THz Transceiver/Two-Photon Absorption
Autocorrelator
by
Juan Montoya
Submitted to the Department of Electrical Engineering and Computer
Science
in partial fulfillment of the requirements for the degree of
Master of Science in Electrical Engineering and Computer Science
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
August 2002
@
Massachusetts Institute of Technology 2002. All rights reserved.
........................
A uthor .....
Department of Electrical Engineering and Computer Science
August 9, 2002
Certified by..
Qing Hu
uter Science
Professor of Electrical Engineering and Co
Thesis Supervisor
.......
Accepted by ............
Arthur C. Smith
Chairman, Department Committee on Graduate Students
HAA~USETS WKS1ITUTE
~TECHWXOGoY
NOV 1 8 2002
BARKER
L1RRE
THz Transceiver/Two-Photon Absorption Autocorrelator
by
Juan Montoya
Submitted to the Department of Electrical Engineering and Computer Science
on August 9, 2002, in partial fulfillment of the
requirements for the degree of
Master of Science in Electrical Engineering and Computer Science
Abstract
In this thesis I will investigate the design of a THz transceiver and explore a novel
application of our device which uses two-photon absorption as a mechanism to detect
ultrafast optical pulses. This thesis naturally divides itself into two separate parts. In
particular, this thesis is in part a continuation of a previous study done in this group
which explores the use of LT-GaAs as a source for opto-electronic generation of highfrequency (- 1THz) signals. In the first part of the thesis, I will present the design
considerations of our device which includes a discussion of material properties and
coplanar waveguide geometry. Furthermore, this part of the thesis will present and
discuss the data which has been obtained through our continued research which has
yielded further insight into the temporal response characteristics of LT-GaAs under
high illumination and bias conditions. The second section of this thesis will explore
a novel application of our device which utilizes a two-photon absorption principle to
detect ultrafast pulses. The theory and merits behind this principle will be discussed,
along with a model which describes our measurements. This is followed by a brief
discussion of the feasibility of using a two-photon absorption excitation mechanism
as a source for THz generation. Finally, our experimental data will be compared with
alternative methods for detecting ultrafast pulses to verify our results. Namely, we
will compare our results with a single-photon absorption measurement technique and
a second harmonic generating crystal measurement.
Thesis Supervisor: Qing Hu
Title: Professor of Electrical Engineering and Computer Science
Acknowledgments
I would like to thank Professor Qing Hu for his leadership, mentorship, and for
granting me the opportunity participate in this exciting project and the flexibility
to look at it from different angles, and different wavelengths. I would also like to
thank all the members in our group for their assistance and invaluable discussions
throughout this project. In particular, I would like to thank Ben Williams and Hans
Callebaut for their help with the wire bonding of the devices, and Sushil Kumar for
the SEM photographs.
I would especially like to thank Professor Rajeev Ram for being so generous as
to allow me to setup in his lab and use his equipment for the two-photon absorption
experiments. I would also like to thank the members in his group, Harry Lee and
Mathew Abraham for their help with the equipment. Finally, I would like to greatly
acknowledge Song Ho-Cho for his help with installing the fs optics in the laser and
for his assistance with the SHG crystal measurements.
The formerly mentioned people had a direct impact on the success of this project.
I would also like to thank Dr. Nader Hozahbri and Professor Kambiz Alavi for helping
me get started in this field, and my family for their encouragement and support.
Contents
1
Introduction
11
2
Low Temperature Grown GaAs
15
3
2.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
2.2
Dark Resistance vs Annealing Conditions . . . . . . . . . . . . . . . .
16
2.3
Carrier Lifetime vs Annealing Conditions . . . . . . . . . . . . . . . .
19
2.4
Shockley Read Hall Rate Equations . . . . . . . . . . . . . . . . . . .
23
27
LT-GaAs Single Photon Absorption CPW Autocorrelator
3.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
3.2
Coplanar Waveguide Geometry
. . . . . . . . . . . . . . . . . . . . .
27
3.3
Single Photon Absorption LT-GaAs Autocorrelator
. . . . . . . . . .
30
3.4
Carrier Lifetime Limited Autocorrelation: Optical Impulse Response .
39
3.5
High Field Effects on Carrier Lifetime . . . . . . . . . . . . . . . . . .
40
High Field Carrier Capture Lifetime Experiments . . . . . . .
49
3.6
Pump and Probe Experiments . . . . . . . . . . . . . . . . . . . . . .
54
3.7
Experimental Setup and Measurements . . . . . . . . . . . . . . . . .
57
3.5.1
61
4 Two-Photon Absorption Autocorrelation
Introduction . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . .
61
LT-GaAs Two-Photon Absorption Motivation . .
. . . . .
62
4.2
Two Photon Absorption : Classical Model . . . . . . . .
. . . . .
64
4.3
Tensor Form of Two-Photon Absorption
. . . . . . . . .
. . . . .
67
4.1
4.1.1
5
4.4
4.5
5
Two Photon Absorption Rate Equations . . . . . . . . . . . . . . . .
68
4.4.1
Two Photon Absorption Circuit Model . . . . . . . . . . . . .
74
Experiment and Conclusions . . . . . . . . . . . . . . . . . . . . . . .
79
4.5.1
79
Two Photon Absorption Discussion of Results . . . . . . . . .
Concluding Remarks
85
A Laser Operation
91
A.0.2
Start-Up Procedure . . . . . . . . . . . . . . . . . . . . . . . .
91
A.0.3
Beam Alignment
. . . . . . . . . . . . . . . . . . . . . . . . .
92
A.0.4
Mode-Locking the Tsunami Ti:Saphirre . . . . . . . . . . . . .
93
A.0.5
Shut-Down Procedure
94
. . . . . . . . . . . . . . . . . . . . . .
B Appendix: Measurement Circuits
95
C Appendix: Linear Delay Stage
99
6
List of Figures
2-1
Annealed LT-GaAs Density of States from [34]. . . . . . . . . . . . .
2-2
Pump and Probe Differential Transmission from [20] for various an-
18
nealing temperatures. Note that the as-grown materialfor the two samples with (.52%) and (.25%) excess arsenic have the fastest response
time when compared to the annealed samples. Also note that the sample with .02 % excess arsenic shows a much slower response time as a
result of trap-filling. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-3
21
Log plot of Differential Transmission from [20]. At low intensity, the
sample with .02% excess arsenic shows a response involving two time
constants. The first time constant corresponds to filling the traps. The
second time constant describes the trap emptying time, and dominates
when the traps are filled. . . . . . . . . . . . . . . . . . . . . . . . . .
22
. . . . . . . . . . . . . . . . .
23
2-4
Electron/Hole Capture and Emission.
3-1
Coplanar Waveguide Geometry illustrating dimensions used for calculating the characteristicimpedence. . . . . . . . . . . . . . . . . . . .
3-2
28
Top view of the coplanar waveguide illustrating the photoconductive
gaps in the center conductor. The shaded region representsgold regions,
while the unshaded region represents LT-GaAs.
3-3
. . . . . . . . . . . .
31
Cross sectional view of the coplanar waveguide photoconductive gap.
The top layer consists of the low-temperature grown MBE GaAs. While
the 620 0 C layer corresponds to normal GaAs.
7
. . . . . . . . . . . . .
32
3-4
Photoconductor Geometry used in calculating photoconductance. The
current direction is denoted as i.
3-5
. . . . . . . . . . . . . . . . . . . .
34
Carrierlifetime limited autocorrelationperformed at an incident wavelength of 850 nm from which a carrier lifetime of
Te
= 1.3 ps is ex-
tracted. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
3-6
InterdigitatedElectrodes, 1.8,um gap size. . . . . . . . . . . . . . . . .
42
3-7
Nonlinear I- V characteristicsfor various CW intensities. . . . . . . .
43
3-8
Poole-FrenkelBarrierLowering. . . . . . . . . . . . . . . . . . . . . .
44
3-9
I-V Characteristic on a (a)linear scale (b) log-log scale.
The solid
curve represents the measured characteristic while the dashed curve is
obtained from our model. In (b), three regions are shown which correspond to an ohmic region, barrier lowering, and an avalanche breakdown. 50
3-10 Autocorrelation measurements taken at three different bias voltages,
showing capture time dependence on applied bias; (a) for time average incident power of Pavg= 4 mW and (b) Pavg=13mW and (c)
Pavg=30mW. In (a) and (b) we note two time constants, as the power
is increased in (c) only one time constant is observed. . . . . . . . . .
52
3-11 Typical pump and probe measurement, Pg = 30 mW, Vc = 30 V, A
= 780 nm........
..................................
56
3-12 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
4-1
Two-Photon Absorption Dynamics in LT-GaAs from [21].
68
4-2
Zscan Measurement used to determine the two-photon absorption coef-
. . . . . .
ficient from [2]. At the position of the beam focus, z=0, the incident
intensity is maximum and two-photon absorption reduces the optical
transmission. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4-3
70
Intensity spectrum of a gaussian input intensity beam with a 100 fs
pulse duration. Also shown is the ideal filter function presented by the
4-4
finite response time of the photoconductor. . . . . . . . . . . . . . . .
76
Circuit for TPA Measurement. . . . . . . . . . . . . . . . . . . . . . .
77
8
4-5
TPA autocorrelationfrom a speaker measurement at Pag=30mW, A =
900 nm, Bias=30 V. A half wave plate was used to minimize coherence
effects and to obtain the minimal pulse width.
4-6
. . . . . . . . . . . . .
80
TPA autocorrelationfrom a speaker measurement with Pavg=170mW,
A = 900 nm, Bias=-30 V. A half wave plate was used to minimize
coherence effects and to obtain the minimal pulse width. . . . . . . . .
4-7
81
TPA Lockin Measurement with A = 900 nm, Pavg=50 mW, Bias =
20V. A half wave plate was used to minimize coherence effects and to
obtain the minimal pulse width. . . . . . . . . . . . . . . . . . . . . .
B-1
82
Transimpedence amplifier used to measure photocurrent to perform autocorrelation and pump-probe experiments. The gain is determined by
Rf and is set to 1M Q. . . . . . . . . . . . . . . . . . . . . . . . . . .
96
B-2 Transimpedence amplifier which uses a dc blocking capacitor to remove
the undesired dc signal. The high pass filter cut-off frequency is determined by choosing the values of R 1 C1 , and the gain is determine by
Rf. ........
....................................
96
B-3 Load resistor (for low frequencies) which may be used to measure the
photo-current. While the resistor loads the low frequency components
of the circuit, it presents an arbitrary termination for the high frequency currents propagating through the transmission line. A typical
load resistor value of R=1 MQ may be accomplished by using the input
resistance of the measuring oscilloscope. . . . . . . . . . . . . . . . .
9
98
10
Chapter 1
Introduction
In this thesis we will investigate the design of an ultrafast transceiver capable of
opto-electronic generation and detection of frequencies with a 3dB bandwidth of up
to 800GHz. This frequency capability has found multiple applications such as optoelectronic characterization of ultrafast laser pulses, communications, spectroscopy,
imaging, semiconductor characterization, and fast A/D conversion. The motivation
for this study is to develop a high-frequency transceiver which may be utilized for
the future development of a high frequency network analyzer capable of producing
S-Parameter measurements of high-frequency
(>
200 GHz) electronic devices.
Prior work in this project by Zamdmer and Verghese et al has established a
framework for describing the operation of a THz transceiver. Our goal in this thesis
is two-fold. First, we would like to present our results to provide a complementary
study which expands on the conclusions which have resulted from previous work by
providing detailed models and novel insight which have resulted from our continued
research. Secondly, we would like to present a novel method of detecting ultrafast
pulses on our transceiver by utilizing a novel principle of operation, namely twophoton absorption.
One of the first questions that needs to be addressed when designing a high frequency transceiver involves frequency generation. One feasible method of generating
a high frequency signal involves opto-electronic generation. Ultrafast lasers and continuous wave lasers may be utilized toward this end. Since large bandwidth optical
11
frequencies are easily obtainable, the bottleneck to high frequency generation is in
the photoconductor.
There are multiple photoconductive alternatives which may be utilized to detect
high frequencies in a circuit geometry. The three basic types of responses from photodetectors may be categorized into transit time limited, external circuit RC time
constant limited, and recombination time limited [5]. The external RC time constant
may limit the response of a device based on the geometry of the photoconductor.
In our devices, which utilize an interdigitated finger geometry with a gap spacing of
1.8pum and finger width of 200 nm on a 10 x 10 pm strip, the capacitance is approximately .4 fF [29]. The RC time constant of our circuit is determined by using the
transmission line impedence as the effective resistance, R=50 Q. Using this value for
R, we find that our device is not limited by the RC time constant which would result
in
TRC =
20 fs. Furthermore, the fastest transit time limited device has been fabri-
cated using GaAs with .5 pim gap spacing resulting in a 4.8 ps FWHM response. For
our material, assuming a saturation velocity of approximately
Vsat =
107 cm/s
the
transit time would be limited toTtt - 20 ps, which is much slower than our observed
transients [8]. Therefore, we conclude that with our geometry our photoconductor
functions as a recombination limited photodetector. The first chapter discusses the
merits of LT-GaAs as an ideal photoconductor with an ultrafast recombination time.
Coplanar Waveguide (CPW) transmission line geometries suitable for the propagation of high frequency signals will be the subject of chapter three. Here we will
discuss the geometrical factors which are involved in the calculation of the characteristic impedence of the transmission line. In addition, this chapter will discuss some
of the advantages of using a coplanar waveguide.
Once the transmission line and photoconductive switch are fully characterized, we
present some applications of the high-frequency transceiver. As discussed in chapter
three, we will explore an application which involves a carrier-lifetime limited autocorrelation of optical pulses. This optical autocorrelator could be used to characterize
pico-second pulses, and could also be utilized as a diagnostic tool to measure the
carrier lifetime of low-temperature grown GaAs. A study of this lifetime will be pre12
sented since it is critical for understanding the limitations of the bandwidth in our
transceiver.
In chapter 4 we will discuss a novel method to detect ultrafast pulses using LTGaAs. This method utilizes a two-photon absorption technique to perform an optical
autocorrelation which is not limited by the carrier lifetime of the material. Since twophoton absorption (TPA) requires large peak intensities, it is important to estimate
the carrier densities which are being generated throughout LT-GaAs. A model is
presented which could be used to estimate the carrier concentrations as a result of
using TPA as an excitation mechanism. Moreover, the implications of this model for a
THz transceiver are described as well as the limitations of the model. In the conclusion
of chapter 4, experimental results will be compared to a second harmonic generating
crystal autocorrelator. This allows for verification of our operation principles, as well
as validation of our results.
13
14
Chapter 2
Low Temperature Grown GaAs
2.1
Introduction
Molecular Beam Epitaxy GaAs grown at temperatures as low as 200'C (LT-GaAs)
has been an attractive material for fast photoconductive switching applications due to
its unique optical properties
[9].
Low temperature grown GaAs incorporates 1%-2%
excess arsenic during growth at temperatures below the regular growth temperature
of 600'C. This excess arsenic manifests itself in the form of As interstitial (Asi), arsenic antisite
(ASGa),
and gallium vacancy (VGa) defects [23]. These defects govern
the ultrafast dynamics of LT-GaAs and allow for the fastest reported carrier trapping
times which have found applications in high-speed electronic devices. The fast trapping time makes LT-GaAs ideal for ultrafast optical switching applications and THz
spectroscopy.
In its as-grown form, LT-GaAs is too conductive for photoconductive switching applications. However, upon annealing at temperatures above 500'C the excess arsenic
atoms precipitate and form arsenic clusters. The corresponding change in resistivity
increases from p = 10 Q cm to 106 Q cm [26]. This increase in resistivity is highly
desirable for optical sampling applications since it suppresses the dark current. For
a device based on a 2x2 pm 2 photoconductive geometry we have measured a dark
resistance greater then 10 MQ. It is important to note that for slow detection devices, this requirement on the dark resistivity could be relaxed by using a reverse
15
biased P-i-N structure. However, for ultrafast switching applications this is not a
suitable alternative due to undesired capacitance effects which would suppress the
fast response.
Moreover, other features such as the high carrier mobility and fast trapping time
make LT-GaAs a superior material for ultrafast optical sampling applications [9]. The
Hall measured electron mobility in annealed LT-GaAs (600 'C) has been reported to
be as high as
e =
3000 cm 2 /V s [35]. Annealing LT-GaAs has the effect of increasing
the mobility from pe =1 cm 2 /V s to pe = 3000 cm 2 /V s [1].
In this section of the thesis, we will discuss some of the growth parameters of
LT-GaAs which govern the three properties of interest for our applications.
The
properties which we would like to optimize for a high-frequency network analyzer
would include the carrier lifetime which is inversely proportional to the bandwidth, the
dark resistance which improves signal to noise performance by reducing any undesired
background signals, and finally the mobility for an improved responsivity. Specifically,
in the section that follows we will discuss material growth temperature parameters
and subsequent annealing conditions which are necessary for our device.
2.2
Dark Resistance vs Annealing Conditions
In order to explore the dark resistance of LT-GaAs we begin by discussing the density
of states for low-temperature grown GaAs. When GaAs is grown at low-temperatures,
as much as 2% excess arsenic may be incorporated into the material. The lower
the substrate temperature, the more excess As is created [10]. Since annealing LTGaAs changes its material properties, it becomes necessary to distinguish between
annealed LT-GaAs and the unannealed form. The convention has adopted to make
the distinction between the two forms by referring to the unannealed LT-GaAs as the
as-grown material, which we will use here.
There are three main defects in the as-grown LT-GaAs. The donor-like defects
consist of As interstitial (Asi) and arsenic antisite
(ASGa)
defects. The acceptor-like
defect is attributed to the gallium vacancy (VGa). All of these defects are incorporated
16
as a result of the excess arsenic during low-temperature growth of MBE GaAs. Far
infrared absorption and electron paramagnetic resonance measurements have been
used to determine the concentration of the various defects. In as-grown LTG-GaAs,
the unionized donor-like concentration consists of [ASGa
ized fraction of about 5% consists of [ASGa]+
= N
0
-
1020 cm- 3 , and the ion-
= N- = 5 x 1018 cm- 3 . In the
latter, the acceptor-like concentration attributed to the gallium vacancy NH = VGa
is taken to be equal to the ionized antisite concentration. This is a result of charge
neutrality and the assumption that the free carriers are negligible in this material
with thermal excitation [23]. Accordingly, LT-GaAs obeys a compensation scheme to
remain charge neutral. For a compensated semiconductor the acceptors and donors
accept and donate electrons from each other and compensate their effects of changing
the free carrier concentrations as shown in equation 2.1 [32].
(2.1)
n+N- = N+±p
With this assumption regarding the free carriers being negligible, it follows that the
dark conductivity in the as-grown LT-GaAs may be attributed to hopping between the
defect states. It is only after annealing that the hopping conduction is decreased and
the resistivity increases to 106 Q cm [42, 9]. After annealing, the overall antisite defect
concentration decreases by an order of magnitude from ASGa
ASGa
- 1019
=
1020
to approximately
[42.
However, it has been discovered that upon annealing the excess As precipitates and
forms large clusters with a diameter of approximately 6 nm and an estimated density
of 1017 cm- 3 [40]. These observations have been confirmed by transmission electron
microscopy and scanning tunneling microscopes [25]. Moreover, the number of ionized
5 x 1018 cm- 3 to AsGa
As+a defects has been shown to reduce from AS+a
1 x
1018 cm- 3 (below the threshold of electron paramagnetic resonance detection). The
annealed density of states is shown in figure 2-1.
Similarly, the gallium vacancies VGa which act as acceptors in LT-GaAs are reduced from VGa = 5 x 1018 cm- 3 to VGa =1
17
X 1018
c-
3
with annealing [42]. Table
As-precipitates
AsGa+ <I0
Ef
E
ASG
EA )VGa
1
1
/cm
3
I0m/cm
3"CM
1
EV
Figure 2-1: Annealed LT-GaAs Density of States from [34].
2.2 below summarizes these parameters.
Defect
As+a
Asa
As-Grown
VGa
5x 10 18
18
5x 10
1 X 10 2 0
Annealed
< I X 10 18
1 x 10 19
< I X 10 18
Table 2.1: Defect Concentrations in As-Grown and Annealed LT-GaAs.
There are two explanations in the literature for the increase in resistivity of LTGaAs upon annealing. The first proposed model attributes the increase of resistivity
of LT-GaAs due to the decreased hopping conduction of electrons between arsenic
antisite defects after annealing. This treatment is similar to the as-grown treatment
of the hopping conduction. Annealing of LT-Gas reduces the excess arsenic defects
which in turn reduces the hopping conduction. Essentially, the defect concentrations
remaining pin the fermi level to the mid-gap [40].
The second suggested model proposes to treat the depletion of charge around the
metallic arsenic precipitates as metallic Shottky barriers in a GaAs matrix [9]. It is
proposed that the overlap in the depletion regions throughout the material result in
18
the insulating behavior of annealed LT-GaAs.
As expected, there have also been suggestions for a unified model which describes
the evolution of the defect model to the as-precipitate model under different annealing
conditions. For weakly annealed undoped LT-GaAs materials, consisting of anneal
temperatures below the threshold of 600 0C, LT-GaAs could be described by a defect
model [10]. However, beyond annealing temperatures of 600 0 C, the precipates tend
to dominate as the model enters the Shottky regime.
These results on the annealing temperature have profound consequences on the
carrier lifetime behavior of LT-GaAs as we will see shortly. In the section that follows,
we would like to model the mid-level defects as carrier trap sites which dominate the
trapping time of LT-GaAs. As we will see in the next chapter, point defect modeling
will allow us to model the potential due to these ionized defects as coloumbic. While
the Shottky model also acts as a capture center for electrons, the potential due to
these defects would be different but could also be described by an effective cross
section. However, at our annealing temperatures below 600 0 C, the point defect model
dominates over the Shottky model. In addition, we have now provided a justification
for annealing LT-GaAs in order to increase the dark resistance. Specifically, we have
concluded that annealing at temperatures above 600 0C increases our resistivity from
p = 10 Qcm--3 to p
=
106 Qc-
3
[26].
In the next section, we will see that this
increased dark resistance comes at the expense of a decrease in capture time.
2.3
Carrier Lifetime vs Annealing Conditions
Since a fast carrier lifetime is desired for a THz transceiver application, we will investigate the carrier lifetime verses annealing conditions for LT-GaAs. Here we will
describe the optical pump and probe measurements which were performed by Melloch
to characterize various LT-GaAs samples under different growth conditions [9].
These types of experiments are important in that they provide a method to characterize the LT-GaAs material after growth. This experiment could be used as a
diagnostic tool to characterize the response time of the material in order to verify
19
growth quality before applying the extra processing steps to develop our devices. In
addition, the pump and probe setup requires only slight modification in order to
perform the autocorrelation experiments to be described in the next chapter.
Finally, the fundamental carrier dynamics are illustrated in this experiment with
various intensity conditions. This will have profound implications to be considered
when explaining our data in the following chapter. The important results which will
be described here will illustrate the effects of saturating the traps at high intensities.
In Melloch's experiments, a differential pump/probe experiment was performed in
order to characterize the carrier capture time of LT-GaAs [20]. In these experiments,
the pump pulse generates electrons in the conduction band and holes in the valence
band. These generated hole-electron pairs result in increased band-filling which increases the transmission of the probe pulse. Essentially, the probe pulse absorbs less
as the available states in the conduction band are decreased. The decreased absorption that the probe pulse encounters could be described by equation 2.2 as given in
[3].
'N,P,E-
In equation 2.2,
f,
and
fc
K
E VET
Eq [f - fc]
(2.2)
are the fermi-dirac distribution functions described by
quasi-fermi levels. These terms describe the carrier dependent absorption. The term
with the square-root dependence comes from a joint-density of states, where E = hv
and the
gap
Venergy
X b
bA.V is
" E
i-g. T+
_LU F
iJii'FJL)
-VVO~
then-x
+hat
as
AU theA
c1%
Ui1.,1i- UJLJLCXU
dio
AJi-U,1~1
bn
stA
"JCk1%I OUCUL%,
il-.11
p
P
1111-U
as a result of optical carrier injection, fc increases as the probability of finding an
electron increases, and the absorption decreases.
The samples used in the experiments which produced the results in figure 2-2
consist of LT-GaAs grown at different temperatures which incorporate more arsenic
as the growth temperature is lowered. The various samples were annealed in-situ
for 30 seconds at different annealing temperatures. In the as-grown samples with
the most excess arsenic (.25% and .52%), a negative transmission dip is seen after
approximately 200 fs. This is a result of building a carrier concentration in the trap
centers beyond their equilibrium values which could now absorb photons [20].
20
0,52%_ excess utrOn
0.8
0Q
0.4
-
-
0.2
-
S0
1 .0
z"
-0.2
4own
3
.0.24SQOf
0.6
0.4
.0
10
203.4.0.0
70
8
time (pe)
Figure 2-2: Pump and Probe Differential Transmissionfrom [20]for various annealing
temperatures. Note that the as-grown material for the two samples with (.52%) and
annealed
(.25%) excess arsenic have the fastest response time when compared to the
slower
samples. Also note that the sample with .02 % excess arsenic shows a much
response time as a result of trap-filling.
Fascinating dynamics occur for the as-grown material which incorporates .02%
In this sample, two time constants are observed for low intensity.
The fast time component is a result of the fast trapping time. The second time
component illustrates the trap emptying time. As the pump intensity increases,
excess arsenic.
the first component saturates quickly as the trap states fill up.
The response is
then dominated by the trap emptying time, and could be described by a single time
constant. The response is illustrated in figure 2-3 in a log scale.
Moreover, the trends shown in the figure 2-2 illustrate that as the annealing temterms
perature is increased the capture time increases. This makes intuitive sense in
of reducing the number of capture sites with increasing temperature. Furthermore,
the absence of a build up in the trap population as the annealing temperature increases, which would result in a negative transmission denotes that the trap emptying
21
0
I
0,O~2%; excess arsenic'
-2
-30
20
40
00
80
100
time (pS)
Figure 2-3: Log plot of Differential Transmission from [20]. At low intensity, the
sample with .02% excess arsenic shows a response involving two time constants. The
first time constant corresponds to filling the traps. The second time constant describes
the trap emptying time, and dominates when the traps are filled.
time (hole-capture) is not significantly different than the trap filling time.
The results of Melloch's experiments express some fundamental relationships which
should be considered when modeling the response of our devices. First, it allows for
a direct measure of the carrier response times which are exclusive of the bias circuit
effects (i.e. contacts, capacitance). Secondly, it illustrates how we could control the
response time of the material by growth and annealing conditions. Finally, it illustrates the importance of trap filling on the dynamic response of the material. As we
will see, this result will play a significant role in explaining our device's I-V curve under a low peak-intensity continuous wave illumination (low-level injection) and under
modelocked illumination (high-level injection).
As we discussed earlier in the chapter, for anneal temperatures over 6000C the
conduction in LT-GaAs is described by a Shottky barrier model which results from
the excess arsenic forming precipitates. It has been shown that increasing the anneal
temperature increases the distance that separates the arsenic clusters. Researchers
have proposed that the carrier lifetime should increase (become slower) with increasing anneal temperatures as a result of the increasing seperation between the arsenic
islands [42, 1].
Here we will describe a model described by Beard which portrays
this behavior using a diffusion model [1]. Accordingly, the carrier lifetime represents
22
the amount of time it takes for a carrier to diffuse before encountering another trap.
The mean diffusion length after a time t may be described by < L >= v Dt where
D is the diffusion coefficient described by the Einstein relationship. Solving for the
carrier lifetime, where < L > is the length to the nearest arsenic cluster, one finds
the relationship
(2.3)
< L >2 e
pekT
Melloch et al have concluded that the carrier lifetime increases as the square of the
seperation distance between arsenic clusters which agrees with the above diffusion
model [42].
2.4
Shockley Read Hall Rate Equations
The steady state dynamics of LT-GaAs could be well described by the band diagram
shown in figure 2-4. The capture and recombination mechanisms all follow from the
Shockley Read Hall Model in steady state. Here we will present a summary of the
results for completeness but will omit a detailed derivation. To describe an electron
trapping process, we will use the following representation adapted from
[38]
EC
ee
Ce
IFe
---
E
Figure 2-4: Electron/Hole Capture and Emission.
N- + Nt+ + e-
(2.4)
No + h+ +-+Nt+
(2.5)
23
. This representation illustrates that the trap center has two charge states of either
being positive or neutral depending on the capture or emission process. The rate
of electron capture from the traps is proportional to the number of electrons in the
conduction band and the number of empty traps [32].
Rnc=
Cun(1 - ft)N
(2.6)
In equation 2.6 Nt+ = (1 - ft)Nt is the number of empty ionized traps, consistent
with our previous notation. The rate of electron emission from the traps, on the other
hand, is proportional to the number of filled traps assuming there are plentiful states
in the conduction band (i.e. neglecting band-filling effects) as shown in equation 2.7
Rne = en(ft)Nt.
(2.7)
Similar equations may be derived for hole capture and hole emmision. In thermal
equilibrium, the net electron recombination process Rn = Rnc - Rne is zero as well
as the net hole recombination process.
We will now focus on a situation that is
out of thermal equilibrium as a consequence of steady state illumination.
steady state illumination, there is no accumulation of charge in the traps.
Under
Note
that this condition differs from the description of Melloch's experiments described
in the previous section in which the transient resulted in a fast population buildup.
Furthermore, with steady-state conditions the net hole and electron recombination
rates must equal each other which allows us to write the following expressions for the
recombination rate [32]
Rne = Rp = R
R =
(2.8)
(2.9)
TP(n + nt) + Tn(P + Pt)
These expressions are difficult to solve in general, but simplify under certain circumstances. For an n-type semiconductor, under low level or high level inject conditions,
the minority carrier recombination rate could be simplified as shown in equation 2.11.
24
Similarly, for a p-type semiconductor the expressions could be simplified as shown in
equation 2.10.
(2.10)
R =
TP
R = $(2.11)
Tn
Since LT-GaAs is a compensated semiconductor, we would like to propose to use
the model originally described by Zamdmer [42] in which both simplifications are
employed. The carrier lifetimes may be written as a product of a carrier thermal
velocity vn, carrier capture cross section an, and the number of traps. A discussion of
the dependences of the carrier capture cross section with an externally applied field
will be left for the next chapter in which we treat such effects to describe our data.
The dependences of the lifetimes are well understood in the expressions below. As the
number of traps increase, there are more recombination sites and the probability of
electron capture should increase. This will lead to a faster capture time. In addition,
as the thermal velocity of the carriers increase more traps will be encountered per
unit time. This will also lead to an increase in capture rate. Finally, the carrier
capture cross section mathematically describes how far the carriers must be from the
recombination sites before they are captured.
n=
(2.12)
1/(vthnnNt+)
(2.13)
Tp= 1/(VthpcrpNt)
Using these expressions for the recombination rate, we may write the follow rate
equations for our device as given in [42].
d
_
IldJe
d- = -I
hv
dt
nN>out -
dp
N0
dt
-=
Ia
hv
e dx
P--p
d
25
+ IdVe
t
ee dx
dx
(2.14)
(2.15)
dN+~
d__ = pN'uovt
- nN> oivt
d
dt
(2.16)
The rate equations shown in equations 2.14, 2.15, and 2.16 are not sufficient to solve
for n(x), p(x), E(x), and Nd (x). In order to find a solution to the four unknowns we
will require another equation. This last equation results from Gauss's law as shown in
equation 2.17. It would be particularly interesting to solve the above rate equations
to determine how well we could model LT-GaAs as an ideal photoconductor. For an
ideal photoconductor, under uniform illumination, we would like to have the carrier
concentrations across the device to be uniform as well. This will allow us to neglect
diffusion currents, and use ohm's law to describe the drift current in our device
J = q(peLn + Php)E. In addition, since we would like to treat the photoconductor as
an illumination controlled resistor, we will require that the electric field across the
device remain linear.
dE
q
- =-(N - N.- + p - n).
(2.17)
Under a low level injection condition, typical for our cw illumination intensities, we
would expect that the carrier concentrations N+ and Nd would not be significantly
altered from their equilibrium conditions. It is interesting to observe the carrier concentrations which result after a long period of continuous wave illumination. This
corresponds to a steady-state condition in which all the time derivatives in the rate
equations are set to zero. Although this steady state simplification eliminates time
from the problem, we must still face four coupled nonlinear differential equations in
the spatial variable x which must be solved in order to obtain the solution for the four
unknowns. Unfortunately, the equations must be solved numerically. Zamdmer has
solved the above equations by using a numerical integration technique which assumed
proper boundary conditions on the electric field and the hole current [42]. Furthermore, with three trial values for n,p, and E at a location as the initial conditions the
solution was numerically obtained for all x. The results obtained in reference [42]
show that the carrier concentrations are fairly uniform throughout the device, and
that the device contains a significant bulk region in which the electric field is linear.
26
Chapter 3
LT-GaAs Single Photon
Absorption CPW Autocorrelator
3.1
Introduction
In order to characterize high-frequency electronic devices it becomes necessary to
develop test equipment capable of receiving and transmitting high frequency signals
without considerable losses and distortion. The device we will discuss in this section
is a transceiver which is capable of transmitting and receiving signals containing a
bandwidth of up to several hundred GHz. This device utilizes a coplanar waveguide
geometry which will facilitate the incorporation of a three terminal device to be tested.
As an application of this transceiver, we will use it to characterize the optical impulse
response of an LT-GaAs photoconductive switch.
3.2
Coplanar Waveguide Geometry
The coplanar waveguide was proposed by C.P. Wen in 1969. This waveguide structure consists of a center conductor and two ground planes separated by a dielectric
as shown schematically in figure 3-1. By choosing the dimensions of the center strip
(S), the separation of the two ground planes (W), as well as the dielectric (Er) and
thickness (h), one could determine the characteristic impedence (Zo) and the at27
tenuation coefficient of the transmission line. Furthermore, by embedding ultrafast
photoconductive switches, also known as Auston switches, one could optically generate high-frequency signals with minimal dispersion and attenuation. In this section,
we will begin by describing the coplanar waveguide devices developed by Verghese et
al [39] which employ LT-GaAs as the source material for both the dielectric substrate
and photoconductive switches.
In order to begin to analyze the coplanar waveguide structure, we need to develop a
way to calculate the characteristic impedence as a function of the various dimensions
in our circuit. Closed form analytical expressions for the characteristic impedence
have been found by using conformal mapping techniques. While the expressions are
developed for low-frequencies, they have been shown to be applicable for millimeter
wave GaAs IC design [33]. A more rigorous approach would involve spectral domain
iterative solutions which would not provide closed form solutions. The characteristic
Figure 3-1: Coplanar Waveguide Geometry illustrating dimensions used for calculating the characteristicimpedence.
impedence in equation 3.1 is expressed in terms of elliptic integrals K(ko), and K(k')
where ko and k' are the modulus of the elliptic integrals [33].
ZO =
Here k' =
307rK(k')0
3
SeffK(ko)
(3.1)
1 - ko and ko may be calculated by choosing the dimensions S and W in
28
the circuit as shown in equation 3.2
ko =
S+2W
(3.2)
.
The effective dielectric constant needed in equation 3.1 which may also be used to
calculate the phase velocity of the signal, vph =
Er
ef
1
is
1 K(k 1 ) K(ko')
2 K(k') K(kko)
-
In the above expression, the last parameters that need to be determined are k'=
(1 - kj), and k, which is provided below [33]
sinh(7r/4h)
sinh(,r(S + 2W)/4h)
In our devices, the center conductor is designed to have a width of S=4.1 pm and
a ground plane separation of W=2.95 pm. The thickness of our dielectric is h
25
mm which is approximately the combined thickness of a molecular beam epitaxy LTGaAs growth structure and a GaAs SI substrate as described later in this chapter.
Combining these values with the relative dielectric value for GaAs of e, = 12.9,
leads to an effective dielectric of Eeff = 17. Using these values in equation 3.1 we
find a characteristic impedance value of Zo = 33 Q which is within 5% of the value
reported in reference [42] (Zo = 34.5Q) which was obtained using a 3D electromagnetic
simulation.
There are several advantages to using coplanar waveguide over microstrip transmission line circuits. By carefully selecting the ratio of the planar dimensions of the
coplanar waveguide one could control the characteristic impedance of the transmission line, allowing one to scale to a desired length for size reduction. Moreover, since
the coplanar waveguide consists of three separate active regions it facilitates incorporation of a three terminal device. Yet another advantage of a coplanar waveguide
embodies the ease of fabrication when compared to a more complicated process involved in fabricating microstrip circuits [33]. In general, it would seem reasonable
29
that developing planar technology would require less processing steps. However, a
comparison of the dispersion characteristics of a microstrip and a coplanar waveguide
indicate that the microstrip has less dispersion at frequencies greater than 700GHz.
On the other hand, longer pulses with less bandwidth are less dispersive on a CPW
due to the more gradual change of the effective index with frequency at lower frequencies [33]. Therefore from a dispersion point of view, the two types of transmission
lines are comparable depending on the bandwidth of interest. On the other hand,
on the basis of allowing for the incorporation of 3-terminal structures and on the
ease of fabrication, the coplanar waveguide geometry appears to be a suitably more
attractive choice for our application.
3.3
Single Photon Absorption LT-GaAs Autocorrelator
An immediate application of the CPW THz transceiver involves characterizing the
carrier lifetime of LT-GaAs. Since the transceiver is designed to use an LT-GaAs
photoconductive switch as a source for the optical generation of high frequency signals,
it is important to characterize the limitations imposed by the response time of LTGaAs.
Furthermore, since the source of the signal generation is an optical pulse
from a modelocked laser, another function of the transceiver involves performing an
optical autocorrelation of the laser source, which is limited by the carrier lifetime of the
material for the single-photon absorption mode of operation. In the following sections,
we will discuss our experimental setup, devices, and results which illustrate the merits
and limitations of our transceiver and its applications. In the next chapter, we will
discuss a novel application of LT-GaAs which is based on a two-photon absorption
principle which allows us to perform a true optical autocorrelationwhich is not limited
by the carrier-lifetime of the material.
The previous section presents the coplanar waveguide geometry in general terms,
and shows how to calculate the characteristic impedance of the transmission line. In
30
this section we will discuss the photoconductive switching operation which allows us
to generate pulses containing high frequency content on our transmission line.
Our discussion begins with the photoconductive switch geometry. The dark shading in figure 3-2 represents the gold metallic regions, while the unshaded region depicts
the semi-insulating LT-GaAs region. As shown, there are two photoconductive gaps
embedded within the center conductor of the coplanar waveguide geometry. These
photoconductive gaps function as optical switches which effectively provide a conducting path when illuminated and allow current to flow through the gap in the center
conductor. In addition, the figure also shows two paths which connect the center conductor to each ground plane. These paths allows us to apply a DC voltage directly
across the gap, while measuring the current through the ground plane. There are a
variety of circuits which could be utilized to measure the current. A discussion of the
alternative methods used to measure the current will be provided in the experimental
setup section of this chapter and in the appendix.
AI
Figure 3-2: Top view of the coplanarwaveguide illustrating the photoconductive gaps
in the center conductor. The shaded region represents gold regions, while the unshaded
region represents LT-GaAs.
In order to begin to discuss the photoconductive switching operation in figure 3-2,
we first need to discuss the LT-GaAs thickness and growth conditions. These devices
are the same devices used by Zamdmer [42] which were grown at Lincoln Labs in a
Molecular Bean Epitaxy system (MBE). The devices were grown on an LEC SI GaAs
substrate. The first layer consists of .2 pam of GaAs grown at a growth rate of 1 p~m
31
per hour at a growth temperature of 620'C. The subsequent layer consists of 1.65 Pm
of LT-GaAs grown at 2201C. Post growth annealing was then performed in - situ for
10 minutes at 5801C under As overpressure. The fine resolution for the device was
achieved by using an electron-beam lithography process, and a lift-off procedure of
20 nm of titanium and 200 nm of gold. The center conductor width of the devices is
S = 4.1 pm, while the separation of the center conductor from the ground planes is
W=2.95 pm. The ground plane widths are 50 pm, which allows them to be treated
as semi-infinite. Various center conductor gap spacing and geometries were tested,
ranging from 10 pm - 2 pm for the standard gap devices. In addition, gap spacings as
small as 1.8 pum were developed for the interdigitated gap geometry shown in figure
3-6. A cross sectional view of the device is provided in figure 3-3.
E=hv
/AU
ji/A
1.65jim
.2pm
220'C GaAs
6200C GaAs
SI GaAs Substrate
Figure 3-3: Cross sectional view of the coplanar waveguide photoconductive gap. The
top layer consists of the low-temperature grown MBE GaAs. While the 620'C layer
corresponds to normal GaAs.
Now we may begin to discuss the current which flows through the center conductor when the gap is illuminated by a pulsed laser. This current, as shown by
Verghese, contains the autocorrelation information of the illuminating pulse. However, if the pulse is shorter than the response time of the photoconductive switch
then the autocorrelation will be limited by the carrier lifetime of the material. This
optical impulse response then allows us to characterize the ultrafast dynamics of the
photoconductor. When a voltage V is applied across the gap in the center conductor,
32
the high frequency photocurrent which propagates down the transmission line is given
in equation 3.5
ip(t =
V0
V
Zo + G(t)-l'
(3.5)
where G(t) is the time varying photoconductance of the gap under illumination. This
equation follows from standard transmission line theory for a pulsed source. Instantaneously, the sending end voltage source sees a voltage divider with the characteristic
impedence of the transmission line. This allows us to solve for the transient current
which then propagates down the line toward the receiving end.
To progress we need to find a dependence on the conductance G(t) in terms of the
incident intensity. First we begin by investigating the conductivity. Since the mobility
of the electrons is much greater than the hole mobility, we will simplify the expression
for the conductivity by neglecting the hole current. In the final analysis, it is only
necessary to keep track of the electron contribution since drift is the major contributor
to our current. We are justified in neglecting the diffusion currents since at the fields
we apply the drift component is much larger than the diffusion current [42]. In order
for the above assumption to be valid we will require two conditions. First, we are
modeling our LT-GaAs photoconductor as being under uniform illumination. This
assumption is valid since our estimated spot size is typically on the order or larger
than the gap dimensions. Secondly, we are treating the contacts as being ohmic and
neglecting any significant concentration gradients throughout the bulk of our device.
a(t) = q(Pen(t) +
MAOp(t))
(3.7)
G(t) = c-A/L
G(t)
=
qpeW/L
j
ST
(3.6)
n(x)dx
The conductivity is written in equation 3.6 for a general semiconductor.
(3.8)
The
conductance is found by taking the product of the conductivity and multiplying it by
the cross sectional area over the length of the device. The total conductance is then
given by integrating a series of infinitesimal parallel conductance sheets with cross
33
X
L
Figure 3-4: Photoconductor Geometry used in calculating photoconductance. The
current direction is denoted as i.
sectional area A=dx W, where we have assumed the geometry given in figure 3-4. In
figure 3-4, the axis parallel to the illumination direction is x which is normal to the
current flow. If we assume steady state is achieved, the carrier concentration becomes
the product of the generation rate with the carrier lifetime
Ib\Jx)
= g (''e
-
aoe-
..
9)
Combining 3.8 and 3.9, we arrive at the following equation for the photoconductance
by carrying out the integration
G(t) = (W/D)(t)(
q(Pee + phTh)
hv
(3-10)
Further simplification is made by approximating the conducting surface area to be
equal,W=D, and by rewriting 3.10 in terms of the quantum efficiency rq
T7 = Pabs/Pn =(1 -
34
R)(1
-
e(aT)).
(3.11)
Finally, combining these results we arrive at an expression for the photoconductance
G(t)
(3.12)
= Ign(t)r/q(peTe + PhTh) = Vi.(t).
Now that the dependence of G(t) on Iin(t) has been established, we wish to illustrate
how we can perform an autocorrelation by measuring the photocurrent of our device.
As shown by Verghese et al [39], the explicit nonlinear dependence of the photocurrent
with intensity is found by taking the taylor series expansion of equation 3.5 with
respect to Ii, in equation 3.12.
This result, shown in general terms in equation
3.13 is particularly important because it shows that a nonlinearity in intensity I
is introduced by utilizing a voltage divider circuit presented by the characteristic
impedence of the transmission line. For instance, without a characteristic impedence
the second derivative of the photocurrent with respect to intensity would be zero.
ZPC =
icO +
di
IO(I
d2i14
- Io) + 2di
o(I _ I0)2 +-
(3.13)
In the above expression, the intensity I is the total intensity illuminating the gap.
By utilizing a beam splitter, the incident beam intensity could be broken up into two
separate components. These components will be labeled I1 and
12.
The magnitude of
the two beams are typically made equal by using a 50/50 beam splitter. This setup
is very similar to one used in interferometry. The difference here being the type of
detection we are making is sensitive to the square intensity, which is an intensity
autocorrelation. Whereas in an interferometer, one is interested in performing an
electric field autocorrelation (i.e. electric field interference).
with two beams out of phase by a variable time delay
I(t) = Ii(t) + 12(t+ T)
Illuminating the gap
T
(3.14)
results in a superposition of the two intensities if the beams are cross - polarized.
For the case of two interfering beams, one would also have to take into account an
additional 1 1 2 (T) term. This term becomes the familiar electric-field autocorrelation
35
when performing a time averaged measurement, and could affect our measurement
of the intensity autocorrelation. Specifically,
< I12(T)
>=< E 1 (t)E2 (t
-
T)
> and if
it is present it will show up mostly as a distorting first order intensity term in the
taylor series expansion shown in equation 3.13. The second order contribution of the
interference term should be weaker than the first as result of the second order taylor
series expansion term being significantly smaller than the first order term contribution. Note that since the nonlinearity in the electric-field is occurring instantaneously
in free-space, the detection is independent of the carrier lifetime of the material. Since
this statement is a bit compact, we will expand on this.
To be more specific, the intensity profile changes spatially where the two beams
overlap as the path length is varied. In our experiments, 112 (T) is then sampled at
the detector location and changes in magnitude as the path length is varied. This
variation occurs when the beams interfere and the path length is less than the coherence length, where l
=
~ 40 pm at 900 nm with a 13 nm bandwidth. In
general, the electric-field autocorrelation should have a longer duration than the intensity autocorrelation since intensity is the magnitude of the electric field squared
I = |E(t) 2. For instance, the width resulting from an autocorrelation of a (sech(±))
with a time delayed version of itself is longer than that which would result from a
(sech( ) 2 ) autocorrelation with itself.
The question arises as to why one would expect the electric field autocorrelation
not to be dependent on the lifetime. At each path delay,
one point in the autocorrelation < 112(T) >.
To,
our device measures
We could think of
'12
as a virtual
beam in free space which contains the information of the electric field autocorrelation
which we could measure. Now let us compare to an intensity autocorrelation. When
performing an intensity autocorrelation, at each path delay (To) in our autocorrelation
we are essentially measuring the autocorrelation of two responses to each beam of the
material which decays with the carrier lifetime. Each response to an individual beam
will be described mathematically in the next section of this chapter.
In general, we would expect that the intensity autocorrelation to have a smaller
duration than the electric field autocorrelation if it could be measured without the
36
carrier lifetime broadening. However, when performing an intensity autocorrelation
that is limited by the carrier response time of the material (Te =1 ps), we would expect
the coherence effect to show up as a small peak on top of our autocorrelation. This
follows from the observation that in an intensity autocorrelation, we are essentially
performing an autocorrelation of the generated carriers (proportional to the intensity)
which relax with the carrier lifetime. In the electric field autocorrelation, however,
we are detecting the autocorrelation of the field which is generated instantaneously
external to the detector, (i.e. I 1 2 (T) is generated independent of the detector).
The intensity-intensity autocorrelation results from the second order term in the
taylor series expansion, which will produce a mixed product term involving I,(t)12 (tT).
The other terms, 11 (t)I1 (t) + 12 (t - r)12 (t -
T)
will result in a constant that does
not depend on the time delay T when taking a time-averaged measurement.
One subtle but important point that needs to be addressed is what it means to
take a DC time averaged measurement. From linear-systems theory, we know that if
a signal has a zero-frequency component, the zero-frequency component contains the
information about the time average of the entire signal. This is most easily expressed
in the fourier transform notation as
X(j0)
=
x(t)e(-M)dt
(3.15)
The subtlety arises because we would like to measure the time average of the highfrequency current in the transmission line which should not have a zero- frequency DC
component. However, as we have seen with the taylor series expansion, the voltage
divider presented by the transmission line produces a nonlinearity which allows the
signal to be mixed to contain a DC component. This is the DC component which we
measure on our equipment which contains the time-average information of the entire
signal. The higher-frequency components radiate or suffer attenuative losses after
leaving the coplanar waveguide before reaching the oscilloscope used to perform the
measurement.
Explicitly, we will now separate the term from the taylor series expression which
37
contains the autocorrelation, since the other terms will contribute to a background
constant (independent of -) when taking a time-averaged measurement.
(I(t)I(t + T))
(iPc(T)) oc (diC
2d1c
(3.16)
A useful figure of merit suggested by Verghese [39] for this autocorrelator is the
second order taylor series coefficient, which is the sensitivity of the response to the
intensity autocorrelation in equation 3.16.
dip
2d1
-Voy 2 Zo
(1±ZOIO)
(3.17)
While the work presented in [39] presents an analysis of the signal to background
ratio, we will present a different analysis which illustrates the same behavior. Namely,
if we compare the magnitude of the current produced by the second order term in
the taylor series, to the third order term, we find that the second order term is
larger by exactly 1/(ZoG(t)). Since the photoconductance G(t) = yI is proportional
to intensity, the limiting behavior of the latter illustrates that as we increase the
intensity the signal to background ratio decreases. Furthermore, equation 3.17 also
shows that as the intensity increases the second order term sensitivity also decreases.
It is therefore tempting to operate at low intensities, however, we could not lower the
intensity arbritrarily since we would also like to have the intensity sufficiently large
to overcome fluctuations in the laser power levels, as well as other noise sources in
our circuit.
We would therefore like to operate at a peak intensity sufficiently high to overcome
the third order contribution by at least one order of magnitude. This corresponds
to setting G(t)Zo = .1 [39]. While this result is given in [39], the values used to
calculate G(t) differed from what we will use here. The values which we will use
for our mobilities are somewhat larger and are updated with what appears to be
the modern consensus in the literature. The reported values for the mobility have
varied from 200 cm 2 V/s to 3000 cm 2 V/s in the literature. These mobility values
rely heavily on the growth and subsequent annealing conditions. In addition, we will
38
neglect the hole contribution to the current which we do not believe to be significant
carriers of current. This is same conclusion reached by Zamdmer [42] based on the
hole boundary conditions imposed on the contacts, as well as results deduced from
Hall measurements. Furthermore, we expect the ratio of the hole to electron mobility
to be approximately 1/20 as it is in regular GaAs [42]. Using our estimated values of
Pe
=
3000 cm 2 /Vs, rT = .5, hv = 1.5 eV,
Te =
500 fs, and a characteristic impedence
of Zo = 50 Q, we calculate a peak intensity value of
peak
.4x1 07 W/cm 2 which
corresponds to G(t)ZO = .1, or equivalently having the second order contribution
to the photocurrent at least a factor of 10 greater than the third order contribution.
Approximating our focal spot to be uniform within a radius of 10 Pm for a conservative
estimate, we find that this peak intensity corresponds to a time average power of 8
mW. Therefore, this analysis shows that for performing an autocorrelation experiment
in which the third and higher order terms are present, we would like to operate at
a time average power of Pyg = 8 mW. There are other experimental techniques
which could be employed to reduce the contribution of the higher order terms in the
taylor series which will be discussed in the experimental results section. Namely, by
chopping the two beams at two different frequencies using an optical chopper, we
could selectively filter out the undesired components of the taylor series.
3.4
Carrier Lifetime Limited Autocorrelation: Optical Impulse Response
The final point that needs to be made is in discussing the difference between a true
autocorrelationand a carrier lifetime limited autocorrelation. The former expressions
in equations 3.12 - 3.17 assumed that steady state was achieved and that the carrier
concentration followed the intensity pulse. However, when the intensity pulse duration
is much less than the carrier response time it becomes necessary to subsitute the
impulse response expression for the intensity. The rate equation describing the carrier
trapping process could be used to determine the impulse response under non-steady
39
state conditions.
dni'
dt
dt
= _a 6 (t)/hv
- n/Te
The rate equation in equation 3.18 contains a number of assumptions.
(3.18)
First, it
assumes that the number of empty traps is not significantly changed throughout
the pump duration.
Otherwise, the above dynamics would be more complex and
would have to account for trap-filling effects. Namely, this implies we are assuming a
low-level injection condition on our intensity. In addition, as before we are assuming
uniform illumination, a single level trap recombination process, and we are once again
neglecting any diffusion current. With these conditions, the carrier concentration
becomes
n'(t) = aIio/hVe-/Te .
(3.19)
In equation 3.19, Ijo is the area of the impulse which approximately equals IpeakAt
where At is the pulse duration. For the carrier-lifetime limited impulse response,
it follows that all the previous expressions could be modified by substituting I(t) =
IpeakAt/Te-'/7_ . A typical autocorrelation denoting the carrier lifetime limited optical
impulse response is provided in figure 3-5. This figure shows the exponential shape of
the resulting autocorrelation and the carrier lifetime extracted using an exponential
fit. Ideally, the autocorrelation signal should be symmetrical. The asymmetry may
result from an asymmetrical illumination of the gap.
3.5
High Field Effects on Carrier Lifetime
While increasing the electric field results in an increased signal, large electric field
carrier transport results in some undesirable consequences in semiconductor devices.
Velocity saturation, impact ionization, avalanche breakdown, space charge limited
current, and other hot-carrier effects may become evident as a result of applying
large voltages which result in strong electric fields across small gaps.
A good way to investigate the high-field effects in semiconductors is to gather the
I-V characteristics of the device. In LT-GaAs photoconductors, a nonlinear I-V char40
0,8-
0.6 0.4-
0.2 0
-8
-6
-4
-2
T(ps)
0
2
4
6
Figure 3-5: Carrierlifetime limited autocorrelationperformed at an incident wavelength of 850 nm from which a carrier lifetime of -re 1.3 ps is extracted.
acteristic has raised curiosity within the scientific community in recent years. Some
groups have suggested space charge limited current as an explanation for the nonlinear I-V behavior. However, Zamdmer has argued that space-charge limited current
would require a much larger acceptor-like concentration than has been observed in
LT-GaAs. Furthermore, Zamdmer argues that the critical voltage required for the
activation of space-charge limited current should be proportional to the square of the
device length L 2 . After testing devices of various lengths, Zamdmer concluded that
space-charge effects are not sufficient to explain the I-V behavior [42].
In this section, we will present our measurements on devices which contain interdigitated photoconductors with gap sizes as small as 1.8 pm which were fabricated
using electron beam lithography. These gap features are slightly smaller than the 2
pm devices in [27], and provide a higher efficiency due to the interdigitated electrode
pattern as shown in figure 3-6. In addition, we will investigate the model proposed by
Zamdmer and verify its validity to our devices. Furthermore, we will develop a similar
model which is based on Zamdmer's findings but also takes into account additional
subtle details. Finally, we will investigate the applicability of the model to larger
intensities where trap filling, auger processes, and other hot carrier effects have been
known to occur. In the next chapter, we will also present another feature which must
41
Figure 3-6: InterdigitatedElectrodes, 1.8pam gap size.
be considered under large illumination intensities, namely two-photon absorption.
figure 3-7 shows the nonlinear I-V characteristics of a device containing an interdigitated electrode pattern across the gap. This pattern contains electrode spacing
distances as small as 1.8 pm, with electrode widths of 200 nm as observed in the
SEM photograph in figure 3-6. These small gaps allow us to generate large electric
fields by applying small voltages. The dark I-V characteristic, which corresponds to
no illumination, is linear throughout the voltages considered with the exception of
a sharp nonlinearity near 60V. The illuminated curves all begin to show a nonlinear
increase at approximately 20V.
One important point to be made which will return to later in this discussion is
that all the I-V characteristics must be taken under continuous wave illumination in
order to be meaningful. This insures that steady state is maintained throughout the
duration of the measurement. The difficulty in comparing the carrier dynamics under
modelocked illumination with that of continuous wave illumination is that the instantaneous peak intensity is very small in the latter. For instance, a 1 mW source when
focused down to 10 x 10 Mm
2
contains a peak intensity of 10 kW/cm 2 . At 840 nm this
corresponds to an instantaneous population density of approximately n' = 2 x 1014
cm-3, using an absorption coefficient value of a = 16000 cm- 1 . For the modelocked
case, we would expect the instantaneous population density to increase to n'=1 x
42
60 r
13mW
50-
40-
30 C4mW
-
201.4m
10Dark
0
-101
0
10
20
30
40
50
Voltage (V)
Figure 3-7: Nonlinear I-V characteristicsfor various CW intensities.
101 cm-3 . Therefore, when comparing our modelocked experiments to the continuous wave I-V characteristics it is important to keep in mind that we are comparing
population densities which vary over 4 orders of magnitude. More importantly, the
population densities which correspond to the modelocked case are on the same order
of magnitude as the density of empty traps. This implies that the carrier densities
generated under modelocked illumination could lead to trap saturation effects.
Zamdmer is the first to explain the nonlinear IV characteristic in LT-GaAs [27]
in terms of a Poole-Frenkel barrier lowering model.
In [27] the nonlinear effects
are ascribed to a modified Frenkel- Poole barrier lowering model suggested by [6]
combined with an electron heating correction as suggested by [28], and then a nearest
neighbor's approximation is used to account for the low-field dependence [42]. While
43
such a model describes all of the key processes involved, here we will use a more
compact model which provides a better fit of our data with fewer fitting parameters.
Moreover, this model will allow for a closed form analytical expression that works
well over a larger bias range.
The original Poole-Frenkel barrier lowering model exists in several modified forms.
First we will describe the Frenkel Poole barrier lowering in its original form, and then
we will discuss the results in [42]. It is important to keep in mind however, that
at the root of all the models one will find the Poole-Frenkel Barrier lowering as the
fundamental mechanism.
EC
rAU
6
AE6
.
....
..
AU
Figure 3-8: Poole-Frenkel BarrierLowering.
2
4-rcr
-qEr
(3.20)
In figure 3-8 the potential energy due to an ionized trap is shown for both a zero field
and an applied electric field. The corresponding potential energy may be written as
shown in equation 3.20. The Poole-Frenkel barrier lowering is defined as the amount
that the maximum in the barrier is reduced with an applied electric field. This
could be calculated by finding the value r where 4
44
- 0 in equation 3.20 in the
absence of an electric field. The resulting distance rAU where this maximum occurs
is rAu = 1/2 q/(rE).
The amount of barrier lowering at the maximum location
corresponding to this value of rAu as a function of the applied electric field E is given
by AU, which is found by using this value of rAU in equation 3.22 in the presence of
an electric field resulting in
3
AU = 2(
)1/2E1/2
4wre
AU = 4f E.1/2
(3.21)
(3.22)
In equation 3.22 we have explicitly defined the Poole-Frenkel coefficient as 4f =
(7 )1/2. According to the Poole-Frenkel model in its original form, the electric field
dependent conductivity is written in terms of an escape probability of an electron in
a trap. This mechanism is similar to a Shottky barrier [14, 13] in which the electrons
may be thermally excited by reducing the barrier. The resulting conductivity for the
Poole-Frenkel effect may be written as a product of the conductivity in the absence
of an electric field mulitiplied by an exponential thermalization dependence on the
barrier lowering as expressed in equation 3.23
a = -oexp(,3fE 1/ 2 /(2kT)).
(3.23)
There have been several modified forms as previously mentioned to the conductivity derived by Frenkel. In its original form, the trap has been written assuming a one
dimensional barrier lowering model. Dussel has modified the model by a treatment
which looks at capture from an effective capture volume point of view, rather than
a thermal escape probability from a capture cross sectional area[6, 42, 281. In this
model, the radius which is critical for capture is considered to reside 2kT below the
Poole-Frenkel barrier lowering maximum (AU), as stated mathematically in equation
3.24. The volume critical for capture is found by calculating the volume enclosed by
the critical capture potential which satisfies equation 3.24. The ratio of the capture
coefficient with an applied field to that in which no field is applied ("('o)
45
which
Dussel derives is given by the change in the effective volume enclosed by this potential
in the presence of barrier lowering. Without providing the mathematical details, the
effective carrier capture cross section which results depends on E3 /2 at high fields.
Zamdmer used this model and modified it by adding another E 3 / 2 term which he
attributed to carrier heating to describe the nonlinear behavior in LT-GaAs. This
correction factor is necessary since the model does not take into account the electron
heating which results from an applied field. The conductivity, which could be derived
from the carrier capture cross section would then result in a current characteristic
which would depend on E' power. However, if saturation velocity effects are taken
into account then the current may decrease to E3 at high fields.
2
U
= 4
- qEr = -2kT - AU
(3.24)
Now that the previously described model has been presented, we see that it essentially
contains four fitting parameters which describe the fundamental processes which are
occurring with an applied field. Namely, these four separate pieces of the model
include electron heating, a capture cross section, a nearest neighbor's model, and
velocity saturation.
What we will now apply is a similar model which better describes our I-V characteristic by accounting for some additional details. This model incorporates the three
tron heating dependence in Zamdmer's model, and the ohmic behaviour at low-biases
which we observe in our data. Finally, it will provide a simple closed form solution
with an empirically observed fitting parameter.
The illustration shown in figure 3-8 shows all of the features of a modified PooleFrenkel Barrier lowering model as proposed in [13, 14]. This modified form extends
the Poole-Frenkel barrier to include a three-dimensional treatment as opposed to its
original ID form. Furthermore, it considers that the electric field only lowers the
barrier to a minimum in a forward direction parallel to the field. The modified form
extends equation 3.20 and replaces the potential change due to the electric field, the
46
Er term, with an angular dependence of Ercos(O). Considering the change in the
barrier height in all angular directions captures the effect of the barrier increase in the
reverse direction, denoted by AE 6 in figure 3-8. Accordingly, Ieda's model suggest
that there is a state of energy 6, corresponding to one of the highly excited states
in the coulombic trap, at which it is more probable for an electron to become a free
carrier by transitioning to a distance rj than it is to become captured. This state 6
may be on the order of kT, which would describe a phonon assisted transition. The
q2 /(47rfr6o6). The increment of the field
corresponding distance r6 is defined as r6
in the reverse direction could be determined by using this value in equation 3.25. The
resulting increase in the barrier height in the reverse direction is as shown in equation
3.26.
-
AE 6
4
qErcos(O)
(3.25)
f32Ecos()/46
(3.26)
2
-
-
In the forward direction, the effective barrier lowering is given as shown in equation
3.27 for the case in which AU > 26. For the case in which AU < 26, the effective
barrier lowering is given in equation 3.28. The intuition behind this approximation
is as follows, for a given capture radius, namely r6 , we would like to determine the
change in the corresponding energy with an applied field. We are interested in keeping
track of this energy because it describes a barrier which could be used to calculate the
thermal escape probability. The capture radius, rb, is used to determine the lowering
of the barrier height in the forward direction which is given in equation 3.27. This
approximation is good as long as the Poole-Frenkel radius which corresponds to the
location of the maximum of the barrier is greater than our choice of the capture radius
r>f > rb. Once the Poole-Frenkel radius is smaller than the capture radius, we must
define a new barrier height which is critical for capture. This effective barrier height in
the forward direction is given by the energy corresponding to an energy 6 lower from
where the maximum of the potential now lies (AU). The reason the critical energy
for capture resides at least 6 below this maximum is because 6 physically corresponds
to the energy in which a phonon interaction will free the electron by providing it with
47
sufficient energy to overcome the barrier.
6
AEforward = AU -
AEforward=
,
For AU > 26
AE6 , For AU < 26
(3.27)
(3.28)
Combining the increment of the barrier in the reverse direction and the lowering
of the barrier in the forward direction Ieda has developed the following equations for
the conductivity shown in equations 3.29 and 3.30 [13].
u = 0 4-Esinh(
a2
4-y
)
, if ceE'/
2
< 27
(3.29)
1
-=
0o-
a2E
[(aE/2 - 1)exp(aE1 / 2
-
y)
-
2yexp(-C 2 E/4-y) + exp(7)
,if aE 1 / 2 > 2-y
(3.30)
In equations 3.29 and 3.30, a =
#f /2kT
and -y = 6/2kT. We used the relative dielec-
tric value of GaAs, E. = 12.9, and our measured gap distance d= 1.8 Mm to determine
the electric field. We further assumed that the electric field is approximately linear
throughout the bulk and used E = V/d to calculate the field. The best fit of our
model is shown in the dashed line in figure 3-9 a) in linear scale and in figure 3-9 b)
in a log scale for the I-V trace in figure 3-7 corresponding to 13mW incident power.
A fit at other intensities provided similar results. The log-log scale is more descriptive sinlc
lt SHOWS tat
jiiee
there are
die thrlelt cagLesllU
ilpe
Wicah WUULU UkreLUspoinUgUl
to three different power laws, which may describe three different processes. The first
two processes are described by the Poole-Frenkel model. Specifically, the change from
the ohmic regime to the exponential dependence regime is due to the barrier lowering
effect. The third power law dependence will be described later in our discussion.
The corresponding value for the energy state in which the carrier becomes a free
carrier is found to be 6 = 2.5 kT, which is a very reasonable value. As a matter of
fact, this is close to the 2kT estimate which described the critical radius for capture
in Dussel's model [6, 42].
The Poole-Frenkel barrier coefficient, Opf was multiplied by a factor of 1.7 in order
48
to provide a best fit. This scaling factor of the Poole-Frenkel coefficient is usually
found to be within the range of 1 - 2, as noted in reference [13, 14]. This could be
explained in terms of the shape of the actual potential. For Shottky barrier potentials,
the scaling factor is exactly 2. On the other hand, for a coulombic potential the PooleFrenkel factor should be exact as given in equation 3.22. It would be interesting to
note what is the cause for this potential deformation. It may be the case that the
metallic arsenic precipates which have been known to act as Shottky potential barriers
have had the effect of producing an effective Poole-Frenkel coefficient.
We will now return again to figure 3-9 which shows the fit of our model in the
dashed curve to the I-V trace under 13mW illumination. We observe in our fit to
the I-V curve that at high bias levels there appears to be a sudden increase in the
conductivity, which is not captured in our model. Note that neither of the previously mentioned models would explain this sudden increase. At these large bias fields
it is possible that the bulk is at the threshold of breakdown, and that we are observing some other hot-carrier effects as we approach the critical breakdown field.
The breakdown field in LT-GaAs has been reported to be as large as
Ecritica
x 10' V/cm. By applying 50V across 2 pm, we estimate the field to be 2.5
3
x 105
V/cm which is close to the critical breakdown field strength [42, 25]. Furthermore,
in annealed LT-GaAs this breakdown process has been associated with an avalanche
impact ionization process [42, 25].
3.5.1
High Field Carrier Capture Lifetime Experiments
As originally proposed by Lax, a trap which is described by a coulombic potential
contains multiple excited states in which a carrier may reside. The capture of a carrier
involves a cascade process in which a carrier funnels down the coulomb potential
through a phonon assisted process. Through each successive transition, the electron
has a certain probability of being re-emitted and being captured. Accordingly, the
effective carrier capture cross section critical for capture is one in which the probability
of being emitted is equivalent to the sticking probability. As discussed in the last
section, Dussel estimated a capture radius to correspond to a potential energy of 2kT
49
(a)
60
50 -
40-
30-
C)
10 -
0
0
10
20
30
40
50
60
Voltage (V)
(b)
102
10 -
10O
10'
Voltage (V)
Figure 3-9: I-V Characteristic on a (a)linear scale (b) log-log scale. The solid curve
represents the measured characteristic while the dashed curve is obtained from our
model. In (b), three regions are shown which correspond to an ohmic region, barrier
lowering, and an avalanche breakdown.
50
under the maximum height of the potential barrier which is subject to change by a
Poole-Frenkel barrier lowering process with an applied electric field [6, 42]. The change
in the capture radius is used to find an effective carrier capture cross section. Once
the carrier capture capture cross section is determined, one may calculate the carrier
capture time as described in chapter one using equation 2.13. Zamdmer modified
Dussel's expression for the capture cross section to include electron heating effects
and found a carrier lifetime which depends on the applied electric field. This bias
dependent carrier capture time has an effect on the current-voltage characteristics of
the device as expressed in equation 3.31. Zamdmer found a fit to the IV curve of his
device, which was attributed to a change in the carrier capture time [42].
I
-
g(P)(Te(E)ve (E) + Th/hE)A
(3.31)
Similarly, we would like to relate our model which describes our nonlinear I-V characteristic to an increase in lifetime. We would expect the lifetime to increase as the
probability of being captured decreases with barrier lowering. We feel our model
well describes the thermal ionization of electrons which is evident by the Maxwell
Boltzmann exponential dependence of our conductivity expressions with an applied
field in equations 3.29 - 3.30. Zamdmer further carried out carrier-lifetime limited
autocorrelation experiments to verify his carrier capture time increase [27]. Here we
will report the results of our experiments. While our data supports the conclusions
drawn in [27], our new data shows some previously unrevealed characteristics which
require further explanation.
Figure 3-10 shows autocorrelation measurements at three different intensities. In
figure 3-10 a) and b), the carrier capture time at first glance appears to be broadening.
This is consistent with what we would expect. However, upon closer inspection it is
observed that there appears to be two distinct lifetimes. The first time constant
is much faster than the second time constant which appears as shoulders in the
plots shown in a) and b). We notice that as the bias is increased, the percentage
of the signal which is described by the first time constant is decreased. This data
51
(a)
1.2-
0.840V
0.6-
20V
<
10V
0.4
0.2
S-j
-0.2'
-8
-6
-4
-2
0
2
4
6
8
1
2
3
4
2
4
6
8
T(ps)
(b)
1.2-
40V
0.8-
20V
0.6-
<
10V
0.4-
0.2-
0-0.2
-4
-3
-2
-1
0
T (ps)
(c)
1.2-
1 -
40V
0.8-
20V
0.610V
0.4-
0.20-0.2'
-8
-6
-4
-2
0
' (ps)
Figure 3-10: Autocorrelation measurements taken at three different bias voltages,
showing capture time dependence on applied bias; (a) for time average incident power
of Pavg= 4 mW and (b) Pavg=13mW and (c) Pavg=30mW. In (a) and (b) we note
two time constants, as the power is increased in (c) only one time constant is observed.
52
suggests that the signal described by the first time constant is associated with barrier
lowering as we will explain.
One possible interpretation of this data is that the
traps are quickly becoming saturated during the first time constant at which point
the traps start emptying due to hole capture which is described by the hole capture
time. It would then follow that as the barrier is decreased, less electrons are captured
before the traps start emptying significantly. This behavior would explain the smaller
percentage of the signal which is described by the first time constant in figure 3-10
a) and b) with increasing bias. Secondly, this model explains why the second time
constant appears to begin at the same time in each plot. This is also consistent
with Melloch's observations involving trap saturation effects using optical-pump and
probe experiments. In Melloch's experiments it was shown that when the traps are
nearly filled, the bottleneck for further decrease of carriers in the conduction band is
limited by the hole capture time. Our estimated peak carrier density corresponding
to our operating intensity is on the order of n' =1018 m-3. As we alluded to earlier
in this section, this is at least four orders of magnitude larger than carrier densities
generated by CW illumination. Furthermore, this carrier density is on the same order
of magnitude as the number of empty traps.
The data in figure 3-10 c) shows our measurements for a more intense beam
corresponding to an average power of P
=
30 mW. These results show that at a
higher illumination intensities the transient is described by a single time constant.
This is consistent with our hypothesis, namely, that as the intensity is increased
the traps saturate in a time scale beyond the resolution of our experiment and the
resulting bottleneck is a single time constant described by the hole capture time.
We have observed in our previous measurements that the sinusoidal speaker motion, and the subsequent averaging, may result in a smoothening of the slope discontinuities. It is a possibility that using this measurement technique, combined with
measuring the full width half maximum of the pulse as opposed to an exponential fit,
could lead to the observation of a single time constant which is significantly broadening. Our measurements were performed using a slow scan technique using a linear
delay stage on a lockin amplifier. The details of our measurement technique will be
53
described in the experimental setup section of this chapter. However, we would like
to emphasize at this point that are results are indicative of a carrier capture time
broadening which is consistent with the results found in reference [27]. Our measurement technique, along with the inclusion of higher intensities have provided additional
insight into the dynamic carrier capture time behavior with bias and illumination.
Lastly, we would like to point out how we ruled out another potential explanation
which we considered which involves a coherence peak interpretation. As mentioned
earlier in this chapter, a coherence peak due to interference will appear as a sharp
peak in the signal when the autocorrelation is carrier lifetime limited. While this
may explain the two time constants, we did not find this explanation to be valid since
we would expect the coherence peak to scale with the applied bias. Therefore, this
behavior would not be consistent with the observation of a reduction in the percentage
of the peak signal with applied bias. In addition, our experiments were performed
with a half-wave plate in one of the arms to cross polarize the two beams in order to
minimize coherence effects.
In conclusion, we find our results to be complimentary to observations drawn from
previous work in the group and we have validated the same conclusions regarding the
increase in the carrier capture time. Namely, that the carrier capture time increases
as the result of the potential barrier lowering in the traps. Our experiments at large
pump intensities, corresponding to modelocked operation, suggest that the hole capture tiImC
(tlap-elllptylllg
timeIC) is non-trivial Uld plays a sglilgicalut role in te
allil
dynamics. Our data further suggests that this time constant may vary, although not
greatly, with bias as shown in figure 3-10 c).
3.6
Pump and Probe Experiments
The optoelectronic pump and probe experiments are similar to the autocorrelation experiments. The key difference between these experiments, is that the pump and probe
experiments use two different photoconductors connected through high-frequency
transmission lines. One advantage of using two different isolated photoconductors
54
in which the two incident beams do not overlap is that optical interference is no
longer an issue. The pump photoconductor is illuminated to generate a pulse which
then propagates down the transmission line toward the probe photoconductor. When
the optical pulse which is illuminating the probe photoconductor, and the electrical
pulse which propagates down the transmission line from the pump photoconductor
coincide, an output is generated. This experiment is best visualized by considering that the probe photoconductor functions as an optical switch, which allows the
pump generated pulse to pass through. In these experiments, both ground planes are
shorted to ground. The output is taken directly from the center conductor output of
the probe switch.
The motivation behind the pump and probe experiments is to investigate the propagation characteristics of our coplanar waveguide. The ultimate goal is to optimize
the signal strength and bandwidth for a high-frequency network analyzer application. Ideally, we would like to optically beat two continuous wave sources with radian
frequencies wi and w2 to generate an electric signal corresponding to the difference
frequency w1
-
w2 . This would allow us to control the frequency of the incident
sinusoidal signal up to several hundred gigahertz for measurement of the 312 (transmission) S-parameter of a device to be tested.
As a first step toward this goal, we would like to optimize and characterize the
waveguide for a pulsed modelocked source illumination. This will allow us to determine and optimize the propagation characteristics of the waveguide, which include
high frequency loss and sensitivity, as well as dispersion. Although for a narrowband
sinusoidal application, the dispersion effects which result from a varying index with
frequency will be minimal. For other potential types of frequency diagnostic applications of our network analyzer, such as determining the time domain impulse response
of a device, we would still like to keep the dispersion to a minimum.
Initially, the pump and probe experiments were begun by Zamdmer using various
circuit geometries. The results of our experiments are shown in figure 3-11, which
were performed using a rapid scan speaker measurement to be described in the experimental setup section of this thesis. The resulting signal is found to be significantly
55
distorted after taking several averages. This could be explained by the photoconductive switch geometry of our devices. These devices differed from the variety used
in the autocorrelation experiments in that the gap spacing was found to be on the
order of 10pm for each device. This large gap geometry poses three detrimental consequences to our signal quality. First, the electric field generated across the gap is
decreased by a factor of five when compared to the previous devices. Secondly, the
benefits in sensitivity from using an interdigitated electrode pattern are no longer
achieved when using a regular gap geometry. Finally, this type of geometry is easily
susceptible to modal distortion which results from asymmetric illumination of the
pulse. One consequence of using a coplanar waveguide is the modal distortion that
occurs between the even and odd modes. These modes of propagation describe the
electric field symmetry across the center conductor to the ground planes.
10.90.8 0.70.60.50.40.30.20.1 -
r (ps)
Figure 3-11: Typical pump and probe measurement, P,
780 nm.
=
30 mW, Vc = 30 V, A
As a suggestion for improvement, it will be noted that Zamdmer achieved significantly better results by using a novel mode discriminator geometry [411. In order to
reduce the modal distortion, Zamdmer devised two photoconductive active regions
symmetrically oriented about the center conductor. This scheme allows for applying a bias signal on each side of the center conductor through the active region for
compensating the modal distortion.
56
While the suggestions for improvements will be summarized in the concluding
remarks of this thesis, it will suffice to say that two immediate improvements to be
made for progress toward a high frequency network analyzer would include using
an interdigitated photoconductive switch geometry and designing new devices which
incorporate modal compensation. Although the devices used in the autocorrelation
experiments contained interdigitated fingers, the center conductor was disconnected
in the middle of the device making them inapplicable for pump and probe experiments. These devices were fabricated this way using a mask which was designed to
incorporate future quantum device experiments in which a quantum device would be
inserted in the center conductor.
In summary, we have presented our initial pump and probe experiments and have
discussed the applications and motivation behind these experiments. Finally, our experimental results indicate the need for redesigning the geometry before proceeding
to perform continuous wave mixing experiments. In addition, two suggestions for immediate improvement were presented as a future step toward making progess toward
designing a THz bandwidth network analyzer.
3.7
Experimental Setup and Measurements
Two different types of modelocked lasers were used in our experiments. Initially, a
Spectra Physics Tsunami Ti:Saphirre modelocked laser with FWHM pulse widths
under 100fs were used to perform autocorrelation and pump and probe experiments.
The tuning range of this laser is from 720 nm-820 nm for the single photon absorption
experiments. In order to achieve a wavelength optimal for two-photon absorption, to
be discussed in the next chapter, and suppression of single photon absorption a Coherent Ti:Saphirre modelocked laser was utilized generating pulses of a FWHM duration
of 100 fs as determined by using a second harmonic generating crystal autocorrelator.
This laser is tunable from 810-910 nm, allowing us to perform both single photon
and two photon absorption experiments. figure 3-12 shows our pump and probe/
autocorrelation experimental setup.
57
Two types of measurements were performed. In the first measurement, a speaker
with a mounted retroreflector was used as a delay stage. The speaker frequency was
set to oscillate at 20Hz, and a synchronized signal with the speaker drive was used to
trigger the oscilloscope. The output of the autocorrelation was displayed in real-time.
Here the signal is in real time in the sense that we could make mirror and device
position adjustments while monitoring the signal on the scope. In order to calibrate
the time scale, a motorized micrometer stage of the second beam was moved a distance
of x=.1 mm, and the movement of the signal on the oscilloscope was monitored. This
motion corresponds to a round trip path delay of T = 2x/c = 2/3 ps which allows us
to calibrate the time scale on the oscilloscope.
A second type of measurement utilizes a chopper and a lockin amplifier combined
with a linear delay stage to detect the signal. The lockin amplifier and motorized
linear delay stage allow for a slow scan of the signal. This technique has certain
advantages over the formerly described measurement since the speaker may create
distorting effects that result from a nonlinear delay, speaker wobble, and gravity.
Indeed, since we are focusing the device onto a 2 pm photoconductive gap a beam
angle deviation from the central axis of the speaker motion could result in a sinusoidal
scan of the gap.
This results in an intensity variation as a function of
is an undesired source of distortion in our measurement.
T
which
During an oscilloscope
measurement, this may be seen by observing a sinusoidal background modulation
with super position of the desired autocorrelation signal. While the latter effects
are undesired, the speaker measurement does offer the advantage over the lockin
measurement of displaying the signal in real time.
The slow scan lockin measurement on the other hand does not suffer from the
same disadvantages as the speaker scan. Although the slow scan may result in a linear
scan of the photoconductive gap for slight angle deviations, this linear effect allows for
simple correction. In the lockin measurement scheme, both beams, 11 (t) + I2 (t -
T),
are chopped at two different frequencies of approximately 1 and 1.5 kHz using the
inner and outer slots on the chopper. The signal is then detected at the sum of the
two frequencies using a lockin integration time constant of 1 s. As a rule of thumb, the
58
sum frequency is used in order to improve the 1/f noise, however, since the difference
frequency is sufficiently large in this case the performance gain may be negligible in
choosing the sum over the difference frequency. The lockin measurement is performed
at each step of the delay stage throughout the range of approximately 1 mm. The
delay stage moves in step sizes of 10 um which corresponds to equal delay increments
of 66 fs.
Another advantage of using a lockin amplifier measurement over the speaker measurement is the reduction of the background signal. During our discussion of the
autocorrelation signal to background ratio, it was observed that a low intensity is
required to increase the autocorrelation signal to background ratio. Reducing the
intensity has the deleterious consequence of reducing the signal strength. The background signal may be viewed as resulting from higher order taylor series terms in the
nonlinear expansion of the photocurrent as a function of intensity. By chopping at
two different frequencies and using the lockin amplifier to detect the sum of the two
frequencies, we are essentially filtering out the higher order harmonics which would
be present in the taylor series expansion. The result is that this type of measurement
reduces the signal to background ratio, and allows us to operate at higher intensities.
59
-
Laser
Me
Attenuator
Speaker Retroreflector
Linear Delay
AL
(~Z2~
BS,
Device
Lens
M3
BS2
5
Chopper
OSA
Figure 3-12: Experimental Setup
60
Chapter 4
Two-Photon Absorption
Autocorrelation
4.1
Introduction
Two Photon Absorption is a nonlinear process which occurs when an incident photon
has energy greater than half the energy gap E,/2 of a semiconductor but less than E,
[15]. In a semiconductor, an electron making a transition from the valence band to
the conduction band by this nonlinear process simultaneously absorbs two-photons
through a virtual state which effectively gives the electron twice the incident photon
energy [21].
This property is described by a two-photon absorption coefficient 3
which determines the strength of this absorption due to the peak incident intensity
I. The advent of commercially available ultrafast lasers capable of producing the
large peak intensities required for two-photon absorption have spurred research in
this area. Recently, two-photon absorption induced changes in conductivity, which
are nonlinear in intensity, have been exploited for commercial ultrafast autocorrelator
applications.
There are several advantages to using two-photon conductivity as a method for
performing an ultrafast optical autocorrelation.
The traditional method of using
second harmonic generating crystals usually requires a stringent phase matching condition which makes it difficult for optical alignment. Moreover, the signal resulting
61
from a SHG crystal is usually much weaker than the fundamental frequency and requires additional components for filtering, sensitive detection using a photomultiplier
tube, and subsequent amplification.
Two-Photon Conductivity (TPC) autocorre-
lators greatly benefit from their simplicity. By using a TPC scheme, the detector
acts as the nonlinear intensity element thereby reducing the number of components.
Moreover, TPC is relatively insensitive to polarization and phase matching.
Two photon Absorption (TPA) has been demonstrated in LT-GaAs by using
transmission based pump and probe experiments at wavelengths with photon energies below the energy gap [21].
Although the applicability of TPA to LT-GaAs
autocorrelation based devices has been suggested [21], it has yet to be demonstrated.
Recently, other groups have developed two-photon absorption based autocorrelators
using different materials and devices such as AlGaAs [16], ZnSe [30], and GaN [36].
Moreover, researchers have recently shown a 451 fs impulse response at 1.55 pm
which they attribute to two-photon absorption effects in LT-GaAs at power levels of
1 mW [11]. However, others have argued that at such low intensities and at that
particular wavelength single photon absorption effects using a two-step mitigated
process from mid-level traps are likely to be the dominant excitation mechanism for
the optical impulse response [37].
In this thesis, the theory for a proposed two-photon absorption based autocorrelator will be developed and demonstrated experimentally. The results will be compared
toa+r
V"'.
iocystAlatcretr.n
mria
Lk
%,"JLJIJ.,L
'.JL
L
this type"nf aut+ocrrelai
aditi
H
"LLkl
..
L j'
"
JUuA. UIL& U".~(.~
L 'JlLLv"X~
.
1.1.1
(,LtA
A
UXl'JXl
,
VXXX
Uj
VJL
(1(
V
nf~
.
will be compared and contrasted with the method discussed in the previous chapter
using single photon absorption.
4.1.1
LT-GaAs Two-Photon Absorption Motivation
An advantage of an LT-GaAs two-photon absorption autocorrelator over the single
photon autocorrelation technique discussed in the last chapter is that it will result in
a true autocorrelation that is not limited by the carrier lifetime of the material. This
is a consequence of the virtual intensity nonlinearity being instantaneous. While the
principles behind the operation will be discussed in greater detail, for the moment it
62
may be advantageous to compare to the similar case of a second harmonic generating
crystal. For a SHG crystal, the nonlinear intensity propagates in free space and a
slow detector is then used to detect the square-intensity. The analogy with a twophoton conductivity autocorrelator is that one could also imagine a virtual squareintensity V being generated instantaneously and also being detected simultaneously.
Interestingly, both principles of operation are described by a nonlinear polarizability.
For a nonlinear medium, the induced polarization may be written as a taylor series
expansion in terms of the incident electric field as
P = XNE + X2EE + X)EEE
(4.1)
In equation 4.1, XM is the first order susceptibility associated with a constant index
of refraction or constant absorption coefficient. The second order susceptibility x(2 ) is
associated with second harmonic generation, which is not significant in our material.
The third order susceptibility which is responsible for two-photon absorption creates
an intensity dependent index of refraction, or an absorption coefficient which depends
linearly on intensity [31]. Frequently, nonlinear optics text books treat the third order
susceptibility as it relates to an intensity dependent index of refraction. While that
particular description is useful in certain applications, in the sections that follow
we will develop a description in terms of how X(3) relates to a TPA induced change
in conductivity of a material since this process forms the basis of operation in our
application.
Another motivating reason to investigate a two photon absorption autocorrelator
encompasses the supplemental range of wavelengths with which we could operate the
LT-GaAs autocorrelator.
The traditional single photon absorption autocorrelator
could now cover a greater spectral range of mid-infrared operation by utilizing TPA.
This is a desired feature for optical communications applications since fiber coupled
devices typically operate at a 1.5 pm wavelength where they have minimal dispersion.
The last chapter discussed how the LT-GaAs CPW autocorrelator has already been
shown to work for above the band gap light A < 870 nm. The TPA regime of operation
63
will allow for it to work with additional photon energies within the mid-gap to the
conduction band. The corresponding additional optical wavelength could then range
from 900 nm - 1550 nm for an upper estimate.
Finally, for an ultrafast THz transceiver, the response of the material is of critical
importance. To optically generate high frequency signals, it is important to characterize the decay time of the optical impulse response of the material. A study of the
capture time of two-photon absorption generated carriers may provide novel insight
into the feasibility of using optical wavelengths with the equivalent photon energy of
a TPA process, (i.e. 450 nm), as a source of THz signals. Moreover, TPA will also
allow us to further characterize the material under the high illumination intensity
conditions in which nonlinear processes may occur.
4.2
Two Photon Absorption : Classical Model
In general, there are several types of symmetry conditions which must be considered
when describing a nonlinear optical interaction within a medium. These symmetry
considerations are important because one may eliminate certain nonlinear processes
solely by examining the symmetry of the medium.
The first symmetry consideration which we will utilize is that which results when
the material is noncentrosymmetric. This property implies that the material does not
contain a symmetry property known as inversion symmetry. This symmetry consideration determines whether or not X(2) exists. GaAs is considered a noncentrosymmetric
medium, and therefore may exhibit a second order susceptibility X
With this consideration in mind, we will choose an appropriate classical model to
describe the second and third order susceptibility. This model is essentially a modified
form of the classical Lorentz model
[4].
The Lorentz model treats the atom - electron
interaction as a radiating dipole, in which the electron motion could be described by
a harmonic potential. In a modified form of the Lorentz model, the electron motion
may be written as
64
+ 2F + w2x + ax 2
(4.2)
-eE(t)/m.
In equation 4.2 the restoring force is depicted as Frest
-mwx - amx2 , and the
damping force is 2mF± [4]. Note that by utilizing a nonlinear restoring force, where
a determines the strength of the nonlinearity, we have modified the original Lorentz
model to account for a nonlinear response due to the electron's displacement from its
equilibrium position [4]. The potential energy due to this nonlinear restoring force
may be found by integration. This will result in the familiar harmonic potential of the
original Lorentz model, as well as a cubic term due to the inclusion of the nonlinear
correction in the restoring force as show in equation 4.3
U
1
2
=
1
+
±Mx
3max3.
(4.3)
The solution to equation 4.2 may be found by utilizing a pertubation expansion
which is a similar procedure to the pertubation theory used in quantum mechanics
[4].
In pertubation theory, the solution may be written in the form of x
Ax() + A2X(3 ) +
. .
_
5) +
where the superscript denotes the order of the expansion.
defining a linear operator, L =
L{x(l) + Ax
-
2
d
By
+ d + o2, we may rewrite equation 4.2 as
) + A2 X(3 )} = -eE(t)/m - aA(x(') + Ax( 2 ) + A2 x(3)) 2
(4.4)
where we have replaced a in equation 4.2 by Aa. By insuring that each component
within the braces on the left hand side of equation 4.4 satisfy the equation individually
while preserving the order of A, one obtains the following three coupled equations
L{x()}
=
-eE(t)/m
(4.5)
=
-a(x( 1 )) 2
(4.6)
-2ax()x( 2 )
(4.7)
L{x( 2 )}
L{x( 3 )}
-
It is interesting to note that the solution to equation 4.5 involving the first order
65
term in the pertubation expansion is the same as the solution to the classical Lorentz
model in its original form. This solution is then squared to provide for a second order
correction in equation 4.6. Finally, the first order and second order corrections are
supplied into the third order term of equation 4.7 which is of interest for calculating
the third order susceptibility. For two-photon absorption processes, we will consider
the electric field to be in the form of E(t) = Eie(jw") + c.c., where c.c. denotes the
complex conjugate. The third order polarizability is written in terms of the number
of atoms N and the third order solution to the coupled equations as
P(3 )(w) = -Nex( 3 .
(4.8)
Since the third order susceptibility may be written in terms of the polarizability as
P( 3)(w) = X( 3)(w)JE(w) 2 |E(w), we need to find the solution to equations 4.5 through
4.7 to calculate the third order susceptibility. The solution for the third order susceptibility is shown in equation 4.9. In equation 4.9 we have defined a function given
by or(z) = (w2
-
z 2 + jFz)- 1 to reduce the notation
2a 2 N
X(3)
4
[7]
(0 (73()-(-Wi))(2-(0)
+ u-(2wi)).
(4.9)
The above calculation of the third order susceptibility is useful because it illustrates the frequency dependence of X(3 ) (w). Furthermore, this simple model is a good
approximation when the excitation frequency w is far from any resonance wo in the
material. Finally, this formalism illustrates the complex nature of X(3). The complex
behavior of X(3 ) is important because the real part of x(3) is associated with a non-
linear refractive index, while the imaginary part is proportional to the two-photon
absorption coefficient
#
[12]. An expression for the two-photon absorption coefficient
in terms of the third order susceptibility is given as
2
2
con Cf
X(3 )',
where X (3)' is the imaginary component Of X(3) [12].
66
(4.10)
A more detailed expression
relating / to X(3 is found in reference [12] which takes into account the tensor nature
of 0.
Tensor Form of Two-Photon Absorption
4.3
Up to this point we have opted to describe the third order susceptibility as a scalar
quantity for simplicity. In this section, we will discuss the true tensor nature of X(.
In general, X() in equation 4.1 is a second order tensor, X(
is a third order tensor,
and X(3) is a fourth order tensor as shown in equation 4.11 [4]
p)
(wO + Wn +
Wm)
=D
Z X1 (WO,
Wn Wm)Ej
(WO)Ek(Wn)E(Wm).
(4.11)
jkl
In equation 4.11, the indices j,k, and 1 represent a summation over the coordinate axis,
and D is a degeneracy factor associated with the distinct permutations of frequencies WO,
Wn, Wm
[4]. In general, there are 81 third order susceptibility tensor elements.
However, calculation of the tensor elements may be simplified by taking into account
crystal symmetry considerations. For the zinc-blende structure of GaAs, (symmetry
class 43m), only 21 of the 81 third order susceptibility elements are non-zero. Furthermore, only four of the 21 elements are independent [12]. These four elements
correspond to X 3)
,3)
(3)
and X(3)
Various approaches have been adopted
to calculate these susceptibility elements by using methods developed in quantum
mechanics. In spite of the simplifications achieved by symmetry considerations, the
fourth order tensor nature of the third order susceptibility remains ill adept for analytical manipulation and a numerical analysis is beyond the scope of this thesis. The
interested reader is referred to a simulation performed by Hutchings et al on regular
GaAs [12]. In the remainder of this thesis, we will continue to treat the two-photon
absorption coefficient as a scalar quantity. We will note, however, that variations on
the two-photon absorption coefficient in LT-GaAs may occur depending on the incident polarization orientation as a result of the anisotropy in the fourth order tensor
nature of X( 3 ) in GaAs.
67
4.4
Two Photon Absorption Rate Equations
In the analysis that follows, we will develop the rate equation description of twophoton absorption and a circuit model which illustrates our measurement. First we
Recently, Smith et al have developed
begin with the diagram shown in figure 4-1.
n
CB
A
T3N
la t
-Cl
T
2hv
hv
4
AL
Et
j2jP
2hu
T
2
VB
Figure 4-1: Two-Photon Absorption Dynamics in LT-GaAs from [21].
a rate equation model which illustrates the two-photon absorption dynamics in LT68
GaAs. The corresponding rate equations are written as follows
di- =dt
+ 1/
hv
2hv
dN
dt
.t
(4.12)
T4
73
I aJo N +n
-=---+-(4.13)
hv
71
73
dNi
-Iait
NT
N
ri
-=
-+ - + dt
hv
T2
71
74
(4.14)
Here Nt is the electron concentration in the traps, N is the electron concentration
in the bottom of the conduction band, and n is the electron concentration in the
upper excited states in the conduction band. It is interesting to note that at 900
nm, the corresponding two photon energy is E
=
2hv which corresponds to 2.75 eV.
Consequently, n electrons excited into this upper state have an excess kinetic energy
of 1.32 eV above the energy gap of E.
=
1.43 eV. The absorption coefficient from the
traps is given as at, and the linear two-photon absorption is described by atpa =
1.
The carriers excited from the mid-level traps at 900 nm are excited to a state of
2.09 eV, which contain an excess kinetic energy of - 662 meV. At this particular
wavelength, the SPA from the traps and the TPA excited carriers are excited into
different regions in the upper conduction band, and we have illustrated this with the
gray region corresponding to n carriers in figure 4-1. For an excitation energy closer
to the mid-gap, near 1500nm, the energy separation between the TPA carriers and
the SPA trap carriers is reduced (~ 130 meV).
The first measurement of the TPA coefficient
/
in LT-GaAs was performed by
Smith [21] using a standard measurement technique known as the z-scan. In this
experiment, a single incident beam is focused onto the sample and the transmitted
optical power is measured. As the position of the sample is translated along the
focusing axis, the incident intensity strength varies on the sample. For single photon
absorption, the transmitted power increases as the input intensity increases due to
absorption saturation effects.
For a two photon absorption process, on the other
hand, the transmitted power decreases as the incident intensity increases as shown in
figure 4-2. This is a result of the increased absorption due to pumping into excited
69
states in the upper conduction band from a TPA process. From these experiments,
the TPA coefficient was determined for various growth and annealing conditions at
a wavelength of 900 nm. In our device, we will assume a nominal value of #3
=
35 cm/GW which corresponds to the value reported by Smith for our growth and
annealing conditions [21].
1.1o
0.9
V
.8
0
-
0. 4
-0.1
0
-0.05
ExperimenoI
0.05
0.1
z (mm)
Figure 4-2: Zscan Measurement used to determine the two-photon absorption coefficient from [2]. At the position of the beam focus, z=O, the incident intensity is
maximum and two-photon absorption reduces the optical transmission.
We would like to use this value of the two photon absorption coefficient, 0, in rate
equations 4.12 through 4.14 which describe the processes shown in figure 4-1. Before
doing so, however, we need to determine the time constants which will allow us to
estimate the resulting carrier concentrations in the bands.
The time constants reported in [2, 21] by Smith et al are shown in table 4.1. It is
worthwhile to examine these time constants since they illustrate the carrier dynamics
of interest in our devices.
The experiment used to obtain the data in table 4.1 involves a pump and probe
optical transmission setup. In this experiment, carriers are pumped with an intense
saturating pump beam consisting of 150 fs pulses at a wavelength of 870 nm. This
intense pump beam saturates the absorption at the bottom of the conduction band
due to band filling. Note that 870 nm is at the edge of the conduction band where both
70
T_
Value (ps)
1.4
T2
3
73
100
_4
.31
Time Constant
Table 4.1: Time constants describing TPA dynamics as reported in [21].
two-photon absorption and single photon absorption processes take place, albeit at
different locations in k-space. The probe beam, which is much weaker than the pump
is then focused onto the same spot. Subsequently, the transmitted output power is
collected as a function of the time delay between the pump and probe optical pulses.
While the time constants extracted from the formerly described experiments show
optimistic results for reducing the carrier capture time with excitation energy (i.e.
T4 <
Ti),
the explanation as to why this occurs is suspect. The explanation for the
reduced carrier capture time with excitation energy provided by Smith et al is given
in terms of the increase in carrier velocity with excitation energy [22].
Applying
the increase in the carrier velocity to a model which relates the carrier lifetime to a
coulombic trap potential cross section and thermal velocity
(4.15)
e
is not sufficient to explain the reduction in capture time. While the thermal velocity
of the carriers vt oc E / 2 , will increase with energy, we expect the carrier capture cross
section to reduce as o- cx E- 1 for an optical phonon transition to o- cX E- 3/ 2 for an
acoustic phonon transition [19]. This implies that rather than having the capture rate
become faster with excitation energy, the capture time actually increases and becomes
slower. This makes intuitive sense in terms of the lessened coulombic attraction from
an ionized site at a further distance in the energy band.
The latter discussion illustrates the importance of analyzing the dynamic processes
behind two-photon absorption excitation. If the time constants were to indeed decrease by a factor of 1/2 for carriers excited higher into the conduction band through
71
a TPA process, when compared to a SPA process, this would have profound consequences for THz devices. This would imply that we could double the bandwidth in
our devices by using high energy excitation. Our interest in such phenomena initiated
our investigation. A recent study of high energy excitation was performed by Beard
et al in which a 400 nm pulsed source was used to study the transient photoconductivity of LT-GaAs. The results from these experiments produced more conservative
values for the time constants with the behavior we would expect [1]. Namely, that
the bottleneck for high-energy excitation relaxation is through an LO phonon-assisted
relaxation into the bottom of the conduction band
(~ 1ps) followed by a carrier
trap-
ping process [1]. We will modify the time constants in table 4.1 by using a value
of
T3
= 1 ps, and T4 = o0 ps. In the latter, we are assuming that a direct capture
into the traps, by a radiative or by other means, is much longer than the other relaxation processes. Table 4.2 shows the time constants which we will use in the steady
state rate equations. The rate equations 4.12 through 4.14 could be used to find the
Time Constant
Ti
Value (ps)
1
3
T2
T3I
1000
T4
Table 4.2: Time constants corresponding to figure 4-1 which are used in the rate
equations to calculate the steady state carrier concentrations.
steady state carrier concentration due to optical excitation. We will calculate the
carrier concentrations which correspond to a total time averaged power due to both
the pump and probe beams of Pav, = 30 mW. The two beams are focused onto an
approximate 10x10 pm 2 area providing us with a time averaged intensity of
'avg
= 30
kW/cm 2 . For a modelocked beam with a 100 fs pulse duration, at a repetition rate
of 100 MHz, this average intensity corresponds to a peak intensity given by
Ipeak
Iavg AT
72
(4.16)
where AT is the pulse duration and T is the period between pulses. For our operating
conditions, we achieve an instantaneous peak intensity of
',eak
= 3 GW/cm2 . The
latter is significant because it allows us to determine the relative strength of the
two photon absorption generation rate relative to the single photon generation from
the traps. Using this calculated value for the peak intensity, the net two photon
absorption is given by atpa =
1#I
=
105 cm-.
Therefore, at these operating conditions
the two-photon excitation mechanism is about an order of magnitude less than the
single photon absorption contribution from the traps. Note that the single photon
absorption for a band to band transition is zero since we are operating at photon
energies below the band gap. The single photon absorption coefficient from the traps
is taken to be at 1 4000 cm- 1 [21]. Using this value for the absorption coefficient,
and the time constants in table 4.2 in the rate equations, one may obtain an estimate
of the peak carrier concentrations shown in table 4.3. In order to estimate the peak
carrier concentrations under pulsed illumination, one may make a few simplifying
assumptions. The first assumption we will make is that the carrier relaxation from
the upper conduction band to the lower conduction band during the pulse duration
(AT) is negligible since AT <
3
< T 4 . This allows us to estimate the initial value of
the carrier concentration in the top of the conduction band, n in equation 4.12. We
find that by assuming a constant generation rate throughout the duration of the pulse,
nr
gAT = 5.8 x 1018 cM-3. After the pulse has passed, the upper conduction band
carriers exponentially relax into the lower conduction band with a time constant 73 in
our model. Since equations 4.13 and 4.14 are linear first order differential equations,
the analytical solution may be found. Table 4.3 shows the resulting peak carrier
concentrations after solving the latter equations and analyzing the peak values in
each of the respective bands.
The above simplified model may be used to produce an estimate of the carrier
concentrations and to illustrate the dynamics involved. However, we must proceed
with caution when using the simplified rate equation model. While the latter model
uses empirically observed time constants, it does not take into account more complicated processes. In particular, we note that to the first order, the model has allowed
73
Steady State Concentration
n = 5.8 x 1018 cm- 3
N = 2.14 x 1018 cm-3
Nt = 2.9 x 1018 cm-3
Table 4.3: Peak carrier concentrations calculated by solving equations 4.12 to 4.14.
us to estimate the carrier concentrations involved. However, since the carrier concentrations are so large, we note that a more accurate model would be required to take
into account the large carrier density (i.e. bandfilling, trap saturation).
4.4.1
Two Photon Absorption Circuit Model
In this section, we will begin to develop a circuit model that describes our measurement. Proceeding as we did in the single photon absorption case, we begin to derive
an equation for the sensitivity by starting with the photoconductivity.
-(t) = q(upen(t) + php(t))
0-(t) = Udark +
(4.17)
'photo(t).
The conductivity above has been written explicitly in terms of the dark conductivity
and the photo-induced change in conductivity. For our DC measurements, its really
the conductance that we are interested in. So we proceed to construct an equation
involving the conductance assuming a square illumination area
G(t) = o-(t)A/L
G(t) =
(4.18)
Gdark + Gphoto(t).
Now we could investigate the steady state carrier concentrations. The electron concentration absorbed beyond the surface into the bulk may be written as
n(x) = g(x)Te.
74
(4.19)
We would expect the intensity to decay into the the bulk exponentially with a decay
constant given by at, since the single photon absorption from the traps is greater
than the two-photon coefficient. To be more quantitative, the differential equation
which describes the intensity absorption depth is written as [17]
d(x)
(-a -
31(x))I(X).
dx
(4.20)
For our conditions, /1(x) is an order of magnitude less than the single photon absorption constant and the volume over which the carriers are generated is essentially
the same as the SPA case. Note that equation contains an analytical solution and
may be solved for the general case in which #1(x) > a. Proceeding to integrate
equation 3.9 leads us to an equation for the desired conductance. Note, that in this
case the quantum efficiency 71 should decrease for our device. This results since our
bulk thickness L
=
1.65 pm was optimized for above the band gap illumination in
which the absorption depth is less than the absorption depth for below the band gap
illumination. For below the band gap illumination, our thickness L is approximately
1/2 the absorption depth L
=
1/(2at). In order to improve the quantum efficiency
for future design considerations, the thickness of the device should be optimized such
that L > 1/at. Expressing our photoconductance below in terms of the quantum
efficiency and material parameters, we develop the following expression
Gphoto(t) = 71q(pe
- Ph) (a + /3o(t))Io(t)
Y(a + NO 0(t)1 0 (t)
(4.21)
Gphoto(t)
Gspa(t) + Gtpa(t).
(4.22)
hva
As noted above, the photoconductance has been written explicitly in terms of the single photon absorption and a two-photon absorption contribution. Similar expressions
have been derived in the literature for other structures [18]. From a systems perspective, it may be advantageous to view the photoconductance in terms of an output of
a system due to an intensity input as is shown in figure 4-3. The impulse response of
the system h(t) decays as an exponential with the dominating carrier lifetime of the
75
material T.
In the frequency domain, the photoconductor acts as a low pass filter
with a cut-off frequency given by
f, =
1/(27T). Figure 4-3 depicts the spectrum due
to a gaussian input intensity of 100 fs pulse duration and an ideal low pass filter with
cut-off frequency
T,
fc.
The filter cut-off frequency corresponds to a carrier lifetime of
= 500 fs, which results in a cutoff frequency
f, =
318.8 GHz. Accordingly, the po-
tential bandwidth due to this cut-off frequency would be BW = 318.6 GHz. In order
Ith(t)e
G (t)
Intensity Spectrum
2
1~~
I
I
I
I
I
I
I
1.51
1
Ideal Filter IH(f)I
0.5
0
-1 1
-10
-8
'
'
'
'
'
0
f (THz)
2
4
6
8
'
I~
-6
-4
-2
10
Figure 4-3: Intensity spectrum of a gaussian input intensity beam with a 100 fs pulse
duration. Also shown is the ideal filter function presented by the finite response time
of the photoconductor.
to continue our development of the autocorrelator model, a few key points need to
be observed. The above intensity spectrum contains a combination of high frequency
76
components, and additional low-frequency components. In traditional communications applications, a signal is typically upconverted to a high frequency where the
entire signal sees a transmission line with a characteristic impedence ZO. Since that
is not the case here, we could take advantage of using superposition to treat the input
as a sum of a high frequency component and a low frequency component in order to
solve for the output due to the broad spectrum.
In our autocorrelator, we observe that the low frequency component of G(t) will
not require a characteristic impedence transmission line model (distributed model)
and the circuit could be treated as a lumped element. However, the high frequency
components will see the characteristic impedence and should be modeled as in the
previous chapter.
<GO>
<Gspa>
V0
<iHF(
RL
Figure 4-4: Circuit for TPA Measurement.
In our new model, as shown in figure 4-4, we depict the high frequency contribution
for the conductance as a voltage dependent current source and the dc component as a
lumped element. The reason a current source is chosen is due to the observation that
changing the macroscopic load (DC resistor RL) should not change the value of the dc
77
current. This result comes from treating the termination as some effective impedence
for high frequencies which does not depend on the macroscopic large load resistor
RL.
Intuitively, one may imagine that most of the energy of the high frequency
signal will radiate or suffer attenuation before reaching the macroscopic load. The
complete circuit model is as shown in figure 4-4, where the high frequency current
source amplitude may be calculated using equation 3.5.
For a d.c. measurement across the resistor RL, the output voltage
VR
VOGTRL
iHFRL
1+RLGT
1+RLGT
VRL
is given by
where GT is the total time averaged photoconductance. For optimal operating conditions, we would like to have the high-frequency current source contribution minimized and a linear output voltage with respect to the time average conductance.
This imposes a constraint on our load resistor RL. Specifically, we will require that
RLGT << 1. With this simplification, we could rewrite equation 4.23 as
VRL
VRL
(4.24)
VoGtRL + iHFRL
V(< Go > +< Gspa > +< Gpa(T) >)RL) +iHF(T)RL
The only terms in the above equation that depend on the delay
(4.25)
(T)
between the
pump and probe beams are the two-photon absorption time averaged conductance
contribution, and the high frequency current source contribution. For a reasonable
estimate, lets approximate the two-photon absorption conductance as being smaller
than the single photon absorption conductance by a factor of 10.
Moreover, lets
approximate 1/ < Gtpa > as being 10 MQ, which corresponds to a single photon
absorption time averaged resistance of 1 MQ. Now we will choose a value of RL
=
100
kQ which satisfies RLGL << 1. This will result in a two-photon absorption peak
signal of V0/10 = 3V. A worse case time averaged high frequency current source
contribution of 1 pA will result in a 100 mV of a background signal. From Verghese's
signal to noise analysis and our discussion in the previous chapter however, we would
78
expect the current source which represents the single photon absorption from the
transmission line nonlinearity to get weaker as we increase the intensity.
4.5
Experiment and Conclusions
In this experiment, the same setup was utilized as in the single photon absorption
experiments discussed in the previous chapter. Namely, an interferometric setup in
which the two beams were cross polarized using a half wave-plate and focused onto the
photoconductive gap in our coplanar waveguide was utilized. A portion of an unused
beam which was transmitted through one of the beamsplitters in our setup was feed
to an HP Optical Spectrum Analyzer to monitor the central wavelength. The laser
was tuned to a central wavelength of 900 nm. In addition, spectral broadening of the
pulse was observed when modelocking was enabled.
Two types of measurements were performed. In the first measurement, a speaker
with a mounted retroreflector was used as a delay stage. The results of this experiment
are shown in figure 4-5 for an incident power of P, 9 = 30 mW and in figure 4-6 for
an incident power of Pg = 170 mW.
For a second measurement, a lockin amplifier is used in conjunction with a linear
delay stage and a chopper as discussed in the previous chapter.
Both beams are
chopped at two different frequencies and the signal is detected at the sum frequency.
The results are displayed in figure 4-7.
4.5.1
Two Photon Absorption Discussion of Results
In order to verify our results, we compared our measurements to a commercial autocorrelator produce by Femtochrome. Femtochrome's autocorrelator uses an LiIO 3
second harmonic generating crystal for an intensity-intensity autocorrelation. Their
setup contains an optical filter which blocks out stray radiation near the fundamental
of 900 nm, which is close to the visible spectrum where ambient light would otherwise
overwhelm the detector. In addition, the filter is a band pass near the frequency of
the second harmonic 450 nm. The detection is performed using a photomultiplier de79
2 -
2 SHG Crystal
-
LT-GaAs Device
1.5-
1 --
0.5 -
-0.5-
- 1111111111
-0.5
-0.4
-0.3
-0.2
-0.1
0
t
0.1
0.2
0.3
0.4
0.5
(ps)
Figure 4-5: TPA autocorrelationfrom a speaker measurement at Pavg=30mW, A
=
900 nm, Bias=30 V. A half wave plate was used to minimize coherence effects and to
obtain the minimal pulse width.
tector. The delay stage comprises of a rotating mirror arrangement at 10 Hz, which
may lead to a more linear scan over our speaker setup. The output of the photomultiplier is then sent to an amplifier with variable gain for subsequent amplification.
The signal is monitored on an oscilloscope which is triggered at the rotating mirror
frequency.
Our measurements were performed with an incident power ranging from 30 mW
to 180 mW. At lower intensities, the signal to noise ratio was too low to obtain a
good measurement. The best measurements occur at the higher incident power levels
where we would expect a greater peak intensity and two-photon absorption signal. In
80
2
1.5-
-
---SHG Crystal
LT-GaAs Device
0.5-
-0.5-
-1
-0.5
1
-0.4
1
-0.3
1
-0.2
1
0
1
-0.1
t
1
0.1
1
0.2
1
0.3
1
0.4
0.5
(ps)
Figure 4-6: TPA autocorrelationfrom a speaker measurement with Pavg=-l 7 0mW,
A = 900 nm, Bias=30 V. A half wave plate was used to minimize coherence effects
and to obtain the minimal pulse width.
addition, as we increase the power we would expect the single photon absorption signal
to decrease as a result of two different mechanisms. The first mechanism responsible
would be the decrease in the absorption coefficient as a result of band-filling. At
these high pump intensities we expect to be significantly releasing carriers from the
traps which results in a decrease of the net trap absorption coefficient as a result of
the reduced available states in the conduction band as discussed in chapter one. The
second mechanism which results in the decrease of the SPA signal follows from our
signal to background ratio analysis of SPA discussed in the previous chapter. In the
analysis in chapter three, we concluded that as we increase the intensity the single
81
2-
SHG Crystal
LT-GaAs Device
1.5-
0.5-
-0.5-
-1
-0.5
1
-0.4
1
1
1
1
1
-0.3
-0.2
-0.1
0
0.1
t
0.2
0.3
0.4
0.5
(ps)
Figure 4-7: TPA Lockin Measurement with A = 900 nm, Pg=50 mW, Bias = 20V.
A half wave plate was used to minimize coherence effects and to obtain the minimal
pulse width.
photon absorption sensitivity should decrease. Furthermore, at low intensities we did
not observe a SPA carrier lifetime limited signal. This is expected since for below the
band-gap illumination the absorption coefficient is lowered and we are generating less
carriers per unit volume. Moreover, since our device thickness is not optimized for
below the band-gap illumination we would expect the SPA autocorrelation signal to
be negligible.
In order to minimize coherence effects, the beams were cross polarized using a
half-wave plate. As the half-wave plate is rotated, the pulse-width of the measured
autocorrelation signal decreases. We have observed the measured FWHM width of the
82
autocorrelation signal to decrease from 500 fs to 300 fs. This is the effect of reducing
the electric field - electric field autocorrelation signal that results from interference.
Since our autocorrelation is not limited by the carrier lifetime, we would expect the
electric field autocorrelation signal to be broader than the intensity autocorrelation.
This result follows since the intensity autocorrelation is essentially the autocorrelation
of the square of the electric field which makes it narrower, which is consistent with
our observations.
The autocorrelation signal performed by using TPA resulted in a FWHM of 300 fs
which is much narrower than what would be possible with a single-photon absorption
carrier lifetime limited autocorrelation. For a lifetime limited autocorrelation, the
carrier lifetime could be extracted from the FWHM by using FWHM =
'[).
This
would result in a carrier lifetime of 216 fs which is much faster than the reported
values for LT-GaAs. We also note that our signal closely matches the SHG crystal
measurement, with an appropriate sech 2 (t/A) shape which gives us confidence in our
results. Using a 1.5 deconvolution factor, we find that the inferred optical pulse width
is 200 fs.
83
84
Chapter 5
Concluding Remarks
In chapter 2 we discussed the material properties of low temperature grown GaAs.
We concluded that low-temperature grown GaAs has a high mobility, a large dark
resistance, and a fast capture time which makes it attractive for our transceiver
application. It is interesting to make a comparison of LT-GaAs to other materials
which have also shown merit for this application. A table comparing the figures of
merit of similar devices from [8] is provided in the table below. On the basis of carrier
Material
CarrierLifetime (ps)
Mobility (cm 2 /Vs)
Cr:doped GaAs
50 - 100
1000
Amprphous silicon
MOCVD CdTe
.8
-
20
.45
1
150
lifetime and mobility, LT-GaAs seems to be the material of choice. When considering
other features such as the dark resistance one may conclude that LT-GaAs is an
even more promising material for our transceiver application. One will find in the
literature that the mobility values of annealed LT-GaAs have been reported to range
from lze = 400 cm 2 /Vs ([24]) - e = 3000 cm 2 /Vs [1, 35]. The reported values may
differ on the basis of annealing and growth conditions. In addition, Zamdmer [42] has
suggested that the discrepancies which arise when comparison is made for the same
growth/anneal conditions may reside on the influence of the semi-insulating substrate
on the Hall measurements. The lower reported mobility values have been obtained
by removing the substrate from underneath the LT-GaAs layer. However, in this
85
thesis we have adopted to consistently use the upper estimates for the mobility since
it seems to represent the measured consensus in the present literature. In either case,
we will note that the mobility is well within a reasonable value when compared to the
electron mobility in regular GaAs y,
=
7000 cm 2 /Vs. As we increase the annealing
temperature, we expect the material properties to converge toward regular GaAs as
the defects introduced during low temperature growth are reduced. The general trend
of mobility should still hold, that is for the as-grown material the mobility is reported
to be pe =1 cm 2 /Vs, whereas for the annealed LT-GaAs this value should increase
considerably.
After discussing the material properties of LT-GaAs, this thesis investigated the
various applications of our ultrafast transceiver. Chapter three focused on autocorrelation experiments which were used to characterize the response time of the circuit.
In this chapter we discussed the factors which effect the sensitivity of our circuit.
One of the schemes to improve the efficiency, is to use a particular geometry in the
photoconductor which includes interdigitated fingers. Our finger spacing is sufficient
to neglect the parasitic RC capacitance which is associated with the external circuit
geometry as opposed to the bulk properties of the material. Future improvements on
this interdigitated finger geometry may lead to improved efficiency at the expense of
a more complex design process. Studies have shown that an optimal electrode width
of 300 nm, with a gap separation between neighboring electrodes of 300 nm, could
lead to an improved efficiency and still remain recombination limited [5]. However,
electrode spacing of less than 200 nm have shown an RC time constant limited response which is larger than the recombination limited response. In addition, by not
noticing a characteristic dependence on the FWHM of the signal with applied bias
a transit time limited response is ruled out for the 300nm electrodes. It would be
interesting to develop these types of devices in the future for an improved efficiency.
Chapter three also discussed the influence of the incident intensity on the carrier
lifetime. It is important to emphasize that the instantaneous carrier densities generated under continous wave illumination and modelocked illumination with pulse
widths on the order of 100 fs will differ by four orders of magnitude under our fo86
cusing and incident power levels. These effects must be taken into account when
making a comparison between continous wave generated data, and modelocked data.
Moreover, the results suggest that under high illumination intensities, trap filling effects must be taken into consideration when resolving the capture time. Under the
higher illumination intensities, which may correspond to incident time average power
level of 30 mW which is only a fraction of the 700mW typically available from a
modelocked laser; the data suggests that hole-capture or trap emptying time is the
bottleneck for the carrier response. With these observations, it becomes necessary to
put everything into the perspective and to discuss the results in terms of the implications for a high-frequency network analyzer design. These results suggest that under
continuous wave photo-mixing, in which the instantaneous intensities are so low as to
make a negligible pertubation on the equilibrium trap densities, the carrier capture
time would be on the order of 200 fs. This could lead to a desired 3dB bandwidth of
800GHz, in which a 1 THz generation could be produced or detected although with
considerable attenuation due to the subsequent roll-off beyond the cut-off frequency.
For other developing applications which may be of interest to this technology such as
time-division mulitiplexing in which the short pulse durations may be exploited, our
results indicate that the incident intensities must be considered when prediciting the
carrier capture time response.
In addition to the intensity experiments, chapter three presented our results on
the bias dependence verses the carrier capture time. These results are in agreement
with the conclusions of Zamdmer et al which state that the capture time is related
to the barrier lowering of the coulombic trap potential with an applied electric field
[27]. We have applied a modified model which takes other subtle details into account,
such as the barrier increase in the reverse direction and a thermal escape probability,
which provides an ohmic fit at a low bias range which is in agreement with our
data. Furthermore, the nonlinear increase in the current verses voltage behavior is
predicted by the model with a fairly good fit. As the applied voltages approach 60V,
it is observed that the model no longer holds and we have suggested impact ionization
to be the dominant mechanism at these applied voltages corresponding to electric field
87
strengths on the order of 10' V/cm.
A novel autocorrelation method using LT-GaAs is presented in chapter 4 which
utilizes two-photon absorption to produce a carrier concentration which is nonlinear in
intensity. Since two-photon absorption has the effect of doubling the incident photon
energy, we have observed that utilizing a wavelength of 900nm places the carriers
high into the conduction band through a TPA process with an excess kinetic energy
of 1.32 eV over the conduction band minimum. In order to account for the carrier
dynamics, we have provided a model which was originally proposed in reference [21, 2]
which utilizes empirically observed time constants. This model allows one to predict
the carrier concentrations under steady-state conditions, and has been suggested to
provide an estimate for our transient experiments.
In developing the model, we
have investigated the response time of carriers excited high into the conduction band
and have concluded that they become trapped with a capture time which is slower
than carriers excited into the conduction band minimum through a single photon
transition. Our conclusions are based on the assumption that new recombination
channels are not introduced at these high energies and that the dominant trapping
processes bottleneck is through the traps which present a coulombic potential.
While our studies and discussion in chapter four have suggested that the mechanism responsible for the increase in capture time with TPA excitation may be related
to a decreased capture cross section, we would like to offer some more interesting
details regarding these high excitation energies. It is interesting to take note that the
carriers excited with this much excess energy (1.32 eV) may scatter into the L or X
valleys which reside at .3 eV and .46 eV above the F valley minimum respectively [1]
in LT-GaAs. Here the electrons have a lower mobility than in the conduction band
minimum due to an increasing temperature, and a larger effective mass due to the different curvature in these valleys. The mobility may be written as Pe
e<
TcoII
>
/m*
where m* is the effective mass, and < r,0u > is the mean scattering time. The lower
mobility implies increased scattering events. It would be interesting to perform UV
experiments with excitation wavelengths at 450 nm to determine if any hot carrier
effects may be involved in creating new recombination channels at these wavelengths.
88
One suggestion for performing such an experiment would be to utilize a frequency
doubler (SHG crystal) at 900nm to characterize the capture time using single photon
absorption experiments. Although experiments have been performed on LT-GaAs at
these wavelengths [1], they have not been performed at intensities large enough to
excite the high carrier densities in which hot-carrier phenomenon become prominent.
Our results have shown that it is possible to use LT-GaAs as a two-photon absorption autocorrelator.
The two-photon absorption coefficient in LT-GaAs /
=
40cm/GW has been reported to be nearly twice as large as it is in regular GaAs. In
addition, other materials such as GaN, and ZnTe, contain a lower value of 4 = 16
cm/GW and
=_6 cm/GW respectively [36, 30]. However, this increase in the two
photon absorption coefficient in LT-GaAs comes at the expense of a residual single
photon absorption (SPA) from the mid-level traps, which is minimal in other materials such as regular GaAs. In conclusion, we have shown TPA may be used to perform
an autocorrelation which does not depend on the carrier lifetime of LT-GaAs. Moreover, this may be a suitable alternative to SHG crystal autocorrelators in terms of
parts reduction.
89
90
Appendix A
Laser Operation
Two different laser systems, in two different labs, were used to perform the experiments described in this thesis. This was necessary in order to cover the broad spectral
range required in our experiments. Namely, the single photon absorption experiments
required a laser tunable with wavelengths less than the band gap of LT-GaAs (A < 870
nm), whereas the two-photon absorption experiments require wavelengths (A > 900
nm). Here we will discuss the laser system used to obtain the single photon absorption
data in Professor Qing Hu's lab.
This laser system comprises of a Spectra Physics Argon-Ion laser and a Tsunami
3960 Ti:Saphirre fs laser. The current optics set in the Tsunami laser allow for a
tunable wavelength of 700 nm - 850 nm. The specifications provided with the laser
state that typical pulse width is between 80-130 fs. The repetition rate of the laser
is 82 MHz. An outline of the procedure to operate the laser is provided below [42].
A.0.2
Start-Up Procedure
1) In order to start the laser system, one must first turn on the chilled water which
flows into the lab by opening the two valves on the left wall when first entering the
lab. One may verify that the water is on by looking at a glass window in the pipe
which contains a spring that will vibrate when there is flow.
2) Next, one may proceed to turn on the mechanical pump located on the floor by
91
the Neslab heat exchanger. This pump increases the flow rate and should be sufficient
to turn off the flow indicator on the Argon-Ion laser status indicator. The pressure
should read 100lb/in2
3) Before proceeding to turn on the Neslab Heat Exchanger, one should verify that
the water is filled up to approximately one inch from the top. This heat exchanger
uses untreated water and may be filled as required. Once the water level is sufficient,
the Neslab heat exchanger may be turned on. This heat exchanger forms a closed
loop which passes through the Argon-Ion power supply. The water temperature of
the laser should decrease to about 60 0F as read on the thermometers on the wall for
both the supply and return readings.
4) Located underneath the optical table is a separate closed loop system for the
Tsunami laser. This system is controlled by a Neslab chiller which should be operated
at 20 0 C. After this system is turned on, the Argon Ion laser is ready to be turned
on.
5) Turn on the Argon Ion Laser and allow for it to warm up for atleast a half
hour before use. The laser power should be set for a 3W warm up temperature. This
should be set by placing the laser in current mode and increasing the current to 3W.
Then the laser should be placed in power mode and the power should be increased to
3W. Once the laser has been allowed to warm up, the power could be increased to the
desired pumping power. The suggested power for modelocking is obtained by setting
the Argon-Jon laser to apower setting between 6W to 7WA.
This is accomplished by
first setting the Argon-Ion laser in current mode and incrementing the current until
the output power is achieved. Subsequently, the laser should once again be placed
in power mode and the power should be increased until 7W is achieved. The power
mode on the laser attempts to maintain a constant output power by stabilizing the
current fluctuations.
A.0.3
Beam Alignment
Beam alignment adjustments may need to be made from time to time in order to
optimize the power output of both the Argon-Ion laser and the Tsunami saphirre
92
laser. If the power output on the Argon-Ion laser is saturated at a low value, the first
adjustment that should be made is located on the external controls at the rear of the
argon ion laser. Using this and the Beam-Lok steering electronics which indicates
the position of the beam, the beam should be centered with the Beam Lok off. Once
the beam is centered on the Beam-Lok stearing module, the Beam Lok should be
turned on in order to allow for beam drift correction. If this does not solve the power
problem, refer to the Argon-Ion laser manual.
Similarly, the output power on the Tsunami laser may be optimized by performing
external adjustments. These adjustments should be made by balancing the output
coupler (M10) adjustments with the high-reflector (MI) adjustments. Please refer to
the Tsunami manual for details about how to optimize the power. On rare occasions,
it may be necessary to make internal alignment adjustments. This should only be
done as a last resort when the performance could not be obtained by the external
adjustments.
A.0.4
Mode-Locking the Tsunami Ti:Saphirre
There are a few alternative methods to determine if the Tsunami laser is modelocked.
The most unambiguous way to determine the quality of the modelocking is to use
an aligned autocorrelator setup in which the zero-path difference is already achieved.
However, since these are not readily available one must usually rely on methods which
will indicate if the laser has initiated modelocking but will not provide information
about the quality of the generated pulses.
To initiate modelocking, turn on the mode locking electronics module. The modelocker enable button on the Tsunami electronics module should be suppressed. The
enable LED will then turn on and the pulsing LED should become stable if a pulse is
detected at the AOM rate. Alternatively, one may monitor the output of the photodiode through a BNC connector on the monitor output located on the 3955 module.
The output should be monitored on a oscilloscope by using the sync output of the
module as the trigger to determine if a signal is being generated at the pulse repetition
rate [42].
93
If the laser is properly modelocking, the output spectrum of the laser pulses should
increase. If one has access to an optical spectrometer, this could be a good indicator of
modelocking. Alternatively, one may us the Jbovin Spex spectrometer located on the
optical bench. This uses a grating/photodetector to determine the output spectrum
as the selected wavelength is tuned by a motor-driven dial. Software was written for
this spectrometer and is available for LabView. Note that Hewlett Packard makes
fiber coupled spectrometers, similar to electronic spectrum analyzers, which would
serve nicely for this purpose since the speed of the acquisition is greatly increased.
The last alternative which serves as an indicator of modelocking is to view the
speckle pattern off of a low intensity portion of a card or object placed in the beam
path. If the laser is modelocked, the beam spot should become less speckled [421.
Note that the laser beam should never be viewed directly, and proper laser safety
precautions should be taken at all times. This indicator is mentioned only because it
may aid the more experienced user who will recognize it. For a new user to the system,
this step should be avoided since it will not be a sufficient indicator of modelocking
performance and is not easy to determine.
A.0.5
Shut-Down Procedure
The shut-down procedure is similar to the reverse of the start-up procedure.
1) First bring the power down to 3W. This is done by decreasing the power in
constant power made to 3W and then by switching to current mode and repeating
the ramp down to 3W. This ensures the laser will start up by ramping up to this
power level during the next start-up.
2) Next, the Argon Ion laser should be turned off. The Tsunami chiller is then
turned off followed by the mechanical pump and Neslab chiller. It is very important
that the cooling system is turned off when not in use to avoid condensation build
up on the laser rod which may permanently damage the laser. Finally, the water
valves should be closed. The mode-locking electronics module should also be turned
off when not in use.
94
Appendix B
Appendix: Measurement Circuits
In order to perform the measurements described in this thesis, it becomes nececessary
to convert the current out of the device into a voltage which we can monitor on an
oscilloscope. In this section, we will illustrate various alternative circuits which we
have used in order to fulfill this task.
The first such circuit, is a transimpedence amplifier as shown in figure B-1. This
configuration allows us to set the gain we require, typically R = 1MQ. It essentially
provides a zero input impedance into the circuit so that it does not load our device.
During our speaker autocorrelation measurements, described in chapter 3, we sinusoidally change the path of one of the two beams. This has the effect of periodically
reproducing the autocorrelation signal with the period determined by the speaker
motion. Typically, the speaker is set to oscillate at 13Hz with an 8V peak-peak driving voltage which allows for a speaker motion of approximately 4 mm peak-peak. In
our taylor series analysis of chapter 2, we noted that along with the autocorrelation
signal (the second order term in the expansion) we also produce a first order dc term
which does not contain any information of the autocorrelation signal.
The circuit illustrated in figure B-1 passes both the sinusoidal signal and the
undesired dc signal. In order to suppress the dc signal, the circuit shown in figure
B-2 is used. This circuit uses a dc blocking capacitor which only allows the ac signal
to pass through. Equivalently, one may see that the overall circuit acts as a high pass
filter with a gain determined by Rf and a corner frequency of
95
f,
=
1 )*
RiO
1
Since the
Rf
<i HF()
V0
Figure B-1: Transimpedence amplifier used to measure photocurrent to perform autocorrelation and pump-probe experiments. The gain is determined by Rf and is set to
1MQ.
speaker oscillates at 20 Hz, and during proper alignment the autocorrelation signal
repeats at twice the speaker frequency, we will provide sufficient margin by choosing a
cut-off frequency of 20 Hz. In other words, since our sampling rate is at 40 Hz without
any aliasing one may conclude that the maximum frequency content in our base band
signal is 20Hz. The sampled signal is then centered at 40Hz, with a bandwidth less
than 20 Hz, which allows us to choose 20Hz as a cut-off frequency.
frequency may be accomplished by using a value of R1
=
This cut-off
500 kQ and C1 = .1 paF.
R,
<i HF(C>,
R1
VO
Figure B-2: Transimpedence amplifier which uses a dc blocking capacitorto remove the
undesired dc signal. The high pass filter cut-off frequency is determined by choosing
the values of R 1 C1 , and the gain is determine by Rf.
For simplicity, the circuit shown in figure B-3 may be used. This circuit comprises
96
of a single load resistor RL. Note, that while this circuit indeed loads our device, the
high frequency current contribution which we are measuring using our measurement
scheme should be independent of this loading value. This is because our macroscopic
resistor does not look resistive at high frequencies. In other words, this load resistance
termination will not significantly alter the load presented to the high frequency signals
on the transmission line. It is our assumption that the high frequency signal will
radiate and will quickly be attenuated upon encountering the mismatch at the end
of the transmission line before reaching our macroscopic load resistor. It follows that
changing the value of the macroscopic load resistor, should not change the degree of
mismatch at the termination of the transmission line to high frequency signals.
The resulting measurement on the load resistor will be a superposition of two
signals. The first signal will be a dc signal that results from the dc component of
the device (a voltage divider between the dark resistance and the load). The second
signal will comprise of a time average of the high frequency signal which propagates
on the transmission line which subsequently becomes mixed back down to dc as
a result of the nonlinearity of the photocurrent. This nonlinearity results from a
voltage divider presented by the characteristic impedance of the line (see chapter 3
for further discussion).
The advantage of using this load resistor for a measurement of the autocorrelation
signal results from its simplicity. This resistor is completely passive and does not
require the dc biasing which is needed in the transimpedance amplifiers to operate
the operational amplifiers. Finally, the desired load resistor value (RL =1 MQ) may
easily be obtained from the input impedence of the measuring oscilloscope. All one
needs to do is to setup the oscilloscope directly to the device to be measured and
the voltage read out will correspond to the voltage across the 1 MQ load (input
impedance).
Another method of performing the autocorrelation measurements is by the use
of a lockin amplifier as discussed in the experimental setup section of chapter three.
The latter circuits were used primarily in the speaker measurement setup. A fourth
alternative is to use a lockin amplifier and an optical chopper to perform the mea97
<iHF(T)>
V0
RL
7
77
Figure B-3: Load resistor (for low frequencies) which may be used to measure the
photo-current. While the resistor loads the low frequency components of the circuit, it
presents an arbitrarytermination for the high frequency currents propagatingthrough
the transmission line. A typical load resistor value of R=1 MQ may be accomplished
by using the input resistance of the measuring oscilloscope.
surement.
The speaker should be turned off in this measurement, and the lockin
amplifier reference should be set to correspond to the sum or difference frequency of
the two chopped beams. The scan is accomplished by using a linear motor driven
delay stage to be described in appendix C. At each step in the linear scan, a lockin
amplifier measurement is performed. The current signal from the device should be
feed directly into the input of the lockin amplifier, since the lockin amplifier contains
internal transimpedence stages. Good measurements on the lockin were accomplished
by setting the integration time to Is.
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Appendix C
Appendix: Linear Delay Stage
In the beginning of this project, labview code had to be written on an IBM Windows
environment in order to control the linear motor driven delay stage. In this section
of the appendix, some of the basic commands will be listed as a reference.
The linear scan used to perform the autocorrelation experiments utilized a motordriven stage manufactured by DynaOptic Motion. This stage allows for 25 mm of
travel (DynaOptic Part Number CTC-163-1) with a resolution of up to .1 pm. In
our experiments, the scan increments were done in steps of 10 pim well beyond the
resolution limit given in the specifications. This corresponds to a temporal increment
of 67 fs.
The motor driven translation stage is controlled by a motor controller
(DynaOptic Part Number CTC-290-102s) which is housed in a computer casing.
In order to communicate with the motor-controller, a cable was designed to establish RS-232 communication with a PC operating under a Windows 98 operating
system. The cable mapped out the 25 pin RS-232 interface on the controller to the
9 pin interface on the personal computer. Only 3 of the 9 pins are utilized which
correspond to RX, TX, and ground. When configuring the RS-232 settings in the
windows environment, it is important to ensure that the Hardware handshaking is
disabled.
Once the communication is established, the motor controller may be programmed
remotely with the programming software of choice. A program was written in National
Instruments LabView which allows for a graphical user interface and simplicity in
99
programming. This program controlled the delay stage motion, and simultaneously
took data readings from a lockin amplifier. The programming sequence consists of
initializing the RS-232 interface, setting the motor parameters, and then programming
the motion commands.
An example of some of the labview motion commands are provided below:
Description
Command
Initialize Settings and Velocity
Move Motor
Read Positon
1SV%d, 1SA10000, 1DS10000, 1SG300, 1DB5, 1DT100
1MN, 1MR%d, 1WT, 1MF
1TP
Table C.1: Example of some of the labview commands to control the linear delay
stage.
In table C, the %d in the command section is the parameter to be input by the
user. For the velocity section, %d should the input of the desired velocity in mm/s
multiplied by 4067109 which is a conversion factor that converts the units of mm/s
into an equivalent motor revolution unit.
For the move motor and read position
commands, %d should be replaced by an input parameter in the units of mm which
must be multiplied by a constant 62059.16 to convert to the required units. Further
details are provided in the DynaOptic Motion manuals.
100
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