical mechanism of the near-field interaction.

sgh PADS PIPED UNO eNO

heii

sons

28

Figure 3.5: Apertureless microscope image of two spheres on plane under different
illuminating polarizations. The wavelength was \ = 630nm and the polarization is
indicated in the upper right corner of each of the four figures. The angular distribution
of the dipole radiation aligned along the axis of polarization is clearly visible as
indicated by the arrows and is in agreement with the simulations.

‘se isi GPS RRO ARDS SISA UMNO

iS a DANN HUI it

angus O Hei gh RANAO ei

29

Figure 3.6: Simulations of the apertureless microscope image of two spheres on plane.
The index of refraction of the sphere on the left in each of the images changes from
1.0 in image A to 1.3 in B, 1.8 in C, and 4.0 in D. The index of the sphere on the
right is held constant at n = 1.6.

sips AG, AG Gh PNOEP INGA OIA DO

30

Figure 3.7: Simulations of the effect of tip size on the resolution of the apertureless
technique. R indicates the radius of curvature of the tip used in the simulations.
Clearly, as the tip increases in size resolution is lost as well as washing out the angular
dependence of the dipole radiation.

31

Bibliography

[1] D. Courjon and C. Bainier, Rep. Prog. Phys. 57, 989 (1994).

(2] H. K. Wickramasinghe and C. C. Williams, Apertureless Near Field Optical Mi-
croscope, U.S. Patent 4,947,034 (April 28, 1989).

[3] F. Zenhausern, M. P. O’Boyle, and H. K. Wickramasinghe, Appl. Phys. Lett. 65,
1623 (1994).

[4] F. Zenhausern, Y. Martin, and H. K. Wickramasinghe, Science 269, 1083 (1995).

[5} M. Born and E. Wolf, Principles of Optics 6” Ed. Cambridge University Press,
1980.

6] B. Hecht, H. Bielefeldt, Y. Inouye, L. Novotny, and D. W. Pohl, J. Appl. Phys.
81, 2492 (1997).

[7] J.D. Jackson, Classical Electrodynamics, 2nd ed. (John Wiley, New York, 1975).
[8] E. Betzig, M. Isaacson, and A. Lewis, Appl. Phys. Lett. 51, 2088 (1987).
[9] N. Garcia and M. Nieto-Vesperinas, Appl. Phys. Lett. 66, 3399 (1995).

(10) Y. Martin, F. Zenhausern, and H. K. Wickramasinghe, Appl. Phys. Lett. 68,
2475 (1996).

[il] Y. Martin, S. Rishton, and H. kK. Wickramasinghe, Appl. Phys. Lett. 71, 1
(1997).

[12] C. Schénenberger and S. F. Alvarado, Rev. Sci. Inst. 60, 3131 (1989).

[13] M. Pluta, Advanced Light Microscopy. Vol. 1 (1988).

32

Sn
yi postmen eu

Chapter 4 Apertureless Microscopy:

Experiment

4.1 Introduction

In this chapter, we describe a series of experiments to explore the limits of spatial
resolution, the measurement of optical properties, and applications of apertureless
microscopy. We feel that there are two important issues. First is the decoupling
of the measured optical signal from topography. Second is the discrimination of
local variations of susceptibility below the diffraction limit. The first issue has been
examined by Hecht et al. [1] for NSOM and is important since crosstalk in the optical
image due to topography can give rise to misleading image artifacts. In their paper,
they give the following criteria to satisfy before a near-field optical (NFO) image can

be “credible”

1. The NFO image is obtained in constant height or constant intensity mode.
Constant height mode is taken to mean that the probe is scanned in a plane
parallel to the average surface of the sample. Constant intensity mode is when
the probe-sample distance is regulated to give a constant intensity at the de-

tector.

2. The NFO image is taken in constant gap mode but has the following character-

istics. Constant gap mode meaning that the probe-sample distance is constant.

2a. Topographic and NFO images are highly uncorrelated. For example, magnetic
force microscopy can also suffer from topographic artifacts; however, images of

magnetic tape show that the tracks are unrelated to the topographic structure.

2b. Correlated structures are displaced by a constant amount.

hi aM i

ira

nah EROS

33

2c. The resolution of the NFO and scanning force images are clearly different.

Although Wickramasinghe has demonstrated apertureless microscopy on dye
molecules and dyed samples at different wavelengths, [2] no attempt was made to
differentiate between objects. Hence, the second issue has not yet been examined in
a controlled set of experiments. We examine the decoupling and differentiation issues

first then introduce applications at the end of the chapter.

4.2 Instrument Description

In our scanning apertureless microscope, an optical microscope focuses a laser to
a diffraction limited spot which is perturbed by an AFM tip operating in tapping
mode where the RMS voltage of an oscillating tip at resonance is kept constant.
Unfortunately, there is some confusion over the use of the term “tapping mode.” The
way it is used here is fundamentally different than the “tapping mode” described in
Reference [9] where the entire cantilever position is modulated at a frequency much
lower than the resonance frequency. When the tip oscillation amplitude being kept
constant, the average tip-sample distance is constant over the lock-in integration
time. Therefore, there is less risk of introducing artifacts that could be due to simply
measuring the cantilever position with light reflected from the cantilever. In previous
experiments, however, the entire cantilever position is being modulated relative to the
sample so there is a great risk that the images are simply a more accurate measurement
of the tip position. (Ref. [10] is a reference to the Tapping Mode patent for the
correct use of the term.) On the return path, a spatial filter blocks light that may be
reflected from the shank of the cantilever and passes that from the tip. A laser line
filter in the return path passes only A = 632.8nm, excluding light from the AFM laser
(\ = 670nm). The light then passes through a Wollaston prism and onto a differential
photodiode where optical intensity or phase is measured with an EG&G 5302 lock-in
amplifier. The drive signal for the AFM is used as the reference frequency [11]. The

SAM used a Nikon Diaphot 200 inverted optical microscope as the platform with a

Digital Instruments Bioscope as the AFM component. In this case, the objective had

iii _obaonbeacpiiotabsbCosMne COM

34
a numerical aperture (NA) of 0.75 and the laser was a Spectra Physics 145-01 HeNe,
A = 632.8nm. A schematic of the optical path in the experiment is shown in Figure
4.1. A critical element of the apparatus is the laser line filter to reject ambient light
and any signal from the AFM control laser. Since the silicon cantilever thickness of
3.dj4m is roughly the light penetration depth at the AFM laser wavelength, stray light

can have a significant impact on the results.

4.2.1 Nanospheres

A proposed explanation for the NFO signal has been described previously in two
theories [12, 13). To reiterate, one is based on a theory of coupled dipoles. The result
of this theory is that the modification of the incident field is due to the interaction
between the tip and sample induced dipoles. The other theory due to Garcia accounts
for refractive index variations of the sample and scattering from a spherical tip. In
either case, the perturbation signal contains a contribution from both the tip and the
sample refractive indices (susceptibility). Measurement of these perturbations as the
tip scans over the sample forms the NFO image. The feature common to both theories
under consideration here is the contribution from the tip and sample susceptibilities.
Since the signal depends on the local susceptibility of the sample, it should be possible
to measure adjacent objects which have different susceptibilities and are smaller than
the diffraction limit.

To address the issue of discriminating the susceptibility below the diffraction limit
it is necessary to determine the resolution of the instrument. To do this in a controlled
way, polystyrene nanosphere size standards in water suspension were deposited on
a glass cover-slip by dilution to an appropriate density, pipetting a small amount
onto the glass, and letting the water evaporate in a dry nitrogen environment. The
nanospheres had a tendency to clump together so some searching was required to find
a reasonable distribution.

Dyed and undyed nanospheres of the same size were imaged to decouple any

potential topographic signal from that due to the near-field optical interaction. Since

30

APM TLE
iicrcecope Objective

Figure 4.1: Schematic of the apparatus. Light from a HeNe laser is split into a refer-
ence beam and a sample beam at the beam splitter 51. The sample beam continues
to the beam splitter, $2, where part of it is dumped and part of it is focussed onto
the AFM tip by a microscope objective (NA 0.75). Since the depth of field of the
microscope objective is only 1 zm, compared to a tip height of 15um, only the apex
of the tip is imaged. Light scattered from the AFM tip is collected by the same
objective and combined with the reference beam (reflected from mirror M1) at the
beam splitter, $3. A laser line filter, LF, then rejects all light except the laser light.
A spatial filter, SF, passes only light from the AFM tip while excluding light that
may be reflected from the cantilever. The light is then split by a Wollaston prism,
WP, and incident on differential photodiodes, A and B.

a es
aiadsNiotHaOAKERDODNINNDHEEASNOSD Ne :

aie es ai

ia

36
any artifacts due to the tip motion will be identical for all the objects (same shape and
size), any differences will be a result of their susceptibilities. We used polysciences
fluoresbrite nanospheres in which the dye resides in the outer 10% of the nanosphere
radius. The fluorescein based dye is propriatory but has a fluorescence spectrum
that peaks at 540 nm and extends out to 700 nm. For this experiment, the dyed
and undyed nanospheres were mixed in equal proportions and then deposited on a
coverslip in the manner described above and imaged with the instrument. Dyed
nanospheres have the additional advantage that they all have the same mechanical
properties. This is important for lock-in detection since both the phase and amplitude
of the tip vibration will change as the tip scans over different materials. To detect

the NFO signal, we measured optical intensity.

Resolution

The optical intensity image of Figure 2 shows the small region at the interface between
two 200 nm nanospheres. The scan size is 250 nm so the entire nanosphere cannot be
seen. From this image we can observe that the edge response of the SAM is 15 nm
and the minimum observable feature is 3 nm in size. As a matter of comparison, the
diffraction limit of the objective lens is approximately 700 nm. [14] Since the FWHM
of a step is a commonly used resolution criterion, this is closer to the predicted
resolution of Garcia rather than Zenhausern.

Figure 4.3 was also obtained by measuring optical intensity and is a scan of two
adjacent, identical 50 nm nanospheres. Since the two are still distinguishable, and
50 nm nanospheres were the smallest available to us at the time, we can say that the
resolution of the SAM is better than 50 nm. Later, we obtained nanospheres 30 nm
in diameter which could also be detected as shown in Figure 4.4; however, 30 nm
spheres clump together significantly and we could not find an instance of only two
adjacent spheres. Notice that the destructive interference on the background for the
measured signal in Figure 4.3 corresponds with the theoretical prediction from the

dipole scattering model. More complicated geometries may not have as simple an

image and are the subject of future simulations.

ieee iil

Figure 4.2: Raw NFO image from the microscope of a region between two adjacent
200nm polystyrene nanospheres with a 3nm minimum observable feature size (A) and
a 15nm step response (B).

38

Figure 4.3: Raw NFO image from the microscope demonstrating 50nm resolution.
The sample is two identical nanospheres adsorbed on a cover slip and imaged by
detecting scattered amplitude. The scan size is 180nm.

ip aides isu sbi sn

Figure 4.4: Raw NFO image from the microscope demonstrating 30nm resolution.
The sample is a layer of 30nm nanospheres adsorbed to a glass cover-slip. The noise
in the AFM image is the tip pushing on the spheres.

Optical phase imaging is shown in Figure 4.5. Although noisy, clusters of 50nm
nanospheres roughly 200 nm in size are just resolved. Resolution here is conserva-
tively taken to mean a two point resolution similar to the Rayleigh criterion where
two sources are considered resolved when the intensity maximum of one falls on the
intensity minimum of the other and not edge sharpness or minimum feature size .

At present, the resolution of the instrument appears to be limited by the AFM
tip radius of curvature since switching to sharper tips gives sharper features.

Both the issues of topographic artifacts and the measurement of local susceptibility
are dealt with in Figure 4.6. Dyed and undyed nanospheres are distinguishable
with adjacent nanospheres appearing as bright and dark. We attribute this to the
properties of the dye since any topographic artifacts that may exist will be identical
for the same size and shape nanospheres. A good indication that the dye does affect
the susceptability is illustrated in Figure 4.7. Samples that were previously imaged
were reused some time later when the dye had leached out of the nanospheres creating
a “halo” around an otherwise dark sphere in the optical image.

Comparing the AFM and SAM images, from the point of view of meeting the

40

Figure 4.5: Clusters of 50 nm nanospheres. Left: Simultaneously acquired AFM data.
Right: Raw NFO image from the microscope demonstrating approximately 200nm
resolution by detecting optical phase.

Figure 4.6: 50nm scale optical property discrimination. False color image of differently
dyed 50nm nanospheres. The left image is AFM data, the right image is the raw NFO
data from the microscope. i) 50nm spheres resolved by the microscope which show
up as “low” next to ii) 50nm spheres appearing as “high.”

Figure 4.7: A. AFM image of an old sample of dyed nanospheres. B. Corresponding
apertureless microscope image indicating that the dye has leached out of the spheres
creating a halo in the near-field optical image.

criteria set down by Hecht et al. [1] for a true NFO image, one finds that several
of them are met. First, the resolutions of the AFM and SAM are clearly different.
Second, in the case of the dyed size standards, the two images are uncorrelated.
Namely, nanospheres that appear identical to the AFM appear different in the NFO
image. Third, the AFM and NFO images are displaced by a constant amount. Finally,
the images were taken in tapping mode which is nearly equivalent to — height
mode (CHM). There is, however, some surface tracking that takes place in tapping
mode operation in order to keep the oscillation amplitude constant. An example of
the artifacts that are introduced in constant gap mode is given in Figure 4.8 where
the optical data was collected when the AFM is lifted off a constant distance (30 nm)
from the sample surface.

To summarize, we have carried out a series of controlled experiments using
nanosphere size standards where we observe significant differences in resolution and
structure between the AFM image and the simultaneously acquired near-field optical

image. For nanospheres 30, 50 and 200 nm in diameter, the two point resolution was

at least 200 nm when detecting optical phase and 30 nm when detecting optical inten-

a aS ge

Siri toga buoy

‘Sains as

“hina eR

Sic iii

ha RMN

IBN v ie vesbaigy sume

42

Figure 4.8: A. AFM image of nanospheres on an anti-reflection film. B. Apertureless
microscope image taken in tapping mode simultaneously with the AFM data. C.
Apertureless microscope image representing constant gap gap contribution to the
optical signal. In this case the tip-sample gap was maintained at 30 nm.

sity. The edge response was typically 15 nm and minimum observable features were
on the order of 3 nm. Further, in experiments employing a mix of dyed and undyed
nanospheres, we find that we can observe differences in the same NFO image for ad-
jacent nanospheres which we attribute to differences in susceptibility. Therefore, we
conclude that near field scanning apertureless microscopy not only meets the criteria
for a NFO image but is also capable of measuring optical properties below the diffrac-
tion limit. We believe that this is the first demonstration that adjacent objects with

different susceptibilities and sizes below the diffraction limit can be differentiated.

4.3 Applications

4.3.1 Anti-reflection films

We have studied anti-reflective thin films with the apertureless microscope as shown
in Figure 4.9. These films were found to be quite sensitive to perturbations in the
interference condition as indicated by Figure 4.10. Although variations in the topog-
raphy of the film are only 9 Ain height, they show up quite clearly as an enhancement

in the near-field image. The smallest areas in Figure 4.9 are 10 nm in size and as a

result could not be seen with conventional optics.

Figure 4.9: Apertureless microscope image of anti-reflection thin film at 633nm.

oan

2nm

AKA
a \ Lil 0 om
my

2nm

Figure 4.10: AFM image and section indicating topography of only 0.9nm.

44

4.3.2 Chromosomes

The Near-field optical structure of the centromere region of undyed polytene chromo-
somes has been observed by using the apertureless microscope in intensity detection
mode. The centromere is of primary importance to the functioning of the chromosome
in the cell during cell division. It is also particularly interesting for structural /optical
studies since its DNA repeat sequences are highly conserved among organisms and
it is possible that they play a part in the centromere self assembly [21-23]. Polytene
chromosomes on glass were obtained commercially (Bioforce labs) and dessicated.
They were imaged by positioning the AFM tip on the chromosome with the inverted
optical microscope, since chromosomes are many microns in size, and then engaging
the SAM.

Figure 4.11 is a result of the measurement of polytene chromosomes. The first
three images (4.11 A, B, C) are a series of AFM scans to indicate where on the
chromosome the near-field optical data was taken. The fourth image in the series is the
raw near-field optical signal which was obtained simultaneously with the AFM data.
The small features are approximately 100nm in size and are believed to represent the
near field structure of the chromosome since they are not in direct correspondence with
the topography as determined by the AFM. Since chromosomes are both structurally
and chemically complicated, it is believed that future spectroscopic studies will be
necessary to extract the function of these features that cannot be determined by single
wavelength illumination.

In summary, we have demonstrated a new application of scanning apertureless
microscopy to the near-field optical imaging of chromosomes. Structure 100nm in
size has been observed and was not simply a measure of the topography. Future ap-

plications in biology could include apertureless imaging of viruses (50 nm) or proteins

(10 nm) since their size is within the demonstrated resolution of the SAM.

A5

Figure 4.11: Apertureless microscopy of polytene chromosomes. A-C) AFM images
of the chromosome with progressively smaller scan sizes of the regions indicated. D)
Apertureless microscope image of a small region of the centromere of the chromosome
simultaneously acquired with the AFM image C.

46

Bibliography

[1] B. Hecht, H. Bielefeldt, Y. Inouye, L. Novotny, and D. W. Pohl, J. Appl. Phys.
81, 2492 (1997).

[2] Y. Martin, F. Zenhausern, and H. K. Wickramasinghe, Appl. Phys. Lett. 68, 2475
(1996).

[3] M. Born and E. Wolf, Principles of Optics 6" Ed. Cambridge University Press,
1980.

(4) D. Courjon and C. Bainier, Rep. Prog. Phys. 57, 989 (1994).
[5] E. Betzig, M. Isaacson, and A. Lewis, Appl. Phys. Lett. 51, 2088 (1987).

[6] L. P. Ghislain and V. B. Elings, Appl. Phys. Lett. 72, 2279 (1998).

[7] H. Hatano, Y. Inouye, and S. Kawata, Opt. Lett., 20 1532 (1997).

[8] H. K. Wickramasinghe and C. C. Williams, Apertureless Near Field Optical Mi-
croscope, U.S. Patent 4,947,034 (April 28, 1989).

[9] F. Zenhausern, M. P. O’Boyle, and H. K. Wickramasinghe, Appl. Phys. Lett. 65,
1623 (1994).

' [10] V. B. Ellings and G. A. Gurley, Tapping Atomic Force Microscope, U.S. Patent
5,412,980 (May 9, 1995).

[11] C. Schonenberger and S. F. Alvarado, Rev. Sci. Inst. 60, 3131 (1989).
[12] F. Zenhausern, Y. Martin, and H. K. Wickramasinghe, Science 269, 1083 (1995).

(13) N. Garcia and M. Nieto-Vesperinas, Appl. Phys. Lett. 66, 3399 (1995).

[14] M. Pluta, Advanced Light Microscopy. Vol. 1 (1988).

AT

[15] H. F. Hamann, A. Gallagher, and D. J. Nesbitt. Appl. Phys. Lett. 73, 1469
(1998).

[16] Y. Martin, S. Rishton, and H. K. Wickramasinghe, Appl. Phys. Lett. 71, 1
(1997).

[17] A. Larech, R. Bachelot, P. Gleyzes, and A. C. Boccara Opt. Lett., 1315 (1996).
[18) R. Bachelot, P. Gleyzes, and A. C. Boccara Opt. Lett., 1924 (1995).

[19] R. Bachelot, G. Wurtz, and P. Royer Appl. Phys. Lett. 73, 3333 (1998).

[20] C. Hubert and J. Levy Appl. Phys. Lett. 73, 3229 (1998).

[21] M.S. Clark and W. J. Wall, Chromosomes Chapman and Hall, London, 1996.

[22] H. F. Willard, Current Opinion in Genetics and development 8, 219 (1998).

[23] T. J. Yen and B. T. Schaar, Current Opinion in Cell Biology 8, 381 (1996).

48

Part II

| Semiconductor Applications of

Force Microscopy

AQ

Chapter 5 Correlation Between the
Surface Defect Distribution and Minority
Carrier Diffusion Lengths in GaN

5.1 Introduction and Motivation

Gallium Nitride based devices are currently of great interest for optoelectronic [1-3]
as well as high power and high temperature electronics [4, 5]. Since many of the the
performance characteristics of bipolar devices are determined by the minority carrier
transport properties (diffusion lengths and lifetimes) [6], it is useful to determine how
they are affected by the defect structure. In the past it had been assumed that linear
dislocations were electrically inert [7-9] since they had little effect on the perfor-
mance or reliability of GaN light emitting diodes. However, the correlation between
cathodoluminescence (CL) and surface morphology observed as dislocations termi-
nating as pits in the surface shown by Rosner et al. indicated that linear dislocations
are important in recombination processes. [10] Electron beam induced current (EBIC)
measurements provide a way to directly measure the minority carrier diffusion length
in semiconductors.

In the EBIC measurement, electron-hole pairs are generated by a high energy
electron beam in an electron microscope near the Schottky contact of a Schottky
diode. The high energy electrons create an excess of minority carriers which diffuse
to the Schottky contact on the semiconductor. The resulting current in the diode is
collected and measured as a function of the distance from the contact. Fitting the
data to an exponential decay gives a direct measurement of the diffusion length.

In this chapter, we correlate the measured diffusion length with the defect struc-

ture measured by atomic force microscopy.

50
5.2 Experiment Outline

In the experiment, we determined both electron and hole diffusion lengths from EBIC
measurements on material that was characterized by atomic force microscopy (AFM).
We then compare the distribution of defect induced depressions on the surface with
the measured diffusion lengths. Because the density of linear dislocations threading
the GaN is believed to be approximately the same as those reaching the top surface
of the film for thin films [7], the 2D AFM data should represent the 3D distribution
of those dislocations. For thicker films, however, the density of threading dislocations
reaching the surface of the film decreases with film thickness. Moreover, the AFM
does not reveal all types of defects. Nevertheless, it is the non-uniform distribution

of the defects and not their absolute number that is considered here.

5.2.1 Details of the AFM and EBIC Experiments

The AFM data was obtained using a Digital Instruments Multimode AFM operating
in Tapping Mode and a Nanoscope IIIa controller. A cross check of the topographic
data was performed using contact AFM with oxide sharpened tips and no significant
differences were found. The EBIC experiments were conducted in a JEOL 6400V
electron microscope with a GW Electronics pre-amplifier followed by GW Electronics
specimen current amplifier or Keithly 486 picoammeter. The entire apparatus was
enclosed in an active electromagnetic interference (EMI) cancellation cage as well as
being mechanically isolated. A schematic of the experiment is illustrated in Figure
5.1. Due to the large concentration of holes in p-type sample (or electrons in UID
n-type sample) compared to the generated electron-hole concentration, only minority
carriers are effectively generated, assuming low electron beam currents. This is the
reason why a p-type sample is required for measurement of electron (as a minority
carrier) transport parameters, and n-type sample is required for measurement of hole
transport properties.

Gold and Ti/Al/Ni/Au were used as the Schottky and ohmic contacts in the

case of n-type GaN while Ni/Au and Ti/Au were used in the p-type case. For more

diffusion
l~exp(-x/L,)

Figure 5.1: A schematic of the EBIC measurement conducted in the SEM. Al and
Au represent the ohmic and Schottky contacts to the GaN film for the diode required
to perform the EBIC measurement. Minority carriers generated by the high energy
electron beam diffuse to the Schottky contact where they are collected and form the
current measured by the amplifier.

Figure 5.2: Line Scan profiles of the EBIC superimposed on the secondary electron
image of the Schottky contact. A) P-type MOCVD grown GaN. The beam cur-
rent was 0.5nA at an accelerating voltage of 20kV. B) N-type MOCVD grown GaN.
The beam current was 1.06nA at an accelerating voltage of 20kV. The profile of the
EBIC as a function of distance from the edge of the Schottky contact is fitted to the
theoretical relation I = kx~'/?exp(—x/L) in order to determine the diffusion length.

detailed discussions of EBIC measurements see References [6] [11] and in general
Reference [13]. A sample of the EBIC data is shown in Figure 5.2. The profile of the
EBIC as a function of distance from the edge of the Schottky contact is fitted to the

theoretical relation J = ka~'/*exp(—a/L) to determine the diffusion length.

5.2.2 GaN Samples

The n-type MOCVD films for this study were commercially grown, unintentionally
doped 2ym thick GaN on sapphire with a carrier concentration in the 10!"cm~? range.
The p-type MOCVD films were commercially grown, Mg doped 2m thick GaN on
sapphire with a carrier concentration in the 10'’cm~? range. The HVPE sample was
a commercially grown, 104m thick GaN layer on sapphire. The 10m layer consisted
of a 8um thick low conductivity (~ 10'®cm~*) layer and a highly conductive bottom
layer.

The molecular beam epitaxy (MBE) samples were grown by E. C. Piquette in
our MBE facility. Ga-polar samples were grown on sapphire using a thin AIN buffer

layer and an RF plasma source for active nitrogen. The film was grown at 800C, near

HN ‘a

53
stoichiometric conditions, to a thickness of 820 nm. Layer thickness were confirmed
by variable angle spectroscopic ellipsometry (VASE). The surface of the film shows
hillocks which may be a result of gallium flux deficiency during growth or the presence

of inversion domains due to the growth on bare sapphire.

5.3 Results

Figure 5.3 shows representative results for n-type MOCVD GaN. The small pits
observed are 30 nm in size as was the case in Reference [10]. Although the two
images are different (in one case the defects appear to lie along the grain boundaries
and in the other terminating steps), the “defect free” regions are typically on the order
of 0.5 wm which also appears to be the case in Reference [10]. Grains of similar size
have also been observed by scanning capacitance microscopy [14]. The corresponding
thresholded images are shown to accentuate the distribution of surface defects. The
average measured hole diffusion lengths for both samples were the same to within
experimental error; L, = 0.28 + 0.02pm.

Figure 5.4 shows results for p-type MOCVD and n-type MBE grown GaN which
also exhibited surface terminated defects. In the p-type sample (left) long trains of
defects clearly outlined the grain boundaries which were in the same size range as
the n-type material, 0.5m. Electron diffusion lengths in this p-type sample were
measured to be L, = 0.2 + 0.054m. The MBE film (right) clearly shows pyramidal
hillocks associated with inversion domains that thread the GaN film [15]. The flat
regions between the hillocks are roughly 0.25ym in size and the hole diffusion length
for this material was L, = 0.22+0.03um. Figure 5.5 shows the n-type HVPE sample
at a boundary between regions of flat and spiral growth. Very small surface pits are
visible at the step boundaries in the spiral region whereas larger pits of the same size
as those in Figures 5.4 and 5.4 are visible in the flat region. A boundary between the
two regions is shown in Figure 5.5. Preliminary measurements of the hole diffusion

length in this sample gave regions of higher and lower L,, which might correspond

to the different growth regions which appear to have less and more surface defects as

asin

500 nm

730 nm

Figure 5.3: Two samples of n-type MOCVD Grown GaN. The top left image is a 3m
AFM scan and the top right image is a 244m scan. Corresponding thresholded images
are shown below to accentuate the defects which appear as 30nm dark areas. Their
distribution does not appear to be random, but decorating the grain boundaries.

e PAROS OREECER TT iets eee .
es 250nm f +1000 nm an \
& . ¥ * . # - : e 4

Figure 5.4: Left: 1m AFM image of p-type MOCVD Grown GaN showing the pits
on the surface from the termination of linear defects at the surface. Right: 44m AFM
| image of n-type MBE grown lym thick GaN film on sapphire. The bottom left and
: right images are the thresholded data to accentuate the distribution of the defects.

Ne
Petey apeseoncate

° 1250: am

Figure 5.5: Left: 54m AFM image of n-type HVPE grown GaN showing the boundary
between the two distinct regions. Right: The corresponding thresholded image to
accentuate the defects.
indicated by the right-hand image in Figure 5.5.

A summary of the EBIC results is shown in Table 5.3. We can notice that the
minority carrier diffusion lengths are always smaller than either the average grain size

or average column size delineated by inversion domains.

5.4 Models for the diffusion length and lifetime

A simple model can be used to explain our observations. By solving the 1D diffusion
equation for minority hole recombination on periodic grain boundaries (due to defects
or inversion domains) in a manner similar to [16], we have
dp Op ()
dx? Ot
with the periodic boundary condition p(m * d) = 0, where m is an integer and d is
the distance between grain boundaries or columns separated by inversion domains.

The boundary condition is set by the assumption that all the carriers recombine at

ov

Sample CC[cm~*] Diffusion length DD{cm~]

n-MOCVD 10"? )—s L, = 0.284 0.02um (2 —5)- 10°
n-MBE lo = LL, = 0.22 + 0.03um 10°
n-HVPE 10% Ly > 2pm 108

p-MOCVD 10 = L, =0.20+0.05um 5-109

Table 5.1: Summary of the EBIC measurements on several GaN samples. The second
column labeled with CC’ represents carrier concentration. The diffusion lengths in
each row of the table are averages over a range of beam currents and different mea-
surement positions on the sample. The last column labeled with DD gives density of
linear dislocations for each sample.

the boundary. The separable solutions are of the form

p(x, t) =e p(x) (2)
where
ple) = posin( (5.1)

At the boundary, p(md) = 0 which gives L, = d/z. Substituting measured values
for d = 0.5um, we find L, = 0.17um which is in good agreement with the measured

values.

5.4.1 2D models for minority carrier diffusion length and life-

time: dislocation density or grain size

If minority carrier recombination on grain boundaries is the limiting mechanism for
minority carrier transport, then a two-dimensional model should give a better rep-
resentation of the observed grain structure. Similar models have been previously

derived in case of GaP [20] and were derived for GaN by Z. Z. Bandi¢ as given in the

following section [21].

38

Random distribution of dislocations

If we assume that linear dislocations are distributed in a hexagonal ” honeycomb-
type” array, then the dislocation density can be expressed as Nyqg = 1/(mr?), where
2r, is the distance between two first-neighbor dislocations. Dislocations are assumed
to have core diameter 279. The minority carrier concentration (holes, for example) is
obtained by solving the two-dimensional diffusion equation for the minority carrier
concentration p:

D,V’p = Op/dt. (5.2)

Boundary conditions at the dislocations are given by:

(7) Pip, = 0 (5.3)
(ii) 2 7, = 9 (5.4)

Boundary condition (7) is for complete recombination at the dislocation. Therefore,
the minority carrier concentration must be zero. Condition (iz) is approximation to
the periodic boundary condition. [20] After solving Eq. 5.2 in cylindrical geometry,
the minority carrier lifetime T,.q: is obtained: [20]

1 2

scat = l — 0.57 5.9
st = Na mVeNe 69)

If the intrinsic minority carrier lifetime without scattering at dislocations is given
by 7, then the total minority carrier lifetime becomes Tt = 7) '+72it. The hole
lifetime and corresponding diffusion length obtained from the model are shown in
Figure 5.6 as a function of dislocation density. For the calculation shown in Figure
5.6, we used the measured value for hole diffusivity, D, = 0.12 cm?/s, obtained from
MOCVD samples, and dislocation core radius of ro = 30 nm, which is typically

observed by AFM measurements.

59
Dislocations occupying grain boundaries

In the majority of samples, experimental observation of the linear dislocation pat-
terns show that they are distributed at the boundaries of otherwise defect-free grains.
Random distribution does occur, but not in the majority of cases.

The schematic of this type of distribution of linear dislocations is also shown in

Figure 5.7. In this case, the boundary conditions for the diffusion equation become:

(1) Dlr, = 0 (5.6)
(ii) 2 yp =O (5.7)

The solution for the minority carrier lifetime in this case is
(5.8)

The hole lifetime and diffusion length obtained from Eq. 5.8 are shown in Figure 5.7,
using T =7)'+72car, Where 7p is the intrinsic lifetime as before.

Both models, either in the case of uniform distribution of linear dislocations, or
in the case of linear dislocations occupying boundaries of defect-free grains, predict
that minority carrier lifetime and diffusion length should be grain size limited for
grain sizes 1 ym or smaller or dislocation limited at dislocation densities of 10°cm~?

and higher. This is in qualitative agreement with our experimental observations as

indicated in Table 5.3.

5.5 Conclusions

We have studied linear dislocations and surface defects in p and n-type metal or-
ganic chemical vapor deposition(MOCVD), hydride vapor phase epitaxy (HVPE)
and molecular beam epitaxy (MBE) grown GaN films on sapphire with atomic force

microscopy. The surface pits due to threading dislocations were found not to be

distributed randomly but on the boundaries of growth columns. The dislocations

60

11

4 LL
ey eo}
2 O
a i on
@ 10f =
= dl
31 D

10° 40° 10° 10°° 10"
Dislocation density [cm]

Figure 5.6: Hole lifetime and diffusion length as a function of dislocation density. a)
Uniform array of linear dislocations. The dislocation core radius is ro, and distance
between dislocation is 2r,. b) Hole lifetime and diffusion length as a function of
dislocation density, assuming uniform distribution of dislocations. The data is plotted
using a diffusivity measured for MOCVD samples. The hole lifetime 7 without
recombination at dislocations is used as an parameter in the plot.

10; eee 7,=30 ns - (D
£, =
a OF o

“ >
! 0.1 1

Cyain size [ium]

Figure 5.7: Hole lifetime and diffusion length as a function of average grain size.

a) Dislocations occupying boundaries of otherwise defect-free grains. The radius of
grains is r;. b) Hole lifetime and diffusion length as a function of average grain size in
the case of linear dislocations occupying grain boundaries of defect-free grains. The
data is plotted using a diffusivity measured for MOCVD samples.

62
are thought to be electrically active since the average distance between them (av-
erage column size) is comparable to minority carrier diffusion lengths as measured
by electron beam induced current experiments on Schottky diodes fabricated with
the same material. Diffusion lengths found for holes and electrons were found to be
Ly = 0.28+0.03um and L, = 0.2+0.05yum. This distance corresponds to the sizes of
regions free from surface dislocations in both cases and can be described by a simple
model of recombination on grain boundaries. A non-uniform distribution of defects
would offer one explanation why, on the assumption that defects are involved in re-

combination, a high “average” dislocation density would not necessarily yield small

diffusion lengths.

63

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69

Chapter 6 Electric Force Microscopy of
GaN

6.1 Introduction

Electric force microscopy (EFM) provides a sensitive way to measure electrostatic
forces and potentials. In the past it has been used to measure buried surface topog-
raphy, dielectric constants [1], deposit and image charge [2, 3], ferroelectric domain
walls [4], and the potential across a pn junction. More recent applications include
imaging and charging nanocrystals [5] as well as the modification of ferroelectric films.

In this chapter, we present several novel applications of EFM. In the first sections,
we study molecular beam epitaxy (MBE) grown GaN films of both polarities using
electric force microscopy to detect sub 1 micron regions of charge density variations
associated with GaN extended defects. The large piezoelectric coefficients of GaN
together with strain introduced by crystalline imperfections produce variations in
piezoelectrically induced electric fields around these defects. The consequent spatial
rearrangement of charges can be detected by electrostatic force microscopy and was
found to be on the order of the characteristic Debye length for GaN at our dopant
concentration. Additionally, the surface charge could be modified by externally ap-
plied strain and illumination. The electric force microscope signal was also found to
be a linear function of the contact potential between the metal coating on the tip and

GaN. Analysis of the data allowed us to measure both the surface state density and

energy.

66
6.2 Theory of Electric Force Microscopy

Electric force microscopy can be performed in two ways: by detecting electrostatic
forces and by detecting the surface potential. To detect the electrostatic forces, a
voltage is applied to a conductive AFM tip (typically coated with metal) which is
then scanned across the surface at a constant tip-sample separation. Phase differences
induced by electrostatic forces on the oscillating tip during scanning are detected and
give a qualitative measurement of the local charge density.

In order to find the force on the tip, we use a model like that for Kelvin force
microscopy. The metal tip is modeled as a small capacitive element, in similar fashion
to Ref. [6-8] only there is no external feedback loop to control the tip voltage. The
energy of the tip is the sum of the Coulomb energy due to free charges and the energy

in the small capacitor formed by the tip and the surface.

B= aC applied ~ Veontac 6.1
Amey z + 5) ( pplied tact) (6.1)

where C' is the sample-tip capacitance, g, are surface charges, gq, are charges induced
on the tip, and Veontact IS the contact potential between the tip metal and the surface
material. The tip-sample separation, z, was set at either 30 nm or 50 nm for the
experiments that will be discussed later. The force felt by the tip under an applied

DC bias will be the derivative of the energy:

= are Va 1€ — Voon ac ° 6.2
inant Dds! pplied tect) (6.2)

Surface Potential

Local surface potential measurements are more complicated than either Kelvin force
or electrostatic force microscopy. In short, to detect the local surface potential, an

oscillating voltage plus a DC bias is applied directly to the AFM tip:

Vapplied =V,.+Vo cos(wt). (6.3)

wenn

67

The tip then feels a force (at frequency w) of

dC , -
R= a! ‘de 7 Veample) Vo (6.4)
where a is the vertical derivative of the tip-sample capacitance. To determine the

surface potential of the sample, the tip voltage is adjusted by an additional feedback
loop to equal the sample potential so that the tip feels no force. The essential dif-
ference between this technique and the one above is that at the zero force condition
there is no tip motion and consequently no charge variation on the capacitor formed
by the tip and the surface. As a result, the image is formed by the surface potential
and not by the charge/contact potential.

For more detail, Appendix A derives the force on the tip from the Maxwell stress

tensor.

6.3. Electric Force Microscopy of GaN

Nitride based devices have been of great interest in the last few years, notably due to
their success in optoelectronics, where lasers and diodes have been demonstrated and
successfully commercialized [9]. Further applications of nitrides are expected in the
arena of high power, high power microwave and high temperature devices [10-12], as
well as solar blind ultra-violet detectors [13]. It has been recently demonstrated that
the large intrinsic piezoelectric coefficients of GaN and AIN are responsible for a high
concentration two-dimensional electron gas at the AlGaN/GaN interface in hetero-
junction field effect transistors (HFET) [14, 15]. Other possibilities exist for the en-
hancement of electric properties of contacts to nitrides by piezoelectric engineering as
recently demonstrated in the case of Schottky contacts [16]. While most of the recent
research has emphasized electronic device aspects of the piezoelectric effect [14-16],
comparatively little work has concentrated on the investigation of fundamental prop-

erties and nanoscale characterization of piezoelectrically induced phenomena. One

consequence of the piezoelectric effect is that it allows electrostatic force imaging

68
of charge redistribution around defects due to local variations in strain caused by
crystalline imperfections. Although the measurement of the magnitude of the charge
density is non-quantitative, electric force microscopy (EFM) of charge density dis-
tributions can provide interesting insight into the nature of defects, the piezoelectric
effect in nitrides, as well as Schottky barrier analysis and surface band bending. On
the other hand, surface potentiometry can quantitatively map the change in surface

potentials due to charge redistribution [1, 6].

6.3.1 GaN Growth

The gallium nitride layers studied here were grown by E. C. Piquette on c-plane sap-
phire substrates by radio frequency plasma assisted molecular beam epitaxy (MBE) in
our MBE facility. Ga-polar GaN films were nucleated using AIN buffer layers whereas
N-polar films were nucleated using a GaN buffer layer. Polarity was determined by
RHEED reconstruction at low temperature [27], and by KOH etching [28, 29]. Other
details of the growth conditions are presented in [24, 25]. Growth conditions for the
Ga-face GaN were slightly Ga-rich, leading to locally flat (0001) Ga-face films which
contain pits on the surface induced by dislocations or most likely (0001) inversion
domains threading along the growth direction. These pits are readily observed in
atomic force microscopy (AFM) images [30] and are sites for the charge accumulation

which will be imaged by the EFM.

6.3.2 Metal Deposition

A variety of different metals were used for coating the AFM tips to vary the metal
work function for electric force microscopy and to provide the contact necessary for
applying a bias to the tip. Cobalt coated AFM tips were obtained commercially
from Digital Instruments. Titanium, Al, Pt, Pd, Ce, W, and Au coated tips were
fabricated in the following manner. Commercial silicon tapping mode AFM tips were
plasma cleaned in a 30W Ar plasma at a pressure of 8 x 10~¢ Torr. A 15 nm metal

layer was then sputter deposited in sputter chamber at a base pressure of 1 x 1077

SH ostmeeen

Figure 6.1: Photo of the Bioscope configured for surface charge studies of strained
piezoelectric materials.

Torr. Electrical contact to the tip was made through the metallic clip on the AFM

tip holder.

6.3.3 EFM Results: Contact Potential

All the EFM data presented here was collected using a Digital Instruments Nanoscope
IIa controller and a Bioscope scanning probe microscope operating in Tapping Mode.
Although mechanically noisy, the Bioscope platform has many advantages for cus-
tomization. For example, Figure 6.1 shows the Bioscope head with a custom stage
for applying strain to the sample during imaging. Moreover access to the internal
jumpers to apply external signals, independent grounds, etc., is simplified compared
to the multimode microscope. This configuration gave us the unique capability for
the strain and light enhancement experiments to be described later.

First, the electric field gradient was measured as a function of tip voltage to rule
out topographical artifacts since they should not depend on the tip bias. Variation

in the induced surface charges result in a force differential between the tip and the

in

ths gg tress

70

surface that increases with tip voltage which can be observed in the series of EFM
images in Figure 6.2. A complication here is that topography can affect the EFM
image for films with a permanent polarization, P, such as GaN. For such films, the
surface charge, 0, = P-n where n is the surface normal, will not be constant over
a rough surface. Here, however, the topography is not severe enough to observe this
effect since the induced pits are approximately 0.5 ym wide and only 25 nm deep
giving a surface normal angle of only 3 degrees. Artifacts at high tip voltages due
to capacitive effects are also problematic. To avoid them, it is necessary to keep
the imaging voltages low which results in weak contrast. Despite these complicating
factors, it is possible to obtain EFM images of the charge distributions.

It was found that the electrostatic force was a function of the magnitude of the
tip voltage and not the sign, consistent with the theoretical V? dependence from
Eq. 6.2. Another feature of Eq. 6.2 we can observe is a force minimum when the
applied bias is equal to the contact potential between the GaN and the metallic tip.
More specifically, Veontacte = Gm — XGan — AE yn — Ao is the contact potential between
metallic tip and the semiconductor. In this formula, ¢,, is metal work function, ¥can
is the electron affinity of GaN (4.2 eV [31]), Ad is band bending caused by surface
states, and AF, is the Fermi level position in the GaN referenced to the bottom of
the conduction band. This was experimentally observed, and Figure 6.2 illustrates
this effect with a signal “null” at a tip voltage of 0.5 Volts in case of cobalt coated tips.
The inset of Figure 6.3 is a plot of the signal RMS roughness (in arbitrary units) as a
measure of contrast against the tip voltage to illustrate the minimum force condition.
Typically, complete cancellation of the signal is not expected due to the first term in
the Eq. 6.2 leaving some residual image due to electrostatic forces.

Figure 6.3 is a plot of the measured tip null voltage V,,,,, as a function of the
difference between metal work function and electron affinity of GaN. The observed
dependence between V,,,,,, and @metal — XGan iS indeed linear. Aluminum and cerium
were found to be anomalous where the opposite sign of the voltage was required to null

the EFM signal. This is attributed to different work functions of oxides which formed

when the tips were exposed to air. A least squares linear fit of this experimentally

ral

Figure 6.2: Electrostatic force image of the surface of MBE grown GaN as a function
of tip applied voltage for a Ga-polar sample. For reference, the top image is the AFM
scan of the same area imaged with EFM. Scans A-D are the EFM data with the tip
bias increasing from A-D. Notice the signal “null” at a tip bias of 0.5 V. The tip
sample separation was 50 nm in all the EFM images.

72

1.0 3 J

S ; g 0.16 ° platinum
psi) } ]
oO 0.87 = 0.124 lad;
oO ; 5 5 ium
© O6F é coe} ° goie J
— o °
O 1 = o0 a5 1D 15 cobalt
> O4F Tip Voltage (V) 4
za 02) tungsten
a 0.0F titanium 4
Wy -0.24 A cerium J
: A aluminum
-0.4 i 1 L

15 -10 05 00 05 10 15 20 25
O neta XGan [eV]

Figure 6.3: Plot of the tip voltage for a minimum force condition vs the work function
difference between the tip metalization and GaN. Inset: Plot of the RMS contrast
against the tip bias in arbitrary units illustrating the “null” condition for the cobalt
coated tips.

observed dependence gives slope of 0.66 + 0.03, and an intercept of —0.04 + 0.03. A
slope less than 1 and indicates presence of the surface states.

The situation will be considered as an electrostatic analysis of the following: 1) An
ideal metal with work function @,,. 2) A dielectric interface region with a thickness
of the tip-sample separation. 3) A semiconductor surface with surface states that fill
up to a particular energy. An analysis of the barrier energy as a function of the metal

work function and semiconductor electron affinity [32] gives the following expression.

dim = a(bm — x) + (1—a) (= - ex) Ad (6.5)

Where ¢g, is the barrier energy between a metal and an n-type semiconductor, dm,

73
is the metal work function, y is the electron affinity, E, is the bandgap, A¢@ is the
barrier lowering, which is assumed constant, and @9 is the maximum energy of the
surface states relative to the valence band. The quantity a arises from collecting

terms while deriving Eq. 6.5 and is written as:

€j

= ——-. 6.6
“ Dog + & ( )

D, is the density of surface states, €; is the dielectric constant of the interface, and
6 is the thickness of the metal-semiconductor interface. For the regression analysis
we write dg, = M(@m — x) + 6 where m and 6 are determined by the slope and
intercept. Regrouping terms in Eq. 6.5 a = m is determined directly by the slope.

The intercept, b, is written as

b=(1—a) (= - en) — Ag. (6.7)

The density and energy of the surface states can now be expressed in terms of the

regression slope and intercept, m and b.

E, b+Ad

eo = 7 Lom (6.8)
dD, = sae (6.9)

Substituting for the slope and intercept, the surface state energy, @o, lies 30 mV + 90
mV above the valence band. This is consistent with an observation of surface states at
or below the valence band maximum using x-ray photoemission spectroscopy [33, 34].

Using an air gap as the dielectric for the interface, the calculated density of surface
states is 9.4+0.5 x 10!°cm~?. If water, ¢; = 80€9, is used as the dielectric to try to
account for a typical surface contaminant, the surface state density becomes 7.5 +
0.4x10!cm~?. Since the density of chargeable defects required to pin the Fermi level

is on the order of 10'*cm~? [35], we conclude that the GaN surface is unpinned in

this case.

74
6.4 Surface Charge Distributions: Debye Length

Figure 6.4 shows that the nature of the charge rearrangement is due to screening of
the piezoelectrically induced charges caused by strain relaxation at numerous defects.
The N-polar (Figure 6.4 A and B) and Ga-polar (Figure 6.4 C and D) films have
different defect structure and hence different surface morphology. Figure 6.4 A and
B show EFM and AFM image and the associated profile for N-polar film. We can
observe steps (approximately 5 nm in height) in the Figure 6.4 B, and associated
charge accumulated on these steps (Figure 6.4 A). In case of Ga-polar films, charge
accumulation (Figure 6.4C) is observed at the edges of the hexagonal pits. However,
in both cases the strain relaxation and consequent charge rearrangement has a spatial
extent of 60 nm. A calculation of the Debye length gives Dp = ,/e,kT/q?N < 100
nm where both films have N > 10!° em73, €, is the dielectric constant of GaN, q is
the elementary charge, and T = 293K. The 60 nm spatial extent of the measured
charge is within the experimental error in the determination of the doping density.
Therefore, since the spatial extent of the charge density surrounding the defects is
approximately equal to the Debye length within experimental error, it is believed that
the observed charge is a screening charge rather than the bare surface charge density
that would be induced on the surface due to the termination of the polarization of the
film. The Debye length observation is probably not precisely correct since a number
of complicating factors exist. First, in the degree of screening at the surface both
the bulk carrier density and the surface mobile carrier density will play a role; the
second is quite difficult to determine, but probably plays a role since EFM is affected
by above bandgap illumination which will be discussed in the next section. Also,
the length scale over which stress relaxation occurs near a large topographic feature
will determine the amount and spatial extent of piezoelectric charge density at the
surface. For the future, a useful, and potentially important, calculation would be to

estimate this and see how it compares with the calculated Debye lengths and observed

contrast in EFM.

aaa
woe

\ yy Wd \ | wo
“525 nm

CoO

‘rt

525 nam

Figure 6.4: A. EFM image of the surface of N-polar GaN and its associated line profile.
The arrows indicate the 60nm spatial extent of the screening charge associated with
strain relaxation at the steps indicated in the following image. B. The AFM and
associated line profile for the same area in A. Arrows indicate the steps of interest.
C. EFM of Ga-polar GaN and its associated line profile. Again, arrows indicate the
spatial extent of the screening charge associated with the defect structure indicated
by the AFM image in D. In all cases the tip-sample separation was 30 nm.

76
6.4.1 Surface Charge Redistribution Due to Optical Gener-

ation and Strain
Light Enhancement Effect

The electric force was found to be light sensitive and was measured at several discrete
wavelengths above and below the GaN bandgap energy (3.4 eV = 365 nm) using lasers
at 635nm, 594.1nm, 543.5nm, and 325 nm as shown in Figure 6.5. The sample was
illuminated at a small glancing angle to eliminate interference with the AFM as shown
in Figure 6.6. The tip voltage was held constant at 5mV, creating weak contrast in
the EFM image without illumination as observed in Figure 6.2. The choice of tip bias
was arbitrary since the experiment was conducted before we knew which tip voltages
were likely to cause artifacts. When the sample was illuminated with a photon energy
below bandgap (Figure 6.5(A-C)), no apparent difference in surface charge could be
observed, even with optical powers above 1mW. However, there is a significant
increase in surface charge when the sample is exposed to light with a photon energy
above the band gap (Figure 6.5 D). This increase is associated with the generation
of electron-hole pairs, which cannot be obtained with photons of energy smaller than
the GaN band gap. We speculate that the separation of generated charges by internal
polarization fields, as well as the increase in the sample conductivity, are responsible
for the observed change.

Figure 6.7 shows the EFM images obtained with tip voltage held constant at
5mV, illuminated with the 325nm laser, as a function of the optical power. The
optical power required to produce a visible change in the EFM image was found to
be as small as 1 zW. No change could be observed for the longer wavelengths even

for optical powers up to three orders of magnitude greater.

Strain Effects

Since the piezoelectric effect will change the magnitude of the internal fields and

consequently the surface charge distribution/potential, a home built stage was used

to externally apply strain to GaN films by bending the sapphire substrate. The

Figure 6.5: Electric field gradient (charge density) images at different illuminating
wavelengths indicated in the upper right of each image. The tip bias was held at 5
mV with 50 nm tip-sample separation in all cases. A) 20 mW red diode laser. B) 1
mW Yellow HeNe laser. C) | mW Green HeNe laser. D) 10 wW from a UV HeCd
laser.

78

Nexitation

Figure 6.6: Ilustration of the illumination geometry for the light enhancement effect.
It is important to minimize the stray light from the external illumination. Light,
other than from the AFM laser, that is collected by the AFM photodiodes affects the
engage offset. Hence, as the intensity is changed during the experiment the AFM can
lose the surface.

induced strain is tensile and approximately 1%. Subsequently, both electric field
gradient and surface potential measurements were made on unstrained and strained
samples and are shown in Figure 6.8. Contrast reversal is observed in the surface
charge of the strained sample as shown in Figures 6.8A and B. Strained samples also
showed regions which had changes in the surface potential of approximately 0.1V as
indicated in Figures 6.8 C and D. One explanation of the observed light and strain
effects is due to inversion domains as mentioned in Section 6.3.1. The spontaneous and
strain-induced polarizations are anti-parallel to that of the bulk crystal within these
inversion domains. Since polarization, which is perpendicular to the sample (0001)
surface, induces free charge separation in such way to cancel the electric field, the
domains of different orientation will induce different surface charges. This will create
regions of opposite surface charge corresponding to inversion domain defect structure.
In the light enhancement effect, opposite internal polarization fields separate the

optically generated holes and electrons to create opposite contrast. The presence of

inversion domains can also explain the observed contrast reversal. Since tensile strain

Figure 6.7: Electric field gradient (charge density) image as a function of optical
power at 325 nm. Optical power increases from A-D. Tip Bias = 5 mV, and the
tip-sample separation was 50 nm.

80

Figure 6.8: A) Electric field gradient (charge density) of an unstrained sample. B)
Electric field gradient of a strained sample. In both cases, the tip voltage was held at
2.0V. C) Surface potential of an unstrained sample. D) Surface potential of a strained

sample. In all cases the sample was unilluminated and the tip-sample separation was
50 nm.

81
will induce a piezoelectric polarization that adds to the spontaneous polarization,
it is believed that the induced polarization charge is sufficient to overwhelm the
available screening charge to reverse the sign of the surface charge. In subsequent
experiments on N-polar films (which were not believed to have inversion domains)
contrast reversal under strain was not observed. This supports the inversion domain
argument; however, a direct observation of the inversion domains with TEM would

be necessary for confirmation.

6.5 Summary

In summary, we have successfully demonstrated that EFM techniques can be used to
detect local variations in piezoelectrically induced charge and potential on the sub 1
micron scale. These charges are believed to be screening charge on the surface since
their spatial extent was comparable to the Debye length. We have also demonstrated
that the EFM signal could be minimized by applying a voltage roughly equal to the
contact potential between the tip metal and the GaN. An analysis of this contact
potential variation gave a surface state density of 9.4+0.5 x 10'°cm~? at an energy of
30 mV above the valence band. This technique also provides a method complementary

to Kelvin probe microscopy for determining work function differences as well as a new

way to determine surface state densities.

82

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Chapter 7 Directed Charge Storage in
Double Barrier CeO2/Si/CeO;/Si
Structures Using Electric Force

Microscopy

7.1 Introduction

In this chapter, an electric force microscope was used to induce and image localized
dots of charge in a double barrier CeQ2/Si/CeO2/Si(111) structure. By applying
large charging voltages and reducing the tip to sample separation to 3-5 nm, dots
50-200 nm in radius of both positive and negative charge have been written. These
charge dots are shown to be stable over periods of time greater than a day, with a
very slow spreading and decrease in total stored charge. It is shown that the dots
may be rewritten and replaced by charge of the opposite sign by application of the
opposite charging voltage. The dependence of dot size on various writing parameters

such as tip voltage, tip to sample separation, and write time is examined.

7.1.1 Cerium Oxide Background

Cerium oxide (CeO) is an insulating material with a lattice mismatch of only 0.35%
to silicon (Si) and has an energy bandgap of ~ 5.5 eV, an attractive set of properties
with the potential to lead to a fully functional silicon heterojunction technology. A
significant amount of work has been done examining the growth and characterization
of CeO» crystals on Si [1-5], and the growth of single crystal Si on to CeO2/Si

heterostuctures has been recently reported [6]. Based on these promising results,

a silicon resonant tunneling diode, an improved silicon-on-insulator (SOI) technology,

86
and stacked silicon electronics have all been proposed. A valuable and interesting
addition to this array of technologies would be the capacity for electrostatic data

storage.

Superparamagnetism

It will be useful to compare the current state of the art density (bit sizes) for magnetic
recording to any proposed data storage scheme. While there are important bench-
marks for recording technology such as signal to noise and data rates, limitations on
the bit size will determine the ultimate areal density. Magnetism has its own, thermo-
dynamically defined, size limit which cannot be subverted to achieve smaller bit sizes.
At very small particle sizes, thermal energy is sufficient to switch the magnetization.
For example, if an ensemble of particles is magnetized by the application of a field

which is then removed, the magnetization decays as [7]:

—t
M(t) = M(O)exp (=) (7.1)
The relaxation time 7 is given by

(7.2)

OM,H.v

kT

When the particle’s energy 0.5.7, Hv is 50 times the thermal energy, the relaxation
time is 100 s. Since the relaxation time is exponential, it changes very quickly with
particle volume, v. Practically, this occurs at particle sizes around 100 nm. The data
storage market may very well push beyond this limit in its development of magnetic
materials. Nevertheless, a realistic upper limit for bit densities in magentic media is

(optimistically) believed to be around 100 Gb/in? or bit sizes around 80 nm. 80 nm

will be the size benchmark for our charge dots.

87
7.1.2 Charge Deposition Experiment

Growth of CeO,/Si Structures

Samples were produced by J. T. Jones from commercially available 3” Si(111) wafers,
n-type with 3.0-4.3 Q-cm resisitivity. After being subjected to a standard acetone,
isopropyl alcohol, de-ionized water degrease in ultrasound, the wafers were etched
in 50:1 HF solution until hydrophobic, rinsed in de-ionized water, and immediately
introduced into vacuum. Prior to growth, samples were introduced to the chamber
from the load lock and the chamber background pressure was brought to less than
5 x 10°! Torr. Two manually shuttered electron beam evaporators were used to
deposit material from an undoped Si charge and a 99.99% CeO» charge to grow the
structures. A reflection high energy electron diffraction (RHEED) setup allowed for in
situ film surface characterization during growth. Initially, a Si buffer layer was grown
by depositing 0.3 A/s Si at 850°C for 60 seconds, and then depositing a 200 A Si film
at 550°C. Buffer layer RHEED patterns were examined to assure the characteristic
(7 x 7) reconstruction was apparent, indicative of a clean Si surface ready for further
growth.

Cerium oxide thin films were grown at a wafer temperature of 550°C, with cham-
ber pressures ranging from 1 x 1077-2 10~® Torr due primarily to outgassing from
cerium oxide pellets. Silicon thin films were also grown at a wafer temperature of
550°C, with chamber pressures of 5x 107-2107" Torr. A double barrier structure
CeO»/Si/CeO2/Si(111) was produced with symmetric CeO, barriers of 35 A. The in-
termediate silicon film thickness was 25 A for the sample and shown by RHEED to

be polycrystalline.

7.1.3 Electric Force Microscopy: Charge deposition and
Imaging

To place charge in the structures, the sample was placed in a conductive holder which

used the AFM ground as a reference as shown in Figure 7.1. Depositing charge in

88

Figure 7.1: Electric force microscope configuration for depositing charge in the layers.
The double barrier structures CeO2/Si/CeO2/Si(111) were produced with symmetric
CeO, barriers of 35 A. The intermediate silicon film thickness was 25 A for each
sample and shown by RHEED to be polycrystalline. Typical tip-sample separations
were 3-5 nm during deposition and 20-30 nm during imaging.

89

Positive Tip Bias

Negative Tip Bias

Figure 7.2: A square array of 150 nm FWHM dots of charge, 3 positive and 1 negative,
written with an EFM to a CeO2/Si/CeO2/Si structure. No topographical changes in
the oxide were detected by AFM after writing, but the dots are clearly visible in the
EFM image. Dots of both positive and negative charge can also be rewritten over
one another by application of the opposite writing voltage.

the structure was performed by reducing the tip - sample separation and applying a
relatively large tip voltage (10 V) for approximately 30s. By applying either positive
or negative bias, regions of either positive or negative charge could be written. Figure
7.2 shows an example of writing a square array of charged regions; 3 positive and 1
negative. Figure 7.3 shows an example of rewriting one of the positive regions with
a negative one. Some residual positive charge remains since the tip piezos did not
return exactly to the write coordinates. In detail, the writing process for depositing

charge in the structure was as follows.

1 Move to the desired position.

90

Figure 7.3: A. Atomic force microscopy of the CeQy layer indicating that it is un-
changed during the deposition of charge of either sign. B. Electric force microscopy of
charge dots of both signs. The dot in the upper right was originally positive and was
rewritten to be negative. Some residual positive charge remains since the tip piezos
did not return exactly to the write coordinates. One interesting feature of the image
is the close proximity of the two types of charge which remained distinct without
leakage.

2 Reduce the scan size to 1 nm or to 0 nm.

Ww

Set the tip-sample distance to 30 nm.
4 Set the “write” voltage by applying the appropriate tip voltage (Typically 10 V).

Reduce the tip-sample distance to approximately 5nm.

Or

6 Wait.

~]

Set the tip voltage to OV and the lift height to 30nm.
8 Repeat.

After the patterns were written, electrostatic force imaging data was taken in
the manner described in Chapter 6, Section 6.2. The tip voltage was held around
1V during imaging since in practice large tip voltages tend to introduce topographic
artifacts at tip biases around 3V. When the phase differences are very small, the

relationship between the phase shift and the frequency shift can be approximated by

a linear relationship. Which, when calibrated for the cantilevers in this experiment,

91
was found to be df ~ 3.5A@ Hz/deg . No changes in the topography were measureable
with the AFM after the charge regions were written.

To compute the total stored charge, Q, we first use an electrostatic analysis
given in Reference [8] to compute the localized charge stored in an insulator, q.
The frequency shift, df, is related to the gradient of the force by the expression
Af = —fof’(zo)/(2k), where z = 30 nm is the tip to sample separation during
imaging, fo = 59.8 kHz is the resonant frequency of the tip, and k = 3 N/m is the
estimated spring constant of the tip. The electrostatic force the tip feels under an
applied DC bias due to charge-charge interactions for charge buried in a dielectric

layer is given by

F(z) = 1 -x(- Too 4 2dce0,dVErM _ coaVeem)
(z + (2dceo,/€ceo,) + (dsi/€si)) CeO E04 CeO, 2
(7.3

where z is the tip to sample separation, d and € are the thickness and dielectric
constant of the CeO, and Si films, as indexed, Vgpay is the bias applied to the tip,
and a is the area of the charged region. The first term in the bracket in Eq. 7.3
is found to be negligibly small, and the last term provides a constant background
independent of the charge. Using only the middle term and the values given above,
an approximation to the localized stored charge is then given by g = 43A0 e/deg. If
this expression is used directly as in the case of Reference [8], we obtain q = 2 to 10e.
Since this was such a low value for the amount of stored charge, we modified the above
model based on the following observation. Simple force modeling predicts the EFM
image of a single localized charge to be 56 nm FWHM, with an area a = 2450 nm’.
This is less than the 150 nm FWHM that is typically observed. Therefore, we estimate
the total stored charge in our EFM images by scaling the expression for g above by
the ratio A/a where A is the experimentally observed area of the charge. Hence, we
estimate the total charge contained in the region as Q = q(A/a) e. For the dots in
Figure 7.2, A§ = 0.23° over an area of A = 1 x 10° nm?, we compute Q = +42 e.

It is not unreasonable to speculate that the amount of charge could in fact be a

single electron which is the case for the smallest dots with a FWHM of 50 nm. For a

92
single charge, the self potential, V = 3kT for room temperature, at reasonable read
distances so thermal noise would not swamp the cantilever. The image charge force of
a single electron on a grounded tip is F= 0.06 pN which is within the AFM’s detection
limit. Therefore, it would be an interesting experiment to look for quantization effects
after depositing a small amount of charge.

To examine the effects of writing parameters on the resultant charge dot size and
intensity, an array of positive charge dots was written at various EFM tip biases, tip
to sample distances, and write times as shown in Figure 7.4. Line scans were taken
across the low-pass filtered image to extract charge dot sizes and relative intensities.
It is found in general that both the size and the intensity of the charge dots scale
linearly with the same slope in relation to the various writing parameters. From a
nominal starting point of 10 V, 60s, and 5 nm, it is found that the size and intensity
of the charge dot may be expected to decrease 10% for each 0.5 V decrease in charging
voltage or 10 s decrease in charging time, and increase 10% for a 2 nm decrease in
tip to sample separation.

To examine the time evolution of stored charge in our system, single charge dots
were written and monitored over time. In all cases, the general trend was for a slow
leakage of charge accompanied by an increase in FWHM of the charge dot, as shown
in Figure 7.5 (A,B). To estimate the lifetime associated with the stored charge, a
single charge dot was written and continuously monitored over several days. After
writing at Very = 10 V, z = 3 nm, and t = 60 s, the resulting charge dot was
continuously imaged at Very = 1 V and z = 30 nm at a read speed of 21 reads/hr
for the first 4 hrs, after which imaging was performed intermittently for the remainder
of the experiment. A plot of the total stored charge, Q, is shown in Figure 7.6. There
is an initial period of charge settling and reorganization during which it is difficult to
reliably extract charge dot profiles in order to determine the stored charge. After this
settling period and over the first 10 hrs, an exponential fit to the charge decay exhibits
a time constant 7 ~ 9.5 hrs, after which the rate of decay slows down considerably to

T > 24 hrs. After a period of t > 40 hrs, the stored charge either leaked away or was

no longer detectable by our instrument. This is a substantially longer time constant

93

Figure 7.4: Electric force microscopy of an array of dots written at different voltages,
tip to sample separations, and writing times as labeled. Dot intensity and size are
strongly dependent on voltage and writing time, and more weakly dependent on tip
to sample seperation.

94

than the 300 s obtained by Yu et al. for charge storage in cobalt nanostructures.

7.2. Conclusions

In conclusion, a novel application of EFM was used to write and image localized dots
of charge in a double barrier CeO2/Si/CeO2/Si(111) structure. By applying relatively
large tip voltages of Very = +(6 — 10) V and reducing the tip to sample separation
to z= 3-—5 nm, charge dots 50-200 nm FWHM of both positive and negative charge
have been written. The total stored charge is found to be @ = +(1—90) e per charge
dot. These charge dots are shown to be stable over periods of time greater than a day,
with an initial charge decay time constant of r ~ 9.5 hrs followed by a period of much
slower decay with + > 24 hrs. The dependence of charge dot size and total stored

charge on various writing parameters such as tip bias, tip to sample separation, and

write time has been examined and linear dependencies extracted.

95

Figure 7.5: Electric force microscopy of deposited charge shortly after deposition (A)
and again (B) after 20 hours. Line scan profiles of the charged regions indicate both
spreading and leakage.

96

100

rare)

CD

7)

uy

te

“Ma | 1 |

O00 300 600 900 12:00 18:00 18:00
Elapsed Time (hr)

Figure 7.6: Decay curve for the deposited charge. After a settling period and over the
first 10 hrs, an exponential fit to the charge decay exhibits a time constant 7 ~ 9.5 hrs,
after which the rate of decay slows down considerably to 7 > 24 hrs. After a period
of t > 40 hrs, the stored charge was no longer detectable by our instrument.

97

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99

Appendices

100

Appendix A Surface Potential
Microscopy

A.1 Derivation of the Force on the Tip from the
Maxwell Stress Tensor

Originally, surface potential microscopy was called scanning Maxwell stress mi-
croscopy since the force on the tip is obtained by integrating the Maxwell stress

tensor 7;; over the tip surface

ti

Where the stress tensor in the absence of a magnetic field is: 5

1.

Since the electric field is always perpendicular to a perfect conductor, the normal

component of the stress tensor at a point on the surface of the tip, r;, reduces to

Toe = 5¢(8e)E(e) Ela) = spi (re) (A.3)

where p;(rz) is the surface charge density on the tip. If there are isolated charge

densities,o(r), polarization fields, P(r), and sample regions at potentials V;, then

p(t) = / [ol(r')] g(te,r’)de’ + So Gi(re)Vj + (te)Vi (A.4)
[=1

where g(rt,r’) is the image charge density induced on the tip surface at ry, by a unit

point charge at r’. The terms c;(r,) and c;(rs) are the differential capacitance between

the I" potential and the self capacitance of the tip.

101
If an oscillating voltage plus a DC bias is applied directly to the AFM tip, Vapptied =
Vac + Vo cos(wt), the tip will feel a force with a DC component plus components at w

and 2w due to the quadratic nature of the stress tensor.

1 N
T= - (/ [e(r’) — VP(r’)] g(t, ede’ + > ci(rs)Vi + ctaVae (rs) Vo cos(wt)
- (A.5)
1 22 - 2
To, = 5,10 c; (rs) sin” (wt) (A.6)

Since Eq. A.6 represents purely capacative forces, only the w component will be

considered here. Therefore, the force felt by the tip at frequency w will become

— T.,cos6dS tip (A.7)

tip

Finally, the voltage Vz, is regulated by an external feedback loop so that the force Fi,

vanishes at

J lett") — VP(r')] fin g(t, P’) cos Od Syipdr’ + 4 Vi $rip Ci(Ps )Cr(Ps) COS OAS pip
yy $rip Ci(Ps)Cr(Fs) COS OAS pip

Vac =
If there are no charge densities and polarizations present, and only one other po-
tential besides the tip, the measurement gives the potential directly. In most of the

studies here, however, there are induced charges at the surface due to spontaneous

polarization and piezoelectricity so the force will be an average of all these effects.

102

Appendix B_ Microellipsometer

B.1 Motivation

Ellipsometry is the standard way to quantitatively determine the optical properties
and thicknesses of thin films. Despite being very accurate, the best ellipsometers
are currently limited to approximately 50 wm spatial resolution. In an attempt to
increase the spatial resolution, we explored a novel scanning probe technique we called
the microellipsometer. The concept was to replace the free space optical path in a
standard ellipsometer with polarization preserving fibers that could be brought close
together and used as a polarizer/analyzer combination. The whole assembly could
then be scanned over the sample. The spatial resolution would then be determined

by the proximity of the two fibers which could approach 1 ym.

B.2 Types of Ellipsometers
There are three primary ellipsometer designs:

Null ellipsometer The null ellipsometer has the following elements:

Source —> Polarizer —+ Compensator —> Sample —> Analyzer —> Detector

The objective of a measurement is to adjust the polarizer, compensator and

analyzer to achieve a signal minimum at the detector. Complicated.

Polarization modulation

Source —+ Polarizer —> Modulator —> Sample —> Analyzer —> Detector

103
Modulations of the input polarization are usually many kHz allowing for fast

measurements but calibration is difficult.

Rotating element It is possible to construct an ellipsometer using only two
polarizers for the polarizer and analyzer components. This method has the

advantage of being simple to construct and align as well as being achromatic.

Source —+ Polarizer —+ Sample —> Analyzer —> Detector

It is this configuration that is used to implement the fiber microellipsometer.
In the actual experiment, however, the analyzer element was rotated manually

rather than continuously spinning.

B.3 Construction of instrument

B.3.1 fiber etching

Elliptical core, single-mode, polarization preserving fiber (Corning PMF-38) was
etched to remove the cladding in order to bring the cleaved ends in close proxim-
ity. The fiber orientation was marked and the fiber was stripped and cleaved. The
cleaved ends were then immersed in a solution of 25 mL 49% hydrofluoric acid and
25 mL 10% buffered HF solution (BOE etchant) and etched for 30 minutes. Since
the radial etch rate is slow at the beginning of the etch and more rapid at the end, it

was essential to carefully monitor the fiber ends.

Detection head assembly

The etched fibers were then mounted to a home built micromanipulator in order to
position them in the holder. The holder was fabricated in lab and consisted of a # 8,
stainless steel, machine washer with a hole drilled end-wise using a # 70 wire drill bit.

The fibers were then threaded through the holes on either end and aligned. For the

alignment, the separation of the cleaved ends and their angle was fixed by observation

104
through microscopes positioned at right angles (plan and profile) to the head assembly.
The entire configuration was then epoxied into place to fix the alignment. A magnet
holds the steel washer to an actuator which controlls its distance to the sample. The

final assembly and a closeup of the fiber ends is shown in Figure B.1.

B.3.2 Control Experiment and Preliminary Results

In order to test the ellipsometer head, a calibration experiment was performed as
shown in Figure B.2. Light from a near IR laser source is chopped for lock in detection
and then polarized with a sheet polarizer. The source was a Melles Griot laser diode
model 56DLB108 of wavelength A = 830nm which was biased at 85.1 mA with a
Keithley 238 high current source measure unit to give an optical power output of
25.5 mW. It then passes through a polarization rotator to set the polarization along
one of the eigen-axes of the fiber. After passing though the fiber, it is incident on
coverslip coated with gold in an evaporater intended as a reference sample. The
reflected light is then collected by the second fiber and is incident on the analyzer
and finally on a photodiode in a transimpedence amplifer configuration. Lock-in
detection was performed with an EG&G 5101 single channel lock in amplifier at the
chopping frequency. The distance to the sample was monitored under a microscope
and controlled by a Newport 855C programmable controller with a Newport actuator
850. Results of the experiment are shown in Figure B.3 and indicate that there
was some polarization sensitivity. Unfortunately locating the fast and slow axes to
launch the polarized mode was not possible by hand. Moreover, the alignment of
the two fibers in the probe assembly was unknown. Therefore, the results are most
likely a mapping of the fiber misalignment rather than measuring the sample. Future

instruments would need a way to better determine the alignment of the fiber axes as

well as rotating polarizers to make fast measurements.

Figure B.1: Close up of the fiber probe.

106

Polarizer Polarization
rotator Fiber
Coupler

aT : _.

MicroEllipsometer

head
Polarizer

Fiber Photodiode

Coupler

Figure B.2: Schematic of the microellipsometer experiment.

107

—O-— Polarizer Angle = 0 deg

0.40 5 —w Polarizer Angle = 60 deg
— 0.38 4 O
_ 7 a ‘
‘ J / \ —
s 0.36 - O_o —~o- 0 OW
a 0.34 4 NN v / \ a
or 0324 9 \ / Ww
— 7] / _
YM o2- \ / “v
c 1 vo
= 0.28 +
m4 4
O 0.26 +
.@) ;
— 0.24 4
0.22
0.20 :
0 20 40 60 80 100

Analyzer Angle (Degrees)

Figure B.3: Preliminary results from the microellipsometer. The lock-in amplifier
signal from the analyzer photodiode is plotted as a function of the analyzer angle
for two input polarizations. The angle of the fiber from the normal to the sample is
roughly 70 degrees.