Efficient THz Lasers and Broadband Amplifiers
Based on Quantum Cascade Gain Media
MASSACHUSES
by
SEP 25 201
Xiaowei Cai
LIBRARIES
B.S., Optical Engineering, University of Rochester (2012)
B.A., Physics, University of Rochester (2012)
Submitted to the Department of Electrical Engineering and Computer
Sciences
in partial fulfillment of the requirements for the degree of
Master of Science in Electrical Engineering and Computer Sciences
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
September 2014
@ Massachusetts Institute of Technology 2014. All rights reserved.
A uthor ...........................
Department of Electrical
Certified by ....
redacted
Signature
.............................
.
ineering and Computer Sciences
August 29, 2014
Signature redacted .................
e o..
Qing Hu
Professor
Thesis Supervisor
Signature redacted
Accepted by.....................L~~.Kldijk
C ani een Kolodze
jsei
SChairman, Department Committee on Graduate Theses
e
2
Efficient THz Lasers and Broadband Amplifiers Based on
Quantum Cascade Gain Media
by
Xiaowei Cai
Submitted to the Department of Electrical Engineering and Computer Sciences
on August 29, 2014, in partial fulfillment of the
requirements for the degree of
Master of Science in Electrical Engineering and Computer Sciences
Abstract
One of the most important applications for Terahertz (THz) quantum cascade (QC)
lasers is to provide compact and powerful frequency-stabilized solid-state sources as
local oscillators in heterodyne receivers for astronomical studies. The first part of
the thesis is dedicated to the device cavity design, fabrication and characterization of
the microstrip antenna coupled third-order distributed feedback QC lasers aimed for
2.060 THz atomic oxygen line.
THz travelling-wave QC amplifiers are highly desired to achieve broadband amplification of THz radiation in free space. The second part of the thesis focuses on the
development of 4.3 THz travelling-wave QC amplifier by monolithically integrating
horn antennas and attaching silicon lenses at the metal-metal waveguide facets.
Thesis Supervisor: Qing Hu
Title: Professor
3
4
Acknowledgments
I want to express my sincere graditude to my advisor Professor Qing Hu, for giving
me the opportunity to work on this project and guiding me in the past two years
with expertise and patience. His open-mindedness, perseverance and dedication have
taught me a lot about being a researcher.
Being in Qing's group, I have had the pleasure of working with many other brilliant minds. In particular, I would like to thank Wilt Kao, who was my mentor in my
first year. Without his patient guidance and extremely comprehensive knowledge, I
would not have been able to transition into graduate research so easily. My labmate
David Burghoff possesses great creativity in experimental work, and has helped me
brainstorm with various problems of my project. I'd also like to thank my labmates
Amir Tavallaee, Ningren Han, Shengxi Huang, Yang Yang, Asaf Albo, and Ali Khalatpour for many useful discussions. In addition, I'd like to thank Dr. John Reno
at Sandia National Laboratory for providing us with the high quality MBE growth
crucial to our work.
Outside of the lab, a large portion of my research falls into fabrication in the
cleanroom. MTL's wonderful staff members were essential to my work. In particular,
I'd like to thank Dennis Ward for repeatedly going out of his way to help me with my
fabrication problems, and also for his great sense of humor during my most miserable
hours.
Outside of research, I am grateful to Prof. Leslie Kolodziejski for her support
and encouragement. It's also truly been a pleasure working with her, Prof. Anantha
Chandrakasan, and the rest of the EECS Graduate Office as a member of EECS GSA.
To all of my friends at MIT, including Samantha Strasser, Reyu Sakakibara, Julian Straub, Koustuban Ravi, Peter Krogen, Joseph Kim, Vincent Xue, Tian Gan,
Stephanie Nam, and many others, thank you for keeping me sane in the last two
years. You guys are awesome!
I'd also like to thank the Siebel Scholars Foundation for the generosity in funding
part of my second year studies at MIT. I am humbled to have been selected for this
5
honor.
I'd also like to thank my previous mentors from my time before MIT, Prof. Bob
Boyd, Dr. Holly Hindman, Prof. Krystel Huxlin, Prof. Thomas Brown, Prof. Scott
Kuo, and Prof. Zhimin Shi. I would not have made it so far without them.
I thank my boyfriend Ivan for his support both in and outside of the lab. This
thesis would have been much harder without him. And I will always remember the
egg tarts.
Finally, and mostly importantly, I would like to dedicate this thesis to my parents, who have always selflessly loved and provided for me, and whose sacrifices have
enabled me to pursue my dreams in life. All that I have and all that I have achieved
I owe to them. Mom, Dad, I love you.
6
Contents
1 Introduction
1.1
Terahertz Gap .......
1.2
THz Quantum Cascade Laser
1.3
Key Components in THz Heterodyne Receivers
1.4
2
.25
3
15
...............................
15
. . . . . . . . . . . . . . . . ......
. . . . . . . . . . . .
1.3.1
THz Quantum Cascade Lasers as Local Oscillators
1.3.2
THz Amplifier Design
16
18
. . . . . .
19
. . . . . . . . . . . . . . . . . . . . . .
21
Thesis overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
Terahertz Waveguides
25
2.1
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2
Surface Plasmon Mode . . . . . . . . . . . . . . . . . . . . . . . . . .
26
2.3
Surface Plasmon Mode in Terahertz Waveguides . . . . . . . . . . . .
27
Microstrip Antenna Coupled Distributed Feedback THz QC Lasers 33
3.1
Third-order DFB Laser .. . . . .
3.2
Microstrip Antenna Coupled Third-order DFB Laser
. . . . . . . . . . . . . . . . . . . .
. . . . . . . . .
33
35
. . . . . . . . . . . . . ... . ....... 35
3.2.1
Wall-Plug Efficiency
3.2.2
Microstrip Antenna Coupled DFB laser . . . . . . . . . . . . .
36
3.2.3
Implementation at the 2.06 THz Atomic Oxygen Line .....
37
4 Design of Travelling-Wave Terahertz QC Amplifiers
43
4.1
Travelling-Wave Amplifier . . . . . . . . . . . . . . . . . . . . . . . .
43
4.2
QC Amplifier Based on Semi-Insulating-Surface-Plasmon Waveguides
45
7
4.3
4.2.1
Facet Reflectivity . . . . . . . . . . . . . . . . . . . . . . . . .
47
4.2.2
Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
QC Amplifier based on Metal-Metal Waveguides . . . . . . . . . . . .
50
4.3.1
Facet Reflectivity . . . . . . . . . . . . . . . . . . . . . . . . .
52
4.3.2
Eigenfrequency Analysis . . . . . . . . . . . . . .....
54
4.3.3
Amplification Simulation . . . . . . . . . . .... . . . . . . . .
58
5 Fabrication of Travelling-Wave Terahertz Quantum Cascade Ampli63
fiers in Metal-Metal Waveguides
63
..............
5.1
General Fabrication Flow ............
5.2
Mechanical Lapping and Polishing .....................
.........
...........
67
. .....
5.2.1
Sources of Scratches
5.2.2
Use of Ultrasonic Cleaning . . . . . . . . . . . . . . . . . . . .
5.2.3
Chemical-Mechanical Polishing
. . . . . . . . . . . . . . . ..
. 69
70
71
5.3
Wet Etch Clean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
5.4
Horn Formation ............
. . . . . . . . . . . . . . . . . .
74
A Design Parameter
79
B Boundary Conditions for Finite-Element Simulations
81
C
C.1 THz DFB Laser with Microstrip Antennae ...............
83
C.2 THz QC Amplifier using MM Waveguides with Horn Antennas . ...
94
C.2.1
D
83
Fabrication Flow
Experimental Parameters for Lapping Process ...........
99
101
Photolithography Masks
8
List of Figures
1-1
The "terahertz gap" in the electromagnetic spectrum . . . . . . . . .
15
1-2
Schematic for quantum cascade laser and its sub-band diagram . . . .
17
1-3
Double-sideband (DSB) noise temperatures of Schottky diode mixers
(circles), SIS mixers (triangles), and HEB mixers (squares) . . . . . .
19
1-4
Comparisons between competing technologies in THz QCL . . . . . .
21
1-5
Schematics for amplifier
. . . . . . . . . . . . . . . . . . . . . . . . .
22
2-1
Schematic of metal-metal (MM) and semi-insulating surface plasmon
(SISP) waveguide structure
2-2
26
2D transverse mode profiles of 4.3 THz SISP waveguides with varying
doping levels . . . . . . . . . . .
......................28
2-3
2D result of confinement, waveguide loss and loss contribution of 4.3
THz SISP waveguides with varying doping levels . . . . . . . . . . . .
2-4
29
Magnetic field magnitude IHyI along the growth direction with varying
doping levels . . . . . . . . . . . . . . . . . . . . . . .
.........30
2-5
Comparison between 1D and 2D result with varying doping levels
3-1
Working principle of third-order DFB lasers
3-2
Schematic of microstrip antenna coupled DFB laser . . . . . . . . . .
3-3
Simulation result of 2.06 THz......
3-4
SEM picture of an antenna coupled DFB laser and simulation of bond-
.
3-5
. . . . . . . . . . . . . . ..
pulsed I - V and L - I curve and spectra data of antenna coupled
D FB lasers . . . . . . . . . . . . . . . . .
9
32
. . . . . . . . . . . ... 34
ing pads . . . . . . . . .. . . .
......................40
................41
. . . . . . . . . . . . . . . . . . . . . . .
37
39
.75
4-1
VB0482 waveguide loss, confinement factor, net gain vs waveguide width 46
4-2
SISP waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
47
4-3
Schematic of QC amplifier based on MM waveguide . . . . . . . . . .
51
4-4 Electric field magnitude comparison with Fabry Perot waveguide . . .
53
4-5
Facet reflectivity versus vertical dimension of the facet
54
. . . . . . ..
4-6 Electric field magnitude with silicon lens of different radii . . . . . . .
55
4-7 E field magnitude vs relative vertical offset between the silicon lens of
4-8
2mm radius and the active region . . . . . . . . . . . . . . . . . . . .
55
2D eigenfrequency Ey
56
4-9 3D eigenfrequency Ez
. . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . .57.
4-10 Ampflier E field magnitude . . . . . . . . . . . . . . . . . . . . . . . .
58
4-11 Power gain versus net modal gain . . . . . . . . . . . . . . . . . . . .
59
4-12 power gain vs vertical offset and HWFM . . . . . . . . . . . . . . . .
60
4-13 power gain vs freq at different net modal gain . . . . . . . . . . . . .
61
5-1
Schematics for THz MM QC amplifier fabrication proess in MM waveguides . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . .
64
5-2
SEM pictures of horn structures . . . . . . . . . . . . . . . . . . . . .
65
5-3
SEM pictures of undercut underneath the horn structure and top metal 66
5-4
SEM pictures after dry etch . . . . . . . . . . . . ... . . . . . . . . .
5-5
Scratches from mechanical lapping
5-6
Damage from ultrasonic cleaning and subsequent lapping . . . . . . .
5-7
SEM pictures of CMP processed wafer after wet etching of the horn
66
. . . . . . . . . . . .. . . . . . . . 69
71
structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . .
72
5-8
SEM picture of a thin amorphous GaAs layer on top of the horn . . .
73
5-9
SEM pictures of crystallographic etch profiles: inwardly and outwardly
sloped sidewall
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-10 SEM pictures of horn structures after wet etch using sulfuric acid
. .
5-11 SEM pictures of horn structure after wet etch using phosphoric acid
76
.
77
D-1 Mask2.2THz . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . .
101
10
D-2 Mask2THz ........................................
103
D-3 Mask-amplifier .....................................
104
11
12
List of Tables
Table of lapping abrasives: Silicon Carbide, Alumina and Diamond
5.2
Comparison between mechanical polishing and CMP
.
67
.
5.1
73
C.1 Table of lapping procedure . . . . . . . . . . . . . . . . . . . . . . . .
99
1 13
. . . . . . . .
14
Chapter 1
Introduction
1.1
Terahertz Gap
Electronics
109
I
10
10
I
I
10112
1013
10
I
I
I
I
30 cm
3 cm
3 mm
300 um
Photonics
1014
10
I
SI
Terahertz
range
Microwaves
is
CLO
Near- and
Mid-infrared
I
30 um
1015
10
1016
1
I
UV
I
3 um
f (Hz)
300 nm
1
30 nm
n
Wavelength
Figure 1-1: The "terahertz gap" in the electromagnetic spectrum. Few natural sources
of radiation exist in this range.
The two major mechanisms to generate coherent electromagnetic radiation in modern engineering are electronic oscillators and conventional lasers. However, electronic
oscillators are limited by the carrier transient time and resistance-capacitance (RC)
time, resulting in power scaling as 1/f4 and frequency < 300 GHz. Conventional lasers
are limited by the material bandgap, which typically is > 40 meV, corresponding to 10
THz. Compared to infrared and microwave, which are well developed cornerstones of
modern engineering, Terahertz (THz) technology is still young and under-developed.
The lack of high quality coherent radiation source between 300 GHz and 10 THz
(wavelength A between 30-1000 pm, and photon energy hw between 1-40 meV) leads
15
to a so-called "THz gap", shown in Fig. 1-1.
Terahertz radiation is attractive and desired for many applications, thanks to
some of its unique properties. A great number of chemical species exhibit distinctive
spectral "fingerprints" in THz range, for example molecular rotational/vibrational
energy levels, and atomic hyperfine structures. As a result, there are many appealing
spectroscopy applications in various areas, ranging from astronomical observation of
the/interstellar medium (ISM) [1-3], atmospheric studies [1], chemical gas sensing [4],
to security detection of explosives and illegal drugs [5]. Another attractive feature of
THz radiation is that it can be transmitted through many materials that are opaque
in the visible spectrum. This allows non-destructive imaging, such as revealing hidden
paintlayers on canvas [6] and pencil letters written on paper inside an envelope [7].
In addition, there is an increasing interest in biomedical diagnostics [8], thanks to
THz radiation's low photon energy (between 1 - 40 meV), which is non-ionizing and
thus safe for biological tissues. T-ray imaging has been used to determine cornea
hydration levels [9], detect cavities in human teeth [10] and breast cancer [11], since
its sensitivity to changes in water content enables high contrast images.
1.2
THz Quantum Cascade Laser
The invention of quantum cascade (QC) laser [12] has provided the possibility of a
promising THz source. Multiple quantum well (MQW) structures of alternating high
and low bandgap materials (i.e. GaAs/AlGai-As) with several monolayer thickness,
are grown by molecular beam epitaxy (MBE). The discontinuity in the conduction
band edge energy at the heterostructure boundaries enables quantum confinement of
carriers in the growth direction and splits the conduction band into subbands, between
which radiative transitions can occur under electrical bias. The same MQW structure
is repeated/cascaded for hundreds of times to enhance the quantum efficiency, as one
electron travelling through the QC structure can potentially emit up to one photon
per period as shown in Fig. 1-2, although the actual efficiency tends to be much
lower due to non-radiative scattering. Com pared to bipolar semiconductor lasers, the
16
emission frequency of QC lasers is no longer limited by the material bandgap, but can
be engineered by carefully designing the thickness of the coupled wells and heights of
the barriers.
(a)
DC Bias
J=Current/Area
I
(b)
Zero Bias ----------.
(C)
xN
Design Bias --------.
xNa
A
h
3'
2'
33
3
2
2.
& 1s
21.
electron
1
3
* 2
. electron
Figure 1-2: Schematic for quantum cascade las er and its sub-band diagram. Figure
is adapted and modified from [13].
Since the first demonstration of a QC laser in THz [14], there have been many
advancements: maximum pulsed temperature Tmax ~ 200 K [15], frequency coverage 1.2-5.1 THz [16,17], >1 W power in pulse [18] and over 300 GHz tunablity [19].
Today, THz QC laser is argubly the only compact solid state source that can deliver continuous-wave (c.w.) THz radiation with greater than milliwatt optical power
and reasonable spectral coverage, which are essential for imaging and spectroscopy
purposes.
17
1.3
Key Components in THz Heterodyne Receivers
An important technique, commonly used in many THz high-resolution spectroscopy
and imaging applications, is heterodyne detection.
The key process contains the
frequency down-conversion in a mixer, where a THz signal W, is mixed with a reference
signal from a local oscillator (LO) WLO and an output signal at the intermediate
frequency (IF)
WIF =
jw,
-
wLoI «W
is generated with an amplitude proportional
to that of the LO. Compared to direct detection; heterodyne detection provides great
sensitivity and spectral resolution, because of the ability to measure high-frequency
signals using mature microwave technologies. The two key components in heterodyne
receivers are the local oscillator (LO) and the mixer.
The development of heterodyne receivers at THz frequency is limited by the availability of suitable LO sources. Candidate THz technologies for use as LO include
Schottky diode based multiplier chains, optically pumped gas laser and quantum cascade laser. Below ~ 2 THz, mutiplier-based microwave sources, such as Schottky
multiplier and power amplifier, are the dominant LO choices [20]. However, output
power drops with both frequency and the number of multiplications. While optically
pumped gas laser is able to deliver tremendous continous wave (c.w.) power >100 mW
at more than 1000 laser lines covering frequency ranage from 150 GHz to 8 THz [21],
it is traditionally bulky and energy hungry, and also lacks frequency tunability due to
the nature of the active medium. Recent development in THz quantum cascade (QC)
laser has offered a compact, high power (> mW) alternative at super-THz range (>
1 THz). A cavity structure that provides single mode operation and narrow far-field
beam pattern is desired for efficient coupling into the mixer.
The most important component in the heterodyne receivers is the mixer, of which
conversion efficiency, IF bandwidth, dynamic range and the detection noise are all
critical to the overall system performance. Fig. 1-3 shows the noise temperature of
different mixers in THz range. Superconductor-insulator-superconductor (SIS) tunnel
junction exhibits almost quantum limited performance up its gap frequency. It is used
in virtually all astronomical heterodyne receivers in THz range below ~ 1.3 THz [22].
18
.
.
. ...
,
100000
15Ohv/k
10000 r
Schottky Diode
0
y
100
--
U.
.---
- -
2hv/k
.. - .Vg
-
0.3
*o U
E
---
-
r
HEB
-
1000
z
W'
0
.
CD
-
.0
-
E
I
0.5
..-
I-
1
2
Frequency (THz)
3
4
5 6
Figure 1-3: Double-sideband (DSB) noise temperatures of Schottky diode mixers
(circles), SIS mixers (triangles), and HEB mixers (squares) [21].
The most sensitive mixer above 1 THz is the superconducting hot-electron bolometer
(HEB), for which LO power as low as ~- 100 nW is sufficient. However, it requires
cryogenic cooling to liquid helium temperatures. A room-temperature alternative is
the Schottky diode (SD), at the expense of low sensitivity and need for relatively large
LO power (>mW). However, the noise temperature of the overall system and the LO
power requirement can be effectively reduced, with a low-noise amplifier (LNA) prior
to mixing, which is still an undeveloped technology in THz range.
This thesis focuses on the development of THz QC lasers as LO and THz amplifier.
1.3.1
THz Quantum Cascade Lasers as Local Oscillators
To be suitable as a local oscillator (LO), the THz quantum cascade (QC) laser needs
to meet a number of essential requirements, including single mode lasing, frequency
selectivity, c.w. operation, high output power (> mW) and narrow beam pattern [23].
THz QC lasers with metal-metal ,.(MM) waveguides have proven to achieve better
performance, in terms of operating. temperature [24]. The strong mode confinement
between the two metal strips enables both the vertical and lateral dimensions to
19
be smaller than the wavelength, which greatly reduces the thermal dissipation and
improves c.w. operation (up to 117 K) [25]. However, due to the sub-wavelength
confinement at the facet, a simple Fabry-Perot MM waveguide often results in a
highly divergent far-field beam pattern and low wall-plug efficiency. In addition, it
does not provide any frequency or mode selectivity.
Many approaches have been explored for shaping the beam pattern of the Fabry
Perot MM waveguide. Attaching silicon hemispherical lenses [26] or horn antennas
[27] at the facet allows mode matching between the laser cavity and free space, but
these approaches still lack control of the lasing frequency and lasing mode.
Instead, the distributed feedback (DFB) laser can provide robust single-mode
operation through its wavelength-selective elements gratings, which can be readily
fabricated through patterning the top metal or opening apertures in the semiconductor. First-order DFB lasers were first explored [28], but they suffered from divergent
beam pattern and low output efficiency. Linear surface-emitting (SE) second-order
DFB lasers [29] improve the beam pattern in the axis parallel to the laser, but beam
remains very divergent in the orthogonal axis. A "Photonic heterostructure" formed
by a grating with adiabatically changing periodicity has been utilized in SE DFB
lasers to suppress the non-radiative mode and improves the power efficiency [30].
Phase-locking arrays of SE DFB lasers creates a tight beam pattern in both axes.
Despite the improvements in power efficiency or beam pattern from these efforts, the
large light emitting area of SE lasers generates large power dissipation and deteriorates the c.w. performance. Thus, a cavity design that can control the laser emission
both spectrally and spatially, with high power efficiency in c.w. operation, is highly
desired.
The invention of third-order DFB laser is truly ingenious, offering edge-emitting
radiation with tight and symmetric far-field beam pattern [31]. The perfectly phasematched DFB laser further improves the power scalability and beam divergence [32].
Integrating microstrip antennas further enhances the wall-plug efficiency of the DFB
laser [33]. Fig. 1-4 shows a summary of" the competing' technologies in the cavity
design of THz QC lasers.
20
Figure 1-4: Comparisons between competing technologies in THz QCL, adapted from
[13].
1.3.2
THz Amplifier Design
Quantum cascade structure provides promising gain medium for amplifying THz radiation. THz amplification has been realized in a master-oscillator/power-amplifier
(MOPA) scheme, where the seed laser and amplifier are fabricated monolithically
and near-field coupled [34]. There has also been THz amplifiers based on gain switching [35]. However, none of these methods are suitable for amplifying continuous-wave
free-space THz radiation, or to serve as a pre-amplifiers prior to mixers in heterodyne
receivers.
There are two types of semiconductor optical amplifiers: Fabry-Perot (FP) amplifier and travelling-wave (TW) amplifier, shown in Fig.
1-5.
Fabry-Perot (FP)
amplifier can achieve narrow-band optical filter and amplification, through feedback
within the cavity, where gain is greatly enhanced at the resonance frequencies through
multiple-pass amplification.
Similar resonance effect can also be realized in a dis-
tributed feedback (DFB) or a distributed Bragg reflector (DBR) cavity. In a TW
amplifier where facet reflectivity is minimal, gain relies on a single-pass amplification
21
and exhibits a broader bandwidth.
(b)
(a)
Gain mediu
R
R
input
AR coating
R<0.1%
output
Gs
input
output
A
Figure 1-5: Schematic for (a) Fabry-Perot amplifiers and (b) Travelling-wave amplifier, with their functional block diagrams, adapted from [13].
Recently, the first free-space light amplifier in THz frequency was developed with
an array of short-cavity SE lasers arranged in a two-dimensional grid [13]. An overall
system power gain of
-
5.6 was achieved at
-
3 THz. However, due to the strong
resonance effect, the bandwidth of amplification was only ~ 1 GHz, which limits
its application to observation of certain spectral lines and single frequency imaging.
In addition, due to the surface-emitting nature of the second-order grating structure,
optical setup of the amplifier is in a reflection mode, where both the input and output
signals share the same half space, making operations more difficult.
A broadband TW amplifier, where the excitation and output signals are in a
collinear layout, is highly desirable in many THz applications. However, THz QC
metal-metal waveguides exhibit strong mirror reflection and poor coupling efficiency
due to its subwavelength mode confinement. The lack of proper anti-reflection (AR)
coating material, which is readily available in the visible and near-IR spectra for
the use of semiconductor optical amplifiers, and isolators, which are commonly used
in microwave technology (for example TW masers [36]), limits the facet reflectivity
reduction and development of TW amplifier in THz frequency range.
22
1.4
Thesis overview
This thesis is dedicated to the development of 2.06 THz quantum cascade (QC) laser
as local oscillator for heterodyne receiver and broadband THz QC amplifier. Chapter
2 reviews the two major types of waveguides in Terahertz: semi-insulating-surfaceplasmon (SISP) waveguide and metal-metal (MM) waveguide. The waveguide knowledge serves as a foundation for the cavity design of THz QC laser and broadband THz
QC amplifier. Chapter 3 discusses the working principle of the microstrip antenna
coupled third-order DFB laser and its implementation at 2.06 THz atomic oxygen
line including its cavity design, fabrication and characterization. Chapter 4 proposes
two designs for travelling-wave THz QC amplifier, one based on SISP waveguide and
the other based on MM waveguide. Chapter 5 details the fabrication flow of THz QC
amplifier based on MM waveguide.
23
24
Chapter 2
Terahertz Waveguides
2.1
Overview
In the visible spectrum, a waveguide often consists of an active region and cladding
layers with lower refractive index to confine the radiation. However, this scheme is
not suitable for terahertz. Since the thickness of the dielectric cladding layer needs
to be on the order of a wavelength in the dielectric, the free carrier absorption, which
increases as A 2 for frequencies above the plasma frequency, will cause large loss due
to the mode overlap with the cladding layer [37].
Instead, there are mainly two types of waveguides in terahertz: semi-insulatingsurface-plasmon (SISP) waveguide and metal-metal (MM) waveguide. Both waveguides operate in the surface plasmon mode, which propagates along the interface
between two materials where the real part of the dielectric constants are of opposite
signs. This not only provides mode confinement in the active region, but also helps
minimize loss due to free carrier absorption in the plasma layer (heavily doped n+
layer for SISP waveguide and metal for MM waveguide). The Drude model can be
introduced to account for the free carrier loss in this plasma layer.
Both waveguide structures are shown schematically in Fig. 2-1. For SISP waveguides, the 10 Mm GaAs/AlGaAs active region is sandwiched between a top metal
contact and a thin (< 1 pm) heavily doped n+ GaAs layer grown on a semi-insulating
GaAs substrate, whereas the n+ layer is replaced with a metal layer for MM waveg25
uides.
+
II
+
_a+jGaAs
metal-metal
waveguide
semi-insulating
surface plasmon
waveguide
Figure 2-1: Schematic of metal-metal (MM) waveguide (left) and semi-insulatingsurface-plasmon (SISP) waveguide structure (right), adapted from [37]
MM waveguides have a highly confined mode in the active region between the two
metal strips (I ~ 1). This sub-wavelength confinement also results in high mirror
reflectivity (R ~ 0.8) and a divergent beam pattern. The strong mode confinement
also allows both the vertical and lateral dimensions to be smaller than the wavelength inside the semiconductor (~ 20 pm at 4 THz), which greatly reduces the heat
dissipation and enables c.w. operation.
On the other hand, in SISP waveguides, the mode extends into the substrate
substantially (F ~ 0.1 - 0.5), resulting in a low mirror reflectivity (R ~ 0.3) and a
beam pattern with low divergence. Semi-insulating substrates are used to minimize
the loss. Waveguide width that is comparable to the free-space wavlength (> 75 pm
at 4 THz) is often needed to maintain a reasonable mode confinement and good beam
pattern.
2.2
Surface Plasmon Mode
According to Drude-Lorentz model [38], a conducting medium has a frequency dependent conductivity and a frequency dependent permittivity, shown as below
u-(w)
c(w)
=
Ecore
-
core
tne 2T
=*1-i
J)(2.1)
m* (1 - iwr)
+
(I
ia
-W
2
1+(wr) 2
26
+
i
2
WP 7-(2.2)
+w(1+(wr)2
where n is the electron density, m* the effective mass for electrons, e the electron charge, r the effective scattering time for electrons, Ecore the permittivity of the
material excluding the electron effect, and wp the plasma frequency of the material.
n2
2
n(2.3)
P
co,
m*
For highly n-doped GaAs n ~ 5 x 1018 cm-3, the plasma frequency fp
=wp/27r
20 THz. Above the plasma frequency, the medium behaves as a dielectric (Re{E} > 0);
below the plasma frequency, the medium behaves as a metal (Re{E} < 0), inside which
the electromagnetic field decays evanescently.
Between two materials where the real part of the dielectric constants are of opposite signs, for example dielectric and metal, coherent electron oscillations that propagate along the interface can exist, so called "Surface Plasmons " (SP).
2.3
Surface Plasmon Mode in Terahertz Waveguides
A 200 pm-wide terahertz SISP waveguide is modelled in COMSOL Multiphysics. A
10 pm active region is sandwiched between the top metal with a thin contact layer
and lower 0.4 pm n+ layer. Detailed design and material parameters are shown in Appendix A. Two-dimensional (2D) finite-element mode solver simulation is performed
to obtain the 2D transverse mode profiles and effective mode indices. Waveguide
loss and confinement factor can be further extracted from the imaginary part of the
propagation constant
f
and the field distributions respectively.
a, = 21m{}
F
= ffactve
IEy 22 dxdy
ff_* EI dxdy
(2.4)
(2.5)
Due to the amphoteric nature of Si doping in GaAs, the maximum achievable
27
Hx
n=
Ev
-3
cm
017
F=0.04
unbounded mode
n = 101cm
F=0.4
SISP mode
n = 101cm
F=0.25
SISP mode
n
=
621
10cm
-3
F=0.9
MM mode
Figure 2-2: Two-dimensional transverse mode profiles of 4.3 THz SISP waveguides,
where the doping levels of the n+ layers are varied.
n+ carrier concentration is ~ 5 x 1018 cm- 3 . Here, the doping level of the lower n+
layer is varied in a wider range to examine its impact on the mode profile, shown in
Fig. 2-2. The 2D transverse mode profiles are shown for different doping levels, 1017
cm- 3, 1018 cm- 3 , 1019 cm- 3, 1021 cm- 3, along with their mode confinement factors
F. The electron concentration is assumed to be n+ for the sake of illustration. As the
doping level of the n+ layer increases, the mode profile changes significantly. At low
doping level 1017 cm- 3 , the mode leaks into the substrate, only bounded by the metal
contacts beneath the substrate instead of the n+ layer. As doping level increases, i.e.
to 1018 cm- 3, 1019 cm-3, the surface plasmon mode is attached to the n+ layer and
decays exponentially into the substrate. At even higher doping level, 1021 cm- 3 , the
lower n+ layer behaves strongly as metal, and the mode is bounded between the top
metal contact and the n+ layer, with F close to unity, approaching the mode profile
in a metal-metal waveguide.
Fig. 2-3 shows the results of mode confinement, waveguide loss and loss contribution from a more detailed scanning of the doping level. Increasing the doping level
is essentially increasing the plasma frequency of the material. At low doping level,
where plasma frequency w,8 < w, the n+ layer behaves just like a dielectric since the
real part of the dielectric constant Re{} is positive. Once the doping level increases
28
f=4.3 THz, heavily doped layer thickness=0.4gm
0.5 --
102
10~
100
2
10
10
101
10
101
102
doping level e18 (cm-3
-
40
-
30
-
20
-
10
102
10
20)
0
15 o
0
3:O
a
10-
a
:
.. I
contact layer loss
active region loss
heavily doped layer loss
total loss
doping level e18 (cm
2
3
.
25...
100
5'I
10-2
p
-
10~1
100
doping level e18 (cm 3
Figure 2-3: Confinement, waveguide loss and loss contribution of 4.3 THz SISP waveguides, where the doping levels of the n+ layers are varied. The calculations are done
with 2D finite-element solver.
29
such that the plasma frequency wo, > W, Re{} changes from positive to negative and
the n+ layer becomes reflective and supports a surface plasmon mode which results
in a higher mode confinement.
One would expect as the doping level of n+ level increases, the layer would become
more and more reflective, or "metal-metal".
However, as noted in both Fig. 2-2
and Fig. 2-3, in the regime of SISP mode, mode confinement factor F drops first
and increases dramatically with increasing doping level, instead of monotonically
increasing.
To further investigate, results from a one-dimensional (ID) MATLAB eigensolver
and two-dimensional (2D) finite-element mode solver are compared. Since the waveguide width in the 2D simulation is 200 pm, which is much greater than the wavelength
inside the semiconductor, results from both simulations should be comparable.
antisymmetric mode
Au n+
1
symmetric mode
substrate
mg
0.5-
-
doping level
1e18 cm
active
0.0
50
100
150
200
250
300
00
350
growth direction (meshing pts)
100
150
200
250
300
350
300
350
300
350
300
350
growth direction (meshing pts)
doping level
5e18 cm-
S0.5-
00
doping level
1e19 cm
50
50
100
150
200
250
300
350
300
350
0
50
100
150
200
250
growth direction (meshing pts)
growth direction (meshing pts)
05
5
00
50
100
150
200
250
0
0
50
growth direction (meshing pts)
100
150
200
250
growth direction (meshing pts)
1.
doping level
5e19 cm'1
0.5
-
Cd
0
50
100
150
200
250
300
350
growth direction (meshing pts)
0
50
100
150
200
250
growth direction (meshing pts)
Figure 2-4: Magnetic field magnitude |H.| along the growth direction for antisymmetric and symmetric modes with varying doping levels.
30
From ID simulation result, shown in Fig. 2-4, there are two competing modes.
One's magnetic field magnitude IH.1 has a null in the center of the n+ layer and the
other has a peak. This can be explained by analogy to a double quantum well. The
n+ layer acts as a barrier between the active region and substrate, forming a two-well
system. At low barrier, there is a strong coupling between the eigenstates of the
individual wells, which form a new set df eigenstates, symmetric and antisymmetric.
As barrier increases, the two wells become decoupled and eigenstates become more
localized in individual wells. In this case, plasmon modes can form at the interface
between the active region and n+ layer, as well as at the interface between the substrate and n+ layer. The two plasmon modes can either be symmetric with respect to
the center of the n+ layer, add up in magnitude and form a peak, or be antisymmetic
and form a null in the center. As the doping level increases, the antisymmetric mode
becomes more confined in the active region (increasing F), whereas the symmetric
mode leaks into the substrate more (decreasing F).
Fig. 2-5 shows the gain threshold, confinement factor and waveguide loss of the two
competing modes from ID eigensolver, and mode from the 2D finite-element solver.
The gain threshold can be calculated as following, without taking into account the
mirror loss.
9threshold "
-
(2.6)
Between the two competing modes, the one with lower gain threshold is favored,
hoping from the symmetric mode to the antisymmetric mode as doping level increases,
shown in the top graph of Fig. 2-5. The symmetric mode has a lower waveguide loss
but also a lower mode confinement. Its gain threshold therefore increases with doping
level, which makes it favorable only at low doping. The antisymmetric mode, on the
other hand, becomes more confined in the active region as the doping level increases.
It has a lower gain threshold at higher doping levels. This mode hopping explains the
initial drop and eventual growth in mode confinement factor seen in the 2D solver
results.
For THz SISP waveguides where the n+ layer doping is < 1019 cm- 3 , the
31
symmetric mode dominates.
f=4.3 THz, heavily doped layer thickness=0.4 gm
E
10
d
:
1x
2D solver 200wide waveguide
1D solver symmetric mode
1D solver antisymmetric mode
x
x
x
Xx
xx
CV
2
CU 10
10
10
10
doping level e18 (cm-3
[-0.5 -
x
1
0
x
x
x
x-
3F
Ux
10
10
10
doping level e18 (cm
10
3
T
E
x
E
x
x
x
xx
x
100
10
10
doping
102
level e18 (cm 3
Figure 2-5: Comparison between ID and 2D results of gain threshold, mode confinement and waveguide loss of 4.3 THz SISP waveguides, where the doping levels of the
n+ layers are varied.
32
Chapter 3
Microstrip Antenna Coupled
Distributed Feedback THz QC
Lasers
3.1
Third-order DFB Laser
The distributed feedback (DFB) laser uses periodic gratings to provide continuous
feedback along the laser cavity [39]. To have constructive interference between reflections by adjacent gratings inside the waveguide, the extra distance of light travelling
through additional grating, which is the length of two grating periods, need to be an
integer of wavelength inside the waveguide.
2A = l
, l = 1, 2,13...
neff
(3.1)
where A is the grating period, 1 is the order of the DFB laser, A is free-space
wavelength and neff is the effective mode index. Wavelength-dependent reflection
from the gratings results in the mirror loss am being a strong function of A (or equivalently, frequency v). Together with the gain spectrum, the mode with the highest
net gain g (v) -a,m (v) will dominate, leading to single-mode emission, assuming unity
confinement factor and similar waveguide loss a,,.
33
(a)
(b)
End-fre Antenna Army
z
Figure 3-1: Working principle of third-order DFB lasers [13]. (a) Electric field distribution inside a corrugated third-order DFB laser operating at the design mode along
with the schematic of that of free-space propagating radiation outside the waveguide.
(b) Schematic of an end-fire antenna array and its far-field beam pattern.
In metal-metal waveguides, the mode is perfectly confined between the two metal
strips in the vertical direction, but not in the lateral direction through the index contrast between the dielectric and air. Thus, the effective mode index can be engineered
through mode overlap with air (refractive index of 1) and semiconductor (refractive
index of GaAs of
-
3.6), since approximately
neff
~ FfnGaAs
+ (1
-
F)nair
(3.2)
where
a
ff_. 1EY 2 dxdy
2
(33)
dxdy
|Ey1
Active
=
Following eqn.
3.1, for third-order DFB lasers, the distance between adjacent
gratings is three-halves of the wavelength inside the waveguide. When the effective
mode index neff approaches 3, the grating periodicity equals half of the free-space
wavelength, and the phase of the free-space radiation aligns with the polarity of the
field inside each grating opening, leading to a "perfectly phase-matched" condition
[32] shown in Fig. 3-1(a). This leads to constructive interference between radiation
through the gratings in free space and a tight edge-emitting beam pattern.
The "perfectly phase-matched" condition
34
(neff
= 3) has been shown to be critical
for the maximum length, power scalability and beam divergence of the DFB laser.
For neff
#
3, the phase errors will accumulate along the laser and emissions from
different grating openings will eventually cancel each other out due to opposite phase
after certain device length, resulting in a decrease in output power and degradation
in beam pattern. Thus, the length over which the relative phase of two collinearly
travelling waves changes by 7r, L, can be defined to indicate the maximum usable
length [32].
Le=Aneff
(3.4)
|Ifef f - 31
The operation of the third-order DFB laser is similar to an end-fire antenna array [40], shown in Fig. 3-1(b). Considering a pair of half-wave antennas fed 1800 out
of phase, maximum cancellation takes place at the centerline between the antennas.
Radiation leaving from one antenna reaches the other after a half cycle (1800) and
reinforces each other (3600 in total, in-phase), leading to maximum radiation bidirectional along the antennas. When such antennas are arranged in an array, tight beam
pattern will form at both ends of the array, so called "end-fire antenna array".
3.2
Microstrip Antenna Coupled Third-order DFB
Laser
3.2.1
Wall-Plug Efficiency
Wall-plug efficiency (WPE), which defines electrical-to-optical power efficiency, is an
important performance metric for lasers. Mathematically, it can be expressed as the
following [41, 42},
WPE = Jma, - Jth dP/dI
Jmax
where
Jmazxt
V
(3.5)
is the dynamic range, dP/dI is the slope efficiency [W/A], and V is
the operating voltage [V]. The slope efficiency, which is the rate of power increase
35
versus current after threshold, can be further expressed as
dP
dI
hw
am
q am+aw
where 77 is the internal quantum efficiency, N is the number of QCL modules, hw is
the photon energy. The out-coupling efficiency
-"-
is a function of the mirror loss
am and waveguide loss a..
To elevate the WPE of QCLs, a waveguide can be designed with a higher mirror
loss, thus with a higher out-coupling efficiency. However, in the limit of infinitely
large mirror loss, the device will not be able to lase considering the finite material
gain.
This is because the lasing threshold has to increase to compensate for the
increased loss, which results in a reduction in dynamic range. To include this effect,
a "modified" out-coupling efficient for a edge-emitting third-order DFB laser can be
written as [13]
d
am _ go 0- aw-am
(3.7)
O.C.modif
=
2 am + aw
9o~am
where go is the gain achievable in the gain medium and 1 is included since power
is collected from only one of two facets for an edge-emitting 3rd-order DFB laser.
Thus, with 60-80 cm- 1 gain and 18 cm-
1
[43] waveguide loss in a metal-metal
waveguide, mirror loss 14-18 cm-1 will maximize the overall efficiency [13]. However,
the mirror losses for the Fabry-Prot cavity, the (imperfectly matched) corrugated 3rdorder DFB and the perfectly matched 3rd-order DFB consisting of serially connected
Fabry-Prot cavities are all very limited, ranging from 1 cm- 1 to 5 cm~ 1 [32,40,44].
3.2.2
Microstrip Antenna Coupled DFB laser
Recently, the integration of microstrip antennas with perfectly matched 3rd-order
DFB laser has shown great enhancement of power out-coupling efficiency, while preserving the single mode continuous wave operation with narrow and symmetric beam
pattern [33].
This work is inspired by antenna designs in microwave engineering. The microstrip
36
Microstrip Antenna
1
L --- I-i
Microstrip Antenna Coupled
3r order DFB laser
-
I
3r order DFB laser
Figure 3-2: Schematic top views of (a) microstrip slot antenna, (b) third-order DFB
laser, and (c) microstrip antenna coupled third-order DFB laser [33]
slot antenna consists of a microstrip transmission line and a slot cut in the metal
ground plane. The current flow through the microstrip line excites the slot such
that a voltage is generated across it and current travels around the slot periphery,
contributing to the radiation [45]. To incorporate similar slot antenna into THz metalmetal waveguide third-order DFB laser, instead of removing parts of the ground plane,
openings with rectangular shape are introduced on the top metal layer and antenna
loops are attached to the both sides of the gaps in the DFB laser, shown in Fig. 3-2.
Apertures along the laser ridge are equivalent to short dipole antennas with radiation resistance Rad
0( (y)2,
using Babinet's Principe [45]. THz metal-metal waveg-
uides often suffer poor power extraction efficiency, due to its subwavelength transverse
dimension w << A. Without changing the sub-wavelength characteristics of the DFB
laser, the integrated antennas significantly increase the effective radiation area and
consequently enhance the power extraction efficiency.
To preserve the distributed feedback provided by the adjacent cavities and the
electric field inside the DFB laser, the physical dimensions of the antenna structure
need to be carefully designed such that the total length of the antenna arm LL on
either side of the ridge is an integer number (m =1, 2, 3...) of AA wavelength travelling
along the antenna arm [33]:
LL = m x Aa
3.2.3
(3.8)
Implementation at the 2.06 THz Atomic Oxygen Line
One of the most important applications for THz QCL is to provide compact, frequencystablized and powerful solid-state sources as local oscillators (LO) in heterodyne
37
receivers for astrophysical and atmospheric studies [24]. Here, we have designed,
fabricated and measured DFB QCLs targeting the 2.06 THz atomic oxygen line.
At the long wavelength corresponding to
-'
2 THz, previously demonstrated 3rd-
order DFB lasers based on either corrugated waveguides [40] or serially connected
Fabry-Prot cavities [32] yield a low power extraction efficiency if narrow ridges are
used to ensure a single lateral mode and to allow an efficient heat removal. Therefore,
we have integrated the 3rd-order DFB structures with microstrip antennas to boost
their power out-coupling efficiency [33].
3D finite-element method (FEM) full wave electromagnetic simulations show that
the grating periodicity is properly designed so that the lasing mode is the lower band
edge (LBE) mode. Its radiation loss am is effectively increased by a factor of 7 from
0.8 cm-
1
for traditional corrugated DFB lasers to 5.8 cm-1 for microstrip antenna
coupled DFB lasers, shown in Fig. 3-3(c). The energy of the LBE mode is mostly
inside the cavity under the top metal, while the upper band edge (UBE) mode is
more localized under the aperture and hence more radiative, am~ 60 cm 1 . The
UBE mode's larger overlap with air also results in a lower neff, which explains its
higher frequency.
To ensure spectrally single-mode lasing on the fundamental lateral mode, a narrow
ridge size of 18 1tm is chosen to avoid the lasing of higher-order lateral modes by
increasing their radiation loss to >50 cm-1, shown in Fig. 3-3(a). By careful choosing
the cavity lengths, arrays of lasers with 10-GHz frequency separation where designed,
ensuring one of the lasers will be within 5 GHz of the target line.
Detailed fabrication flow is included in the Appendix C. Fig. 3-4 (a) and (b) show
the scanning electron microscope (SEM) pictures of microstrip antenna coupled DFB
lasers. To provide bias current to such a narrow and long device, side bonding pads
are connected with each cavity of the laser through contact fins, which are formed with
air bridges by removing part of the GaAs (~-' 15 rim) using wet etch. The side bonding
pads are placed 90 pm (> A/2) away from the laser, in order to avoid possible mode
coupling between the laser and side bonding pads when the distance between them is
< A/2, shown in Fig. 3-4 (c). Devices were fabricated from two gain media, FL175M38
d
a
10
'7
E
I
e
SHigher- Iorder laterlal mode
Radiati n loss > 50 cm-1
/
-
80
0
UBE mode
RadiatiIU 1U=s
~1
- J0 m111
0
-
Cl)
--
I
I
4
0-
C
Lasing mode: LBE mode
Frequency 2.0608 THz
1
Radiation loss ~ 5.8 cm
2
I
2
2.1
2.2
I
2.3
FREQ (THz)
I
2.4
hi
2.5
2.6
2.7
b
Antenna couple
3rd-order DFB
lasing mode
am~5. 8 cm-1
3rd-order DFB
am~0. 8 cm-1
z -+
Figure 3-3: (a) Gain-loss vs. frequency plot. (b) Magnetic and electric field of
the lasing antenna coupled third-order DFB mode, and far-field beam pattern, and
magnetic field of the corresponding corrugated third-order DFB mode.
39
M3 (wafer # EA1222) which is a resonant phonon design [43] and OWI1185E-M1
(wafer #VB0244) which is based on scattering-assisted (SA) injection [46,47].
(a)
(b)
Figure 3-4: SEM pictures of an antenna coupled DFB laser (a) DFB laser with side
bonding pads and contact fins. (b) zoomed-in picture of the air bridge. (c) Magnetic
fields of the lasing antenna coupled third-order DFB mode when the distance between
the laser and side bonding pads is 60 pm (< A/2) (top) and when the distance is 90
pm (> A/2)(bottom).
Fig. 3-5(a) shows the pulsed I - V and L - I curves and spectral data of three
adjacent antenna-coupled third-order DFB lasers fabricated with wafer# EA1222 and
different cavity lengths. As predicted, their lasing frequency differs by about 10 GHz,
and device 2 lases at 2058.48 GHz (within 2 GHz of 2060 GHz). The maximum
lasing temperature Tmax of device 2 is 80.6 K (pulse). Unfortunately, none of these
three lasers achieves lasing in c.w. mode because of the large power dissipation of the
FL design. Fig. 3-5 (b) shows the pulsed I-V and L-I curves and spectra data of a
40
similar antenna-coupled third-order DFB, lasing around 2.25 THz, which is closer to
the gain peak of the gain medium. It reaches 1.92 mW peak power in c.w. mode at
14 K. Thus, with the same EM design and a superior gain medium, QCLs with high
output power can be achieved and used as local oscillators for heterodyne detection
to observe the atomic oxygen line at 2.06 THz.
Cuj
50
0
150
lnt
(mA)
-o
200
1 0-
150
200.
-j
1 02
9-
-
9
8
82
7
2058.48 GHz
6
2
a
0
CV)
0
5
(a
Cu
E
6
0
0-
4
0
0
3
2--
22.02 2.04 2.06 2.08
Frequency (THz)
- . . ..
A. . ....-.
0
100
2.1
200
300
400
Current Density (A/cm
2.1 2.15 2.2 2.25 2.3 2.35 2.4
Frequency (THz)
u
-
2
2
1
500
0
2
100
01
200
300
400
500
606
Current Density (A/cm2)
)
(a
CurSgt (mA)
50
hr
datal
data2
data3
Figure 3-5: pulsed I - V and L - I curve and spectra data of antenna coupled DFB
lasers. (a) antenna coupled DFB lasing around 2.06 THz with different cavity lengths,
thus different lasing frequency ~ 10 GHz apart (b) a similar antenna coupled DFB
lasing around 2.25 THz.
41
42
Chapter 4
Design of Travelling-Wave
Terahertz QC Amplifiers
Travelling-Wave Amplifier
4.1
The amplifier gain for a Fabry-Perot (FP) cavity can be expressed as [48]
(1 - Rj)(1 - R 2 )G,
(1 - Gs,
8 R1i
)2
+ 4Gsv/R1YR2sin 2 [ir(v
-
vm)/
iLL]
where the facet reflectivities are R1 and R 2 , cavity resonance frequencies vm, frequency
spacings AvL and single-pass gain G,
G, = exp(gnetL) = exp((gmI - a.)L)
r = ffaguve
ffjE,
IE,|2 dxdy
2 dxdy
(4.2)
(4.3)
where a., is the waveguide loss, F is the mode confinement factor in the active region,
gnet
[cm-1] is the net modal gain, and L is the cavity length.
In order to achieve broadband amplification, any feedback in the cavity needs
to be eliminated. Thus, a travelling-wave (TW) amplifier, which relies on minimal
mirror reflection and gain from a single-pass, is desired. Ideally, a TW amplifier has
43
gain
GTW ~ (input coupling efficiency) x G, x (output collection efficiency)
(4.4)
where optimum coupling between the input signal and the amplifier can be achieved
with a seed laser of similar beam pattern as the amplifier. The coupling efficiency
could be potentially calculated through an overlap integral of the beam patterns in
space between the seed laser and the amplifier.
To suppress self-lasing, the amplifier cannot be biased beyond the lasing threshold
condition, which can be deduced through the round-trip gain and loss balance,
R1 R2 exp(29thrL) exp(-2aL)
=
(4.5)
1
9th =
(4.6)
where am is the total mirror loss; assuming the mirror reflectivities of the two facets
are the same (R 1 = R2 = R) then
am2 =
1
-- log R,
2L
2L
1
_
log R 2 -
log R
L
(
am = am, +
The material gain at the gain peak frequency for THz QCL is approximately
gpeak
where
An3D
An3D 3
70 x 1015
cm-
cm- 1
fij
Av/THz
(4.8)
[Cm- 3 ] is the three-dimensional population inversion density,
fi,
the
oscillator strength scaled by the effective mass of GaAs, and Av [THz] the bandwidth,
which is typically 1 THz. For a vertical QCL design, oscillator strength
fj
~ 1 and
when there is about 16% of the total population inversion 6 x 1015 cm- 3 , the peak
70
cm- 1
.
gain is
For a given cavity length, when mirror reflection is so minimal that gain threshold
exceeds the material gain, the amplifier can be biased at its peak material gain and
achieve the maximum amplification. When the gain threshold is lower than the ma44
terial gain, the amplification is determined by the gain threshold, in other words the
mirror loss. This relationship can be incorporated into the single-pass gain formalism
and simplifies Eqn. 4.2 into
{e
(rg-a,)L
e(rgth-aw)L
= eamL
=
for 9m
< 9th
for g.
> 9th
()
The amplification is fundamentally limited by the mirror reflectivity shown in the
analysis above. Whether gth < gm or 9th > gm can be easily reversed by changing the
cavity length, since 9t is a function of cavity length. It is beneficial to have 9th just
below gm, since self-lasing of the amplifier will facillitate the experimental alignment
of the seed laser and the amplifier. In other words, even with low material gain,
high amplification is achievable by increasing the cavity length. The reason that the
cavity cannot be infinite long is that the amplifier will reach lasing threshold and
start oscillate at some point. From the lasing threshold condition, we can derive
L
logR
(4.10)
g.I' - aw
which shows mirror reflectivity limits the maximum cavity length. However, due to
the lack of good anti-reflection coating material in THz, developing a THz travellingwave QC amplifier is very challenging.
4.2
QC Amplifier Based on Semi-Insulating-SurfacePlasmon Waveguides
QC amplifier based on SISP waveguides is designed based on a resonant phonon active
region FL183R-2 and uses a similar active region described in Ref. [49]. The quantum
cascade structure is grown on top of a heavily doped layer of 0.4 Jim thickness and
doping level n = 5 x 1018 cm- 3 , on a semi-insulating substrate.
The design bias
.
voltage is ~ 13 V and current density is ~ 850 A/cm2
Waveguide loss and mode confinement factor are calculated using two-dimensional
45
finite-element solver for varying waveguide widths, as described in Chap. 2.
f=4.3 THz, heavily doping 5e18 cm-3 ,thickness=0.4 grm
"
-1
8
E
0,
6
50
40
60
70
waveguide width (pm)
80
90
10 0
80
90
100
0.31
0.2
0.1
07o
50
60
70
waveguide width (pm)
In
15
E
C-)
-.
......
..
. .-
-........
10
-............-.....
5
IC
.....................
0 -
-
C
04
50
60
70
waveguide width (ptm)
80
90
100
Figure 4-1: Waveguide loss, confinement factor and net gain vs waveguide width for
4.3 THz SISP waveguides. The calculations are done with 2D finite-element solver.
From Fig. 4-1, confinement factor drops significantly as waveguide width narrows.
When waveguide width is less than 50 pm, mode confinement is so low that net
modal gain gnet = g. x r - a, < 0 (assuming peak material gain is
-
70 cm- 1).
Power expects to exponentially decay as propagating through the waveguide. Possible
amplification gain is only available when waveguide is wider than 50 pm, as get >
0. The single-pass gain becomes dependent on the mirror reflectivity, shown in the
previous section.
46
4.2.1
Facet Reflectivity
In semi-insulating surface-plasmon (SISP) waveguides, the two-dimensional mode profile and far field beam pattern is shown in Fig. 4-2. The mode is bound between the
upper metal layer and the heavily doped n+ layer beneath the active region and above
the semi-insulating substrate. Since the n+ layer is thinner than the skin depth, the
mode extends substantially into the substrate. This spatially extended mode results
in an approximate plane-wave like transmission, a narrow beam pattern (full-wdth
at half maximum ~ 20') and mirror reflectivity close to the Fresnel reflection coefficient R ~ 0.3, simply due to the index contrast mismatch between the dielectric
GaAs-AlGaAs (n~3.6) and air (n=1).
(b)
Figure 4-2: SISP waveguide's (a) two dimensional mode profile (b)far field beam
pattern with FWHM ~ 200
To reduce facet reflectivity of SISP waveguides, a high-resistivity hyper-hemispherical
silicon lens (HR-Si, >10 kQ-cm, refractive index n~ 3.4) can be placed at the facet,
to improve the mode transition from the dielectric to the air. The spacing between
the facet and silicon lens can be adjusted with double-side polished, high-resitivity
silicon spacer so that the facet is at the R/n aplanatic point of the lens to avoid any
spherical aberration.
The lens can be further anti-reflection (AR) coated with parylene to reduce reflections between the lens and air. Parylene's refractive index of n = 1.62 is lower
than the ideal value of single-layer AR coating n =
47
ngs = 1.85. However, its low
water absorption, thermal stability, good adhesion and conformal vacuum deposition
makes it suitable as an AR coating material for silicon lens at terahertz frequency.
Gatesman et al has observed a transmission close to 90% for a parylene coated silicon
or the Si/parylene/air interface at the design frequency ~ 2 THz, with FWHM of
~ 2 THz [50]. Only 3% - 4% of transmission loss is estimated due to the non-ideal
refractive index of parylene, while the remaining 6% - 7% is predicted to be the loss
in silicon and parylene [50]. A TDS study by Rungsawang et al has also confirmed a
drop in reflectivity from 0.32 to 0.052 for 2.8 THz QC laser in SISP waveguide with
the aid of parylene AR coating [51].
To investigate the transmission/reflection at the interface between the waveguide
facet and Si interface, scattering parameters (S-parameter) analysis can be performed
in three-dimensional (3D) finite-element simulations. To prevent any reflections from
the end of the silicon, port boundary conditions can be used to absorb any linear
combination of a set of eigenmodes, or a perfectly matched layer (PML) can be defined
as an additional layer surrounding the silicon to absorb any incident radiation. More
information can be found in Appendix B.
Two-dimensional (2D) eigenmodes can first be foundon a boundary port through
eigenmode analysis. The port is excited with one of the 2D fundamental modes with
electric field distrbution Eex. The computed electric field E, on the port includes
both the excitation and the reflected field. The S-parameter then can be calculated
as the normalized integral of the excited electric field and calculated electric field.
The time average power reflection/transmission can be obtained as IS1|2 (reflection
when i=j; transmission when ifj). For example, the reflection parameters S11 is given
by
ff,((Ec - Ex) - E*)dA
Eex 2 dA
ffport
In this case, 32% reflectivity is found for an open facet waveguide. When the facet is
attached to silicon, the reflectivity drops below 1%.
According to Eqn. 4.9, the maximum single-pass gain would be about G, ~
48
R1
~
100. However, this would require the lasing threshold slightly smaller than the peak
g
9m1'Qw
.
material gain and the device length can be calculated through Eqn. 4.10: L ~
For a 100 pm wide waveguide, the optimum device length is close to 2.7 mm. As the
waveguide width decreases, the preferred device length increases significantly due to
the rapid drop in confinement factor. For a waveguide of width 50 Am, 14 mm long
device length is needed to achieve maximum gain.
4.2.2
Limitations
A narrow waveguide (< 40 pm) is desired for efficient heat removal in continous wave
(c.w.) operation, but such a device is unable to provide any amplification since the
waveguide loss exceeds material gain (gin - am/P < 0) due to low confinement factor
(F < 0.1).
When the waveguide is wide enough so that there is a reasonable modal gain to
provide amplification, the single-pass gain is maximized at long device length shown in
the previous section, given a theoretical low mirror reflectivity is achievable (R<1%)
through attaching a AR coated hyperhemispherical silicon lens at the end facets. A
2.5 mm long and 100 pm wide SISP waveguide based on FL183-R2 will dissipate
electric power close to 28 W at its designed bias. With such large power dissipation,
the device temperature will rise and material gain will drop subsequently. Current
design scheme and gain medium will be suitable only if the amplifier is operated in
pulsed mode.
To ease the heat dissipation burden of wide and long waveguides, a bound-tocontinuum (BTC) active region design can be considered thanks to its low bias voltage
and current density. Despite the fact that it has much worse temperature performance
compared to resonant phonon designs, it will provide reasonable material gain at low
temperature [52].
In addition, the performance of travelling-wave amplifier based on SISP waveguides is expected to drop as the wavelength increases. This is due to the fact that
free-space coupling and mode matching between the free space and the waveguide will
become worse as the free-space wavelength increases. More importantly, the mode
49
confinement factor IF will decrease at long wavelengths for a given width.
4.3
QC Amplifier based on Metal-Metal Waveguides
In metal-metal (MM) waveguides, in addition to the index mismatch between the
air and semiconductor, the sub-wavelength mode confinement also causes a modal
mismatch between the confined mode between the 10 pm spaced metal strips and the
near-field mode at the aperture (AO ~ 70 pm at 4.3 THz) and increases the mirror
reflectivity to -0.7.
There are two main challenges for MM waveguide to be suitable as a travellingwave amplifier. First, the strong mirror reflectivity induces strong feedback inside the
cavity, which makes MM waveguides suitable as standing-wave amplifiers with narrow
bandwidth. If it is used as travelling-wave amplifier, its single pass gain (< -) will
be low due to this strong mirror reflection. Efforts such as angled facets have been
employed on amplifier section in a master-oscillator power-amplifier (MOPA) scheme
to reduce the cavity feedback and increase the mirror loss [53]. Second, light coupling
in and out of the sub-wavelength aperture will be very inefficient.
A metal-metal waveguide with broadband horn antennas monolithically fabricated
at the two ends and anti-reflection (AR) coated silicon lenses attached to the facets
is proposed here. Fig. 4-3 shows the three-dimensional (3D) and two dimensional
(2D) views of the proposed QC amplifier based on metal-metal waveguides.
The
active region is grown on semi-insulating GaAs substrate, and is metal-metal bonded
to a n+ GaAs receptor substrate (see Appendix C). Horn structures are formed on
both ends of the waveguide using the semi-insulating substrate and expand the mode
vertically. The waveguide can also be defined laterally, flaring from the center towards
the two ends. Hyper-hemispherical silicon lenses (and silicon spacers if necessary)
are attached to the two facets.
A thin metal layer can be deposited on the top
of the cavity and bottom of the receptor substrate for bias purpose. Despite the
50
Figure 4-3: Schematic of QC amplifier based on MM waveguide. (a) 3D view. (b)
2D side view: active region (red) and receptor n+ substrate (grey) are metal-metal
bonded (yellow). Horn structures are formed on both ends of the waveguide, using
semi-insulating substrate (grey). The entire structure is sandwiched between a top
and bottom metal layer (yellow). AR coated silicon lens (blue) are attached to the
two facets. (c) 3D top view: the waveguide is flared from the center towards the two
ends.
lateral conductivity of GaAs in the active region (n
-
1015 cm-), the active region
underneath the horn structure/semi-insulating substrate will not be biased or have
any gain. This structure will not only reduce the facet reflectivity, but also improve
the radiation coupling between the sub-wavelength waveguides and free space.
In
fact, such monolithically integrated antenna structure has been employed in terahertz
time-domain spectroscopy (THz-TDS) studies [54] and has shown improved free-space
coupling efficiency and effective mode expansion. AR coated silicon lens can be used
further to improve the mode matching from the dielectric to the air shown in the
previous analysis.
The performance of the proposed metal-metal waveguide travelling-wave THz QC
amplifier strongly depends on three key parameters: facet reflectivity, lasing gain
threshold and amplification power gain. The calculations are done with finite-element
method (FEM) simulations, since the estimation of reflectivity using effective index
method is no longer valid. However, if silicon lenses of 2 mm radius are used, the
dimension of the entire structure far exceeds the dielectric wavelength (- 20 pm
51
at 4.3 THz). The number of elements in three-dimensional (3D) meshing will on
the order of ~ 10', which significantly reduces the computation efficiency. While
the lateral dimension of the waveguide can be easily made comparable to free-space
wavelength, the mode expansion in the vertical direction (growth direction) from the
active region to the free space through the horn structure and silicon lens becomes
the limiting factor to achieve low facet reflection and efficient light coupling. Thus,
most of the FEM simulations are done in the two-dimensional (2D) environment with
the geometry shown in the side view in Fig. 4-3. In the 3D FEM simulations, in
order to avoid the computation overhead associated with the silicon lens, a perfectly
matched layer (PML) is used surrounding a thin silicon spacer to absorb all the
incident radiation. However, this is appropriate only if the transmission from the
dielectric lens to the air is perfect.
In the 2D simulations, considering the fabrication limits and computation efficiency, the center ridge which contains the 10 pim active region is made 1 mm long,
the horn structures on the two ends of the ridge expands the vertical dimension from
10 pim to 100 Mm with a 450 rising slope, and the silicon lenses of 2 mm in radius with
parylene AR coating of appropriate thickness (nAR=1.62, t = 4fl,,) are attached to
the two facets.
4.3.1
Facet Reflectivity
Low facet reflectivity is desired for large power amplification, since it results in a large
mirror loss, and consequently high gain threshold. To analyze the facet reflectivity, the
fundamental mode is excited at the center of the 10 pm tall ridge and S-parameter
for the reflected wave S1 is calculated in the 2D FEM simulations. For a simple
Fabry-Perot waveguide, facet reflectivity is ~ 0.7 due to the sub-wavelength mode
confinement at the facet and a standing wave is formed in the cavity due to this strong
feedback, shown in Fig. 4-4(c). With monolithic horn structures and silicon lenses,
the facet reflectivity can be effectively reduced to ~ 0.1% t 0.5% and the boundary
mode propagates through the cavity in a travelling-wave manner, shown in Fig. 4-4
(a) and (b). An uncertainty of
0.5% in facet reflectivity calculation is due to the
52
Electr.
fI.Id
nom(V/.)
500 pm
(b)
(a)
(C)
(d)
Figure 4-4: Electric field magnitude of (a) active region with monolithic horn structure
and silicon lens attached at the facet. (b) zoomed in of (a) at the transition from the
active region to horn structure. (c) active region of a Fabry-Perot waveguide. (d) line
graph of E field magnitude across the lens output
numerical discretization.
Horn structures with different slopes and different final heights are simulated.
Facet reflectivity is found to be rather insensitive to the horn angle, while it significantly decreases with increasing horn height until the facet vertical dimension exceeds
the dielectric wavelength A/nsi (~ 20 pm at 4.3 THz). This shows that the AR coated
silicon lens effectively reduces the wavelength at the facet. Despite the fact that 30
pm facet height is sufficient to reduce the facet reflectivity to < 0.5%, shown in Fig.
4-5, it is still too close to the diffraction-limited spot size (diameter
=
sina)
and
coupling efficiency will be very low. Thus, larger horn structures (100pm in growth
direction) are simulated and fabricated to achieve more efficient coupling.
Also, the radiation pattern is found to be sensitive to the size of the silicon lens and
also the position of the silicon lens with respect to the ridges. A silicon lens of larger
radius gives a better radiation beam pattern because it is more forgiving of various
optical aberrations, shown in the radiation pattern comparison between silicon lenses
of 0.5 mm and 2.0 mm radii (see Fig. 4-6). However, even with a 2 mm radius
silicon lens, misalignment of the silicon lens relative to the facet can deteriorate beam
pattern. As the vertical offset between the ridge and silicon lens increases (shown
53
5
0
S4
0
0
10
20
30
40
50
60
70
vertical dimension of the facet h (jim)
80
90
Figure 4-5: Facet reflectivity versus vertical dimension of the facet, assuming a 450
slanted angle. Facet reflectivity is reduced to < 0.5% when the facet vertical dimension exceeds 30 ,um.
in Fig. 4-7) the beam pattern becomes more tilted due to severe coma aberration,
despite the fact that the facet reflectivity remains relatively constant. As the gap
between the facet and silicon lens increases, the effect of the silicon lens reduces and
facet reflectivity expects to increase significantly
[551.
This shows that the alignment
of the silicon lens to the facet is critical.
4.3.2
Eigenfrequency Analysis
To achieve the maximum possible single-pass gain, it is desired to bias the amplifier
to the point of maximum material gain, without the amplifier self-lasing and consequently gain clamping. However, for alignment, it is important to make sure that the
lasing threshold is slightly below the maximum available gain.
From 2D eigenfrequency analysis, without taking into account the waveguide loss
and metal loss, the gain threshold for a structure with 1 mm long active region is~
65 cm-1 , shown in Fig. 4-8. This is consistent with the previous facet reflectivity
54
Figure 4-6: Electric field magnitude of (a) a waveguide with AR coated silicon lens of
0.5 mm radius (facet reflectivity R ~ 0.06%) (b) a waveguide with AR coated silicon
lens of 2 mm radius (facet reflectivity R
no offset
-
0.05%).
100 pm offset
200 pm offset
Figure 4-7: Electric field magnitude vs relative vertical offset between the center of
the AR coated silicon lens and that of the active region. When offset=0, R ~ 0.05%;
when offset=100 pm, R ~ 0.08%; when offset=200 pm, R ~ 0.27%;
55
simulation. Assuming unity confinement factor, the gain threshold is determined by
the mirror loss gth =
e
R am = -1g.
The 0.1 % facet reflectivity calculated
previously is expected to help achieve gain threshold
69 cm- 1 for a 1 mm long
device.
Figure 4-8: E field in the growth direction of the lasing mode in 2D eigenfrequency
analysis
However, the 2D environment assumes infinite lateral dimension, in other words,
no lateral variations. It does not capture the behavior of the higher order lateral
modes. Thus, it is important to verify the results in the 3D environment. Perfectly
matched layers (PML) surrounding a thin silicon spacer is used in 3D simulations
to represent the nearly perfect transmission from the silicon lens to free space. As
expected, when the waveguide width exceeds the material wavelength (~
20 pm at
4.3 THz), higher order lateral modes start to appear. When the waveguide is 100
pm wide, the gain threshold of the higher order mode is much lower than the gain
threshold found from 2D simulations. One way to increase the loss of these parasitic
lateral modes is to narrow the waveguide width, which is also desired for efficient heat
removal in continuous wave (c.w.) operation. Thus, the waveguide is narrowed in the
center (30 pm wide), flaring laterally towards the two ends (100 pm wide) to ensure
the lateral dimension at the facet exceeding the free space wavelength for efficient
56
1
,
light coupling. The gain threshold of the higher lateral modes increases to 43 cm
shown in Fig. 4-9, much closer to the peak material gain that THz QC gain medium
is able to provide, ~ 50 cm-
Lasing mode
-
2-
E
4
C
6
z
810
-1 2-1 4
4.2
4.22
4.24
4.26
4.28
4.3
4.32
FREQ (THz)
200
4.34
4.36
4.38
4.4
200,
100
100
600
400
400
200
200'0
0
2
200
2000
-600
-600
100
-0
Figure 4-9: Net gain versus frequency plot with active region material gain 43 cm-1
(top). Electric field in the growth direction inside the cavity where the center is
narrow (30 [tim wide) and flares laterally to the two ends (100 Mm wide) (bottom).
57
4.3.3
Amplification Simulation
From the previous simulation, the radiation beam pattern is shown most similar to
Gaussian and have an offset dependent on the lens size. In reverse, similar beam
pattern will be coupled into the amplifier most efficiently.
(a)(
(c)
(b)
Figure 4-10: Electric field magnitude of (a) background/input field (b) amplified/excited field (c) zoomed in of (b)
To simulate the performance of the amplifer, a wave with electric field
Eb
of a
Gaussian transverse profile of FWHM ~ 500 pm, 150 pm vertical offset relative to
the center of the facet and normalized total electric field energy is used to excite the
waveguide.
Its E-field is polarized in the
y
direction and it propagates in the +x
direction, shown in Fig. 4-10 (a). The electric field is coupled into the amplifier
cavity and amplified, shown in Fig. 4-10 (b) and (c). The amplifier power gain can
be expressed as G =
=
E
I= dE
-
f2dy, since f IEbI2dy is normalized to
be unity.
Assuming the facet reflectivity is sufficiently low, the power on the output end is
mostly the amplified input after single pass through the waveguide Pott ~ Pbrlcouptinge
and the input end is mostly the amplified input after two passes through the waveguide
58
e
12001
0
simulated power gain
calculated power gain
assume 17% coupling efficiency
1000800Q
600-
0
400-
200__-g..
0
10
20
- -_
30-
40
50
60
net modal gain (cm-)
70
80
90
Figure 4-11: Power gain versus net modal gain plot. Red: simulated data; blue:
calculated power gain G = ?couplingegnetL assuming ricoupling=17%. The center ridge is
1 mm long, horns on the two ends are 100 pm tall with 450 slanted angle and the
silicon lenses of 2 mm radius are AR coated.
Pin
~ P7coupling egnetLg
gnetL.
The ratio of the power on the input end to that on the
output end is roughly RegnetL, which also determines the lasing condition of the cavity.
At relatively low bias/material gain, the amplifier itself does not lase and the output
end has much more power gain than the input end (RegnetL < 1). As the bias/material
gain increases, amplifier's power gain rises exponentially G ~
7couplng
L
and the
power ratio approaches 1. When the power gain is larger than the single-pass gain
(red line above blue line in Fig. 4-11), it indicates that the input signal oscillates
inside the amplifier cavity for more than one single-pass before leaving the cavity. A
higher power gain can be achieved at the cost of a narrower bandwidth. At sufficient
high bias, the material gain is able to overcome the mirror loss and R x egnetL
>
Physically, the amplifier will start to lase and gain should be clamped R x
= 1.
egnetL
1.
Since the FEM simulation cannot incorporate this nonlinear effect, the radiation continues to oscillate in the cavity and be amplified. This is no longer a steady-state,
which is an assumption in the frequency domain analysis. Numerically, the power
gain starts to drop, shown in Fig. 4-11, which will not happen in actual experiments.
59
Considering the theorectical relationship between the amplifier's power gain versus
net modal gain G ~ rlempjjgegnetL, a coupling efficiency 17% is be found to be a good
fit between data from the simulation and theorectical calculation. However, since the
2D simulation assumes infinite lateral dimension, actual finite lateral dimension is
expected to further reduce the coupling efficiency and the power gain.
The 2D FEM simulation predicts that with net modal gain gnet = 70 cm-1,the
designed amplifier can achieve power gain ~ 200. However, the peak material gain
1
gm for THz QCL with a vertical design is only about 70 cm- . Excluding waveguide
loss and metal loss and assuming unity confinement factor, the active region is able
.
1
to provide a net modal gain of guet = glF - a,, ~ 50 cm-
With 50 cm- 1 net modal gain, FWHM (full width at half maximum) and vertical
offset of the input Eb field are then sweeped in detailed. Fig. 4-12 shows a twodimensional surface plot of amplifier gain versus different input field FWHM and
offset. Power gain is found to be sensitive to the input field, and can be maximized
to ~ 22. This shows that experimental alignment/coupling of the seed laser and
amplifier is critical.
Power Gain
22
700
20
=600
0
18
00-j 500
16
a)o 400
14
12
3O$50
300
350
400
500
450
550
600
650
FHWM of the input E field (pm)
Figure 4-12: Surface contour plot of power gain with input E field at different vertical
offset relative to the facet and of different FWHM, with 50 cm' net modal gain.
Power gain versus frequency is plotted in Fig. 4-13. Since the AR coating thickness
of the silicon lenses is only optimized for the design frequency 4.3 THz (t = 4fAR ), the
60
power gain shows a nonuniform frequency response which is consistent over different
values of net modal gain.
100
-
90
material gain 50cm
material gain 55cm]
80
70
C
60
a)
50
0
40
13-
30
20
II
-
10
"'
4.1
4.2
4.3
4.4
4.5
4.6
Freq (THz)
Figure 4-13: Power gain versus frequency for different net modal gain.
For building a short-cavity amplifier (< 1 mm long), the material gain of a typical
THz QCL gain medium may not be sufficient to reach the IR limit. In this case,
it is desirable to have gain media optimized for maximum low temperature gain,
independent of Tmax performance.
61
62
Chapter 5
Fabrication of Travelling-Wave
Terahertz Quantum Cascade
Amplifiers in Metal-Metal
Waveguides
The 10 pim-thick quantum cascade structures are grown by molecular beam epitaxy
(MBE) on top of a semi-insulating GaAs substrate with a 0.2 pim-thick AlO. 5 Ga0 .5As
etch stop layer in between by Dr. John Reno of Sandia National Laboratories. All
fabrication takes place at the MIT's Microsystems Technology Laboratory (MTL),
except the lapping and polishing process in Prof. Qing Hu's laboratory.
The fabrication process for the metal-metal (MM) quantum cascade (QC) travellfingwave amplifier is similar to MM QC laser, up to the wafer bonding step. The overall
fabrication flow will be discussed with details for the steps unique to the QC amplifier.
5.1
General Fabrication Flow
The gain medium wafer is first cleaved into the correct size and with correct crystal
orientation. After metal deposition of a layer of Ti/Au (100/3000
A),
the wafer is
Au-Au wafer-bonded to an n+ GaAs receptor substrate of slightly bigger size for
63
2 Horn formation
Ti/Au
3. Top metal definition
Ti/Au
Ti/Au
4. Dry etch
Ti/Au
Figure 5-1: Schematics for THz MM QC amplifier fabrication proess in MM waveguides. (Left column) Top view. (Right column) Side view.
64
convenient wafer handling. Note that the Ti acts as an adhsion layer between the
semiconductor and Au. For metal with higher stress level, for example Ni, a thickness
ratio with respect to the adhesion layer of 10:1 is recommended. A thin layer ~ 0.3 Am
of SiO 2 is deposited on both sides of the bonded wafer using the plasma-enhance
chemical vapor deposition (PECVD) tool STS-CVD. The SiO 2 protects the bottom
of the receptor substrate and the sidewalls of the wafer from the following mechanical
lapping and wet etch of the horn structure.
The semi-insulating substrate is thinned and polished to a thickness of
-
100 Am
with < 1 Am surface roughness and no obvious scratches. The horn antenna (shown
in Fig.
5-2) is patterned by contact photo-lithography using positive photoresist
(MicroChem Shipley 1813) and defined by wet etch using two chemical etchants,
H 2 SO 4 : H 2 0 2 : H 2 0
=
1: 8 : 1 and citric acid : H 2 0 2 : H 2 0 = 3 : 2 : 3 (citric acid
concentration of 1 g/mL). The citric acid based etchant is a selective etchant and
"stops" once reaching the Alo.Ga. 5 As layer. The 0.2 pm etch stop is then removed
using a 10 sec dip in HF etchant, which creates an under-cut near the bottom of the
horn structure, shown in Fig. 5-3(a).
Figure 5-2: SEM pictures of (a) the horn structure using wet etch with etchants
H 2 SO4 : H 2 0 2 : H 2 0
=
1 : 8 : 1 and citric acid : H 2 0 2 : H 2 0 = 3 : 2 : 3. (b) Zoom-in
of the sidewall of the horn structure
The ridges are defined by a second contact photo-lithography using an image
reversal photoresist (MicroChem AZ 5214E), followed by metal deposition Ti/Au
(150/3500 A) and lift-off process. A slightly thicker metal is used to cover the gap
between the horn and the gain medium created by the etch stop removal, shown in
65
kD)
Figure 5-3: SEM pictures of (a) undercut underneath the horn structure after HF
removal of the 0.2 pm-thick etch stop (b) continuous top metal covering the 0.2 pm
gap from the gain medium to the horn structure
Fig. 5-3 (b). Then, the top metal layer can act as a self-aligned etching mask for the
subsequent anisotropic dry etch based on Cl 2 /SiCl 4 /Ar gas mixture, shown in Fig.
5-4. The passivation layer on the sidewall (mainly SiO 2 ) can be removed by a 3-5
min Silox Vapox dip, or 4 min BOE dip, or an isotropic SF6 plasma etch. A 5-10 sec
dip in a very diluted ammonia-based etchant (NH 4 0H : H202 : H 2 0
1: 3 : 300)
can be used to clean the grass-like features due to micromasking.
Figure 5-4: SEM pictures (a) after 10 pm-deep dry etch (b) after 100 pm-deep dry
etch using the top metal as a self-aligned etching mask
The last step of the fabrication is backside lapping and backside metal deposition.
The receptor substrate is mechanically lapped to a remaining thickness of 150-200
66
,um. 400 grit SiC sandpaper is firstly used to remove majority of the material and
9 pLm A1 2 0 3 lapping film is then used to improve the surface roughness for better
cleaving result. Lastly, a Ti/Au (150/2500 A) layer is deposited on the backside of
the device.
The wafer is then cleaved or die sawed into smaller sub-chips.
The individual
chips will be edge-polished and In/Au die-bonded to a copper chip carrier with the
correct length. Hyper-hemispherical silicon lens will be attached to both facet of the
device. The device will be wire-bonded for further measurement.
5.2
Mechanical Lapping and Polishing
Mechanical lapping and polishing is a process to remove material using abrasive particles, which can be in the form of free abrasive lapping and fixed abrasive lapping.
Free abrasive particles can be used with a cloth for polishing a fine surface, while fixed
abrasive lapping refers to the use of sandpapers or abrasive lapping films which abrasive particles are attached to. Common abrasive particles include Alumina (A1 2 0 3 ),
Silicon Carbide (SiC), Diamond and etc. Their hardness, shape and usage are discussed in Table 5.1 [56]. Free abrasive polishing with fine Alumina particles ~ 0.3 14m
has been observed to leave a hazy passivation layer on the surface and low removal
rate. All mechanical lapping and polishing are done with SiC paper and Alumina
abrasive lapping films.
Material
Silicon Carbide (SiC)
Alumina (A12 0 3 )
Diamond (C)
Hardness
(KNOOP
100)
2450
2000
6000
Structure and Usage
blocky and sharp
rarely used for smooth surface finishes
blocky and angular
commonly used for fine, surface finishes since
it breaks down over time
sharp and angular
Useful in produce excellent surface finish and
high removal rates
Table 5.1: Table of lapping abrasives: Silicon Carbide, Alumina and Diamond
67
Au-Au bonded pieces (1.5 cm x 2 cm) are fixed to the center of a the mounting
block (5 cm diameter) using Crystalbond wax at ~ 150 'C . Wax needs to cover
the edge of the substrate to prevent the corners from breaking during lapping. A
lapping fixture (Model 155 from South Bay Technology) holds the sample during
processing. The thickness control of the lapping fixture helps to lap the sample with
~ 10 pm accuracy. A micrometer can be used to determine the lapping thickness more
precisely. Different weights can be applied to the lapping fixture to provide various
pressure and speed of lapping. Silicon carbide (SiC) paper or aluminum oxide abrasive
lapping film is fixed to the lapping plate (Model 920 from South Bay Technology)
with a metal ring.
The semi-insulating substrate with orginal thickness of ~ 650 pm is first mechanically lapped with 400-grit SiC paper with average particle size ~,-, 35 pm until a
thickness of ~ 200 pm. Alumina abrasive lapping films with reducing particle size
from 20 pm to 1 pm are used, to further thin the substrate until a final thickness of
~ 100 pm and reduce the surface roughness. The detailed experimental parameters
for lapping process is included in Appendix C.
A scratch-free surface with roughness <1 pm and thickness variation < 5 pm is
desired. Since the substrate needs to be patterned by photoresist
-
1.4 pm thick,
any big scratch or surface roughness more than 1 pm will affect the adhesion of the
photoresist during wet etch of the horn structure formation. The edge of the wafer
will always be thinner than the center after mechanical lapping.
If the thickness
variation exceeds 10 pm, it's possible that the gain medium on the edge of the wafer
will be etched through during wet etch before the center part reaches the etch stop.
Small surface roughness can be achieved using abrasive lapping films with fine particle
sizes and flatness can be improved with less pressure and slow wheel speed with the
trade-off of slow removal rate, but scratches are almost unavoidable during mechanical
lapping and polishing.
68
5.2.1
Sources of Scratches
Scratches are consistently observed after lapping with 3 Mm alumina film and cannot
be removed with finer alumina films. The scratches can either be at random positions
or uniformly distributed on the surface, shown in Fig. 5-5. The latter suggests the
source of scratch is from particles stuck on the abrasive lapping films.
Figure 5-5: Pictures of two bonded wafers (of size
1.5 x 2 cm) after mechanical
lapping: left one has a few light scratches near the edge of the surface and right one
has many deep scratches uniformly distributed on the surface
A few sources of scratches are identified. Also, two possible reasons are also found
to explain why abrasive films with finer particle size are unable to remove scratches.
1. Free particles in the lapping environment. Thus, the lapping process is done
in a fume hood to prevent outside contamination.
2. Uneven abrasive particles on the lapping films or too much pressure on the
sample.
3. Lapped GaAs or abrasive alumina with big particle size from previous lapping
are stuck in the wax and fall out to cause scratches as wax is being removed during
lapping. This has become the source of scratches most difficult to avoid.
The only way to avoid this is to either use intense ultrasonic cleaning to shake
out the particles stuck in the wax, or use acetone and isopropanol to wash away these
particles along with part of the wax. The former method may run into the risk of
damaging the metal-semiconductor interface (details in the next section). The latter
is done at the cost of loss of wax which protects the corners of the substrate from
69
breaking and reduces the edge effect of lapping. This is only recommended in the
very last few steps of lapping.
4. The scratches are bigger than abrasive film's particles and cannot be lapped
away. Thus, before switching to a lapping film with a finer particle size, the substrate
surface need to be lapped free of obvious features.
5. Lapped material GaAs or abrasive materials alumina with fine particle size
are stuck in the scratches and filled scratches get deeper as being lapped. Ultrasonic
cleaning can be used to detach particles from the scratches.
5.2.2
Use of Ultrasonic Cleaning
The use of ultrasonic cleaning has greatly improved the yield rate of scratch-free
surface. However, it is possible and has been observed that the metal-semiconductor
interface breaks after short but intensive ultrasonic cleaning (20 second ultrasonic
cleaning at 40 KHz and average power 140 W/gallon) and subsequent lapping, shown
in Fig. 5-6. Ultrasonic cleaning uses cavitation bubbles induced by high frequency
waves to agitate the solution and detach fine particles from the surface.
If such
cavitation bubbles implode near a surface and induce a shock wave, surface can be
damaged [57].
Ultrasonic Model CP230D is able to provide a control of heat and average sonic
power as low as 4 W in a 0.75-gallon tank. Between different lapping films, the sample
is immerse in the water in a plastic beaker and ultrasonic cleaned for 20 sec at power
level 2. No damage has observed.
An alternative could be using a megasonic cleaner. Megasonic cleaning which operates at a much higher frequency above 0.8-1.2 MHz has shown more controlled cavitation or less cavitation since cavitation threshold increases with frequency. Due to its
effectiveness in removing contamination without inflicting surface damage, megasonic
cleaning has been widely accepted in semiconductor manufacture industry [57]
70
Figure 5-6: Damage to an Au-Au bonded wafer from ultrasonic cleaning and subsequent lapping. The outer area (yellow) is Au on top of the receptor substrate. The
center area (grey) is the top of the S.I. substrate. Part of the gain medium and S.I.
substrate break from the metal, leaving the adhesion layer Ti (red) exposed
5.2.3
Chemical-Mechanical Polishing
An alternative way to produce scratch-free polished surface other than mechanical
lapping and polishing is through chemical-mechanical polishing (CMP).
A common solution for CMP of GaAs, dibromine (Br 2 )-methanol (MeOH) is
avoided due to its poor surface finish [58], decomposition over time [59] and the
presence of toxic bromine vapors. Hydrogen peroxide (H 2 0 2 ) ammonium hydroxide
(NH 4 0H) solution, on the other hand, has shown to be able to achieve nanometer
surface finish in the pH range 6-8.5 [60].
A three-step mechanism is proposed for GaAs CMP using peroxide-ammonia solution [61].
Hydrogen peroxide oxidizes the surface and form a layer of insoluble
oxohydroxidation products of Ga and As. Then these oxohydroxides are dissolved
with aqueous (aq.) NH 3 and finally removed from the surface with mechanical wiping. Since the pH of the solution is close to neutral, hydrogen peroxide composes
majority of the solution and provides abundant oxidation agent. Thus, the limiting
factor of the process will be the concentration of the aq. NH 3 and the efficiency of
mechanical wiping. Mckeekin et al shows the removal rate rises exponentially with
71
pH [60].
250 mL 30% H 2 0 2 is mixed with 0.1 mL 30% NH 4 0H to achieve pH
-
8.3. Since
peroxide does decompose over time and the decomposition accelerates with increasing
pH [61], the solution should be mixed about half an hour before the CMP process.
A synthetic velvet polishing cloth is soaked with the mixed solution. Acetone is used
to rinse off the wax covering the edge of the substrate, because wax will not dissolve
or etch in peroxide-amonium solution.
The wax beneath the sample will still be
able to hold the sample to the mounting block during CMP. Sample load is about
360 g/cm 2 . However, compared to literature [60], a much slower removal rate (~_.1
pm/hr) is observed. After 1 hr CMP, surface looks smooth and scratch-free under
the microscope.
However, after the following step wet etch of horn structure with sulfuric acid
and citric acid, short line features show up uniformly distributed on the surface of
the SI substrate and translates into sidewall waviness under SEM, shown in Fig. 57. Dyment et al has also reported similar dislocations defects observed with high
resolution reflection X-ray [59].
Figure 5-7: SEM pictures of (left) CMP processed wafer after wet etching of the horn
structure, (right) zooom-in on the top surface of the horn structure
Table 5.2 shows a comparison between mechanical polishing and CMP. In the
actual fabrication, two pieces are processed. One has gone through both mechanical
polishing and CMP, while the other has only been mechanically polished.
72
Pros
Cons
mechanical polishing
remove big surface roughness and
CMP
remove small surface roughness
deep scratches > 1 Mm
and scratches < 1 pm
hard to avoid scratches
surface damage with features of
short lines
Table 5.2: Comparison between mechanical polishing and CMP
5.3
Wet Etch Clean
A wet etch clean is found to be crucial between the process of mechanical lapping (or
CMP) and wet etching of the horn structure. Without this step, a thin layer of GaAs
(< 1 pm thick) that is etched irregularly, is observed on top of the horn structure,
shown in Fig. 5-8. The zig-zag edge of this layer translates into a wavy sidewall for
the entire horn structure.
Figure 5-8: SEM picture of a thin amorphous GaAs layer on top of the horn structure.
The piece is previously mechanically lapped without wet etch clean.
A thorough ultrasonic clean with 3-solvent is performed right after mechanical
lapping (or CMP) to remove additional wax or dust on the surface. However, this
layer of amorphous GaAs layer is still consistently observed, which suggests this could
be a thin damaged surface layer from lapping.
73
Piranha (H 2 SO 4 : H202: H 2 0 4:1:1), a common cleaning etch to prepare substrate
prior to MBE growth [62], is used here. To have a reproducible etch rate and mirrorlike surface finish, the solution is carefully prepared with the sequence of H 2 0, H 2 SO4
.
and H202, and the sample is dipped in the solution for 30 s at temperature ~ 70'C
5.4
Horn Formation
After mechanical lapping (or CMP) and piranha clean, the semi-insulating substrate
needs to be patterned with photoresist by contact photolithography and wet etched
to form the horn structure. Since the horn structure will be ~ 100 Am tall, it is
important to use photoresist with good adhesion as a mask during wet etch and
etchants that will produce reasonable etch rate and good sidewall profile with little
erosion to the photoresist.
Two positive photoresists have been investigated. The 10 Asm thick positive photoresist AZ 4620 is ideal for covering all the scratches and surface roughness. However,
high thermal stress is expected for such a thick photoresist and causes cracking after
postbake if any surface defect is present. Any cracking in the photoresist leads to
peeling during wet etch which is highly undesired. The thin positive photoresist (~
1.4 pm thick) Shipley 1813 has proven to have good adhesion during wet etch, but it
requires a smooth surface with roughness and scratchess < 1 pm.
Care must be taken in aligning the mask with respect to the crystallographic axes
of the wafer, since different crystal axes will have different etch profiles.
For US
(100) wafers with (100) facing up, for example, the fabrication of SISP waveguides,
outwardly sloped sidewalls are produced along the (01T) (parallel to the major flat)
and undercut sidewalls along the (011) (parallel to the minor flat on US (100) wafers),
shown in FIg. 5-9. However, when the wafer is flipped upside down, for example,
during the fabrication of metal-metal waveguides, the relationship is reversed.
The wet etching of GaAs is often a two-step reaction, consisting of the oxidation
of the surface (typically by H202) and the dissolution of these oxides with acids or
bases. The second step usually determines the reaction type, whether it is diffusion
74
Figure 5-9: SEM pictures of crystallographic etch profiles: (left) inwardly-sloped and
(right) outwardly-sloped sidewall, using 1:8:10 H 2 SO 4 /H 2 0 2 /H 2 0 etchant (mostly
diffusion limited).
limited (the supply/transport of acid/base to the surface) or reaction-rate limited (the
activation energy of the dissolution reaction), and subsequently the etching profile
[63].
Diffusion limited etching dominates when the solution is of high viscosity or has
low acid/base concentration. The etching is sensitive to agitation, but not to temperature. The etching profile tends to be more isotropic and surface finish looks
"polished". Reaction-rate limited etching, on the other hand, has sufficient supply of
reagents and is instead sensitive to temperature. It can produce anisotropic profiles
with respect to certain crystallographic orientations and magnify surface defects or
damages. Thus, a diffusion limited etching is preferred considering its surface polishing effect and isotropic profile which helps mode expansion from the ridges. Various
etchants are investigated and results are compared.
Sulfuric acid etchant (H 2 SO 4 /H 2 0 2 /H 2 0). Mirror-like surface finish is only produced at high sulfuric acid (ie. 4:1:1 H2 SO 4 /H 2 0 2 /H 2 0) or high hydrogen peroxide
(ie.
1:8:1 H 2 SO 4 /H 2 0 2 /H 2 0) concentrations [64]. Solution with high sulfuric acid
concentration is often referred to as piranha etch, which attacks organics such photoresist and is not suitable for device etch.
Thus, a solution with high peroxide
concentraion 1:8:1 H 2 SO 4 /H 2 0 2/H 2 0 at room temperature is used for wet etching of
the horn structure. It produces the highest etch rate (~
75
7-9 pm/min), most isotropic
sidewall profile and best surface polishing effect, shown in Fig. 5-10. However, its
etch rates and sidewall slope are not only time-dependent, but also crystal orientationdependent which results in an uneven bottom surface. It's important to prepare the
solution with a consistent method, calibrate the etch rate before processing the real
wafer, and account for different etch rate for different crystallographic orientation.
(a)
(D)
C)
tu)
Figure 5-10: SEM pictures of horn structures after wet etch using sulfuric acid etch
1:8:1 H 2 SO 4 /H 2 0 2 /H 2 0 (diffusion limited). (a) shows an uneven bottom. (b) zoom-in
of (a). (c) shows the smooth sidewall. (d) zoom-in of (c).
Phosphoric acid 1:1:5 H 3 PO 4 /H 2 0 2 /H 2 0. It produces smooth and straight sidewall with negligible waviness and slope ~ 450, shown in Fig. 5-11. The etch rate is
reasonable ~ 85 pm/hr and uniform across the entire wafer. However, despite the
high viscosity of the phosphoric acid, the etching is still reaction-limited and deepens
any surface defect, thus undesired.
76
(a)
tW
ka)
Figure 5-11: SEM pictures of horn structure after wet etch using phosphoric acid etch
1:1:5 H 3 PO 4 /H 2 0 2 /H 2 0 (reaction limited). (a) shows an even bottom. (b) zoom-in
of (a). (c)shows the smooth sidewall. (d) zoom-in of (c).
77
Citric acid citric/H 2 0 2 /H 2 0 is often used as a selective etchant for GaAs/AlGaAs.
Solution mixture of 3:1 citric/H 2 02 with stirring is often used for substrate removal.
However, it is observed experimentally that stirring causes sidewall roughness and deteriorates photoresist adhesion. Instead, a solution mixture of 3:2:3 citric/H 2 0 2 /H 2 0
without stirring is used and produces reasonable etch etch
-
20 Am/hr.
After various testing, the horn structures are patterned by contact photo-lithography
using positive photoresist (MicroChem Shipley 1813) and then defined by wet etch using two chemical etchants, H 2 SO4: H202 : H20
3 : 2 : 3 (citric acid concentration of 1 g/mL).
78
=
1: 8: 1 and citric acid: H 2 0 2 : H 2 0 =
Appendix A
Design Parameter
Design parameters for two-dimensional finite-element mode solver in COMSOL Multiphysics.
Thickness
Material
n
r
0.4 pm
Au
5.6 x 1022 cm- 3
0.05 ps
0.1 pm
n+ GaAs (top contact)
5 x 1018 cM-
10 pm
3
0.1 ps
GaAs (active region)
0
0.4 pm
n+ GaAs
5 x 1018 Cm-3
0.1 ps
200 pm
GaAs
0
0.4 pm
Au
5.6 x 1022 cM-
79
3
0.05 ps
80
F
Appendix B
Boundary Conditions for
Finite-Element Simulations
Since it's impossible to model the infinite space or the open boundary in the finiteelement simulations, choosing the right type of absorbing boundary condition is critical to avoid unwanted relfection. The Radio Frequency (RF) Module of COMSOL
provides a absorbing domain, perfectly matched layers (PMLs), and two possible absorbing boundary conditions, scattering boundary condition and port boundary condition [65].
1. Scattering Boundary Condition, a first order absorbing boundary condition
for a plane wave, a cylindrical wave or a spherical wave. Since the radiation from a
semi-insulating-surface-plamon waveguide is mostly plane wave due to its spatially
extended mode profile, scattering boundary condition is enough to absorb the outgoing radiation from the waveguide. The edges of an air box that are several wavelength
away from the waveguide can be defined with scattering boundary conditions.
2. Port Boundary Condition, a perfectly absorbing condition for eigen modes
of known mode profiles and propagation constants calculated through eigenmode
solver. One physical boundary can be defined with several port boundary conditions
to represent a linear combination of several corresponding orthogonal modes.
Port boundary condition is often used in scattering parameter (S-parameter) calculations.
At least one physical boundary of the waveguide is defined with port
81
boundary condition. When port i has wave excitation, Sji will be the S-parameter for
transmitted wave and Sii will be the S-parameter for reflected wave.
3. Perfectly Matched Layer (PML), an additional domain that absorbs the incident
radiation without producing reflections. When the radiation pattern of the waveguide
is no longer a plane wave, a cylindrical wave or a spherical wave, for example, metalmetal waveguide, PML surronding the finite air box can be used to absorb the almost
omnidirectional radiation from the waveguide. Similarly, PML can be defined as a
domain surrounding other domain of any material.
The thickness of the PML is also set to be at least a wavelength to fully absorb
the incident wave. The scaling factor and scaling curve parameter of the PML are
set to be 1 in most studies. Except for eigenfrequency study, the wavelength factor
is removed from the scaling expression for the PML formulation, to avoid nonlinear
dependence in eigenfrequency value. Thus, a scaling factor of value approximately a
wavelength (75 * 10-6 for 4 THz) needs to be used instead of 1.
82
Appendix C
Fabrication Flow
C.e
THz DFB Laser with Microstrip Antennae
Starting materials:
1. GaAs wafers with MBE grown heterostructures from Sandia National Laboratories).
2. Bare 3" n+ GaAs wafers (thermocompression receptor wafers) from AXT.
Overview:
Part 1. Thermocompression bonding
Part 2. Substrate lapping and removal
Part 3. Silicon dioxide definition
Part 4. Top metal definition
Part 5. Mesa definition
Part 6. Air Bridge
Part 7. Backside metallization
83
Part 1. Thermocompression bonding
Step
Description
1.
Cleave
and
Lab
name
Machine
TRL
Comments
Sample size
--
1x2 cm.
Gently
scribe MBE wafer name onto one
MBE samples
edge (for identification following
ebeam deposition).
2.
Cleave 3" n+ GaAs
Cleave into halves for ebeam load-
TRL
ing.
wafers into halves
3.
TRL
Predeposition
acid-hood
oxide strip
4.
Deposit
dip in BOE
thermo-
TRL
ebeamAu
compression metal
5.
scribed
Cleave
edges
off
7.
A,
deposited at
Scribed edges will not be flat, so
TRL
must be removed prior to thermo-
MBE
Cleave 3" n+ GaAs
Ta/Au 100/2500
1 A/s
compression.
samples
6.
30 s dip in 1:1 HCl:H20, or 10 s
Pieces
TRL
should
be
moderately
halves into smaller
larger than MBE samples (at
pieces
least 0.2 cm longer on each side).
Thermocompression TRL
EV501
Replace quartz
pressure
plate
with steel plate.
On 4" wafer chuck, align edges of
MBE and receptor samples, face
to face (use glass slide).
Place 4" steel electrode (no bow)
on
top of wafer
stack
with
graphite spacers.
Bond for 60 min at ~ 300*C and
~ 4 MPa pressure, in vacuum.
(recipe: bwilliam-cu300.aba)
84
Step
Description
Lab
8.
Name bonded sam-
TRL
Machine
Comments
Scribe MBE wafer number on exposed receptor wafer around the
ple
edges of bonded sample, This is
for identification following anneal
step.
9.
TRL
Anneal
EV501
Place all bonded pieces in EV501.
Place graphite spacers on top of
pieces, and top with 4" steel electrode stack with graphite spacers.
Anneal for 45min at 300*C , in N2
ambient.
(recipe: bwilliam-anneal300.aba)
10.
MBE sidewall and
receptor
protective
TRL
STS-CVD
Deposit 4000 ALFSIO2 on front
and back of bonded samples.
backside
dielec-
tric deposition
85
Part 2. Substrate lapping and removal
Step
Description
Lab
11.
MBE substrate lap-
Hu
Affix bonded sample to steel
ping
Lab
chuck using Crystal Bond wax.
Machine
Comments
Lap MBE substrate using 400 grit
sandpaper until ~ 100 pm substrate remains.
Dissolve wax in acetone, remove
sample.
Soak in clean acetone for ~.1 hr
to remove wax residues.
Rinse in 3 solvents.
12.
Ultrasound clean
TRL
Ultrasound
Ultrasound samples for 10 s in 3
solvents. (setting: degas)
13.
Backside
sist
photore-
coating
TRL
Coater
(op-
(Optional step,
generally used
only use if STS-CVD is down).
tional)
Manually swab Shipley 1813 photoresist onto receptor backside.
Postbake 20min.
14.
Wet etch removal
TRL
acid-hood
Selective etch of GaAs MBE re-
of remaining sub-
ceptor stopping on AlGaAs etch
strate
stop.
Put all samples in citric
acid:H 2 0 2 3:1 solution.
Etching solution is strongly diffusion limited and must be kept agitated to achieve reasonable etch
rates. Use a stir bar and magnetic
stirrer.
86
Step
Lab
Description
Machine
Comments
Etch speed and selectivity degrades with time.
Change solu-
tion every r~14 hr.
15.
Receptor photore-
TRL
photo-wet
If backside photoresist is used earlier, strip this off in acetone, fol-
sist removal
lowed by MeOH and IPA.
16.
Etch stop removal
TRL
acid-hood
HF, ~-,15-30 s (rate ~,,20 nm/sec).
Dip in and out every 5 s to release the bubbles. AlGaAs layer
appears as a pretty rainbow colored layer; GaAs is a dull gray.
Removal is visually obvious.
17.
Top
contact
re-
TRL
acid-hood
For
high
pulsed
ture performance,
moval (optional)
temperaremove the
doping layer for the top contact.
Etch away
H 3 PO 4 : H 2 0 2 : H2 0
pm/min;
enough).
87
typically
in 1:1:25
(0.25
1 min is
Part 3. Silicon Dioxide Definition
Step Description
Lab
Machine
Comments
18.
Use 3 solvent clean immediately
Positive resist coat-
TRL
coater
ing
before coating.
HMDS primer (setting 5)
Shipley1813
Dispense/Spread/Spin
for
6/8/30s at 0.5/0.75/3.90 krpm
Follow with
15 min prebake
(95 0C).
19.
Photoresist
expo-
TRL
MA-6
75 s low vacuum exposure.
TRL
photo-wet
MIF319 for 45 s. Follow by two
sure
20.
Development
rinses in DI water for 45 s each.
Follow by
20
min post-bake
(120 0C ).
Wait an hour.
21.
Wet etch
TRL
acid-hood
Dip samples in BOE. For 2500 A,
it takes 100 sec. Do not agitate
the solution.
Rinse and agitate in water for
twice.
Acetone to get rid of the photoresist on the silicon dioxide. 3 solvent clean.
Asher for 15 min.
88
Part 4. Top metal definition
Step
Description
Lab
Machine
Comments
22.
Image reversal re-
TRL
Coater
Use 3 solvent clean immediately
before coating.
sist coating
150'C dry in the HMDS machine
for 15 min.
AZ5214E
Dis-
photoresist,
pense/Spread/Spin
for 6/8/30s
at 0.5/0.75/3.95 krpm
Follow
with
15 min
prebake
(95 0C ).
23.
Exposure
TRL
MA-6
7 s low vacuum exposure.
24.
Image reversal bake
TRL
hotplatel
120*C bake for 1 min.
(setting
top of a silicon dummy, monitor
113-114)
temperature using contact ther-
Bake on
mometer.
25.
TRL
Flood exposure
MA-6
Flood expose all samples for 135
s.
26.
TRL
Development
photo-wet
AZ422MIF for 2:30.
Follow by
two rinses in DI water for 1 min
each.
27.
Post
development
TRL
Asher
evenness of photoresist
clean
28.
Predeposition
ox-
TRL
acid-hood
Top metal deposi-
TRL
ebeamAu
Lift-off
Ta/Au 100/3000 Adeposited at 1
A/s
tion
30.
30 s dip in 1:1 HCl:H20 or 10 s
dip in BOE
ide strip (optional)
29.
Ash for 5 min to remove the un-
Soak all pieces for r~-2 hr in ace-
TRL
tone. 3-solvent clean afterwards.
89
Part 5. Mesa definition
Step
Description
Lab
Machine
Comments
31.
Post liftoff clean
TRL
Plasmaquesl Ash for 15 min
Plasmaquest SiO2 WK1 for 700
sec to take off the silicon dioxide
not covered by metal
Ash for 30 min to take off the
polymer formed by 02 and CF 4
during plasmaquest
32.
Mesa dry etch
TRL
SAMCO
Run standard Cl clean,
then
precondition chamber using 3*3
inch
GaAs dummy
(cut into
half) for 30 min using recipe 7
(ICP120W, RF 40W, 0.5/3/16
sccm C12/SiCl4/Ar, 1 Pa)
Leaving dummies inside,
etch
samples using recipe 7 for 70 min
(for 10 pm MBE layer).
Top
metallization (gold) acts as selfaligned mask,
thermocompres-
sion layer (bottom gold) acts as
etch-stop.
Chamber needs to be chlorine
cleaned and reconditioned every
3-4 runs, preventing redepositing.
33.
Sidewall
vation
passi-
TRL
acid-hood
Dip samples in BOE for 4 min. If
passivation is not removed, lasers
removal
ridges will shatter later during
(wet)
cleaving.
90
Step
Description
34.
Sidewall
vation
passi-
Lab
Machine
Comments
TRL
plasmaquest If sample is not BOE safe (eg.
have SiO 2 ),
removal
use dry removal in
plasmaquest
(dry)
600 sec recipe: SF6_WK2.rcp(70
mtorr
/100
sccm
SF6/
ECR500W/RF OW)
If there is grass, wet etch cleaning
for 5- 10 sec NH 4 0H : H 2 0 2 : H 2 0
10:6:980ml
91
Part 6. Air bridge
Step
Description
Lab
Machine
Comments
35.
Positive resist coat-
TRL
Coater
Use 3 solvent clean immediately
before coating.
ing
150'C dry in the HMDS machine
for 10 min
AZP
4620
Dis-
photoresist
pense/Spread/Spin for 0/9/60-at
0/1.5/2 krpm
Follow with 45 min
prebake
(95 0C ).
Wait for an hour.
36.
Photoresist
expo-
TRL
MA-6
150 sec HARD CONTACT
TRL
photo-wet
MIF405 for 2:30 min.
sure
37.
Development
Follow
by two rinses in DI water for 1
minute each.
Follow
by
15
min post-bake
(95 0 C ) (use pre-bake oven).
Wait for an hour.
38.
Wet etch
TRL
acid-hood
Etch
air bridge
in 90:30:300
NH 4 0H: H 2 0 2 : H 20
1pam/min).
(~
Adjust the etch-
ing time according to the width
of the air bridge.
For 2 pm air
bridge width, 1 min is enough
since etching comes from both
directions.
Gentle agitation.
92
Part 7. Backside metallization
Machine
Comments
Step
Description
Lab
39.
Backside substrate
Hus
Affix bonded
lapping
lab
chuck using Crystal Bond wax.
sample to steel
Lap MBE substrate using 400 grit
sandpaper until ~-.' 100 pm sub-
strate remains.
Dissolve wax in acetone, remove
sample.
Soak in clean acetone for --1 hr
to remove wax residues.
Rinse in 3 solvents.
40.
Backside metal de-
TRL
ebeamAu
Deposit Ti/Au 150/1500 Aat 1
A/s.
position
Samples need to be device-side
down.To avoid scratching devices,
samples should be placed on top
of unscratched GaAs (or Si) dummies.
41.
DieSaw
ICL
diesaw
Wax and die saw.
Take off the
diesaw tape with UV light
93
C.2
THz QC Amplifier using MM Waveguides with
Horn Antennas
Starting materials:
1. MBE grown heterostructures grown on semi-insulating GaAs substrate from
Sandia National Laboratories).
2. Bare 3" n+ GaAs wafers (thermocompression receptor wafers) from AXT.
Overview:
Part 1. Thermocompression bonding
Part 2. Substrate lapping and polishing
Part 3. Horn definition
Part 4. Top metal definition
Part 5. Mesa definition
Part 6. Backside metallization
The fabrication procedures for Part 1, 5 and 6 are same as those in the fabrication
for THz QC Laser using MM waveguides. Please refer to Appendix A.
94
Part 2. Substrate lapping and polishing
Step
Machine
Comments
Description
Lab
MBE substrate lap-
Hu
Affix bonded sample to steel
ping
Lab
chuck using Crystal Bond wax.
Lap MBE substrate until r.,100
pm substrate remains with ~l
pm surface roughness.
Dissolve wax in acetone, remove
sample.
Soak in clean acetone for -1 hr
to remove wax residues.
Rinse in 3 solvents.
Ultrasound clean
TRL
Ultrasound
Ultrasound samples for 10 s in 3
solvents. (setting: degas)
Backside
photore-
TRL
Coater
Manually swab Shipley 1813 photoresist onto receptor backside.
sist coating
Postbake 20 min.
Wet etch clean
TRL
acid-hood
30 s dip in H 2 SO 4 : H 2 0 2 : H20
4:1:1
--2 pm etch (etch rate
is temperature dependent, mix
properly)
Receptor
photore-
TRL
photo-wet
strip the backside photoresist off
in acetone, followed by MeOH
sist removal
and IPA.
95
Part 3. Horn definition
Step
Description
Lab
Machine
Comments
Positive resist coat-
TRL
coater
Use 3 solvent clean immediately
before coating.
ing
95'C dry on a hotplate for 10
min.
Shipley
Dis-
1813
pense/Spread/Spin
for 6/8/30s
at 0.5/0.75/3.90 krpm
Photoresist
30min prebake (95'C ).
TRL
Prebake
expo-
TRL
MA-6
75 s low vacuum exposure.
TRL
photo-wet
MIF319 for 45 s (gentle stirring,
sure
Development
followed by two rinses in DI water
for 45 s each.
Postbake
Manually swab Shipley 183 on the
TRL
back. 30 min post-bake (120'C).
Wait an hour.
96
Description
Lab
Machine
Comments
Wet etch
TRL
acid-hood
Dip
in
1:8:1
H 2 SO 4 : H 2 0 2 : H 2 0
(etch
rate
is
dependent,
samples
temperature
~,.9pm/min).
3:2:3
by
Followed
citric:H 2 0 2 : H 2 0 (r~ 20 pm/hr).
solution.
Do not agitate the
When photoresist adhesion is not
good, can bake the sample on the
hotplate for 1 min at 115*C
.
Step
Etch stop removal
TRL
acid-hood
Acetone to remove the photoresist, followed by 3-solvent clean.
Dip in HF for -10 s for 0.2 pm
thick AlO. 5Ga 0 .5As etch stop. AlGaAs etch appears as a pretty
rainbow colored layer; GaAs is a
dull gray. Removal is visually obvious.
Top
contact
re-
TRL
acid-hood
For
high
ture performance,
moval (optional)
tempera-
pulsed
remove the
doping layer for the top contact.
in 1:1:25
Etch away
(0.25
H3 PO 4 : H2 0 2 : H 2 0
pm/min;
typically
enough).
Post clean
TRL
Asher
97
Asher for 15min
1
min
is
Part 4. Top metal definition
Step
Description
Lab
Machine
Comments
22.
Image reversal re-
TRL
Coater
Use 3 solvent clean immediately
before coating.
sist coating
95'C dry on the hotplate for 10
min.
AZ5214E
photoresist,
pense/Spread/Spin
Dis-
for 6/8/30s
at 0.5/0.75/4.95 krpm
Follow with
15 min
prebake
(95 0C ).
Exposure
TRL
MA-6
7 s low vacuum exposure.
Image reversal bake
TRL
hotplatel
120*C bake for 1 min. Bake on
(setting
top of a silicon dummy, monitor
113-114)
temperature using contact thermometer.
Flood exposure
TRL
MA-6
Flood expose all samples for 135
S.
Development
TRL
photo-wet
AZ422MIF for 2:30 or longer.
Follow by two rinses in DI water
for 1 min each.
Post
development
TRL
Asher
evenness of photoresist
clean
Predeposition
TRL
acid-hood
30 s dip in 1:1 HCl:H20 or 10 s
dip in BOE
oxide strip
Top metal deposi-
Ash for 5 min to remove the un-
TRL
ebeamFP
Ti/Au 180/3700
A
tion
Lift-off
Soak all pieces for ~-2 hr in ace-
TRL
tone. 3-solvent clean afterwards.
98
C.2.1
Experimental Parameters for Lapping Process
Lapping machine Model 920
Lapping fixture Model 155
Speed: workstation speed ~ 1-2 and lapping wheel ~1
Weight of the load: 200g steel cylinder
Weight of the lapping fixture center part: 560g
Overal pressure on the sample: ~ 360 g/cm2
Ultrsonic Cleaning: Crestsonic Model 275D, power level 2 for ~ 20 sec
Lapping
Film/Paper
Abrasive Particle Size
Speed
Remaining Substrate
Thickness
400 grit ~ 35 pm
20 pm
9 pLm
3 pm
1 pm
100 pm/10 min
50 pim/10 min
40 jim/10 min
4 pm/10 min
<1 pm/10 min
300
200
130
110
105
Material
SiC paper
Alumina film
Alumina film
Alumina film
Alumina film
Table C.1: Table of lapping procedure
99
pm
ptm
pm
Am
pm
100
Appendix D
Photolithography Masks
Figure D-1: Mask label: 2.2 THz
Microstrip antenna coupled DFB lasers targetting 2.06 THz atomic oxygen line.
The devices are fabricated with the gain medium FL175-M3 (wafer EA1222), a reso101
nant phonon design.
Devices varies in grating periodicity (from 65 to 82 pm) while maintaining other
physical parameters in the same column. The first four columns cover frequency from
1.86 to 2.25 THz with 10 GHz incrementation. The last column covers frequency
from 1.94 to 2.08 THz with 10 GHz incrementation. Devices in different columnes
vary slightly in antenna length (20 and 21 jim) and ridge width (19.5 and 20 pm), to
tune lasing threshold and frequency.
The mask is 1.5 cm along the vertical direction (along the ridge) x 1.25 cm along
the horizontal direction. It has three layers. The first layer is designated for patterning
SiO 2 , the insulation layer. The second layer is for patterning the top metal, followed
by mesa etch using ICP-RIE. The last layer is for creating the air-bridge structures
using thick photoresist.
102
Figure D-2: Mask label: 2 THz
A similar mask is designed for gain medium OW1185E-M1 (wafer VB0244), a
scattering assisted design peak at ~2 THz.
103
In
nit
pI
EE
I
Ii
I.
J.
At
[1W
~
!.Jii
i:!IJ
+
III 1~fT
J
LI
WI
....
.. . ...
....
. ......
,
~fj
ill
.~1.
I
I..
J
aII
11jjj
.........
.............
.......
....
..
........
....
.....
....
..
....
....
..
..
...
..
...
..
....
.1'''' '' ''.
4 ...
..
.......
lf Nil ~
B
.
4.
111
1111
1~W
~H+
Eli
III!
Itli 11T
ill
1
11
til LIII
1111
tIll
JTH TTff
1
il p
1
Figure D-3: Mask label: Amplifier 4 THz
THz travelling-wave amplifier at 4 THz. Devices in different rows varies in lengths
(from 1 to 3 mm) and devices in different columns varies in ridge and horn shape.
The mask is 1.05 cm along the horizontal direction x 1.54 cm along the vertical
direction (along the ridge). It has two layers. The first layer is for patterning the horn
with standard photo lithography and wet etch. The second layer is for patterning the
top metal, followed by mesa etch using ICP-RIE. The mask has be to be properly
aligned with the crystal axis of the chip that the ridges are parallel to the minor flat,
in order to create a rising slope of the horn during wet etch.
104
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