I. The Mode Locked Dye Laser. II. Picosecond Photoconductivity of Semi-Insulating Gallium Arsenide - CaltechTHESIS

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LJ

Q | +

0.5 : 1

500 550 600 650 700
(nm)

Figure 2.2 Absorption spectrum of a typical mixture of DODCI and

malachite areen, used to mode lock the dye laser.

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-19-

mixture of DODCI and malachite green in ethylene glycol. The third
waist is occupied by an acousto-optic Bragg cell for single pulse ex-

‘traction from the cavity.

The argon laser pumping beam is focused to a 50 micron spot
on the Rhodamine 6G dye jet. The cavity waist at that point is 42
microns in diameter, which results in efficient energy conversion.
The absorber spot size is 27 microns in diameter in order to be
more easily saturated by the picosecond pulse than the gain medi-
um. The dumper spot size is 30 microns in order to establish fast

acousto-optic pulse extraction.

The mirrors are coated for broad-band high reflectivity for the
range 5500angstroms to 6500angstroms, and the pump focusing mirror is
coated for 5145 angstromsas well. The cavity mirrors’ placements and
radii of curvature are chosen to optimize the stability of the cavity
[16]. The mirrors are held in high-resolution angular orientation
mounts, and one of the mounts at each cavity waist is placed ona

translation stage for fine adjustments of the cavity length.

Each dye circulation system consists of a pump which draws
dye from a reservoir and forces it through a 0.8um filter. The dye is
passed through a vibration damper and up to a stainless steel noz-
zle. The dye is forced through the nozzle, which has rectangular

aperture dimensions of 1.58 x 0.39 mm. The resulting jet is flat and

-20-

optically clear, and relatively vibration frec. The nozzle is held ina
x-y-z translation stage as well as in an angular rotation mount
which orients the plane of the jet at the Brewster angle with

respect to the dye laser beam [17]

A prism is placed in the cavity to ensure that the laser oscil-

lates at a wavelength within the effective mode locking range of the

saturable absorbers. This range is 5900 to 6150 angstroms. The prism
is cut at a full Littrow angle of 69° so that the dye laser is in-

cident upon the prism at the Brewster angle at both faces.

If the output of the laser were obtained with a partially
transmitting mirror, optimum output coupling considerations
would dictate that the transmission be quite low, approximately
two or three percent. In our system, the output coupling is per-
formed with an acousto-optic cavity dumper with a maximum
diffraction efficiency of 47%. As a result, we obtain at least ten
times the output power that is obtained with conventional mirror

coupling techniques.

The cavity dumper, or Bragg cell, consists of a block of fused
Silica oriented at the Brewster angle. An acoustic transducer is
bonded to the bottom face of the block; when the transducer is en-
ergized by an rf electrical pulse, the resulting periodic strain wave

acts as a transient grating. The cell is oriented at the Bragg angle

-21-

as well, and the laser beam is deflected out of the cavity for as long

as the grating remains in the path of the beam [5b].

The cavity dumper used in the laser is a commercial argon
laser acousto-optic dumper obtained from Spectra-Physics (Model
365). It is energized with an rf wave at 470 Mhz. This rf power
comes from the Spectra-Physics driver, which is capable of emit-
ting twelve watts of rf power with a rise time of five nanoseconds.
The risetime of the laser output envelope is a convolution of the
acoustic wave risetime and the transit time of the acoustic wave
across the laser beam. The Bragg cell is placed at the third waist
in the cavity, which has a beam diameter of 30um. Since the veloci-
ty of sound in the fused silica cell is 5.95210° cm/sec, the transit
time of the wave is five nanoseconds. Thus, the overall risetime is
sufficient to bring the acoustic wave to full power in the path of the
laser beam within one cavity round trip time. Hence, a single pulse
may be extracted from the cavity with minimal dumping of the

preceding and succeeding pulses.

The dumper has a diffraction efficiency 7 given by

nL~/MI,
ave

7=sin 2.2

where L is the interaction length, M is the acousto-optic figure of

merit, and J, is the acoustic intensity. Using the peak acoustic

~22-

power available from the transducer, 16MW /cm*, and a figure of
merit.of 1.512107'§ [18], the maximum 7 becomes 98%; in practice,
only a 47% diffraction efficiency is obtained into a single diffraction
order. The Bragg cell actually dumps two output beams from the
cavity (see Figure 2.4), One of the beams passes once through the
cell; it is Doppler up-shifted according to the configuration shown.
Its power is 7P, where P is the intracavity power. The other beam is
Doppler down-shifted, and passes through the cell twice. This beam
consists of that cavity energy that is undiffracted upon the first
pass and diffracted upon the second pass. Its power is n(1-7n)P,

which is always less than the power of the first beam.

The action of the dumper perturbs the mode locked laser away
from its steady state condition of optimum pulse width and power.
In order to extract the highest quality picosecond pulses from the
laser, the gain medium must be given time to amplify the intracav-
ity energy back to its original level. The saturation effects must be
given an opportunity to restore the short pulse width of the pulses
as well. According to Yasa [19], the minimum time required for
complete restoration of the attributes of the pulses is 200 round
trips. We allow our system 2048 round trips of recovery in case the
stability of the laser falls short of the theoretical model used by

Yasa.

It is necessary to synchronize the cavity dumper with the single

-23-

R=lOcm

Figure 2.4 The dumper arm. P is the primary beam extracted from

‘the cavity, S is the secondary one (see text).

-24-

pulse traveling within the laser(See Figure 2.5). This is done by
directing some of the spurious reflections from the prism to a fast
(200 picosecond risetime) photodetector[20]. The amplified output
of this photodetector acts as a clock for the rest of the electronics
in the system. The electrical pulse train is fed into a tuned
amplifier resonant with the cavity round trip frequency, and count-
ed down by 2048 [26]. This produces a pulse every 22usec.. This
pulse activates the rf driver for the cavity dumper, which produces
a burst of 470 Mhz power to the acoustic transducer. The acoustic
wave is now synchronized with the picosecond pulse in the cavity.
The simplest way to adjust the relative delay between the light
pulse and the acoustic wave is to move the transducer toward or
away from the beam while monitoring the dumped output light
pulse. The delay is increased when the sound wave has farther to
travel, and as long as the total distance from the transducer to the
laser beam is kept small, the acoustic wave maintains a clean wave-
front. Proper adjustment gives the result shown in Figure 2.6. This
oscilloscope trace is the output of the fast (200 psec) photodiode

and is distinctly detector limited in its temporal response.
2.6 The Operation and Control of the Dye Laser

The mode locked dye laser is composed of an unusually com-
plex cavity. The cavity consists of seven mirrors and four optical

elements, all of which must be within microns of their optimum po-

-25-

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-26-

100 4
mV

é 4

<4—10 nsec —»>

Figure 2.6 A detector limited display of a
dumped picosecond pulse. Note remnants of the
previous and following pulses at +10 nsec from
the main pulse.

-2f-

sition for successful production of picosecond pulses. Each of the
seven mirrors has two angular and two positional degrees of free-
dom. The two dye jets must be precisely centered on the appropri-
ate cavity waist and oriented at the Brewster angle. The acousto-
optic dumper must be oriented at the Brewster angle and the
Bragg angle, and have its transducer placed precisely at the cavity
waist of the dumper arm. Thus, it is necessary to establish a
dependable means of converging on the small "volume” in a 37-
dimensional space of cavity element co-ordinates that could pro-
duce a stable train of short pulses. Further, once the laser oscil-
lates, it is important to be able to interpret the behavior of the

laser to remedy departures from perfect alignment.

The first steps toward alignment of the laser involve a four
mirror cavity which includes the tuning prism. Here, the DODCI
and dumper cavity arms are replaced with flat mirrors at the loca-
tion of beam waists of the seven mirror cavity. The four mirrors
are placed in the approximate positions specified by a complete
cavity stability analysis [16]. The concave mirrors placed about
the Rhodamine 6G jet collimate the fluorescence, and direct it to-
ward the flat mirrors. Lasing is directly forthcoming, and through
cavity adjustment, the threshold is lowered to a few hundred mil-
liwatts of argon power. The remaining two arms and the Bragg cell

are introduced into the cavity; with each addition to the cavity,

-2B-

there is an increase in threshold and a4 decrease in the tolerance of
the cavity to misalignment. When the seven mirror cavity is com-
plete, the threshold is 700 mW of argon power and the angular mir-
ror tolerance-is tens of microradians. Since the saturable absorber
is only effective within a range of 8000 angstromsto 6150angstroms, the

laser is tuned with the prism to oscillate in that spectral region.

The saturable absorber jet is first introduced into the cavity
with no dyes in solution. As the dyes are introduced, the laser in-
tensity begins to oscillate at the round trip frequency. As the dye
concentrations are increased to their optimum level, the lasing
pump threshold reaches roughly five watts, and the intensity
modulation sharpens to form pulses. The optimum dye concentra-
tions are determined empirically, and correspond to the absorp-
tien curve shown in Figure 2.2. The pulses become detector limit-
ed; a typical display is shown in Figure 2.7. We use two means of
obtaining more precise knowledge of the laser operation. The most
direct method is second harmonic generation pulse measurement,
but a more convenient technique that has proven to be a very reli-
able indicator of the pulse quality is the real-time spectral mea-

surement using the optical multichannel analyzer.

When the the power of the argon pump laser is raised just
beyond the threshold of the dye laser, the dye laser spectrum

shows a broad, stable profile (see Figure 2.8). This is indicative of

Figure 2,7 Detector-limited pulses generated by the passively mode

locked CW dye laser.

(=30-

OMA
DISPLAY
SHAPE ?
SINGLE - ~ SINGLE LONG PULSE A PAIR OF
ULTRASHORT SHORT
PULSE _» PULSES

INCREASING PUMPING POWER

Figure 2.8 Some typical laser pulse shapes and the related spectra at

various pump levels.

-31-

short output pulses. If the argon power is raised further, or if the
concentration of the saturable absorber is too low, the spectrum
narrows, and shows a spike in a spectral region where the saturable
absorber is being excessively bleached. When this happens, the ab-
sorber is incapable of adequately attenuating the leading edge of
the pulses, the inversion in the amplifier is incompletely depleted,
and the pulses broaden to a few hundred picoseconds. If the pump-
ing power is raised still further, the laser begins double pulsing.
Here, the gain is sufficient to support two fairly short pulses, each
capable of saturating the absorber. The spectrum broadens some-
what as well. With continued increase of the pumping power, the
pulses disappear entirely, and are replaced with the modulation
observed with small absorber concentrations. At this and higher
power levels, the spectrum narrows to no more than a few
angstroms. Finally, all modulation disappears if the dye laser is
given sufficient gain to saturate the absorber on a CW basis. While
there is some tradeoff between pumping power and absorber con-
centration, the shortest pulses are only obtained with the proper

saturable absorber concentration designated in Figure 2.2.
2.7 Summary of the Operation Characteristics

The operating parameters of the passively mode locked dye
laser can be summarized as follows: The argon laser is stabilized

for constant light output, and emits five watts of continuous power

-3e-

at 5145 angstroms. The dye laser generates pulses of 1-2 pi-
cosecond duration, with peak powers of about 1 kW. This
‘corresponds to about 1 nanojoule of energy per pulse, or 10° pho-
tons per pulse. A pulse is dumped from the laser every 2048 round

trips of the cavity, or every 22 microseconds.

-ga-

Chapter 3

Picosecond Pulse Width Measurements

3.0 Introduction

Figure 2.6 in the previous chapter showed the output of the
mode locked dye laser using a fast photodetector. This detector
was far too slow to resolve the pulse shape. While significantly fas-
ter photodetectors have been developed and are commercially
available, the fastest real time electronic means of measuring the
picosecond pulses is no faster than ten to twenty-five picoseconds.
The fastest measurement techniques involve sampling oscilloscopes
or streak cameras for the final signal display, and to this date, no
such devices have shown sufficiently fast response to resolve a sub-

picosecond pulse.

The fastest direct pulse measurement system is the streak
camera. Recent improvements in the response time of these de-
vices has resulted in a temporal response of a few picoseconds{21].
The drawback of streak cameras is their high cost and their single-
shot nature. If multiple shot averaging is desired, a signal averag-

ing system, such as an optical multichannel analyzer, is necessary.

Less costly methods of pulse measurement include two-photon

fluorescence (TPF) and second harmonic generation (SHG) [22,23].

-34-

TPF requires.a fluorescent dye to absorb light in a two photon pro-
cess from two counterpropagating beams. Where the pulses coin-
cide in space, there will be maximum TPF, and the profile of the
pulse’s autocorrelation is obtained. A similar principle is invoked
‘in SHG, where the only resulting information regarding the tem-
poral shape of the pulse is the autocorrelation integral. As will be
seen, this gives the actual pulse width to an accuracy of within a
factor of two. In our situation, the TPF technique would suffer due
to low signal strength; the SHG method provides easily detectable
signals, and is generally regarded as a superior means of dye laser

pulse measurement.

3.1 The Second Harmonic Generation Technique

of Pulse Width Measurement

SHG picosecond pulse width measurements involve splitting the
pulses in two with a beamsplitter (See Figure 3.1). Each beam is
sent down a separate arm of a Michelson interferometer, where
each pulse experiences a delay r proportional to the length of the
particular arm. The two pulses
are focused on, and coincide in a crystal of KDP (potassium dihy-
drogen phosphate), a second harmonic generating medium. Since
SHG is a nonlinear phenomenon, there is disproportionately more
average second harmonic energy produced when the pulses arrive

at the crystal simultaneously than when they arrive separately.

-35-

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-36-

At= 2ps(fwhm)

I i i 8

L] ' t | I |

-2 =1 0 1 2
DELAY (mm)

Figure 3.2 A typical trace of a noncollinear
second harmonic generation pulse width
measurement.

-37-

Thus, by measuring the average SHG as a function of optical delay,
one can deduce the spatial (i.e., temporal) extent of the pi-
cosecond pulse. The spatial extent of a 1 picosecond pulse in space

is 0.3 mm.

If an optical wave is incident upon a crystal with a nonlinear
susceptibility, there will be a polarization induced with a com-
ponent oscillating at double the frequency of the incoming wave.
This polarization drives a second harmonic optical field, and if
proper phase matching is established, the superposition of all
these driven fields is a coherent frequency-doubled beam[5c].

Specifically, a wave polarized in the g direction
E(t)=¥L[E Fet+c.c. 3.1

generates a polarization oscillating at 2w in the a direction

ad
us af tut 2
P? 4 [E get“t+c.c. } 3.2

where dagg is the nonlinear susceptibility.

In the case of picosecond pulse width measurements, the elec-
tric field amplitude £f is the pulse envelope, and thus varies with

time.

Eputse (t )=¥LE F(t )+c.c. ] 3.3

-38-

Tf two pulses are delayed in time by a relative amount 7, and
superimposed at the SHG crystal, the resulting nonlinear polariza-
tion is

3.4

oat at Je t(otek), p ae +r)e to(t+r)ek yr) e. t

P dt )=d abe foe

The component of this polarization oscillating at 2x is

d .
pee (t )=— SSE [Ete t (ut +E#)4 7 2e B(alt+ T)+E-P)

3.5
+ 2B EF eM (ut +r) eters oo, ]

where £ is &y (t) and £, is & (¢+7).

This polarization drives a SHG electric field. The derivation of
this field from the inhomogeneous wave equation yields the expres-

sion [5]

2 ethkl=t
Esuc & Capek rea ihe 3.6

where Ak=kz,-2k, represents a mismatch in the phase velocities of
the fundamental and SHG waves, L is the interaction length of the

process, and Eiw, is the superposition field of the two pulses.

The SHG power is proportional to the squared amplitude of the

SHG electric field

Powersue @ EsucE suc 3.7

-39-

-For the moment, let us assurme perfect phase matching: sAk=o.
Combining Equations 3.6 and 3.7, and keeping only the slowly vary-

ing terms (compared to optical frequencies), we obtain

Powersye af?+ie +4 = +(E®B 2 e742 (747, )ER- e-*T40.¢.)

3.8
where the intensity /=F£f£°, and /,#£,£}.

The process of SHG pulse width measurement consists of
sweeping r roughly linearly through an interval centered at r=0. A
photomultiplier detects the SHG, and its output is integrated with
a low-pass filter to obtain an electric current representing the
average contribution of many pulses. The rate f at which r=ft is
swept is such that wf exceeds the cutoff frequency of the filter.
Hence, the terms in Equation 3.8 which oscillate at wr and 2ur aver-
age to zero, leaving only the first three terms. The cutoff frequen-
cy of the filter is also well below the repetition rate of the pi-
cosecond pulses, so the SHG current may be accurately represent-
ed by the integral of the slowly varying terms in Equation 3.8 over

some interval containing many picosecond pulses.
ilr)= [Ut )4/%(t47)44 (1 (2 +7)at 3.9

Integrating and normalizing so that limi(r)=1, Equation 3.9 becomes

i(r)=1+26@X(r) . 3.10

-40-

where G is the autocorrelation integral, given by

[Te Wle+r)ae

z=
ont) f 1?(t) dt

3.11

The range of G is 0 for r+ and 1 for r=0, so the ratio of the peak

value of i(t) to the minimum baseline is 3:1.

Thus, the SHG data will give information about the pulse, but
only through the autocorrelation integral of the pulse. In practice,
the shape of the pulse is assumed, and the analytic autocorrelation
integral is compared to the experimental SHG curve. In chapter
two, it was stated that the theoretical prediction of I(t) was a
squared hyperbolic secant. If the autocorrelation integral is per-
formed on the theoretical function, the ratio between the FWHMs of
the integral and the function is 1.55. In the same manner, the ra-
tio of the width of the experimental SHG curve and the actual pulse
width would be 1.55. Regardless.of the choice of the function used
to describe the pulse width, the ratio of FWHMs is on the order of
unity, and for rough measurements, the difference between the two

widths is ignored.

One of the arms of our Michelson interferometer is movable by
means of a precision stepping motor and translation stage, and the
other arm has a rapidly oscillating (60 Hz) optical delay apparatus.

These features of the interferometer allow either a slow and accu-

-41-

‘rate variable delay to be introduced between the two pulses, or a
fast, approximate delay suitable for real time observation of the
pulse width. The rapid delay apparatus has an analog output signal
roughly proportional to the delay. This signal is used to drive the
horizontal axis of an oscilloscope, and the SHG signal drives the
vertical axis. The display is a real time pulse measurement, which
is a valuable monitor of the pulsewidth for use in cavity alignment
and pumping power optimization. The slow and accurate SHG
measurement data are loaded into a Nicolet 1174 signal averager
and are averaged over many traversals of the translation stage.
This lowers the noise in the signal, and provides a numerical record
of the autocorrelation data on magnetic tape for later analytical

studies.

Figure 3.3 shows the general characteristics of SHG traces,
and how the technique indicates the quality of mode locking that
prevails in a laser. When the laser is unlocked, and the modes os-
cillate with random relative phases, the SHG shows a coherence
spike at r=0. If the laser is completely locked, then the modes are
coherently related to each other, and the coherence length in-
creases to the extent of the pulse width. At intermediate stages of
mode locking, the SHG is a superposition of the two extreme cases

[24].

A significant reduction in the noise of the SHG analysis is pos-

hee

FREE RUNNING NOISE BURST SINGLE PULSE

_ B
= 3

3 oO

sé 35

fos a?

S | ~
_ et
bw N

rN) a
e) fe) 0 +

Figure 3.3 Autocorrelation traces for pulses with varying
degrees of coherence. The left ordinate is for
noncollinear SHG, and the right ordinate is for

collinear SHG.

-43-

sible if the input beams are non-collinear. This results in the com-
plete absence of phase matching when only one pulse is present in
the nonlinear crystal. So, instead of a peak of three units on a
baseline of one unit of SHG power, the non-collinear SHG peak is
obtained on a zero baseline. Moreover, the fundamental beams are
physically separated from the SHG beam at the detector, allowing
spatial filtering to reject the noise. One drawback of the non-
collinear approach is that the interferometer must be set for
near-zero delay when aligning the KDP crystal, since one beam
alone does not generate the SHG. Without SHG, it is difficult to
know where the zero delay point is; consequently, a simutaneous
search of delay and KDP orientation must be made to find the SHG.
With the collinear method, the SHG baseline can be found first,then

the delay is varied to find the maximum.

The limitations of the SHG pulse measurement technique in-
clude the fact that the autocorrelation integral of a pulse need in
no way resemble the actual pulse. For example, the autocorrela-
tion of a pulse is always symmetric about r=0, regardless of any
asymmetry of the pulse. Further, the averaged SHG data is biased
toward the detection of short pulses [25]. Due to the nonlinear na-
ture of SHG, the broader pulses that may exist in a pulse train
make less of a contribution to the average SHG power than the

sharper pulses. For example, the dye laser frequently develops

-44.

spontaneous pulse height modulation at a 200 kHz frequency. In all
likelihood, the pulse width is being modulated as well. With some
effort in adjusting the cavity, this modulation can be suppressed.
Such steps must be taken to establish a stably oscillating cavity in
order to rely on the pulse width determined by SHG. Another
difficulty with the autocorrelation measurement is the requirement
of a clean, nearly Gaussian transverse mode in the output of the
laser. Slight transverse misalignments of two fundamental modes
will not greatly decrease the intensity product required for SHG.
However, if high order modes suffer transverse displacement dur-
ing the delay sweep, the intensity product could vary considerably,

and completely destroy the accuracy of the SHG measurement.

This nonlinear method of correlating a fast pulse with another
signal (including itself) through variable delay is a powerful tech-
nique suitable for application in a broad range of experiments. If
the beam of picosecond pulses were split into a strong pump beam
and a weak probe beam, the probe could be used to determine the
lifetime of effects that the pump beam had on a sample. If the
pump were sufficiently intense to bleach a fast saturable absorber,
for example, the detection of the transmission of an obliquely in-
troduced probe would demonstrate the persistence of the bleach-
ing. If the probe pulse arrived at the absorber before the pump, it

would be absorbed; if it arrived after the pump, the probe would

-45-

pass through the bleached absorber. By varying the delay between
the two pulses, the bleaching lifetime could be measured with pi-
cosecond resolution. The same principles apply to reflection or
polarization rotation studies in semiconductors and other materi-

als.
3.2 The Experimental Set-up for Pulse Width Measurement

Qur second harmonic generation system is shown in Figure
3.1. It is based upon the system first developed at Bell Labora-
tories by Ippen and Shank(3]. it consists of the interferometric de-
lay system, a KDP crystal, and a detection and signal processing

system.

The interferometer consists of the two delay arms mentioned
earlier. The accurate arm has a resolution of 21 femtoseconds in
optical delay, and a total range of 500 picoseconds. The oscillating
arm has a resolution of about 0.5 picoseconds (limited by the speed

of the detection system), and a range of 100 picoseconds.

In order to produce significant quantities of second harmonic
output, it is necessary to match the phases of the fundamental
beams and the second harmonic beam[5c]. This ensures a
coherent superposition of all the second harmonic wavelets creat-
ed throughout the crystal. This is possible in the KDP crystal, since

it possesses birefringence. The input and output beams are of a

AB.

different polarization, so the refractive index of an ordinary ray at
6100 angstroms can be matched to an extraordinary ray at
3050 angstroms. If the input and output wavevectors are not matched,
the second harmonic output over an interaction length L is re-
duced by a factor

sin®(AkL ) 3.12
(AkL )?

where Ak=ky,-ki.-ko,, i.e., the difference between the SHG
wavevectors and the two fundamental wavevectors. If Ak can be

made equal to zero, the maximum SHG can be obtained.

dé can be made equal to zero by specifying the orientation of
the crystal relative to the input beams. The input beams are non-
collinear; so the phase matching requirement is satisfied in the
direction of the angle bisector of the two beams. If the input
beams are separated by an angle 2g, then the phase matching con-

dition becomes k»2,,=2k,,cosé or

n&+(3)=nfcose 3.13

where ¥ is the angle that the bisector makes with the optic axis of
the crystal. ne” (3) is the extraordinary refractive index at 2a at an
angle ¥ to the optic axis, and n,“ is the ordinary refractive index at
frequency w. The angle # is determined from an expression of the

refractive index ellipsoid [5c]:

-47-

A) =-20 255-2
ein’v= (n/cosB)-*-(n,*)

14
nya) °

In this case, A=6100 angstroms, 77%=1.496752, n?*=1.543934,
andn= 1.508818. The crystal was obtained from Cleveland Crystals,
and was cut at v=60° 28’ , so the half angle of the input separa-

tion is f=2°5/

The phase mismatch has been set to zero through appropriate
orientation of the crystal. However, the phase matching has only
been established at the center wavelength of the pulse. In order to
reduce the overall phase mismatch arising from the nonzero
bandwidth of the pulse, the interaction length L must be short
enough to make the product AkL small. The spread of
Ak=k, o,-2k,,,cosB at 6100 angstroms over a spectral range of 12

angstroms (a 1 psec pulse) is
en
bAk = (n 2(u+du)(8) ~The, w+de) 3.15

Let ¢=n, 2,(8)-2n,.. For rough calculations, we assume @¢/ad is a con-

stant. Thus,

= f6A)m 2g 1
64k = » ar 3.16

Using established data for the wavelength dependence of the ordi-

nary and extraordinary refractive index in KDP [5c], the maximum

-48-

interaction length L is

en
SAG TOoC™. 3.17

Since the beams are non-collinear, and focused by a5cm. lenstoa

spot size of 15 microns, the actual interaction length is

L= spot diameter

sing

=0.045cm. 3.18

Thus, the SHG can be expected to experience adequate phase

matching over the entire interaction length.

The second harmonic beam is detected with an RCA 1P28 pho-
tomultiplier with a Schott UG-5 ultraviolet transmitting filter. The
fundamental beam is rejected by the glass filter as well as by an
aperture placed in front of the photocathode of the detector which
allows only the normally incident second harmonic beam (see Fig-
ure 3.1). The integrated current from the photomultiplier is stored
on a Nicolet 1174 signal averager. The signal averager contains
4096 addresses which can be loaded separately. Each address is
associated with a given position of the translation stage (ie., a
given value of the delay time + between the two incident pulses)
through a master controller of the stepping motor and signal
averager[26]. The stage is swept through the pulse width and the

SHG signal is accumulated in the signal averager for processing

-49_

and interpretation.

Fourier transform considerations dictate that in order to pro-
duce short optical pulses, the lasing spectrum must be correspond-
ingly broad. The spectral range is given by

re
c T pulse

AA=

3.19

For 6100 angstrom pulses with a duration of 1 picosecond, the spec-
tral bandwitith of the laser must be 12angstroms. In order to monitor
the real time spectrum of the dye iaser, we couple spurious
reflections from the Bragg cell into an optical fiber. The fiber car-
ries the light to the entrance slit of a grating spectrometer (GCA
Mcpherson 2051). The exit slit of the spectrometer is replaced with
the vidicon of an optical multichannel analyzer (OMA). The vidicon
(Princeton Applied Research 1205A)has 512 optical elements which
are variously iNuminated by the spectral components of the laser.
These elements are connected to a set of addressable memories
which are displayed on a CRT. This display indicates the real time
spectrum of the dye laser. The spectral range of the system is
100 engstroms, and the resolution is 0.186angstroms. The center
wavelength of the display is determined by the orientation of the
spectrometer grating; the calibration of the spectrometer-OMA sys-
tem is checked with a He-Ne and an argon laser. The information

yielded by the real-time spectral measurements gives valuable in-

-50-

sight into the operating conditions of the mode locked dye laser.

10.
11,
12.
13,
14,
15.

16.
17.

~50a-

References for Part I

. E. Hargrove, R. L. Fork, and M. A. Pollack, Appl. Phys. Lett. 5,
(1964).

oO - rm

. V. Shank and E. P. Ippen, Appl. Phys. Lett. 24, 373 (1974).

mm

. P. Ippen and C. V. Shank, Appl. Phys. Lett. 27, 488 (1975).

E. P. Ippen and C. V. Shank in Topics in Applied Physics, ed. by
S. L. Shapiro (Springer-Verlag, 1977), Ch. 4.

A. Yariv, Quantum Electronics (John Wiley and Sons, Inc., New York,
2nd ed, 1975), a) p. 256; b) p. 356; c) p. 421.

J. P. Laussade, Ph.D. Thesis, California Institute of Technology,
1969.

H. A. Haus, IEEE J. Quant. Electron. QE-11, 736 (1975).
C. P. Ausschnitt, IEEE J. Quant. Electron. QE-13, 321 (1977).

M. Bass, T. F. Deutsch, and M. J. Weber, Lasers, Vol. 3, Levine and
DeMaria, eds. (Marcel Dekker, Inc., New York, 1971), Ch. 3.

B. B. Snavely, Proc. IEEE 57, 1374 (1964).

M. E. Mack, J. Appl. Phys. 39, 2483 (1968).

G.H.C. New, IEEE J. Quant. Electron. QE-10, 115 (1974).

C. V. Shank and E. P. Ippen, Appl. Phys. Lett. 26, 62 (1975).

G. £. Bush, R. P. Jones, and P. M. Rentzepis, Chem. Phys. Lett. 18,
178 (1973).

E. P. Ippen, private communication.
P. Agmon, Ph.D. Thesis, California Institute of Technology, 1980.

The mirrors were obtained from CVI Corp. or from Spectra Physics.

The pump was obtained from the Weldon Tool Co. The vibration damper
is the #A71530-200 from Greer Olaer Inc. The stainless steel nozzles
are from Coherent, Inc. The x-y-z stages were obtained from the Line

18.
19.
20.
al.
22.
23.
24.

25.
26.

-50b-

Tool Co. The rotation mounts for the dye jets were designed and
constructed by L. Begay.

R. W. Dixon, J. Appl. Phys. 38, 5149 (1967).

Z. A. Yasa, et al., Opt. Comm. 15, 354 (1975).

G. H. McCall, Rev. Sci. Instrum. 43, 865 (1972).
Hamamatsu Corporation.

. Weber, J. Appl. Phys. 38, 2231 (1967).
Armstrong, Appl. Phys. Lett. 10, 16 (1967).

. Ippen and C. V. Shank in Topics in Applied Physics, ed. by
. Shapiro (Springer-Verlag, 1977), Ch. 3.

m “nim cu pa a
= c- oO = me]

. Van Stryland, Opt. Commun. 31, 93 (1979).

The pulse extraction timing system was designed and constructed by
Desmond Armstrong.

-51-

PART IT. PICOSECOND PHOTOCONDUCTIVITY OF
SEMI-INSULATING GALLIUM ARSENIDE
Chapter 4

The Opto-electronic Switch
4.0 Introduction

The introduction of deep impurity levels into gallium arsenide
has been an effective means of producing semi-insulating samples
of the material. Resistivities of 10°9-cm are typical for GaAs in
which chromium or oxygen has been introduced. The great majori-
ty of our experiments have been performed on chromium doped
material, but the general description of Cr:GaAs fits oxygen doped
material as well. The addition of these dopants is designed to com-
pensate for the presence of low level impurities such as silicon. Sil-
icon contamination of GaAs is a common side-effect of growing the
erystal in quartz (silicon dioxide) boats. The dopants also act as a
recombination center for free electrons and holes, thus reducing
the free carrier concentration by reducing the recombination life-
time. As a result, the concentration of electrons and holes in
Cr:GaAs is typically as low as 108em7*, and the bulk recombination

lifetime is well under a nanosecond.

It is due to these two properties of Cr:GaAs that this material

-52-

was chosen for photoconductivity studies. Our dye laser has 108
photons per pulse; for typical geometries of fast photoconductivity
measurements, the highest possible photocarrier density would be
10'4cm-*, It was necessary to select a material for which the intro-
duction of that concentration of photocarriers could be easily
detected. Hence, the low free carrier concentration of Cr:GaAs was
ideal; the ratio of dark to illuminated carrier densities (and
corresponding currents) could be as much as eight orders of mag-
nitude. In principle, then, such measurements could be taken with
a high signal to noise ratio. Further, the subnanosecond recombi-
nation lifetime of the material was a feature that required the high
temporal resolution of the mode locked dye laser. Thus, Cr:GaAs
accommodated both the analytical strengths and weaknesses of
the mode locked dye laser. Further, the use of Cr:GaAs in mi-
crowave devices and as a substrate material in opto-electronic de-
vices motivated these studies in understanding ultrafast phenomena

in the material.

High speed photoconductivity experiments have been per-
formed on Cr:GaAs by a number of investigators [1-4]. The meas-
urement technique generally consisted of mounting a chip of
Cr:GaAs in the middle of a high-speed transmission line, applying a
voltage to one end of the line, and observing the current pulse

through the chip upon illumination by a fast optical pulse. The

-53-

risetime of these current pulses is typically as fast as the optical
pulse risetime, or as fast as the line will permit. The falltime is dic-
tated by the lifetime of the photocarriers, and the height of the
current pulse is determined by the intensity of the photoexcita-
tion. The efforts of these investigators have generally been direct-
ed toward the production of the fastest possible current pulses, or
the highest possible output voltages. Since the devices "switch”
the input voltage on or off the output terminals, they are common-
ly known as opto-electronic switches. The fastest switches have
shown a 70 picosecond full-width at half maximum (FWHM) [1], and

high voltage devices have switched several kilovolts [4].

The fast response time of these devices was generally attributed
by the observers to the presence of chromium in the material.
However, the presence of chromium alone as a recombination
center cannot account for the high speed of the Cr:GaAs devices. A
more accurate depiction of the dynamics of the switches must in-
clude the effect of surface recombination. Since the excitation
pulses are completely absorbed within the first micron of the ma-
terial, it is clear that surface effects could play a profound role in

determining the effective lifetime of free carriers.

Our experiments have demonstrated fast photoconductivity of
these switches; the fastest response time (FWHM) of the switches to

picosecond pulses has been 70 psec. We have also seen that the

response of the switches depends upon surface effects. From ex-
periments designed to exploit the distinct nature of surface carrier
recombination, we have shown these results to be consistent with
established measurements of bulk recombination and surface

recombination velocity.

The second part of this thesis deals with the theory and
development of the ultrafast optoelectronic switch. This includes
the preparation of the GaAs, fabrication of the microstrip line, and
measurement techniques. This is followed by a theoretical treat-
ment of the carrier dynamics under picosecond light pulse excita-
tion and a comparison between the predicted and observed height
and width of the current pulse. Finally, the means of separately
determining the surface and bulk recombination parameters will

be discussed.
A.1 Development of Switch Design

There were several stages in the development of the fast
opto-electronic switches. The objective of the development was to
produce a switch configuration suitable for measuring the fast pho-
toconductivity of Cr:GaAs. Rather than work toward high output
voltages, we strove to eliminate artificial limitations on the speed
of the switches, so that their temporal response would reflect the

inherent speed of the semiconductor material as much as possible.

55-

It was necessary to work in the context of stripline technology in
order to provide a well matched circuit at high frequencies to cou-
ple into the sampling oscilloscope. The term “stripline” is reserved
for a conductive strip imbedded in a dielectric which is sandwiched
‘between two ground planes. A "microstripline” is a metal strip
which is separated from a single ground plane by a dielectric medi-
um (see Figure 4.1). Since the strip in a stripline is obscured by
the ground planes, the more practical configuration of the switches
is the microstripline. Its electrical isolation is not as good as that
of the stripline, but accessibility for optical excitation was preem-
inent in importance. At first, in order to minimize impedance
discontinuities in the circuit, an entire microstripline was fabricat-
ed from Cr:GaAs. A later design replaced the semiconductor mi-
crostripline. with commercial stripline materials, and several
different approaches were taken to insert the Cr:GaAs chip into the
transmission line. Various coaxial arrangements were investigated

as well.

The semiconductor microstriplines were constructed from
wafers of Cr:GaAs (see Figure 4.2). The size of the chip used was
typically 3 x 1 x 0.036 cm. Eutectic gold-germanium was evaporat-
ed on the chip to provide a fairly good ohmic contact, and pure
gold was evaporated on top to increase the conductivity of the mi-

crostripline. The microstripline itself was etched from this metal-

~56-

GROUND PLANE STRIP CONDUCTOR

€ DIELECTRIC

D N
SUBSTRATE GROUND PLANE

‘STRIP
CONDUCTOR

a 9 — DIELECTRIC
fh ; y SUBSTRATE

GROUND PLANE

Figure 4,1 A stripline (top), and a microstripline (bottom).

-5?-

Figure 4,2 An opto-electronic switch with a

semiconductor microstripline.

Metal Contacts

Cr:GaAs

_58-

lized layer according to dimensions specified by time-domain
reflectometry measurements as well as from published microstrip
impedance formulas (see Section 4.2). The Cr:GaAs microstripline
was mounted on a gold plated copper block and held in place by
‘OSM miniature connectors with 0.010” diameter terminals [5]. The
copper block served as the ground plane of the transmission line.
The terminals were soldered to the ends of the transmission line. A
gap was etched into the transmission line during fabrication with

dimensions of 70, 100, and 400 microns.

The semiconductor microstripline switches were fast (70
psec), but they consumed considerable amounts of Cr:GaAs. Fur-
ther, it was necessary to cut the wafer to a specified size to match
the copper block. A gap caused by a short wafer would generate an
impedance discontinuity, and if the wafer were slightly too large,
attaching the connectors to the block would shatter the micro-
stripline. For these reasons, it was decided that the microstriplines
be constructed from commercially available materials, and that
efforts be made to minimize the discontinuities at the connections
to the Cr:GaAs chip. The speed of the switches made from com-
mercial substrates was as great as that of the semiconductor sub-

strate switches.

The design of these switches was similar to that of the sem-

iconductor switches (see Figure 4.3). The material consisted of a

-59-

46pm COPPER
(a)
fo SAMPLE

L—*.

(b)

Figure 4,3 An opto-electronic switch with a polystyrene

microstrip: (a) the microstrip substrate

(bd) a side view of the switch

(a) (b) | (c)

Figure 4.4 Assembly configurations of the Cr:GaAs chip
in the polystyrene microstripline: (a) the
exposed, (b) the covered, and (c) the buried
sample. SI= Cr:GaAs sample, g= retallic
contacts, C = copper strip, gp = ground
plane, d = dielectric medium, and s = solder

or conductive epoxy.

-60-

dielectric, most frequently a highly homogeneous polystyrene
(1/16" thick), with copper sheets bonded on each side [6]. The
support block was 2” long by 3/4” wide, and was constructed from
various materials. The composition of the block, now no longer
used as a ground plane, had no observable effect on the operation
of the switches. A transmission strip with a gap was either cut or
photolithographically etched from the top conductive plane. The
technique of photo-etching the substrate consisted of spinning pho-
toresist (Shipley 1350J) onto one side of a sheet of stripline materi-
al and exposing the resist through a mask. The photoresist was
developed, more photoresist was painted on the back of the sub-
strate to protect the ground plane, and the substrate was etched in
a hot saturated solution of either ferric chloride or ammonium per-
sulfate. OSM miniature connectors were attached to the ends of
the block; their terminals were 0.050” gold plated tabs. The termi-
nals were soldered to the ends of the striplines. To ensure good
ground plane continuity, the ends of the ground plane were folded
over on the block and held in place with the ground flanges of the
miniature connectors. Wafers of Cr:GaAs were prepared (see Sec-
tion 4.3) with metallic contacts of Au, Au-Ge, Au-Zn, In, or Cr. The
contacts were prepared with 75 micron gaps. Then the wafers were
cleaved into appropriately sized chips (1.9 x 1.9 mm) for mounting

on the gap in the transmission strips. .

~§1-

Several methods of mounting the chips in the microstripline
were investigated, all with an effort at reducing the impedance
discontinuities of the line (Figure 4.4). Although the illuminated
resistance of: the Cr:GaAs chip never dropped below a few kN, it was
important to minimize the impedance mismatch in the line from
the gap to the 50N sampling head. In most of the cases, the chips
were mounted directly on top of the gap in the line, and the electri-
cal contacts were made with indiurm-silver solder (90% In, 10% Ag)
or with conductive (gold or silver) epoxy (Fig 4.4a). In some
switches, the transmission line strips were peeled back from the
substrate and used to establish direct contact to the chip (Fig
4.4b). In a few cases, the chip was buried in a rectangular pit cut
into the dielectric. The strips of the transmission line were then
soldered directly onto the contacts (Fig 4.4c). The measures that
were taken beyond the first method described had no noticeable
effect on the speed of the switches. One possible explanation for
this might lie in the 25 picosecond resolution of the sampling sys-
tem, which corresponds to 4 mm of propagation length. Since any
untreated discontinuity in the impedance at the chip could not
have been larger than 1 mm, it probably never would have been
seen by the detection system. The first mounting technique was
the method of choice, being easiest to perform, and allowing con-

venient chip replacement.

-62.

Another switch design was the coaxial switch, patterned after
a fast photodiode package developed by McCall [7]. This design
(Figure 4.5) featured a Mylar sheet capacitor on the biased end of
the chip. The other end of the chip was mounted on the terminal of
a miniature connector. It was hoped that the low impedance
source of charge would provide a ready supply of current; howev-
er, there was no improvement over the switch in Figure 4.4a. The
resistance of the chip was always too high to make use of the low

impedance input.
4.2 The Microstrip Line

The most fundamental attribute of a high speed transmission
system of electrical signals is the impedance. The impedance of
such a systern is the ratio of voltage to current in a traveling wave.
Wherever an impedance discontinuity appears in a transmission
system, the boundary conditions of electric field and current con-
servation cannot be satisfied without the creation of a reflected
wave at the discontinuity. In a poorly impedance matched system,
the superposition of reflected signals at a detector does not exhibit
the true nature of the original signal. For example, a short pulse
would appear broad due to the presence of multiply reflected and
delayed pulses that arise at the impedance discontinuities. It is
important, therefore, to design a transmission system with a uni-

form impedance in order to facilitate the accurate interpretation

-63-

\ A
\ 7 4—— Aluminum
| at —— Brass
Vo +— Mylar
LL. i
f Praud
Pyyl
Inner conductor tp | | * Aluminum
Teflon —! ! H
i J
Miniature __ Bil
connector

Figure 4.5 A coaxial switching unit.

-64-

of the transmitted signal.

The sampling system has a characteristic impedance of 50
ohms. This determines the impedance of the microstripline, and
the first task in developing the device is to determine the dimen-
sions needed to fabricate a 50 ohm microstripline. A very rough
estimate of the impedance of a microstripline is Z=z//(cew), where
c is the speed of light, « is the dielectric constant, and h and w are
shown in Figure 4.1. This formula is only good for w>>aA; in our
case, we need a more sophisticated analysis. There is a wealth of
data in the literature; both theoretical and empirical expressions
have been developed to describe the impedance of a microstripline
given its dimensions, and vice versa [For examples, see Refs. 8-11].
Unfortunately, there is very little agreement between any of these
sources; there is a range of a factor of two in which the results lie
[12]. For our experiment, we used a time-domain reflectometer to
determine the impedance of microstrips that were fabricated ac-

cording to the rough consensus of the literature.

In a time domain refiectometer (TDR), a fast risetime voltage
pulse is launched into an electrical system from a 50 ohm cable. If
there is any impedance discontinuity in the system, the resulting
reflection returns to the TDR, and is displayed on the voltage step.
From the height of the reflected signal, and frorn its delay relative

to the voltage step, the magnitude, sign, and location of the im-

-65-

pedance discontinuity may be determined (Figure 4.6).

We constructed a number of microstriplines using rough esti-
mates of the correct strip width. From TDR measurements of
these microstriplines, we interpolated to determine the correct
strip width for a 500 device. This width for the polystyrene mi-
crostripline was 0.188 cm; for the Cr:GaAs microstripline, the
correct width was .036 cm. It turned out that Kaupp’s empirical
formula [11] showed excellent agreement with our experimental
data. His expression is

w | 5.97 t
——=1.25 =
h lexp(zVet1.41/87) h

41

where the symbols are defined in Figure 4.1.

Even an impedance matched microstripline cannot transmit
high speed signals without distortion. Sources of this distortion in-
clude the frequency dependence of the group velocity, the high fre-
quency loss tangent of the dielectric, and the ohmic loss of the
conductor due to decreasing skin depth at high frequencies [13-

15].

When switch measurements were taken in a magnetic field
(See Section 6.3), the oscilloscope sampling head was placed at a
distance from the switch. This was done to avoid any influence of

the high magnetic field on the components within the sampling

———

Reflection

ry

VOLTAGE

10 mil rad
STRIP CONDUCTOR

Wii eo COPPER BLOCK

Figure 4,6a) Time domain reflectometer display of a

semiconductor microstripline. The micro-

stripline is connected on the left to a

50 ohm line.

{.63mm w =|.88mm | w= 2.03mm
532 z= 502 z= 472

Ut

b) Voltage reflection (vertical axis) from

impedance discontinuities along a polystyrene

microstripline. The discontinuities occur

at the transitions between the line and the

connectors.

-67-

head. The interposition of a high-speed signal cable between the
switch and the sampling head resulted in further signal dispersion
over the microstripline dispersion. Rather than calculate the
overall bandwidth of the microstripline and signal cable, we mea-
Sured the increase of the width of a fast pulse upon passage through
a microstripline without a gap and then through the cable. We pro-
duced the fast pulse by differentiating the fast risetime step from
the time domain reflectometer pulse generator. This fast pulse
was a small amplitude pulse with a full width at half-maximum of 40
picoseconds. The risetime of the sampling head was 25 pi-
coseconds. The pulse broadened to 43 picoseconds upon passage
through the transmission line; assuming that the bandwidths are
Gaussian, and the convolutions are quadratic, the risetime of the
entire system was 30 picoseconds. We used this figure in the curve

fitting described in Chapter 6.
4.3 Surface Preparations

The high absorption coefficient of Cr:GaAs (4.3x10tem-! [22]) at
the visible wavelength of the mode locked dye laser implies that
photocarrier lifetimes will be greatly affected by the conditions at
the surface of the semiconductor. In order to explore the effects
of surface preparation on the photocarrier lifetime, switches with
various surface preparations were constructed. This discussion of

surface preparation techniques applies specifically to Cr:GaAs

-68-

chips in switches with polystyrene microstriplines. In all, over six-

ty switches were investigated.

The tests performed on these switches measured the surface
recombination velocity s; we investigated the relationship between
various surface preparations and the resulting observed value of s.
Surface recombination velocity is defined as the observed constant
of proportionality relating the rate of carrier recombination at the
surface (carriers per unit time per unit area) with the carrier con-
centration at the surface (carriers per unit volume). The magni-
tude of s is determined by the conditions at the surface of the ma-
terial, including the lattice termination, lattice defects, and ad-
sorbed impurities. The concept of surface recombination will be

treated in more detail in Section 5.3.

In the early stages of switch production, the technique of chip
preparation was a typical photolithographic method. After the sur-
face of the chip was treated according to some prescription, a me-
tal or metal alloy, such as gold, gold-germanium, or gold-zinc was
evaporated onto the entire wafer. The wafer was spun with positive
photoresist (Shipley 1350J), and exposed with UV light through a
mask. The mask consisted of an array of slits, 75 microns wide.
After development, the wafer was immersed in a gold etch solution
(KI J 9:20 =275:150:250 by weight), and the exposed metal regions

were etched away to form 75 micron gaps in the contacts. The

-69-

wafer was then alloyed in a hydrogen atmosphere at 400 °C to es-
tablish a good electrical contact and strong mechanical bond
between the metal and the semiconductor. The wafer was cleaved
into appropriately sized chips for the switches, soldered to the
stripline, and then tested. Some of the results of these tests are
tabulated in [12]. There was virtually no relationship between the
surface preparation and the speed of the device. It was hoped that
by preparing the surface in such a way as to increase the surface
recombination velocity, the photocarrier lifetime would decrease
accordingly. Such results were not seen in switches with GaAs crys-

tals which were prepared by the above technique.

The difficulty in demonstrating a connection between the sur-
face conditions and carrier lifetime lay in the sample preparation.
The gold etch not only removed the metallic contact over the gap,
it attacked the Cr:GaAs as well. Further, the chips were heated in
the alloying oven, which promoted chemical reactions between the
Cr:GaAs and any adsorbed impurities, as well as causing the subli-
mation of arsenic from the surface. So, regardless of the surface
preparation established on the chip prior to switch fabrication, the
surface conditions were determined by the gold etch and the heat
of alloying oven. It was necessary to develop a technique of apply-
ing metallic contacts to the chip without etches, and preferably |

without the application of any coating, such as photoresist. Fur-

-70-

ther, the electrical and mechanical bond between the Cr:Gads and
evaporated metal would have to be of high quality without alloying.
It was found that chromium satisfied the requirements imposed on
the contact material. The non-alloyed Cr:GaAs-chromium contact
provided the highest output signal for the switches, and was ex-
tremely durable. An evaporation mask was developed which strung
15 micron stainless steel wires across the chip, with sufficiently
close contact to the chip that no evaporation shadowing took place.
The result was a clean gap in the contacts with minimal contamina-
tion of the surface. Indium-silver solder was used initially to bond
the chip to the stripline; to eliminate that source of surface heat-
ing, conductive epoxies were then used exclusively. Magnetophoto-
conductivity tests showed that the surface recombination velocity
was determined by the initial surface preparation; there was good
agreement between this data and luminescence studies which

determined the surface recombination velocity independently [16].

The surface recombination velocity s in Cr:GaAs can be varied
from 450 cm/sec to more than 10° em/sec, by means of appropri-
ate surface preparations. s has been reduced to 400-500 cm/sec
when the surface is passivated by an epitaxially grown layer of
Al,Gay.2As. Low values of s are also obtained with chemical solu-
tions, such as one causing the chemisorption of ruthenium ions

[17] (s = 3.5x10*) , and etches, such as solutions of citric acid [16]

-7i-

or phosphoric acid [18] ( 6 = BX 105). The highest surface recom-
bination velocities are obtained from mechanical polishing with
abrasive grits ($s > 10°). The various surface preparations used in
our experiments include the AlGaAs passivating layer grown with
molecular beam epitaxy [19], a citric acid etch (saturated citric
acid in water: nitric acid: water= 2:1:2 by volume) [16], and

mechanical polishing (3 micron alumina grit applied until a matte

finish is obtained).
4.4 The Experimental Set-up for Switch Measurements

The experimental set-up is shown in Figure 4.7. A chip of
Cr:GaAs has metallic contacts evaporated on its surface. The chip
i¢ mounted on a microstripline, and ea voltage is applied across a
gap in the metallic contacts. Ordinarily there is very little current
flow due to the high resistivity of the material. When the gap is il-
luminated with a picosecond light pulse, photocarriers are created
in the gap, and current flows for the duration of the photocarriers’

existence.

The detection system for measuring the current waveform
consisted of a Tektronix 7904/ 7S11-7T11 sampling oscilloscope
system with a 25 picosecond risetime sampling head, the 8-4 or the
5-6. The sampling system required a trigger to arrive 80

nanoseconds before the signal. In order to minimize jitter from

-72-

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-73-

‘pulse to pulse, we triggered the oscilloscope with a current pulse
from a photodiode which detectedaportion of the laser pulse. The
remainder of the light pulse traveled down an 80 nanosecond delay
line in air before reaching the switch. Miniature high-speed con-.
nectors and semi-rigid cable were used in carrying the signal from
the switch to the sampling head, and all connections were made as ”
short as possible. The data from the sampling system was stored
digitally on the Nicolet 1174 signal averager. The sweep of the sam-
pling head was controlled by the signal averager, and the voltage of
the vertical signal of the oscilloscope was stored into memory.
Thus, the inherently large noise of the sampling head was averaged
away, and the signal could be stored for processing. In this
manner, many signals could be stored on magnetic tape for pro-

cessing on Caltech’s 1BM 370 computer.

4.5 Experimental Photoconductivity Results

We constructed switches according to the method described
above. The switches were tested by applying an electric field of
4x107 v/ern to one end, illuminating the gap with a picosecond pulse
from the dye laser, and measuring the current flow with a 25 pi-
cosecond sampling head. A typical result of one of the fastest
switches is shown in Figure 4.8. The risetime is limited by the sam-

pling head, and the falltime by the effective photocarrier lifetime

VOLTAGE

i€-100 mV-> |

-74-

rf

abn 4

0 400 200 300 400
PICOSECONDS

Figure 4.8 Output of an opto-electronic
switch upon illumination by 4 picosecond

pulse.

~75-

in the Cr:GaAs. This photocarrier lifetime is determined by both

the bulk recombination rate and the surface recombination velocity.

Ideally, the bulk recombination rate should not vary too
greatly from one sample of Cr:GaAs to another. If this were the
case, the surface conditions could be altered on different samples,
and the effects of these alterations could be investigated with the
knowledge that the other material parameters were constant. Un-
fortunately, this situation does not always exist; a common prob-
lem of doing measurements on Cr:GadAs is the variability of speci-
mens obtained from different growth techniques, or even from
different locations in the same ingot [20]. Our Cr:GaAs was general-
ly obtained from Crystal Specialties Inc. [21]. The measurements
done on these samples indicated fairly constant material charac-
teristics. The variability that we saw in several ingots, and many
different wafers from these ingots implies that the accuracy of our
results is about 10% within a single wafer, and about 30% for

Cr:GaAs as a whole.

The photocarrier lifetimes of carefully made switches depend-
ed strongly on the surface preparation. The lifetimes were meas-
ured according to the 1/e point on the current decay curve. This
time was deconvolved with the response time of the entire electri-

cal system. The fastest switches were constructed using the early

-76-

technique of construction; thus the gold etch in the presence of
the contacts coming into solution provided the most active surface
for recombination. The photocarrier lifetime was about 70 pi-
coseconds. The switches whose surfaces were prepared by
mechanical polishing showed the next shortest lifetime of 80 pi-
coseconds. The citric acid passivating etch reduced the surface
recombination velocity to the point where the lifetime was 100 pi-

coseconds.

The switch with the most passivated surface, that with the
GaAlAs cap, was the slowest of all, with a 450 picosecond lifetime.
This last switch displayed the properties of pure GaAs rather than
Cr:GaAs. The reason for this was that the passivating properties of
GaAlAs only appear at an epitaxial interface. If the GaAlAs were
grown directly on the Cr:Gads substrate, the recombination at the
interface would reflect the lattice defects and adsorbed impurities
of the sawn, lapped, polished, and inevitably contaminated surface
of the Cr:GaAs, rather than the Cr:GaAs-GaAlAs interface. So, an
epitaxial layer of pure GaAs was grown on the substrate, and then
the GaAlAs layer was grown on top of that. It was not practical to
grow Cr:GaAs instead of the pure material. Thus, the measure-
ments of this switch provided data on the effect of chromium in

GaAs as a recombination center.

Some switches were constructed using O:GaAs, where oxygen

-77-

is used as a recombination center instead of chromium. There was
no noticeable difference between the behavior of the oxygen doped
material and Cr:GaAs. Experiments were done with semi-insulating
Fe:InP; The photocarriers showed comparable lifetimes at a pas-
sivated surface (100 picoseconds), but the most significant proper-
ty of the InP switch was its large throughput. We have defined
throughput as the ratio of input voltage to peak output voltage
measured on a 50 ohm load. Typical throughputs for Cr:GaAs
switches were 0.1% for gold and gold alloy contacts, and 0.8% for
chromium contacts, constant over a bread range of input voltage.
Throughputs for InP switches were typically four or five percent,

making them attractive candidates for fast current pulse sources.
4.6 Conclusion

Opto-electronie switches can have pulse widths of less than
100 picoseconds. As a result, they have at least three major appli-

cations.

(1) First, they are very fast photodetectors; they are among
the fastest detectors available. They are simple, have large sensi-
tive areas, and have a fairly good signal to noise ratio (40 dB). They
are not very sensitive, however, generating 30 microamps per watt

of incident optical power.

(2) A second application of these switches is as a fast current

-78-

source to drive devices such as diode lasers (See Figure 4.9). In
order to reduce impedance matching problems between the 50
ohm line and a 2-3 ohm diode laser, the switch and laser could be
integrated on a single chip. Nevertheless, detector limited pulses
(<200 psec.) have been observed with our switches connected to Hi-
tachi diode lasers through 50 ohm lines. Accurate temporal meas-
urements can be done by mixing the dye laser pulse with the much
weaker diode laser pulse in a non-linear crystal. This would be
more effective than performing SHG on the diode laser pulse, since
the greater power and higher resolution of the dye laser pulse

would make nonlinear measurements easier and more accurate.

(3) Finally, and most importantly for this discussion, these
switches allow measurements of the material parameters in semi- |
conductors. By investigating the overall photocarrier lifetimes |
under different conditions, a quantitative determination of the car-

rier recombination parameters can be undertaken.

We have constructed photoconductive switches that are capa-
ble of producing current pulses that reflect the photocarrier life-
time in the constituent semiconductor. Such lifetimes are deter-
mined in the semiconductor by surface and bulk carrier recombi-
nation. There was an explicit dependence of photocarrier lifetime
on surface preparation, and evidence of the effect of chromium on

the bulk recombination rate. It is now necessary to investigate these

-79-

‘IJOATIP Jasel[ e&@ Se YOJTMS OTUOTZOSTAa-O4dO aU, 6°h sAINeTY

3d09SOT19SO
ONMdNVS

¥OLD3R 13d
-OLOHd
298d 001 —=. =
+. :
uasvl 94u01}99;9
-01dO |
asd 5

LHOMI : q
998c 08 VW (y oot = vy)

3$1Nd LNaYHND — esd 5

asind
LHS

-80-.

phenomena in Cr:GaAs to establish the analytical dependence of
photocarrier lifetime on the surface and bulk recombination

parameters.

~81-

Chapter 5

The Theory of Ultrafast Photoconductivity
of Semi-insulating Gallium Arsenide

5.0 Introduction

In order to interpret the behavior of the photoconductive
switches, we need to examine the processes that determine the
lifetime of photocarriers. In Cr:GaAs, electron-hole pairs recom-
bine through direct band to band transitions, through Auger
processes, and through intermediate interband states. These in-
termediate states can be present in the form of recombination
center impurities, or as states that arise in the forbidden gap due
to the lattice termination at the surface. The carriers migrate
through the semiconductor due to the electric field as well as

through diffusion.

In this chapter, the different recombination processes will be
investigated to form estimates of their magnitude. Further, a
diffusion equation describing the dynamics of the photocarriers will
be developed which includes the effects of the electric field, ambi-
polar diffusion, bulk recombination, and surface recombination
velocity. Using known values of recombination rates, we will com-

pare the results of this analysis with the experimental photocon-

-82-

ductivity data that we have obtained.

5.1 Carrier Recombination in the Bulk

The resistivity of Cr:GaAs can be very high; it is generally 10°
ohm-cm. It is possible to calculate the concentration of thermally
excited carriers from simple considerations of the Fermi distribu-
tion of electrons and holes in the material. The concentrations of

electrons and holes are given by the expressions

em [92
erm,kT eho E er

5.1

. 5 Ver]
p.=2 erm, kT ger Eula
.=2|\——_—

where m; are the effective masses of electrons and holes. These
effective masses are m, = 0.07 m,, and mis 0.5m,. #,, £;, and £,
are the energies of the conduction band, the Fermi level and the
valence band of the semiconductor. The band gap is 1.43 eV, and
the Fermi level is generally taken to be 0.74 eV above the valence
band. The Fermi level is very nearly in the center of the sernicon-

ductor, so the calculations proceed directly to obtain

Nig aX 10%em 73

5.2
Pozi 107em7*

83-

as approximate values for the free carrier concentration. The

—_—__——___. We take the electron mo-
NE Unt Pe fy

- resulting bulk resistivity is p=

bility to be 3000cm?2/V-sec, and the hole mobility to be 170cm?/v-sec.
Thus, p=5x10° ohm-cm, within the observed range. Our photoexcita-

tion carrier density is

$a 5.3
laser spot area

n=p=

where #=10° is the number of photons in the laser puise, and a=
1/2300 angstroms is the absorption coefficient of GaAs at 6100
angstroms. Thus, the photocarrier density is approximately
10'tcm-5. We see that the equilibrium carrier concentration is negli-
gible compared to the optically excited population, so only these

carriers need to be considered as participants in recombination.

Recombination takes place through unassisted band to band
transitions (including Auger transitions) and at recombination
centers such as oxygen and chromium. The carrier lifetime due to
the former process has been estimated to be about 3 nanoseconds
[22]. This process alone is too slow to be responsible for the fast
bulk recombination rate observed in our Cr:GaAs switches (r = 250
psec., see Chapter 6); the rate must be strongly determined by the

recombination centers.

As we saw above, the equilibrium concentration of free car-

riers is negligible compared to the photoexcited population creat-
ed by the picosecond light pulse. Consequently, the initial carrier
population, composed almost exclusively of photoexcited electron-
‘hole pairs, is made up of an equal number of electrons and holes.
The band to band recombination rate for electrons, for example, is
then

Sn

at Cnrp=-Cn

A result of this situation would be a dependence of carrier lifetime

on the initial excitation level.

—— 5.5

n(t)=

where no is the initial carrier concentration. We saw no depen-
dence of decay time on the intensity of the picosecond pulse, lead-
ing us to conclude that the band to band process of recombination
does not play a significant role in carrier lifetime determination.
We then must consider the effect of the chromium dopant as a

recombination center in the material.

Deep levels in semiconductors, such as chromium in GaAs, in-
crease the rate of carrier recombination. This can be seen through
an uncertainty principle argument by recognizing that an electron,

trapped and highly localized by a recombination center, has a

-85-

correspondingly broad range in momentum-space. As a result, a
hole with a relatively narrow wavevector may recombine with the
trapped electron; the momentum conservation criterion of the
‘recombination process is readily met without the necessity of

creating a phonon.

The concentration of chromium in Cr:GadAs is highly variable,
even within a single wafer of the material [23]. Much of this varia-
tion is due to a large solubility difference of chromium in the liquid
and solid states of GaAs; as the crystal is grown, chromium mi-
grates toward the liquid portion of the GaAs. Thus, the regions that
solidify last have the highest concentrations of chromium, and the
first regions to solidify have the least. As a result, the chromium
concentration can vary from 10'* to more than 10'’atoms/cm’. For

our analysis, we will assume a concentration of 10"atems /em?.

The recombination of carriers through a recombination center
takes place through a two step process. First, an unionized center
captures a carrier, an electron, for example. Now the center is ion-
ized, and the capture of a hole is greatly enhanced by the Coulomb
attractive force. This second step will occur almost immediately
after the first step. Thus, the limiting process in the recombina-
tion, the unionized capture, will establish the recombination rate
at the centers. Thus, the recombination rate will depend on the

product of the concentration of the species to be captured, and the

-86-

concentration of the chromium.

an _
ae ou 5.6

where o is the unionized capture cross section, vy, is the thermal
velocity, and N is the chromium concentration. Thus the decay

time is

5.7

T=
GUyN

Note that this decay time is independent of the initial electron con-
centration, which is consistent with our observation. Using typical
values for the cross section o=3x107!"cm?® [24], and thermal velocity
v=4.5x10” em/sec, we obtain a recombination lifetime of 8
nanoseconds. This rate is too low to explain the bulk recombina-
tion rate observed in Cr:Gads. Either the recombination rate
through chromium is higher than we just calculated, or there are
other recombination centers such as oxygen in the material, or
both. Since we did not see any dependence of carrier lifetime on
the excitation intensity, we must assume that the dominant recom-
bination process is monomolecular, i.e., through a recombination

center.

The GaAlAs switch was identical to the other polystyrene mi-

crostripline switches, except that the gap of the GaAs chip was

-87-

capped first with an epitaxially grown layer of pure GaAs, and then
with another layer of GaAlAs for surface passivation (Figure 5.1)£19]
We chose the concentration of aluminum in the GaAlAs to be
’ sufficiently high (55%) to be transparent to the 6150 angstrom light
pulse. The interface between the pure GaAs and the GaAlAs served
as the photosensitive region. The concentration of chromium in
the pure GaAs layer was estimated to be less than 10*atoms /cm' at
the very most. Further, the observed decay time was 450 pi-
coseconds, the longest observed. It might be expected, then, that
the observed recombination at the highly passivated GaAs-GaAlAs
interface would be associated with unassisted band to band transi-
tions, and not be due to recombination center effects. Thisis not a
reliable assumption, however. The GaAlAs cap was oxygen doped
semiinsulating material. The passivating layer was made semiinsu-
lating in order to eliminate current leakage through that layer.
The diffusion coefficient of oxygen at the temperatures of molecu-
lar beam epitaxial growth is roughly 10-"cm*/sec [19]. The top
layer growth took approximately one hour; the diffusion length
of oxygen into the originally undoped GaAs would have been ap-
proximately 2000 angstroms. So, a significant portion of the top of
the GaAs sensitive layer was oxygen doped material; recombination
processes would be strongly affected by the presence of oxygen as
a recombination center. Thus, we can assume only that the longer

decay time in the GaAlAs switch was due to a lower concentration

-88-

Figure 5.1

Metal

Contacts

Picosecond
Light Pulse

Bias dt
Voltage—~> ——

Geometry

Metal

Contacts wr

[1

«co @e-—

Cr:GaAs

Sampling
Oscilloscope

Picosecond
Light Pulse

Photo-

Carriers

Cr:GaAs
Substrate

of the Opto-electronic Switch

wa 1.5um 0:GaAlAs

undoped GaAs

The Heterostructure Opto-electronic

Switch

-89.

of recombination centers, including those at the interface, and not

to their complete absence.
5.2 Surface-Recombination

Surface recombination of free carriers in GaAs is a frequent
impediment to successful electronic device fabrication. The free
surface of GaAs acts as a powerful recombination agent for a
number of reasons. The surface of GaAs, as well as that of any oth-
er material, necessarily consists of a lattice termination. The elec-
tronic states of a semiconductor are segregated into bands as a
result of the periodicity of the crystal lattice; where this periodici-
ty is disrupted, such as at the surface, electronic states may ap-
pear in the middle of the band. It is through these states that
enhanced electron-hole recombination may take place. Further,
whatever impurities there are at the surface of the material can
act as recombination centers. Moreover, GaAs does not have a na-
tural passivating oxide, as silicon does, for example. The arsenic
sublimes from the surface, upsetting the stoichiometric balance,
which further perturbs the lattice. Hence, the surface of materi-
als, especially that of GaAs, can be the site of interband states

which aid in the recombination of photocarriers.

Surface traps in GaAs immobilize large numbers of electrons

at the surface of the material. As a result, a space charge region is

-90-

created in a shallow layer near the surface which consists of a pop-
ulation of holes coulombically attracted to the trapped electrons.
The thickness of this layer has been found to be on the order of
tens of angstroms [16], whereas the typical extent of the photocar-
rier population in our switches is roughly a diffusion length, or 5000
angstroms. Thus, the space charge effect is essentially a surface
phenomenon in our experiment. There will be an enhanced elec-
tron recombinaton rate at the surface due to the increased free
hole concentration, and a reduced hole recombination rate for the
same reason. Due to the greater electron mobility compared to
hole mobility (4/u, = 20), the Cr:GaAs can be treated as an n-type
material; the altered recombination rates at the surface have a net
effect of decreasing the conductivity at the surface. The
phenomenological surface recombination velocity is a combination
of the effects of the space charge region and recombination
centers at the surface. Photoconductivity and luminescence mea-
surements taken over a broad spectrum can discriminate between
these two contributions by demonstrating a wavelength shift of the
luminescence and photoconductivity peaks toward longer
wavelengths [16]. Since our measurements were all taken within a
narrow band of excitation wavelengths well above the energy gap,
we were unable to resolve any of the details of the two surface
recombination processes. We did obtain results, which, when inter-

preted in the context of phenomenological surface recombination

-91-

velocity, agree well with these luminescence studies.

The usual analytic description of surface recombination velo-
city begins by assuming that there are p recombination centers per
unit area in a thin layer near the surface of a material, with some
capture cross section ¢. Assume that a material has a uniform car-
rier concentration n throughout its volume, and that c=o. If a non-
zero o is suddenly “turned on”, carrier recombination will begin at
the surface, and according to the diffusion coefficient D, there will
be a current flow toward the surface. Specifically, this particle

current per unit area just beneath the surface can be expressed
-D22 (y=0)=n-ovnp
ay th 5.8

where uv, is the thermal velocity of carriers [25]. We see that the
product ovisp is equal to the surface velocity, and that this: product
is a constant of the material specimen at a given temperature.
This constant is identical to the surface recombination velocity s
defined earlier; Equation (5.8) is used as a boundary condition for
differential equations of free carrier dynamics. A typical value of s
for GaAs is 10° cm/sec; generally there is assumed to be one
recombination center per atom at the lattice termination. Conse-
quently, the magnitude of the capture cross section ¢ is roughly

107 '®cm,*.

-92-

5.3 A Diffusion Model of the Switch

Photocarriers created in Cr:GaAs initially follow the profile of
oY, where a is the optical absorption coefficient of the material,
and y is the distance into the medium. The carriers recombine at
the surface and throughout the bulk, while diffusion acts to smooth
out the distribution. We assume a monomolecular bulk recombina-
tion rate according to Section 5.1. The geometry of this analysis is

shown in Figure 5.1. The currents follow the continuity equations

on 77

ee Ye .
ot J T 5.9
j=-D Wn+ub 5.10

Combining the two above equations gives the differential equation

for the charges
On. yen, — 5.11
at =D T

This equation is subject to the boundary conditions

n(o,t)=0, n(y,t<0)=0 nly, O)=nge"w 5-12
on _s
By yao D™ 5.13

where r is the bulk recombination rate, uw is the carrier mobility, D

is the ambipolar diffusion coefficient, E is the applied electric field,

-93-

and s is the surface recombination velocity. We assume that n is
uniform in the x and z directions. Since the light pulse has a dura-
tion of 1-2 picoseconds, and since the resulting photocarriers relax
from the high energy levels of the appropriate band to the low level
of the band within a few (subpicosecond) collision times, we are
justified in treating the carrier generation as a delta function in

time. We have also assumed charge neutrality for ambipolar diffusion [12].

We begin the solution of Equation 5.11 by observing that the
term n/r may be temporarily eliminated if the final result is multi-
plied by e~'“*. We then perform a Laplace transform on the rernain-

ing expression. We obtain

- a°n (y, 5.14
noe “¥+qn (yg y= Anya)

where q is the Laplace transform variable, conjugate to the "time”

variable Dt. The homogeneous solution to Equation 5.14 is
n(y.g)=A (g)eF¥+5 (q)e"VB¥ 5.15

where only the second term satisfies the boundary condition at

y=~, hence, A(q)=0. The particular solution of Equation 5.14 is

n(y.g)=Ce-w 5.16

where

-94-

Tq

C=
at—g 5.17

Thus, the solution is

"ge 7*¥
nty.q)= = +B (q)e-Vav 9.18

Inserting Equation 5.18 into the surface boundary condition Equa-

tion 5.13, we obtain an expression for B(q):

—no(aty) 5.19
(a®~q )(7+V4q )

B(q)=

where y=s//D. In order to find n(y,t), we perform the inverse La-

place transform

1 fme™ __ no(aty) -V¢x DIY 5.20
rtaas Sate tae vy ee

This expression has a removable singularity at g=a?2, and no other
singularities on the single sheet of the complex plane. We choose a
branch cut on the negative axis, and choose the square roots to be
positive imaginary above the cut, and negative imaginary below the
cut. The only contribution to the contour integral is from the two

paths above and below the branch cut. We obtain

nly.t)=ri. frelatzie Sais’ Maka d ot ands 6.21
¥ ~ ari 45 a+¢2z ® riz i .

where we have introduced the variable z*=-g. Equation 5.21 be-

-95-
comes
5.22

—2r9 = . | 1 1
Gaal fe * (2 coszy +ysinzy) | zir| dz

nly,t)=

The four terms in this integral are found in Reference [26]; simpli-

fying, and including the term ezp(-t/r), we obtain

n{y,t =n (0, c)exp(-t nL (av BE Her) (aN BE + oa

where 7 is s/D and W(z)=erp(z"erfc(z). Curves of Equation 5.23 are

shown in Figure 5.2.

The total current passing through the carrier field described

above is

i(t)eeubu [nce dy 5.24

where w is the width of the stripline. This integral is

i(t =e ukwm (0, O)ezp (-t fy

[ow (aVat )-a¥ (Vat | 5.25
a(a-7)

n(0,0) is related to the illumination level, and is

aN | 2nad_

7 (0, 0)= Aredgan ATECpuise

5.26

arate

é.is the number of photons in the optical pulse, N= 227 is the

0006 = =oohs = gost oe 9 oS Th OZ OTE =— EZ

‘uMTpow 249 OUT BsoUeISTp puB

owt} JO uoTZOUNT e Se UOTZeAZUaDUOD JeTIIeN Z°S aandTd
SHOULSONY Cos

- =n read i]: as 4-}-4- he EE PTET CTT eR LPR Ebel --T ied 4- |.

Seti biter OY oooh, Kn One

‘ +H

a+

an y

-96-

on See me a
itt

a ee oe t rc =f ~j}- -l- -
—_ a

on cor ;

ee nnd
fe ee

oos'6

loos

o0e°o 002°0 vie) Ga} 0°09

ooh'9

go3"0

: : ge-}2 aie fn ee
ab aa on op a

006°6

mi

CO’ OON/CL* AON

00L°o

008°0

000°}

-97-

total number of photocarriers initially in the medium, and i-y is
the Fresnel reflectivity of the medium. The laser spot just covers
the entire gap; the above expression includes this geometrical cov-
erage of the gap by the spot. Equation 5.25 is shown in Figure 5.3,
as well as a filtered Equation 5.25 that would simulate an observed

signal through a finite bandwidth detection system.

We now have an expression for the ultrafast photoconductivity
of Cr:GaAs. In order to relate this expression (Equation 5.25) to ob-
served data, we filter the theoretical pulse to simulate the finite
bandwidth of the detection system. Thus, we can compare the de-
cay time generated by various carrier recombination parameters
to observed decay times, and hopefully use this data to deduce the
recombination parameters themselves. If typical values of surface
and bulk recombination constants are inserted into Equation 5.25,
there is good agreement with observed photoconductivity pulses.
However, the pulse shape alone cannot uniquely determine the
recombination parameters [12]. For almost any given value of sur-
face recombination velocity, there can be found a bulk recombina-
tion rate to force agreement between theoretical and experimental
data. In order to measure the parameters with any accuracy,
more information must be extracted from the photoconductivity of

the switches. As it turns out, magnetophotoconducivity measure-

tu 0.33 3
2 10° E
© 40.27 Lu
wn 2
tu <
aa 40.20 E
uy 8
4 40.13 a
> =
a ro)
= 40.07 ©
rs) &
a 00 n ! ! I 00 «©
“Oo 50 100 150 200 250 300
t (ps)
1.0 i v t 7 1.2
> .
pa |
2 R. = 502 &
OQ so
> S
Ee 8
j 0.25- 40.3 >
ti
cc
0.04 1 i

-50 fe) 50 100 150 200 250°"

t (ps)

Figure 5.3 Theoretical curves of current as a function

of time. The top curve is the unfiltered
current, and the bottom curve is the current

after passing through a Gaussian filter.

-99-

ments supply sufficient information for a reliable determination of

s and r.

-100-

Chapter 6
Recombination Parameter Determination:

Ultrafast Magnetophotoconductivity
of Semi-insulating Gallium Arsenide

6.0 Carrier Dynamics in a Magnetic Field

In Chapter 5, it was shown that the diffusion equation that in-
cludes the effects of surface and bulk recombinaton could explain
the behavior of the photoconductive switch. However, there is a
high degree of correlation between the surface and bulk recombi-
nation rates that prevail in the semiconductor. The two phenomena
act in concert; in order to determine the separate recombination
parameters to any degree of accuracy, the recombination
processes must be decoupled in some way. This decoupling can be
accomplished by applying a magnetic field perpendicular to the
electric field and to the surface of the semiconductor (See Figure

6.1).

Without the magnetic field, the carriers are simply drawn to
the appropriate electrode by the action of the applied electric
field: When the magnetic fleld is applied, the electrons and holes
(traveling in opposite directions and bearing opposite charges) are
both impelled toward or away from the surface according to the
direction of #xf. The carriers always experience bulk recombina-

tion; when the signs of the fields are such that the carriers are

PTaty oTzeuseyW
B UT YOXTMS OTUOIZDeTY-09dO eyL T1°9 sanetY

-101-

sye5:-1i9 .
adoasojj}989 “O18 oe OR RHOA
Buljdwes “4-8 O-:->
t =] + [+ ‘I

A? ® ® \

$198}u05

asind 14614
puosasooig

P1914-

-102-

drawn, toward the surface, more carriers experience surface
recombination as well. When the fields force the carriers into the
medium, fewer carriers recombine at the surface. The net result
of the magnetic field is the increase or decrease of the overall life-
time of all the carriers. Thus, the observed photoconductivity
trace will show an increase or decrease in pulse width, according to
the signs of the fields. Such a phenomenon has been observed.
This effect is known as magnetophotoconductivity (MPC). By this
method, the two recombination processes can be decoupled, and
the respective recombination parameters can be determined with

reasonable accuracy.

Another basic photo-electric measurement undertaken in a
magnetic field is the magnetophotoelectric effect (MPE). MPE
measurements involve the detection of a short circuit current
through the illuminated switch or a voltage across the switch in the
absence of an applied electric field. The current flow arises from
the average motion of carriers normal to the surface. Initially, the
carriers are created at the surface; diffusion carries them into the
bulk. Since both carriers are initially traveling into the bulk, the
magnetic field bends the paths of electrons in one direction, and
holes in the other (See Figure 6.2). Thus, a pulse of current is pro-

duced according to the direction of the magnetic field.

We derive the carrier dynamics necessary to describe the PME

qoasJq OTAPOoToopYousewoqzoud YSeseszyiIn suL z°*g oanstTy

syen:id
ado9s0411960 sioqse9 Ni i
Suljdwes Md LO 6 U 0S
i , ¢
S ee

@ ® |@®@ \
piesa < $l281U09
aT |

asind 146;
PuodIasodid

-104-

and MPC effects by following the treatment of Beer [27a]. The
current density j that arises from electric and magnetic fields is

given by

jroyh*+agh"xB 8.1

where £" is defined as

B'=f'+ vt /e 8.2

and where # and 4 are the applied electric and magnetic fields. ¢
is the chemical potential, which, in the case of a classical (nonde-
generate) Maxwellian semiconductor is related to particle gra-

dients by
—im Vn
Ve=kT-—- 6.3

For sufficiently small magnetic fields, that is, for the cyclotron fre-

quency eB/m small compared to the collision time r, oy and ay are

given by
e® p_ de ofa 05
2 a
e ae Sfo eT 78, 6.5

On he ak, de m*

where f. is the carrier distribution function, r is the collision time,

-105-

‘k& is a single component of the momentum, and m’ is the effective
mass of the charge carrier. We assume a Maxwellian distribution

function, fo=ef-*“*" and evaluate oy and ay

e*h® e2n
= ar k*a 3k =——_—__——
78 anime Tho 3kT 6.6
eth? 2 233 e°n
= —— 2 ftp yk? eal Be
Oe anim el Fo 3mk1 8.7

We have used the relationships e=A*k?2m*, and k=m‘v/h, and a
Maxwellian form for f,. The brackets <> represent an average
value obtained from integrating the term within the brackets with

the distribution function fp.

We insert Equations 6.6, 6.7, and 6.2 into Equation 6.1, and ob-

tain

- ne®*f | e®¥n
SAT 3

6.8

. nerun xB
8m *kT 3m."

We recognize the first term in Equation 6.8 as the common expres-

sion j=nez£, where »is the carrier mobility. Thus, we have

_e
3kT 8.9

The second term is the diffusion expression joenD 2. By compar-

-106-

ing the first two terms, we then have the Einstein relation

pa Hk?

@ 6.10

The third term describes a current flow in the direction of #xd,
that is, toward or away from the surface (according to the
geometry specified in Figure 6.1). This is the MPC effect. The mag-

nitude of the current density toward or away from the surface is

+ ner= = . 6.11
JMPC 3m eT =ne uw pylxe

where py is the Hall mobility, defined to be [27b]

2

om 6.12

The fourth term in Equation 6.8 involves a current perpendicular to
the magnetic field and the carrier gradient, i.e., in the x-direction
(See Figure 6.2). This current density is present in the absence of

an electric field; it is the PME effect. Its magnitude is

» _etun x8
-_ *

=epupBDVn 6.13
JPME am HH.

Let us compare the relative magnitudes of the photoconduc-

tive PC and PME current densities. The ratio of jpyr and jp, is

jpur _ euyBDVn _ BD vn
Jpc ne ut ne 6.14

-107-

Here, we take the conductivity mobility and Hall mobility to be
equal. In our experiment, E was typically 5x10° v/m, and D was tak-
en to be 8.2x10~m?/sec. The initial (t=0) value of ¥n//m is -a, the ab-
sorption coefficient; we can take this figure for an upper limit on
Vn /n, since the overall gradient of the carrier distribution will de-
crease with time due to diffusion. The magnetic field was 15 kilo-
gauss. Thus, the ratio of the current densities is approximately
1072. Hence, the current due to the PME effect will be small com-
pared to conduction current due to the applied electric field. Con-

sequently, the PME effect will only be observed when E=0.

We have derived expressions for the current density arising
from the application of a magnetic field to a semiconductor. The
result for the MPC effect will be included in the differential equa-
tions which relate current flow toward the surface to enhanced sur-
face recombination. The PME current pulse that is produced upon
illumination of the opto-electronic switch is directly proportional

to the current density described above.
6.1 Ultrafast PME; Theory and Experiment

The PME effect under ultrafast illumination can be described
in terms of the carrier concentration expression developed earlier.
The result obtained above can be seen intuitively by assuming that

the carriers have an average diffusion velocity in the y-direction

-108-

= —2 an

Uy= n dy 6.15

where n(v,t) is given in Equation 5.23, and D is the ambipolar
diffusion. In the presence of the magnetic field B, the carriers gain

a velocity component in the x-direction

Uz = Uy By =U, UB 6.16

where @,=8 i8 the Hall angle. Thus, the current density in the x-

direction at a depth y is
dy

which is the same result as Equation 6.13. In our analysis, we take
the magnitude of the Hall mobility and the conductivity mobility to
be the same; Philadelpheus and Euthymiou [28] find that the two
mobilities are nearly identical in samples of Cr:GaAs with nearly
equal electron and hole concentrations. We assume that during the
time of cbservation (<100 psec), the concentrations of electrons
and holes remain nearly the same. Thus, we use their result of
#=3000cm*/u-sec for electron mobility, and a ratio of 20 for u,/~,.
To an accuracy of five percent, then, we can ignore the contribu-

tion of holes to conduction.

The total current i passing into the contacts is the integral

-109-

on
i(¢)= i(y dy =ew wBD ——d 6.18
i(t)=wfi(y)dy=ewuBD foo dy

where e is the charge of an electron, and w is the width of the con-

tact. We intégrate directly to obtain
i(t )=ew uBD {n(0,t)—n(~,t )}=ew wBDn (0,t) 6.19
or, using Equation 5.23,

i(t)= ZewunabBD | -1.aW (av Dt \-y¥ (yv0t ) 6.20
"AT CGpuise any

where r is the bulk recombination lifetime, and the other constants

are the seme as in Chapter 5.

The PME pulse reflects only the preponderance of carrier
movement into the bulk; the pulse only exists for as long as there
is a preferred direction of the diffusion velocity. Since this
diffusion velocity is proportional to the slope of the curves shown in
Figure 5.2, the diffusion velocity ceases having that preferred
direction when there is (roughly) as much of the curve n(y,t) on
the left of the maximum as there is on the right. Thus, the average
diffusion velocity can approach zero while there are still plenty of
photocarriers present in the material. Consequently, the PME
pulse is faster than the magnetophotoconductivity (MPC) pulse. It
is so much faster, in fact (theoretical FWHM=5 psec), that our pro-

pagation and detection system was completely incapable of resolv-

-110-

ing any of its features. An instrument limited pulse wes seen with a
FWHM of 50 psec; the amplitude was low (160 microvolts across 50
ohms), and was most effectively monitored with the signal averag-

ing systern.

Since there was no method of resolving the PME pulse shape
or width, the only useful data emerging from the experiment was
the total charge in the current pulse. The PME pulse passed
through a filtering process which presumably did not attenuate the
DC component of the pulse. Thus, the integral of Equation 6.20

should match the total charge observed in the experiment.

The integral of Equation 6.20 is

rer = Zew pnaeBD Tt
tet ATC Opuice (@VD T+ 1)(yVD r+1) 6.21

The pulse contained ¢@=2x10° photons, B was 15 kilogauss, the

diffusion coefficient D is 6.2x10~cm?/sec, the Fresnel reflectivity

=0.32, the absorption length 1/a = 2300 angstroms,

1-1 =

nol
nmi

the mobility ~=3000 cm®/volt-sec, and y=s/D, where the surface
recombination velocity s=5x10§ em/sec. The bulk recombination
rate was r= 250 picoseconds, so the diffusion length VDr was 4500
angstroms. The microstripline width WwW, was equal to the diameter

of the laser spot, which was 2mm.

-111-

The total Q, therefore, was 1.1 x 10-5 coulombs. The total ob-
served charge was 160 microvolts across 50 ohms for 50 pi-
coseconds, which corresponds to 1.6 x 10° coulombs. Since the
carriers were not forced into the contacts to be detected, many
carriers simply diffused under the contacts and recombined. For
those carriers that were so deep into the crystal that no replace-
ment charge could be drawn from the contacts, a local field would
build up as the charges separated that would arrest the motion of

the carriers. This may account for the small observed signal.
6.2 Ultrafast MPC-Theory

The analysis of MPC parallels that of the photoconductivity
derivatior. in Chapter 5. It is necessary to include ihe magnetic
drift term in the diffusion equation and in the surface boundary

condition that was derived in Section 6.0. —
jupc = new®hxB | 8.22
This expression is added to the current equation (5.10)
j=-eD int+enul tne pti xB 8.23

(here, £=£7, and #=B8F) and to the surface boundary condition

Eqn. 5.13 at the y=0 surface

-112-

pit eg HEB =ns 6.24

ayy

We recall that the surface recombination velocity is the ratio of
. carriers that recombine per unit time and area to the surface car-
rier concentration. The right hand side of Equation 6.24 is this rate
of carrier recombination per unit time and area. This must be
equal to the number of carriers that arrive at the surface per unit
time and area, which is given by the sum of the diffusion current

and the magnetic drift.

The continuity equation remains the same as Equation 5.9 ,

on

=-vj- 8.25

4|3

and the other boundary conditions are unchanged as well. Assum-
ing that n is constant in the x and z directions, the resulting

differential equation is

an _ 7, 3®n an _n 6.26
vam, ay? Ok ay =
where
pall Be 6.27
2D

The solution of Equation 6.26 is related to the B=0 solution in

a straightforward manner [29]. Assume that a function h(y,t)

-113-

satisfies the B=0 differential equation and boundary conditions,
Equations 5.11-5.13. h(y,t) will be equal to Equation 5.23. Now con-

sider a function n(y,t), such that
n(y,t =e FWD )h (yt, ara-k, yry—k) 6.28

where the constants a and y are replaced with a-k and y-k, as indi-
cated. We will now show that the function n(y,t) as defined in Equa-
tion 6.28 is a solution to the differential equation (Equation 6.26)

and its boundary conditions. First, we note thal the presence of
the term + in Equation 6.26 merely introduces a factor e~'/T in

the result; since both differential equations have this terrn, we
need not carry it through the derivation of n(y,t). Inserting Equa-

tion 6.28 into Equation 6.26, we obtain

—— =D |———— 2 -—— + +2Dk—~—- 8.239

Using our assumption that h(y,t) satisfies Equation 5.11, we see
that the equality in Equation 6.29 holds. Now we must verify that

n(y,t) in Equation 6.26 satisfies the boundary conditions.

First, we show that n(~,t)=0. Since the B=0 carrier concentra-
tion decreases at least as fast as e-¥"““)t according to Equation 5.23,
then, regardless of the sign of k in the exponential in Equation 6.28,

n{y,t) will always vanish for sufficiently large y.

-114-

The initial profile of h at t=0 is noe. We substitute a-& for a,

and see that
ny, O)=e ~*¥h(y, O)=n9 ef-*-(9-* Wan pe 6.30

Thus, the t=0 initial condition is satisfied. Since h=0 for t less than

zero, n will be zero prior to ilumination as well.

The last boundary condition is the surface recombination ex-

pression Equation 6.24. We rewrite Equation 6.24 in terms of k and

y=s /D
io . 6.31
n ay y=0
Inserting Equation 6.28 into 6.24, we obtain
1 ah 6.32
—f +—~——— oye
k Rk By ys0 72k

Since h satisfies the surface boundary condition, we may replace

1 oh

h By with y-k, and observe that the boundary condition is satisfied.

Hence, the relationship between the B=0 case and the MPC effect

stated in Equation 6.28 is valid.

The function n(y,t) taken from Equation 6.28 is shown graphi-
cally in Figure 6.3 as a function of the distance into the material
with the time t as a parameter. The three sets of curves show the

carrier concentration profile at successive times under a magnetic

NORMALIZED CARRIER DENSITY

~115-

B= 15 kilogauss
S=5 x 105 cm/sec
T= 250 psec
es ae —+ 3
! i i “ |
Oj 1 ' 8.200. | O.400 0.600 0.800 1.000
| \teo-peee-—--——}_— | - -. ... MICRONS

ft: 9.200, |) «9.400 0.600 0.600 1 .Ga0
____.'_. MICRONS

B= -15 kilogauss

0.400 e.60c 0.800 1.cac0
MICRONS

Figure 6.3 Theoretical curves of carrier concentration as
a function of time, distance into the medium, and
applied magnetic field.

-116-

field B=15kgauss, B=0, and B=-15kgauss. The geometry is such
that the carriers are impelled toward the surface for positive B,
and pushed into the bulk for negative B. It is clear that the surface
recombination rate, which is proportional to s-n(0,£), is greatest in
the top curves, and least in the bottom curves. In fact, since n(0,t)
is drawn almost immediately to zero in the bottom trace, the sur-
face recombination is almost completely suppressed. The condition
for suporession of surface recombination is Dk>>Dy, that is, the
magnetic drift velocity must be much greater than the surface

recombination velocity. Thus, the B-field must be much greater

than a. In our experiment, this condition was satisfied if the B-
it

field greatly exceeded 12 kgauss. Since we used 15 kgauss, the sur-
face recombination was not entirely suppressed; however, the data
obtained in a negative B-field closely approximated the character

of a s=0 measurement.

The data obtained from photoconductivity tests is sensitive to
the total charge present in the material. Thus, the current pulse

will be proportional to the integral of the charge distribution:

i(t)=we uk fn (y.t)dy 6.33

where w is the stripline width, and n(y,t) is the carrier concentra-
tion under the influence of the magnetic field. Performing the in-

tegrai, we obtain

~-117-

6.34 i(t)=

2we pi noe /-0F tk (a hy AW praly Dk Ue t yk Soh |
Are puss (ame NE= Vaal)

where W,=W(ivDt ), with W(z) defined above, and where the above
-substitutions for a and y must be performed. Plots of Equation
6.34 are shown in Figure 6.4. Shown are curves of current versus
time; this would be the output of aninfinitely fast oscilloscope. Ac-
tual data will reflect the finite bandwidth of the transmission and
detection system. Since the carriers experience enhanced recom-
bination when they are forced to the surface, a B-field of the prop-
er sign wiil decrease the width of the current pulse, and vice versa.
The effect of the finite bandwidth of the detection system will be to

reduce the apparent height of the narrow pulse as well.
6.3 Ultrafast MPC-Experiment

The MPC data was obtained by repeating the photoconductivi-
ty experiments in the presence of a magnetic field. Special pole
faces were constructed for the magnet in order to maximize the
field in the region of the GaAs chip. The separation of the conical
pole faces was 2mm (the width of the chip), and clearance for the
microstripline was cut into the pole faces. This maximized the lo-
cal B-field at the chip, and minimized the impedance contribution
from the grounded metal pole faces. The magnet drew 10 amperes
at 100 volts, and produced 15kgauss at the location of the chip as

measured with a gaussmeter.

Current (Arbitrary Units)

-118-

B= -15 kilogauss

S= 5x10°cm /sec
T= 250 psec

B= +15 kilogauss

t 1 {
1.010

Nanoseconds

1.0

Figure 6.4 Theoretical curves of current as a function

of time and magnetic field

-119-

Early measurements involved storing several separate photo-
conductivity traces on magnetic tape. Each trace represented
data obtained using different magnetic field intensities, and each
was the average of several seconds of sampling oscilloscope sweeps.
The dye laser pulse amplitude, however, did not always remain
stable over the time necessary to acquire the several traces. As a

result, the first traces were inconsistent with the last traces.

A means of data acquisition was devised that was insensitive to
dye laser fluctuations. Since it is the product EB that determines
the nature of the magnetic effect, it was decided that the magnetic
field be kept constant, and the electric field (the voltage across the
gap) switched rapidly frorn one polarity to the other. Rapid switch-
ing of the magnetic field was deemed impractical. A routing circuit
was devised which passed the positive E-field photoconductivity
pulse trace to one half of the memory of the signal averager, and
inverted and passed the negative data to the other half of the
memory. Thus, two traces were simultaneously stored into
memory, one demonstrating the effect of carriers driven into the
bulk of the semiconductor, and the other showing enhanced sur-
face recombination. The amplitude was recorded with 12-bit reso-
lution, and the sweep was digitized to a density of four channels
per picosecond. This data was written onto magnetic tape to be

processed on a computer. Each sample was previously tested to

-120-

verify that it was isotropic to current flow in either direction in

order to ensure accurate interpretation of the data.

The FORTRAN program used to analyze the data read a record
from the tape and smoothed, normalized and sampled the data into
a 128 elernent array. Another array was generated using Equation

6.34 . This analytical array was filtered with a Gaussian filter hav-
ing a bandwidth associated with a risetime of 30 picoseconds (the
risetime of the detection system). The filtered array was com-
pared to the experimental data by means of a least-squares non-
linear parameter curve fitting routine. The adjustable parameters
given to the fitting routine were the vertical scale, the horizontal
position, the bulk recombination rate, and the surface recombina-
tion velocity. The results of such calculations are shown in Figure
6.5 and 6.6 for switches of different surface preparations; the solid
lines are the experimental data, the symbols indicate the analyti-

cal curves.

It is clear that the magnetic field increases or decreases the
overall lifetime of the carriers. We see in Figure 6.5 that the width
of the first pulse is approximately double that of the second pulse.
The height difference is a result of the finite speed of the detection
system; both pulses have the same initial amplitude at the gap, but
the narrower pulse is more broadened and reduced in height due

to the attenuation of its high frequency components.

-121-

spuodasoueN

s * e e ° e ® Z2°O 0°0
oj 249 9,70 4140 250 0°0/p°t B40 9,°0 4720 °

9asdgsz =1,
998/W9 OLXSZ= §

; *9081}, puodas ayy uy adezans ay. paeMo4
pue ‘aol, SITS ay, uy TeySA19 eya Jo yTNq ayy OUUT
peot0F Ste SLazIIVQ *ALPOOTSA UOT eUTQUODeA aoesans

(sun Aseayiquy) yuadiNnd

USTU B ayerTZUET 04 peysttod ATTwoTueYyoeu sem syenray
ey} fO adejains sug *seaano A4TATLONpUCSO}oYdoy suse
(SToquks) TeoTxa209uN4 pues (®arnd py{Tos) Teyuewuyzedxq G*9g aaNet

SPUuOdsasSOURN

ot 80 90 vo 20 00/01 80 90 +0 20 00

gesd osz =2L

-122-

9938/9 OLx6=S

*390819 puodcsas sy UT edeJaunS ayy paeMoy pue ‘aoRIy
YSATT BYyQ UT TeVISAID ayy Jo YTnq ayy o4Uy paosoys

Ble SIaTIIVD *APTOOTSA UOTZBUTQUODSaA sdeJaANS |ayuy
sonpser Of YO¥S PTO" OTAZTO eB YYTM pdazvaTy SEM Syeng
ayy JO sdeJANS ay, “Saaano AZTATZONpUuO.OYZoUdOZsUFEeU
(SToquAS) [wOTZaZ0aY44 PUB (@AAND PT{Os) [Te usuTIedxy 9°9 eanzty

(sHun Asesjiquy) yuaing

-123-

6.4 Summary of the Experimental Results

We see that the fit between the theoretical and experimental
curves ig very good, and, equally as important, the fit is inflexible
to variations of sand r. Without the magnetic field, the parameters
were extablished to within an accuracy of an order of magnitude
for r, and to many orders of magnitude for s [12]. The magnetic
field nearly eliminated this flexibility of the fitting process, and
determined both parameters such that a satisfactory fit was ob-
tained only within a range of ten percent of the parameters. This
range was found by providing the fitting program with a wide
variety of initial estimates for s and r. Regardless of the initial esti-

mates, the final best-fit parameters fell within a ten percent range.

The parameters returned from the fitting routine compare
favorably with material parameters determined by other investiga-
tors. The bulk recombination rate was quite uniform over the col-
lection of switches tested; +r was determined to be 250450 pi-
coseconds. Our value of + agrees well with CW photoconductivity
measurements taken under high illumination intensity (7r=250
psec. [30]). Lower intensity CW measurements show longer life-
times (many nanoseconds) due to the presence of traps in the ma-
terial with long occupation times [30-32]. A trap can be regarded
as a recombination center with a higher probability of thermal emis-

sion of a captured electron (or hole) than ionized capture of a

~-124-

hole (or electron). Thus, a trap will extend the lifetime of one
species of carrier by isolating it from recombination with the other
species. The higher the concentration of traps, the greater this
‘lifetime extension [33]. Under high level optical excitation, there
will be a sufficient number of free carriers to populate all the traps
without depletion of the free carrier supply. Hence, the free car-
rier lifetime will be unaffected by the presence of the traps. Under
6 -functicn illumination, the occupation of these long-lived trap
states is negligible for the hundred picoseconds of observation, so
our good agreement with the high intensity measurements is ex-

pected.

The surface recombination velocity was calculated to be from
8x10 cm,/sec at a surface passivated with a citric acid etch [16]
(See Figure 6.6), to 7.5x10§ cm/sec at a mechanically polished sur-
face (See Figure 6.5). These values are in good agreement with
luminescence studies which determined s to be §&x10* and 10°
em/sec, for the respective surface preparations. We saw no mag-
netic field effects for the GaAlAs switch; this observation was con-
sistent with theoretical predictions using the established value of s
at the heterostructure interface. Hence, that switch reflected the

recombination activity of the bulk and not the surface.

We have seen that the fast photoconductivity of Cr:GaAs can

be explained with a model of carrier dynamics that involves surface

-125-

and bulk recombination processes. However, the uncertainty in
determining recombination parameters through ultrafast photo-
conductivity alone can be as high as several orders of magnitude.
The combination of a high surface recombination velocity and low
bulk rate may yield photoconductivity pulses indistinguishable
from those produced by a low surface rate and a high bulk recom-
bination rate. The introduction of the magnetic field reduces this
uncertairty for a single device to approximately 10%. There is a
measure of the degree of correlation between two parameters that
is used in nonlinear parameter fitting. This correlation coefficient
(an element of a matrix in numerical analysis commonly called "r’

ranges between i and -1, with the extreme values designating high
correlation and with 0 indicating complete lack of correlation [34].
When the fitting routine is performed on a single pulse, the correla-
tion coefiicient between the surface and bulk parameters is 0.96.
When two pulses obtained under different magnetic fields are treat-
ed simultaneously by the routine, the coefficient drops to 0.16.
This indicates the dramatic improvement in parameter estimation
when the ultrafast photoconductivity of a material is studied in a

magnetic field.

Thus, the technique of ultrafast magnetophotoconductivity is
a useful new tool for the succesful determination of recombination

parameters in semiconductors. Recent advences in mode locked

-126-

dye laser technology, such as broadband tunability and Gigawatt
output pulse powers, will enable an expansion of this diagnostic
method to a wider range of materials to learn more about carrier

recombination phenomena on a picosecond time scale.

ao oO FSF WwW FP

- 10.
11.
12.
13.
14,

15.
16.
17.
18.
19.
20.
21,
22.
23.

-127-

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~~

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-128-

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