Surface-Emitting Distributed Feedback Terahertz
Quantum-Cascade Phase-Locked Laser Arrays
by
Tsung-Yu Kao
Submitted to the Department of Electrical Engineering and Computer
Science
in partial fulfillment of the requirements for the degree of
Master of Science in Computer Science and Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
September 2009
c Massachusetts Institute of Technology 2009. All rights reserved.
°
Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Department of Electrical Engineering and Computer Science
September, 2009
Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Qing Hu
Professor
Thesis Supervisor
Accepted by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Terry P. Orlando
Chair, Department Committee on Graduate Students
2
Surface-Emitting Distributed Feedback Terahertz
Quantum-Cascade Phase-Locked Laser Arrays
by
Tsung-Yu Kao
Submitted to the Department of Electrical Engineering and Computer Science
on September, 2009, in partial fulfillment of the
requirements for the degree of
Master of Science in Computer Science and Engineering
Abstract
A new approach to achieve high-power, symmetric beam-pattern, single-mode THz
emission from metal-metal waveguide quantum-cascade laser is proposed and implemented. Several surface-emitting distributed feedback terahertz lasers are coupled
through the connection phase sectors between them. Through carefully choosing the
length of phase sectors, each laser will be in-phase locked with each other and thus
create a tighter beam-pattern along the phased-array direction. A clear proof of
phase-locking phenomenon has been observed and the array can be operated in either
in-phase or out-of-phase mode at different phase sector length. The phase sector can
also be individually biased to provide another frequency tuning mechanism through
gain-induced optical index change. A frequency tuning range of 1.5 GHz out of 3.9
THz was measured. Moreover, an electronically controlled “beam steering” device
is also proposed based on the result of this work. This thesis focuses on the design,
fabrication and measurement of the surface-emitting distributed feedback terahertz
quantum-cascade phase-locked laser arrays.
Thesis Supervisor: Qing Hu
Title: Professor
3
4
Acknowledgments
I would like to acknowledge my research advisor Prof. Qing Hu for his guidance and
support. I am indebted to Sushil Kumar for being a fabulous colleague and mentor
to me. I learned a lot from him. His prudence, diligence and the deep understanding
in physics set up a role model as a researcher for me to follow.
I wish to thank Alan Lee for his always useful suggestions and broad knowledge
about almost everything. He is the one I would like to discuss with whenever I am in
a deadlock. I thank Qi Qin for sharing the experiences and techniques in fabrication
and all the bitter yet fruitful time spent in the clean room with me. I am also grateful
for the staffs and students in MTL for their enthusiasm for helping me solve a lot
of fabrication problems. I wish to thank David Burghoff for our conversations on
many different aspects of life and also the good competition between us. I also thank
Allen Hsu and Ivan Chan for the discussions on the quantum well design and the
experiment setup. I would like to thank my friends here in MIT. They drag me out
of the lab and save me from being totally stressed out by the research work.
I am grateful for the support from my parents and my sister back home. This
thesis could never be done without the love from them. Last, I want to express my
gratitude to ChuanKang. It is she who gives me sound advice when I sorely need it.
She is my ballast. She is my conscience.
5
6
Contents
1 Introduction
17
1.1
Motivation and Background . . . . . . . . . . . . . . . . . . . . . . .
17
1.2
Surface-Emitting 2nd order DFB THz QCL Phase-Locked Array . . .
19
1.3
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
2 Commonly Used Coupling Method
23
2.1
Evanescent Wave Coupled Scheme . . . . . . . . . . . . . . . . . . . .
24
2.2
Diffraction Wave Coupled Scheme . . . . . . . . . . . . . . . . . . . .
25
2.3
Y-junction Coupled Scheme . . . . . . . . . . . . . . . . . . . . . . .
28
2.4
Leaky-Wave Coupled Scheme . . . . . . . . . . . . . . . . . . . . . .
29
2.4.1
Mode discrimination mechanism between different modes . . .
30
Among all Commonly Used Coupled Methods . . . . . . . . . . . . .
33
2.5
3 Design of 2nd Order DFB Surface-Emitting Phased-Array Laser
3.1
3.2
37
Review on DFB Operation and Surface-Emitting Laser . . . . . . . .
37
3.1.1
Distributed feedback operation - coupled-wave theory . . . . .
37
3.1.2
2nd order surface-emitting DFB laser . . . . . . . . . . . . . .
44
2nd order Surface-Emitting DFB THz Quantum-Cascade Laser
. . .
45
3.2.1
Effect of boundary condition . . . . . . . . . . . . . . . . . . .
51
3.2.2
Surface loss induced by metal grating - a different point of view 53
3.2.3
A more physical view of DFB operation
. . . . . . . . . . . .
55
3.3
How to Couple Two Metal-Metal Waveguide DFB Lasers . . . . . . .
59
3.4
Practical Design Issues . . . . . . . . . . . . . . . . . . . . . . . . . .
63
7
3.5
3.4.1
Phase sector design . . . . . . . . . . . . . . . . . . . . . . . .
63
3.4.2
Taper design
. . . . . . . . . . . . . . . . . . . . . . . . . . .
65
3.4.3
Voltage controlled gain in phase sector . . . . . . . . . . . . .
65
3.4.4
Electrical isolation between phase sector and laser ridges . . .
67
3.4.5
Thermal simulation of array devices . . . . . . . . . . . . . . .
68
3.4.6
Far-field beam pattern . . . . . . . . . . . . . . . . . . . . . .
68
3.4.7
Design flow . . . . . . . . . . . . . . . . . . . . . . . . . . . .
70
Simulation Methods and Environment . . . . . . . . . . . . . . . . .
73
3.5.1
COMSOL Multiphysics . . . . . . . . . . . . . . . . . . . . . .
73
3.5.2
HFSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
4 Fabrication and Measurement
79
4.1
Fabrication Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
79
4.2
Issues in the first fabrication - during the fab process . . . . . . . . .
81
4.2.1
The quest of thick photoresist . . . . . . . . . . . . . . . . . .
83
Issues in the First Fabrication - during the measurement . . . . . . .
84
4.3.1
The lossy bonding pad . . . . . . . . . . . . . . . . . . . . . .
87
4.4
Result from the First Fabrication . . . . . . . . . . . . . . . . . . . .
89
4.5
Things Improved in the Second Fabrication . . . . . . . . . . . . . . .
93
4.5.1
Improvement in fabrication process . . . . . . . . . . . . . . .
93
4.5.2
Improvment in the design . . . . . . . . . . . . . . . . . . . .
95
4.3
4.6
Issues in the Second Fabrication
. . . . . . . . . . . . . . . . . . . .
95
4.7
Results from the Second Fabrication . . . . . . . . . . . . . . . . . .
97
4.7.1
The grating operation . . . . . . . . . . . . . . . . . . . . . .
97
4.7.2
The gain-induced optical index change . . . . . . . . . . . . .
99
4.7.3
Direct proof of phase locking . . . . . . . . . . . . . . . . . . .
99
4.7.4
Discussion on the poor device performance . . . . . . . . . . . 103
4.8
Conclusions, Summary and Future Work . . . . . . . . . . . . . . . . 108
8
List of Figures
1-1 The “terahertz gap” in the electromagnetic spectrum. . . . . . . . . .
18
1-2 Typical beam pattern measured from a surface-emiting 2nd order DFB
THz laser. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
19
1-3 A five-ridge 2nd order DFB surface-emitting MM THz QCL PhaseLocked Array. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
2-1 The Quantum wells analogy of mode splitting. . . . . . . . . . . . . .
25
2-2 The Overlapping area between different modes and the intermediate
region in evanescent-wave coupled scheme. . . . . . . . . . . . . . . .
25
2-3 The Optical Talbot Carpet. . . . . . . . . . . . . . . . . . . . . . . .
26
2-4 The working principle of Talbot cavity. . . . . . . . . . . . . . . . . .
27
2-5 Schematics for Y-junction operation. . . . . . . . . . . . . . . . . . .
28
2-6 Modes supported in a periodic index structure. . . . . . . . . . . . . .
31
2-7 Mode Intensity distribution for mode (0,3), (0,2) and (0,4). . . . . . .
32
2-8 Different coupling schemes in this chapter. . . . . . . . . . . . . . . .
34
3-1 A graphic description of DFB operation. . . . . . . . . . . . . . . . .
38
3-2 Typical DFB reflectivity against different wavelengths. . . . . . . . .
39
3-3 Typical threshold gain v.s. frequency of a gain-coupled DFB laser. . .
42
3-4 Spatial intensity distribution of the lowest threshold modes at different
coupling strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
3-5 Representation of different orders of DFB operation. . . . . . . . . . .
46
3-6 The typical structure of MM waveguide 2nd order DFB surface-emitting
laser with metal covered facet. . . . . . . . . . . . . . . . . . . . . . .
9
47
3-7 Typical Surface Loss plot against frequency of 2nd order DFB in MetalMetal waveguide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
3-8 (a)(b) is the detailed surface loss and frequency against different facet
length condition. (c)(d)(f) show the field intensity distributions for
different modes inside the cavity. (e) shows the Hx field for first lower
6
Λ.
16
. . . . . . . . . . . . . . . . . . . . .
52
3-9 Different Hx field sampling points. . . . . . . . . . . . . . . . . . . . .
54
3-10 The concept of ”center π shift” . . . . . . . . . . . . . . . . . . . . .
55
3-11 The competition between DFB and Fabry-Pérot cavity. . . . . . . . .
56
band-edge mode when δ =
3-12 Hx field mode shapes for modes close to the bandgap at different facet
length condition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
57
3-13 Hx field mode shape for Mode 43 44 and 45. . . . . . . . . . . . . . .
61
3-14 Mode discrimination mechanism for coupled array. . . . . . . . . . . .
61
3-15 ”Chain-link” and ”sneak” configurations . . . . . . . . . . . . . . . .
63
3-16 Different phase sector configurations. . . . . . . . . . . . . . . . . . .
64
3-17 (a) shows the taper design from the top. The attacking angle is 12◦ .
(b) shows the extension of grating on the taper and also the electrical
isolation gap between phase sector and laser ridges. . . . . . . . . . .
65
3-18 Electronically control loss can induce mode hopping. . . . . . . . . .
66
3-19 Calculated optical index change due to the gain in the medium using
Kramers-Kronig relation. . . . . . . . . . . . . . . . . . . . . . . . . .
67
3-20 The three-dimensional heat flow calculation using a finite-element solver
for the c.w. temperature performance for array with different ridge
width and ridge numbers. . . . . . . . . . . . . . . . . . . . . . . . .
69
3-21 Far-field beam patterns from different numbers of in-phase point sources
under different distance between sources. . . . . . . . . . . . . . . . .
70
3-22 Simulated near-field and far-field patterns for different ridge numbers
phased-array. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
72
3-23 COMSOL Multiphysics simulation environment. . . . . . . . . . . . .
75
3-24 Typical HFSS simulation environment and its result. . . . . . . . . .
77
10
4-1 The Photoresist undercut indicator used in mesa etch step. . . . . . .
81
4-2 The “bubble” issue. (a) shows a typical bubble on the wafer. (b)
shows the bubble can go beneath the mesa and make ridges “floating”
on nothing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
4-3 The distribution thickness of photoresist on GaAs substrate under different mesa profiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
83
4-4 Some result of thick negative photoresist NR71-3000P. . . . . . . . .
85
4-5 The mesa undercut on the phase sector. . . . . . . . . . . . . . . . .
86
4-6 The wet etched profiles along crystal plane on GaAs substrate. . . . .
86
4-7 The poor SiO2 coverage problem. . . . . . . . . . . . . . . . . . . . .
87
4-8 (a)(b) the amplitude scattering matrix coefficient S11 and S12 for 63 deg
and 45 deg sloped end facet. (c) shows the effective mirror loss (sum
of both facet) for a 330 µm long F-P device using facet reflectivity
calculated in (a) and (b). . . . . . . . . . . . . . . . . . . . . . . . . .
88
4-9 SEM pictures of devices after die sawed. . . . . . . . . . . . . . . . .
89
4-10 Some c.w. measurement results for a best surface-emitting device on
wafer VB052. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
90
4-11 Beam pattern measurements from a 3-ridge and a single ridge device.
91
4-12 A close comparison of between beam pattern from single ridge and
3-ridge device. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92
4-13 Beam pattern and spectrum measurement for two 3-ridge devices. . .
92
4-14 SiO2 coverage on the top of the mesa. (a) shows the SEM picture of
poor SiO2 coverage example. The SiO2 retreated too much to the sidewall. This will cause the current bypass the first few modules of MWQs
and also a worse current uniformity. (b) shows the good SiO2 coverage. SiO2 stays on the top of the mesa even at the narrow taper tip
(∼ 20 µm wide). (c) shows the pictures under optical microscope, the
greenish color is SiO2 . . . . . . . . . . . . . . . . . . . . . . . . . . .
94
4-15 Unexpected gain medium undercut after the wet etch on Ta/Au/Ta/Cu
bottom metal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
96
4-16 The non-sticky second Au layer. . . . . . . . . . . . . . . . . . . . . .
96
4-17 (a) shows the pulse spectra for three different grating devices (each
color corresponding to a device with different Λ), plotted in log scale.
Spectra for different bias are plotted starting from near-threshold bias
at bottom to high bias at top. (b) shows the L-I and I-V curves for different devices. From left to right are devices with Λ = 24.5, 23.5, and , 22.5 µm.
The demensions for each device is 50 × 735, 710, 680 µm. The Jth for
each device is 610, 575, 600 A/cm2 , and the Tmax,pul is 94, 116, 105 K.
(c) λ0 versus Λ variation (in solid red). A line going through origin
and corresponding to nef f ≈ 3.29 is also plotted (in dashed blue). . .
98
4-18 (a) shows the pulse L-I curve for a 7-ridge array device. The dimensions of this device are 50 × 710 µm × 7. Jth is 770 A/cm2 , and the
Tmax,pul is 35 K. Power and beam pattern were not measured. (b) shows
the spectra of the this device, plotted in log scale. Spectra for different
bias are plotted starting from near-threshold bias at bottom to high
bias at top. This device remains single-frequency at all bias (c) Peak
of the spectra of device against different c.w. bias point on the phase
sector. The main laser ridges were biased near the peak current. It
shows a 1.5 GHz tuning range. . . . . . . . . . . . . . . . . . . . . . . 100
4-19 The L-I curves for several 2-ridge array device with different phase
sector lengths. The length starts with 11.5 µm for device #1 and
extends to 18 µm for device #14. The spectra measured from different
devices at different bias point are showed on the center right in the
figure. The mode-hoping event is clearly showed on the spectra. All
the L-I curves and spectra are taken with the phase sector unbiased
(floating). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4-20 Beam patterns from the two 2-ridge devices with different phase sector
length measured 20 cm away from the device using a He-cooled Ge:Ga
photo-detector with angular resolution < 1◦ . . . . . . . . . . . . . . . 102
12
4-21 GIV curves of devices on wafer FL183S-VA0094 from different fabrication batches (a) shows the c.w. I-V curve of a 100 µm × 1.34 mm
Fabry-Pérot dry-etch device without sidewall or end facet covered with
metal and its GIV curve. (b) shows the pulse I-V curve of a 50×735 µm
surface-emitting wet-etch device and its GIV curves. . . . . . . . . . . 105
4-22 The best Tmax,pul tested so far from different types of devices in the
second fabrication on wafer FL183S-VA0094 (best Tmax,pul = 161 K)
plotted out with its corresponding threshold current (red circle). A
fitted line from those data point can be extrapolated to Tmax 160−170 K
when Jth is around 400 A/cm2 (in dashed-blue). . . . . . . . . . . . . 106
4-23 A comparison between pulse spectra of wide Fabry-Pérot devices from
different fabrication batches on the FL183S-VA0094. . . . . . . . . . . 107
4-24 SEM pictures from FL183S-VA0094 chip #20 surface-emitting device. 107
13
14
List of Tables
4.1
Summary of best performance of different types of devices tested so far
on gain medium FL182C-M11-VB052, FL183S-VA0094 and OWI222GVB0240. “F-P” stands for Fabry-Pérot cavity laser, and “S-E” stands
for surface-emitting. The typical F-P device does not have sidewall
or facet covered with metal. “sidewall-covered” means the device is
covered with metal along the longitudinal edge. “no end facet metal”
means the S-E device doesn’t have metal covered on two ends. “Taperend” means the device is terminated by the taper section used to connect phase sector but without the phase sector attached to it, nor covered with metal. “7-ridge Array” means the device is a phased-array
structure consists of the single ridges with dimensions listed before. . 104
15
16
Chapter 1
Introduction
1.1
Motivation and Background
The THz gap, loosely defined as 300 GHz to 10 THz (Fig. 1-1), got its name due
to the difficulties to obtain good radiation source in this frequency range. Electronic
device is normally limited by transient time and resistance-capacitance time constant
and thus hard to operate at this frequency. Traditional laser generated in bandgap
material is not suitable either, since THz photon has only ∼ 10 meV energy, which is
below the minimum bandgap of material system in any diode laser. The invention of
quantum-cascade laser (QCL) [1]—a well-designed multiple quantum wells structure
operates at designed bias to achieve population-inversion between inter-subband and
then lasing—provides another possibility. The emitted photon energy can be modified
by adjusting the energy difference between two radiation subbands. The first THz
QC Laser [2] came seven years later after the first QC Laser. Since then, a lot of
improvements have been demonstrated in this field: frequency coverage from 1.2 −
5 THz, pulse maximum operating temperature Tmax at 186 K [3] , c.w. Tmax at
117 K [4] , maximum pulse power 246 mW/ c.w. 138 mW [5] . All these pushed
THz QC Laser one step closer to real-world application. Perhaps one of the most
promising applications for THz QCL in near future is using THz QCL as the Local
Oscillator (LO) source for submillimeter-wave heterodyne receivers [6, 7, 8]. Several
groups have demonstrated and confirmed that THz QCL has the same or even better
17
performance than the conventional gas laser - along with lower power consumption
and smaller form factor make it very desirable for application in astrophysics and
space-science. But the divergent and rapidly changing phase front of beam pattern
from Fabry-Pérot Metal-Metal (MM) ridge [9] waveguide raises the difficulties in
actual measurement setup [8].
Figure 1-1: The “terahertz gap” in the electromagnetic spectrum.
Several groups searched to improve the beam pattern using distributed-feedback
surface-emitting grating [10, 11] , which preserves the superior temperature performance of MM waveguide and also provides single mode operation. But even though
a tighter beam pattern was observed along the grating direction in these devices, the
beam pattern is still far from symmetric.
Symmetric beam pattern and single mode laser emission from MM waveguide
have been demonstrated using two-dimensional photonic-crystal (PC) structures recently [12] , but the large current required to pump the bulky contiguous gain medium
deteriorates the c.w. operation, which is crucial for practical LO application.Despite
much progress, more improvements are still needed to meet the standard for real instrument application (symmetric beam pattern, single mode, milli-Watt c.w. power
at 77 K with reasonable power dissipation).
18
1.2
Surface-Emitting 2nd order DFB THz QCL
Phase-Locked Array
The surface-emitting 2nd order DFB laser provides a good starting point to meet
those requirements mentioned in the previous section. But perhaps the most urgent
challenge now is to improve the beam pattern of such devices. Due to the physical
dimension of light emitting area, the far-field beam pattern is tighter along the grating
direction, but much broader in another (see Fig. 1-2).
60
1
50
Intensity (a.u.)
0.8
40
0.6
30
0.4
20
0.2
0
−45 −35 −25 −15 −5
5
15
Angle (degrees)
10
25
35
45
Figure 1-2: (a) Typical beam pattern measured from a surface-emiting 2nd order DFB
THz laser using a He-cooled Ge:Ga photo-detector with angular resolution < 1 ◦ . The
beam pattern is much tighter along the z direction (the grating, or the longitudinal
direction) and broader along the x direction (the lateral direction).(b) The real-time
snapshot of the radiation pattern from the same device. After Ref. [13]
In order to create a symmetrical beam-pattern, one needs to increase the emitting
area in both directions. The lateral dimension of a single laser ridge, and thus the
width of aperture, is restricted by several performance requirements. For a wider
device, one has to satisfy c.w. temperature performance considering that the heat
dissipation is poorer; wider ridges might also support more than one lateral mode.
The presence of the high-order lateral modes hinders the normal operation of 2nd
19
order DFB (This will be discussed more in Chapter 3). The laser then will not lase
at the desired DFB mode.
Figure 1-3: A five-ridge 2nd order DFB surface-emitting MM THz QCL Phase-Locked
Array.
The approach proposed in this thesis is aiming to solve such dilemma. By coupling different DFB laser ridges through carefully designed “phase sector”, each laser
is engineered to be “in-phase” locked with each other—forming a two-dimensional
phase-locked array (see Fig. 1-3). The distance between laser ridges is chosen closed
to the free space wavelength of laser (∼ 80−100 µm), creating a tighter beam pattern
along the phased-array direction. The heat dissipation problem is also less astringent
as the gap between ridges is kept equal or larger than the ridge width (∼ 25 − 50 µm)
to ensure good heat removal from gain medium (see Section 3.4.5 for heat flow simulation result3).
These phase sectors can be individually-biased (see Section 3.4.3), which provides
another way to fine tune the frequency of phased-array through the gain-induced
optical index change. This mechanism might be more favored than the commonly
used temperature tuning or the Stark-shifting at high bias since it provides another
degree of freedom of tuning without too much impact on the laser array output power.
20
1.3
Overview
This thesis is organized into several chapters. Chapter 2 reviews some commonly
used coupling methods in phased-array diode laser. The working principle behind each
method, as well as its benefit and disadvantage will be compared and briefly discussed.
The first part of Chapter 3 explains the distributed feedback (DFB) operation and
attempts to clarify the origin of mode discrimination in a surface-emitting 2nd order
DFB laser while the second part focuses on the design of “phase sector” and how to
correctly couple MM waveguide lasers. Some practical design issues and simulation
methods used in this thesis will be also covered in this chapter. Chapter 4 describes
the detailed steps in fabricating these devices and the difficulties encountered during
the fabrication. Important measurement results will be also analyzed and explained.
21
22
Chapter 2
Commonly Used Coupling Method
Extensive and persistent efforts had been made in developing phase-locked diode laser
array to achieve high coherent power. Since most diode lasers have emitting facets
larger than their wavelengths (500 nm−3 µm), and thus have better beam pattern
(compare to THz Metal-Metal waveguide edge emitting laser), the main drive behind
the development is to distribute the total output power over several lasers to prevent
the facets from catastrophic meltdown in high power application. Even though the
motivations and wavelength range are not the same, there are still many good concepts
and ideas can be borrowed or modified for achieving phase-locked laser array in THz
frequency.
There are four commonly used coupling schemes in integrated diode laser system–
laser ridges are coupled through their exponentially decaying field outside the high
index dielectric core (Evanescent wave coupled [14], see Section 2.1), or through
the Talbot effect feedback from external reflector (Diffraction wave coupled [15], see
Section 2.2), or by feeding laser from two ridges into one single-mode waveguide
(Y-junction coupled [16], see Section 2.3), or through lateral leaky propagating wave
(leaky-wave coupled [17], see Section 2.4).
23
2.1
Evanescent Wave Coupled Scheme
Most of diode lasers have cores with higher optical index than cladding for utilizing the total internal reflection (TIR) from core/cladding interface to achieve better
optical confinement factor (the Γ factor), which results more overlapping between
electromagnetic mode and the gain medium (usually the core), and so reduces the
threshold gain of lasing. The favored lasing mode of this type of structure does not
have real propagating constant in those lower optical index intermediate cladding.
This means the fields in those regions are evanescent wave, exponentially decaying
from the interface. When two laser ridges are placed close enough to each other, new
eigenmodes will form due to the interacting between these evanescent fields. Similar
analogy can be found when placing two finite height quantum wells close together.
New eigenmodes emerge and eigenvalues of the system will split (see Fig. 2-1). From
Fig. 2-1, it is self-evident that these eigenmodes represent the “in-phase” and “out-ofphase” modes of laser array. The same concept is still valid for multiple ridges. One
can solve the coupled-mode equation for an array of N coupled, identical laser ridges
and obtain N distinct “supermodes” [18]. It is important to point out that in the
evanescent-wave coupled scheme, only nearest-neighbor interactions are taking into
account, considering the fact that the evanescent wave decays exponentially outside
the core and thus would have negligible coupling beyond nearest-neighbor. This is not
ideal for stable phase-locking operation when the number of ridges N is large, since
fabrication fluctuations in one element can split the phased-array into two separated
regions, lasing with random phase difference.
Besides, evanescent-wave coupled devices tend to favor “out-of-phase” mode since
it has less overlapping with the relatively lossy intermediate material between laser
cores and thus is intrinsically not ideal for single-lobe operation (see Fig. 2-2).
24
Figure 2-1: The Quantum wells analogy shows the mode splitting when
modes are coupled together. When two
identical wells are far apart, the ground
states of the system have two-fold degeneracy. For two adjacent quantum
wells, the ground states will split into
even and odd solution with different energies.
Figure 2-2: The Overlapping area between different modes and the intermediate region in evanescent-wave coupled scheme. The shaded area marks
the overlapped region. The out-ofphase mode usually has less energy resides in the intermediate region since
the mode envelope has to cross the zero
point in order to flip the sign.
2.2
Diffraction Wave Coupled Scheme
There are at least two types of diffraction wave coupled devices. The first one is by
arranging the longitudinal spacing and lateral offset between two or more sets of laser
arrays to reject out-of-phase spatial mode; the second type uses external reflector
placed at the end of phased-array with the “correct” distance to only reflects electromagnetic emission from in-phase mode back to the laser ridges while the emission
from out-phase-mode is reflected to the intermediate gap. The out-of-phase mode
will then be surpassed due to the lack of optical feedback.
25
Figure 2-3: The Optical Talbot Carpet. The four brighter spots represent the periodic coherent source. The
same wavefront reappears in Z2T with
the same periodicity but shift by a halfperiod (a π shift). The exact same pattern shows again at ZT without any
phase shift. Note that the patterns
with shorter periodicity are generated
along the path. After Ref. [19].
The origin of this spatial filter property is from the so called “Talbot effect”. For
a laterally periodic wave source, its “pattern” will reappear at certain distances away
from the source plane (see Fig. 2-3). This distance is called the Talbot distance Z T .
At half of the Talbot distance, the same pattern also reappears with a half-period
shifted version. This Talbot effect is actually the direct result of diffraction theory
and the Talbot distance can be derived with this simple formula:
ZT =
2 a2 nef f
λ
(2.1)
Where a and λ are the spatial period and the wavelength of a source, respectively.
nef f is the effective index. For the “in-phase” mode, the spatial period is just the
distance between two laser ridges, but for the “out-of-phase” mode, this period is
doubled. One can arrange two sets of laser array with ZT /2 apart and shifted half
the spatial period to form a geometry that only supports “in-phase” mode (see Fig. 24(a,b)). The similar effect happens when the second set of array is replaced with a
perfect reflector which also sits at ZT /2 position. The exact same pattern, or called
26
“self-image” will be reflected back to the array aperture and provide feedback for
lasing (see Fig. 2-4(c)).
Figure 2-4: The working principle of Talbot cavity. (a) shows the in-phase mode
operation and (b) shows the out-of-phase operation. The out-of-phase mode has
higher radiation loss. (c) shows another configuration utilizing Talbot effect. The
mirror placed at ZT (in) /2 will feed the in-phase wavefront back to the laser array, and
the out-of-phase wavefront to the intermediate space.
The diffraction wave coupled scheme relies on the optical feedback from outside
of individual laser ridge. This might be doable in mid-IR or visible frequency, but
for a moderate width (50 µm) THz Metal-Metal waveguide, the reflectivity of a facet
can be as high as 90% [20], compare to 30% − 40% for mid-IR lasers. This makes
sufficient external feedback difficult to achieve. Furthermore, the external reflector
for diffraction coupled devices requires carefully designed mechanic part to maintain
27
Figure 2-5:
Schematics
for
Y-junction operation.
Case 1
depicts the in-phase operation.
When the amplitudes in two ridges
are in-phase, the fundamental
mode will be excited in the single
mode waveguide. Case 2 shows
when laser ridges are out-of-phase,
radiation mode will be excited at
the junction. This explains why
the Y-junction structure prefers
the in-phase mode. Modified from
Ref. [21]
its stability, which is rather challenging in cryogenic temperature.
2.3
Y-junction Coupled Scheme
The Y-junction coupled method got its name from the “Y” shape splitter which combines two identical laser ridges into one single mode output waveguide (see Fig. 2-5).
The operation of Y-junction can be explained as such: When fields in two laser ridges
are in-phase, the electromagnetic field from two ridges will constructively add up and
excite the fundamental lateral mode inside the output waveguide, but when fields
from two ridges are out-of-phase, high-order lateral mode, which does not supported
by the single-mode waveguide, will be excited at the junction. The high-order lateral
mode then escapes the waveguide and couples to free-space radiation, which increases
the radiation loss, and thus the lasing threshold of this configuration. Hence, the inphase mode will be the preferred one in Y-junction structure.
One thing needs to be mentioned is that even though the Y-junction substantially suppresses out-of-phase mode, when multiple ridges are included in the system,
due to the similar reason in evanescent-wave coupled scheme, the lack of global cou28
pling reduces the discrimination (the difference in lasing threshold ) between adjacent
modes.
Y-junction structure may also show sustained self-pulsation between in-phase and
out-of-phase mode [22]. The mechanism can be understood as follows. When the
in-phase mode is building up its intensity, it will strongly deplete the carrier in the
center of waveguide, cause the so-called “spatial hole burning” effect and reduce the
gain in the center. Then the out-of-phase mode will have a better overlapping with
the gain medium and start to lase. Once the intensity of the out-of-phase mode starts
to grow, the output power in the in-phase mode drops and the carriers in the center of
waveguide gets replenished again and then the same process repeats itself indefinitely.
Besides all these problems, making a prefect Y-junction is also quite challenging.
A Y-junction (a perfect splitter) typically requires small splitting angles between two
laser ridges to reduce the reflection from a junction. This will result making a sharp
tip in the fabrication step. These sharp tips require higher resolution in lithography
process, which is often not desired.
2.4
Leaky-Wave Coupled Scheme
The leaky-wave method got its name since it couples multiple laser ridges through
the propagating wave leaking from the sides. While most of diode lasers confine the
field inside the core utilizing total internal reflection (see Section 2.1), some lasers
achieve the modal confinement just by the partial reflection from interface [23] or by
gain guiding [24]. For such structures, the propagating constant outside the ridges
is real, which means that even though the mode is confined inside the waveguide, it
is still emitting power to the side. One single ridge of such device is not very useful
since the poor confinement factor and the extra radiation loss from the side uplifts the
lasing threshold, but when multiple ridges placed adjacently to form a laser array, the
radiation loss actually drops, for now only the ridges on the edge of array suffers from
the side radiation. Coupling through the propagating wave possess many advantages.
First, unlike the exponentially decayed evanescent wave, the coupling strength will
29
be much stronger since the aptitude of propagating wave decreases polynomially with
distance. This also makes long-distance coupling possible. Secondly, since the propagating constants in different region are all real, the phase information is well-preserved
across the array, which means a small change in phase caused by local perturbation,
such as a defect in single ridge or a flip from in-phase mode to out-of-phase mode in
one spot, will “propagate” through the whole array, provide a more robust “global”
coupling.
It might be worth mentioning that one can think the leaky-wave coupled laser
array as a two-dimensional cavity in which the confinement provided by traditional
Fabry-Pérot cavity in the longitudinal direction, but by distributed feedback reflection
from the interchanging high/low index structure along the array direction [25].
2.4.1
Mode discrimination mechanism between different modes
Fig. 2-6 shows the mode profile along the coupling direction of a laser array with infinite ridges. We can see that in this periodic structure, both in/out phase evanescent
wave coupled mode and in/out phase leaky-wave mode are supported. The favored
lasing mode is determined by the total loss of each mode, or the so-called threshold
gain. The mode with the lowest threshold gain will build up its amplitude first and
then quench other modes from lasing. If gain is placed in the higher index region,
the evanescent-coupled mode will be favored (Fig. 2-6(b,c)), but when gain is placed
preferentially in the lower optical index region, the leaky-wave mode will become the
lasing mode since it has better overlapping with gain medium.
From the profiles of leaky-wave modes (Fig. 2-6(d,e)) one observation can be made:
the mode is “in-phase” when there are odd numbers of half-cosine in the intermediate
region (high-index region), and “out-of-phase” for even numbers of half-cosine. The
definition of numbers of “half-cosine” is the numbers of zero-crossing events plus 1.
Now the problem falls on how to selectively excite in-phase mode against out-of-phase
mode. The mode selectivity mechanism will be much clear if we take a closer look at
the mode profile.
Suppose the optical index and the width of high/low index regions and also the
30
Figure 2-6: Modes supported in a periodic index structure.
(a) shows
the high/low index region. (b,c) are
the evanescent wave coupled modes
where the stronger field stays inside
the high-index core. (b) shows the
in-phase coupled mode and (c) shows
the out-of-phase coupled mode. Note
that there is no zero-crossing point
in the in-phase mode. (d)(e) shows
the leaky-wave coupled in-phase and
out-of-phase mode, respectively. The
strong field is in the low-index region.
For in-phase mode, there are three
(odd) half-cosines in the intermediate
region while there are four (even) for
out-of-phase mode. After Ref. [26]
31
frequency of the system are chosen to just fit the fundamental mode in the low-index
region and three half-cosines in the high-index region, which is noted as mode (0,3).
There are two adjacent modes with different eigenfrequencies which have two and
four half-cosines (mode (0,2) and (0,4)). Fig. 2-7 depicts the intensity profile (not
amplitude) for mode (0,3), (0,2), and (0,4). From the previous observation, mode
(0,3) is in-phase mode and the other two are out-of-phase modes.
Figure 2-7: Mode Intensity distribution for mode (0,3), (0,2) and (0,4). The index and
the geometry is adjusted to just make mode (0,3) match the resonance condition. The
shaded regions mark the overlapping area between the mode intensity and the gain
medium. Mode (0,2) and (0,4) both have stronger field outside the gain medium, but
the upper number off-resonance mode has higher field “trapped” in the intermediate
region. After Ref. [27]
The shaded regions in Fig. 2-7 marks the overlapping area between the mode
profile and the region with gain. It is not hard to see that the confinement factor Γ,
which is defined as the ratio of the mode in the active gain medium to the complete
mode profile in the structure, will be higher for mode (0,3) since this mode has
minimum intensity in the intermediate region while mode (0,2) and (0,4) both have
more energy outside the active medium.
32
This phenomenon can be understood with a little guide from transmission line
theory. When a wave coming from region with impedance Z0 enters region with
impedance Z1 and length s and then escapes to another region with impedance Z0 , the
total reflectivity from two Z0 −Z1 interfaces will drop to zero when s equals the integer
multiples of one half-wavelength inside the Z1 region. That is: s = mλ1 /2, where
m is an integer number, which is called the “resonance condition” in reference [25].
When this condition is met, all the energy will just pass through the interface as if it
doesn’t exist, but deviation from this condition will increase the reflectivity and then
“trap” more energy inside Z1 region. This explains why mode (0,2) and (0,4) have
higher modal intensity in the intermediate region than mode (0,3) since the configure
was set to let mode (0,3) just match the s = mλ1 /2 condition.
Besides the confinement factor Γ, one can bring in another mode selective mechanism by introducing material loss in intermediate regions. Based on the same effect
described in the previous part, modes satisfy the resonance condition will have minimum field inside the intermediate region and thus suffer the least from this additional
loss.
If we further exam the mode selective mechanism here, it is actually independent from the in-phase or out-of-phase mode and either one can be excited through
choosing the right length (or the optical index) of intermediate region. This is very
different from the evanescent-wave coupled method, where the coupled method intrinsically prefers out-of-phase operation.
2.5
Among all Commonly Used Coupled Methods
Clearly, among all commonly used coupled methods, the leaky-wave coupled method
is the most ideal scheme, which is indeed the case for the best performance phasedarray of diode lasers. Despite all the advantages it has, this coupled method is still
not ready to use for coupling Metal-Metal waveguide THz QC Lasers. The key feature of leaky-wave coupled scheme is that laser are coupled through the propagating
wave leaking to high-index region from the low-index gain medium. For Metal-Metal
33
waveguide THz QC Laser, the gain medium is a GaAs/Alx Ga1−x As multilayer structure with optical index 3.5 ∼ 3.6 in THz frequency. High quality, low loss intermediate
material with index higher than 3.5 ∼ 3.6 is hard to find at THz, and even if there
is such a material, to incorporate it into the current fabrication technique might be
another challenging subject to study itself.
Figure 2-8: Different coupling schemes in this chapter. The guided mode is in the
white region and the intermediate space is the shaded region. The optical index
profile is also showed beneath each figure. Note that in leaky-wave coupled scheme,
the guided mode resides in the low-index region while in other three schemes, it is in
the high-index region. After Ref. [26]
The evanescent-wave coupled method doesn’t require the high-index intermediate
material, but in order to have enough coupling strength between laser ridges, the distance between ridges has to be kept small. For instance, some coupling phenomenon
34
start to show when two 40 µm wide MM waveguides are placed 5 − 10 µm away from
each other in a preliminary simulation. This shows the impracticability of applying
this scheme in THz MM QCL. This short coupling length is a direct result of strong
confinement by the MM waveguide and the total internal reflection from GaAs-Air
interface. Filling up the intermediate region with lower index material might remedy
this problem, but then the same fabrication challenge comes up again. Besides, the
narrow gap between laser ridges also hinders the c.w. temperature performance since
heat is generated too close to each other.
As mentioned before, both Y-junction and Talbot effect are hard to achieve with
Metal-Metal waveguide. Prefect Y-junction requires small splitting angle between
adjacent ridges, which leads to undesired sharp tip in the pattern; external feedback
is also difficult due to the high reflectivity of MM waveguide.
All above sound very pessimistic, but the key factor that makes leaky-wave coupled method the most wanted scheme is that the coupling is taken place though the
“propagating-wave” which preserves the phase information across the whole array. If
we can manage to couple Metal-Metal waveguides through propagating wave, then
the same design principle of leaky-wave coupled method might be still valid. This
leads to the next chapter.
35
36
Chapter 3
Design of 2nd Order DFB
Surface-Emitting Phased-Array
Laser
3.1
Review on DFB Operation and Surface-Emitting
Laser
3.1.1
Distributed feedback operation - coupled-wave theory
Before getting into the subject of how to design a phased-array with MM waveguide
using propagating-wave coupled scheme, some reviews on the distributed feedback
(DFB) operation will help to understand the working principle better.
The distributed feedback effect comes from the Bragg reflection from the periodic
variation of characteristics of waveguide. The variation can be in the real part of
permittivity ²0 (index coupled ) or the imaginary part of permittivity ²00 (gain or loss
coupled or complex-coupled ) as long as it brings in periodic change in the effective
refractive index of the structure. The reflection from alternating interfaces causes
a very wavelength-dependent feedback. The maximum reflection occurs when the
37
Bragg condition is satisfied.
λB = 2Λne
(3.1)
where Λ is the period of the variation and ne is the effective index of the waveguide.
Fig. 3-1 might explain the origin of DFB better. Consider a wave incident from the
left to a infinite long waveguide which has some type of grating-induced effective index
variation with periodicity Λ. Some parts of incident wave will be reflected backward
in every interface along its way passing the waveguide. When Λ is just half of the
wavelength of incident wave, all the backward reflection will constructively add up
and thus result higher reflectivity. This is exactly the first order Bragg’s law in X-ray
scattering under normal incident condition. The periodic grating gives the waveguide
a spectral filter characteristic. Fig. 3-2 shows a typical reflection characteristic of
such a structure.
Figure 3-1: A graphic description of DFB operation. The incident beam comes from
the left, and is reflected back partially by every interface between na and nb . When
the periodicity of the structure just matches 1/2 wavelength of the incident beam
inside the medium, a strong constructive interference will occur. After Ref. [28]
Incorporating the periodic variation in laser waveguide provides great spectral selectivity and thus single-mode laser can be made. For small perturbations in effective
index, perhaps the coupled-wave model is the most widely used analysis approach.
The formulation in this part basically follows the Kogelnik and Shank’s derivations
in [29].
38
Figure 3-2: Typical DFB reflectivity against different wavelengths. λB is the Bragg
wavelength. After Ref. [28]
Suppose we only consider a scalar wave equation for electric field, propagating
along the z-axis inside a DFB waveguide. Assume the system is independent of x and
y direction.
∂2
E + k2E = 0
∂z 2
(3.2)
The periodic variation in index n(z) or gain/loss α(z) can be expressed as
2π
z)
Λ
2π
α(z) = α0 + α1 cos( z)
Λ
n(z) = n0 + n1 cos(
(3.3)
where n0 and α0 are the average index and gain/loss of the system and n1 and α1 are
the amplitudes of the periodic variation. Λ is the periodicity of the perturbation.
When the Bragg condition is met, λ0 = 2Λn. It is convenient to define a new
parameter β0 ,
β0 ≡ n0 ω0 /c =
2π
π
=
λ0
Λ
(3.4)
where β0 is just the wavenumber and ω0 is the angular frequency of the scalar wave
function in Bragg condition. If the perturbation is small and we are only interested
39
in frequency close to the Bragg condition, that is,
α0 , α 1 ¿ β 0 ,
n1 ¿ n
(3.5)
ω ≈ ω0
and the wavenumber in scalar wave equation k can be rewritten as
k 2 = β 2 + 2jαβ + 4κβ cos(2β0 z)
(3.6)
where κ is defined as
κ=
πn1 1
+ jα1
λ0
2
(3.7)
κ is called the “coupling constant” which is proportional to the amplitude of periodic
perturbation n1 and α1 . This coupling constant describes the “strength” of coupling
between forward and backward wave in the structure.
Since we only concern the modes close to the Bragg condition (β ≈ β0 ). We can
write the solutions of the system with the linear composition of forward and backward
waves
E(z) = R(z)e−jβ0 z + S(z)ejβ0 z
(3.8)
where R(z) and S(z) are the z-dependent envelope function of forward (R) and backward (S) wave. By substituting Eq. (3.8) into the scalar wave equation Eq. (3.2) and
neglecting the second derivatives R00 and S 00 (since only small perturbation are taken
into account so the envelope function should have negligible high-order derivatives),
we have
−
∂R
+ (α − jδ)R = jκS,
∂z
∂S
+ (α − jδ)S = jκR
∂z
where δ is defined as
40
(3.9)
δ≡
(β + β0 )(β − β0 )
(β 2 − β02 )
=
≈ β − β0
2β
2β
(3.10)
It’s clear that under small perturbation approximation, δ is a good measurement
of the deviation from Bragg condition. Eq. (3.21) is often referenced as the “coupledwave equation”
It’s not hard to guess the general solutions with form like
R(z) = r1 eγz + r2 e−γz
S(z) = s1 eγz + s2 e−γz
(3.11)
After substituting Eq. (3.11) into Eq. (3.21), and matching up all the coefficients, one
will find γ has to be
γ 2 = κ2 + (α − jδ)2
(3.12)
Assume the length of waveguide is L and its center is placed z = 0, for symmetry
reason we can derive more constraints on the coefficients r1,2 and s1,2 , which are
r1 = ±s2
(3.13)
r2 = ±s1
One normally applied boundary condition is
1
1
R(− L) = S( L) = 0
2
2
(3.14)
This means the forward wave or the backward wave starts with zero energy at the
edge of the waveguide and then build up its amplitude from the gain medium and
the backward scattering. With Eq. (3.13), and (3.14), we can solve the coupled-wave
equation and get
1
R(z) = sinh(γ(z + L))
2
1
S(z) = sinh(γ(z − L))
2
41
(3.15)
with more algebras, one can get
κ=±
jγ
sinh(γL)
(3.16)
α − jδ = ±jκ cosh(γL)
The mode shape and the threshold information are embedded in the previous equations. These transcendental equations only have numerical solutions. A typical
threshold against frequency plot is in Fig. 3-3
Figure 3-3: Typical threshold gain v.s. frequency of a gain-coupled DFB laser. Mode
which is closet to the Bragg frequency has the lowest threshold. Note that the spacing
between adjacent modes roughly equals to Fabry-Pérot mode spacing (c/2L). After
Ref. [29]
There are several important points need to be mentioned. First, κL is an essential
parameter that measures the feedback strength provided by the DFB structure. L
in the expression shows the distributed nature of the system. From Eq. (3.11) and
Eq. (3.12) we know that the shape of envelope function R and S are markedly determined by parameter γ (and thus by κ). Fig. 3-4 shows the mode intensity distribution
under different coupling strength κL. When κL ¿ 1, the reflectivity comes from the
DFB structure is not strong enough to keep the energy in the center; when κL À 1,
the reflectivity from DFB is too strong and thus the energy is localized in the center
of device. Neither of them is desired since in both scenarios the laser might suffer
more from the spatial hole burning effect. In a more complex system, where there is
no closed form solution but only numerical simulation result, the concept of coupling
42
Figure 3-4: Spatial intensity distribution of the lowest threshold modes
at different coupling strength. After
Ref. [29].
strength is still valid. It is also an important factor in choosing the optimized length
for 2nd order DFB surface-emitting laser (see Section 3.4). Another worth noting
point is that in the definition of κ (Eq. (3.7)), not only the real index, but the loss
of gain variation of the system also contributes to the coupling strength. In the following section, this loss can be extended to include the radiation loss in higher order
surface-emitting laser.
Secondly, the mode selectivity of DFB laser comes from the frequency dependent
reflectivity of the structure. The mode with higher reflectivity will reach the lasing
threshold first, and thus the mode closest to the Bragg wavelength λB = 2π/β0 is
always the lasing mode. In Fig. 3-3, we can see the mode sits right on the Bragg
frequency has the lowest threshold. This mode selectivity ensures the single mode
operation of the laser. Another observation is that even through we call these modes
the “DFB” modes, the frequency and the mode shape of these modes are not that
different from their Fabry-Pérot counterpart. Actually, it will be useful to think
these modes as the perturbed version of the Fabry-Pérot modes since if one shuts off
this periodic perturbation gradually, the “DFB” modes will change back to the F-P
modes.
Third, in a differential equation like Eq. (3.21), the boundary condition greatly
determines the properties of the solution. As we will see in the next section, the facet
43
condition at the boundary plays a dominating role in choosing the right spatial mode.
3.1.2
2nd order surface-emitting DFB laser
There is another point of view of seeing DFB operation. For a infinite long DFB
waveguide, the periodic variation, or the “grating”, brings one more translational
symmetry into the system. The conservation of translational momentum will induce
this relationship:
~ Bragg
β~backward = β~f orward ± G
(3.17)
where β~backward and β~f oward are the wavenumber of forward and backward wave and
~ Bragg is the “Bragg” wave vector, which equals 2π/Λ and Λ is the periodicity of the
G
~ Bragg | is twice of | βbackward |, it just
grating. When | βbackward |=| βf orward |, and | G
satisfies the Bragg condition and the backward and forward wave are linked by the
grating.
When the Bragg wave vector is not large enough to directly connect backward and
forward wave, it is possible that multiple Bragg wave vectors involve in the process.
These processes are called high-order DFB operation. For high-order DFB operation,
radiation modes can be excited in the intermediate stage. Assume the laser system
consists of three different materials with index n1 , n2 and n3 , where n1 is the index
of laser core and n2 and n3 are the indexes of cladding materials. Also assume the
core has the highest optical index among the three, so n1 > n2 , n3 . Radiation mode
~ Bragg <=
is possible at frequency f0 (free space wavelength λ0 ) if β~ ± mG
2πn3
λ0
or
2πn2
λ0
since both the phase-matching condition and the dispersion relationship in cladding
~ Bragg |=| βf |∼
material have to be satisfied. For the first order DFB, | β~f ± G
2πn2,3
λ0
2πn1
λ0
>
so it will not excite radiation mode in n2 and n3 , but for a 2nd order DFB
~ Bragg |≈ 0 and thus a radiation modes with almost zero wavenumber
process, | β~f − G
along the interface direction, that is, a radiation emission normal to the waveguide,
upward and downward is possible. After the forward wave excites the radiation mode,
the radiation mode will excite back the backward wave. Fig. 3-5 shows the graphical
44
representation for different orders of DFB operations.
For 3rd order DFB, the radiation emits to an angle θq from the waveguide. The
actual value of θq is determined by the ratio between the magnitude of
2πni
,
λ0
i = 2, 3
~ Bragg . It is possible that for a third or higher orders of DFB, no radiation
and β~f ± G
~ Bragg is
solution can exist in the cladding area if n2 or n3 is too small so that β~ ± mG
larger than
2πn2
λ0
or
2πn3
.
λ0
The vertical surface-emitting property of 2nd order DFB laser is very desirable for
integrated optics because it is more compatible with the current packaging techniques.
For MM waveguide THz QC Lasers, which is suffered from the bad far-field beam
pattern and low mirror loss caused by the sub-wavelength facet size, 2nd order DFB
not only effectively enlarges the emitting area, and thus improves the far-field beam
pattern, but also increases the mirror loss and so brings up the slope efficiency of
laser, which means more power can be delivered.
The 2nd order DFB grating has been widely implemented in lasers at many frequencies [30, 31], but for THz Metal-Metal waveguide QCL, this technique became
mature much later. The high reflectivity of end-facet requires precise control of facet
condition and the commensurate Γ factors between high-order lateral and fundamental mode due to strong mode confinement in MM waveguide [10] both make it difficult
to excite the right mode that emits the ideal beam pattern.
3.2
2nd order Surface-Emitting DFB THz QuantumCascade Laser
Fig. 3-6(a) shows the typical structure of 2nd order DFB surface-emitting MM THz
QC Laser. Metal-Metal waveguide which consists of the gain medium (multiple quantum wells, MQWs) sandwiched by the bottom metal plane and the top metal layer.
The normal dimensions of MM waveguide are about 50 − 120 µm in width and few
hundreds µm to 1 − 2 mm in length. The thickness of MQW is typically set to be
10 µm, which is roughly the optimized value considering we need enough modules of
45
Figure 3-5: Representation of different orders of DFB operation. In the 1st order
DFB, one grating Bragg vector can connect forward and backward wave, while in the
2nd order DFB operation, the forward wave is first converted to radiation mode (1st
order effect) through one Bragg vector and then reconverted back through another
Bragg vector to the backward wave (2nd order effect). After Ref. [28]
46
Figure 3-6: (a) The typical structure of MM waveguide 2nd order DFB surfaceemitting laser with metal covered facet. (b) The profile of E field on the plane across
the center of MM waveguide along longitudinal centerline. It shows how E field is
bent by the aperture on the top metal, convert Ey into Ez field. After Ref. [10]
MQWs to provide gain while keeping the heat dissipation in control. (More MQWs
means higher voltage drop across the device, which means more power will be dissipated.) The grating of 2nd order DFB is formed by opening apertures on the top
metal along the longitudinal direction of waveguide. The periodicity of the grating
is Λ and the “filling-factor” or the duty cycle means the ratio of the un-opened top
metal over Λ. So for 80% Duty Cycle and Λ = 30 µm, it means the aperture is 6 µm
wide and un-opened metal is 24 µm. The boundary condition can be adjusted by
changing the length of two ends of device. This extra length is define as δ, which will
be referred as the “facet length”. As it will show in the following section, the facet
length plays the central role of mode selectivity. The aperture size along the lateral
direction is kept as large as possible to prevent the so-called “anti-guide” effect [32],
but the upper limit of value is often limited by the fabrication, which will be discussed
in Chapter 4. The total length of such a device then equals to the number of periods
times the periodicity plus two facet length at two end (L = N × Λ + 2 × δ).
Metal commonly used for MM waveguide, such as Au and Cu, have electric permittivity as high as ²r ≈ −103−4 in THz frequency) [33]. Hence, the disrupt opening
on the top metal induces strong effective index change in the waveguide [34, 35, 36]
47
which provides strong coupling between the guided mode and the radiation mode.
This coupling strength is largely affected by the duty cycle of the aperture. Intuitively, wider apertures tend to provide stronger perturbation and thus more surface
emission, but strict numerical analysis using the Floquet-Bloch theorem [37] showed
duty cycle close to 50% gives greatest surface mirror loss. Such a low duty cycle is
hard to achieve in real device since the top metal also serves as the electrical contact, provides the right voltage bias and current through the MQWs structure. The
lack of the metal affects the current uniformity beneath the aperture, which leads to
different voltage bias across the gain medium or even push some parts of the gain
medium into early NDR (Negative Resistance Region), both will significantly degrade
the performance of lasers. A safe value for duty cycle should be at least above 75%
according to previous experience [10, 32].
The opening in metal let radiation escape from the waveguide to the far-field. Due
to the inter-subband transition nature, QCL only supports modes with polarization
along the MQW growth direction. Hence, inside the MM waveguide, Ey and Hx
are two dominating fields (see Fig. 3-6 for the coordinates definition). Clearly, the
Poynting vector which is proportional to Ey × Hx ẑ, will align with the z direction.
But from Fig. 3-6(b), we can see that the metal on the edge of aperture “bends” the
strong Ey field to the z direction near the aperture. Now at least some part of the
Poynting vector is along the y direction (Ez × Hx ŷ), which explains the origin of
surface-emitting radiation.
Even though the 2nd order DFB grating makes the normal surface emission possible, the far-field beam pattern is still determined by the actual E field distribution of
individual aperture. Fig. 3-7(d) shows the near field E field distribution of the lowest
surface loss mode (thus, the lasing mode) of a typical 2nd order DFB MM waveguide
laser. As mentioned before, the far-field energy comes from the Ez component. If for
every aperture on the device the E field distribution looks more or less like Fig. 37(d), then the total Ez distribution will have odd-symmetry along the y axis, and the
far-field beam pattern has to have a null in the center. This unwanted feature can be
remedied by incorporating the “center π shift” purposed by D. Botez et al. [38] into
48
Figure 3-7: (a) Typical Surface Loss plot against frequency of 2nd order DFB in
Metal-Metal waveguide. (b,c) The mode intensity distribution inside the waveguide
for the lower and upper band-edge modes. The gray line indicates the position of
grating. (d),(e) The electric field distribution for both modes. The mode just shifts
Λ
from lower to upper band-edge mode. The stronger Ez field for upper band-edge
4
mode explains the higher surface loss. After Ref. [10]
the grating design to obtain single lobe far field beam pattern. The concept is by
moving the positions of half of the apertures
Λ
2
further or closer to the other half. It
will “flip” the phase of Ez field inside half of apertures on the device. This operation
will covert the odd-symmetry to even, and consequently, dual-lobe to single lobe.
S. Kumar et al. [10] reported a single mode surface-emitting DFB THz quantumcascade laser (Λ = 30 µm, 30 periods and 80% duty cycle, center around 3 THz) with
almost no degradation in pulse temperature performance (Tmax = 149 K compares to
153 K for the multi-mode Fabry-Pérot device on the same die). The measured c.w.
49
power is about 6 mW, which is near by two times higher than the measured power of
edge emitting lasers with comparable sizes.
Several important findings and innovations are involved in the developing of such
a device. First, S. Kumar et al. found that the lasing will be killed if the highly doped
n+ GaAs layer beneath the top metal, which serves as the ohmic contact layer [39]
between the top metal and the MQWs, is still left inside the aperture. The thickness
of the doped layer is typically around 500−1000 Å, but since the E field is bent by the
edge of metal inside the aperture, the interaction distance between the Ez component
and the optically lossy contact layer become longer (∼ several µm), which consumes
all the radiation power and pushes the threshold higher than the maximum material
gain and then stops the lasing.
Second, the design uses a sloped sidewall covered with thin SiO2 and then metal,
which forms a lossy side pad to selectively excite the fundamental lateral mode. This
technique relies on the fact that the maximum field intensity of high-order lateral
modes resides closer to the sloped sidewall and thus those modes have stronger interaction with the lossy side bonding pad while the fundamental mode has negligible
intensity near the sidewall. The effect of end/side bonding pad will be discussed more
in Section 4.3.1.
Third, due to the sub-wavelength geometry, MM waveguide has facet reflectivity
as high as 0.7−0.9 [20] and this value is sensitive to the actual structure—the shape of
facet and the surface roughness, etc.—which is significantly affected by the fabrication
quality. In order to reduce this uncertainly, in mid-IR or visible light laser, normally
the facet is coated with Anti-Reflection (AR) coating to eliminate this reflection, but
for sub-wavelength waveguide in THz frequency where the reflection is not dominated
by the index mismatch on the facet, but the “modal-mismatch” between the guided
and free-space mode, AR coating is not that effective. Another approach is to cover
the end facet with High-Reflection (HR) coating. In MM waveguide, a facet covered
with metal serves well as this purpose. Metal provides almost 100% reflectivity to all
the lateral modes. With this controllability, S. Kumar et al. can obtain the desired
surface loss and mode shape by adjusting the facet length δ.
50
3.2.1
Effect of boundary condition
Fig. 3-8(a) shows the surface loss plot of the lowest loss mode (typically, the lasing mode) in the 2nd order DFB against different facet length (δ, as defined in
Section 3.2). If we assume the mode confinement factor and waveguide loss in different modes are almost the same in MM waveguide (which is a good approximation),
then the lowest surface loss mode will be the lasing mode. Clearly the curves in
Fig. 3-8(a) are all roughly periodic in δ with periodicity
Λ
.
2
This is because when the
cavity length increases a full Λ, the same boundary condition will repeat again. Note
that this is different from the transmission line theory where the boundary condition
(impedance) will reappear for every Λ/2 due to the fact that the DFB grating imposes
another translational symmetry property. This will become clear in the next section.
When δ = Λ4 , the surface loss is at its minimum and the mode energy distribution is
quite flat (point I in Fig. 3-8(a)). When δ increases, the surface loss also increases
and the mode energy distribution becomes more and more localized in the center (see
Fig. 3-8(d)). This agrees with the intuition since one can treat the surface loss as
the periodic perturbation in the imaginary part of optical index (α1 ). The coupling
strength κL will increase if α1 goes up (see Eq. (3.7)), and Fig. 3-4 also shows pushing
κL higher will concentrate the field intensity in the center. Another point of view is
that if the surface loss increases, the mode is losing more energy traveling back and
forth inside the waveguide and thus will decay faster, which leads to a more localized
mode shape.
When δ advanced near
Λ
,
2
two high surface loss modes show up near the upper
band-edge side (see point III in Fig. 3-8). The maximum field intensity of these “facet
modes” both reside on the two end of waveguide (see Fig. 3-8(f)). From δ =
3
Λ,
4
Λ
2
to
these two modes start to move across the bandgap to the lower band-edge and
then finally mixed up with the lower band-edge mode. The surface loss of these two
modes monotonously drops in this course (see the blue line in Fig. 3-8(a)).
When δ increase from
Λ
4
to
Λ
,
2
the frequency of the lowest surface loss mode first
drops. At a certain δ value between
Λ
2
− 34 Λ, the frequency hops to a higher value and
51
Figure 3-8: (a)(b) is the detailed surface loss and frequency against different facet
length condition. (c)(d)(f) show the field intensity distributions for different modes
6
inside the cavity. (e) shows the Hx field for first lower band-edge mode when δ = 16
Λ.
52
then falls again for bigger δ. Once δ crosses 34 Λ, the frequency abruptly jumps back
to its previous value when δ was
Λ
.
4
The discontinuities in the frequency against δ
indicate different “mode hopping” events (see Fig. 3-8(b) near δ = 10/16 − 12/16Λ).
Fig. 3-8(a)(b) shows the surface loss and frequency against different facet length
δ for the first lower band-edge mode and the two“facet modes”. Two curves cross at
point where δ ≡ ∆A . For δ < ∆A , the lowest surface loss mode is the same FabryPérot-like mode and since the total length of the cavity increases with δ, its frequency
also drops with the change of δ. At δ > ∆A , the “facet mode” become the lowest loss
mode. This explains the first discontinuity point. When δ = 43 Λ, the cavity length
just increases a full Λ and the same boundary condition reappears, so the lowest
surface loss mode “hops” back to the Fabry-Pérot-like mode which accounts for the
second frequency discontinuity.
When changing the facet length, the mode evolution of DFB laser is rather complicated. In order to fully understand this rich and elaborate behavior, it requires a
closer look on the actual electromagnetic field pattern.
3.2.2
Surface loss induced by metal grating - a different point
of view
There might be a more intuitive way to link the field inside the waveguide and the
surface loss it generated. Recall the Maxwell equations for complex amplitude field
with radial frequency ω,
~ ∝∇×H
~
ωE
(3.18)
Inside the MM waveguide, Hx is the dominant H field (again, see Fig. 3-6 for the
coordinates). For far-field radiation loss, we only care about the Ez component, and
then Eq. (3.18) can be reduced to
Ez ∝
∂Hx
∂y
53
(3.19)
Figure 3-9: (a)(b) shows different Hx sampling points. (a) samples the strongest
H field and thus will have strong surface loss while (b) sampled the null point. (c)
shows the mode “slipping” inside the waveguide. The red arrows point the position
of aperture openings. The sampling point gradually shifts from the center to the side.
which means the magnitude of Ez field is determined by the Hx field gradient in y
direction and the Hx strength.
When opening a aperture on the top metal, the Hx field beneath it will leak
out from the waveguide. This will induce a strong Hx field gradient in y direction
(upward). Hence, one can treat the aperture as a sampling tool which converts the
sampled Hx field into Ez field. If a strong H field sampled by the aperture, this
aperture will contribute stronger far-field energy (See Fig. 3-9(a)).
From this sampling H field point of view, the concept of “center π shift”[38]
becomes easier to understand since shifting half period ( Λ2 ) is merely moving the
sampling point to sample H field with different polarity. This will consequently
change the polarity of Ez field in one half of the apertures and thus brings the beam
pattern from dual lobe to single lobe. Fig. 3-10 shows a graphical explanation to this
effect.
Another very interesting point here is that inside a laser cavity, due to the
standing-wave nature of a oscillator, there is actually only zero or ±π difference
54
Figure 3-10: The concept of ”center π shift” (b) shows the Hx mode shape of the
first lower band-edge mode inside the 2nd order DFB waveguide when facet length δ
is Λ/4. The Ez induced by the aperture is the main contributor of far-field intensity.
Without the center π shift, the Ez field has odd symmetry and thus the far-field beam
pattern has to have a null in the center. With the center π shift, the polarity of E z
field in half of the apertures will flip and the system will now have even symmetry
and thus peak-in-the-center far-field beam pattern. (a) the far-field beam pattern
from surface-emitting DFB laser.
between any two sampling points. The field is either in-phase (phase difference zero)
or out-of-phase (±π) or null (just at the node of standing-wave). With this understanding, one can choose a shift amount differs from
Λ
2
as long as it still samples the
right field polarity.
3.2.3
A more physical view of DFB operation
For 2rd order DFB metal-metal waveguide with metal covered facets, the strong reflectivity provided by the facet imposes FP (Fabry-Pérot)-like modes. The distributed
feedback grating opens a bandgap around the Bragg frequency, and brings new mode
selectivity mechanisms (surface loss and reflection from the grating) to the system.
If the reflectivity of facet is weak, the lasing mode will be completely determined
by the DFB operation, but for high-reflection facet, the favored lasing mode can be
55
Figure 3-11: The competition between DFB and Fabry-Pérot cavity. The total mode
selectivity is the sum of both mechanisms. Since the facet is highly reflective, the
depth of F-P selectivity is much deeper than DFB operation. Thus the actual lasing mode can be pulled and pushed by the F-P cavity length, moving along the
DFB threshold curve. (a) shows the mode selectivity from DFB operation, which
can be approximated by the red curve. (b) the sum of mode selectivity from DFB
(dark red line) and F-P cavity, the total selectivity is still dominated by the F-P
cavity (green line).
“pushed and pulled” by changing the Fabry-Pérot cavity length (the facet length δ).
See Fig. 3-11 for more detailed explanation.
Assume the angle of facet is a simple vertical face coated with ideal metal. Since
the ideal metal forces the Ey field at the facet to be zero ( Ek,waveguide = Ek,metal = 0)
and also for a electromagnetic resonator, (in our case, the DFB laser cavity) the H
field is always “orthogonal” to the E field, that is, the Hy reaches its maximum
amplitude at the facet. Since the condition has to be maintained at all time, one can
imagine the field is attached to the metal facet and moving the facet length could
squeeze or pull the mode inside the waveguide.
When δ = Λ4 , the waveguide is just at the right length to accommodate an integer
number of “half-cosines” and also ensure the node point of Hy field is just beneath
the aperture. For device with 10 periods, − Λ2 center phase sift and δ =
Λ
,
4
we know
the number of “half-cosines” that satisfies the requirement above equals to 20 and the
wavelength of this mode is just the Bragg wavelength Λ (see Mode 20 in Fig. 3-12,
56
Figure 3-12: Hx field mode shapes for modes close to the bandgap at different facet
length condition.
δ = 1/4 Λ). From the previous discussion of the origin of surface loss, we know such
a configuration has the lowest surface loss. Hence, this mode is also corresponding
to the lower band-edge mode in Fig. 3-8. We named this mode as Mode 20. The
adjacent mode Mode 19 is corresponding to the second lower band-edge mode and
Mode 21 is the upper band-edge mode. The loss of Mode 21 is higher since almost
every aperture samples the largest H field.
When δ is between
Λ
4
and
Λ
,
2
the facets stretch the mode inside the waveguide.
So the frequency of Mode 20 drops. The surface loss goes up since every aperture
start to sample stronger H field. The wavelength of Mode 20 is longer than Λ now
and thus the relative position between “half-cosines” and aperture is slipping away.
The surface loss of Mode 21 also goes up and when δ =
Λ
2
it reaches its peak. At this
facet length, every aperture is sampling the highest H field (the anti-node of standing
wave) (see Mode 21 in Fig. 3-12, δ = 1/2 Λ).
When δ = Λ2 , there are actually three modes near the upper band-edge, Mode 21
57
Mode 22 and Mode 23 (see δ = 1/2 Λ − 5/8 Λ). Once δ is larger than
Λ
,
2
Mode 23
will become the new upper band-edge mode, while Mode 21 and Mode 22 become the
“facet mode” and start traveling through the bandgap to the lower band-edge. Since
these two modes are inside the bandgap, and wave propagates inside the DFB grating
region should be strongly decaying (see Fig. 3-2 for DFB reflectivity function), one
can think these facet modes are trapped inside a cavity formed by the DFB reflector
and the metal facet. Since we have two identical facet ends, the system will then
have even and odd solutions. Here, Mode 22 is the even one and Mode 21 is odd (see
Fig. 3-12, δ = 5/8 Λ). The surface loss of facet mode is high due to the short effective
cavity length. When two facet modes move closer to the lower band-edge, the DFB
reflectivity will drop and then effective cavity length will increase, which leads to the
lower surface loss.
When δ reaches 34 Λ, the waveguide is again able to just accommodate an integer
number of “half-cosines” which gives the lowest surface loss. This integer becomes 22
(Mode 22). Mode 21 converts to the new second lower band-edge mode and Mode 23
becomes the upper band-edge mode. The process will repeat itself with a periodicity
of δ = Λ2 .
The explanation above clarifies the complicated surface loss behavior against various δ values and also gives out a detailed discussion about the origin of different
modes and a consistent view to link the surface loss, mode intensity distribution, and
the relative mode-aperture position together.
Also note that the facet mode is often referred as the “surface mode” in Photonic
Crystal (PC) language, which only exists on the boundary between PC and continuous
material (like air) under certain interface condition. In our case, the DFB grating is
a 1-D PC and the extra end-facet section is the continuous material and 43 Λ ≥ δ ≥
Λ
2
is the interface condition for surface mode to exist. The feature of “surface mode”
is that it will move across the bandgap by changing the interface condition. This is
exactly the same behavior that “facet mode” has.
58
3.3
How to Couple Two Metal-Metal Waveguide
DFB Lasers
Now we have enough tools and understanding to design MM waveguide surfaceemitting DFB phased-arrays. As mentioned in Section 2.5, if we want to incorporate
leaky-wave coupled method to the system, we need coupling through “propagatingwave”, which, for MM waveguides, doesn’t exist in the lateral direction. A solution
to that is as following: Suppose we have two identical surface-emitting DFB Lasers
that lase at the same frequency (the grating will ensure the single mode operation),
but with arbitrary phase relation. If one feeds the output of lasers into a section of
waveguide by connecting the lasers to the two ends of waveguide, since two lasers have
the same frequency, a standing-wave will form inside the waveguide. This standingwave links two DFB lasers together and forces the phase relation between them to be
either zero or π.
The system can be better understood if one draws a analogy between this and
the leaky-wave coupling method. Since the DFB region and the connecting waveguide have very different wave-guiding properties, they can be treated as regions with
different effective indexes. The system is just like laser cores (DFB laser) coupled by
the intermediate material (waveguide) through propagating wave, and thus the same
design principle derived from the leaky-wave coupled method will be still valid here,
which is, the “resonance condition” in Section 2.4.1
s=m
λ(waveguide)
2
(3.20)
where m is an integer number, and s is the length of waveguide. Since this waveguide
controls the phase relation like what the intermediate region between diode laser
ridges does in leaky-wave coupled method, it is natural to name it as the “phase
sector”.
We need to clarify the mode discrimination mechanism between the mode that
satisfies resonance condition and its adjacent modes. In order to couple DFB laser
59
from the end, the facets can not be covered by metal, but for simplicity reason, we
still assume the H field reaches its maximum point at the original facet position.
For a 10 periods long 2nd order DFB laser with − Λ2 center phase sift and δ ≥
Λ
,
4
there are total 20 half-cosines inside the waveguide for the lower band-edge mode.
Let’s note this mode as Mode 20 (see Fig. 3-12(a)). If we couple two of such lasers
together through a phase sector with length = 4 ×
λ(waveguide)
,
2
since the resonance
condition is exactly satisfied with m = 4 (an even number), these two laser ridges
will be “in-phase” coupled (this is different from Section 2.4, where even number is
for “out-of-phase” coupling. The reason for this is clear on the graph). The mode
shape and the positions of half-cosines will be intact, and thus all apertures are still
sampling the same Hx field. If we neglect the small decrease in facet radiation loss and
the Γ factor caused by connecting the phase sector, the threshold of this “in-phase”
mode will be virtually the same as the original single DFB laser. For this in-phase”
mode, there are total 20 × 2 + 4 = 44 half-cosines inside the structure. We note it as
Mode 44. There are two adjacent modes near this mode, Mode 43 and Mode 45 (see
Fig. 3-13(a)), which simply means there are 43 and 45 half-cosines in the structure,
respectively. Since the total length of the structure doesn’t change, the wavelength
will be slightly longer in Mode 43 and shorter in Mode 44. This effectively lengthens
the facet length of DFB laser in Mode 43, and shortens the facet length for Mode 45
(see Fig. 3-13(b)). Changing the facet length will change the lowest surface loss mode
in the DFB laser.
The change in surface loss can be easily read out in the graph like Fig. 3-14(a).
If we mark Mode 44 (in resonance) at δ =
and
Λ
4
Λ
+,
4
and Mode 45 and 43 at δ =
Λ
4
+ ∆L
− ∆H , ∆H and ∆L are the changes in facet length for higher and lower mode
number side. The exact value ∆ is determined by many parameters in the structure,
but typically around the Fabry-Pérot mode spacing. It is clear that Mode 44 sits on
the lowest point in the curve, while Mode 43 moves upward ∆L and increases the
surface loss, and Mode 45 moves downward ∆H and then hops to another curve with
higher loss.
If one starts with a higher δ value like
60
7
Λ
16
for Mode 44, after the coupling is
Figure 3-13: Hx field mode shape for Mode 43 44 and 45. (a) shows mode shape
for “in-phase” mode (Mode 44) and two adjacent “out-of-phase” modes. The length
phase sector = 2 Λ. (b) shows the zoomed in version of phase sector. Mode 45 and 43
effectively pushes or pulls the facet length, respectively. δ = 1/4Λ in all three modes.
Figure 3-14: Mode discrimination mechanism for coupled array. (a) shows the surface
loss of Mode 44 (mode at resonance) and the two adjacent modes at δ = Λ/4. Mode 44
7
has the lowest surface loss. (b) shows the same graph but with δ = 16
Λ. Mode 44 is
not guaranteed to be the mode with the lowest loss. (c) by introducing loss in phase
sector, Mode 44 is the lowest mode again. The loss is “lifted-up” from the hollow
green circle to solid green dot.
61
formed, it is plausible that Mode 45 moves to a lower loss point (see Fig. 3-14(b)).
This problem can be saved by introducing another mode selective mechanism in the
system. Since for Mode 43 and 45, the resonance condition is not valid any more,
there will be stronger field “trapped” inside the phase sector, while for Mode 44, the
field intensity inside the phase sector is much smaller. By adding loss in the phase
sector, one can selectively increase the loss for modes not at resonance. Taking this
extra loss into account, then the loss plot will become Fig.3-14(c) where Mode 44
is the lowest loss mode again. The extra loss for the Mode 45 is larger since from
Fig. 2-7 we know the trapped field intensity is higher in the higher mode number side
and thus it suffers more from this additional material loss.
The typical surface loss of 2nd order DFB MM waveguide laser is around 1 − 10 cm−1
from δ = 14 Λ to 43 Λ and the loss curve is flatter in the first
Λ
4
region. Hence the extra
mode discrimination we need is roughly 3 − 4 cm−1 . If a material loss of 60 − 70 cm−1
can be added in the phase sector and 5−10% of energy is trapped in the phase sector,
we could expect an additional loss of 3 − 7 cm−1 for Mode 45, which should be enough
to increase the loss of Mode 45 higher than that of Mode 44.
This hybrid mode discrimination mechanism from both DFB grating and the
Γ factor ensures the stable operation of phased-array. The same coupling method
can apply to system with multiple ridges and since the coupling is though propagating wave, it preserves the robustness of the leaky-wave coupled scheme. It’s worth
mentioning that the actual geometry of the phase sector is not important in this
coupling scheme, as long as it allows enough energy to pass through it and then fix
the phase condition between two laser ridges. If we bend the phase sector from a
straight waveguide to a half circle, the geometry of the laser array will change from
a “chain-link” to the “sneak” shape (see Fig. 3-15(a)(b)). If two laser ridges lase
in-phase, we then have a narrower beam pattern along the “array direction” (the
lateral direction). One can add in more laser ridges to expand the lateral emitting
area and obtain more symmetric beam pattern. One thing needs to be noted is that
when one bends the phase sector by 180 deg, the polarity of x axis will flip its sign.
Since the far-field energy comes from sampling the Hx field beneath the aperture
62
(Section 3.2.2), which also flips its sign in the process. Hence, the “in-phase” mode
in “chain-link” configuration will become “out-of-phase” when it changes to “sneak”
shape (see Fig. 3-15(c)).
Figure 3-15: ”Chain-link” and ”sneak” configurations
3.4
Practical Design Issues
The coupling mechanism is described in the previous section, but there are more
practical details in each part of the system, such as the actual geometry of the phase
sector and how to choose the distance between adjacent ridges. These practical design
issues will be discussed in this section.
3.4.1
Phase sector design
Since the propagating-wave coupled scheme relies on the length of phase sector, it
is crucial to make sure the phase sector only supports one lateral mode. Otherwise,
high-order lateral mode might be excited in the phase sector when we bend the
63
waveguide to form the sneak shape configuration. The final sector ridge width is
between 15 − 25 µm for operation between 3 − 3.5 THz.
There are different ways to bend the phase sector, one can directly turn the
waveguide by 90◦ , or a full half-circle, or the combination of the two (see Fig. 3-16).
From the simulation, the right angle one does not provide enough coupling and the
mode behavior is rather complex and frequency dependent in the corner. The halfcircle has good property, but the geometry makes it difficult to bias the phase sector.
The final design is the hybrid type, consists of three parts: the extension part, the
half-circle, and bias part (see Fig. 3-16(c)). This design can adjust the total length
of phase sector by changing the length of extension part, while keeping the distance
of ridges the same.
Figure 3-16: Different phase sector configurations.
Another concern is that at certain condition, the mode can be trapped inside the
phase sector by the Bragg reflectors (the DFB grating on the laser ridges) at two ends.
This mode typically has low surface loss (since the cavity length can be quite long)
and might become the lasing mode. In order to increase the loss, several approaches
were investigated. Grating can be opened on the top of structure to increase the
surface loss of certain mode. This approach is very effective in the simulation, but it
requires precise fabrication to match up the grating period of the phase sector and
64
Figure 3-17: (a) shows the taper design from the top. The attacking angle is 12 ◦ .
(b) shows the extension of grating on the taper and also the electrical isolation gap
between phase sector and laser ridges.
the grating on the laser ridges. Another approach is to open the side metal of the
phase sector. Since the half-circle section of phase sector has small radius (∼ 30 µm),
radiation can escape from side.
The grating method was adopted in the first fabrication, but then switched to
open-side metal method in the second fabrication for it simplicity and less stringent
fabrication requirement (see Section 4.5.1).
3.4.2
Taper design
The ridge width of lasers were chosen to be 25−60 µm, which is wider than the width
of phase sector (15 − 25 µm). Hence, a taper structure is needed to connect them
together. The final design is a taper with 12◦ attacking angle (see Fig.3-17(a)). The
grating on the laser ridge is extended to the taper part to prevent forming another
cavity between the laser ridge and the phase sector (see Fig.3-17(b))
3.4.3
Voltage controlled gain in phase sector
In Section 3.3, we mentioned the possibility to bring in another mode discrimination mechanism by introducing extra material loss in the phase sector. This can be
achieved by selectively biasing the main laser ridges and keeping the phase sector
unbiased. The total loss in the main laser ridges can be estimated as ∼ 15 − 20 cm−1
65
Figure 3-18: Electronically control loss can induce mode hopping. By biasing the
phase sector, one can control the gain in the phase sector and thus move the loss of
the Mode 45 up and down (the orange circle). Once the orange circle is lower than
the red circle, the lowest loss mode of the system will change and the lasing will hop
from Mode 44 to Mode 45. See Fig. 3-14 for definitions of different modes.
(typical MM waveguide loss is ∼ 10 − 15 cm−1 and another ∼ 5 cm−1 for the surface
loss). The unbiased MQWs might have higher material loss and the narrow and bent
geometry will also increase waveguide loss in the phase sector. All these sum up to a
loss difference around 30 − 40 cm−1 or more.
Furthermore, it is also possible to control the array to lase at different coupling
modes, through changing the loss in phase sector electronically. Fig. 3-18 shows the
possibility of mode hopping from in-phase mode to out-of-phase mode when changing
the phase sector bias. This also makes the far-field beam pattern change from single
lobe in the center to null in the center.
In addiction, since any change in the imaginary part of the index (gain or loss)
will induce corresponding change in the real part as well through the Kramers-Kronig
relation, this gain-induced optical index change can provide another way to fine tune
the laser array frequency. Fig. 3-19 shows some preliminary calculations of this effect. For a gain medium with 60 cm−1 peak gain at 3.8 THz and 1 THz Lorentzian
linewidth, ∼ 0.4 − 0.6% change in optical index can be achieved. Assume 10% of
field intensity resides in the phase sector, then this change in optical index will induce 10%× ∼ 0.5% ≈ 0.05% change in frequency. For a laser works in 3.5 THz, this
66
Figure 3-19: Calculated optical index change due to the gain in the medium. (a)
shows the imaginary part of electric susceptibility (χ00 ) and corresponding change in
the real part of electric susceptibility (χ0 ) using Kramers-Kronig relation. The gain
was assumed to be 60 cm−1 at 3.8 THz with 1 THz Lorentzian linewidth. (b) shows
the calculated change in optical index.
means a tuning range of 1.75 GHz. The relationships between gain, electric susceptibility and optical index change are:
² = ² r ²0
= (²1 + i²2 )²0
= (1 + χ0 + i χ00 )²0
g nef f c
²2 = −
2π f0
√
n = ²1 + i²2
(3.21)
where ²1 and ²2 are the real and imaginary part of relative permittivity. χ0 and χ00
are the electric susceptibility. f0 is the frequency of the peak gain and nef f is the
effective index of the system.
3.4.4
Electrical isolation between phase sector and laser ridges
In order to provide electrical isolation between the phase sector and the main laser
ridges, a complete cut on the top/side metal and the bonding pad is required. The
67
gap is placed on the end of taper where the width of the waveguide narrowest and
support only one lateral mode to prevent the excitation of undesired high-order lateral
mode. The EM simulation shows a gap width smaller than 6 − 7 µm will not cause
too much perturbation to the field by eye-ball judgment. The final value is 5 µm,
considering it is less challenging for fabrication (see Fig. 3-17(b)).
3.4.5
Thermal simulation of array devices
In order to evaluate the thermal properties of the laser array, heat-flow out of the
laser array was modeled by solving the heat-equation in three dimensions using a
finite-element solver. Laser array is placed on a 1 µm Cu ( κCu ∼ 4 W/cm·K) on a
150 µm n+ GaAs substrate (κ ∼ 1 − 2 W/cm·K) followed by a 40 µm In/Au bonding
surface (κ ∼ 0.1 − 1 W/cm·K) attached to a heat sink with temperature fixed at
100 K (see Fig. 3-20(a)), the density of power dissipation in the active region is about
104 V/cm × 1000 A/cm2 = 107 W/cm3 . The temperature of structure is defined as
the maximum temperature inside the laser ridge array, which typically happens in
the ridge in the center. For 50 µm ridge width and 100 µm distance between ridges,
Fig. 3-20(c) shows that the temperature increases with ridges number but will saturate
after certain ridge numbers, while in Fig. 3-20(e), the temperature keeps on rising
for wider devices. For comparison, a three-ridge array which has 250 µm effective
emitting area will have a temperature increment about 75%·T0 (T0 is the temperature
difference between the maximum temperature and the heat sink temperature when
there is one ridge), but for a 250 µm wide single ridge, the temperature increment is
near 200%·T0 . This clearly shows the advantages of array device in c.w. performance.
3.4.6
Far-field beam pattern
The far-field beam pattern of the array device can be roughly predicted by the simple
point source model. Fig. 3-21 shows the far-field beam pattern for different distances
and numbers of point source. Assume all point sources are in-phase, when the distance
between ridges is smaller than free space wavelength of laser, there is always one
68
Figure 3-20: (a) cross-section of a three-dimensional heat flow calculation using a
finite-element solver for the c.w. temperature performance for array with different
ridge width and ridge numbers. (b) shows the temperature profile of a 2-ridge device
and the contribution from each ridge. (c) shows the maximum temperature inside
the ridges against different ridge numbers. (d)shows the temperature against different
distance between ridges. (e) shows the temperature against different ridge width.
69
D/λ = 0.7
I (a.u.)
1
2
3
7
0.5
0
−80
−60
−40
−20
0
Angle (deg)
20
40
60
80
D/λ = 1
I (a.u.)
1
2
3
7
0.5
0
−80
−60
−40
−20
0
Angle (deg)
20
40
60
80
D/λ = 1.3
I (a.u.)
1
2
3
7
0.5
0
−80
−60
−40
−20
0
Angle (deg)
20
40
60
80
Figure 3-21: Far-field beam patterns from different numbers of in-phase point sources
under different distance between sources. When distance d < λ, there is only one
lobe in the center; when d < λ, multiple modes are observed.
strongest single lobe in the center and two weaker side lobes at ±90◦ . When the
distance is larger than the free space wavelength, the center lobe stays, but the
two side lobes start to move toward the center. Taking into account the fact that
the surface-emitting laser is not a real point source, so the radiations beyond ±45 ◦
are getting weaker, the system can be considered as in single-lobe operation even
the distance is larger than the free space wavelength. The final distance chosen for
the design is between 90 − 100 µm since a larger distance will improve the c.w.
performance (see Fig. 3-20(d)).
3.4.7
Design flow
There are several essential parameters in designing the phased-array. The grating
period (Λ), ridges width (W ) and duty cycle (or filling factor F F ) basically determine
the lasing frequency of the structure. The total number of periods in single ridge (N )
and the facet length (δ) determine the field intensity distribution in the cavity and
70
the surface loss of lasers (see Section 3.2.1). The phase sector length determines
the system coupling mode (“in-phase” or “out-of-phase”) (see Section 3.3) and the
distance between two ridges determines the heat removal property and the far-field
beam pattern.
The whole design process of the 2nd order surface-emitting DFB laser phasedarray is done with full-wave three-dimensional simulations using a finite-element
eigenmode solver. The detailed simulation environment will be discussed in the next
section.
The design typically starts with a single ridge. For each lasing frequency, once the
width and the duty cycle are chosen, different structure will be simulated to find the
correct grating period. The facet length is then detailedly scanned to map the surface
loss plot like Fig. 3-8(a). A δ value between Λ/4 − Λ/2 is chosen to ensure stable
operation of lower band-edge mode. Multiple ridges are coupled together through the
phase sector and then the length of phase sector is scanned to find the “in-phase”
resonance condition. The whole process then goes through multiple iterations with
small variation in all important parameters, since there are many uncertainties in the
fabrication, such as the actual geometry of the sloped sidewall, the aperture duty
cycle and the actual width of the structure, etc., this step is to test the robustness of
the design.
Fig. 3-22(b)(c) shows the simulated Ez intensity 15 µm above of a single ridge
device and the far-field pattern. Fig. 3-22(a) shows Ey field and Hx field of the
simulated 3-ridge device coupled in “in-phase” mode. It is clear that field in three
ridges are phase-locked with each other. Fig. 3-22(d)(e) shows the Ez intensity 15 µm
above the 3-ridge structure and the far-field beam pattern.
The simulated device has 10 periods with Λ/2 center phase shift, 40 µm ridge
width and the distance between ridges is 90 µm. Each ridge is about 300 µm long. The
mode showed in the figures is the lower band-edge mode which lases around 3.4 THz
with 3 − 4 cm−1 surface loss. The simulated far-field beam pattern is calculated from
the two-dimensional Fourier transformation of the Ex field 45 µm above the device.
The distance is chosen to be larger than ( 41 λ(in
71
f ree space) )
for avoiding near field effect.
Figure 3-22: Simulated near-field and far-field patterns for different ridge numbers
phased-array. (a) shows the Hx and Ey field of a 3-ridge in-phase coupled phasedarray. (b)(c) shows the near-field (15 µm above) and far-field beam pattern of a
single ridge device. The beam pattern contracts along the grating direction, but is
still broad in another direction. (d)(e) shows the similar graph but for in-phase 3-ridge
device. The beam pattern also contracts along the phased-array direction.(f) shows
the in-phase far-field beam pattern for 5-ridge device. The beam pattern becomes
symmetric.
72
The beam pattern can be further improved by coupling more ridges. Fig. 3-22(f)
shows the 5-ridge configuration and its far-field beam pattern.
3.5
Simulation Methods and Environment
As mentioned before, the design of phased-array relies heavily on numerical simulations. The Finite Element Method (FEM) is proved to be a very useful numerical
tool in simulating THz device and its interaction with metal[32, 10, 40]. The only
drawback is that the FEM method needs great computation power to digitize the
space with finite meshes and then map a continuous system to its discrete counterpart. A good use of the symmetry property of the system can normally cut the
system to one half or more, but in our proposed structure there is no such symmetry.
Hence, a full structure three-dimensional full-wave simulation is required to design
the phased-array. In the following sections I will describe the simulation environment
and techniques used in this thesis.
3.5.1
COMSOL Multiphysics
Most of the simulations in this thesis are done with a commercial FEM solver COMSOL Multiphysics, RF Module , which provides easy implementation to add loss
or gain to a material and many features in meshing and also equipped with different
quick solvers for handling large numerical model.
The purpose of simulation is to find the modes supported in the cavity and also
the loss of each mode. The lasing mode will then be the mode with the lowest loss.
If we first assume there is no material loss (like metal loss or scattering loss from
GaAs) in the laser cavity and a absorbing layer is placed infinitely far, since the only
lossy part of the system is from the absorbing layer outside the laser, for a solved
eigenmode with most of its energy confined inside the laser cavity, the loss must come
from the power it radiates outward to the infinity. The radiation loss can then be
retrieved from the imaginary part of the eigenfrequeny.
Since it is impossible to simulate the whole space, the system has to be terminated
73
at certain boundaries. It is crucial to make these boundaries reflection-less and absorb all the radiated power from the structure. Otherwise the surface loss will not be
accurate and the reflected wave might couple back to cavity and then induce unreal
simulation result. The best solution to this problem in three-dimensional full-wave
EM simulation is the so called “Perfect Matched Layer” (PML)[41, 42] , which consists
of several boundary regions with artificial anisotropic absorbing material that effectively transform the propagating waves to exponentially decaying waves. The PML is
placed around the structure at least 50 µm away (∼
1
2
of the freespace wavelength)
to avoid absorbing the near-field energy. Once the PML is set, it takes a few round
of iterations to find the best absorption coefficients[42] and the distance between the
PML and the device. The energy flow of eigenmode is plotted and then searched for
the trace of unusual standing wave pattern between PML and the device. With the
correct PML setting, we can minimize the simulated space and reduce the simulation
time.
The mesh density is another factor that affects the accuracy and the required time
of the simulation. Low mesh density cannot capture the effect of small features but
setting the density too high will result practically unsolvable problem since a FEM
problem is usually with O(n3 ) complexity. In order to use least computation power
while maintaining the accuracy of solutions, the structure will be first solved in higher
mesh density, and then reduced the mesh density until some significant changes in
frequency and loss start to show. The normal mesh density is then set 1 − 2 times
higher than this critical density.
Another technique is to mesh different regions with different densities according
to the geometry and the optical index of each region. The rule of thumb is to have
10 mesh points within one wavelength in the material. For two adjacent regions with
great differences in geometry dimensions, the small geometry often induces meshes
too fine for the large geometry. It usually helps if one adds another auxiliary layer in
between as a buffer layer which let the mesh density “relax” from one to another.
Fig. 3-23 shows a typical structure simulated in COMSOL. The device is surrounded by the PML layer except the bottom metal plane. The vacuum region above
74
Figure 3-23: COMSOL Multiphysics simulation environment. (a) the purple regions
are the PML for the system. It covers the whole structure except the bottom metal
plate. (b) the pink region is the simulated device. There are at least 40 − 50 µm from
the device to the PML layers.
the device is divided into two: the one next to the device is the buffered layer between the much heavily-meshed device and the other vacuum space (not showed in
the graph).
With all the techniques listed above and the latest Paradiso Solver [43], which
saves half of the memory and more than half in consumed time than the default
UMFPACK[44] solver, a 5-ridge device embedded in a 500 µm × 500 µm × 100 µm
space can be simulated under 1.5 million degree of freedom (D.O.F.) and be solved for
50 eigenvalues around 3.5 ± 1 THz in a machine with 32 gigabytes RAM in roughly
60 minutes.
The loss from materials can be also added to the simulation by introducing the
Drude model[13], but for lossy metal, due to the extreme small dimension (∼ 3000 Å)
of metal thickness, it will be very inefficient to mesh the interior space of metal. The
solution is to use “Impedance boundary” and “Transition boundary” in COMSOL to
model a thin sheet of metal with finite conductance. With this approach, almost no
penalty has to pay for the D.O.F and it only adds a slightly longer time to solve the
eigenvalue problem (< 10%).
75
3.5.2
HFSS
Another simulation tools used in this thesis is HFSS, which is also a 3-D full-wave
electromagnetic field simulator but specialized in handling microwave structure with
metal components, such as waveguides or antennas. It also has a well-designed drawing tool for fast modeling a structure, but the less-controllable mesher and solver
and the lack of the ability to add gain in material restrict it from solving eigenvalue
problems of the phased-array system.
The main use of this software is to find the scattering matrix of a simple component, such as the Y-junction or the sloped sidewall end bonding pad (see Section 4.3.1), to quickly verify certain characteristics of this element.
Fig. 3-24 shows a typical simulation example in HFSS. A rectangular metal waveguide with 10-aperture grating on the top. The wave is fed in through the ports on two
ends to calculate the scattering matrix. Like in COMSOL, it also needs an absorbing
boundary to absorb the radiation loss. It shows simulated amplitude reflection (S 11 ),
p
transmission (S12 ) and radiation loss ( 1 − S11 2 + S12 2 ) at different frequencies and
different duty cycles.
76
Figure 3-24: Typical HFSS simulation environment and its result. The simulated
structure is a rectangular metal waveguide with cross-section 10 × 40 µm. A aperture
grating was opened on the top of the waveguide to find the optimized grating duty
cycle for surface-emission. From Duty=80 result, the 2nd order DFB structure reaches
its strongest reflectivity (blue line) between 3.5 − 3.6 THz. The surface-emission
reaches its maximum at Duty=50.
77
78
Chapter 4
Fabrication and Measurement
This chapter will cover the fabrication process and techniques developed along the
way in pursuing surface-emitting DFB MM waveguide QCL phased-array. The measurement result of each fabrication will also be covered and discussed.
So far two runs of fabrication have been done. In the first fabrication, many
unperceivable problems emerged during the process and dramatically reduced the
yield rate and device quality. The second fabrication fixed many problems in the first
run. Both “in-phase” and “out-of-phase” phase-lock phenomenon have been observed
and frequency tuning through gain-induced optical index change in the phase sector
is also identified.
4.1
Fabrication Steps
The fabrication process of MM waveguide DFB Laser can be summarized as followed.
The whole fabrication process involves three stages. The first one is mainly Cu-Cu
wafer bonding. The MBE-grown gain medium wafer and the receptor n+ GaAs wafer
are first cleaved into the right size and then coated with Ta/Cu layers (250/5000 Å)
by electron-beam deposition. The gain medium is then flipped and placed on top of
the receptor wafer. The crystal lines of both wafers are carefully aligned for future
cleaving purpose. The Cu-Cu bonding then takes place in the EV Group 501 wafer
bonder, under vacuum at 400 ◦ C and 4 − 6 M P a for 60 minutes. After cooling to the
79
room temperature, the device then undergoes a 30 minutes annealing at 400 ◦ C in
N2 gas. The purpose of annealing is to release the boundary stress between Cu and
GaAs wafer. A thin SiO2 is deposited to both sides of device for protection before
the device is taken out of the clean room for lapping. The GaAs substrate of MBEgrown gain medium is mechanically lapped down, leaving 150 − 200 µm of substrate.
A thick layer of photoresist is applied on the receptor wafer, protecting it from the
following chemical etch (wet etch). The etchant is a NH4 OH : H2 O2 1:9 solution,
which is a selectively etchant that stops at the Al0.55 Ga0.45 As etch stop layer (etch
rate 1-3 µm/min). A quick HF etch is used to remove the etch stop layer, followed
by the highly-doped top contact layer etch in H3 PO4 : H2 O2 : H2 O 1:1:25 (etch rate
0.2-0.3 µm/min). As mentioned before, it is crucial to remove this highly-doped layer
for surface-emitting device. A Ta/Au (or Ti/Au) metal grating is then defined using
image reversal photoresist AZ5214 and lift-off process.
The second stage is about defining the gain medium laser ridges. In order to
incorporate sloped sidewall described in Section 3.2, all mesas are aligned along at
45◦ angle to the cleave direction on the GaAs substrate. A pattern using positive
photoresist Shipley 1813 is defined first with contact lithography and then the device
is wet etched in H2 SO4 : H2 O2 : H2 O 1:8:80 solution (etch rate 0.5-0.7 µm/min) to
create a smooth and sloped sidewall. Since this mesa defining etch is isotropic, the
etchant will attack the gain medium beneath the photoresist from the edge of it. This
undercut value determines the actual mesa ridge width which is a critical value in
controlling the lasing frequency. An array photoresist undercut indicator consisted
of different sizes of squares was placed on every sub-chip for in-situ monitoring the
undercut value. (see Fig. 4-1). When the undercut value reaches one half of the length
of the square, the photoresist on the top will be released from the wafer, leaving a
visible change under optical microscope.
After that, a thin layer of SiO2 (∼ 3200 − 4000 Å) is blanket deposited on the
devices as the electric isolation layer. A quick buffered oxide etch (BOE) opens up
the SiO2 on the top of mesa followed by another Ta/Au (250/2500 − 3500 Å) lift-off
process which defines the bonding pad and the metal on sidewall which connects to
80
Figure 4-1: The Photoresist undercut indicator used in mesa etch step. (a) shows the
picture of photoresist cap from the top under optical microscope. (b) shows the SEM
picture after the photonresist removal. For pyramids without flat mesa on the top,
the photoresist will flow away during the etch step.
the metal grating in the first lift-off process.
The last stage is backside lapping and back side contact deposition. The finished
device is taken out for another mechanical lapping on the GaAs substrate, leaving on
150−200 µm of substrate for better c.w. temperature. Finally, a Ti/Au (250/2500 Å)
layer is deposited on the backside of the device, serving as the bottom electric contact
and also providing Au for the next In/Au die-bonding process. The device is then
cleaved, die sawed into smaller sub-chips, In/Au die-bonded to a copper chip carrier
and wire-bonded for further measurement.
4.2
Issues in the first fabrication - during the fab
process
In the first fabrication, after finishing the Cu-Cu bonding and substrate lapping, in the
substrate removal step, etchant breached through the etch stop layer along the edge
of wafer and some parts of gain medium were lost in this accident. After examining
the process, this problem was contributed to the large device wafer (> 2 cm × 2 cm)
81
and the thicker substrate left in lapping process. The lapping leaves a slightly concave
profile, that is, the substrate in the center is thicker than that along the edge. The
substrate along the edge is consumed by the etchant first and the etch stop layer
is exposed. Since the etch does not actually “stop” at the etch stop layer, it just
slows down the etch process, for large and thick substrate, when the etch stop layer
finally shows up, the etchant already etched through the stop layer along the edge
and started to attack the MQW gain medium beneath it. However, there were ∼ 60%
of gain medium still intact and thus it was reasonable to go on.
In the mesa defining etch, in order to reach the desired photoresist undercut value,
a slightly longer etch time was used after the bottom metal showed up (60 − 90 sec,
compares to typical 30 sec over etch time). This extra 30−60 sec is enough for etchant
to breach through the thin tantalum (Ta) metal (250 Å) and etch the Cu-Cu bonding
layer. Since the etch rate of copper is fast (> 1 µm/min), and the Galvanic effect
also enhances the etch rate, once a pin hole is formed on the tantalum, the copper
under it will be rapidly etched away, creating a empty hole which can even extend
into the bottom of mesa, leaving some part of the device “floating” on nothing. The
whole wafer had these “bubbles” everywhere (see Fig. 4-2).
Figure 4-2: The “bubble” issue. (a) shows a typical bubble on the wafer. (b) shows
the bubble can go beneath the mesa and make ridges “floating” on nothing.
82
Figure 4-3: The distribution thickness of photoresist on GaAs substrate under different mesa profiles. (a) shows the PR coverage on positive slope sidewall. The
thinnest PR is on the edge the mesa. (b) shows the PR coverage for negative sidewall
(undercut) substrate. After Ref.[45].
4.2.1
The quest of thick photoresist
New issue emerged in the last metal lift-off process. At this stage, 10 µm high mesa
structures were formed on the wafer. This unplanarized surface leads to different
photoresist thickness on different structure. The thickness of photoresist (PR) on the
edge of mesa (marked as thickness “b” in Fig. 4-3(a)) is the thinnest part on the wafer
and is sensitive to the width of mesa [45]. For a small mesa, this thickness b could be
as thin as zero, leaving no PR on the edge. This problem starts to manifest when the
mesa width is smaller than ∼ 40 µm, which is far smaller than the previous fabricated
surface-emitting device (60 µm), but in my design, the smallest mesa width is 15 µm
and thus new photoresist or coating technique has to be adopted here.
After trying a slow spin speed AZ5214, a double layer, even a triple layer photoresist coating. The coverage problem was not fully solved and the PR thickness on the
top of the mesa was not thick enough for the next lift-off process. More difficulties
comes from the fact that the design has a pattern with thin lines run through the
bottom continuously to the top of mesa, which requires PR with straight sidewall and
83
high aspect ratio. This was finally achieved with a negative photoresist NR71-3000P
(Futurrex, Inc.). A 9 − 12 µm thick photoresist was coated followed by a lithography
with precisely controlled exposure and development time. The result PR covered all
the desired region and also thick enough (2 − 3 µm) on the top of mesa. See Fig. 4-4
for the result.
4.3
Issues in the First Fabrication - during the
measurement
The bubble issue mentioned in the previous section was proved to be more problematic
than expected during the measurement. Since these bubbles are ∼ 1 µm deep and
the SiO2 used as the electric isolation layer is only 400 nm, once the last metal layer
for bonding pad touches the bubble, it is very likely that the bonding pad will be
shorted to the bottom metal through the rim of the bubble, where the SiO2 coverage
is bad, and completely bypasses the current through device, makes the device useless
(see Fig. 4-2). Most of the devices in the first fabrication were unmeasurable due to
this problem.
Besides the bubble issue, all phase sectors were shorted to the ground. The SEM
picture shows great undercut in half-circle section of phase sector (see Fig. 4-5). The
phase sector is likely shorted through these parts. The undercut comes from the
different etch speed and thus profile on different crystal plane of GaAs in etchant.
Fig. 4-6 shows the etch profile of GaAs along different crystal plane. Great undercut
on the bottom of GaAs is formed when the ridge is aligned perpendicular to the h100i
directions.
Some strange I-V behaviors were observed during the measurement. Fig. 4-7(a)
shows the I-V curves for four very similar simple surface-emitting single ridge devices.
At the same bias voltage, the current is very different in every device. This indicates
there is another current flowing path parallel to the gain medium or some part of
the gain medium is biased at higher electric field. After checking the scan tunneling
84
Figure 4-4: Some results of thick negative photoresist NR71-3000P. (a)-(d) shows the
SEM picture of photoresist after a 5000 Å metal deposition. (e)(f) shows the optical
microscope picture of the thick PR. A 6 µm wide PR strip can run all the way down
from the 10 µm high mesa to the bottom SiO2 layer.
85
Figure 4-5: The mesa undercut on the phase sector. The red arrows point out the
undercut point. The size of this undercut is roughly 1 µm height, which makes
SiO2 coverage bad at these point and thus after the metal deposition, some short
path formed at these spots.
Figure 4-6: The wet etched profiles along crystal plane on GaAs substrate. The arrow
shows the h100i directions on GaAs substrate. A larger undercut can be seen on the
direction perpendicular to h100i.
microscope (SEM) picture (see Fig. 4-7(b)), it is confirmed that the differences in
I-V curves is from the bad SiO2 coverage on the sidewall, which may be due to
over-etching in the SiO2 opening BOE dip.
86
Figure 4-7: (a) the I-V curves of several almost identical devices. The current differs
in each device at the same bias. This indicates the existence of different current paths.
(b) SEM picture show bad SiO2 coverage on the tip for those device in (a).
4.3.1
The lossy bonding pad
When testing the short (10 Periods), single ridge surface-emitting devices, even
though none of them have the bubble issue or the bad SiO2 coverage problem, only
very few of them lased yet with unexpectedly high Jth . The I-V curve looks normal
which means the electron transportation should not be the cause of the problem and
the high surface loss (∼ 10−15 cm−1 in simulation) of short device also cannot match
the loss needed to kill lasing. Besides, a longer version (30 Periods) of device with
the same grating period and duty cycle lased up to Tmax 123 K and with much lower
Jth . These all point to a length-dependent unknown loss mechanism.
After rechecking the design, the end bonding pad is the most suspicious part of
the structure. Due to the wet etch, the sidewall of end facet is not vertical. The
angle of the facet end is normally considered between 30 − 70 deg and is sensitive to
the actual wet etching condition (time and the environment during the etch) and also
the substrate orientation. The sloped sidewall end facet covered with metal can be
thought as a “taper” in vertical direction. A model was built in HFSS EM simulator
to fathom this point of view. The simulated structure is a waveguide filled with
GaAs, with cross-section 10 µm high × 40 µm wide. One end of the waveguide is
tapered down to 0.4 µm high × 40 µm wide and then attaches to a SiO2 waveguide
87
Figure 4-8: (a)(b) the amplitude scattering matrix coefficient S11 and S12 for 63 deg
and 45 deg sloped end facet. (c) shows the effective mirror loss (sum of both facet)
for a 330 µm long F-P device using facet reflectivity calculated in (a) and (b).
with the same cross-section and a 20 µm extension waveguide. The whole structure
is covered in ideal metal except the input and output ports. Scattering matrix of the
structure in different frequencies and different taper angles were simulated to capture
the reflectivity of the bonding pad. Fig. 4-8 shows the amplitude scattering matrix
coefficient S11 (reflection) and S12 (transmission) for different facet angles.
From Fig. 4-8(c), it shows the bonding pad can be a good mode converter at
certain angle/ frequency combination. Since the SiO2 waveguide is very lossy due to
its small height, energy converted into the SiO2 will be heavily damped. For longer
grating devices, the coupling strength κL is stronger and the mode intensity is more
localized in the center (see Section 3.1.1) and the effective mirror loss for longer device
is also lower, so this lossy bonding pad effect is not obvious, but for short device, the
loss from the end bonding pad (for a 330 µm device the effective facet loss can be as
high as 45 cm−1 ) will even kill lasing.
To validate this assumption experimentally, we cut out the bonding pad out of
several measured short devices (see Fig. 4-9(a)) using die saw and remeasure the
device, but all devices were shorted to the ground after the die saw. SEM picture
(Fig. 4-9(b)) confirmed it is due to the side metal touched the bottom metal after the
die saw. It requires further investigation in future to clarify this puzzle.
88
Figure 4-9: SEM pictures of devices after die sawed. (a) shows the die saw cut street,
which is about 30 − 40 µm. (b) shows the profile of a cut along h110i. The facet is
rather porous as compared to a much smoother facet in (c) where the cut is along
h100i direction.
4.4
Result from the First Fabrication
Two different gain medium were fabricated into devices in this run: one is FL183SVB0112 (Tmax 169 K, peak gain around 3.85 THz) and another is FL182C-M11-VB052
(Tmax 140 K, peak gain around 3.3 THz). Due to the many issues described above,
almost none of the devices in VB0112 can be measured. The best surface-emitting
device on VB052 is a 40 × 756 µm, 30 Periods, duty cycle 80% single ridge device
lases up to a maximum heat-sink temperature (Tmax ) of 123 K in pulse mode at
3.55 THz and the threshold current density (Jth ) was 745 A/cm2 at 8 K. Only a 17 K
drop in Tmax from the upper limit the gain medium (140 K) shows the quality of the
fabrication considering the device is shorter, narrower, and the frequency is off the
peak gain. Fig. 4-10 shows the c.w. I-V curve and the spectrum at different biased
89
Figure 4-10: Some c.w. measurement results for a best surface-emitting device on
wafer VB052–40 × 756 µm, 30 Periods, duty cycle 80% single ridge device, Tmax,pul =
123 K. (a) shows the c.w. I-V curve and the L-I curve in the inset. (b) shows the
c.w. spectrum at different bias point. A red shift in lasing frequency at higher bias
is observed. It is believed the optical index of gain medium increases due to the c.w.
heating.
points. The measured pulse power of this device was around 1 mW.
For those short devices, the Tmax all drop dramatically to 20−54 K, which are listed
as followed: 60 × 330 µm single ridge device with end bonding pad (Tmax 40 K), 25 ×
330 µm single ridge device without end bonding pad (Tmax 35, 53 K), 40 × 330 µm 3-ridge
array device (Tmax 27, 34, 52, 54 K).
Despite the poor performance, some types of coupling between ridges were observed. Fig. 4-11(b) shows the beam pattern measurement of a single ridge device
and a 3-ridge array device. Beam narrowing is observed in the array device along the
array direction (see Fig. 4-12).
Fig. 4-13 shows beam pattern measurement along the array direction of another
3-ridge device with different phase sector length. A clear dual-lobe beam pattern
was observed, but the spectrum information revealed different frequencies in left and
right lobe. This dual-lobe beam pattern undoubtedly proved the existence of coupling
between ridges, but the multi-mode behavior is undesirable.1
1
For the short devices, all measurements were done in pulse mode at 8 K.
90
Figure 4-11: Beam pattern measurements from a 3-ridge (left-hand side) and a single
ridge (right-hand side) device. (a) shows the I-V curve (blue), L-V curve (green),
and L-I curve (red, inset) from both devices. The dimensions of a single ridge are
40×400 µm. 3-ridge device suffered more SiO2 coverage problem and thus the current
density is higher than the single ridge device at the same voltage bias. The spectra
were not taken for these devices due to its weak power. (b) shows the two-dimensional
beam pattern measured with He-cooled Ge:Ga photo-detector using two-axis scanning
mirror, the distance between the device and the sensor is effectively 30 cm. It also
shows the 1-D beam pattern along the phased-array direction (lateral direction) in
linear and log scale. Single lobe beam patterns were observed in both devices.
91
Figure 4-12: A close comparison of between beam pattern from single ridge and 3ridge device. The 3-ridge device shows a slightly narrower beam pattern along the
lateral direction.
Figure 4-13: Beam pattern and spectrum measurement for two 3-ridge devices. (a)
shows dual-lobe behavior. Note that two lobes have different spectrum components.
(b) shows a roughly single lobe beam pattern. The spectrum measurement on the
center of the lobe and the edge of the lobe are also different.
92
4.5
Things Improved in the Second Fabrication
From the information gathered during the first fabrication and measurement, several
changes need to be made in the design and fabrication technique need to be improved,
which is described as followed.
4.5.1
Improvement in fabrication process
In the first fabrication, gain medium close to edge of the wafer were etched away
during the substrate removal step. A more careful lapping step was taken in the
second run. The substrate was first lapped down to ∼ 175 µm and then further
lapped with fine sand paper (grid size 30 µm) for the last 25 µm. This process
insures the flatness of the substrate and thus minimizes the time that etch stop layer
on the edge exposes to the etchant.
A four metal composite layer consists of Ta/Au/Ta/Cu (250/1000/250/5000 Å)
was used for the Cu-Cu bonding in the second run instead of the old Ta/Cu recipe.
When the gain medium is flipped and Cu-Cu bonded to the receptor wafer, the Ta/Au
layer will be on the top. During the mesa etch step, the gold layer will protect the
copper bonding layer beneath it from the etchant. Tantalum serves as an adhesion
layer between Au and Cu. The Cu-Cu wafer bonding was successful and no bubble
issue was observed in the second fabrication. The gold layer works well as a protection
layer but also introduces another problem which will be discussed later.
A double layer Shipley 1813 was used to improve the poor SiO2 coverage problem
on small features and the lithography recipe was adjusted to improve the adhesion
between PR and SiO2 to prevent the over-etch. With these alterations, good SiO2 coverage was obtained and there was no SiO2 over-etch to the sidewall. Fig. 4-14 shows
the microscope picture from the top of the device and the SEM pictures of some poor
SiO2 coverage devices.
93
Figure 4-14: SiO2 coverage on the top of the mesa. (a) shows the SEM picture of
poor SiO2 coverage example. The SiO2 retreated too much to the sidewall. This will
cause the current bypass the first few modules of MWQs and also a worse current
uniformity. (b) shows the good SiO2 coverage. SiO2 stays on the top of the mesa
even at the narrow taper tip (∼ 20 µm wide). (c) shows the pictures under optical
microscope, the greenish color is SiO2 .
94
4.5.2
Improvment in the design
The major design change is to increase the length of individual laser ridge from 10
Periods to 16 Periods. This should reduce the effective loss from end bonding pad.
Meanwhile, in order to compensate the smaller surface loss of longer device, the duty
cycle is reduced to 75% to boost up the surface loss. A slightly wider device width
(from 25 − 40 µm to 50 µm) is also adopted in the design for further reducing the
current non-uniformity in wet-etch device while keeping the laser still lasing in the
fundamental lateral mode. The coupled ridge number also increases to 7 to keep the
beam pattern more symmetric.
The phase sector is also redesigned to avoid the shorted problem caused by the
undercut in the half-circle section. The metal on the side of phase sector is now
completely removed except the side for biasing purpose.
Another modification is that the estimate photoresist undercut value in the mesa
etch step is reduced by 1.5 µm according to the experience in the first fabrication.
This reduces the extra etch time required to meet the desired device width.
4.6
Issues in the Second Fabrication
The four metal composite layer consists of Ta/Au/Ta/Cu used for the Cu-Cu bonding
resolved the bubble issue, but the wet-etch ridge profile also changed due to the gold
layer. Fig. 4-15 shows the SEM pictures of the wet-etch ridge on the Ta/Au/Ta/Cu
bottom metal. Clear deep undercut along the edge of ridge near the bottom metal
can be seen. This can be explained by the Galvanic effect, which states the etch
rate of etchant will be enhanced due to the proximity of metal. For copper bottom
metal this enhancement just gives out the desired ridge profile. Since gold is more
noble than copper, the Galvanic effect is also stronger. This leads to the dramatically
enhancement on the lateral etch rate of GaAs near the bottom metal and thus the
deep undercut we observed.
This undercut forms a gap about 0.5 µm high between the sidewall and the bottom
metal which makes the following lift-off process rather tricky. The final solution is
95
Figure 4-15: Unexpected gain medium undercut after the wet etch on Ta/Au/Ta/Cu
bottom metal.
Figure 4-16: The non-sticky second Au layer.
96
to first deposit thick Ta/Cu/Ta/Au layer (250/4500/250/1000 Å = 6000 Å) from the
top, filling up the gap between the sidewall and the bottom plane and then redeposit
another 2000 Å of Au using planetary rotation plane to cover the sidewall. The result
turns out good, no bonding pad shorted to the ground and all laser ridges can be
biased. The only drawback of this “patch” deposition method is that the second layer
of Au doesn’t stick well to the first one and some bonding pads got peeled off (see
Fig. 4-16) during the wire-bonding. This reduces the yield-rate of the process.
4.7
Results from the Second Fabrication
The general yield-rate of second fabrication is much higher than the first one since
most of the fabrication problems are solved. Here shows some important measurement
results from the second fabrication.
4.7.1
The grating operation
Fig. 4-17 shows the spectrum measurement of three second-order surface-emitting
DFB lasers with different grating periods and the L-I and I-V curves of each device.
The lasing frequency basically follows the grating period, and the deviations from the
curves are due to the variations in facet length and more importantly, the finite width
of the laser ridge. Since for electromagnetic modes, this equation is always valid
2
2
2
kx + k y + k z =
µ
2π
(λ/n)
¶2
(4.1)
where kx,y,z are the wave vectors in three directions inside the cavity, λ is the free
space wavelength and n is the effective index of material in the waveguide. For MM
waveguide in THz frequency, the fundamental mode has ky = 0 and kx =
2π
,
2a
where
a is the width of the waveguide. Since the DFB operation will fix the kz =
2π
,
2Λ
where
Λ is the period of grating, Eq. (4.1) can be further simplified to
sµ ¶
µ ¶2
2
1
1
1
1
+
=
(λ/n)
2
Λ
a
97
(4.2)
Figure 4-17: (a) shows the pulse spectra for three different grating devices (each
color corresponding to a device with different Λ), plotted in log scale. Spectra for
different bias are plotted starting from near-threshold bias at bottom to high bias
at top. (b) shows the L-I and I-V curves for different devices. From left to right
are devices with Λ = 24.5, 23.5, and , 22.5 µm. The demensions for each device is
50 × 735, 710, 680 µm. The Jth for each device is 610, 575, 600 A/cm2 , and the
Tmax,pul is 94, 116, 105 K. (c) λ0 versus Λ variation (in solid red). A line going
through origin and corresponding to nef f ≈ 3.29 is also plotted (in dashed blue).
98
Eq. (4.2) clearly shows the wavelength of lasing mode is not directly proportional
to the grating period but offset by the width of the waveguide. This pulls down the
lasing wavelength λ0 .
4.7.2
The gain-induced optical index change
Since the phase sector can be biased in the second fabrication, we are able to verify
the frequency tuning mechanism through gain-induced optical index change in the
phase sector. Fig. 4-18(a)(b) show the pulse L-I curve and the spectra at different
bias of a 7-ridge phase array. The 7-ridge device lased at a single frequency at all
bias. Fig. 4-18(c) shows the change of lasing frequency of the phase array against
different phase sector bias points. The frequency first red-shifted at lower bias and
then blue-shifted after the material gain started to grow. The gain medium of this
device has peak gain around 3.8 THz, so from Fig. 3-19(b), the gain will induce a
decrease in optical index, which also agrees with the blue-shift in the frequency. When
the phase sector is biased over the NDR point, the frequency abruptly dropped (like
the MQWs gain after NDR). The curve stops just beyond the NDR point to prevent
the phase sector from melting since it was biased in the c.w. mode. Also note that
the measured frequency tuning range is about 0.05 cm−1 ≈ 1.5 GHz, which is closed
to the estimated value in Section 3.4.3.
Restricted to the measurement equipment, the phase sector was biased in c.w.
mode. Although the c.w. heating effect may also alter the optical index of the device,
its effect was excluded due to: First, at all biasing values, maximum power dissipated
in the device was smaller than 3 W and the heat-sink temperature only rose less than
2 K. Secondly, the heating should cause monotonic and smooth red-shift while the
device showed blue-shift. This shows the heating is not the dominating mechanism.
4.7.3
Direct proof of phase locking
In order to verify the coupling mechanism in phased-array, a series of 2-ridge devices
with different phase sector lengths were fabricated and tested. The favored lasing
99
Figure 4-18: (a) shows the pulse L-I curve for a 7-ridge array device. The dimensions
of this device are 50 × 710 µm × 7. Jth is 770 A/cm2 , and the Tmax,pul is 35 K. Power
and beam pattern were not measured. (b) shows the spectra of the this device, plotted
in log scale. Spectra for different bias are plotted starting from near-threshold bias
at bottom to high bias at top. This device remains single-frequency at all bias (c)
Peak of the spectra of device against different c.w. bias point on the phase sector.
The main laser ridges were biased near the peak current. It shows a 1.5 GHz tuning
range.
mode changes from “out-of-phase” mode to “in-phase” mode when the phase sector
length varies from 11.5 µm to 18 µm. See Fig. 4-19 for more detailed result. The
devices were numbered from #1 to #14, ranged from 11.5 µm to 18 µm with a 0.5 µm
step.
Fig. 4-20 shows the out-out-phase and in-phase 1-D beam pattern along the array
100
Figure 4-19: The L-I curves for several 2-ridge array device with different phase
sector lengths. The length starts with 11.5 µm for device #1 and extends to 18 µm
for device #14. The spectra measured from different devices at different bias point are
showed on the center right in the figure. The mode-hoping event is clearly showed on
the spectra. All the L-I curves and spectra are taken with the phase sector unbiased
(floating).
101
(a)
(b)
Beam Pattern of VA0094 chip1 Device 1, along phased−array direction
out−of−phase, λ = 127.5 cm−1, Distance between ridges = 100 µm
Beam Pattern of VA0094 chip1 Device 13, along phased−array direction
in−phase, λ = 127.5 cm−1, Distance between ridges = 100 µm
measured data
simulation
1
0.8
Intenisty (a.u.)
Intenisty (a.u.)
0.8
0.6
0.4
0.6
0.4
0.2
0.2
0
0
−60
measured data
simulation
1
−40
−20
0
20
Angle (deg)
40
−60
60
−40
−20
0
20
Angle (deg)
40
60
Figure 4-20: Beam patterns from the two 2-ridge devices with different phase sector
length measured 20 cm away from the device using a He-cooled Ge:Ga photo-detector
with angular resolution < 1◦ . (a) shows dual-lobe behavior. (b) shows a single lobe
beam pattern. The data was fitted to a point-source modal simulation with the
measured frequency of the device (127.5 cm−1 ) and the actual distance between ridges
(100 µm). The beam pattern is cut off by the cryostat window beyond ±45◦ which
explains the abruptly dropped intensity.
direction from dev#1 and dev#13, respectively. The lasing wavelength for two devices
are both around 127.5 cm−1 , which indicates the laser ridges are still in the same DFB
mode while two ridges coupled in different spatial modes.
It is worth mentioning that for devices with phase sector length between 12.5 −
15.5 µm (device #3 and device #8), there are two regions in the L-I curves (see Fig. 419). After investigating the spectrum and beam pattern, it is clear that the device
went through mode-hopping from one spatial mode to another. This phenomenon can
be explained as followed. For these “unstable” devices, the phase sector length is far
from the resonance condition and thus even though the laser ridges were designed to
lase at effective facet length near δ = Λ/4, the mismatched phase sectors push or pull
the effective facet length to a different value. Recall that in Fig. 3-14(a)(b), moving
the facet length δ to higher value will make the system more unstable. Even though
the loss in phase sector can compensate this effect (see same figure(c)), but at a certain
facet length condition, the loss of Mode 44 and Mode 45 are just commensurate. Since
the peak of gain spectrum shifts when changing the bias point, it alters the relative
loss of adjacent mode and leads to mode-hopping. The mode-hopping events showed
102
in Fig. 4-19 hops from lower to higher frequency also supports this explanation. For
these devices, it is very likely that the mode-hopping will be also induced by changing
the bias point of phase-sector like what is suggested in Section 3.4.3. This requires
more measurements in the future to verify.
The measured dual-lobe beam pattern agrees well with the point-source model
simulation, which is a strong evidence of phase-locking between MM waveguide laser
ridges; in addition, the fact that the beam pattern is controlled by the phase sector
length (same DFB mode for each laser ridges, but coupled in different spatial modes)
shows the coupling is though propagating-wave coupled scheme. The mode-hopping
behavior reveals more information about the coupling mechanism and the changes in
Jth (a good indication of loss) on devices with different phase sector length also supports the “resonance condition” idea. Devices which show mode-hopping behaviors
(device #3, 8) are higher in threshold current than those who only show singe mode
behavior (see Fig. 4-19).
4.7.4
Discussion on the poor device performance
Even though several fabrication issues were solved in the second fabrication, and
also the gain medium (OWI222G-VB0240 (Tmax 186 K, peak gain around 3.9 THz)
and FL183S-VA0094 (Tmax 161 K, peak gain around 3.8 THz)) are better than the
FL182C-M11-VB052 (Tmax 140 K) used in the first fabrication, the overall device
performance in the second fabrication was much worse than the first one. See Table 4.1
for more measurement results from both gain medium.
The best measured device in the first run is a 80 × 400 µm F-P device without
sidewall or facet covered with metal. The device lased up to Tmax 129 K (a 11 K
drop from 140 K, the best recorded temperature on that gain medium), while in
the VA0094 the device with the same dimensions has a 20 K drop. A comparison
on surface-emitting devices also shows the same trend. In VB052, the best surfaceemitting device lased up to 123 K (40 × 756 µm, 17 K drop) but a device with wider
width and similar length only lased to 116 K (50 × 710 µm, 45 K drop) in VA0094.
The first suspected cause to this extra loss was the undercut on laser ridges during
103
Summary of the best Tmax,pul from devices tested so far
(FL182C-M11-VB052 and FL183S-VA0094)
Gain Medium
Device
Dimensions
Tmax,pul Temperature note
Type
(K)
Degradation
FL182C 140 K
F-P
80 × 400 µm
129
−11 K
FL183S
161 K
F-P
80 × 400 µm
154
−7 K
FL183S
161 K
F-P
120 × 800 µm
141
−20 K
FL182C 140 K
S-E
40 × 756 µm
123
−17 K
FL183S
161 K
S-E
50 × 710 µm
116
−45 K
FL183S
161 K
F-P
50 × 670 µm
132
−29 K
sidewall-covered
F-P
50 × 280 µm
124
−37 K
sidewall-covered
S-E
50 × 670 µm
110
−51 K
no end facet metal
S-E
50 × 480 µm
66
−95 K
Taper-end
S-E
50 × 480 µm
43
−118 K
7-ridge Array
OWI222G 186 K
F-P
120 × 800 µm
155
−31 K
F-P
80 × 400 µm
152
−34 K
F-P
40 × 800 µm
63
−123 K
S-E
50 × 670 µm
70
−116 K
no end facet metal
S-E
50 × 670 µm
50
−136 K
with end facet metal
S-E
50 × 735 µm
33
−153 K
none of the tested taper-end or array device lased in OWI222G
Table 4.1: Summary of best performance of different types of devices tested so far
on gain medium FL182C-M11-VB052, FL183S-VA0094 and OWI222G-VB0240. “FP” stands for Fabry-Pérot cavity laser, and “S-E” stands for surface-emitting. The
typical F-P device does not have sidewall or facet covered with metal. “sidewallcovered” means the device is covered with metal along the longitudinal edge.
“no end facet metal” means the S-E device doesn’t have metal covered on two ends.
“Taper-end” means the device is terminated by the taper section used to connect
phase sector but without the phase sector attached to it, nor covered with metal.
“7-ridge Array” means the device is a phased-array structure consists of the single
ridges with dimensions listed before.
the mesa wet etch on the Ta/Au/Ta/Cu bottom metal (Section 4.6). If this undercut went deep into the laser ridge, it will hinder the proper biasing of the device
and change the properties of gain medium. Such biasing problems should affect the
electron transportation behavior of gain medium and be revealed in the I-V curve,
yet a comparison between I-V curves of these lossier devices and F-P devices on the
same gain medium but from different fabrication batch disputes this possibility (see
Fig. 4-21). Notice that two graphs have different scales. The current density of both
104
Figure 4-21: GIV curves of devices on wafer FL183S-VA0094 from different fabrication
batches (a) shows the c.w. I-V curve of a 100 µm × 1.34 mm Fabry-Pérot dry-etch
device without sidewall or end facet covered with metal and its GIV curve. (b) shows
the pulse I-V curve of a 50 × 735 µm surface-emitting wet-etch device and its GIV
curves.
devices can not be directly compared since the actual size of the wet-etch device is
hard to define and the existence of top contact layer and the quality of the top metal
deposition will also affect the voltage drop across the device. The important things
is to see if the “humps” in the GIV curve are well preserved. These humps indicate
the alignment of energy levels in different quantum wells and thus can provide crucial
information of the gain medium property. Both two signature humps of FL-series are
still clear in the I-V curve (the wet-etch device usually does not have clear NDR in the
I-V curve). Besides, if one plots out the maximum heat-sink temperature (Tmax ) and
the threshold current (Jth ) of all devices from the second fabrication (see Fig. 4-22),
it roughly spreads along a straight line which can be extrapolated to Tmax 160−170 K
when Jth is around 400 A/cm2 (the Jth of the Tmax 161 K device). This also shows
the gain medium is not changed by the fabrication and the bad performance is from
some unknown loss.
From Table 4.1, the grating devices from second fabrication suffer more Tmax
drops than previous fabrication. This suggests that the extra loss might come from
something related to the aperture. The current non-uniformity[13] itself could not
explain the huge Tmax drop and apertures look clean under the SEM pictures.
105
900
measured data point
fitted curve
th
2
J (A/cm )
800
700
600
500
400
0
20
40
60
T
80 100 120 140 160 180
(K)
max,pulse
Figure 4-22: The best Tmax,pul tested so far from different types of devices in the
second fabrication on wafer FL183S-VA0094 (best Tmax,pul = 161 K) plotted out with
its corresponding threshold current (red circle). A fitted line from those data point
can be extrapolated to Tmax 160 − 170 K when Jth is around 400 A/cm2 (in dashedblue).
From Section 3.2, it is known that the un-removed highly-doped top contact layer
inside the aperture can be extremely lossy and even stop surface-emitting device
from lasing.Since the wet etched F-P devices all have regions uncovered by metal
along the edges of devices due to fabrication restrictions, if the top contact layer has
not been completely removed, the opened regions will act like the lateral loss section
or the side-absorbers[46] used to kill high-order lateral modes. Fig 4-23 shows the
spectrum measurement of a F-P device (100 µm×1.34 mm) from previous fabrication
on VA0094 and the F-P device (120 × 800 µm) from the second fabrication on the
same wafer. While clear multiple lateral modes behavior is observed in the 100 µm
wide device, the even wider 120 µm device only shows longitudinal modes. This
is a strong evidence that the bad performance of the second fabrication is due to
not-completely-removed top contact layer.
Several devices were then brought back to redo the top contact layer removal step.
However, this was considered impractical after several trials. Since the etching rate is
strongly enhanced by metals near the aperture, it is difficult to predict the required
etch time and the size of finished sub-chip (3 mm × 3 mm) is also hard to handle.
106
Figure 4-23: A comparison between pulse spectra of wide Fabry-Pérot devices from
different fabrication batches on the FL183S-VA0094. (a) shows the spectra of a
100 µm × 1.34 mm F-P device from previous fabrication (b) shows the spectra of a
100 × 800 µm F-P device from the second fabrication. In (a), there are unequally
spacing modes in the spectra while in (b) these modes are strongly suppressed. All
spectra are plotted in log scale.
Figure 4-24: SEM pictures from FL183S-VA0094 chip #20 surface-emitting device.
(a) before the patch top contact layer etch, the aperture was clean and smooth. (b)
after the etch, aperture became porous.
107
Fig. 4-24 shows the SEM picture inside the aperture before and after the patch wet
etch. The aperture changed from smooth to porous and the Tmax of devices on this
sub-chip also dropped ∼ 10 K after the etch (116 K to 109 K, 66 K to 45 K).
The other gain medium used in the second medium shows more Tmax drop. Compare to 186 K for the best device on that wafer, the best device from the second
fabrication only lased up to 150 K (F-P device, 120 × 800 µm) and for surfaceemitting devices, the best Tmax is only 70 K and none of the tested array devices
lased (see Table 4.1). This extra loss might be due to the fact that this wafer had
been through one more long BOE dip (∼ 180 secs) to redo the SiO2 deposition step.
This will induce more roughness on the side and the top of the ridge, which leads
to more loss. The thin SiO2 layer (< 2000 Å compare to 3200 − 4000 Å for devices
on VA0094) used in this wafer is another possible cause. Recall in Section 4.3.1, the
metal-covered sloped sidewall will convert mode into the lossy bonding pad. Since
the waveguide loss of bonding pad is inverse proportional to its thickness, a huge
decrease in thickness will have big impact on the loss. More measurements of devices
on this wafer are needed before drawing any definite conclusion.
4.8
Conclusions, Summary and Future Work
New approach for obtaining symmetric beam pattern from terahertz quantum cascade laser through phased-array has been proposed and initial proof of phase-locking
phenomenon has been observed. This is the first phase locked array implemented in
terahertz quantum cascade laser. The approach involves a carefully designed “phase
sector” which connects different laser ridges and then imposes definite phase relationship between lasers through the forming of standing-wave in the phase sector. The
phase difference between different laser ridges can be either zero or ±π, corresponding to “in-phase” or “out-of-phase” operation by changing the length of phase sector.
The frequency tuning mechanism through gain-induced optical index change was also
verified and the tuning range agrees well with the initial calculation.
The operation principle behind the 2nd order surface-emitting distributed feed108
back laser was thoroughly discussed in Section 3.2. A more physical “H field sampling” point of view on the origin of surface-emission was given and the complicated
mode behavior against different boundary conditions were also detailedly explained.
This provides a consistent view to link the surface loss, mode intensity distribution,
and the relative mode-aperture position together. The method to couple metal-metal
waveguide terahertz quantum-cascade lasers was given in section 3.3. The stable
operation of phased-array was guaranteed by introducing extra loss in the phase sector. An electronically mode selection method was also proposed based on this mode
selection mechanism.
A three-dimensional full structure, full-wave simulation environment was built
within a commercial finite element method solver (COMSOL Multiphysics). With
the latest quick eigenmode solver and meshing techniques, it is capable of solving
large structures within reasonable time. This provides a powerful tool for designing
the complex geometry and quickly identifying the feasibility of each approach. The
work reported in this thesis can never been done without this numerical tool.
The first part of Chapter 4 covered the problems emerged during the fabrication
process and then the improvement. Ample experiences were learned and many new
techniques were developed during this process, especially the development of lift-off
process using thick negative photoresist, which opened more possibilities of fabricating
grating structure. This technique will be very useful in future projects.
Despite these quite fruitful results, there are still many key progress needed to be
done. Restricted by the time constraint of this thesis, the electronically-controllable
mode-hopping and the symmetric beam pattern from phased-array (which requires a
7-ridge device coupled in correct phase sector length) have not been demonstrated.
Beyond this, the design of current phased-array may need further modifications. It
was unfortunate that both two batches suffered from different fabrication problems
which significantly degraded the device quality. But, even the fabrication problem
alone cannot fully explain the poor performance of phased-array devices. From Table 4.1, it shows that the sidewall-covered Fabry-Pérot device only lost several Kelvins
of Tmax when the length was shrunken from 670 µm to 280 µm, while the Tmax dropped
109
50 K from a 710 µm long surface-emitting device to a 480 µm long taper ended surfaceemitting laser ridge. It is likely the complex geometry of the taper part has the same
effect of end bonding pad and converts power to the lossy bonding pad waveguide.
With the clear evidence of phase-locking and the confirmation of that the coupling is
through the designed mechanism, more aggressive designs can be adopted in future.
A wider and longer laser ridges can be used to reduce the metal loss from the covered
sidewall and the taper part. A simpler taper geometry or even a taper-less structure
can be tried to avoid more loss. The final goal is to improve the maximum working
temperature and the power output of the laser phased-array to bring this technique
a step closer to the practical applications aimed by the terahertz QCLs.
110
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