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Modulated cap thin P-clad antoguided array lasers

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Modulated cap thin P-clad antoguided array lasers
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O, Jeong-Seok, 1962-
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viii, 108 leaves : ill. ; 29 cm.

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Electrons ( jstor )
Etching ( jstor )
Laser arrays ( jstor )
Laser beams ( jstor )
Laser modes ( jstor )
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Lasers ( jstor )
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Thesis (Ph. D.)--University of Florida, 1998.
Bibliography:
Includes bibliographical references (leaves 102-107).
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Typescript.
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Vita.
Statement of Responsibility:
by Jeong-Seok O.

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MODULATED CAP THIN P-CLAD ANTIGUIDED ARRAY LASERS

















By

JEONG-SEOK O












A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1998













TO MY MOTHER AND FATHER,

AND MY LATE SISTER













ACKNOWLEDGEMENT


First and foremost, my deepest thanks for this work should go to Dr. Peter S. Zory, Jr., my advisor. In addition to his support for my graduate study, his excellent academic and technical knowledge in the field of semiconductor lasers has been the greatest encouragement of my graduate research. He has inspired me not only academically but also spiritually. The largest part of my achievement in this work is attributed to his guidance with great inspiration.

I would like to thank the members of my committee; Dr. Gijs Bosman, Dr. Fredrik A. Lindholm, Dr. Ramu V. Ramaswamy, and Dr. Chris J. Stanton. It is my great privilege to have these honorable professors as my committee members and to be guided by them. Their keen suggestions and corrections have been very helpful for making this work better. I would also like to thank Dr. Dan Botez at the University of Wisconsin, Madison, who is a world expert on antiguided array lasers. Most of my basic knowledge of antiguided array lasers was initiated by his educational discussions on the subject with me. He was always very willing to give his valuable advice to me and I was encouraged very much by him.

I thank the U.S. Air Force Research Laboratory for sponsoring this work. Dr. Mark A. Emanuel at Lawrence Livermore National Lab., Dr. Bradley D. Schwartz and Dr. Richard S. Setzko at Hughes Danbury Optical Systems are also given my appreciation for providing the thin p-clad laser materials used in this study. I thank Mr. Steve Shein of the



iii







Microelectronics Lab. and his predecessor, Mr. James Chamblee, for all their technical support over the years. I would also like to thank the department staff, particularly Mr. Bob McClain and Ms. Linda Kahila. 'I truly appreciate all the things that are done everyday to make our department run and allow us to do our research.

I would like to thank all my colleagues that I have worked with or studied with while at the university; Chi-Lin Young, Chih-Hung Wu, Chia-Fu Hsu, Carl Miester, John Yoon, and Jong-jin Kim. Particular thanks go to Jong-jin Kim for help with basic experiments for this work and valuable information about material growth techniques and other material properties.

I would also like to thank my friends for their spiritual support with lifetime friendships. Thanks go to Dr. Craig C. Largent and his wife, Donna, for encouraging me with their heartwarming friendship. My deep appreciation is to be expressed to Geun-hyo An and Kee-woo Kim for their encouragement in many aspects of my life. I would also like to express my special appreciation to Henry J. Walker, Jr., for encouraging me to do my best for this work. He has been a great inspiration to me and given me great helps.

Finally, I certainly want to thank my mother and father for all their love and support. I also want to thank my brother and two sisters. They are always my greatest supporters and friends. My very special thanks go to my late sister for giving me the courage to resume my graduate study after her death. Without all the love and underpinning of my family, I could never be at this point.








iv














TABLE OF CONTENTS

page

ACKNOW LEDGMENTS ....................................................iii

A BSTRA CT ........................................................ ..... vii

CHAPTERS

1 INTRODUCTION ............................................... 1

1.1 Historical Perspective on Semiconductor Lasers ..................... 1
1.2 Basic Operating Principles ...................................... 3
1.3 M otivation .................................................. 11
1.4 Overview ................................................... 13

2 FOURIER OPTICS AND SEMICONDUCTOR LASER ARRAYS ....... 16

2.1 Introduction .................................................. 16
2.2 Fourier Optics and Far Field Patterns............................... 17
2.3 Far Field Patterns from Arrays of Light Sources .................... 22
2.4 Monolithic Semiconductor Laser Arrays ....................... 31
2.5 Array M ode Stability ......................................... 34

3 ANTIGUIDED ARRAYS .......................................... 36

3.1 Introduction .................................................36
3.2 Single Real Refractive-Index Antiguides ........................ 37
3.3 Antiguided Arrays ............................................ 39
3.4 Antiguided Array Fabrication Techniques ........................ 46

4 MODULATED CAP THIN P-CLAD ANTIGUIDED ARRAY LASERS .. .5(

4.1 Introduction .................................................. 50
4.2 Thin P-clad Laser Structure..................................... 51
4.3 Modulated Cap Thin P-clad (MCTC) Antiguided Array Lasers. ....... 55 4.4 Design Aspects of Thin P-clad Epitaxial Structures for MCTC Antiguided
Array Lasers ................................................. 62
4.5 Design Aspects of MCTC Antiguided Array Lasers ................ 68




V








5 FABRICATION OF MCTC ANTIGUIDED ARRAY LASERS ........... 73

5.1 Introduction ..................................................73
5.2 Pulsed Anodization Etching .....................................74
5.3 Electroplating ............................... ................... 78
5.4 Fabrication of MCTC Antiguided Array Lasers ..................... 79

6 CHARACTERIZATION OF MCTC ANTIGUIDED ARRAY LASERS ... 84

6.1 Introduction ..................................................84
6.2 Device Characterization .................. .................... 86

7 SUMMARYAND FUTURE STUDIES .............................94

7.1 Sum m ary ....................................................94
7.2 Recommendations for Future Study. ..............................97

REFEREN CES ........................................................... 102

BIOGRAPHICAL SKETCH ..............................................108

































VI













Abstract of Dissertation Presented to the Graduate School of the
University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

MODULATED CAP THIN P-CLAD ANTIGUIDED ARRAY LASERS By

Jeong-Seok O

December, 1998

Chairman: Peter S. Zory
Major Department: Electrical and Computer Engineering


The use of a thin p-clad laser structure with a modulated cap thickness for the fabrication of spatially coherent high-power phase-locked antiguided array lasers is proposed and demonstrated. Also presented are design aspects, fabrication techniques and characterization of these modulated cap, thin p-clad (MCTC) antiguided array lasers.

The work began with understanding the fact that minor contouring of the contact surface of the cap layer of thin p-clad laser structures causes significant changes in the complex effective refractive-index of the transverse lasing mode. Since large refractiveindex variations are required to fabricate monolithic antiguided array lasers, it was proposed that thin p-clad laser structures might be suitable for this purpose.

MCTC antiguided array lasers operating at a wavelength of 950 nm were fabricated in thin p-clad InGaAs/GaAs single quantum well material. The edge emitting arrays had 23 lasers on 7 pm centers with 5 gm wide gain regions (elements). The spatially coherent output beam from the best arrays had an 0.80 wide central lobe containing


vii







about 75% of the beam power at 1.2 times the pulsed current threshold (Ith). At 10 Ith, the central lobe contained about 60% of the beam power and was 1.60 wide. Although this performance level was quite good, the yield of devices with these high quality beam characteristics was very low (- 5 %). This could be attributed partially to the fact that the fabrication tolerances for the etched profile in the cap thickness required to achieve these results were quite small. Another reason for the low yield could be attributed to thickness non-uniformities in the laser material used.

In order to improve the yield, the pulsed anodization techniques used to etch the structures were improved and new electrolytes for faster and precise etching were developed. In addition, new designs which were less sensitive to cap thickness variations were developed.

In order to quantify the predicted performance of new designs, a "process window" concept was developed. In essence, the process window is an area in an "array mode gain / cap thickness variation" space which must be maximized in order to maximize fabrication tolerances for in-phase mode operation. The three major factors which affect the process window size are refractive index profile of the epitaxial layer structure, array dimensions and transverse mode loss. The effects of these three factors on the process window are presented and a new thin p-clad structure which employs a multilayer cap design is proposed.












Vi1l













CHAPTER 1
INTRODUCTION


1.1 Historical Perspective on Semiconductor Lasers

The first documented discussion of the possibility of light amplification by the use of stimulated emission in a semiconductor was made in an unpublished manuscript written by John von Neumann in 1953 [1]. He sent the manuscript to Edward Teller along with a letter to ask some questions concerning specific points in the manuscript. In this paper, von Neumann discussed using carrier injection across a p-n junction as one possible means of achieving stimulated emission in semiconductors. During the late 1950s and early 1960s, a number of theoretical and experimental papers were published on the subject of the injection laser [2-4] prior to the actual demonstrations of injection laser operation in 1962 [5,6]. Practical utility of these early devices was, however, limited since a large value of the threshold current density (Jth > 50 kA/cm2) inhibited their continuous operation at room temperature.

As early as 1963, it was suggested [7,8] that the threshold current density of semiconductor lasers might be lowered significantly if a layer of one semiconductor material was sandwiched between two cladding layers of another semiconductor material having a relatively wider bandgap. Laser devices consisting of two dissimilar semiconductors are commonly referred to as heterostructure lasers, in contrast to the single-semiconductor devices which are labeled as homostructure lasers. Heterostructure lasers capable of continuous wave (CW) operation at room temperature were first demonstrated in 1969 [9-11].


1




2


The factors largely responsible for this breakthrough was the exceptional and fortuitous close lattice match between AlAs and GaAs, which allowed heterostructures consisting of layers of different compositions of AlxGal_-xAs to be grown on GaAs substrate.

The first major application of semiconductor lasers was optical-fiber communication. It utilizes the fact that the laser output power can be modulated easily by modulating the injection current. Giga-hertz data transmission rates are now possible. The development of semiconductor lasers whose operating wavelengths are 1.3 ptm and 1.55 jim was motivated by the optical-fiber communication application, since optical-fiber dispersion is minimum at 1.3 jtm and optical loss in the fiber is minimum at 1.55 jtm. Laser amplifiers were also developed due to the need for repeaters in optical-fiber communication systems. Distributed feedback (DFB) and distributed Bragg reflector (DBR) lasers were also developed for optical-fiber communications to achieve frequency multiplexing of transmission signals and frequency stability.

As semiconductor laser technologies were advanced, more applications were generated. The optical memory (CDs: audio and video discs) industry has created a large demand for semiconductor lasers. Surface emitting two-dimensional arrays are demanded for optical data processing and computing. High power semiconductor lasers are needed for printers and copiers, and they are also being used as efficient pumping sources for solid state lasers and machining/cutting operations. When even higher power is reliably available, the list of applications will expand to include free space communication, laser radar, laser fusion, and more.




3


1.2 Basic Operating Principles

The purpose of this section is to provide a qualitative understanding of the physics underlying semiconductor laser operation. Two things are required to operate a laser: (i) a gain medium that can amplify the electromagnetic radiation propagating inside it and provide the spontaneous emission noise input and (ii) a feedback mechanism. As the name itself implies, the gain medium for a semiconductor laser consists of a semiconductor material. The optical feedback is obtained using the cleaved facets that form a FabryPerot (FP) cavity and the mode confinement is achieved through dielectric waveguiding. In order to provide optical gain, a semiconductor laser needs to be externally pumped, and both electrical and optical pumping techniques have been used for this purpose. A simple, practical, and most commonly used method employs current injection through the use of a forward-biased p-n junction. Such semiconductor lasers are sometimes referred to as injection lasers or laser diodes.

A p-n junction is formed by bringing a p-type and an n-type semiconductor into contact with each other. When they first come in contact, their Fermi levels do not match since the two are not in equilibrium. An equilibrium is, however, quickly established through diffusion of electrons from the n-side to the p-side, while the reverse occurs for holes. These diffusing electrons and holes recombine in the junction region. Eventually a steady state is reached in such a way that further diffusion of electrons and holes is opposed by the built-in electric field across the p-n junction arising from the negatively charged acceptors on the p-side and positively charged donors on the n-side. The Fermi level is then continuous across the p-n junction, as shown in Figure 1-1 (a) where the energy-band diagram of the p-n homojunction is shown. When a p-n junction is forward-biased by applying an external voltage, the built-in electric field is reduced,












p n






ED @@eSS$ ee EED)((E))(EALc Ef: Fermi level Ec: Conduction band edge Eg: Band-gap energy Ev: Valence band edge E,


(a) zero bias: V = 0





p n




-hv = Eg

-eeeeeeeee r



(b) forward bias: V = Eg / q







Figure 1-1. Energy-band diagram of a p-n junction at (a) zero bias
and (b) forward bias





5


making possible a further diffusion of electrons and holes across the junction. As shown in Figure 1-1 (b), both electrons and holes are present simultaneously in a narrow "active" region and can recombine ether radiatively or non-radiatively. Photons of energy hv = Eg are emitted through radiative recombination. However, these photons can also be absorbed through a reverse process that generates electron-hole pairs. When the external voltage exceeds a critical value, the rate of photon emission exceeds that of absorption. The p-n junction is then able to amplify the electromagnetic radiation and is said to exhibit optical gain. However, for a homojunction the thickness of the region where gain is sufficiently high is very small since there is no mechanism to confine the charge carriers (electrons and holes).

The carrier-confinement problem is solved with the use of a p-n heterojunction. Figure 1-2 (a) shows the schematic energy-band diagram for a double-heterostructure laser wherein the thin active region has a lower band-gap compared to that of the p-type and n-type cladding layers. Electrons and holes can move freely to the active region under forward bias. However, once there, they cannot cross over to the other side because of the potential barrier resulting from the band-gap difference. This allows for a substantial build-up of the electron and hole populations inside the active region, where they can recombine to produce optical gain. The successful operation of a laser requires that the generated optical field should remain confined in the vicinity of the gain region. In double-heterostructure semiconductor lasers the optical confinement occurs by virtue of a fortunate coincidence. As shown in Figure 1-2 (b), the active layer with a smaller band-gap also has a higher refractive index (na) compared with that (nc) of the surrounding cladding layers. Because of the index difference, the active layer in effect












p-clad active n-clad

C


E _1 hv = Eg




(a) schematic energy band diagram for carrier confinement






p-clad active n-clad na


nc nc nc na nc












(b) refractive-index diagram for optical confinement




Figure 1-2. Carrier and optical confinement scheme of a double-heterostructure




7


acts as a dielectric waveguide. The physical mechanism behind the confinement is total internal reflection (TIR), as illustrated in Figure 1-2 (b). When a ray traveling at an angle 0 hits the interface, it is totally reflected back if the angle 0 exceeds the critical angle

(0) given by



c = sinl n (1.1) Thus, rays traveling nearly parallel to the interface are trapped and constitute the waveguide mode.

When the current flowing through a semiconductor laser is increased, electrons and holes are injected into the active region, where they recombine through radiative or non-radiative mechanisms. As one may expect, non-radiative recombinations are not helpful for laser operation, and attempts are made to minimize their occurrence by controlling point defects and dislocations. However, a non-radiative recombination mechanism, known as the Auger process, is intrinsic and becomes particularly important for long-wavelength semiconductor lasers operating at room temperature and above. Physically speaking, during the Auger process the energy released by electron-hole recombination is taken by a third charge carrier (electron or hole) and is eventually lost to lattice phonons.

During a radiative recombination, the energy Eg released by the electron-hole recombination appears in the form of a photon whose frequency v or wavelength ?, satisfies the energy conservation relation Eg = hv = hc/A. This can happen through two optical processes known as spontaneous emission and stimulated emission. In the case of spontaneous emission, photons are spontaneously emitted in random directions with no




8


phase relationship among them. Stimulated emission, by contrast, is initiated by an already existing photon, and the emitted photon matches the original photon not only in its wavelength but also in direction of propagation. It is this relationship between the incident and emitted photons that renders the light emitted by lasers coherent.

Although stimulated emission can occur as soon as current is injected into the semiconductor laser, the laser does not emit coherent light until the current exceeds a critical value known as the threshold current (Ith). This is so because stimulated emission has to compete against the absorption processes during which an electron-hole pair is generated at the expense of an absorbed photon. Since the electron population in the valence band generally far exceeds that of the conduction band, absorption dominates at a low level of the injection current. At a certain value of the current, a sufficient number of electrons are present in the conduction band to make the semiconductor optically transparent. With a further increase in current, the active region of the semiconductor laser exhibits optical gain and can amplify the electromagnetic radiation passing through it. Spontaneously emitted photons serve as the noise input for the amplification process.

However, optical gain alone is not enough to operate a laser. The other necessary ingredient is optical feedback which can be obtained by placing mirrors at the ends of the gain medium. The cavity formed by the mirrors is called Fabry-Perot (FP) cavity. In A1GaAs semiconductor lasers, the cleaved facets are about 30% reflective mirrors and form the FP cavity. Figure 1-3 (a) shows a schematic of a typical heterostructure stripe laser.

Because of the optical feedback, the number of photons traveling perpendicular to the facets increases when the current is large enough to satisfy the condition of net




9


stimulated emission. However, some photons are lost through the partially transmitting facets and some get scattered or absorbed inside the cavity. If the loss exceeds the gain, stimulated emission cannot sustain a steady supply of photons. This is precisely what happens below threshold, when the laser output consists of mainly spontaneously emitted photons. At threshold, gain equals loss and stimulated emission begins to dominate. Over a narrow current range in the vicinity of the threshold current, the output power jumps by several orders of magnitude and the spectral width of the emitted radiation narrows considerably. In the above threshold regime, laser output increases almost linearly with the injection current as shown in Figure 1-3 (b). Details as to the processes which determine Ith and the slope of P-I curve can be found in several excellent textbooks [12 -14].




10





p-contact oxide
p+-cap

p-clad
active layer n-clad


near-field n-substrate


n-contact


far-field: g\em os
Light output 500 gm
= 100 x 400 500 m
Lateral direction 1.09,

(a) schematic of a heterostructure stripe laser










0






Igh Injection current, I

(b) P-I curve: relation between the laser output power (P) and injection current (I)



Figure 1-3. Schematic of a heterostructure stripe laser and P-I curve.




11



1.3 Motivation

High brightness semiconductor lasers (high power, spatially coherent sources) are of considerable interest for use in applications such as efficient pumping of solid-state lasers, fiber amplifiers and lasers, high speed optical recording and printing, and free space communications. Conventional narrow-stripe (-5 .tm wide) single-spatial-mode lasers provide at most 200 mW reliably because of the limitation of the optical power density at the laser facet. For reliable operation at higher power levels, large-aperture (2 100 ptm) sources which operate in a single-spatial mode are necessary. However, single-stripe large-aperture lasers are inherently operating in multi-spatial modes since the number of allowed spatial modes is increasing with the stripe width. Thus, achieving single-spatialmode operation from large-aperture devices at high-power levels has proved challenging.

One way to achieve such devices is to phase-lock an array of narrow-stripe singlespatial-mode lasers. Such a phase-locked array (coherent array) of diode lasers operates as a single coherent source at a power level that can be one to two orders of magnitude higher than a standard single-element device. The phase-locked array structures which have been studied to date include the antiguided array (leaky-wave coupled array), the positive-index waveguide array (evanescent-wave coupled array), the Y-junction coupled array, and the diffraction coupled array. Of these, the antiguided array laser [15] has demonstrated the best performance. Since the effective refractive-index of the optical gain regions (elements) in these antiguided array lasers is lower than that of the interelement regions, the individual antiguided lasers (elements) in the array can be coupled to all others by lateral leaky waves through the interelement regions. An example of the beam quality which has been achieved with a 23 element antiguided array laser (150




12


p.m wide) is shown in Figure 1-4 (a). The vertical axis is beam power and the horizontal axis is lateral beam direction. For comparison a beam profile of a typical 100 p.m aperture laser is shown in Figure 1-4 (b).










































phase-locked antiguided array lasers fabricated using the above techniques were . . . . : : : : i.. .. i... .. .......




13


achieved, commercialization of antiguided array lasers has not been realized because of the difficulties in reproducing the required lateral refractive-index modulation with those complex processes and very small fabrication tolerances of the devices.

In order to commercialize antiguide array lasers, easier fabrication techniques should be employed, which will also ease fabrication tolerances. Utilizing a thin p-clad laser structure [22, 23], the required lateral index modulation for antiguided array lasers can be easily obtained by modulating the cap layer thickness which can be done with a simple etching process without regrowth and dopant diffusion. Modulated-cap thin p-clad (MCTC) antiguided array lasers are, therefore, easily fabricated with standard post-growth processing steps such as pulsed anodization etching [24], photolithography, and metallization. The MCTC structure will be very likely employed to make practical antiguided array lasers when the necessary technologies have been fully developed. In this dissertation, the use of a thin p-clad structure for the fabrication of antiguided array lasers is proposed and demonstrated [25]. Based on theoretical and experimental research, this dissertation is also devoted to developing the fabrication technologies of MCTC antiguided array lasers.


1.4 Overview

This dissertation is a systematic study of the thin p-clad laser structure for fabricating antiguided array lasers which produce spatially coherent high power output beams.

In Chapter 2, Fourier optics is introduced in order to understand the output beam (far-field) behaviors of laser arrays. Fourier optics calculations of the far-field distribution from the near-field of an array of light sources show the need of phase-locking




14


between array elements for a single main peak far-field pattern and array dimension effects on full width at half maximum (FWHM) of the far-field main lobe and power percentage in the lobe. Then different types of monolithic semiconductor arrays are introduced. Previous fabrication techniques of monolithic semiconductor arrays are presented with a brief discussion of device stability.

Chapter 3 reviews antiguided array theory in order to explain basic concepts. First, a single antiguide structure is discussed to show lateral mode discrimination due to the lateral radiation loss. The wavelength of the lateral leaky-wave of a single antiguide is also derived. This wavelength is related to the required lateral array dimensions for maximum coupling (resonant coupling) between array elements of antiguided arrays. Near-field modes (array modes) of antiguided arrays are then shown and defined to be used for discussion of array mode discrimination. Finally, previous antiguided array results are addressed which are involved with complicated growth or impurity disordering technologies.

Chapter 4 describes how to achieve antiguided array lasers with a thin p-clad laser structure and how to design a thin p-clad structure for antiguided arrays. After a brief explanation of a thin p-clad laser structure, two major characteristics of the structure for fabricating antiguided arrays are introduced. They are drastic changes in refractive-index and mode loss of a transverse lasing mode with small changes in the p+-cap layer thickness, which make it easy to induce the required index modulations for antiguided array lasers with a simple modulations of the p+-cap layer. A new concept, "processwindow," is also introduced, and with the concept, various design aspects of epitaxial structures and array dimensions are explored.




15


Chapter 5 is assigned for device fabrication. First, an etching technique of pulsed anodization is explained with details of basic set-up, electrolytes and their preparation, circuit parameters, oxide thickness and etch rate. Electroplating for gold metallization is used for making shiny contacts (low metal loss contact) along with the electron beam evaporation technique. The electroplating technique is also described and the fabrication sequence of MCTC antiguided array lasers is shown with brief explanations.

In Chapter 6, device characterizations are presented. Starting with a near- and farfield measurement set-up, measured near-field and corresponding far-field patterns are shown. Beam widths of the far-field main lobes and power percentage in the main lobes are discussed. Then, other electrical-optical characteristics such as P-I curve and slope efficiency are shown and discussed.

Chapter 7 summerizes this work and future work is addressed. For easier fabrication of more stable antiguided array lasers, a new thin p-clad epitaxial structure is proposed. This new structure employes a design of a three layer cap including a lossy quantum layer sandwiched between two p- cap layers.












CHAPTER 2
FOURIER OPTICS AND SEMICONDUCTOR LASER ARRAYS


2.1 Introduction

In order to understand the behavior of the output beam (far-field) from a laser array, the relation between the near-field at the laser facet and the far-field using Fourier optics was studied. In Sec. 2.2, the basic concepts of Fourier optics are explained briefly, and the Fraunhofer approximation is used for practical calculations of far-field patterns. In Sec. 2.3, the computation formalism of the far-field from an array of light sources is introduced. Several far-field patterns from different near-field patterns are calculated and the resulting plots are shown. This calculation shows the need for phase-locking between array elements to have a narrow central lobe in the far-field patterns which contains most of the beam power. The phase-locked mode for this type of operation is called 'in-phase' array mode. Basically, the phase-locking condition is said to be 'in-phase' when the fields in each element are cophasal and 'out-of-phase' when the fields in adjacent elements are a ;r phase-shift apart. For an out-of-phase array mode, the corresponding far-field has two main lobes. For most applications using semiconductor laser arrays, in-phase mode operation is desirable, and hence the characteristics of in-phase far-field patterns are focused on to investigate the effects of array dimensions on FWHM of the central main lobe and power percentage in the main lobe.

Once the necessary conditions for achieving an in-phase near-field distribution are known, the next question is how to achieve these conditions in laser array devices.


16




17


Section. 2.4 has the answer to this question. Individual element lasers in an array should be able to "talk to" the other element lasers in order to have the same phase with others (phase-locking). This means that the optical field of each element laser should reach to the other lasers and interact with them (coupling). Several coupling schemes used in semiconductor array lasers are presented as well as fabrication techniques.

In Sec. 2.5, array mode stability with thermal and/or carrier-induced refractiveindex variations in the array structures is addressed. This leads to antiguided array lasers for more stable in-phase operation with increasing drive level.


2.2 Fourier Optics and far-field Patterns

Fourier optics provides a description of the propagation of light waves based on harmonic analysis (the Fourier transform) and linear systems. Harmonic analysis is based on the expansion of an arbitrary function of timef(t) as a superposition (a sum or an integral) of harmonic functions of time of different frequencies. The harmonic function F(v) exp(j2'rvt), which has frequency v and complex amplitude F(v), is the building block of the theory. Several of these functions, each with its own value of F(v), are added to construct the functionf(t). The complex amplitude F(v), as a function of frequency, is called the Fourier transform of f(t). This approach is useful for the description of linear systems. If the response of the system to each harmonic function is known, the response to an arbitrary input function is readily determined by the use of harmonic analysis at the input and superposition at the output.

An arbitrary function f(x,y) of the two variables x and y, representing the spatial coordinates in a plane, may similarly be written as a superposition of harmonic functions of x and y of the form F(V,,vy) exp[-j2zr(Vxtx+vy)], where F(vx,vy) is the complex




18


amplitude and v. and vy are the spatial frequencies (cycle per unit length) in the x and y directions, respectively. The harmonic function F(v,, vy) exp[-j27(vx+ vyy)] is the twodimensional building block of the theory.' It can be used to generate an arbitrary function of two variables f(x,y).

The plane wave U(x,y,z) = A exp[-j(kx+kyy+kzz)] plays an important role in wave optics. The coefficients (kx, ky, kz) are components of the wave-vector k and A is a complex constant. At points in an arbitrary plane, U(x,y,z) is a spatial harmonic function. In the z=O plane (near-field plane), for example, U(x,y,O) is the harmonic function, Aexp[j2rvnx+ vyy)], where vx = kJ2r and vy = ky/27r are the spatial frequencies and kx and ky are the spatial angular frequencies. There is a one-to-one correspondence between the plane wave U(x,y,z) and the spatial harmonic function U(x,y,O), provided that the spatial frequency does not exceed the inverse wavelength 1/A. Since an arbitrary functionf(x,y) (near-field) can be analyzed as a superposition of harmonic functions, an arbitrary traveling wave may be analyzed as a sum of plane waves. The plane wave is the building block used to construct a wave of arbitrary complexity.

Apparently, there is a one-to-one correspondence between the plane wave U(x,y,z) and the harmonic function U(x,y,O). Given one, the other can be readily determined if the wavelength X is known. Given the wave U(x,y,z), the harmonic function U(x,y,O) is obtained by sampling in the z=O plane. On the other hand, the wave U(x,y,z) is constructed by using the relation U(x,y,z) = U(x,y,O) exp(-jkzz) with


2 2 2 1/2 2 2 ) 1/2
kz = (k -kx -ky ) =2 l1 = 2/t(1/ -v -v ) k=2t/. (2.1)




19


An arbitrary function fN(x,y) of a near-field distribution at the z=O plane can be written as a superposition integral of harmonic functions f1vx,y) = FN(vx, Vy) exp[j2,(vx+ vyy)], and the complex amplitudes FN(vx, vy) can be found by the Fourier transform of fN(x,y);

FN(vx, vy) = I fN(x, y) exp[j 2r (vxx + vyy)] dx dy (2.2) and then

fN(x,y) = ffv(x,y) dvxdvy

= fFN(Vx, Vy) exp[-j2t (vx + Vyy)] dvdvy. (2.3)


The response functions Ufx,y) at the z=1 plane (far-field plane) to the harmonic functions fax,y) can be obtained by the relation described above, U(x,y) = flx,y) exp(jkzl), and the far-field distribution function fF(x,y) at the z=1 plane, corresponding to the near-field function f(x,y), is obtained as a superposition integral of the response functions UVx,y);


fF(x,y) = IfUv(x,y) dvdvy

= fFN(v.,v ) exp[-j2t(vxx +v y)] exp(-jkzl) dv dvy (2.4) where kz is a function of v. and vy given in equation (2.1).

Although the far-field distribution due to an arbitrary near-field distribution can be evaluated with equation (2.4), the real computation of the far-field can be very complicated. The Fraunhofer approximation, however, can be used when the propagation distance 1 is sufficiently long (see Figure 2-1). With the approximation, fF(x,y) is proportional to the Fourier transform FN(vx, Vy) of the near-field functionfN(x,y), evaluated




20


at the spatial frequencies v,x = x/M) and vy = y/M:



f,(x ,y) =j exp(-jkl) exp-jx F (-, ) (2.5) This approximation is valid if fN(x,y) is confined to a circle of radius b satisfying b2/)d <1, and this condition is easily satisfied for practical far-field calculation. The details of the Fraunhofer approximation can be found in most Fourier optics textbooks [26, 27].

The expression for the far-field intensity distribution IF(x,y), which is an actual measurement with experiments, is obtained by multiplying the complex conjugate of fF(x,y) with fF(x,y);
1 (X y)'2
IF(x,Y) fF(x,y) f *(x,y) () F -, ). (2.6) Then, the angular distribution pattern for the far-field intensity FF(Ox,Oy) can be defined by the absolute value of the Fourier transform FN(x/2d,y/2) with replacing x/l and yll with tanOx and tanO, respectively (see Figure 2-1);

FF (0, 0y) FN (v, vy) 2, vx = tan0x/k vy = tan0 y/X. (2.7) Figure 2-2 shows an example of a far-field pattern from a single one dimensional slit of uniform near-field (constant amplitude with constant phase). The width of the slit is D and the amplitude of the near-field is A. The near-field functionfNr(x) can be expressed as follows (see Figure 2-2 (a)):
A -D D
fN (x) = 2 2, (2.8)
0 ;otherwise

and then the Fourier transform FN(v) of fN(x) is found using equation (2.2):

D/2 sin (tvD)
FN(V) = /A exp (ji2cvx) dx =AD (2.9)
o=C1 xvD




21
The angular far-field pattern function FF(9), ignoring a constant value of AD, is obtained using equation (2.7) (see Figure 2-2 (b)):

FF (O) = sin (7D tan O/X) 2 (2.10) cD tan9/X
The first zero point (0d) in the far-field pattern plot is found from sin(7rD tan / 2) = 0 and 0d is approximately the same with the full width at half maximum (FWHM) of the main central lobe (FWHM = -0.9 Od):

d=Tan- =) ,if D >> X. (2.11)


The angle 0d is called a divergence angle (well known as a diffraction characteristic of a single slit source) and the divergence angle reduces as the slit width D increases.









X, Y)
x1







Near-field (f(x,y)) plane


Far-field (fF x,y)) plane

Figure 2-1. When the distance I is sufficiently long,fF(x,y) is proportional to
the Fourier transform FN(vx, vy) of the near-field function fN(x,y),
evaluated at the spatial frequencies vx = x/Xl and vy = y/Al.

fN/x) FF(0) A /

SFWHM
/ \

-D/2 D/2 x Od 0
(a) (b) Figure 2-2. Far-field pattern (b) from a single slit source of uniform near-field (a)




22



2.3 Far-Field Patterns from Arrays of Light Sources

Consider a one dimensional array of N equally spaced identical elements corresponding to individual laser-array elements. Assuming that the near-field distribution functions of the individual array elements are the same and can have different complex amplitudes (see Figure 2-3), which is applicable to most practical cases, the near-field functionfNa(x) for the array can be expressed as follows:

M
fNa(x) = AnfN(x-nT) (2.12)
n = -M

where the total number of array elements is N = 2M + 1,fN(x) is the near-field distribution for the center element at the center of which the origin of the coordinate system is located, An is the complex amplitude of the n-th element, and T is the center-to-center distance between two adjacent array elements.




-MT -T -d/2 0 d/2 T MT


A_Mf(x+MT) AfN(x+T) AOfN(x) AfN(x-T) AfN(x-MT)


Figure 2-3. One dimensional array of N (2M+1) equally spaced identical elements.




The Fourier transform offNa(x) is, then, obtained using equation (2.2):

M
FN(v) = f_AnfN(x-nT) exp(j27rvx)dx. (2.13)
n = -M

By replacing x nT with a new variable u, that is u = x nT, the above equation can be separated into an integral and a summation:




23



FN (v) = f (u) exp (j 2nvu) du] Anexp ( 2nrvT). (2.14) n =-M

From the above expression of FN(v), the far-field pattern for an array of N equally spaced identical elements can be expressed as follows:

FF (6) = Fs(O) F () (2.15)

2 tan 0
Fs (0) fN(x) exp (j 27vx) dxv (2.16)

M 2
Fg () =- Anexp (j 2nvT) ,v = an (2.17)
n = -M

As can be noticed, Fs(O) is the far-field intensity distribution for one of the array elements, and Fg(O) is a function (the so-called grating function) characterizing the array and representing the interference effect of the elements in the array. The far-field pattern of the array is a product of Fs(O) and Fg(O). Since the grating function Fg(O) has periodic major peaks and the angular period of the peaks (9p =Tan -(;T)) is always smaller than the divergence angle of Fs(O) (d = Tan-1(Ald) and Tan- (1.5Ald) for the near-fields of fN(x) = 1 and fN(x) = cos(rx/d) respectively, where-d/2 x < d/2), Fs(O) is the envelope function of the major peaks of the far-field pattern of the array.

In Figure 2-4, an example of the array far-field pattern FF(6) is shown with Fs(6) and Fg(O) forfN(x) = 1, where -d/2 _x _d/2, An = 1, A = 0.95 gm, d = 5 p.m, T = 7 lm, and N = 7, which can be obtained from a uniformly illuminated grating of equally spaced slits. All the functions are normalized and Figure (a) shows the grating function Fg(O) and the single-element far-field pattern Fs(O) while Figure (b) shows the array far-field pattern FF(O) (the product of Fs() and Fg(O)) with Fs(O) which is the envelope function of the far-field major peaks. For this particular case, 0p of Fg(O) is -7.730, 0d of Fs() is




24


-10.760, and the FWHM of the central lobe of the array far-field is -0.990. The peak position of the first major side lobe of the array far-field is -7.600 which is a little shifted from Op (-7.730) because Fs(O) is not constant.



1.2 ... 1.2 ........
Fg(8) F,(8)



0.4 0.4 0.2 1 0.2
0 -- 0.
z
-0.2 : :* I -0.2
-20 -15 -10 -5 0 5 10 15 20 -20 -15 -10 -5 0 5 10 15 20
Lateral angle 0 (degree) Lateral angle 0 (degree)
(a) (b) Figure 2-4. far-field pattern FF(O) (b) with the single-element far-field Fs(O) and the
grating function Fg(O) (a) for an array of 7 uniform near-field slits with the slit width of 5 Jpm, the array period of 7 pim, and the wavelength of 0.95 p.m.


Although a uniform near-field of the slits can be obtained for a diffraction experiment by illuminating the slits with a wide laser beam, the near-fields of semiconductor lasers are not uniform and their near-field profiles are usually approximated to Gaussian or sinusoidal profiles. Therefore, it is not appropriate to use a uniform near-field profile for elements of a semiconductor laser array. Since the lateral near-field profile of antiguided lasers are described as sinusoidal,fu(x) = cos(nrx/d) for the fundamental lateral mode will be used for far-field calculations of antiguided array lasers, where d is the antiguide width. For comparison, the array far-field patterns for the two different cases of the uniform and sinusoidalfN(x) profiles are shown in Figure 2-5. The values for other parameters are the same with the above example: A. = 1, L = 0.95 um, d = 5 Jim, T= 7 im, and N = 7. As




25


shown in the figure, when the sinusoidal fN(x) is used, the width of Fs(6) profile is increased and hence so are the heights of the side lobes of the array far-field. This is because the slit width for the sinusoidal fN(x) is effectively reduced, compared with that for uniform fN(x): the divergence angle of a single slit far-field increases as the slit width reduces. The divergence angle (Od) for fN(x) = cos(nx/d) is Tan-(1.52Jd) (-15.910 for this case) instead of Tan'(bld) (~10.760 for this case) forfN(x) = 1.



1 .2 I 1,,, ,1

1 F(O) for fN(x) = cos(n/d)


0.8
Fs(/) forfN(x)= 1

S0.6

0.4

0.2

0



-20 -15 -10 -5 0 5 10 15 20 Lateral angle 0 (degree)

Figure 2-5. Array far-field pattern forfN(x) = cos(x/xld) compared with that forfN(x) = 1
: An = 1, = 0.95 pm, d = 5 tm, T= 7 .m, and N = 7.

For the above two cases, the complex amplitudes (An) of the element (slit) nearfields were assumed to be uniform across the array. For monolithic semiconductor laser arrays, however, the amplitudes are usually nonuniform across the array because the element lasers of the array are optically coupled to each other. According to the




26


coupled-mode analysis for an array of N coupled, identical elements [28, 29], an array of N emitters has N normal modes or eigenmodes which are called array modes. Each array mode has a field-amplitude (An) configuration that is nonuniform across the array.

Four array modes of a 7 element array are schematically depicted in Figure 2-6 (a) with sinusoidal element near-fields. There is a succession from the fundamental array mode, K = 1, the 00-phase-shift mode defined in Figure 2-6 (a), to the last high-order array mode, K = N (7 for this case), the 1800-phase-shift mode also defined in the figure. The common names of the fundamental (K = 1) and the highest order (K = N) modes are inphase and out-of-phase modes respectively. Shown with a dashed line are the envelope functions of the array-mode near-field amplitude profiles, which correspond to the modes of an infinite potential well of width (N + 1)T.

The far-field patterns corresponding to each array mode are shown in Figure 2-6 (b). The single-element far-field distribution Fs(O) for the sinusoidal element near-field distributionfN(x) = cos(ctr/d) is the dashed curves in the figure and can be obtained using equation (2.16):

Fs (0) = cos (d v) 2 tan (2.18)
(2d v) 2
From this equation, the divergence angle ed is easily proved to be Tan-'(1.SAId). The grating function Fg(O) for the array modes can be calculated using equation (2.17) and the array-mode near-field amplitude (An) profiles shown in Figure 2-6(a): sin (N+ 1) xTv+K tan
F 9,(9) = 2 t 6 K= 1, 2, ...,N (2.19) cos cos (27Ty)
where K is the array mode number, and this equation is not a normalized ex where K is the array mode number, and this equation is not a normalized expression.




27




K= 1; in-phase mode pk =Tan-l(1 )


-WHM



-0pk 0ad 0pk Lateral angle (0)

K= 2; adjacent-in-phase mode










K = 6; adjacent-out-of-phase mode










K = 7; out-of-phase mode








(a) Array modes (b) far-field patterns

Figure 2-6. (a) near-field amplitude profiles: four of the seven array modes of a seven
element array. The dashed curves are the envelope functions of the near-field profiles. (b) far-field patterns corresponding to each array mode: the dashed
curves correspond to the single-element far-field pattern.




28


As mentioned earlier, the angular positions of the array far-field peaks do not exactly coincide with those of the grating function, but the differences are negligible and the peak positions of the far-field can be obtained more easily from the grating function than from the exact far-field function which is a product of the single-element far-field and the grating functions. The peak positions (0pk) from the grating function are


0pk = Tan-(Q ) ;for K = 1 (2.20)



6Pk = Tan- 2 (N+ 1)) ;for 2 5 K N-1, (2.21)



Pk Tan Q -a ] ;for K = N (2.22) where Q is an integer number and K is the array mode number.

From the above results and the array far-field figures, it is obvious that only the K=1 mode (in-phase mode) has a main central lobe at 0 = 00 (straight-forward beam) in its farfield pattern. From a practical point of view, the in-phase mode far-field pattern is desired because the output energy of the array is primarily contained within the main central lobe which is straight-forward and whose FWHM can be very small. Therefore, for semiconductor laser array devices, achieving in-phase mode operation has been the main goal, and this work is also focused on in-phase operation.

A simple expression for FWHM of a main central lobe of an in-phase far-field can not be easily obtained from the expression (FF(O)) of the array far-field pattern. However, the dependence of the FWHM on array parameters such as array dimensions and number of elements in an array is the same with that of divergence angle (0a) of the central lobe, as one might expect. The divergence angle (named 'an array divergence angle')





29


can be obtained from the expression of the grating function and it is

Oad= Tan- (N+I )T 2(N +)T3 [rad]. (2.23) For comparison, the following expression of an array divergence angle is for a uniform amplitude profile (An = 1):


ad =Tan-1 [rad] (2.24) As shown in the above expressions, an array divergence angle depends on the wavelength and the total array width and hence so does the FWHM of the central lobe. For arrays of a few elements (less than 10), the FWHM is almost the same as )NT (loosely defined as the diffraction-limited beam width), and it becomes a little larger than A/NT (1.1 1.2 2/ NT) as the number of array elements increases. More accurate values of the FWHM are obtained from the numerical data of the array far-field pattern calculation which can be easily done using the expressions of Fs(O) and Fg(O).

Since the goal of laser arrays is to obtain high output power in a narrow straight-forward beam, it is necessary to suppress the side lobes in an in-phase far-field pattern. In order to do that, one needs to know the determining parameters of power rate of the main central lobe. The power contained in a far-field lobe is proportional to the area of the lobe. The FWHM's of the lobes in a far-field are basically all the same and hence the power contained in a lobe is simply proportional to the height of the lobe. The heights of far-field lobes are determined by the single-element far-field function Fs(O) (the envelope function of an array far-field). Using the expressions of Fs(O) (equation (2.18)) and Opk (equation (2.20)), the ratio (Pc) of the central lobe power to the total power can be expressed as follows:




30



F, (0) csQ T d
P F()+2 F k) = 0.81 (2.25)
Pc= 0 d1_2 1
Fs (0) + 2 Fs (Opk) Q = 1 2 1 Q= 1

The central lobe power rate Pc depends on d/T and, in Figure 2-7, it is plotted as a function of d/T. As shown in the figure, the plot is very linear and Pc can be approximated very closely to 0.81(d/T); Pc can not exceed 0.81 for the sinusoidal element-near-field. For comparison, the expression of Pc for a uniform element-near-field is shown in the following equation and it is also plotted in Figure 2-7:



P= 1+2 (=inQ (2.26)
1 d T







4 0.8
For uniform element-near-field
0 0.6
o

0.4

.." For sinusoidal element-near-field
0.2



0 0.2 0.4 0.6 0.8 1 dlT


Figure 2-7. Central lobe power rate for sinusoidal and uniform element-near-fields




31



2.4 Monolithic Semiconductor Laser Arrays

In order for a laser array to operate in the in-phase array mode, the first condition is that the optical field of the each element laser of the array should reach to those of the other element lasers and interact with them (coupling). In a typical positive-indexguided laser array, for which the near-field intensity peaks are in the high-index array regions (also optical gain regions), this condition is obtained by evanescent fields of the elements when the element lasers are close enough to each other (see Figure 2-8 (a) evanescent-wave coupled array). Three more basic types of coupling schemes are depicted in Figure 2-8: Y-junction coupled array, diffraction coupled array, and leaky-wave coupled array.

Evanescent-wave coupled array devices were the subject of intensive research over the 1983 1988 time period. It has been proved that it is difficult to achieve the in-phase operation with evanescent-wave coupled arrays because they tend to operate in the out-ofphase mode [30, 31]. In order to overcome this problem, several techniques were tried and they included preferential interelement pumping [32], buried-rib-guide element arrays for higher transverse optical-mode confinement in the interelement regions [33 35], chirped arrays [36 -39], and using xt phase-shifters in front of alternate array elements [40 42]. Even though some good results were obtained with those techniques, they were from arrays of a few elements, not from arrays of many elements which are required for high power devices. Performances of those devices were not stable for high pover operations.

As a consequence of the difficulties encountered in obtaining stable in-phase operation from evanescent-wave coupled arrays, alternative coupling schemes were proposed




32


for ensuring in-phase operation. The two basic approaches were Y-junction coupled arrays (interferometric devices) and diffraction coupled arrays. For Y-junction coupled arrays [43 46], Y-shaped single-mode waveguides were utilized (see Figure 2-8 (b)). At each Y-shaped junction, fields from adjacent waveguides couple efficiently to a single waveguide only if they are in phase with each other. If they are out of phase with each other, they are simply lost as a radiation loss because of their destructive interference. Thus Y-junction coupled arrays severely suppress out-of-phase mode operation. Initial results of those arrays were encouraging, but the output beams were rather broad, mainly due to poor discrimination against adjacent modes. In order to improve the mode discrimination, an interferometric array composed of Y-shaped and X-shaped branches has been proposed [47], and Whiteaway et al. have proposed a tree-array device [48]: a fanout of light via Y branches starting from a single waveguide and ending with a large linear array of emitters. However, the implementation of such devices is impractical because of the difficulty of fabricating low-loss, symmetric Y-junctions.

Diffraction-coupled arrays were based on the concept that fields from adjacent waveguides can be made to oscillate in-phase by placing a feedback mirror at an appropriate distance from the waveguides' apertures (see Figure 2-8 (c)). The most complete analysis of such devices was performed by Mehuys et al. [49]. However, just as for Yjunction coupled arrays, due to poor intermodal discrimination, the best results were single-lobe far filed patterns of beam-widths several times the diffraction limit [49].

The three types of laser arrays described above are positive-index-guided devices, for which the near-field intensity peaks and optical gains are in the high-index array regions. Optical coupling between two positive-index-guided elements is not strong




33


because the optical modes in the elements are strongly guided. The weak coupling was the major reason for the failure of positive-index-guided arrays. It is possible to get a strong coupling with those devices by reducing the refractive-index step between element and interelement regions. However, those array devices with a smaller refractive-index step are more susceptible to thermal and/or carrier induced refractive-index variation which leads to unstable device operation.











_I i' .......... i .......... L ..........L
(a) (b)










..... . .. ."
(c) (d) Figure 2-8. Schematic diagrams of basic types of phase-locked linear arrays of
semiconductor lasers. The bottom traces correspond to refractive-index
profiles. (a) Evanescent-wave coupled array. (b) Y-junction coupled array.
(c) Diffraction coupled array. (d) Leaky-wave coupled array.


Strong coupling and large refractive-index step can be obtained with negativeindex-guided arrays for which the near-field intensity peaks and optical gains are in the





34


low-index array regions. Since optical modes of those arrays are confined in low-index regions, the modes are antiguided and leaked to the lateral directions. Hence, a very strong coupling can be obtained by the leaky waves propagating through interelement regions in negative-index-guided arrays (called leaky-wave coupled arrays or more commonly, antiguided arrays, see Figure 2-8 (d)). More detailed discussions about the antiguided arrays will be given in the next chapter.


2.5 Array Mode Stability

As mentioned in the previous section, the weak coupling due to the refractive-indexstep, An, was the major reason for the failure of evanescent-wave coupled arrays (positiveindex-guided), and it is possible to get a strong coupling with those devices by reducing An. There is, however, one major limitation: the built-in index-step, An, has to be below the cutoff for high-order lateral modes in the element regions since the elements should have only the fundamental lateral mode for single-lobed far-field patterns. Since An 5 5 x 10-3 for typical devices, the devices are susceptible to thermal and/or carrier induced refractive-index variation and gain spatial hole burning which lead to unstable device operation as drive level increases.

Due to the weak coupling, the near-field profile of the in-phase array mode of a uniform evanescent-wave coupled array has a raised-cosine-shaped envelope (from coupledmode theory). Thus, with increasing drive above threshold, gain saturation due to local photon density is uneven: so-called gain spatial hole burning. The gain is saturated mostly in the central elements, which, in turn, creates a local increase in the refractiveindex profile due to a decrease in carrier density. As the refractive-index of the central elements increases, the optical modes in the elements are more strongly guided, which




35


results in higher near-field peaks in the central elements. The net effect on the in-phase mode is self-focusing, which further accentuates the mode-profile non-uniformity. Thus a positive feedback mechanism is created, which, with increasing drive, narrows the nearfield and broadens the far-field beam-width. At the same time, since the area of the array is uniformly pumped, more and more gain is available for the high-order modes (adjacent modes) which can reach threshold and cause further broadening of the far-field beamwidth. Therefore, the in-phase mode of evanescent-wave coupled arrays is fundamentally unstable with increasing drive level.

Unlike evanescent-wave coupled arrays, there is no limitation on An for antiguided arrays (leaky-wave coupled); that is, no matter how high An is, the fundamental lateral mode is favored to lase in the elements. This fact makes it possible to fabricate in-phase operating arrays with high index-steps (2 0.01) which are stable against thermal and/or carrier induced refractive-index variation. Since the elements can be strongly coupled by leaky waves in antiguide arrays, the envelope of the near-field profile of the in-phase mode can be nearly flat unlike the prediction of coupled-mode theory which is for weakly coupled devices. Hence, gain spatial hole burning can be prevented in antiguided arrays. In conclusion, for high-power devices, antiguided arrays are what ensure stable in-phase operation to high drive levels.













CHAPTER 3
ANTIGUIDED ARRAYS


3.1 Introduction

A monolithic array of phase-coupled diode lasers can be described simply as a periodic variation of the real part of the refractive-index. Such a system can have two classes of modes: evanescent-type array modes, for which the near-fields are peaked in the highindex array regions; and leaky-type array modes, for which the near-fields are peaked in the low-index array regions. An array of the leaky-type array modes is called an antiguided array. When the high index array regions are pumped, evanescent-type array modes are favored to lase, while antiguided array modes are favored to lase when the lowindex array regions are pumped. Another distinction is that the effective refractive-index of antiguided modes are below the low refractive-index value while those of evanescenttype modes are between the low and high refractive-index values. For both classes of modes, the phase-locking condition is said to be 'in-phase' when the fields in each element are cophasal, and 'out-of-phase' when fields in adjacent elements are phase-shifted by 1800.

In this chapter, the basic properties of a single antiguide are first discussed in Sec 3.2. Then antiguided arrays are introduced and the details of the arrays are discussed in Sec 3.3: resonant leaky-wave coupling, antiguided array modes with far-field patterns, grating functions for antiguided arrays and mode discrimination mechanisms. Finally, fabrication techniques of antiguided array lasers are presented in Sec 3.4.


36




37



3.2 Single Real Refractive-Index Antiguides

The basic properties of a single real refractive-index antiguide are schematically depicted in Figure 3-1. The refractive-index of the antiguide core is denoted as ne which is lower than that (ni) of the cladding. The typical index depression, An, is (1 2) x 10-3 for simple gain-guided lasers and (2 5) x 10-2 for strongly index-guided lasers. The effective refractive-index of the fundamental lateral mode is lower than the core refractive-index. By contrast, the effective index of the fundamental mode in a positive-index guide is between the low index of the cladding and the high index of the core. Whereas, in a positive-index guide, optical mode is confined in the core via total internal reflection, in an antiguide, optical mode is partially confined in the core and partially leaked out to the cladding (see Figure 3-1 (c)). The lateral wavelength k1 of the leaky wave can be obtained using the equations with the diagram shown in Figure 3-1 (c), where ke and ki are the propagation vectors in the core and the cladding, re and Ki are their lateral components respectively, P is the longitudinal component of the propagation vectors which is the same in both regions and 0 is the vacuum wavelength:


t 27u (3.1)
S [ni -ne] + [ (J + l),/ (2d) ]2

where J is the lateral mode number (J = 0 for the fundamental mode). The radiation leaking to the cladding can be considered as a radiation loss a [50]:

(J + 1)2 X02 2
ar = x Fl (3.2)
d3 e 2ne (ni ne)

where Fis the lateral propagation confinement factor.




38






i





(b)




.... ..... .... .. .. ......... .. ..... = nk..... ....



Ke = ke cos e

ii = ki cos0i
(c) = k sin0e = ki sin0i (keS 2t) keS2 = J (27r) D AB = S1 ne cose = (J + 1)X0 / (2d) CD = S2 where J = 0, 1, 2,...






Figure 3-1. Schematic diagrams of a real refractive-index antiguide: (a) real refractiveindex profile; (b) near-field amplitude profile of the fundamental lateral mode,X1 is the lateral wavelength of leaky-wave; (c) ray-optics picture.



Since the radiation loss UT is proportional to (J + 1)2, the antiguide acts as a lateralmode discriminator, that is, the fundamental lateral mode is favored to lase in the antiguide. In Figure 3-2, shown are the radiation losses as a function of lateral index step An for the fundamental (J = 0) and the first order (J = 1) lateral modes with d = 5 tm, X0 =




39


0.95 pm, ne = 3.263 and antiguide core gain ge of 20 cm"1. The loss difference between the two modes is ~60 cm- at An = 0.2, which is a quite large discrimination against the first order mode.



500 1 1 1. 1 1.


400 --- J=


8 300
0
200 100



0 0.05 0.1 0.15 0.2 An

Figure 3-2. Radiation loss as a function of lateral index step An for J = 0 and J = 1 lateral
modes with d = 5 .tm, ;.0 = 0.95 m, ne = 3.263 and antiguide core gain ge of
20 cm-1.




3.3 Antiguided Arrays

Owing to lateral radiation, a single antiguide can be considered as a source of laterally propagating travelling waves of wavelength X1 (see Figure 3-1 (b)). Then in an array of antiguides, elements will be resonantly coupled in-phase or out-of-phase when the interelement spacings (s) correspond to an odd or even integral number (m) of half the lateral wavelength (X- / 2), respectively. From this condition and the expression of X1 (equation (3.1)), the resonant phase-locked coupling condition is




40




s = m -X ;m = 1,2,3,...,
(2)


2 n 2 = ( 2 ( (J + 1) (3.3)
i e 2s 2d

where d is the element width, ne and ni are the real refractive-indices of element and interelement regions, respectively and J is the lateral element mode number. In order to have a single central lobe in a far-field pattern, J should be 0 with in-phase coupling (m = odd). As examples, in-phase (m = 1) and out-of-phase (m = 2) array modes of a 5-element antiguided array are shown in Figure 3-3. For these and all other examples in this work, d =

5 p.m, s = 2 pm and kg = 0.95 p.m are used.



d s

---i n








(a) (b) Figure 3-3. Near-field amplitude profiles of array modes of a 5-element antiguided array:
(a) m = 1 in-phase mode; (b) m = 2 out-of-phase mode; m also corresponds
to number of near-field intensity peaks in the interelement regions.




When the resonance condition is met, the interelement regions act like Fabry-Perot resonators and the lateral coupling between elements is maximized. The envelope function of the near-field peaks of in-phase or out-of-phase modes becomes uniform as the




41


lateral coupling strength increases. In Figure 3-4, two near-field amplitude profiles of

resonant and non-resonant m = 3 in-phase array modes and the corresponding far-field

patterns of a 5 element antiguided array are compared. As shown in the figure, the

envelope function of the near-field profile of the resonant mode is uniform while that of

the non-resonant mode is cosine-shaped. This difference in the envelope function of the

near-field peaks mainly affects the FWHM of the far-field pattern and it does not strongly



1.2
FWHM = 1.390


(aI\ i\ \
(a /\ 0.4 01 =7.620
'2 i i'" Il ,,


-0.2 I I
-20 -15 -10 -5 0 5 10 15 20 Resonant in-phase mode Lateral angle (0)


1.2
A FWHM = 1.60:


I\ 0.6
(b)
\ / 0.41 = 7.590
-- Y 0 a.2\


-0.2
-20 -15 -10 -5 0 5 10 15 20 Non-resonant in-phase mode Lateral angle (0)


Figure 3-4. Near-field amplitude profiles of resonant (a) and non-resonant (b)
m = 3 in-phase array modes and their corresponding far-field patterns:
for the resonant mode, ne = 3.263 and ni = 3.339; for the non-resonant mode
ne = 3.263 and ni = 3.370.




42


affect the angular positions of the side lobes and the central lobe power rate since they mostly depend on the array geometry (see Sec. 2.3). For this particular case, the difference in FWHM between the resonant and non-resonant far-fields is -0.210, while the difference in the angular position of the side lobes is only -0.030, and the central lobe power rates are virtually the same for both modes.

The envelope functions of the near-field profile of the in-phase and out-of-phase modes in an antiguided array can be generalized with a cosine function: for in-phase array modes, An = Aocos (ntT/L) and An = A(-1) ncos (nxtT/L) for out-of-phase modes, where An is the height of the n-th near-field amplitude peak from the center of the array and L > NT. The value of L for a mode can be obtained from the near-field profile. It is a measure of the coupling strength of the mode and becomes infinite for a resonant mode. Using equation (2.17) with the above expressions for An, the grating functions for the in-phase and out-of-phase modes of an antiguided array are obtained as follows:

for in-phase modes;

F (0) = [sin (Nu) + sin (Nv)2,+ 2Tv),v 2Tv (3.4)
Ssinu sinv 2 L2 L

for out-of-phase modes;
Fg() = Fcos (Nu) cos (Nv) 2, = (T
S L cosu cosv = + 2Tv ,v= -2TV (3.5)
S 1cosu cosy 2 L 2 L

where v = tan6 / X. Thus the far-field patterns of antiguided in-phase and out-of-phase modes can be explained with the above expressions of Fg(O) and equation (2.18) for the expression of Fs(O) (single-element far-field pattern).

Although a resonant in-phase mode is the most desirable mode because the uniform envelope of the near-field profile makes the device insensitive to gain spatial hole burning




43


and thus stable with high drive levels (see Sec 2.5), it is not always the most favorable mode to lase, since it is not always the mode which has the lowest mode loss. On the contrary, the radiation loss of an in-phase mode becomes maximum when the index step An approaches the resonance point. As shown in the Figure 3-5, for the in-phase (m = 3) mode, resonant coupling occurs when the radiation loss is maximum (the point indicated with the vertical dashed line). At the resonant coupling point, however, the out-of-phase mode is the most favorable mode to lase because it has the lowest loss.




12 i''

10 --adjacent in-phase

8 out-of-phase
-t 6
S'in-phase

4

2 -'



0.04 0.06 0.08 0.1 0.12 An

Figure 3-5. Mode radiation loss as a function of lateral refractive-index step An (= ni ne)
for a 5 element antiguided array: ne = 3.263, d = 5 Lm, s = 2 tm, and
o = 0.95 tm



In order to make the in-phase mode lase, some mode discrimination against the outof-phase and adjacent modes should be provided. One way to enhance the mode discrimination against the out-of-phase and adjacent modes is to make the interelement




44


regions lossy. Figure 3-6 shows significant enhancement in the mode discrimination when the interelement regions are lossy. In this figure, an interelement loss (Ci; material loss in the interelement regions) of 200 cm"1 was used and the array dimensions and the element refractive-index were the same with those used for the radiation loss plot (Figure 3-5). The mode loss of the in-phase mode near the resonant coupling point is almost not affected by the interelement loss while that of the other modes is significantly affected. The mode loss of the in-phase mode at the resonance point (the point indicated with the left vertical dashed line in Figure 3-6) increases from -6 cm-1 (radiation loss when ai = 0 cm-1) to -7 cm-1 (combination of radiation loss and array mode loss due to ci when oi = 200 cm-1). By contrast, the maximum difference (at the point indicated with the right



70 I I ' I .

60 50

E 40 adjacent in-phase

: 30 out-of-phase

20
in-phase
10


0.04 0.06 0.08 0.1 0.12 An

Figure 3-6. Mode loss (radiation + interelement loss (cti)) as a function of lateral
refractive-index step An (= ni ne) for a 5 element antiguided array:
n, = 3.263, d = 5 p.m, s = 2 p.m, X = 0.95 pm, c = 200 cm-1.




45


dashed line in Figure 3-6) in the mode losses between the in-phase mode and the mode which has the next lowest mode loss increases from -5 cm- (when oq = 0 cm1-) to -25 cm-1 (when oai = 200 cm-1).

The mode discrimination enhancement with interelement loss does not degrade when gain, which is necessary in real devices, is placed in the element regions. Shown in Figure 3-7 are the mode losses for the same array with a material gain (ge) of 40 cm-1 in the element region, in addition to ai = 200 cm-1. The mode loss profiles do not change much and simply down-shift due to the element gain, and the maximum difference in the mode losses is still -25 cm-1.



30 ,

20 ..out-of-phase

10
S adjacent in-phase
-" 0

S-10
-o
-20
in-phase
-30

-40 I I I I
0.04 0.06 0.08 0.1 0.12 An

Figure 3-7. Mode loss (radiation + interelement loss (ai) element gain (ge)) as a function
of lateral refractive-index step An (= ni ne) for a 5 element antiguided array:
ne = 3.263, d = 5 pm, s = 2 jim, X = 0.95 jim, cl = 200 cm-1 ge = 40 cm-.



From these mode loss profiles, it should be noticed that the resonant coupling point does not coincide with the position of maximum mode discrimination against the




46


out-of-phase and adjacent modes and that the in-phase mode is favored to lase only in a certain range of the lateral refractive-index step, where the in-phase mode is the lowestloss mode. The mode loss (or gain) profiles also depend on the array dimensions because the dimensions directly affects the lateral mode confinements in the element (gain) and interelement (loss) regions (this will be discussed in a later chapter). Therefore, for designing antiguided array devices, the mode loss (or gain) profiles should be calculated to find the An range where the in-phase mode operation is most favored.


3.4 Antiguided Array Fabrication Techniques

Historically, the first arrays of antiguided lasers were gain-guided arrays [51] (Figure 3-8 (a)) since an array of current-injecting stripe contacts provides an array of carrierinduced refractive-index depressions for which the gain is highest in the depressed-index regions. While the radiation losses can be quite high for a single antiguide [52], closely spacing antiguides in linear arrays reduces the device loss significantly [53], since radiation leakage from individual elements mainly serves the purpose of coupling the array elements.

The first real-index antiguided array was realized by Ackley and Engelmann [54]. This was an array of buried heterostructure (BH) lasers designed such that the interelement regions had higher refractive indices than the effective refractive indices in the buried active mesas (Figure 3-8 (b)). Since the high-index interelement regions had no gain, only leaky array modes could lase. The device showed definite evidence of phase locking (in-phase and out-of-phase) but had relatively high threshold-current density (5 7 kA / cm2) since the elements were spaced far apart (13 -15 gpm), not allowing for effective leaky-wave coupling.




47




Gain-guide Arrays

~~ proton implant p-clad layer
S-, -. active region optical model n-clad layer

(a)

Buried-heterostructure Arrays

oxid---. p-cap layer
-._. p-c.ad layer active region
n-claa layer
high-index regrowth n-substrate

(b)


Figure 3-8. Schematic diagrams of early antiguided arrays: (a) gain-guided arrays;
(b) buried-heterostructure arrays.



For practical devices, the high-index interelement regions have to be relatively narrow (1 3 pm), which is virtually impossible to achieve using BH fabrication techniques. Instead, one can fabricate narrow, high-effective-index regions by periodically placing high-index waveguides in close proximity (0.1 0.2 ptm) to the active region [16, 50]. In the newly created regions (interelement regions), the fundamental transverse mode is primarily confined to the passive guide layer (high-index waveguide layer) and thus the transverse mode gain in the interelement regions is low. In order to further suppress oscillation of evanescent-wave modes, an optically absorbing material can be placed in the interelement regions.

The first closely spaced, real-index antiguided array was realized by liquid-phase epitaxy (LPE) over a patterned substrate [16]. Initially, a passive-waveguide structure




48


(Al0.3Ga0.7As / A101Gao.9As) is grown on top of a GaAs substrate. Then channels are etched and a planar DH (double-heterostructure) laser structure is regrown, taking advantage of the LPE-growth characteristics over patterned substrates [55]. Each buried interchannel mesa had both higher effective refractive-index and lower transverse mode gain than the channel regions. Devices made in late 1980's and early 1990's were fabricated by metal-organic chemical vapor deposition (MOCVD) and can be classified into two types: the complimentary-self-aligned (CSA) stripe array [15, 50] (Figure 3-9 (a)); and the self-aligned stripe (SAS) array [18, 19] (Figure 3-9 (b)).



Complimentary-self-aligned Arrays
p-GaAs
p+-GaAs (cap layer) p-A10.6Ga0 4As clad layer) p-A10.3Ga0.7As (passive guide) S p-A10.6Ga0.4As (clad layer) active region
n-A10 6GaO 4As (clad layer)
(a)

Self-aligned-stripe Arrays
p-GaAs
p-Al0.6Ga0.4As (clad layer) S _ ___ p-Alo.3Ga0.7As (passive guide) . ctive region
-A10.6Ga0.4As (clad layer)
(b)


Figure 3-9. Schematic diagrams of present antiguided arrays: (a) complimentary-selfaligned (CSA) arrays; (b) self-aligned-stripe (SAS) arrays.


In CSA-type arrays, preferential chemical etching and MOCVD regrowth occur in the interelement regions. For SAS-type arrays, the interelement regions are built-in




49


during the initial growth and then etching and MOCVD regrowth occur in the element regions. Note that, for SAS-type arrays, the passive guide and loss regions (interelement regions) can be incorporated in one layer [18].

Although CSA-type and SAS-type arrays have been demonstrated with significant results, the fabrication yields of in-phase device are very low. The reason for the low yields is that the etching and regrowth techniques are too complicated to precisely control the array parameters such as the effective refractive-indices of the element and interelement regions which strongly depend on material compositions of epitaxial layers and thicknesses of the layers.

In principle, the effective refractive-index of the transverse mode can be easily affected by simply changing the thickness of the cap layer if the p-clad layer is thin enough to achieve a significant transverse-mode-overlap with the cap layer which has a higher index than the clad layer: this type of an epitaxial structure is called a thin p-clad laser structure. Therefore, the periodic index variations can be obtained by periodically modulating the cap thickness of a thin p-clad structure with simple etching techniques. We have already demonstrated this type of array (modulated cap thin p-clad antiguided array lasers) [25] and they are the subject of this work.













CHAPTER 4
MODULATED CAP THIN P-CLAD ANTIGUIDED ARRAY LASERS


4.1 Introduction

In most diode laser applications, it is desirable that the laser devices have low threshold current density and high differential quantum efficiency. In order to fulfill these two requirements, semiconductor laser structures must be designed to have both high optical field and carrier confinements in the active region. Normally this is obtained by making the cladding layers thick, usually greater than the lasing wavelength. However, as the name indicates, thin p-clad laser structures have a thin p-clad layer with a thick n-clad layer for different device purposes.

Since the p-clad layer of thin p-clad structures is thin, the separation distance between the active region and the p-contact layer can be small enough to cause a strong interaction between lasing modes (transverse modes) and the contact layer. Utilizing this characteristic of thin p-clad structures, one can easily affect the lasing modes by affecting the cap-layer (changing the cap-layer thickness or contact metal). This has been shown in several publications relating the utilization of thin p-clad laser structures with the fabrication of surface-emitting [56, 57] and edge-emitting [58] distributed feedback (DFB) lasers.

In Sec 4.2, the basic properties of thin p-clad laser structures are discussed which include cap-thickness dependence of effective refractive-index and mode loss for transverse modes. Utilizing those properties, modulated cap thin p-clad (MCTC) antiguided


50




51


arrays are introduced in Sec 4.3. In this section, array mode gain profiles are presented, and a new concept called 'process-window' is defined, and the matter of epitaxial layer design of thin p-clad structures for MCTC antiguided arrays is addressed. Sec 4.4 is devoted to design aspects of MCTC antiguided arrays for optimum device performance.


4.2 Thin P-clad Laser Structure

Figure 4-1 shows the thin p-clad laser structure used in this study which consists of a 1400 nm n-Al0.6Ga0.4As clad layer grown n-GaAs substrate, a -420 nm active region, a 200 500 nm p-Alo.6Ga0.4As clad layer and p+-GaAs cap layer whose thickness is modulated between -100 nm and -250 nm for MCTC antiguided array devices. The active region is composed of a 8 nm In0.15Ga0.85As undoped strained quantum well (QW) layer sandwiched between two 7 nm GaAs barrier layers, 200 nm graded p- and n-AlxGal_-As guide layers (x = 0.3 0.6) above and below the sandwich layers respectively. The emission wavelength of this structure is 950 nm. Note that the p-clad is much thinner than the n-clad, which has a typical thickness. Figure 4-1 also shows the refractive-index profile of the structure and the fundamental transverse mode (TEO mode) profiles corresponding two different cap-thicknesses. It should be noticed that the refractive-index of the cap layer is greater than those of the clad and guide layers. In the following discussion, it will be apparent why the higher refractive-index of the cap layer is important.

Since the transverse mode profile can extend to the cap layer because of the thin pclad layer and the refractive-index of the cap layer is larger than that of the p-clad layer, the mode becomes trapped in the cap layer as the cap-thickness increases. When this occurs, the mode-overlap with the cap layer becomes significant. The effective refractive-index of the mode is proportional to the integral of the product of the layer refractive




52




refractive-index

100 nm p+-cap: GaAs

p-clad: A10.6Ga0.4As 200 500 nm active region
.nGaAs/GaAs SQW, AlGaAs guid

TE, mode TEO mode

n-clad: Al0.6Gao.4As 1400 nm





n-substrate: GaAs





Figure 4-1. Epitaxial layer structure of thin p-clad InGaAs single quantum well lasers;
and fundamental transverse mode (TEo mode) profile change with cap
thickness change; refractive-index profile of the layer structure.




index and mode-overlap with the layer. When the cap layer thickness is small, the mode profile overlaps mostly with the active and clad layers, as shown in the figure, and most of contributions to the effective mode index come from those layers. As the cap thickness increases, the mode overlap with the cap increases, and the contribution of the cap layer to the effective mode index also increases. This results in a higher effective mode index since the cap layer index is higher than those of the clad and guide layers (ignoring the contributions of the thin barrier and quantum well layers). If the cap layer is lossy, the




53


loss of the transverse mode also increases as the cap thickness increases. However, if the cap layer has a lower refractive-index than the p-clad layer or if it is too lossy, these can not occur since the mode intensity can not build up in the cap layer.

Using the structure shown in Figure 4-1 with a 500 nm p-contact metal layer of gold and with a 100 nm oxide layer between the cap layer and the gold layer, the effective mode index and loss of the TE0 mode were calculated with a cap thickness range from 50 nm to 500 nm and the results are shown in Figure 4-2. This calculation was done with the program MODEIG [59] for multi-layer waveguide structures. For this calculation, the p-clad layer thickness was 465 nm, 950 nm was used for the wavelength and a free carrier absorption loss of 120 cm-lin the cap layer was used. As can be seen in the figure, both the effective index and the mode loss start to increase rapidly when the cap thickness increases beyond 150 nm. For the structure with an oxide layer (100 nm) between the cap layer and the gold layer (500 nm), both the effective index and the mode loss start to increase earlier than those for the structure without the oxide layer. This is because the refractive-index of the oxide layer (-1.8) is lower than that of the cap layer (-3.5) and thus the oxide layer helps the mode intensity build up in the cap layer. The mode loss is composed of the cap loss and the metal loss. Most of the loss for the structure with the oxide layer is due to the free carrier absorption loss in the cap layer.

Utilizing the characteristic of large effective index change with a small variation of the cap thickness of thin p-clad structures, the required large index step between the element and interelement regions of antiguided arrays can be easily fabricated by simply etching the cap layer.





54





Effective index /Au ....... Effective index /Oxide/Au
3.5


o 3.45

3.4 ,
(a) E
3.35

3.3


3.25 100 200 300 400 500
Cap thickness (nm)

-- Loss /Au .....-- Loss/Oxide/Au
200


150


(b) 100


S 50



100 200 300 400 500
Cap thickness (nm)



Figure 4-2. (a) Effective refractive-index of the fundamental mode (TEo) as a function
of cap layer thickness; (b) Mode loss of the TEO mode as a function of cap
layer thickness; p-clad thickness = 465 nm, oxide thickness = 100 nm
Au (gold) thickness = 500 nm




55


4.3 Modulated Cap Thin P-clad (MCTC) Antiguided Array Lasers

A cross section of a typical MCTC antiguided array laser structure is shown in Figure 4-3 (a). The cap layer for p-metal contact is highly p-doped GaAs and the structural variation is etched into cap layer to induce the index modulation as shown in Figure 4-3

(b). The oxide layer in the interelement regions is used to confine carriers and hence optical gain in the element regions. The thickness of the oxide is usually -100 nm. The oxide is a GaAs native oxide and can be formed on the cap layer with pulsed anodization technique which will be discussed in the next chapter. The metal contact can be different in the element and interelement regions, but the metal contact in the element regions should be "shiny" in order to reduce the optical loss due to mode overlap with the metal layer [60]. The symbols, te and ti, are designated for cap layer thicknesses in element and interelement regions, respectively. As used before, d and s are element and interelement dimensions, respectively. For the p-clad thickness, the symbol tcE is used. The associated lateral effective refractive-index variation (index step: An0) for a TEO mode, to a first approximation, is given by the difference in effective index between the TE0 mode in each region of the structure. In addition to the higher index, the mode loss of theTE0 mode in the interelement regions is higher than that in the element regions as shown in Figure 4-3

(b). This is another merit of the thin p-clad structure since higher mode loss in the interelement regions is required to discriminate against out-of-phase and adjacent modes as discussed in Chapter 3. The interelement loss can be further increased by using a very lossy metal with a thinner oxide layer for the metal contact in the interelement regions. In this work, noe and noi are the effective refractive-indices for a TE0 mode in the element and interelement regions, respectively and % and ci are the TEO mode losses in the element and interelement regions, respectively.





56




:interelement: element region region s d
4 ----- *-+:4 -------------p+- cap: GaAs : te


p clad: Al.6Ga.4As : tcl optical mode

~QW: InCA guide: AldaX
- O:In ...G -uide: AlbaAs

n clad: Al.6Ga.4As
(a)





> nbi 4 c0 b
d s
0
"0 noe. V Oo eN


position

(b)




Figure 4-3. (a) Modulated-cap thin p-clad (MCTC) antiguide array laser structure;
(b) TEo modal refractive-index and loss profile for (a).



In order to discuss MCTC antiguided arrays, we need to define antiguided array modes more descriptively than the simple definition of in-phase, out-of-phase and




57


adjacent modes. Botez et al. used the number of null points (within an array) in the nearfield profiles to define antiguided array modes [50]. Their definition, however, does not include the array modes which are composed of the first or higher order lateral modes in the element regions because the null number of an array mode which consists of the fundamental lateral modes in the element regions can be the same with that of an array mode which has the first or higher lateral mode in the element regions.

With three numbers, an antiguided array mode (AM) can be defined as AMiml, where j and m are the numbers of intensity peaks in the element and interelement regions and I is the number of null points of the envelope of the near-field profiles. Four example array modes for a 5-element array are shown in Figure 4-4. Figure 4-4 (a) is an AM130 mode (in-phase mode): it has one peak in the element regions and three peaks in the interelement regions, the envelope profile of the array mode doesn't cross the axis within the array (zero null point). For the other array modes shown in the figure, the mode numbers can be figured easily. Note that the total numbers of null points of AM131 (Figure 4-4 (c)) and AM220 (Figure 4-4 (d)) modes are the same and hence the two modes can not distinguished from each other with Botez's definition of array modes.

This new definition of array modes, however, will be used only when it is necessary. The common terms, in-phase, out-of-phase and adjacent in- or out-of-phase will be mostly used since those terms have been used for the descriptions of far-field patterns. An inphase far-field pattern has a single central lobe while an out-of-phase far-field has two main lobes separated from each other by the angular distance of -Tan-l((XT), and an adjacent in- or out-of-phase far-field has twin lobes located at the same lobe positions of the in-phase or out-of-phase far-field pattern, respectively (see Figure 2-6).





58


For in-phase modes, the array mode numbers (j, m, 1) should be (1, odd-number, 0) and the modes which have (1, even-number, 0) or (j > 1, m, 0) have out-of-phase-type farfields. A (j, m, I > 0) mode is called the l-th adjacent (j, m, 0) mode.





d s : s





























Figure 4-4. Antiguided array modes: (a) AM130 mode (in-phase);
(b) AM120 mode (out-of-phase); (c) AM131 mode (adjacent in-phase);
(d) AM220 mode (out-of-phase).




The first thing to do when fabricating MCTC antiguided array lasers with a given epitaxial structure is to decide the values of array geometry parameters (cap thicknesses te




59


and ti in the element and interelement regions, element width d, and interelement spacing s). The array dimensions d and s are related to the lateral index step An0 which should be relatively large for stable device performance with high drive levels. There are some constraints on d, s and achievable An0 in a thin p-clad structure, and the dimensions d and s have to be optimized with those constraints. This subject will be discussed in the next section.

Since the lower refractive-index and optical loss in the element region are desired, the cap thickness te in the element regions should be chosen less than 150 nm from the index and mode loss change profiles shown in the figure 4-2 (100 nm for this study). In order to decide the value of ti with the te value and given array dimensions d and s, the mode gain profiles of in-phase, out-of-phase and adjacent array modes have to be calculated as a function of the interelement cap thickness. As mentioned in Sec 3.3, an inphase mode is favored to lase only in a certain range of the lateral refractive-index step An0 where the in-phase mode is the lowest-loss mode. Since An0 corresponds to the interelement cap thickness, with a fixed element cap thickness, it can be said that an inphase mode is favored to lase only in a certain range of the interelement cap thickness. Once the range of the interelement cap thickness is calculated, a value of ti can be chosen in the range where the mode discrimination is maximum.

The effective index method can be employed to calculate the mode gain profiles of the two dimensional (2-D) array structure (transversal and lateral structures). First, the transverse structure is calculated to obtain the effective refractive-index and mode gain or loss of the TE0 mode with different cap thicknesses for the element and interelement regions. Then, those values obtained from the calculation are used for calculating the




60


complex mode indices of the one dimensional (1-D) lateral array structure of the element and interelement regions, which is another simple 1-D multi-layer waveguide structure. From the imaginary part of the complex mode indices of various array modes, array mode gain (loss) profiles are obtained. Since the TE mode is calculated for the transverse structure, TM mode should be assumed for the 1-D lateral structure, although there are no major differences in the results between TM and TE mode assumptions.

In Figure 4-5, calculated mode gain profiles are shown as a function of the interelement cap thickness for two different antiguided array structures: a 5 element and a 18 element array. For the 5 element array structure, d = 6 .m and s = 3.5 pm were used with a 250 nm p-clad thickness (tcl) while for the 18 element array structure, d = 5 p.m and s = 2 pm were used with tcl = 465 nm. For both cases, the element cap thickness was fixed at 100 nm, a 500 nm gold layer was used for the metal contact, and the material gain in the active QW layer was assumed to be 2000 cm-1 for the element regions and 0 cm-1 for interelement regions. At the wavelength of 950 nm, a free-carrier absorption loss of 120 cm-1 was used for the p+-GaAs cap layer.

In these plots of the profiles, the shaded areas are for the interelement cap thickness range where the in-phase mode has the highest mode gain and thus is the most favored mode to lase. The shaded areas also show the mode gain difference between in-phase mode and the mode which has the next highest mode gain. The interelement cap thickness ti to be used for the fabrication of MCTC antiguided array lasers should be within the shaded range. The closer ti is to the point indicated with a vertical arrow in the plots, the more stable in-phase operation with high drive levels will be, because the mode discrimination against the other mode is maximum at the point.





61




50 .

0 in-phase out-of-phase
30

20
Adjacent in-phase
10 -E process-windoxw


160 180 200 220 240 Interelement cap thickness (nm)
(a)

50 ,,
out-of-phas
40
v in-phas

d 30 adjacent in-phase-.

S20

[] process-window


140 160 180 200 220 240 Interelement cap thickness (nm)
(b)


Figure 4-5. Process-windows calculated for two different antiguided array s with te = 100 nm and 2000 cm1 QW material gain in the element regions:
(a) 5 element array with d = 6 gm, s = 3.5 gm, and tcl = 250 nm; (b) 18 element array with d = 5 gm, s = 2 Jim, and tcl = 465 nm.


Since the shaded areas are the range for which MCTC antiguided arrays should be processed, we have named this area the "process-window". For the above particular cases, the widths of the process-windows are less than 20 nm, which indicates that the





62


etching for the interelement cap thickness should be performed very precisely. With the pulsed anodization technique, the etching process can be done with a precision of -10 nm. In addition to the narrow process-window, the thicknesses of epitaxial layers are not generally uniform to such a degree, thus low fabrication yields result. MCTC antiguided arrays were fabricated with both the structures and the fabrication yield of the 5 element arrays operating in the in-phase mode was ~50%, while that of the 23 element arrays, made with the same epitaxial structure used for the calculation of the 18 element arrays, was -5% as can be expected from the process-window differences. Detailed results will be in Chapter 6.


4.4 Design Aspects of Thin P-clad Epitaxial Structures for MCTC Antiguided Array Lasers

For high fabrication yields of stable in-phase mode devices, a large process-window is required: wide width and large mode discrimination. The width and the position of a process-window are related to the slope of the effective refractive-index profile of TE mode and the knee position of the profile (see Figure 4-2 (a)) as well as array dimensions d and s. For a wider process-window, the effective refractive-index of the TEo mode should increase slowly as the cap thickness increases. This leads to the requirement that the refractive-index of the cap layer be smaller than that of the active region, but still larger than that of the clad layer. This can be done theoretically by using ternary material AlGaAs for the cap layer instead of GaAs. By changing mole fractions of the ternary material, the refractive-index of the cap layer can be changed, which leads to a change in the slope of the "refractive-index vs. cap thickness" curve. The thickness of a thin p-clad layer is also an important parameter to engineer the effective mode-index profiles.





63


In Figure 4-6, shown are the changes in the mode-index curve for the interelement regions when the Al composition of AlGaAs material used for the cap layer increases for a fixed p-clad thickness (a) and when the p-clad thickness changes for a GaAs cap layer (b). For this calculation, the graded AlGaAs guide layers (in the active region) described in Sec 4-2 for the structure shown in Figure 4-1 were replaced with Al0.3Ga0.7As layers. The refractive-index of AlGaAs material gets smaller as the Al composition increases. As shown in Figure 4-6 (a), when the Al composition increases while the p-clad thickness is fixed at 400nm, the slope of the mode-index curve decreases, the knee of the curve shifts toward the larger interelement thickness side, and the radius of the knee curvature increases. The shift of the knee causes a shift of the process-window and the increasing radius of the curvature results in a wider process-window. Thus, the combination effects of the decreasing slope and the increasing radius of the knee curvature result in a wider process-window. The radius of the knee curvature can be further increased by reducing the p-clad layer thickness. Figure 4-6 (b) shows the changes of the knee curvature with decreasing p-clad thickness. For this calculation, a GaAs cap layer was used. It is observable that the radius of the knee curvature increases significantly when the p-clad thickness decreases from 400 nm to 200 nm.

In Figure 4-7, a process-window (w2) enhanced by combining the two aspects of larger Al composition of AlGaAs cap layer and smaller p-clad thickness is compared with a process-window (wl) for a typical thin p-clad structure. For window w1, a typical p+GaAs cap layer and a p-clad thickness of 400 nm were used and for window w2, a p+Al0.15Ga0.85As cap layer was assumed with a p-clad thickness of 200 nm. As shown in the figure, the interelement cap thickness range corresponding to the mode-index range




64





3.44 400 nm p-clad a 3.42
3.4 GaAs cap S Al0.05Ga0.95As ca S3.38 AlIo.Ga0.9As ca 7

3 3.36 3.34

3.32
50 100 150 200 250 300 350 400
Interelement cap thickness (nm)
(a)

3.4
3.39 i GaAs cap 3.38 S3.37
3.36
3.35 400 nm p-cla /
3.- 300 nm p-clad/ ,, 200 nm p-cla & 3.33
3.32
50 100 150 200 250 300
Interelement cap thickness (nm)
(b)


Figure 4-6. TE0 mode effective refractive-index profiles for the interelement regions:
(a) with an AlxGal_xAs cap layer (x = 0, 0.05, 0.1) and p-clad thickness of
400 nm; (b) with an GaAs cap layer and p-clad thicknesses of 400, 300,
and 100 nm


indicated with the shaded areas is almost three times wider for the 'Alo.15Gao.85As cap /

200 nm p-clad' structure than that for the 'GaAs cap / 400 nm p-clad' structure. Although

the real process-window width is a function of both the mode index and the mode loss, the





65


mode loss dependence of the process window width can be ignored unless the mode loss is very large. Hence, comparison of the process-window widths between different thin p-clad structures can be done by comparing the mode-index profiles of the two structures.




3.48 I . I . I . . .
3.46 -A10.15Ga0.85As cap / 200 nm -clad
3.44 -GaAs cap / 400 nm p-clad
S3.42
3.4
S 3.38 0 3.36
S3.34
3.32
100 200 300 400 500
Interelement cap thickness (nm)


Figure 4-7. Enhanced process-window (w2) with a AlGaAs cap layer and a reduced
p-clad thickness (200 nm) compared with a process-window of a typical
thin p-clad structure with GaAs cap layer and p-clad thickness of 400 nm.




In order to estimate a process-window width roughly, one has to know the interelement mode-index range corresponding to the process-window. The interelement modeindex range can be estimated using the resonant coupling condition (equation (3.3)) with given values of d, s and noe. The interelement mode-index (noi) range for the processwindow of the m = q in-phase mode (J = 0) is approximately between the two resonance noi values for the m = q in-phase and m = q+1 out-of-phase modes. This gives an easy way to design a thin p-clad structure for MCTC antiguided array lasers since the calculation of the array mode gain profiles is a very time-consuming process.





66

Alternatively, for a wide process-window, a very lossy material can be used for the cap layer because the large loss of the layer suppresses the out-of-phase and adjacent modes severely in the vicinity of the process-window and hence the mode gain profiles of those mode are pushed down. However, there are some limitations to using a very lossy material for a cap layer. If the cap loss is beyond a certain value (it depends on the index profiles of the epitaxial layers and wavelength), the mode intensity in the cap layer cannot be built up enough to give sufficient index change as the cap thickness is increased. Therefore, the loss in the cap layer should not be beyond the limit.

As shown in Figure 4-8, the process-window of an 18 element array of a typical thin p-clad structure is significantly enlarged by replacing the typical GaAs cap layer with a very lossy cap layer. Other than the cap layers, the epitaxial structures for both cases are the same and, for the guide layers, Al0.3Ga0.7As was used instead of the graded AlGaAs layers as used for the interelement mode-index calculation. For the lossy cap layer, the same material with the QW well, InGaAs, was used, assuming that the cap loss is 2000 cm-1 (this number is a random value and was chosen simply to see the loss effects on the process-window). The loss value used for the typical GaAs cap layer is 120 cm-1 which is a practical number at the wavelength of 950 nm. For the lossy cap layer case, the element cap thickness was fixed at 50 nm to reduce the loss in the element region while, for the typical cap layer case, it was fixed at 100 nm. The width of the process-window where the mode discrimination is greater than 2.5 cm-1, for comparison, is -5 nm for the typical cap layer case and that of the lossy cap layer case is -24 nm which is -5 times wider. The mode discrimination, which is an indication of stable in-phase operation, is also greatly improved for the lossy cap layer case. As mentioned in Chapter 3, a large interelement loss increases the mode discrimination significantly as well as the processwindow.





67




40
in- hase
30

20
adjacent in-phase 10
Sout-of-phas
-10
0 El process-window
-10 I . I * 120 140 160 180 200 220 Interelement cap thickness (nm)
(a)

50 I I I I out-of-phase-in-phas
30 adjacent in-phase -.20

N 10
< process-window
0 I * I * I 140 160 180 200 220 240 Interelement cap thickness (nm)
(b)

Figure 4-8. Comparison of the process windows of two 18 element arrays with :
(a) a very lossy cap layer (cap loss = 2000 cm-1); (b) a typical cap layer
(cap loss = 120 cm-1); d = 5 pm, s = 2 Jim, and tcl = 465 nm.


Combining all the aspects discussed in this section with the process-window concept, one can engineer thin p-clad structures for high fabrication yields of stable in-phase

operating MCTC antiguided array lasers with consideration of practical growth and fabrication procedures. One such an epitaxial structure will be proposed in the last chapter.




68



4.5 Design Aspects of MCTC Antiguided Array Lasers

The array mode discrimination is a strong function of the interelement dimension, as well as the interelement loss, because of the lateral array mode confinement effect in the interelement regions. As shown in Figure 4-9, the maximum array mode discrimination is reduced by a factor of two when the interelement width decreases from 2 pm to 1.5 p.m, while maintaining the same array period (7g1m). The reason for this can be explained as follows. The lateral array mode confinement in the interelement regions decreases when the interelement width is reduced, and so does the array mode loss due to the interelement loss. Since the overall array mode gain is the difference between the array mode gain due to the element gain and the array mode loss due to the interelement loss, and the major difference in the overall array mode gain between two array modes comes from the difference in the array mode loss due to the interelement loss. Therefore the array mode discrimination decreases when the interelement width is reduced. On the contrary, the process-window width does not change significantly and the window position is shifted to larger interelement thicknesses. This is due to the fact that the window width mainly depends on the index slope and the window position is determined by the resonance coupling condition which is related to the element and interelement dimensions. Considering these effects, to achieve stable in-phase mode operation, the interelement should be relatively wide and have large interelement loss. However, when the interelement dimension increases, the output power percentage in the central lobe of farfield pattern decreases as discussed in Sec 2.3 since the central lobe power rate is proportional to d/T (= 1/(1+(s/d)). In designing MCTC antiguided array lasers, one has to compromise between wider width for stable operation and narrower width for higher




69


power in the central main lobe unless interelement loss is high enough to get sufficient mode discrimination.





40
AM110 (in-phase)






10 AM210 AM120,



120 140 160 180 Interelement cap thickness (nm)
(a)



AM1 1(in-phase)


.8 30

0AM210
6 20 AM


AM120


140 160 180 200 Interelement cap thickness (nm)
(b)

Figure 4-9. Array dimension effects on the process-window: process-windows for two
19-element arrays with; (a) d = 5 p.m and s = 2 pm; (b) d = 5.5 p.m and
s = 1.5 Lm, obtained using the same epitaxial structure.




70


The basic constraints in designing MCTC antiguided array lasers relate to element and interelement cap thicknesses and their widths. The first constraint is on the refractive-index difference (Ano) for the TE0 mode between the element and interelement regions. The index step, An, should be large enough (An0 2 0.01) for the devices to be insensitive to thermal and/or carrier induced refractive-index variations (see Sec 2.5); this constraint places a lower limit on An0 and hence the interelement cap thickness. The second constraint, which places an upper limit on An0, is that the interelement regions should not lase. As the cap thickness of a thin p-clad structure is increased, the vertical epitaxial structure becomes a twin-waveguide structure which has two eigen modes; in-phase (TEO) and out-of-phase (TE1) modes. The TE1 mode is a radiation mode which has a big mode loss until the cap thickness reaches cut-off for the mode and hence one can ignore theTE1 mode when the cap thickness is smaller than the cut-off thickness. However, beyond the cut-off thickness, the TE1 mode becomes a guided mode and can lase. As the cap thickness increases, both the effective index and the loss of the TE0 mode are also increased. Eventually, the loss of the TE0 mode becomes larger than that of the TE1 mode and the TE1 mode lases (see Figure 4-10). Hence, the cap thickness of the interelement regions should be thin enough that the TE1 mode can not lase; this places an upper limit on the interelement cap thickness and hence Ano. The third constraint regards element and interelement widths. Element width (d) should accommodate only a single fundamental lateral mode (J = 0) for in-phase array mode operation, which limits d to a maximum value (d,.). Interelement width (s) is limited to a minimum value (smin) by photolithography and consideration of array mode discrimination. As discussed before, the ratio r (r= d/s) directly affects the fraction of the output power in the main lobe of the far-field




71


pattern, with a larger ratio producing higher power in the main lobe. On the contrary, array mode discrimination decreases as r increases as mentioned earlier in this section.

Once Ano, da and smin are determined from the basic constraints, optimum values for d and s can be calculated using the following procedure. The resonant coupling condition for J = 0 from equation (3.3) is

mo2 )02
h = n2 n2 O An2. (4.1)
2s 2d

An optimum range of r can be calculated by using equation (4.1) and the third constraint (d 1ma, smin and r=d/s) along with Ano. Combining these equations, one obtains 1r 1 + (2dma/Xo) 2An (4.2)
< r < (4.2) m2_ (2Smin/kO) 2AnO m

From the above range of r, a desired minimum value rmin can be chosen, and an optimum range of s calculated using the resonance condition again;

() 1 (2dm 2
2 1(m2 1 s md /1 + An2 (4.3)
2 YAn rmn max

Then, a desired value of s is chosen from the above range and a corresponding value of d is calculated as follows


d = s/ m2( 0) An (4.4)


After d and s are thus chosen, the corresponding process-window should be calculated to determine the correspondence, or lack thereof, between the resonance condition and the maximum array mode discrimination, thus optimizing the interelement cap thickness.





72


From the inequality (4.2), it should be noticed that an array mode with a larger m number produces a smaller r value, and therefore, lower power in the main lobe of the farfield pattern. Therefore, a smaller m number array mode is desirable.





3.4 .. *.* i ... 700 600



-400
S3.3
300

3.25 /n 200 100

3.2 I II','l-- , 0
100 150 200 250 300 350 400 450 500 Interelement cap thickness (nm)




Figure 4-10. Effective mode index (n) and mode loss (a) of TE0 and TE1 modes as a function of interelement cap thickness













CHAPTER 5
FABRICATION OF MCTC ANTIGUIDED ARRAY LASERS


5.1 Introduction

The most crucial process in fabricating MCTC antiguided array lasers is the etching process to obtain the precise interelement cap thickness required for in-phase operation. As discussed in Chapter 4, process-windows for the interelement thickness to be processed are quite narrow for typical thin p-clad structures: 10 30 nm. Therefore, the etching process for the required interelement thickness should be controlled with a precision of less than 10 nm. There are quite a few etching techniques such as chemically assisted ion beam etching (CAIBE) [61, 62], reactive ion etching (RIE) [63, 64], electron cyclotron resonance (ECR) discharge etching [65, 66], and Ar(+) ion milling [67]. However, these techniques are not suitable for MCTC antiguided array devices because the rms roughness values of the techniques are beyond the precision required for MCTC devices. For fabrication of MCTC antiguided array lasers, the pulsed anodization technique has been improved with developing a new electrolyte. The details of the pulsed anodization etching technique are presented in Sec 5.2.

Since the p-clad thickness of thin p-clad structures is relatively small, the metal loss of a thin p-clad device can be very high, depending on p-metallization. To minimize the metal loss, a shiny gold contact is necessary and the electroplating technique is simple to employ and good for the requirement. In Sec 5.3, the electroplating technique is discussed. Finally, the fabrication sequence is presented in detail in Sec 5.4.


73




74



5.2 Pulsed Anodization Etching

As discussed earlier, controlling the cap thicknesses (tc and ti) involves an etching process which is crucial for obtaining in-phase laser operation in MCTC antiguided arrays. In addition to the etching process, making a GaAs native oxide layer over the cap layer in the inter-element regions is necessary to confine the optical gain only in the element regions. Both procedures can be done at the same time using a pulsed anodization etching technique.

The pulsed anodization etching set-up is composed of two electrodes immersed in an electrolyte, a pulsed voltage source, two resistors and an oscilloscope (see Figure 5-1). The cathode is a platinized titanium grid and the anode is the sample to be etched. An electrically conducting metal vacuum tube is used to hold a sample horizontally to make the sample surface parallel with the cathode grid. The electrolyte which is called GWA is a mixture of ethylene glycol (G), deionized water (W) and 85% phosphoric acid (A). Changes in shape of the pulsed current waveform during the etching process are displayed on the oscilloscope using the 10 ohm power resistor. Figure 5-2 shows a typical current pulse shape measured on the oscilloscope during pulsed anodization etching. Initially, the pulse shape is square with a negative undershoot. As the etching proceeds, the leading edge of the pulse remains constant, but the magnitude of the trailing edge current decreases. Typically, a pulser voltage Vp = 80 V, a repetition rate of 100 Hz, a pulse width between 0.3 and 1 msec, and Rva = 0 0 are used; a high value of Rv, can cause non-uniform etching, particularly for a big wafer.

The electrolyte, GWA, has a property of etching GaAs native oxide and the etch rate depends on the acid concentration of the electrolyte. When pulsed bias is applied to the




75


circuit, a native oxide is growing on the sample surface due to chemical reactions between surface material of the sample and OH- ions attracted to the sample surface in the electrolyte while the pulse is on, and the oxide is also constantly dissolved. Initially, the overall oxide growing rate overcomes the overall dissolving rate because there is no oxide on the sample surface at the beginning. As the oxide becomes thicker, the growing rate decreases because the circuit resistance is increasing due to the oxide. When the growing rate becomes equal to the dissolving rate, the oxide layer is constantly travelling into the sample with a constant thickness. The trailing edge current of the pulsed current waveform displayed on the oscilloscope also becomes constant. The final oxide thickness depends mainly on the bias voltage, and, for example, a blue oxide (-100 nm thick) is obtained with 80 V.





Pulse
Generator V 10. Q P Resistor Oscilloscope


Metal vacuum tube

PAE sample


Electrolyte
Cathode ............




Figure 5-1. Basic pulsed anodization etching set-up




76






Leading edge
current \ t > 0
Trailing edge current

Time




Figure 5-2. Typical current pulse shape during pulsed anodization etching.




Two different acid concentration GWA's have been developed for fabrication of MCTC antiguide array lasers: one is for slow etching, the other is for relatively fast etching. The ratio of G:W:A for the slow etching is 40:20:1 (which is named GWA) while that for the fast etching is 8:4:1 (which is named GWA841). The electrolyte GWA is a slower and more precise etchant than GWA841, so both electrolytes are used to fabricate MCTC antiguided array lasers due to their merits. GWA is used to perform a slower etch of the whole wafer surface to obtain the right cap thickness for interelement regions, which must be precise, with the remaining oxide not being removed quickly in the electrolyte after the process is done and the circuit is off. For the groove etching of element regions, GWA841 is used because it is faster and produces smaller undercut, resulting in better control of array dimensions and steeper side walls.

The etch rate for pulsed anodization is not constant with time t and etch depth, h(t), can be predicted with the following expression:

h (t) = vot + h [ 1 exp (-ct)] (5.1)





77


The parameters, vo, ho, and a, depend on anodization materials (GaAs or AlGaAs) and electrolytes (GWA or GWA841). Once those parameters are determined based on experiments for a given anodization material and given circuit parameters with an electrolyte, the formula produces accurate predictions (within 10 nm) for etch depth of the material. Since the etching process for MCTC antiguided array lasers should be performed precisely, determining the values of the etch depth parameters is very important and etch depths should be measured precisely. For this study, an atomic force microscope (AFM) was used for etch depth measurements (see Figure 5-3). The rms roughness of the etched surface performed with pulsed anodization etching was measured -1 nm with an AFM.


















Figure 5-3. AFM surface profile for an antiguide array laser with d = 5 pm and s = 2 p.m.



The lapse of time after making the electrolyte is also an important parameter for pulsed anodization etching; etch rate of a fresh electrolyte is higher than that of an aged electrolyte. The time required for chemical stabilization of the ingredients is approximately 24 hours; the anodization results were quite consistent and reproducible using mately 24 hours; the anodization results were quite consistent and reproducible using





78


electrolytes between two and four days old. Hence, for device fabrication, the electrolytes should be prepared a day before they are used and it is desired that preliminary etching test to determine the etching depth parameters and the etching process for interelement and element cap thicknesses should be performed on the same day.


5.3 Electroplating

For p- and n-metallization in fabricating semiconductor lasers, electroplating is a very simple and quick process, compared with other techniques such as electron-beam evaporation, and it can be performed without complicated apparatus. The necessary setup for electroplating process is basically the same with that for pulsed anodization etching except for opposite circuit polarity and a different electrolyte (gold solution). Since gold ions in the gold solution are positive and attracted to the negative electrode, a sample for electroplating should be connected as the cathode. Unlike the pulsed anodization process, the variable resistor is needed to control the current in the circuit because gold thickness on the sample depends on the current and electroplating time (t). With pulsed bias, the gold thickness can be controlled more easily and the typical bias used is a 0.3 msec pulse width at a 100 Hz repetition rate. The pulser output voltage should be controlled along with the variable resistor for the necessary current density (J) flowing through the sample. The thickness (Ta) of the electroplated gold can be controlled with a formula for the thickness which is: Tau = P J p f t, where p is the pulse width, f is the repetition rate, and P is the gold growth rate per unit current density. The experimental value of 0 is

-490 [A/min][cm2/mA]. For uniform electroplating, the electroplating process should be started at a low current density (10 20 mA/cm2) and the current density can be gradually increased up to 100 mA/cm2 to speed up the process. When the current density is too





79


high, bubbles are generated on the sample surface. This should be avoided because the bubbles are stuck on the sample surface and obstruct further electroplating on the area under the bubbles. As the electroplated gold is getting thicker, the color of the electroplated area becomes shiny bright yellow, brownish yellow then rusty brown. The electroplating process should be finished before the electroplated area becomes brownish yellow since too thick gold stripes on the sample can be peeled off easily when the sample is cleaved into bar forms for test.


5.4 Fabrication of MCTC Antiguided Array Lasers

A fabrication procedure of MCTC antiguided array lasers is presented in sequence as follows.

1. Wafer cleaning is performed by boiling the wafer with TCA, acetone, and methanol in

sequence. Some tough stains which are difficult to clean with TCA, acetone and methanol can be removed by leaving the wafer in a developer solution for photolithography for a couple of minutes and repeating the first boiling step. Note that GaAs

oxide is easily dissolved in a developer.

2. Pulsed anodization etching on the whole cap layer surface is performed for required

interelement cap thickness and the oxide layer in interelement regions. This step is for



cap layer ti

converting the top part of the cap layer into a GaAs native oxide layer (-100 nm) and making cap thickness ti at the same time. Since the oxide is -100 nm thick, the initial cap thickness should be bigger than ti at least by 100 nm. This first pulsed anodization





80


etching process is the most important step of the whole fabrication process because the inter-element cap thickness ti should be in the vicinity of the maximum mode discrimination point in the process-window. Therefore, a relatively slow anodization process

with GWA is needed to control ti precisely.

3. First photolithography is creating the antiguide array patterns on the oxide layer formed s d
photoresist
S oxide
cap layer ti


in Step 2. Element regions are open stripes to be etched to a cap thickness te.

4. Pulsed anodization etching of the open stripes in the photolithography pattern is per: s : d
photoresist
oxide
cap layer (te

formed to obtain the required element cap thickness te. This etching process is performed with the faster etchant GWA841 since the element cap thickness is not necessary to be controlled as precisely as interelement cap thickness; the mode index is not sensitive to cap thickness in the vicinity of element cap thickness (-100 nm). More important factor of this step is to achieve steep side walls since array dimensions affect the mode discrimination.

5. Stripping out the remaining oxide in the element regions is the following step after etching the element regions. This process is done by letting the wafer sit in the etching electrolyte after disconnecting the circuit.





81













s d
photoresist
....... --oxide





gold
cap layer


electroplating, the wafer should be checked if the oxide in the element regions has been

removed completely. If not, Step 5 should be repeated.





s d

gold
cap layer


cleaning process for the photolithography removes the photoresist. Since the oxide remaining in the interelement regions should not be removed, any acid solution and

photolithography developer should be avoided in the cleaning procedure.

8. Second photolithography is for defining the device stripe pattern:a is the dimension for



gold photoresist oxide cap layer

probe contact area. Since the oxide layer in the inter-element region still remains to




82


confine gain to the element regions, the individual elements of the arrays have to be connected to each other. The second photolithography is for both connecting the coreelements and defining device stripe pattern, and this should be carefully done without removing the remaining oxide in the inter-element regions. Since normal developing solutions can dissolve the oxide quickly, developing time is very critical for the second

photolithography.

9. Second p-metallization is for connecting elements and prove contact area. Electronp-metal: Ni /Au photoresist oxide



cap layer


beam evaporation is used. A metal which has a good adhesion to the oxide, such as Ni, should be deposited first because adhesion between gold and the oxide is not good enough to hold the metal stripes firmly; otherwise, the metal connections between elements can be destroyed later. Then gold is deposited over the first metal deposition. 10. Lift-off process is performed to separate individual array stripes. After the lift-off p-metal oxide



cap layer


process, another gold electroplating over the p-metal deposition may be necessary to

secure the connections between elements.

11. Lapping substrate is for reducing device thickness down to -100 gm for a lower

device resistance and easy cleaving process.





83


12. N-metallization is done by electroplating gold on the n-substrate. 13. Cleaving the wafer into bar forms for test is the final step of the fabrication.




Top view H [U




Front view Oxide Cap layer













CHAPTER 6
CHARACTERIZATION OF MCTC ANTIGUIDED ARRAY LASERS


6.1 Introduction

In this chapter, the experimental results of MCTC antiguided array lasers are presented. In Figure 6-1, shown is a schematic diagram for characterizing near-field and farfield patterns of array lasers. The major components of the experimental set-up are a scaled screen, a CCD camera, a video analyzer, a monitor and a personal computer, a cylindrical lens for far-field measurement and an objective lens (50x) for near-field characterization.

The function of a cylindrical lens for far-field characterization is focusing the laser output beam on the scaled screen in the vertical direction. Then the camera catches the far-field image on the screen and sends the image to the monitor through the video analyzer. The basic function of the video analyzer is displaying the far-field intensity profile along the horizontal line on the monitor which can be moved in the vertical direction. The vertical line on the monitor can be moved in the horizontal direction and allows measuring the position of far-field peaks using the image of the scaled screen. Once the distance on the screen between two major peaks of far-field pattern is measured using the vertical line and the image of the scale, the angular distance between the two peaks can be calculated easily along with the distance between the laser and the screen. The typical distance between the laser and the screen used is -25 cm. The image signal of the CCD camera is also sent to the computer where the image is analyzed to generate the intensity


84




85


profile of the image using an image processing software such as Frame Grabber. The intensity profile generated on the computer can be printed out and the distance of the two











Computer Monitor Video analyzer Far field measurement Antiguided array laser


------Cylindric lens CCD camera Scaled screen



Near field measurement Antiguided array laser

/ ------50x objective lens CCD camera Scaled screen


Figure 6-1. Schematic diagram of the set-up for far-field and near-field intensity patterns.




86


peaks is also measured from the print-out. Then the scale of the print-out can be calibrated with the angular distance calculated from the distance measured with the monitor. Using the calibrated print-out as a reference scale, far-field beam width (FWHM) can be measured quite accurately by measuring the central peak width on a print-out.

For near-field characterization, an objective lens is used to form the laser facet image (near-field zone) on a screen. Since the magnification of the image is the ratio of the distance between the lens and the screen to the distance between the laser facet and the lens, the focal length of the lens should be very short, otherwise the distance between the screen and lens is too long. With a 50x objective lens, the distance between a -30 cm wide screen and the laser is -2 m for observing the distinguishable individual element images of a 150 .tm wide array facet within the screen. The near-field image is sent to the computer and can be printed to analyze.


6.2 Device Characterization

Five element MCTC antiguided array lasers with three different cap thickness modulation depths, dm, were fabricated and characterized at the early stage of this study to prove that thin p-clad structures had the characteristics of refractive index modulation. The thickness of thin p-clad layer of the material used for these devices was 250 nm. The modulation depth dm is the difference in cap layer thickness between element and interelement regions. The element width was 6 gm and the interelement spacing was 3.5 pm. For all the devices, the cap thickness in the element regions was -90 nm and the oxide thickness in the interelement regions was -100 nm.

For dm = 100 nm, the calculated index modulation An0 was 0.025. The measured near-field and far-field intensity patterns of a typical dm = 100 nm array laser with cavity




87


length L = 500 pm is shown in Figure 6-2 (a). The beam width (FWHM) of the central lobe of the far-field is 1.30 at 15% above threshold, which is nearly diffraction-limited. This indicates in-phase operation at that drive level.

For dm = 150 nm, the calculated Ano was 0.07 and out-of-phase operation occurred as shown in Figure 6-2 (b). The threshold current and slope efficiency of these lasers were essentially the same as for the in-phase lasers, 70 mA and 0.42 W/A respectively. With increasing current, the two far-field lobes were somewhat more stable with respect to broadening than for the central lobe of the in-phase lasers.

For the devices with dm = 210 nm, the calculated Ano was 0.12 and the typical threshold current was -110 mA. As shown in Figure 6-2 (c), one wide central lobe was observed in the far-field pattern indicating that the individual elements in the array were not strongly coupled. This lack of coupling is probably the reason for the nearly 60% increase in threshold current relative to the in-phase and out-of-phase mode lasers. In this case the lasing modes cannot adjust so as to avoid the lossy thick cap sections.

As shown with the above results, MCTC antiguided array device performances are greatly dependent on cap thickness modulation. This indicates that a large refractiveindex modulation can be obtained by modulating cap thickness of a thin p-clad structure.

With the encouragement from the 5 element devices results, 20 element devices were also fabricated and characterized. While they had been designed for an in-phase operation with 5 -tm wide elements and 2 gm interelement spacing, the devices were mostly operating in out-of-phase mode possibly because of etch-depth errors for interelement cap thickness. The typical near-field and far-field patterns of 20 element out-of-phase array lasers are shown in Figure 6-3. These array lasers were made from 465 nm




88


p-clad material. In the near-field profiles, 20 peaks of individual element laser beams are distinguishable and the far-field pattern is quite stable with increasing current level. The typical threshold current (Ith) was -140 mA and a total P-I slope efficiency was -0.52W/A with a pulse width and a frequency of 40 sec and 1 kHz, respectively. This second fabrication confirmed again the phase-locked operation of MCTC antiguided array devices.

Finally, with improved pulsed anodization technique, stable in-phase mode operation was achieved with 23 element MCTC antiguided array lasers. The elements were 5 gm wide and the interelement regions were 2 gm wide. Unlike the 5 element MCTC antiguided array lasers fabricated with the 250 nm p-clad material, 465 nm p-clad material was used to improve a better P-I slope efficiency. Other than the p-clad layer thickness, the rest of the wafer structure was the same with the structure for the 5 element arrays. For these lasers, the array pattern was created over the entire surface of the wafer and then stripes for individual array lasers were defined; in the 5 and 20 element array lasers, the array pattern was fabricated only inside the stripe area. The cap thickness in the element regions and in the interelement regions were 100 nm and 230 nm respectively. The thickness of the oxide in the interelement regions was 100 nm.

These 23 element MCTC antiguided array lasers were designed for m = 3, in-phase operation and the required An0 was 0.076. The measured near-field and far-field intensity patterns of one of the lasers with cavity length L = 500 lm are shown in Figure 6-4. The beam width (FWHM) of the central lobe of the far-field was 0.80 at 1.2 x Ith (Ith =

-200mA) and 1.60 at 10 x Ith. The far field behavior with increasing current, as shown in Figure 6-4, is greatly improved compared with that of the 5 element lasers. Up to 10 x It current level which is the limit of our pulser, the far field pattern of in-phase operation was





89


very well maintained. In addition to the more stable far-field behavior with increasing current, the side lobes of the far-field patterns were significantly suppressed due to the higher ratio of element to interelement width. The central lobe contained -75% of the beam power at 1.2 x Ith and -60% of the beam power at 10 x Ith. As shown in Figure 65, the total P-I slope efficiency was -0.4 W/A with a driving frequency and a pulse width of 1 kHz and 2 gpsec respectively. The slope efficiency is smaller than that of a regular 100 gm wide, 500 im long laser made from the same material (typically 0.52 W/A). This is mainly due to the loss in the interelement regions, which is required to obtain stable in-phase operation.

Although stable in-phase operation was achieved with 23 element MCTC antiguided arrays, the fabrication yield of the in-phase operating devices was very low (-5%) because the process-window of the thin p-clad structure used for the devices was very narrow as shown in Figure 4-5 (b). On the other hand, the fabrication yield of in-phase 5 element devices was relatively high (-50%) which can be expected from Figure 4-5 (a).

From these experimental results, it is clear that thin p-clad structures should be designed to have a large process-window for high fabrication yields of in-phase devices. In the next chapter, such a thin p-clad structure for a large process-window is proposed.




90




Near field intensity Far field intensity

FWHM =1.30
9.5 itm
(a) In-phase dm= 100 nm
I= 80 mA






FWHM =2.40


(b) Out-of-phase dm = 150 nm 9.5 m
I= 80 mA H






FWHM =4.20


(c) Random phase 9.5 Wm dm = 210 nm I = 120 mA







Figure 6-2. Near-field and far-field patterns of 5 element MCTC antiguided array lasers
d = 6 gm, s = 3.5 utm





91







Near-field Far-field



.....................::::::::::::::::: ...., .. .. ... ................ .. .

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lasers (out-f-phae. opeation.d.=....ms=
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............ .......... ..................... .......






92








Near-field Far-field


.. . . .......... ....... ......iiii:i : :::: i:i::i::::::i:::i!i!i!: :!:~!!:!i!: ::ii!:::: nr :iii !i:!!! i !i:iii~iiiiiiiiniii :i-~i ........ .... ......: ..... ..




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. .............................................................



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Full Text
86
peaks is also measured from the print-out. Then the scale of the print-out can be cali
brated with the angular distance calculated from the distance measured with the moni
tor. Using the calibrated print-out as a reference scale, far-field beam width (FWHM)
can be measured quite accurately by measuring the central peak width on a print-out.
For near-field characterization, an objective lens is used to form the laser facet
image (near-field zone) on a screen. Since the magnification of the image is the ratio of
the distance between the lens and the screen to the distance between the laser facet and the
lens, the focal length of the lens should be very short, otherwise the distance between the
screen and lens is too long. With a 50x objective lens, the distance between a ~30 cm
wide screen and the laser is ~2 m for observing the distinguishable individual element
images of a 150 (im wide array facet within the screen. The near-field image is sent to
the computer and can be printed to analyze.
6.2 Device Characterization
Five element MCTC antiguided array lasers with three different cap thickness mod
ulation depths, dm, were fabricated and characterized at the early stage of this study to
prove that thin p-clad structures had the characteristics of refractive index modulation.
The thickness of thin p-clad layer of the material used for these devices was 250 nm. The
modulation depth dm is the difference in cap layer thickness between element and interele
ment regions. The element width was 6 (tm and the interelement spacing was 3.5 (am.
For all the devices, the cap thickness in the element regions was ~90 nm and the oxide
thickness in the interelement regions was ~100 nm.
For dm = 100 nm, the calculated index modulation An0 was 0.025. The measured
near-field and far-field intensity patterns of a typical dm = 100 nm array laser with cavity


33
because the optical modes in the elements are strongly guided. The weak coupling was
the major reason for the failure of positive-index-guided arrays. It is possible to get a
strong coupling with those devices by reducing the refractive-index step between element
and interelement regions. However, those array devices with a smaller refractive-index
step are more susceptible to thermal and/or carrier induced refractive-index variation
which leads to unstable device operation.
'
m
5m
_n n
(c)
(d)
Figure 2-8. Schematic diagrams of basic types of phase-locked linear arrays of
semiconductor lasers. The bottom traces correspond to refractive-index
profiles, (a) Evanescent-wave coupled array, (b) Y-junction coupled array,
(c) Diffraction coupled array, (d) Leaky-wave coupled array.
Strong coupling and large refractive-index step can be obtained with negative-
index-guided arrays for which the near-field intensity peaks and optical gains are in the


104
[25] J. S. O, C. F. Miester, J. Yoon, P. S. Zory, and M. A. Emanuel, Modulated-Cap Thin
p-Clad Antiguided Array Lasers, SPIE Proceedings 3284, pp. 36 40, Jan. 1998.
[26] B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, John Wiley & Sons,
New York, p. 123, 1991.
[27] J. W. Goodman, Introduction to Fourier Optics, McGrow-Hill, New York, p. 57,
1968.
[28] J. K. Butler, D. E. Ackley, and D. Botez, Coupled-Mode Analysis of Phase-Locked
Injection Laser Arrays, Technical Digest of the Optical Fiber Communication Con
ference, Paper TuF2, pp. 44 46, New Orleans, LA, Jan. 23-25, 1984.
[29] J. K. Butler, D. E. Ackley, and D. Botez, Coupled Mode Analysis of Phase-Locked
Injection Laser Arrays, Appl. Phys. Lett., Vol. 44, pp. 293 295, Feb. 1984: see also
Appl. Phys. Lett., Vol. 44, p. 935, May 1984.
[30] W. Streifer, A. Hardy, R. D. Burnham, and D. R. Scifres, Single-Lobe Phased-Array
Diode Lasers, Electron. Lett., Vol. 21, pp. 118 119, 1985.
[31] J. K. Butler, D. E. Ackley, and M. Ettenberg, Coupled-Mode Analysis of Gain and
Wavelength Oscillation Characteristics of Diode Laser Phased Arrays, IEEE J.
Quantum Electron., Vol. QE-21, pp. 458 464, 1985.
[32] Y. Twu, A. Dienes, S. Wang, and J. R. Whinnery, High Power Coupled Ridge
Waveguide Semiconductor Laser Arrays, Appl. Phys. Lett., Vol. 45, pp. 709 711,
1984.
[33] S. Mukai, C. Lindsey, J. Katz, E. Kapon, Z. Rav-Noy, S. Margalit, and A. Yariv,
Fundamental Mode Oscillation of a Buried Ridge Waveguide Laser Array, Appl.
Phys. Lett., Vol. 45, pp. 834 835, 1984.
[34] E. Kapon, L. T. Lu, Z. Rav-Noy, M. Yi, S. Margalit, and A. Yariv, Phased Arrays of
Buried-Ridge InP/InGaAsP Diode Lasers, Appl. Phys. Lett., Vol. 46, pp. 136 138,
1985.
[35] N. Kaneno, T. Kadowaki, J. Ohsawa, T. Aoyagi, S. Hinata, K. Ikeda, and W. Susaki,
Phased Array of AlGaAs Multistripe Index-Guided Lasers, Electron. Lett., Vol. 21,
pp. 780-781, 1985.
[36] E. Kapon, C. Lindsey, J. Katz, S. Margalit, and A. Yariv, Chirped Arrays of Diode
Lasers for Supermode Control, Appl. Phys. Lett., Vol. 45, pp. 200 202, 1984.
[37] C. P. Lindsey, E. Kapon, J. Katz, S. Margalit, and A. Yariv, Single Contact Tailored
Gain Phased Array of Semiconductor Lasers, Appl. Phys. Lett., Vol. 45, pp. 722 -
724, 1984.


77
The parameters, v0, h0, and a, depend on anodization materials (GaAs or AlGaAs) and
electrolytes (GWA or GWA841). Once those parameters are determined based on exper
iments for a given anodization material and given circuit parameters with an electrolyte,
the formula produces accurate predictions (within 10 nm) for etch depth of the material.
Since the etching process for MCTC antiguided array lasers should be performed pre
cisely, determining the values of the etch depth parameters is very important and etch
depths should be measured precisely. For this study, an atomic force microscope (AFM)
was used for etch depth measurements (see Figure 5-3). The rms roughness of the etched
surface performed with pulsed anodization etching was measured ~1 nm with an AFM.
Figure 5-3. AFM surface profile for an antiguide array laser with d = 5 [im and s = 2 jam.
The lapse of time after making the electrolyte is also an important parameter for
pulsed anodization etching; etch rate of a fresh electrolyte is higher than that of an aged
electrolyte. The time required for chemical stabilization of the ingredients is approxi
mately 24 hours; the anodization results were quite consistent and reproducible using


90
(a)In-phase
djn = 100 nm
I = 80 mA
Near field intensity
Far field intensity
(c) Random phase
dm = 210 nm
I = 120 mA
Figure 6-2. Near-field and far-field patterns of 5 element MCTC antiguided array lasers
d = 6 (im, s = 3.5 (im


7
acts as a dielectric waveguide. The physical mechanism behind the confinement is total
internal reflection (TIR), as illustrated in Figure 1-2 (b). When a ray traveling at an
angle 0 hits the interface, it is totally reflected back if the angle 0 exceeds the critical angle
(0c) given by
0 = sin
-1 (n '
\naJ
(1.1)
Thus, rays traveling nearly parallel to the interface are trapped and constitute the
waveguide mode.
When the current flowing through a semiconductor laser is increased, electrons and
holes are injected into the active region, where they recombine through radiative or
non-radiative mechanisms. As one may expect, non-radiadve recombinations are not
helpful for laser operation, and attempts are made to minimize their occurrence by
controlling point defects and dislocations. However, a non-radiative recombination
mechanism, known as the Auger process, is intrinsic and becomes particularly important
for long-wavelength semiconductor lasers operating at room temperature and above.
Physically speaking, during the Auger process the energy released by electron-hole
recombination is taken by a third charge carrier (electron or hole) and is eventually lost to
lattice phonons.
During a radiative recombination, the energy Eg released by the electron-hole
recombination appears in the form of a photon whose frequency v or wavelength X
satisfies the energy conservation relation Eg = hv = hc/X. This can happen through two
optical processes known as spontaneous emission and stimulated emission. In the case
of spontaneous emission, photons are spontaneously emitted in random directions with no


MODULATED CAP TUTU F-CLAD ANTIGUIDED ARRAY L ASERS
By
JEONG-SEOK O
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1998


12
[im wide) is shown in Figure 1-4 (a). The vertical axis is beam power and the horizontal
axis is lateral beam direction. For comparison a beam profile of a typical 100 (J.m aper
ture laser is shown in Figure 1-4 (b).
Lateral angle
(a)
Figure 1-4. Lateral far-field patterns from
(a) a 150 [im wide phase-locked antiguided array laser, and
(b) a conventional 100 (im wide stripe laser
Several techniques have been used to obtain the required periodic lateral refractive-
index variations in fabricating antiguided array lasers. These include growth over
channeled substrates [16], regrowth after etching the element regions in the upper clad
layer [17], regrowth after etching of thin waveguide layers embedded in the clad layer
[18 20], and impurity-induced disordering [21], Although coherent powers from
phase-locked antiguided array lasers fabricated using the above techniques were


8
phase relationship among them. Stimulated emission, by contrast, is initiated by an
already existing photon, and the emitted photon matches the original photon not only in its
wavelength but also in direction of propagation. It is this relationship between the
incident and emitted photons that renders the light emitted by lasers coherent.
Although stimulated emission can occur as soon as current is injected into the
semiconductor laser, the laser does not emit coherent light until the current exceeds a
critical value known as the threshold current (1^). This is so because stimulated emis
sion has to compete against the absorption processes during which an electron-hole pair is
generated at the expense of an absorbed photon. Since the electron population in the
valence band generally far exceeds that of the conduction band, absorption dominates at a
low level of the injection current. At a certain value of the current, a sufficient number
of electrons are present in the conduction band to make the semiconductor optically
transparent. With a further increase in current, the active region of the semiconductor
laser exhibits optical gain and can amplify the electromagnetic radiation passing
through it. Spontaneously emitted photons serve as the noise input for the amplification
process.
However, optical gain alone is not enough to operate a laser. The other necessary
ingredient is optical feedback which can be obtained by placing mirrors at the ends of the
gain medium. The cavity formed by the mirrors is called Fabry-Perot (FP) cavity. In
AlGaAs semiconductor lasers, the cleaved facets are about 30% reflective mirrors and
form the FP cavity. Figure 1-3 (a) shows a schematic of a typical heterostructure stripe
laser.
Because of the optical feedback, the number of photons traveling perpendicular to
the facets increases when the current is large enough to satisfy the condition of net


37
3.2 Single Real Refractive-Index Antiguides
The basic properties of a single real refractive-index antiguide are schematically
depicted in Figure 3-1. The refractive-index of the antiguide core is denoted as ne which
is lower than that (n¡) of the cladding. The typical index depression, An, is (1 2) x 10
for simple gain-guided lasers and (2 5) x 10'2 for strongly index-guided lasers. The
effective refractive-index of the fundamental lateral mode is lower than the core refrac
tive-index. By contrast, the effective index of the fundamental mode in a positive-index
guide is between the low index of the cladding and the high index of the core. Whereas,
in a positive-index guide, optical mode is confined in the core via total internal reflection,
in an antiguide, optical mode is partially confined in the core and partially leaked out to
the cladding (see Figure 3-1 (c)). The lateral wavelength of the leaky wave can be
obtained using the equations with the diagram shown in Figure 3-1 (c), where ke and k¡
are the propagation vectors in the core and the cladding, Kg and k¡ are their lateral compo
nents respectively, P is the longitudinal component of the propagation vectors which is the
same in both regions and Xq is the vacuum wavelength:
*/ =
2k
K- J[n¡2-ne2] + [(J+l)X0/(2d)]2
where J is the lateral mode number (7 = 0 for the fundamental mode).
The radiation leaking to the cladding can be considered as a radiation loss oq [50]:
(J+ 1)V 2
ttr = "I XTl *
d nej2ne{ni-ne)
(3.1)
(3.2)
where r¡ is the lateral propagation confinement factor.


60
complex mode indices of the one dimensional (1-D) lateral array structure of the element
and interelement regions, which is another simple 1-D multi-layer waveguide structure.
From the imaginary part of the complex mode indices of various array modes, array mode
gain (loss) profiles are obtained. Since the TE mode is calculated for the transverse struc
ture, TM mode should be assumed for the 1-D lateral structure, although there are no
major differences in the results between TM and TE mode assumptions.
In Figure 4-5, calculated mode gain profiles are shown as a function of the interele
ment cap thickness for two different antiguided array structures: a 5 element and a 18 ele
ment array. For the 5 element array structure, d = 6 p.m and s = 3.5 |im were used with a
250 nm p-clad thickness (tcl) while for the 18 element array structure, d = 5 Jim and s = 2
(im were used with tcl = 465 nm. For both cases, the element cap thickness was fixed at
100 nm, a 500 nm gold layer was used for the metal contact, and the material gain in the
active QW layer was assumed to be 2000 cm'1 for the element regions and 0 cm"1 for
interelement regions. At the wavelength of 950 nm, a free-carrier absorption loss of 120
cm"1 was used for the p+-GaAs cap layer.
In these plots of the profiles, the shaded areas are for the interelement cap thickness
range where the in-phase mode has the highest mode gain and thus is the most favored
mode to lase. The shaded areas also show the mode gain difference between in-phase
mode and the mode which has the next highest mode gain. The interelement cap thick
ness t¡ to be used for the fabrication of MCTC antiguided array lasers should be within the
shaded range. The closer tj is to the point indicated with a vertical arrow in the plots, the
more stable in-phase operation with high drive levels will be, because the mode discrimi
nation against the other mode is maximum at the point.


BIOGRAPHICAL SKETCH
Jeong-Seok O was bom in South Korea in 1962. He received his B.S. degree in
electronic engineering from Kon-Kuk University, Seoul, Korea, in 1990 and his M.S.
degree in electrical and computer engineering from the University of Florida in 1995.
After his graduation he was teaching mathematics at a preliminary school for
college in Seoul until he was accepted as a graduate student at the University of Florida in
August 1993. He pursued a nonthesis option for his M.S. degree and his research was in
the area of photonics. In May of 1994, he was assigned to be a graduate research assis
tant at the Photonics Research Laboratory in the Department of Electrical and Computer
Engineering. During his M.S. study, he was engaged in research on semiconductor
lasers, particularly intersubband lasers and distributed feedback (DFB) lasers as well as
device fabrications. He also participated in a contract research of Blue Light Emitting
Material and Injection Devices (DARPA/ONR) and performed research on degradation
of CdZnSe blue-green lasers and etching of nitride (InGaN, GaN) material.
Since May of 1995, he has been pursuing his Ph.D. degree in electrical and
computer engineering in the semiconductor laser research group (photonics) at the
University of Florida. As a graduate research assistant, he is performing contract
research of Modulated Cap Thin p-Clad Lasers (Air Force Research Lab.). His current
research area involves spatially coherent high power semiconductor lasers using thin
p-clad antiguided array structures.
108


54
Cap thickness (nm)
Figure 4-2. (a) Effective refractive-index of the fundamental mode (TE0) as a function
of cap layer thickness; (b) Mode loss of the TE0 mode as a function of cap
layer thickness; p-clad thickness = 465 nm, oxide thickness =100 nm
Au (gold) thickness = 500 nm


57
adjacent modes. Botez et al. used the number of null points (within an array) in the near
field profiles to define antiguided array modes [50]. Their definition, however, does not
include the array modes which are composed of the first or higher order lateral modes in
the element regions because the null number of an array mode which consists of the fun
damental lateral modes in the element regions can be the same with that of an array mode
which has the first or higher lateral mode in the element regions.
With three numbers, an antiguided array mode (AM) can be defined as AM¡ml,
where j and m are the numbers of intensity peaks in the element and interelement regions
and / is the number of null points of the envelope of the near-field profiles. Four example
array modes for a 5-element array are shown in Figure 4-4. Figure 4-4 (a) is an AM130
mode (in-phase mode): it has one peak in the element regions and three peaks in the inter
element regions, the envelope profile of the array mode doesnt cross the axis within the
array (zero null point). For the other array modes shown in the figure, the mode numbers
can be figured easily. Note that the total numbers of null points of AM131 (Figure 4-4 (c))
and AM220 (Figure 4-4 (d)) modes are the same and hence the two modes can not distin
guished from each other with Botezs definition of array modes.
This new definition of array modes, however, will be used only when it is necessary.
The common terms, in-phase, out-of-phase and adjacent in- or out-of-phase will be mostly
used since those terms have been used for the descriptions of far-field patterns. An in-
phase far-field pattern has a single central lobe while an out-of-phase far-field has two
main lobes separated from each other by the angular distance of ~Tan_1(X(/r), and an
adjacent in- or out-of-phase far-field has twin lobes located at the same lobe positions of
the in-phase or out-of-phase far-field pattern, respectively (see Figure 2-6).


105
[38] J. E. A. Whiteaway, G. H. B. Thompson, and A. R. Goodwin, Mode Stability in
Real Index-Guided Semiconductor Laser Arrays, Electron. Lett., Vol. 21, pp. 1194 -
1195,1985.
[39] J. Ohsawa, S. Hinata, T. Aoyagi, T. Kadowaki, N. Kaneno, K. Ikeda, and W. Susaki,
Triple-Stripe Phase-Locked Diode Lasers Emitting 100 mW CW with Single-Lobed
Far-Field Patterns, Electron. Lett., Vol. 21, pp. 779 780, 1985.
[40] J. R. Heidel, R. R. Rice, and H. R. Appelman, Use of a Phase Corrector Plate to
Generate a Single-Lobed Phased Array Far Field Pattern, IEEE J. Quantum Elec
tron., Vol. QE-22, pp. 749 752, 1986.
[41] S. Thaniyavam, and W. Dougherty, Generation of a Single-Lobe Radiation Pattern
from a Phased-Array Laser using a Near-Contact Variable Phase-Shift Zone Plate,
Electron. Lett., Vol. 23, pp. 5 7, 1987.
[42] M. Matsumoto, M. Taneya, S. Matsui, S. Yano, and T. Hijikata, Single-Lobed Far-
Field Pattern Operation in a Phased Array with an Integrated Phase Shifter, Appl.
Phys. Lett., Vol. 50, pp. 1541 1543, 1987.
[43] D. F. Welch, W. Streifer, P. S. Cross, and D. Sciffes, Y-Junction Semiconductor
Laser Arrays: Part II Experiments, IEEE J. Quantum Electron., Vol. QE-23, pp.
752-756, 1987.
[44] M. Taneya, M. Matsumoto, S. Matsui, S. Yano, and T. Hijikata, 0 Phase Mode
Operation in Phased Array Laser Diode with Symmetrically Branching Waveguide,
Appl. Phys. Lett., Vol. 47, pp. 341 343, 1985.
[45] W. Streifer, Analysis of a Y-Junction Semiconductor Laser Array, Appl. Phys. Lett.,
Vol. 49, pp. 58 60, 1986.
[46] A. E. Bazarov, I. S. Goldobin, P. G. Eliseev, O. A. Kobilzhanov, G. T. Pak, T. V. Petra -
kova, T. N. Pushkim, and A. T. Semenov, Sov. J. Quantum Electron., Vol. 17, p. 551,
1987.
[47] W. Streifer, A. Hardy, D. F. Welch, D. R. Scifres, and P. S. Cross, Improved Y-X
Junction Laser Array, Electron. Lett., Vol. 26, pp. 1730 1731, 1990.
[48] J. E. A. Whiteaway, D. J. Moule, and S. J. Clements, Tree Array Lasers, Electron.
Lett., Vol. 25, pp. 779 781, 1989.
[49] D. Mehuys, K. Mitsunaga, L. Eng, W. K. Marshall, and A. Yariv, Supermode Con
trol in Diffraction-Coupled Semiconductor Laser Arrays, Appl. Phys. Lett., Vol. 53,
pp. 1165 1167, 1988.


28
As mentioned earlier, the angular positions of the array far-field peaks do not
exactly coincide with those of the grating function, but the differences are negligible and
the peak positions of the far-field can be obtained more easily from the grating function
than from the exact far-field function which is a product of the single-element far-field and
the grating functions. The peak positions (Qpk) from the grating function are
\for K = 1
(2.20)
%k = Tan
Q
K
2(N + 1) JTj
X
for 2 (2.21)
%k = Tan~
Q \)f
for K = N ,
(2.22)
where Q is an integer number and K is the array mode number.
From the above results and the array far-field figures, it is obvious that only the K= 1
mode (in-phase mode) has a main central lobe at 9 = 0 (straight-forward beam) in its far-
field pattern. From a practical point of view, the in-phase mode far-field pattern is
desired because the output energy of the array is primarily contained within the main cen
tral lobe which is straight-forward and whose FWHM can be very small. Therefore, for
semiconductor laser array devices, achieving in-phase mode operation has been the main
goal, and this work is also focused on in-phase operation.
A simple expression for FWHM of a main central lobe of an in-phase far-field can
not be easily obtained from the expression (FF(6)) of the array far-field pattern. How
ever, the dependence of the FWHM on array parameters such as array dimensions and
number of elements in an array is the same with that of divergence angle (0^) of the cen
tral lobe, as one might expect. The divergence angle (named an array divergence angle)


51
arrays are introduced in Sec 4.3. In this section, array mode gain profiles are presented,
and a new concept called process-window is defined, and the matter of epitaxial layer
design of thin p-clad structures for MCTC antiguided arrays is addressed. Sec 4.4 is
devoted to design aspects of MCTC antiguided arrays for optimum device performance.
4.2 Thin P-clad Laser Structure
Figure 4-1 shows the thin p-clad laser structure used in this study which consists of
a 1400 nm n-Al0 gGa^ 4As clad layer grown n-GaAs substrate, a -420 nm active region,
a 200 500 nm p-Al^ 6GaQ 4As clad layer and p+-GaAs cap layer whose thickness is mod
ulated between -100 nm and -250 nm for MCTC antiguided array devices. The active
region is composed of a 8 nm In0 ^Ga^ g5As undoped strained quantum well (QW) layer
sandwiched between two 7 nm GaAs barrier layers, 200 nm graded p- and n-A^Ga^As
guide layers (x = 0.3 0.6) above and below the sandwich layers respectively. The emis
sion wavelength of this structure is 950 nm. Note that the p-clad is much thinner than the
n-clad, which has a typical thickness. Figure 4-1 also shows the refractive-index profile
of the structure and the fundamental transverse mode (TE0 mode) profiles corresponding
two different cap-thicknesses. It should be noticed that the refractive-index of the cap
layer is greater than those of the clad and guide layers. In the following discussion, it
will be apparent why the higher refractive-index of the cap layer is important.
Since the transverse mode profile can extend to the cap layer because of the thin p-
clad layer and the refractive-index of the cap layer is larger than that of the p-clad layer,
the mode becomes trapped in the cap layer as the cap-thickness increases. When this
occurs, the mode-overlap with the cap layer becomes significant. The effective refrac
tive-index of the mode is proportional to the integral of the product of the layer refractive


45
dashed line in Figure 3-6) in the mode losses between the in-phase mode and the mode
which has the next lowest mode loss increases from ~5 cm'1 (when oq = 0 cm'1) to ~25
cm'1 (when oq = 200 cm'1).
The mode discrimination enhancement with interelement loss does not degrade
when gain, which is necessary in real devices, is placed in the element regions. Shown in
Figure 3-7 are the mode losses for the same array with a material gain (ge) of 40 cm'1 in
the element region, in addition to oq = 200 cm'1. The mode loss profiles do not change
much and simply down-shift due to the element gain, and the maximum difference in the
mode losses is still ~25 cm'1.
An
Figure 3-7. Mode loss (radiation + interelement loss (cq) element gain (ge)) as a function
of lateral refractive-index step An (= n ne) for a 5 element antiguided array:
ne = 3.263, d = 5 [im, s = 2 (im, Xq 0.95 pm, oq = 200 cm"1 gc = 40 cm'1.'
From these mode loss profiles, it should be noticed that the resonant coupling point
does not coincide with the position of maximum mode discrimination against the


107
[63] I. Adesida, A. Mahajan, E. Andideh, M. A. Khan, D. T. Olsen and J. N. Kuznia,
Reactive Ion Etching of Gallium Nitride in Silicon Tetrachloride Plasmas, Appl.
Phys. Lett., Vol. 63, pp. 2777 2779,1993
[64] A.T. Ping, I. Adesida, M.A. Khan, and J. N. Kuznia, Reactive Ion Etching of Gal
lium Nitride Using Hydrogen Bromide Plasmas, Electron. Lett., Vol. 30, pp. 1895 -
1897,1994.
[65] S.J. Pearton, C.R. Abernathy, and C.B. Vartuli, ECR Plasma Etching of GaN, AIN
and InN Using Iodine or Bromine Chemistries, Electron. Lett., Vol. 30, pp. 1985 -
1986, 1994.
[66] SJ. Pearton, C.R. Abernathy, and F. Ren, Low Bias Electron Cyclotron Resonance
Plasma Etching of GaN, AIN and InN, Appl. Phys. Lett., Vol. 64, pp. 2294 2296,
1994.
[67] S.J. Pearton, C.R. Abernathy, F. Ren, and J.R. Lothian, Ar+-Ion Milling Characteris
tics of III-V Nitrides, J. Appl. Phys., Vol. 76, pp. 1210 1215, 1994.


REFERENCES
[1] J. von Neumann, Notes on the photon-disequilibrium-amplification scheme, an
unpublished manuscript written before September 16, 1953. The original is located
in the von Neumann Collection of the Manuscript Division of the Library of Con
gress of the United States, James Madison Memorial Building, Room 101, Washing
ton, DC. Also, IEEE J. Quantum Electron., Vol. QE-23, No. 6, pp. 659 671, June
1987.
[2] N. G. Basov, O. N. Krokhin, and Yu. M. Popov, Production of negative-temperature
states in P-N junction of degenerate semiconductors, Zh. Eskp. Theor. Fiz., Vol. 40,
pp. 1879 1880, 1961.
[3] M. G. A. Bernard and G. Duraffourg, Laser conditions in semiconductors, Phys.
Stat. Sol., Vol. 1, pp. 699 703, 1961.
[4] C. Benoit a la Guillaume and Mme. Trie, Les semi-conducteurs et leur utilisation
possible dans les lasers, J. de Physique, Vol. 22, pp. 834 836, 1961.
[5] R. N. Hall, G. E. Fenner, J. D. Kingsley, T. J. Soltys, and R. O. Carlson, Coherent
light emission from GaAs junctions, Phys. Rev. Lett., Vol. 9, pp. 366 -368, 1962.
[6] M. I. Nathan, W. P. Dumke, G. Bums, F. H. Dill, Jr., and G. Lasher, Stimulated emis
sion of radiation from GaAs p-n junctions, Appl. Phys. Lett., Vol. 1, pp. 62 64,
1962.
[7] H. Kroemer, A proposed class of heterojunction lasers, Proc. IEEE Vol. 51, pp.
1782-1783, 1963.
[8] Zh. I. Alferov, and R. F. Kazarinov, Semiconductor laser with electrical pumping,
U.S.S.R. Patent 181737, 1963.
[9] Zh. I. Alferov, V. M. Andreev, V. I. Korolkov, E. L. Portnoi, and D. N. Tretyakov,
Injection properties of n-A^Ga^As p-GaAs heterojunctions, Fiz. Tekh. Poluprov.,
Vol. 2, p. 1016, 1968.
[10] H. Kressel and H. Nelson, Close confinement gallium arsenide PN junction lasers
with reduced optical loss at room temperature, RCA Rev., Vol. 30, p. 106, 1969.
[11] I. Hayashi, M. B. Panish, P. W. Foy, A low threshold room temperature injection
laser, IEEE J. Quantum Electron., Vol. QE-5, pp. 211 212, 1969.
102


2
The factors largely responsible for this breakthrough was the exceptional and fortuitous
close lattice match between AlAs and GaAs, which allowed heterostructures consisting of
layers of different compositions of AlxGdi_xAs to be grown on GaAs substrate.
The first major application of semiconductor lasers was optical-fiber communica
tion. It utilizes the fact that the laser output power can be modulated easily by modulat
ing the injection current. Giga-hertz data transmission rates are now possible. The
development of semiconductor lasers whose operating wavelengths are 1.3 (im and 1.55
(im was motivated by the optical-fiber communication application, since optical-fiber
dispersion is minimum at 1.3 Jim and optical loss in the fiber is minimum at 1.55 Jim.
Laser amplifiers were also developed due to the need for repeaters in optical-fiber com
munication systems. Distributed feedback (DFB) and distributed Bragg reflector (DBR)
lasers were also developed for optical-fiber communications to achieve frequency multi
plexing of transmission signals and frequency stability.
As semiconductor laser technologies were advanced, more applications were
generated. The optical memory (CDs: audio and video discs) industry has created a large
demand for semiconductor lasers. Surface emitting two-dimensional arrays are
demanded for optical data processing and computing. High power semiconductor lasers
are needed for printers and copiers, and they are also being used as efficient pumping
sources for solid state lasers and machining/cutting operations. When even higher power
is reliably available, the list of applications will expand to include free space communica
tion, laser radar, laser fusion, and more.


72
From the inequality (4.2), it should be noticed that an array mode with a larger m
number produces a smaller r value, and therefore, lower power in the main lobe of the far-
field pattern. Therefore, a smaller m number array mode is desirable.
2
a
n>
o
C/2
C/2
cT
3
100 150 200 250 300 350 400 450 500
Interelement cap thickness (nm)
Figure 4-10. Effective mode index (n) and mode loss (a) of TE0 and TEj modes
as a function of interelement cap thickness


30
^(0)
Pc=
^(0)+2/yeM)
2=1
-
2-1
oo
COS Q 7C-
1+2I
V l J
( dV
2=1
L(f) J
0.81
(2.25)
The central lobe power rate Pc depends on d/T and, in Figure 2-7, it is plotted as a function
of d/T. As shown in the figure, the plot is very linear and Pc can be approximated very
closely to 0.81 (d/T)-, Pc can not exceed 0.81 for the sinusoidal element-near-field. For
comparison, the expression of Pc for a uniform element-near-field is shown in the follow
ing equation and it is also plotted in Figure 2-7:
P_ =
1+2 I
2=1
sin\Q%f
' d
QKf
I 21-1
d
T
(2.26)
Figure 2-7. Central lobe power rate for sinusoidal and uniform element-near-fields


78
electrolytes between two and four days old. Hence, for device fabrication, the electro
lytes should be prepared a day before they are used and it is desired that preliminary etch
ing test to determine the etching depth parameters and the etching process for interelement
and element cap thicknesses should be performed on the same day.
5.3 Electroplating
For p- and n-metallization in fabricating semiconductor lasers, electroplating is a
very simple and quick process, compared with other techniques such as electron-beam
evaporation, and it can be performed without complicated apparatus. The necessary set
up for electroplating process is basically the same with that for pulsed anodization etching
except for opposite circuit polarity and a different electrolyte (gold solution). Since gold
ions in the gold solution are positive and attracted to the negative electrode, a sample for
electroplating should be connected as the cathode. Unlike the pulsed anodization pro
cess, the variable resistor is needed to control the current in the circuit because gold thick
ness on the sample depends on the current and electroplating time (t). With pulsed bias,
the gold thickness can be controlled more easily and the typical bias used is a 0.3 msec
pulse width at a 100 Hz repetition rate. The pulser output voltage should be controlled
along with the variable resistor for the necessary current density (J) flowing through the
sample. The thickness (Tau) of the electroplated gold can be controlled with a formula
for the thickness which is: Tau = p J p f t, where p is the pulse width, f is the repetition rate,
and P is the gold growth rate per unit current density. The experimental value of P is
-490 [/min][cm2/mA], For uniform electroplating, the electroplating process should be
started at a low current density (10-20 mA/cm2) and the current density can be gradually
increased up to 100 mA/cm2 to speed up the process. When the current density is too


65
mode loss dependence of the process window width can be ignored unless the mode loss is
very large. Hence, comparison of the process-window widths between different thin
p-clad structures can be done by comparing the mode-index profiles of the two structures.
100 200 300 400 500
Interelement cap thickness (nm)
Figure 4-7. Enhanced process-window (w2) with a AlGaAs cap layer and a reduced
p-clad thickness (200 nm) compared with a process-window of a typical
thin p-clad structure with GaAs cap layer and p-clad thickness of 400 nm.
In order to estimate a process-window width roughly, one has to know the interele
ment mode-index range corresponding to the process-window. The interelement mode-
index range can be estimated using the resonant coupling condition (equation (3.3)) with
given values of d, s and n0e. The interelement mode-index (n0i) range for the process-
window of the m = q in-phase mode (7 = 0) is approximately between the two reso
nance n0 values for the m = q in-phase and m = q+1 out-of-phase modes. This gives an
easy way to design a thin p-clad structure for MCTC antiguided array lasers since the cal
culation of the array mode gain profiles is a very time-consuming process.


67
Interelement cap thickness (nm)
(a)
Interelement cap thickness (nm)
(b)
Figure 4-8. Comparison of the process windows of two 18 element arrays with :
(a) a very lossy cap layer (cap loss = 2000 cm'1); (b) a typical cap layer
(cap loss =120 cm'1); d = 5 p.m, s = 2 |lm, and tcl = 465 nm.
Combining all the aspects discussed in this section with the process-window con
cept, one can engineer thin p-clad structures for high fabrication yields of stable in-phase
operating MCTC antiguided array lasers with consideration of practical growth and fabri
cation procedures. One such an epitaxial structure will be proposed in the last chapter.


98
can be sandwiched between two other cap layers of the ternary material, but the absorption
loss layer should be thicker than the QW gain layer to ensure band-to-band absorption in
the loss layer. As the loss layer thickness increases, a larger mode loss is obtained, but
the index slope is also increased (which leads to a narrower process-window) because the
refractive index of the loss layer is higher than those of other layers. Therefore, the mole
fraction of the ternary material and the loss layer thickness should be optimized together
to obtain a wide process-window with large array mode discrimination.
With the idea of the above three cap-layer structure, a new epitaxial structure for
MCTC antiguided array lasers has been designed (Figure 7-1). The cap layers of the pro
posed structure are 100 nm p+-GaAs lower cap layer, 15 nm In0 15GaQ 85As loss layer, and
270 nm p-Al0 2Gao 8As upper cap layer. The p-clad thickness is 300 nm. The calcu
lated process-window for a 19 element device (5 (im wide elements with 2 |im wide inter
elements) with this structure is shown in Figure 7-2. For this calculation, 10000 cm'1
absorption loss was assumed for the InGaAs loss layer, and the element cap thickness was
fixed at 50 nm. The process-window width (where array mode discrimination is larger
than 2 cm'1) is about 28 nm, which is large enough for a high fabrication yield. The max
imum array mode discrimination is about 7.5 cm'1.
Since the proposed p-cap structure is not a common structure and the related growth
and fabrication techniques have not yet been developed, those techniques need to be stud
ied further. Especially, the growth of well defined p-cap QW loss layer is important to
achieve high fabrication yields of stable in-phase array devices.
There are several other things to be studied further for transferring the MCTC antigu
ided array technology to industry. They include facet coating, thermal effects in CW


11
1.3 Motivation
High brightness semiconductor lasers (high power, spatially coherent sources) are of
considerable interest for use in applications such as efficient pumping of solid-state lasers,
fiber amplifiers and lasers, high speed optical recording and printing, and free space
communications. Conventional narrow-stripe (~5 fim wide) single-spatial-mode lasers
provide at most 200 mW reliably because of the limitation of the optical power density at
the laser facet. For reliable operation at higher power levels, large-aperture (> 100 Jim)
sources which operate in a single-spatial mode are necessary. However, single-stripe
large-aperture lasers are inherently operating in multi-spatial modes since the number of
allowed spatial modes is increasing with the stripe width. Thus, achieving single-spatial
mode operation from large-aperture devices at high-power levels has proved challenging.
One way to achieve such devices is to phase-lock an array of narrow-stripe single-
spatial-mode lasers. Such a phase-locked array (coherent array) of diode lasers operates
as a single coherent source at a power level that can be one to two orders of magnitude
higher than a standard single-element device. The phase-locked array structures
which have been studied to date include the antiguided array (leaky-wave coupled
array), the positive-index waveguide array (evanescent-wave coupled array), the Y-junc-
tion coupled array, and the diffraction coupled array. Of these, the antiguided array laser
[15] has demonstrated the best performance. Since the effective refractive-index of the
optical gain regions (elements) in these antiguided array lasers is lower than that of the
interelement regions, the individual antiguided lasers (elements) in the array can be cou
pled to all others by lateral leaky waves through the interelement regions. An example of
the beam quality which has been achieved with a 23 element anti guided array laser (150


31
2.4 Monolithic Semiconductor Laser Arrays
In order for a laser array to operate in the in-phase array mode, the first condition is
that the optical field of the each element laser of the array should reach to those of the
other element lasers and interact with them (coupling). In a typical positive-index-
guided laser array, for which the near-field intensity peaks are in the high-index array
regions (also optical gain regions), this condition is obtained by evanescent fields of the
elements when the element lasers are close enough to each other (see Figure 2-8 (a) eva
nescent-wave coupled array). Three more basic types of coupling schemes are depicted
in Figure 2-8: Y-junction coupled array, diffraction coupled array, and leaky-wave coupled
array.
Evanescent-wave coupled array devices were the subject of intensive research over
the 1983 1988 time period. It has been proved that it is difficult to achieve the in-phase
operation with evanescent-wave coupled arrays because they tend to operate in the out-of-
phase mode [30, 31]. In order to overcome this problem, several techniques were tried
and they included preferential interelement pumping [32], buried-rib-guide element arrays
for higher transverse optical-mode confinement in the interelement regions [33 35],
chirped arrays [36-39], and using k phase-shifters in front of alternate array elements
[40 42], Even though some good results were obtained with those techniques, they
were from arrays of a few elements, not from arrays of many elements which are required
for high power devices. Performances of those devices were not stable for high power
operations.
As a consequence of the difficulties encountered in obtaining stable in-phase opera
tion from evanescent-wave coupled arrays, alternative coupling schemes were proposed


25
shown in the figure, when the sinusoidal f^x) is used, the width of Fs(6) profile is
increased and hence so are the heights of the side lobes of the array far-field. This is
because the slit width for the sinusoidal f^x) is effectively reduced, compared with that
for uniform f^x): the divergence angle of a single slit far-field increases as the slit width
reduces. The divergence angle (6d) for f^x) = cos(jncld) is Tan1 (1.5Jd) (-15.91 for
this case) instead of Tan1 (kid) (-10.76 for this case) for fN(x) = 1.
Lateral angle 6 (degree)
Figure 2-5. Array far-field pattern for f^x) = cos(Kxld) compared with that for f^x) = 1
:An= 1, A = 0.95 |im, d- 5 (im, T 7 |im, and N = 7.
For the above two cases, the complex amplitudes (An) of the element (slit) near
fields were assumed to be uniform across the array. For monolithic semiconductor laser
arrays, however, the amplitudes are usually nonuniform across the array because the ele
ment lasers of the array are optically coupled to each other. According to the


I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
Peter S. Zory, Chair (
Professor of ElectricaTand
Computer Engineering
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
Professor of Electrical and
Computer Engineering
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standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
/TU Fredrik. A. Lindholm
Professor of Electrical and
Computer Engineering
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standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy
CAjIAA.
Ramu V. Ramasvvamy
Professor of Electrical and
Computer Engineering
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standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy. ^
£
! £
Chris J. Stanton
Professor of Physics


79
high, bubbles are generated on the sample surface. This should be avoided because the
bubbles are stuck on the sample surface and obstruct further electroplating on the area
under the bubbles. As the electroplated gold is getting thicker, the color of the electro
plated area becomes shiny bright yellow, brownish yellow then rusty brown. The elec
troplating process should be finished before the electroplated area becomes brownish
yellow since too thick gold stripes on the sample can be peeled off easily when the sample
is cleaved into bar forms for test.
5.4 Fabrication of MCTC Antiguided Array Lasers
A fabrication procedure of MCTC antiguided array lasers is presented in sequence
as follows.
1. Wafer cleaning is performed by boiling the wafer with TCA, acetone, and methanol in
sequence. Some tough stains which are difficult to clean with TCA, acetone and
methanol can be removed by leaving the wafer in a developer solution for photolithog
raphy for a couple of minutes and repeating the first boiling step. Note that GaAs
oxide is easily dissolved in a developer.
2. Pulsed anodization etching on the whole cap layer surface is performed for required
interelement cap thickness and the oxide layer in interelement regions. This step is for
oxide
converting the top part of the cap layer into a GaAs native oxide layer (~100 nm) and
making cap thickness t¡ at the same time. Since the oxide is -100 nm thick, the initial
cap thickness should be bigger than t¡ at least by 100 nm. This first pulsed anodization


CHAPTER 2
FOURIER OPTICS AND SEMICONDUCTOR LASER ARRAYS
2.1 Introduction
In order to understand the behavior of the output beam (far-field) from a laser array,
the relation between the near-field at the laser facet and the far-field using Fourier optics
was studied. In Sec. 2.2, the basic concepts of Fourier optics are explained briefly, and
the Fraunhofer approximation is used for practical calculations of far-field patterns. In
Sec. 2.3, the computation formalism of the far-field from an array of light sources is intro
duced. Several far-field patterns from different near-field patterns are calculated and the
resulting plots are shown. This calculation shows the need for phase-locking between
array elements to have a narrow central lobe in the far-field patterns which contains most
of the beam power. The phase-locked mode for this type of operation is called in-phase
array mode. Basically, the phase-locking condition is said to be in-phase when the
fields in each element are cophasal and out-of-phase when the fields in adjacent elements
are a n phase-shift apart. For an out-of-phase array mode, the corresponding far-field
has two main lobes. For most applications using semiconductor laser arrays, in-phase
mode operation is desirable, and hence the characteristics of in-phase far-field patterns are
focused on to investigate the effects of array dimensions on FWHM of the central main
lobe and power percentage in the main lobe.
Once the necessary conditions for achieving an in-phase near-field distribution are
known, the next question is how to achieve these conditions in laser array devices.
16


87
length L = 500 (im is shown in Figure 6-2 (a). The beam width (FWHM) of the central
lobe of the far-field is 1.3 at 15% above threshold, which is nearly diffraction-limited.
This indicates in-phase operation at that drive level.
For = 150 nm, the calculated An0 was 0.07 and out-of-phase operation occurred
as shown in Figure 6-2 (b). The threshold current and slope efficiency of these lasers were
essentially the same as for the in-phase lasers, 70 mA and 0.42 W/A respectively. With
increasing current, the two far-field lobes were somewhat more stable with respect to broad
ening than for the central lobe of the in-phase lasers.
For the devices with dm = 210 nm, the calculated An0 was 0.12 and the typical thresh
old current was ~110 mA. As shown in Figure 6-2 (c), one wide central lobe was
observed in the far-field pattern indicating that the individual elements in the array were
not strongly coupled. This lack of coupling is probably the reason for the nearly 60%
increase in threshold current relative to the in-phase and out-of-phase mode lasers. In this
case the lasing modes cannot adjust so as to avoid the lossy thick cap sections.
As shown with the above results, MCTC antiguided array device performances are
greatly dependent on cap thickness modulation. This indicates that a large refractive-
index modulation can be obtained by modulating cap thickness of a thin p-clad structure.
With the encouragement from the 5 element devices results, 20 element devices
were also fabricated and characterized. While they had been designed for an in-phase
operation with 5 p.m wide elements and 2 (im interelement spacing, the devices were
mostly operating in out-of-phase mode possibly because of etch-depth errors for interele
ment cap thickness. The typical near-field and far-field patterns of 20 element out-of-phase
array lasers are shown in Figure 6-3. These array lasers were made from 465 nm


76
t = 0
Leading edge
current
V t>0
Trailing edge current
Time
Figure 5-2. Typical current pulse shape during pulsed anodization etching.
Two different acid concentration GWAs have been developed for fabrication of
MCTC antiguide array lasers: one is for slow etching, the other is for relatively fast etch
ing. The ratio of G:W:A for the slow etching is 40:20:1 (which is named GWA) while
that for the fast etching is 8:4:1 (which is named GWA841). The electrolyte GWA is a
slower and more precise etchant than GWA841, so both electrolytes are used to fabricate
MCTC antiguided array lasers due to their merits. GWA is used to perform a slower etch
of the whole wafer surface to obtain the right cap thickness for interelement regions,
which must be precise, with the remaining oxide not being removed quickly in the electro
lyte after the process is done and the circuit is off. For the groove etching of element
regions, GWA841 is used because it is faster and produces smaller undercut, resulting in
better control of array dimensions and steeper side walls.
The etch rate for pulsed anodization is not constant with time t and etch depth, h(t),
can be predicted with the following expression:
h (t) = v0t + h0[ 1 exp (-at) ] .
(5.1)


26
coupled-mode analysis for an array of N coupled, identical elements [28, 29], an array of
N emitters has N normal modes or eigenmodes which are called array modes. Each array
mode has a field-amplitude (An) configuration that is nonuniform across the array.
Four array modes of a 7 element array are schematically depicted in Figure 2-6 (a)
with sinusoidal element near-fields. There is a succession from the fundamental array
mode, K 1, the 0-phase-shift mode defined in Figure 2-6 (a), to the last high-order array
mode, K = N (7 for this case), the 180-phase-shift mode also defined in the figure. The
common names of the fundamental (K = 1) and the highest order {K = N) modes are in-
phase and out-of-phase modes respectively. Shown with a dashed line are the envelope
functions of the array-mode near-field amplitude profiles, which correspond to the modes
of an infinite potential well of width (N + 1 )T.
The far-field patterns corresponding to each array mode are shown in Figure 2-6 (b).
The single-element far-field distribution Fs(6) for the sinusoidal element near-field distri-
bution/^j:) = cos(jDdd) is the dashed curves in the figure and can be obtained using equa
tion (2.16):
FA 6) -
cos (ndv)
,v =
tan0
X
(2.18)
(2dv)2- 1
From this equation, the divergence angle 6d is easily proved to be Tan1 (1.5X1d). The
grating function Fg(9) for the array modes can be calculated using equation (2.17) and the
array-mode near-field amplitude (An) profiles shown in Figure 2-6(a):
F/0) =
sin
{N + 1) nTv +K ^
cos
K 71
N+ 1
- cos (2jiTv)
)V = m0 ^=ll2, ,
(2.19)
where K is the array mode number, and this equation is not a normalized expression.


91
Figure 6-3. Near-field and far-field patterns of 20 element MCTC antiguided array
lasers (out-of-phase operation) d = 5 p.m, s 2 |im.


35
results in higher near-field peaks in the central elements. The net effect on the in-phase
mode is self-focusing, which further accentuates the mode-profile non-uniformity. Thus
a positive feedback mechanism is created, which, with increasing drive, narrows the near
field and broadens the far-field beam-width. At the same time, since the area of the array
is uniformly pumped, more and more gain is available for the high-order modes (adjacent
modes) which can reach threshold and cause further broadening of the far-field beam-
width. Therefore, the in-phase mode of evanescent-wave coupled arrays is fundamen
tally unstable with increasing drive level.
Unlike evanescent-wave coupled arrays, there is no limitation on An for antiguided
arrays (leaky-wave coupled); that is, no matter how high An is, the fundamental lateral
mode is favored to lase in the elements. This fact makes it possible to fabricate in-phase
operating arrays with high index-steps (> 0.01) which are stable against thermal and/or
carrier induced refractive-index variation. Since the elements can be strongly coupled by
leaky waves in antiguide arrays, the envelope of the near-field profile of the in-phase mode
can be nearly flat unlike the prediction of coupled-mode theory which is for weakly cou
pled devices. Hence, gain spatial hole burning can be prevented in antiguided arrays.
In conclusion, for high-power devices, antiguided arrays are what ensure stable in-phase
operation to high drive levels.


18
amplitude and vx and vy are the spatial frequencies (cycle per unit length) in the x and y
directions, respectively. The harmonic function F(vx, vy) exp[-j2n(v,^* vyy)] is the two-
dimensional building block of the theory.' It can be used to generate an arbitrary function
of two variables f(x,y).
The plane wave U(x,y,z) = A exp[-j(k^+kfl+k^)] plays an important role in wave
optics. The coefficients (kx, ky, kz) are components of the wave-vector k and A is a com
plex constant. At points in an arbitrary plane, U(x,y,z) is a spatial harmonic function. In
the z=0 plane (near-field plane), for example, U(x,y,0) is the harmonic function, Aexp[-
j2it(vxx+ vyy)], where = k^n and Vy = ky!2n are the spatial frequencies and kx and ky
are the spatial angular frequencies. There is a one-to-one correspondence between the
plane wave U(x,y,z) and the spatial harmonic function U(x,y,0), provided that the spatial
frequency does not exceed the inverse wavelength 1 fk. Since an arbitrary function f(x,y)
(near-field) can be analyzed as a superposition of harmonic functions, an arbitrary travel
ing wave may be analyzed as a sum of plane waves. The plane wave is the building
block used to construct a wave of arbitrary complexity.
Apparently, there is a one-to-one correspondence between the plane wave U(x,y,z)
and the harmonic function U(x,y,0). Given one, the other can be readily determined if the
wavelength X is known. Given the wave U(x,y,z), the harmonic function U(x,y,0) is
obtained by sampling in the z=0 plane. On the other hand, the wave U(x,y,z) is con
structed by using the relation U(x,y,z) = U(x,y,0) exp(-jkzz) with
2 2 2 1/2 22? 1/2
k=(k-kx-kv) = 2k(\/X -v-vv) ,k = 2n/X.
x y x y
(2.1)


CHAPTER 4
MODULATED CAP THIN P-CLAD ANTIGUIDED ARRAY LASERS
4.1 Introduction
In most diode laser applications, it is desirable that the laser devices have low
threshold current density and high differential quantum efficiency. In order to fulfill
these two requirements, semiconductor laser structures must be designed to have both
high optical field and carrier confinements in the active region. Normally this is obtained
by making the cladding layers thick, usually greater than the lasing wavelength. How
ever, as the name indicates, thin p-clad laser structures have a thin p-clad layer with a thick
n-clad layer for different device purposes.
Since the p-clad layer of thin p-clad structures is thin, the separation distance
between the active region and the p-contact layer can be small enough to cause a strong
interaction between lasing modes (transverse modes) and the contact layer. Utilizing this
characteristic of thin p-clad structures, one can easily affect the lasing modes by affecting
the cap-layer (changing the cap-layer thickness or contact metal). This has been shown
in several publications relating the utilization of thin p-clad laser structures with the fabri
cation of surface-emitting [56, 57] and edge-emitting [58] distributed feedback (DFB)
lasers.
In Sec 4.2, the basic properties of thin p-clad laser structures are discussed which
include cap-thickness dependence of effective refractive-index and mode loss for trans
verse modes. Utilizing those properties, modulated cap thin p-clad (MCTC) antiguided
50


93
Injection current, I (mA)
Figure 6-5. P-I curve of a 23 element MCTC antiguided array laser (in-phase operation);
d = 5 pm, s = 2 p.m.


63
In Figure 4-6, shown are the changes in the mode-index curve for the interelement
regions when the A1 composition of AlGaAs material used for the cap layer increases for a
fixed p-clad thickness (a) and when the p-clad thickness changes for a GaAs cap layer (b).
For this calculation, the graded AlGaAs guide layers (in the active region) described in
Sec 4-2 for the structure shown in Figure 4-1 were replaced with Al^Ga^As layers.
The refractive-index of AlGaAs material gets smaller as the A1 composition increases.
As shown in Figure 4-6 (a), when the A1 composition increases while the p-clad thickness
is fixed at 400nm, the slope of the mode-index curve decreases, the knee of the curve
shifts toward the larger interelement thickness side, and the radius of the knee curvature
increases. The shift of the knee causes a shift of the process-window and the increasing
radius of the curvature results in a wider process-window. Thus, the combination effects
of the decreasing slope and the increasing radius of the knee curvature result in a wider
process-window. The radius of the knee curvature can be further increased by reducing
the p-clad layer thickness. Figure 4-6 (b) shows the changes of the knee curvature with
decreasing p-clad thickness. For this calculation, a GaAs cap layer was used. It is
observable that the radius of the knee curvature increases significantly when the p-clad
thickness decreases from 400 nm to 200 nm.
In Figure 4-7, a process-window (W2) enhanced by combining the two aspects of
larger A1 composition of AlGaAs cap layer and smaller p-clad thickness is compared with
a process-window (wj) for a typical thin p-clad structure. For window wl5 a typical p+-
GaAs cap layer and a p-clad thickness of 400 nm were used and for window w2, a p+-
Al0 15GaQ 85As cap layer was assumed with a p-clad thickness of 200 nm. As shown in
the figure, the interelement cap thickness range corresponding to the mode-index range


20
at the spatial frequencies vx = x/Xl and Vy = y/Ai:
This approximation is valid iff^x,y) is confined to a circle of radius b satisfying b2l?d 1,
and this condition is easily satisfied for practical far-field calculation. The details of the
Fraunhofer approximation can be found in most Fourier optics textbooks [26, 27].
The expression for the far-field intensity distribution Ip(x,y), which is an actual mea
surement with experiments, is obtained by multiplying the complex conjugate of fp(x,y)
with fp(x,y);
(2.6)
Then, the angular distribution pattern for the far-field intensity FF(9x,6y) can be defined
by the absolute value of the Fourier transform Fp¡(xl?J,yl?J) with replacing x/l and y/l with
tan6x and tanOy respectively (see Figure 2-1);
(2.7)
Figure 2-2 shows an example of a far-field pattern from a single one dimensional slit
of uniform near-field (constant amplitude with constant phase). The width of the slit is D
and the amplitude of the near-field is A. The near-field function f^x) can be expressed as
follows (see Figure 2-2 (a)):
(2.8)
_ 0 ;otherwise
and then the Fourier transform F^v) offp¡(x) is found using equation (2.2):
kvD
(2.9)


13
achieved, commercialization of antiguided array lasers has not been realized because of
the difficulties in reproducing the required lateral refractive-index modulation with those
complex processes and very small fabriction tolerances of the devices.
In order to commercialize antiguide array lasers, easier fabrication techniques
should be employed, which will also ease fabrication tolerances. Utilizing a thin p-clad
laser structure [22, 23], the required lateral index modulation for antiguided array lasers
can be easily obtained by modulating the cap layer thickness which can be done with a
simple etching process without regrowth and dopant diffusion. Modulated-cap thin
p-clad (MCTC) antiguided array lasers are, therefore, easily fabricated with standard
post-growth processing steps such as pulsed anodization etching [24], photolithography,
and metallization. The MCTC structure will be very likely employed to make practical
antiguided array lasers when the necessary technologies have been fully developed. In
this dissertation, the use of a thin p-clad structure for the fabrication of antiguided array
lasers is proposed and demonstrated [25]. Based on theoretical and experimental
research, this dissertation is also devoted to developing the fabrication technologies of
MCTC antiguided array lasers.
1.4 Overview
This dissertation is a systematic study of the thin p-clad laser structure for
fabricating antiguided array lasers which produce spatially coherent high power output
beams.
In Chapter 2, Fourier optics is introduced in order to understand the output beam
(far-field) behaviors of laser arrays. Fourier optics calculations of the far-field distribu
tion from the near-field of an array of light sources show the need of phase-locking


3
1.2 Basic Operating Principies
The purpose of this section is to provide a qualitative understanding of the physics
underlying semiconductor laser operation. Two things are required to operate a laser: (i)
a gain medium that can amplify the electromagnetic radiation propagating inside it and
provide the spontaneous emission noise input and (ii) a feedback mechanism. As the
name itself implies, the gain medium for a semiconductor laser consists of a semiconduc
tor material. The optical feedback is obtained using the cleaved facets that form a Fabry-
Perot (FP) cavity and the mode confinement is achieved through dielectric waveguid-
ing. In order to provide optical gain, a semiconductor laser needs to be externally
pumped, and both electrical and optical pumping techniques have been used for this pur
pose. A simple, practical, and most commonly used method employs current injection
through the use of a forward-biased p-n junction. Such semiconductor lasers are some
times referred to as injection lasers or laser diodes.
A p-n junction is formed by bringing a p-type and an n-type semiconductor into
contact with each other. When they first come in contact, their Fermi levels do not match
since the two are not in equilibrium. An equilibrium is, however, quickly established
through diffusion of electrons from the n-side to the p-side, while the reverse occurs for
holes. These diffusing electrons and holes recombine in the junction region. Eventually
a steady state is reached in such a way that further diffusion of electrons and holes is
opposed by the built-in electric field across the p-n junction arising from the negatively
charged acceptors on the p-side and positively charged donors on the n-side. The Fermi
level is then continuous across the p-n junction, as shown in Figure 1-1 (a) where the
energy-band diagram of the p-n homojunction is shown. When a p-n junction is
forward-biased by applying an external voltage, the built-in electric field is reduced,


96
the ternary material, the refractive-index of the cap layer can be changed and the trans
verse mode overlap with the cap layer can be affected by changing p-clad layer thickness.
Employing these effects, a wider process-window can be obtained Another way to create
a wide process-window is to use a very lossy material for the cap layer because the large
loss of the layer suppresses out-of-phase and adjacent modes severely in the vicinity of a
process-window and pushes down the mode gain profiles of those modes.
Controlling the cap thicknesses of element and interelement regions, which involves
the etching process, is cmcial for obtaining in-phase laser operation in MCTC antiguided
arrays. In addition to the etching process, making a GaAs native oxide layer over the cap
layer in the interelement regions is necessary to confine the optical gain only in the ele
ment regions. An improved pulsed anodization etching technique was used for both pro
cedures. The electrolyte used in pulsed anodization etching is GWA, which is a mixture
of ethylene glycol, deionized water and phosphoric acid. Two different acid concentra
tion GWAs have been developed for slow and fast etching: GWA and GWA841, respec
tively. GWA is used to perform a slower etch of the whole wafer surface to obtain the
right cap thickness and a native oxide layer for interelement regions. For the groove
etching of element regions, GWA841 is used because it is faster and produces smaller
undercut, resulting in better control of array dimensions and steeper side walls. For p-
and n-metallization, electroplating technique has been used along with electron-beam
evaporation. To minimize p-metal loss, a shiny gold contact (no annealing) is necessary
and the electroplating technique is simple and good for the requirement.
Five element MCTC antiguided array lasers fabricated with three different cap
thickness modulation depths at the early stage of this study showed the characteristics of


48
(Al0 3GaQ 7As / Al0 jGaQ 9As) is grown on top of a GaAs substrate. Then channels are
etched and a planar DH (double-heterostructure) laser structure is regrown, talcing advan
tage of the LPE-growth characteristics over patterned substrates [55]. Each buried inter
channel mesa had both higher effective refractive-index and lower transverse mode gain
than the channel regions. Devices made in late 1980s and early 1990s were fabricated
by metal-organic chemical vapor deposition (MOCVD) and can be classified into two
types: the complimentary-self-aligned (CSA) stripe array [15, 50] (Figure 3-9 (a)); and the
self-aligned stripe (SAS) array [18, 19] (Figure 3-9 (b)).
Complimentary-self-aligned Arrays
p-GaAs
p+-GaAs (cap layer)
p-Al0 gGa^ 4As (clad layer)
p-Alg^Gao^As (passive guide)
p-AloeGap^As (clad layer)
/ ' / active region
n-Al0 gGa^ 4As (clad layer)
(a)
Self-aligned-stripe Arrays
p-GaAs
p-Al0 6Gao 4As (clad layer)
p-Al0 3GaQ 7As (passive guide)
active region
n-Al0 6Ga<) 4As (clad layer)
Figure 3-9. Schematic diagrams of present antiguided arrays: (a) complimentary-selF
aligned (CSA) arrays; (b) self-aligned-stripe (SAS) arrays.
In CSA-type arrays, preferential chemical etching and MOCVD regrowth occur in
the interelement regions. For SAS-type arrays, the interelement regions are built-in


TABLE OF CONTENTS
page
ACKNOWLEDGMENTS iii
ABSTRACT vii
CHAPTERS
1 INTRODUCTION 1
1.1 Historical Perspective on Semiconductor Lasers 1
1.2 Basic Operating Principles 3
1.3 Motivation 11
1.4 Overview 13
2 FOURIER OPTICS AND SEMICONDUCTOR LASER ARRAYS 16
2.1 Introduction 16
2.2 Fourier Optics and Far Field Patterns 17
2.3 Far Field Patterns from Arrays of Light Sources 22
2.4 Monolithic Semiconductor Laser Arrays 31
2.5 Array Mode Stability 34
3 ANTIGUIDED ARRAYS 36
3.1 Introduction 36
3.2 Single Real Refractive-Index Antiguides 37
3.3 Antiguided Arrays 39
3.4 Antiguided Array Fabrication Techniques 46
4 MODULATED CAP THIN P-CLAD ANTIGUIDED ARRAY LASERS .. .50
4.1 Introduction 50
4.2 Thin P-clad Laser Structure 51
4.3 Modulated Cap Thin P-clad (MCTC) Antiguided Array Lasers 55
4.4 Design Aspects of Thin P-clad Epitaxial Structures for MCTC Antiguided
Array Lasers 62
4.5 Design Aspects of MCTC Antiguided Array Lasers 68


88
p-clad material. In the near-field profiles, 20 peaks of individual element laser beams are
distinguishable and the far-field pattern is quite stable with increasing current level. The
typical threshold current (1^) was ~140 mA and a total P-I slope efficiency was -0.52W/A
with a pulse width and a frequency of 40 Jisec and 1 kHz, respectively. This second fabri
cation confirmed again the phase-locked operation of MCTC antiguided array devices.
Finally, with improved pulsed anodization technique, stable in-phase mode opera
tion was achieved with 23 element MCTC antiguided array lasers. The elements were 5
Jim wide and the interelement regions were 2 Jim wide. Unlike the 5 element MCTC
antiguided array lasers fabricated with the 250 nm p-clad material, 465 nm p-clad material
was used to improve a better P-I slope efficiency. Other than the p-clad layer thickness,
the rest of the wafer structure was the same with the structure for the 5 element arrays.
For these lasers, the array pattern was created over the entire surface of the wafer and then
stripes for individual array lasers were defined; in the 5 and 20 element array lasers, the
array pattern was fabricated only inside the stripe area. The cap thickness in the element
regions and in the interelement regions were 100 nm and 230 nm respectively. The thick
ness of the oxide in the interelement regions was 100 nm.
These 23 element MCTC anti guided array lasers were designed for m 3, in-phase
operation and the required An0 was 0.076. The measured near-field and far-field intensity
patterns of one of the lasers with cavity length L = 500 |im are shown in Figure 6-4. The
beam width (FWHM) of the central lobe of the far-field was 0.8 at 1.2 x 1^ (Ith =
~200mA) and 1.6 at 10 x 1^. The far field behavior with increasing current, as shown in
Figure 6-4, is greatly improved compared with that of the 5 element lasers. Up to 10 x 1^
current level which is the limit of our pulser, the far field pattern of in-phase operation was


14
between array elements for a single main peak far-field pattern and array dimension
effects on full width at half maximum (FWHM) of the far-field main lobe and power per
centage in the lobe. Then different types of monolithic semiconductor arrays are intro
duced. Previous fabrication techniques of monolithic semiconductor arrays are presented
with a brief discussion of device stability.
Chapter 3 reviews antiguided array theory in order to explain basic concepts.
First, a single antiguide structure is discussed to show lateral mode discrimination due
to the lateral radiation loss. The wavelength of the lateral leaky-wave of a single antigu
ide is also derived. This wavelength is related to the required lateral array dimensions
for maximum coupling (resonant coupling) between array elements of antiguided
arrays. Near-field modes (array modes) of antiguided arrays are then shown and defined
to be used for discussion of array mode discrimination. Finally, previous antiguided
array results are addressed which are involved with complicated growth or impurity disor
dering technologies.
Chapter 4 describes how to achieve antiguided array lasers with a thin p-clad laser
structure and how to design a thin p-clad structure for antiguided arrays. After a brief
explanation of a thin p-clad laser structure, two major characteristics of the structure for
fabricating antiguided arrays are introduced. They are drastic changes in refractive-index
and mode loss of a transverse lasing mode with small changes in the p+-cap layer
thickness, which make it easy to induce the required index modulations for antiguided
array lasers with a simple modulations of the p+-cap layer. A new concept, process-
window, is also introduced, and with the concept, various design aspects of epitaxial
structures and array dimensions are explored.


5
making possible a further diffusion of electrons and holes across the junction. As shown
in Figure 1-1 (b), both electrons and holes are present simultaneously in a narrow
active region and can recombine ether radiatively or non-radiatively. Photons of
energy hv ~ Eg are emitted through radiative recombination. However, these photons can
also be absorbed through a reverse process that generates electron-hole pairs. When the
external voltage exceeds a critical value, the rate of photon emission exceeds that of
absorption. The p-n junction is then able to amplify the electromagnetic radiation and is
said to exhibit optical gain. However, for a homojunction the thickness of the region
where gain is sufficiently high is very small since there is no mechanism to confine the
charge carriers (electrons and holes).
The carrier-confinement problem is solved with the use of a p-n heterojunction.
Figure 1-2 (a) shows the schematic energy-band diagram for a double-heterostructure
laser wherein the thin active region has a lower band-gap compared to that of the p-type
and n-type cladding layers. Electrons and holes can move freely to the active region
under forward bias. However, once there, they cannot cross over to the other side
because of the potential barrier resulting from the band-gap difference. This allows for a
substantial build-up of the electron and hole populations inside the active region, where
they can recombine to produce optical gain. The successful operation of a laser requires
that the generated optical field should remain confined in the vicinity of the gain region.
In double-heterostructure semiconductor lasers the optical confinement occurs by virtue of
a fortunate coincidence. As shown in Figure 1-2 (b), the active layer with a smaller
band-gap also has a higher refractive index (na) compared with that (nc) of the
surrounding cladding layers. Because of the index difference, the active layer in effect


Abstract of Dissertation Presented to the Graduate School of the
University of Florida in Partial Fulfillment of the Requirements for the
Degree of Doctor of Philosophy
MODULATED CAP THIN P-CLAD ANTIGUIDED ARRAY LASERS
By
Jeong-Seok O
December, 1998
Chairman: Peter S. Zory
Major Department: Electrical and Computer Engineering
The use of a thin p-clad laser structure with a modulated cap thickness for the
fabrication of spatially coherent high-power phase-locked antiguided array lasers is
proposed and demonstrated. Also presented are design aspects, fabrication techniques
and characterization of these modulated cap, thin p-clad (MCTC) antiguided array lasers.
The work began with understanding the fact that minor contouring of the contact
surface of the cap layer of thin p-clad laser structures causes significant changes in the
complex effective refractive-index of the transverse lasing mode. Since large refractive-
index variations are required to fabricate monolithic antiguided array lasers, it was pro
posed that thin p-clad laser structures might be suitable for this purpose.
MCTC antiguided array lasers operating at a wavelength of 950 nm were fabri
cated in thin p-clad InGaAs/GaAs single quantum well material. The edge emitting
arrays had 23 lasers on 7 (im centers with 5 Jim wide gain regions (elements). The spa
tially coherent output beam from the best arrays had an 0.8 wide central lobe containing
vii



PAGE 1

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106
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46
out-of-phase and adjacent modes and that the in-phase mode is favored to lase only in a
certain range of the lateral refractive-index step, where the in-phase mode is the lowest-
loss mode. The mode loss (or gain) profiles also depend on the array dimensions because
the dimensions directly affects the lateral mode confinements in the element (gain) and
interelement (loss) regions (this will be discussed in a later chapter). Therefore, for
designing antiguided array devices, the mode loss (or gain) profiles should be calculated to
find the An range where the in-phase mode operation is most favored.
3.4 Antiguided Array Fabrication Techniques
Historically, the first arrays of antiguided lasers were gain-guided arrays [51] (Fig
ure 3-8 (a)) since an array of current-injecting stripe contacts provides an array of carrier-
induced refractive-index depressions for which the gain is highest in the depressed-index
regions. While the radiation losses can be quite high for a single antiguide [52], closely
spacing antiguides in linear arrays reduces the device loss significantly [53], since radia
tion leakage from individual elements mainly serves the purpose of coupling the array ele
ments.
The first real-index antiguided array was realized by Ackley and Engelmann [54].
This was an array of buried heterostructure (BH) lasers designed such that the interele
ment regions had higher refractive indices than the effective refractive indices in the bur
ied active mesas (Figure 3-8 (b)). Since the high-index interelement regions had no gain,
only leaky array modes could lase. The device showed definite evidence of phase lock
ing (in-phase and out-of-phase) but had relatively high threshold-current density (5 7 kA
/ cm2) since the elements were spaced far apart (13 -15 fim), not allowing for effective
leaky-wave coupling.


39
0.95 Jim, ne = 3.263 and antiguide core gain ge of 20 cm'1. The loss difference between
the two modes is ~60 cm"1 at An = 0.2, which is a quite large discrimination against the
first order mode.
Figure 3-2. Radiation loss as a function of lateral index step An for 7 = 0 and 7=1 lateral
modes with d = 5 Jim, X0 = 0.95 Jim, ne = 3.263 and antiguide core gain ge of
20 cm'1.
3.3 Antiguided Arrays
Owing to lateral radiation, a single antiguide can be considered as a source of later
ally propagating travelling waves of wavelength \¡ (see Figure 3-1 (b)). Then in an array
of antiguides, elements will be resonantly coupled in-phase or out-of-phase when the
interelement spacings (s) correspond to an odd or even integral number (m) of half the lat
eral wavelength (k¡ / 2), respectively. From this condition and the expression of (equa
tion (3.1)), the resonant phase-locked coupling condition is


ACKNOWLEDGEMENT
First and foremost, my deepest thanks for this work should go to Dr. Peter S. Zory,
Jr., my advisor. In addition to his support for my graduate study, his excellent academic
and technical knowledge in the field of semiconductor lasers has been the greatest
encouragement of my graduate research. He has inspired me not only academically but
also spiritually. The largest part of my achievement in this work is attributed to his guid
ance with great inspiration.
I would like to thank the members of my committee; Dr. Gijs Bosman, Dr. Fredrik
A. Lindholm, Dr. Ramu V. Ramaswamy, and Dr. Chris J. Stanton. It is my great
privilege to have these honorable professors as my committee members and to be guided
by them. Their keen suggestions and corrections have been very helpful for making this
work better. I would also like to thank Dr. Dan Botez at the University of Wisconsin,
Madison, who is a world expert on antiguided array lasers. Most of my basic knowl
edge of antiguided array lasers was initiated by his educational discussions on the subject
with me. He was always very willing to give his valuable advice to me and I was encour
aged very much by him.
I thank the U.S. Air Force Research Laboratory for sponsoring this work. Dr. Mark
A. Emanuel at Lawrence Livermore National Lab., Dr. Bradley D. Schwartz and Dr. Rich
ard S. Setzko at Hughes Danbury Optical Systems are also given my appreciation for
providing the thin p-clad laser materials used in this study. I thank Mr. Steve Shein of the


CHAPTER 6
CHARACTERIZATION OF MCTC ANTIGUIDED ARRAY LASERS
6.1 Introduction
In this chapter, the experimental results of MCTC antiguided array lasers are pre
sented. In Figure 6-1, shown is a schematic diagram for characterizing near-field and far-
field patterns of array lasers. The major components of the experimental set-up are a
scaled screen, a CCD camera, a video analyzer, a monitor and a personal computer, a
cylindrical lens for far-field measurement and an objective lens (50x) for near-field charac
terization.
The function of a cylindrical lens for far-field characterization is focusing the laser
output beam on the scaled screen in the vertical direction. Then the camera catches the
far-field image on the screen and sends the image to the monitor through the video ana
lyzer. The basic function of the video analyzer is displaying the far-field intensity profile
along the horizontal line on the monitor which can be moved in the vertical direction.
The vertical line on the monitor can be moved in the horizontal direction and allows mea
suring the position of far-field peaks using the image of the scaled screen. Once the dis
tance on the screen between two major peaks of far-field pattern is measured using the
vertical line and the image of the scale, the angular distance between the two peaks can be
calculated easily along with the distance between the laser and the screen. The typical
distance between the laser and the screen used is ~25 cm. The image signal of the CCD
camera is also sent to the computer where the image is analyzed to generate the intensity
84


56
: interelement:
element
; region ;
region
¡ s .
d
p clad: Al 6Ga4As
optical mode
-guide: AlGaXs -" ~ '
Qy?' ^n-15^a-85^. guide: AlGaAs -T"
n clad: A16Ga4As
(a)
(b)
C/5
c/5
O
n
*~o
o
Figure 4-3. (a) Modulated-cap thin p-clad (MCTC) antiguide array laser structure;
(b) TE0 modal refractive-index and loss profile for (a).
In order to discuss MCTC antiguided arrays, we need to define antiguided array
modes more descriptively than the simple definition of in-phase, out-of-phase and


23
MV) [f>00 exp (J 27tvw) duj
m
Anexp (j 2nnvT)
L/j = -AY -J
From the above expression of F¡Av), thefar-field pattern for an array of N
identical elements can be expressed as follows:
(2.14)
equally spaced
FF(0) f,(0) 7(0) ,
FA 9) =
^(0) s
r fN(x) exp (j 2%vx) dx
oo
,V =
tan0
IT
M
^ Anexp (j 2kkvT)
,v =
tan0
T~'
(2.15)
(2.16)
(2.17)
n = -M
As can be noticed, Fs(6) is the far-field intensity distribution for one of the array elements,
and Fg(6) is a function (the so-called grating function) characterizing the array and repre
senting the interference effect of the elements in the array. The far-field pattern of the
array is a product of Fs(6) and Fg(6). Since the grating function Fg(6) has periodic major
peaks and the angular period of the peaks (6p -Tan1 (XJT)) is always smaller than the
divergence angle of Fs(9) (6d = Tan1 (XJd) and Tan]( 1.5Jd) for the near-fields of f^(x) =
1 and fj^x) = cos(Kxld) respectively, where-J/2 of the major peaks of the far-field pattern of the array.
In Figure 2-4, an example of the array far-field pattern FF(6) is shown with Fs(6)
and Fg(6) forf^x) = 1, where -d/2 N = 7, which can be obtained from a uniformly illuminated grating of equally spaced slits.
All the functions are normalized and Figure (a) shows the grating function Fg(9) and the
single-element far-field pattern Fs(9) while Figure (b) shows the array far-field pattern
FF(6) (the product of Fs(6) and Fg(6)) with Fs(6) which is the envelope function of the
far-field major peaks. For this particular case, 6p of Fg(6) is ~7.73, 6d of Fs(6) is


92
Near-field
Far-field
Figure 6-4. Near-field and far-field patterns of 23 element MCTC antiguided array
lasers (in-phase operation) d = 5 pm, s = 2 pm.


99
operation, array geometry effects on device performance and uniform etching for large
size wafers. Since the main goal of array lasers is to obtain spatially coherent high power
output beams from one facet, facet coating is required. The role of facet coating in deter
mining array operating modes needs to be studied.
When array lasers are in CW operation, the heat generated inside lasers can degrade
device performance. Although the heating problem of CW operation can be reduced by
using a heat-sink with p-side down packaging, thermal effects in CW operation on device
performance is still a necessary topic to be investigated.
Array geometry could also affect device performance. In this study, antiguided array
devices with two different array geometries were fabricated. Five and twenty element
devices had array patterns only inside the device stripes; on the contrary, 23 element
devices had array patterns both inside and outside the device stripes. Although 23 ele
ment devices showed better results, it is not clear whether this is due to the geometry or
not since the effects of the different geometries have not been theoretically studied. It is
conjectured that the array geometry can affect the phases of the near-fields of individual
array element lasers as well as the array mode discrimination. Since they are crucial fac
tors for stable performance of antiguided array devices, the geometry effects should be
studied.
For industry production of these devices, uniform etching for large size wafers is
essential. A high energy etching technique such as reactive ion etching (RIE) can pro
duce a uniform etch overall, but it is not appropriate for fabrication of MCTC antiguided
array devices because the etched surface resulting from a high energy etching technique is
too rough for these devices (the rms value of the etched surface roughness of RIE is


100
~50 nm). The rms value of the etched surface roughness of pulsed anodization etching is
~1 nm and hence pulsed anodization etching technique has been employed. However,
with our laboratory pulsed anodization etching set-up for small size wafers ( < 1 inch
diameter), the etching of large size wafers ( > 2 inch diameter) tends to be non-uniform
due to the edge electric field effects on the wafers. This problem may be solved by using
a bigger electrolyte container and a larger size cathode plate or investigating different
electrolytes. Without a proper technique for uniform etching with large size wafers,
industry production of these devices will not be practical.
p-cap: Al0 2Gao 8As
270 nm
SQW:p-In(mGa08 ' 15 nm
p+-cap:GaAs
100 nm
p-clad: Al0 6Ga<) 4As
300 nm
p-guide: AIq 3Gao 7 As
200 nm
barrienGaAs
7 nm
III SQWdriQ 15GaQ 85As <
. -'7. 8 nm
barrienGaAs
7 nm
n-guide:Al<) 3Ga<) 7As
200 nm
n-clad: Al0 gGa*) 4As
1400 nm
Figure 7-1. A proposed epitaxial structure for a large process-window


49
during the initial growth and then etching and MOCVD regrowth occur in the element
regions. Note that, for SAS-type arrays, the passive guide and loss regions (interelement
regions) can be incorporated in one layer [18].
Although CSA-type and SAS-type arrays have been demonstrated with significant
results, the fabrication yields of in-phase device are very low. The reason for the low
yields is that the etching and regrowth techniques are too complicated to precisely control
the array parameters such as the effective refractive-indices of the element and interele
ment regions which strongly depend on material compositions of epitaxial layers and
thicknesses of the layers.
In principle, the effective refractive-index of the transverse mode can be easily
affected by simply changing the thickness of the cap layer if the p-clad layer is thin
enough to achieve a significant transverse-mode-overlap with the cap layer which has a
higher index than the clad layer: this type of an epitaxial structure is called a thin p-clad
laser structure. Therefore, the periodic index variations can be obtained by periodically
modulating the cap thickness of a thin p-clad structure with simple etching techniques.
We have already demonstrated this type of array (modulated cap thin p-clad antiguided
array lasers) [25] and they are the subject of this work.


85
profile of the image using an image processing software such as Frame Grabber. The
intensity profile generated on the computer can be printed out and the distance of the two
Computer Monitor Video analyzer
Far field measurement
CCD camera
Near field measurement
Figure 6-1. Schematic diagram of the set-up for far-field and near-field intensity patterns.


10
p-contact
oxide
p+-cap
p-clad
active layer
n-clad
n-substrate
n-contact
(a) schematic of a heterostructure stripe laser
(b) P-I curve: relation between the laser output power (P) and injection current (I)
Figure 1-3. Schematic of a heterostructure stripe laser and P-I curve.


95
narrower element width for stable operation and wider element width for higher power in
the central main lobe. Element and interelement widths can be optimized with the reso
nant coupling condition considering basic constraints of device operation and fabrication.
Design for the m=l array mode is desirable since it produces the highest power in the
main lobe of the far-field pattern.
In order to ensure stable in-phase array mode operation, large mode discrimination
against out-of-phase and adjacent modes should be provided. Radiation loss due to lat
eral leaky waves in antiguided arrays is only a small contribution to mode discrimination.
By making interelement regions lossy, mode discrimination can be enhanced and the
enhancement with interelement loss does not degrade with element gain. The array mode
discrimination is a strong function of the interelement dimension, as well as interelement
loss, because of the lateral array mode confinement effect in the interelement regions.
For fabrication of stable in-phase mode operating MCTC antiguided array lasers, epitaxial
layer structures with a sufficiently high interelement loss should be designed.
An in-phase mode is favored to lase only in a certain range of the lateral refractive-
index step where the in-phase mode is the lowest-loss (or highest-gain) mode. This
implies that there is a certain range of interelement cap thickness where the in-phase mode
is favored to lase. This range of interelement cap thickness was named process-win
dow since MCTC antiguided arrays should be processed for interelement thickness to be
in this range. For high fabrication yields of stable in-phase mode devices, a large pro-
cess-window (wide width and large mode discrimination) is required. The process-win
dow can be engineered by using AlGaAs ternary material in the cap layer along with
tailoring of the p-clad layer thickness and composition. By changing mole fractions of


21
The angular far-field pattern function FF(6), ignoring a constant value of AD, is obtained
using equation (2.7) (see Figure 2-2 (b)):
FF(Q) =
sin (itDtanG/^)
(2.10)
7tDtan0/X
The first zero point (6d) in the far-field pattern plot is found from sin(nD tanO/ X) 0 and
6d is approximately the same with the full width at half maximum (FWHM) of the main
central lobe (FWHM = ~0.9 0d):
e.-JYm-Mg)-! if
D X.
(2.11)
The angle 6d is called a divergence angle (well known as a diffraction characteristic of a
single slit source) and the divergence angle reduces as the slit width D increases.
x
Figure 2-1. When the distance / is sufficiently long,fF(x,y) is proportional to
the Fourier transform F^(vx,vy) of the near-field function fu(x,y),
evaluated at the spatial frequencies vx = x//U and vy = ykl.
fId*)
-D/2
D/2
J
/
VFF(Q)
/
/
\
\
\
/
/
/
h*-
1
1
\
\
^FWHM
\
/
i
l
'
V.
n a
(a) (b)
Figure 2-2. Far-field pattern (b) from a single slit source of uniform near-field (a)


66
Alternatively, for a wide process-window, a very lossy material can be used for the
cap layer because the large loss of the layer suppresses the out-of-phase and adjacent
modes severely in the vicinity of the process-window and hence the mode gain profiles of
those mode are pushed down. However, there are some limitations to using a very lossy
material for a cap layer. If the cap loss is beyond a certain value (it depends on the index
profiles of the epitaxial layers and wavelength), the mode intensity in the cap layer cannot
be built up enough to give sufficient index change as the cap thickness is increased.
Therefore, the loss in the cap layer should not be beyond the limit.
As shown in Figure 4-8, the process-window of an 18 element array of a typical thin
p-clad structure is significantly enlarged by replacing the typical GaAs cap layer with a
very lossy cap layer. Other than the cap layers, the epitaxial structures for both cases are
the same and, for the guide layers, A1q 3GaQ 7As was used instead of the graded AlGaAs
layers as used for the interelement mode-index calculation. For the lossy cap layer, the
same material with the QW well, InGaAs, was used, assuming that the cap loss is 2000
cm'1 (this number is a random value and was chosen simply to see the loss effects on the
process-window). The loss value used for the typical GaAs cap layer is 120 cm'1 which
is a practical number at the wavelength of 950 nm. For the lossy cap layer case, the ele
ment cap thickness was fixed at 50 nm to reduce the loss in the element region while, for
the typical cap layer case, it was fixed at 100 nm. The width of the process-window
where the mode discrimination is greater than 2.5 cm'1, for comparison, is ~5 nm for the
typical cap layer case and that of the lossy cap layer case is ~24 nm which is ~5 times
wider. The mode discrimination, which is an indication of stable in-phase operation, is
also greatly improved for the lossy cap layer case. As mentioned in Chapter 3, a large
interelement loss increases the mode discrimination significantly as well as the process-
window.


58
For in-phase modes, the array mode numbers (j, m, I) should be (1, odd-number, 0)
and the modes which have (1, even-number, 0) or (j > 1 ,m, 0) have out-of-phase-type far-
fields. A (j, m, l > 0) mode is called the /-th adjacent (j, m, 0) mode.
(c) (d)
Figure 4-4. Antiguided array modes: (a) AMi30 mode (in-phase);
(b) AM12q mode (out-of-phase); (c) AM131 mode (adjacent in-phase);
(d) AM22o mode (out-of-phase).
The first thing to do when fabricating MCTC antiguided array lasers with a given
epitaxial structure is to decide the values of array geometry parameters (cap thicknesses tg


75
circuit, a native oxide is growing on the sample surface due to chemical reactions between
surface material of the sample and OH' ions attracted to the sample surface in the electro
lyte while the pulse is on, and the oxide is also constantly dissolved. Initially, the overall
oxide growing rate overcomes the overall dissolving rate because there is no oxide on the
sample surface at the beginning. As the oxide becomes thicker, the growing rate
decreases because the circuit resistance is increasing due to the oxide. When the growing
rate becomes equal to the dissolving rate, the oxide layer is constantly travelling into the
sample with a constant thickness. The trailing edge current of the pulsed current wave
form displayed on the oscilloscope also becomes constant. The final oxide thickness
depends mainly on the bias voltage, and, for example, a blue oxide (-100 nm thick) is
obtained with 80 V.
Figure 5-1. Basic pulsed anodization etching set-up


69
power in the central main lobe unless interelement loss is high enough to get sufficient
mode discrimination.
(a)
(b)
Figure 4-9. Array dimension effects on the process-window: process-windows for two
19-element arrays with; (a) d = 5 pm and s = 2 pm; (b) d = 5.5 pm and
s = 1.5 pm, obtained using the same epitaxial structure.


Microelectronics Lab. and his predecessor, Mr. James Chamblee, for all their technical
support over the years. I would also like to thank the department staff, particularly Mr.
Bob McClain and Ms. Linda Kahila. I truly appreciate all the things that are done
everyday to make our department run and allow us to do our research.
I would like to thank all my colleagues that I have worked with or studied with
while at the university; Chi-Lin Young, Chih-Hung Wu, Chia-Fu Hsu, Carl Miester, John
Yoon, and Jong-jin Kim. Particular thanks go to Jong-jin Kim for help with basic
experiments for this work and valuable information about material growth techniques and
other material properties.
I would also like to thank my friends for their spiritual support with lifetime friend
ships. Thanks go to Dr. Craig C. Largent and his wife, Donna, for encouraging me with
their heartwarming friendship. My deep appreciation is to be expressed to Geun-hyo
An and Kee-woo Kim for their encouragement in many aspects of my life. I would
also like to express my special appreciation to Henry J. Walker, Jr., for encouraging
me to do my best for this work. He has been a great inspiration to me and given me
great helps.
Finally, I certainly want to thank my mother and father for all their love and
support. I also want to thank my brother and two sisters. They are always my greatest
supporters and friends. My very special thanks go to my late sister for giving me the
courage to resume my graduate study after her death. Without all the love and underpin
ning of my family, I could never be at this point.
IV


81
s d i
*+
cap layer \ te w 1
photoresist
oxide
6.First p-metallization is electroplating element regions with gold. Before starting the
photoresist
oxide
gold
electroplating, the wafer should be checked if the oxide in the element regions has been
removed completely. If not, Step 5 should be repeated.
7.Removing the remaining photoresist is for the second photolithography. The standard
s i d
-* <
oxide
-gold
cap layer
cleaning process for the photolithography removes the photoresist. Since the oxide
remaining in the interelement regions should not be removed, any acid solution and
photolithography developer should be avoided in the cleaning procedure.
8.Second photolithography is for defining the device stripe patterns is the dimension for
^photoresist oxide
probe contact area. Since the oxide layer in the inter-element region still remains to


103
[12] L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits,
John Wiley & Sons, New York, 1995.
[13] P. S. Zory ed., Quantum Well Lasers, Academic Press, San Diego, 1993.
[14] W. W. Chow, S. W. Koch, and M. Sargent III, Semiconductor-Laser Physics,
Springer-Verlag, New York, 1997.
[15] D. Botez, L. J. Mawst, G. Peterson, and T. J. Roth, Resonant optical transmission
and coupling in phase-locked diode laser arrays of antiguides: The resonant optical
waveguide array, Appl. Phys. Lett., Vol. 54, No. 22, pp. 2183 2185, 1989.
[16] D. Botez, L. J. Mawst, P. Hayashida, G. Peterson, and T. J. Roth, High-power,
diffraction-limited-beam operation from phase-locked diode-laser arrays of closely
spaced leaky waveguides (antiguides), Appl. Phys. Lett., Vol. 53, No. 6, pp. 464 -
466, 1988.
[17] L. J. Mawst, D. Botez, T. J. Roth, and G. Peterson, High-power, in-phase-mode
operation from resonant phase-locked arrays of antiguided diode lasers, Appl. Phys.
Lett., Vol. 55, pp. 10 12, 1989.
[18] T. H. Shiau, S. Sun, C. F. Schaus, K. Zheng, and G. R. Hadley, Highly stable strained
layer leaky-mode diode laser arrays, IEEE Photon. Technol. Lett., Vol. 2, pp. 534 -
536, 1990.
[19] L. J. Mawst, D. Botez, C. Zmudzinsky, M. Jansen, C. Tu, T. J. Roth, and J. Yun,
Resonant self-aligned-stripe antiguided diode laser array, Appl. Phys. Lett., Vol. 60,
pp. 668 670, 1992.
[20] J. S. Major, Jun., D. Mehuys, and D. F. Welch, 11.5 W pulsed operation of
antiguided laser diode array, Electron. Lett., Vol. 28, pp. 1101 1102, 1992.
[21] J. M. Gray, and J. H. Marsh, 850-nm antiguided laser array fabricated using a zinc
disordered superlattice, CLEO96, Paper CTuC3, p. 78, 1996.
[22] C. H. Wu, P. S. Zory and M. A. Emanuel, Contact reflectivity effects on thin p-clad
InGaAs single quantum well lasers, IEEE Photon. Technol. Lett., Vol. 6, pp. 1427-
1429,1994.
[23] C. H. Wu, P. S. Zory and M. A. Emanuel, Characterization of thin p-clad InGaAs
single-quantum-well lasers, IEEE Photon. Technol. Lett., Vol. 7, pp. 718-720, 1995.
[24] M. J. Grove, D. A. Hudson, P. S. Zory, R. J. Dalby, C. M. Harding, and A. Rosenberg,
Pulsed anodic oxides for III-V semiconductor device fabrication, J. Appl. Phys.,
Vol. 76, pp. 587-589, 1994.


6
p-clad
active
n-clad
yt'QQQQQQQQ e
/TN /Tn /Tn /Tn /T> /TS ^
vX7 \17 vi/ v vt/ \I7 vE/ U7
10 0
hv-E
g
'Ey
(a) schematic energy band diagram for carrier confinement
p-clad
active
na
n-clad
nc
nc
nc
na \
nc
Xe
(b) refractive-index diagram for optical confinement
Figure 1-2. Carrier and optical confinement scheme of a double-heterostructure


83
12. N-metallization is done by electroplating gold on the n-substrate.
13. Cleaving the wafer into bar forms for test is the final step of the fabrication.
Top view
£:
| 1
il J
>i x
1 I
1 1
1 1
1 n
1 L
|
1 1
i 1
1 "


CHAPTER 7
SUMMARY AND FUTURE STUDIES
7.1 Summary
Phase-locked antiguided array lasers were demonstrated with modulated cap thin p-
clad structures. For single central lobe far-field operation, individual element lasers of a
laser array should be phase-locked, that is, phase difference of near-fields between adja
cent element lasers should be zero (in-phase). This phase-locking condition is achieved
by controlling the refractive-index step between element and interelement regions of the
laser array. Utilizing modulated cap thin p-clad structures, the required refractive-index
step can be easily obtained by controlling cap layer thicknesses of element and interele
ment regions with pulsed anodization etching.
Since the goal of laser array fabrication is to obtain high power in a low divergence
lateral beam, the fraction of the total output power contained in the central main lobe of an
in-phase far-field is of great interest. The ratio of the central lobe power to the total out
put power is linearly proportional to the lateral dimension ratio of element width to array
period. Theoretically, the central lobe power rate cannot exceed 0.81 for semiconductor
laser arrays for which the element near-field distribution is assumed to be sinusoidal. In
order to achieve high power in the central main lobe, the ratio of element width to array
period is desired to be large, but wider element width leads to smaller array mode discrim
ination. Hence, unless interelement loss is high enough to obtain sufficient mode dis
crimination in designing MCTC antiguided array lasers, one has to compromise between
94


17
Section. 2.4 has the answer to this question. Individual element lasers in an array should
be able to talk to the other element lasers in order to have the same phase with others
(phase-locking). This means that the optical field of each element laser should reach to
the other lasers and interact with them (coupling). Several coupling schemes used in
semiconductor array lasers are presented as well as fabrication techniques.
In Sec. 2.5, array mode stability with thermal and/or carrier-induced refractive-
index variations in the array structures is addressed. This leads to antiguided array lasers
for more stable in-phase operation with increasing drive level.
2.2 Fourier Optics and far-field Patterns
Fourier optics provides a description of the propagation of light waves based on har
monic analysis (the Fourier transform) and linear systems. Harmonic analysis is based
on the expansion of an arbitrary function of time f(t) as a superposition (a sum or an inte
gral) of harmonic functions of time of different frequencies. The harmonic function F(v)
exp(j27Wt), which has frequency v and complex amplitude F(v), is the building block of
the theory. Several of these functions, each with its own value of F(v), are added to con
struct the function/(r). The complex amplitude F(v), as a function of frequency, is called
the Fourier transform of/(r). This approach is useful for the description of linear sys
tems. If the response of the system to each harmonic function is known, the response to
an arbitrary input function is readily determined by the use of harmonic analysis at the
input and superposition at the output.
An arbitrary function f(x,y) of the two variables x and y, representing the spatial
coordinates in a plane, may similarly be written as a superposition of harmonic functions
of x and y of the form F(vx,vy) exp/-y'27r(vxx+Vyy)/, where F(vx,vy) is the complex


24
-10.76, and the FWHM of the central lobe of the array far-field is -0.99. The peak
position of the first major side lobe of the array far-field is -7.60 which is a little shifted
from 6p (-7.73) because Fs(6) is not constant.
(a) (b)
Figure 2-4. far-field pattern FF(6) (b) with the single-element far-field Fs(6) and the
grating function Fg(6) (a) for an array of 7 uniform near-field slits with the
slit width of 5 pm, the array period of 7 (im, and the wavelength of 0.95 pm.
Although a uniform near-field of the slits can be obtained for a diffraction experi
ment by illuminating the slits with a wide laser beam, the near-fields of semiconductor
lasers are not uniform and their near-field profiles are usually approximated to Gaussian or
sinusoidal profiles. Therefore, it is not appropriate to use a uniform near-field profile for
elements of a semiconductor laser array. Since the lateral near-field profile of antiguided
lasers are described as sinusoidal, f^x) = cos(TVdd) for the fundamental lateral mode will
be used for far-field calculations of antiguided array lasers, where d is the antiguide width.
For comparison, the array far-field patterns for the two different cases of the uniform and
sinusoidal f^x) profiles are shown in Figure 2-5. The values for other parameters are the
same with the above example: An = 1, X = 0.95 pm, d = 5 pm, 7=7 pm, and N = 7. As


5 FABRICATION OF MCTC ANTIGUIDED ARRAY LASERS 73
5.1 Introduction 73
5.2 Pulsed Anodization Etching 74
5.3 Electroplating 78
5.4 Fabrication of MCTC Antiguided Array Lasers 79
6 CHARACTERIZATION OF MCTC ANTIGUIDED ARRAY LASERS ... 84
6.1 Introduction 84
6.2 Device Characterization 86
7 SUMMARY AND FUTURE STUDIES 94
7.1 Summary 94
7.2 Recommendations for Future Study 97
REFERENCES 102
BIOGRAPHICAL SKETCH 108
VI


74
5.2 Pulsed Anodization Etching
As discussed earlier, controlling the cap thicknesses (tc and tj) involves an etching
process which is crucial for obtaining in-phase laser operation in MCTC antiguided
arrays. In addition to the etching process, making a GaAs native oxide layer over the cap
layer in the inter-element regions is necessary to confine the optical gain only in the ele
ment regions. Both procedures can be done at the same time using a pulsed anodization
etching technique.
The pulsed anodization etching set-up is composed of two electrodes immersed in
an electrolyte, a pulsed voltage source, two resistors and an oscilloscope (see Figure 5-1).
The cathode is a platinized titanium grid and the anode is the sample to be etched. An elec
trically conducting metal vacuum tube is used to hold a sample horizontally to make the sam
ple surface parallel with the cathode grid. The electrolyte which is called GWA is a mixture
of ethylene glycol (G), deionized water (W) and 85% phosphoric acid (A). Changes in
shape of the pulsed current waveform during the etching process are displayed on the oscil
loscope using the 10 ohm power resistor. Figure 5-2 shows a typical current pulse shape
measured on the oscilloscope during pulsed anodization etching. Initially, the pulse shape
is square with a negative undershoot. As the etching proceeds, the leading edge of the
pulse remains constant, but the magnitude of the trailing edge current decreases. Typically,
a pulser voltage Vp = 80 V, a repetition rate of 100 Hz, a pulse width between 0.3 and 1
msec, and Rvar = 0 Q are used; a high value of Rvar can cause non-uniform etching, particu
larly for a big wafer.
The electrolyte, GWA, has a property of etching GaAs native oxide and the etch rate
depends on the acid concentration of the electrolyte. When pulsed bias is applied to the


22
2.3 Far-Field Patterns from Arrays of Light Sources
Consider a one dimensional array of N equally spaced identical elements corre
sponding to individual laser-array elements. Assuming that the near-field distribution
functions of the individual array elements are the same and can have different complex
amplitudes (see Figure 2-3), which is applicable to most practical cases, the near-field
function fNa(x) for the array can be expressed as follows:
M
/*(*)= I (2-i2)
n = -M
where the total number of array elements is N = 2M + l,fu(x) is the near-field distribution
for the center element at the center of which the origin of the coordinate system is located,
An is the complex amplitude of the n-th element, and T is the center-to-center distance
between two adjacent array elements.
-T -d/2 0 d/2 T
MT
-MT
Amn(x-MT)
A_Mx+MT)
Figure 2-3. One dimensional array of N (2M+1) equally spaced identical elements.
The Fourier transform off^a(x) is, then, obtained using equation (2.2):
M
FN(V) = V r AnfN(x-nT) exp (j2nvx)dx. (2.13)
* oo
n = -M
By replacing x nT with a new variable u, that is u = x nT, the above equation can be sep
arated into an integral and a summation:


9
stimulated emission. However, some photons are lost through the partially transmitting
facets and some get scattered or absorbed inside the cavity. If the loss exceeds the gain,
stimulated emission cannot sustain a steady supply of photons. This is precisely what
happens below threshold, when the laser output consists of mainly spontaneously emitted
photons. At threshold, gain equals loss and stimulated emission begins to dominate.
Over a narrow current range in the vicinity of the threshold current, the output power
jumps by several orders of magnitude and the spectral width of the emitted radiation
narrows considerably. In the above threshold regime, laser output increases almost lin
early with the injection current as shown in Figure 1-3 (b). Details as to the processes
which determine 1^ and the slope of P-I curve can be found in several excellent textbooks
[12-14],


52
Figure 4-1. Epitaxial layer structure of thin p-clad InGaAs single quantum well lasers;
and fundamental transverse mode (TEq mode) profile change with cap
thickness change; refractive-index profile of the layer structure.
index and mode-overlap with the layer. When the cap layer thickness is small, the mode
profile overlaps mostly with the active and clad layers, as shown in the figure, and most of
contributions to the effective mode index come from those layers. As the cap thickness
increases, the mode overlap with the cap increases, and the contribution of the cap layer to
the effective mode index also increases. This results in a higher effective mode index
since the cap layer index is higher than those of the clad and guide layers (ignoring the
contributions of the thin barrier and quantum well layers). If the cap layer is lossy, the


53
loss of the transverse mode also increases as the cap thickness increases. However, if the
cap layer has a lower refractive-index than the p-clad layer or if it is too lossy, these can
not occur since the mode intensity can not build up in the cap layer.
Using the structure shown in Figure 4-1 with a 500 nm p-contact metal layer of gold
and with a 100 nm oxide layer between the cap layer and the gold layer, the effective
mode index and loss of the TE0 mode were calculated with a cap thickness range from 50
nm to 500 nm and the results are shown in Figure 4-2. This calculation was done with
the program MODEIG [59] for multi-layer waveguide structures. For this calculation,
the p-clad layer thickness was 465 nm, 950 nm was used for the wavelength and a free
carrier absorption loss of 120 cm_1in the cap layer was used. As can be seen in the figure,
both the effective index and the mode loss start to increase rapidly when the cap thickness
increases beyond 150 nm. For the structure with an oxide layer (100 nm) between the
cap layer and the gold layer (500 nm), both the effective index and the mode loss start to
increase earlier than those for the structure without the oxide layer. This is because the
refractive-index of the oxide layer (~1.8) is lower than that of the cap layer (~3.5) and thus
the oxide layer helps the mode intensity build up in the cap layer. The mode loss is com
posed of the cap loss and the metal loss. Most of the loss for the structure with the oxide
layer is due to the free carrier absorption loss in the cap layer.
Utilizing the characteristic of large effective index change with a small variation of
the cap thickness of thin p-clad structures, the required large index step between the
element and interelement regions of antiguided arrays can be easily fabricated by simply
etching the cap layer.


89
very well maintained. In addition to the more stable far-field behavior with increasing
current, the side lobes of the far-field patterns were significantly suppressed due to the
higher ratio of element to interelement width. The central lobe contained -75% of the
beam power at 1.2 x 1,^ and -60% of the beam power at 10 x 1^. As shown in Figure 6-
5, the total P-I slope efficiency was -0.4 W/A with a driving frequency and a pulse width
of 1 kHz and 2 (isec respectively. The slope efficiency is smaller than that of a regular
100 p.m wide, 500 (im long laser made from the same material (typically 0.52 W/A).
This is mainly due to the loss in the interelement regions, which is required to obtain sta
ble in-phase operation.
Although stable in-phase operation was achieved with 23 element MCTC antiguided
arrays, the fabrication yield of the in-phase operating devices was very low (-5%) because
the process-window of the thin p-clad structure used for the devices was very narrow as
shown in Figure 4-5 (b). On the other hand, the fabrication yield of in-phase 5 element
devices was relatively high (-50%) which can be expected from Figure 4-5 (a).
From these experimental results, it is clear that thin p-clad structures should be
designed to have a large process-window for high fabrication yields of in-phase devices.
In the next chapter, such a thin p-clad structure for a large process-window is proposed.


34
low-index array regions. Since optical modes of those arrays are confined in low-index
regions, the modes are antiguided and leaked to the lateral directions. Hence, a very
strong coupling can be obtained by the leaky waves propagating through interelement
regions in negative-index-guided arrays (called leaky-wave coupled arrays or more com
monly, antiguided arrays, see Figure 2-8 (d)). More detailed discussions about the antigu
ided arrays will be given in the next chapter.
2.5 Array Mode Stability
As mentioned in the previous section, the weak coupling due to the refractive-index-
step, An, was the major reason for the failure of evanescent-wave coupled arrays (positive-
index-guided), and it is possible to get a strong coupling with those devices by reducing
An. There is, however, one major limitation: the built-in index-step, An, has to be below
the cutoff for high-order lateral modes in the element regions since the elements should
have only the fundamental lateral mode for single-lobed far-field patterns. Since An < 5
x 10~3 for typical devices, the devices are susceptible to thermal and/or carrier induced
refractive-index variation and gain spatial hole burning which lead to unstable device
operation as drive level increases.
Due to the weak coupling, the near-field profile of the in-phase array mode of a uni
form evanescent-wave coupled array has a raised-cosine-shaped envelope (from coupled
mode theory). Thus, with increasing drive above threshold, gain saturation due to local
photon density is uneven: so-called gain spatial hole burning. The gain is saturated
mostly in the central elements, which, in turn, creates a local increase in the refractive-
index profile due to a decrease in carrier density. As the refractive-index of the central
elements increases, the optical modes in the elements are more strongly guided, which


about 75% of the beam power at 1.2 times the pulsed current threshold (Ith). At 10 1^,
the central lobe contained about 60% of the beam power and was 1.6 wide. Although
this performance level was quite good, the yield of devices with these high quality beam
characteristics was very low (~ 5 %). This could be attributed partially to the fact that the
fabrication tolerances for the etched profile in the cap thickness required to achieve these
results were quite small. Another reason for the low yield could be attributed to thick
ness non-uniformities in the laser material used.
In order to improve the yield, the pulsed anodization techniques used to etch the
structures were improved and new electrolytes for faster and precise etching were devel
oped. In addition, new designs which were less sensitive to cap thickness variations were
developed.
In order to quantify the predicted performance of new designs, a process window
concept was developed. In essence, the process window is an area in an array mode
gain / cap thickness variation space which must be maximized in order to maximize fab
rication tolerances for in-phase mode operation. The three major factors which affect the
process window size are refractive index profile of the epitaxial layer structure, array
dimensions and transverse mode loss. The effects of these three factors on the process
window are presented and a new thin p-clad structure which employs a multilayer cap
viii
design is proposed.


71
pattern, with a larger ratio producing higher power in the main lobe. On the contrary,
array mode discrimination decreases as r increases as mentioned earlier in this section.
Once An0, dmax and smin are determined from the basic constraints, optimum values
for d and s can be calculated using the following procedure. The resonant coupling con
dition for / = 0 from equation (3.3) is
irJ -UJ
(4.1)
An optimum range of r can be calculated by using equation (4.1) and the third constraint
(d^d,^, smin V1 +
m
(4.2)
Jm2- (2sm¡n/X0)2An¡
From the above range of r, a desired minimum value rmin can be chosen, and an optimum
range of s calculated using the resonance condition again;
r~
f2d 1
2
1 +
max
An2
K ^0 ,
(4.3)
Then, a desired value of s is chosen from the above range and a corresponding value of d
is calculated as follows
d = s /
2-'r:)2^
m
(4.4)
After d and s are thus chosen, the corresponding process-window should be calcu
lated to determine the correspondence, or lack thereof, between the resonance condition
and the maximum array mode discrimination, thus optimizing the interelement cap thick
ness.


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70
The basic constraints in designing MCTC antiguided array lasers relate to element
and interelement cap thicknesses and their widths. The first constraint is on the refrac
tive-index difference (An0) for the TE0 mode between the element and interelement
regions. The index step, An0, should be large enough (An0 >0.01) for the devices to be
insensitive to thermal and/or carrier induced refractive-index variations (see Sec 2.5); this
constraint places a lower limit on An0 and hence the interelement cap thickness. The sec
ond constraint, which places an upper limit on AnQ, is that the interelement regions should
not lase. As the cap thickness of a thin p-clad structure is increased, the vertical epitaxial
structure becomes a twin-waveguide structure which has two eigen modes; in-phase (TEq)
and out-of-phase (TEj) modes. The TEj mode is a radiation mode which has a big mode
loss until the cap thickness reaches cut-off for the mode and hence one can ignore tlieTE}
mode when the cap thickness is smaller than the cut-off thickness. However, beyond the
cut-off thickness, the TEj mode becomes a guided mode and can lase. As the cap thick
ness increases, both the effective index and the loss of the TEq mode are also increased.
Eventually, the loss of the TE0 mode becomes larger than that of the TEj mode and the
TEj mode lases (see Figure 4-10). Hence, the cap thickness of the interelement regions
should be thin enough that the TEj mode can not lase; this places an upper limit on the
interelement cap thickness and hence An0. The third constraint regards element and
interelement widths. Element width (d) should accommodate only a single fundamental
lateral mode (/ = 0) for in-phase array mode operation, which limits d to a maximum
value (dmax). Interelement width (s) is limited to a minimum value (smin) by photolithog
raphy and consideration of array mode discrimination. As discussed before, the ratio r
(r= d/s) directly affects the fraction of the output power in the main lobe of the far-field


29
can be obtained from the expression of the grating function and it is
Qad = Tan
2(W+1)7J 2 (A+1)7
[rad] .
(2.23)
For comparison, the following expression of an array divergence angle is for a uniform
amplitude profile (An = 1):
(2.24)
9- = Tan~'iwr^rirad]-
ad
As shown in the above expressions, an array divergence angle depends on the wavelength
and the total array width and hence so does the FWHM of the central lobe. For arrays of
a few elements (less than 10), the FWHM is almost the same as A/AT (loosely defined as
the diffraction-limited beam width), and it becomes a little larger than A/AT (1.1 1.2 A/
AT) as the number of array elements increases. More accurate values of the FWHM are
obtained from the numerical data of the array far-field pattern calculation which can be
easily done using the expressions of Fs(6) and Fg(6).
Since the goal of laser arrays is to obtain high output power in a narrow straight-for
ward beam, it is necessary to suppress the side lobes in an in-phase far-field pattern. In
order to do that, one needs to know the determining parameters of power rate of the main
central lobe. The power contained in a far-field lobe is proportional to the area of the
lobe. The FWHMs of the lobes in a far-field are basically all the same and hence the
power contained in a lobe is simply proportional to the height of the lobe. The heights of
far-field lobes are determined by the single-element far-field function Fs(6) (the envelope
function of an array far-field). Using the expressions of Fs(6) (equation (2.18)) and
(equation (2.20)), the ratio (Pc) of the central lobe power to the total power can be
expressed as follows:


15
Chapter 5 is assigned for device fabrication. First, an etching technique of pulsed
anodization is explained with details of basic set-up, electrolytes and their preparation,
circuit parameters, oxide thickness and etch rate. Electroplating for gold metallization is
used for making shiny contacts (low metal loss contact) along with the electron beam
evaporation technique. The electroplating technique is also described and the fabrication
sequence of MCTC antiguided array lasers is shown with brief explanations.
In Chapter 6, device characterizations are presented. Starting with a near- and far-
field measurement set-up, measured near-field and corresponding far-field patterns are
shown. Beam widths of the far-field main lobes and power percentage in the main lobes
are discussed. Then, other electrical-optical characteristics such as P-I curve and slope
efficiency are shown and discussed.
Chapter 7 summerizes this work and future work is addressed. For easier
fabrication of more stable antiguided array lasers, a new thin p-clad epitaxial structure is
proposed. This new structure employes a design of a three layer cap including a lossy
quantum layer sandwiched between two p- cap layers.


44
regions lossy. Figure 3-6 shows significant enhancement in the mode discrimination
when the interelement regions are lossy. In this figure, an interelement loss (cq; material
loss in the interelement regions) of 200 cm'1 was used and the array dimensions and the
element refractive-index were the same with those used for the radiation loss plot (Figure
3-5). The mode loss of the in-phase mode near the resonant coupling point is almost not
affected by the interelement loss while that of the other modes is significantly affected.
The mode loss of the in-phase mode at the resonance point (the point indicated with the
left vertical dashed line in Figure 3-6) increases from ~6 cm'1 (radiation loss when cq = 0
cm'1) to ~7 cm"1 (combination of radiation loss and array mode loss due to oq when cq =
200 cm'1). By contrast, the maximum difference (at the point indicated with the right
An
Figure 3-6. Mode loss (radiation + interelement loss (cq)) as a function of lateral
refractive-index step An (- n¡ ne) for a 5 element antiguided array:
ne = 3.263, d = 5 pm, s = 2 pm, Xq = 0.95 pm, cq = 200 cm"1.


82
confine gain to the element regions, the individual elements of the arrays have to be
connected to each other. The second photolithography is for both connecting the core
elements and defining device stripe pattern, and this should be carefully done without
removing the remaining oxide in the inter-element regions. Since normal developing
solutions can dissolve the oxide quickly, developing time is very critical for the second
photolithography.
9.Second p-metallization is for connecting elements and prove contact area. Electron-
p-metal: Ni /Au photoresist oxide
Au / / /
cap layer
beam evaporation is used. A metal which has a good adhesion to the oxide, such as
Ni, should be deposited first because adhesion between gold and the oxide is not good
enough to hold the metal stripes firmly; otherwise, the metal connections between ele
ments can be destroyed later. Then gold is deposited over the first metal deposition.
10.Lift-off process is performed to separate individual array stripes. After the lift-off
process, another gold electroplating over the p-metal deposition may be necessary to
secure the connections between elements.
11.Lapping substrate is for reducing device thickness down to -100 (im for a lower
device resistance and easy cleaving process.


68
4.5 Design Aspects of MCTC Antiguided Array Lasers
The array mode discrimination is a strong function of the interelement dimension, as
well as the interelement loss, because of the lateral array mode confinement effect in the
interelement regions. As shown in Figure 4-9, the maximum array mode discrimination
is reduced by a factor of two when the interelement width decreases from 2 (im to 1.5 (im,
while maintaining the same array period (7 pm). The reason for this can be explained as
follows. The lateral array mode confinement in the interelement regions decreases when
the interelement width is reduced, and so does the array mode loss due to the interelement
loss. Since the overall array mode gain is the difference between the array mode gain due
to the element gain and the array mode loss due to the interelement loss, and the major dif
ference in the overall array mode gain between two array modes comes from the differ
ence in the array mode loss due to the interelement loss. Therefore the array mode
discrimination decreases when the interelement width is reduced. On the contrary, the
process-window width does not change significantly and the window position is shifted to
larger interelement thicknesses. This is due to the fact that the window width mainly
depends on the index slope and the window position is determined by the resonance cou
pling condition which is related to the element and interelement dimensions.
Considering these effects, to achieve stable in-phase mode operation, the interelement
should be relatively wide and have large interelement loss. However, when the
interelement dimension increases, the output power percentage in the central lobe of far-
field pattern decreases as discussed in Sec 2.3 since the central lobe power rate is pro
portional to d!T (= 1/(1 +{sld)). In designing MCTC antiguided array lasers, one has to
compromise between wider width for stable operation and narrower width for higher


42
affect the angular positions of the side lobes and the central lobe power rate since they
mostly depend on the array geometry (see Sec. 2.3). For this particular case, the differ
ence in FWHM between the resonant and non-resonant far-fields is ~0.21, while the dif
ference in the angular position of the side lobes is only ~0.03, and the central lobe power
rates are virtually the same for both modes.
The envelope functions of the near-field profile of the in-phase and out-of-phase
modes in an antiguided array can be generalized with a cosine function: for in-phase array
modes, An = AQcos (mzT/L) and An = AQ (-l)cos (n%T/L) for out-of-phase
modes, where An is the height of the n-th near-field amplitude peak from the center of the
array and L > NT. The value of L for a mode can be obtained from the near-field profile.
It is a measure of the coupling strength of the mode and becomes infinite for a resonant
mode. Using equation (2.17) with the above expressions for A, the grating functions for
the in-phase and out-of-phase modes of an antiguided array are obtained as follows:
for in-phase modes;
f8(6) =
sin (Nu) sin (Nv)
L sinu sinv
\u = l(Tz + 2Tv),v = lll-2Tv\, (3.4)
for out-of-phase modes;
(0) = [
I"cos (Nu) cos (Nv)
cos u
cosv
<3-5>
where v = tan9 / X. Thus the far-field patterns of antiguided in-phase and out-of-phase
modes can be explained with the above expressions of Fg(0) and equation (2.18) for the
expression of Fs(6) (single-element far-field pattern).
Although a resonant in-phase mode is the most desirable mode because the uniform
envelope of the near-field profile makes the device insensitive to gain spatial hole burning


19
An arbitrary function ff/x.y) of a near-field distribution at the z-0 plane can be
written as a superposition integral of harmonic functions f^/x.y) = F^v^Vy) exp[-
j2n(vxx+vyy)], and the complex amplitudes FN(vx,vy) can be found by the Fourier trans
form of fti(x,y)\
Fn(vx' V = J7 /*(*. y) exPU 2k (vxx + V) ] dx dy (2.2)
oo
and then
oo
fN(x,y) = J j/v(x ,y) dvxdvy
oo
oo
= J JFaKVx Vy ) exP[-7 271 (v + V ) ] dvy (2.3)
oo
The response functions UJx,y) at the z-l plane (far-field plane) to the harmonic
functions fjx,y) can be obtained by the relation described above, U^x,y) = fj(x,y) exp(-
jkzl), and the far-field distribution function fp(x,y) at the z-l plane, corresponding to the
near-field function f^(x,y), is obtained as a superposition integral of the response functions
UJx,y);
oo
fF(x,y) = J Jtfv(r,y) dvxd\y
oo
oo
= 1 vy) exp[-j2n (vxx + v^y) ] exp(-jkj) dvxdvy (2.4)
oo
where kz is a function of vx and vy given in equation (2.1).
Although the far-field distribution due to an arbitrary near-field distribution can be
evaluated with equation (2.4), the real computation of the far-field can be very compli
cated. The Fraunhofer approximation, however, can be used when the propagation dis
tance / is sufficiently long (see Figure 2-1). With the approximation, fp(x,y) is
proportional to the Fourier transform F^{ vx,vy) of the near-field function f^(x,y), evaluated


32
for ensuring in-phase operation. The two basic approaches were Y-junction coupled
arrays (interferometric devices) and diffraction coupled arrays. For Y-junction coupled
arrays [43 46], Y-shaped single-mode waveguides were utilized (see Figure 2-8 (b)). At
each Y-shaped junction, fields from adjacent waveguides couple efficiently to a single
waveguide only if they are in phase with each other. If they are out of phase with each
other, they are simply lost as a radiation loss because of their destructive interference.
Thus Y-junction coupled arrays severely suppress out-of-phase mode operation. Initial
results of those arrays were encouraging, but the output beams were rather broad, mainly
due to poor discrimination against adjacent modes. In order to improve the mode dis
crimination, an interferometric array composed of Y-shaped and X-shaped branches has
been proposed [47], and Whiteaway et al. have proposed a tree-aixay device [48]: a fan
out of light via Y branches starting from a single waveguide and ending with a large linear
array of emitters. However, the implementation of such devices is impractical because
of the difficulty of fabricating low-loss, symmetric Y-junctions.
Diffraction-coupled arrays were based on the concept that fields from adjacent
waveguides can be made to oscillate in-phase by placing a feedback mirror at an appropri
ate distance from the waveguides apertures (see Figure 2-8 (c)). The most complete
analysis of such devices was performed by Mehuys et al. [49]. However, just as for Y-
junction coupled arrays, due to poor intermodal discrimination, the best results were sin
gle-lobe far filed patterns of beam-widths several times the diffraction limit [49].
The three types of laser arrays described above are positive-index-guided devices,
for which the near-field intensity peaks and optical gains are in the high-index array
regions. Optical coupling between two positive-index-guided elements is not strong


27
K = 1; in-phase mode
Lateral angle (0)
K = 6; adjacent-out-of-phase mode
A' = 7; out-of-phase mode
(b) far-field patterns
Figure 2-6. (a) near-field amplitude profiles: four of the seven array modes of a seven
element array. The dashed curves are the envelope functions of the near-field
profiles, (b) far-field patterns corresponding to each array mode: the dashed
curves correspond to the single-element far-field pattern.


CHAPTER 3
ANTIGUIDED ARRAYS
3.1 Introduction
A monolithic array of phase-coupled diode lasers can be described simply as a peri
odic variation of the real part of the refractive-index. Such a system can have two classes
of modes: evanescent-type array modes, for which the near-fields are peaked in the high-
index array regions; and leaky-type array modes, for which the near-fields are peaked in
the low-index array regions. An array of the leaky-type array modes is called an anti
guided array. When the high index array regions are pumped, evanescent-type array
modes are favored to lase, while antiguided array modes are favored to lase when the low-
index array regions are pumped. Another distinction is that the effective refractive-index
of antiguided modes are below the low refractive-index value while those of evanescent-
type modes are between the low and high refractive-index values. For both classes of
modes, the phase-locking condition is said to be in-phase when the fields in each element
are cophasal, and out-of-phase when fields in adjacent elements are phase-shifted by
180.
In this chapter, the basic properties of a single antiguide are first discussed in
Sec 3.2. Then antiguided arrays are introduced and the details of the arrays are discussed
in Sec 3.3: resonant leaky-wave coupling, antiguided array modes with far-field patterns,
grating functions for antiguided arrays and mode discrimination mechanisms. Finally,
fabrication techniques of antiguided array lasers are presented in Sec 3.4.
36


40
s = 1 ];m = 1, 2, 3, ...,
ni ~ne
2 fwM2 r(/+l)M2
2s
2d
(3.3)
where d is the element width, ne and n¡ are the real refractive-indices of element and inter
element regions, respectively and / is the lateral element mode number. In order to have
a single central lobe in a far-field pattern, J should be 0 with in-phase coupling (m = odd).
As examples, in-phase (m = 1) and out-of-phase (m = 2) array modes of a 5-element anti
guided array are shown in Figure 3-3. For these and all other examples in this work, d =
5 (im, j = 2 (im and Xq = 0.95 (im are used.
(a) (b)
Figure 3-3. Near-field amplitude profiles of array modes of a 5-element antiguided array:
(a) m = 1 in-phase mode; (b) m = 2 out-of-phase mode; m also corresponds
to number of near-field intensity peaks in the interelement regions.
When the resonance condition is met, the interelement regions act like Fabry-Perot
resonators and the lateral coupling between elements is maximized. The envelope func
tion of the near-field peaks of in-phase or out-of-phase modes becomes uniform as the


TO MY MOTHER AND FATHER,
AND MY LATE SISTER


64
(a)
(b)
Figure 4-6. TE0 mode effective refractive-index profiles for the interelement regions:
(a) with an AlxGai_xAs cap layer (x = 0, 0.05, 0.1) and p-clad thickness of
400 nm; (b) with an GaAs cap layer and p-clad thicknesses of 400, 300,
and 100 nm
indicated with the shaded areas is almost three times wider for the Alo.15Gao.s5As cap /
200 nm p-clad structure than that for the GaAs cap / 400 nm p-clad structure. Although
the real process-window width is a function of both the mode index and the mode loss, the


59
and t¡ in the element and interelement regions, element width d, and interelement spacing
s). The array dimensions d and s are related to the lateral index step An0 which should be
relatively large for stable device performance with high drive levels. There are some
constraints on d, s and achievable An0 in a thin p-clad structure, and the dimensions d and
s have to be optimized with those constraints. This subject will be discussed in the next
section.
Since the lower refractive-index and optical loss in the element region are desired,
the cap thickness te in the element regions should be chosen less than 150 nm from the
index and mode loss change profiles shown in the figure 4-2 (100 nm for this study). In
order to decide the value of tj with the ^ value and given array dimensions d and s, the
mode gain profiles of in-phase, out-of-phase and adjacent array modes have to be calcu
lated as a function of the interelement cap thickness. As mentioned in Sec 3.3, an in-
phase mode is favored to lase only in a certain range of the lateral refractive-index step
Ahq where the in-phase mode is the lowest-loss mode. Since An0 corresponds to the
interelement cap thickness, with a fixed element cap thickness, it can be said that an in-
phase mode is favored to lase only in a certain range of the interelement cap thickness.
Once the range of the interelement cap thickness is calculated, a value of t¡ can be chosen
in the range where the mode discrimination is maximum.
The effective index method can be employed to calculate the mode gain profiles of
the two dimensional (2-D) array structure (transversal and lateral structures). First, the
transverse structure is calculated to obtain the effective refractive-index and mode gain or
loss of the TEq mode with different cap thicknesses for the element and interelement
regions. Then, those values obtained from the calculation are used for calculating the


43
and thus stable with high drive levels (see Sec 2.5), it is not always the most favorable
mode to lase, since it is not always the mode which has the lowest mode loss. On the
contrary, the radiation loss of an in-phas mode becomes maximum when the index step
An approaches the resonance point. As shown in the Figure 3-5, for the in-phase (m = 3)
mode, resonant coupling occurs when the radiation loss is maximum (the point indicated
with the vertical dashed line). At the resonant coupling point, however, the out-of-phase
mode is the most favorable mode to lase because it has the lowest loss.
Figure 3-5. Mode radiation loss as a function of lateral refractive-index step An (= n ne)
for a 5 element antiguided array: ne = 3.263, d = 5 |im, s = 2 (im, and
Xq = 0.95 Jim
In order to make the in-phase mode lase, some mode discrimination against the out-
of-phase and adjacent modes should be provided. One way to enhance the mode
discrimination against the out-of-phase and adjacent modes is to make the interelement


62
etching for the interelement cap thickness should be performed very precisely. With the
pulsed anodization technique, the etching process can be done with a precision of ~10 nm.
In addition to the narrow process-window, the thicknesses of epitaxial layers are not gen
erally uniform to such a degree, thus low fabrication yields result. MCTC antiguided
arrays were fabricated with both the structures and the fabrication yield of the 5 element
arrays operating in the in-phase mode was -50%, while that of the 23 element arrays,
made with the same epitaxial structure used for the calculation of the 18 element arrays,
was -5% as can be expected from the process-window differences. Detailed results will
be in Chapter 6.
4.4 Design Aspects of Thin P-cIad Epitaxial Structures
for MCTC Antiguided Array Lasers
For high fabrication yields of stable in-phase mode devices, a large process-window
is required: wide width and large mode discrimination. The width and the position of a
process-window are related to the slope of the effective refractive-index profile of TE0
mode and the knee position of the profile (see Figure 4-2 (a)) as well as array dimensions
d and s. For a wider process-window, the effective refractive-index of the TE0 mode
should increase slowly as the cap thickness increases. This leads to the requirement that
the refractive-index of the cap layer be smaller than that of the active region, but still
larger than that of the clad layer. This can be done theoretically by using ternary material
AlGaAs for the cap layer instead of GaAs. By changing mole fractions of the ternary
material, the refractive-index of the cap layer can be changed, which leads to a change in
the slope of the refractive-index vs. cap thickness curve. The thickness of a thin p-clad
layer is also an important parameter to engineer the effective mode-index profiles.


101
Figure 7-2. Process-window of the proposed structure for 19-element arrays
with d = 5 (J.m and s = 2 |im


47
Gain-guide Arrays
proton implant
p-clad layer
active region
n-clad layer
Buried-heterostructure Arrays
p-cap layer
p-clad layer
active region
n-clad layer
n-substrate
Figure 3-8. Schematic diagrams of early antiguided arrays: (a) gain-guided arrays;
(b) buried-heterostructure arrays.
For practical devices, the high-index interelement regions have to be relatively nar
row (1 3 (im), which is virtually impossible to achieve using BH fabrication techniques.
Instead, one can fabricate narrow, high-effective-index regions by periodically placing
high-index waveguides in close proximity (0.1 0.2 (im) to the active region [16, 50]. In
the newly created regions (interelement regions), the fundamental transverse mode is pri
marily confined to the passive guide layer (high-index waveguide layer) and thus the
transverse mode gain in the interelement regions is low. In order to further suppress
oscillation of evanescent-wave modes, an optically absorbing material can be placed in the
interelement regions.
The first closely spaced, real-index antiguided array was realized by liquid-phase
epitaxy (LPE) over a patterned substrate [16]. Initially, a passive-waveguide structure


61
(a)
Interelement cap thickness (nm)
(b)
Figure 4-5. Process-windows calculated for two different antiguided array s with
te = 100 nm and 2000 cm'1 QW material gain in the element regions:
(a) 5 element array with d = 6 (im, s = 3.5 Jim, and tcl = 250 nm;
(b) 18 element array with d = 5 (im, s = 2 fim, and tcl = 465 nm.
Since the shaded areas are the range for which MCTC antiguided arrays should be
processed, we have named this area the process-window. For the above particular
cases, the widths of the process-windows are less than 20 nm, which indicates that the


80
etching process is the most important step of the whole fabrication process because the
inter-element cap thickness t¡ should be in the vicinity of the maximum mode discrimi
nation point in the process-window. Therefore, a relatively slow anodization process
with GWA is needed to control tj precisely.
3.First photolithography is creating the antiguide array patterns on the oxide layer formed
' s d
*-*
cap layer '|t
photoresist
oxide
in Step 2. Element regions are open stripes to be etched to a cap thickness te.
4.Pulsed anodization etching of the open stripes in the photolithography pattern is per
formed to obtain the required element cap thickness te. This etching process is per
formed with the faster etchant GWA841 since the element cap thickness is not necessary
to be controlled as precisely as interelement cap thickness; the mode index is not sensitive
to cap thickness in the vicinity of element cap thickness (~ 100 nm). More important fac
tor of this step is to achieve steep side walls since array dimensions affect the mode dis
crimination.
5.Stripping out the remaining oxide in the element regions is the following step after etch
ing the element regions. This process is done by letting the wafer sit in the etching elec
trolyte after disconnecting the circuit.


97
corresponding refractive-index modulation: in-phase, out-of-phase and random phase oper
ations. Twenty element out-of-phase and 23 element in-phase array lasers have also been
fabricated. For the 23 element array lasers, unlike 5 and 20 element array lasers, the array
pattern was created over the entire surface of the wafer and then stripes for individual array
lasers were defined; for 5 and 20 element devices, the array pattern was fabricated only
inside the stripe area. The spatially coherent output beams of the 23 element in-phase
arrays had 0.8 wide central lobe with -75% of the beam power at 1.2 times the pulsed cur
rent threshold (1^). At 10 x 1^, the central lobe contained -60% of the beam power and
was 1.6 wide.
7.2 Recommendations for Future Study
Although the device performance was quite good for the 23 element devices, the fab
rication yield for in-phase mode operation devices was very low(~5%) because the pro-
cess-window of the material used for the devices was very narrow (less than 10 nm). A
large process-window for high fabrication yields of stable in-phase mode devices can be
obtained using the idea of ternary material along with tailoring p-clad thickness. A high
mode loss in the interelement regions is also necessary for stable in-phase operation in the
process-window range. In principle, by using the active quantum well (QW) material for
a cap layer, the mode loss can be very high in the interelement regions due to band-to-
band absorption loss in the cap layer. However, there are some limitations to using active
QW material for a cap layer. If the absorption loss is beyond a certain value (it depends
on the index profiles of epitaxial layers and wavelength), the mode intensity in the cap
layer cannot be built up enough to give sufficient index change as the cap thickness is
increased. In order to avoid this problem, a thin absorption loss layer of the QW material


38
(a)
x
t>
a
c
I
o
cd
(b)
(c)
Figure 3-1. Schematic diagrams of a real refractive-index antiguide: (a) real refractive-
index profile; (b) near-field amplitude profile of the fundamental lateral
modc,X¡ is the lateral wavelength of leaky-wave; (c) ray-optics picture.
Since the radiation loss is proportional to (7 + l)2, the antiguide acts as a lateral
mode discriminator, that is, the fundamental lateral mode is favored to lase in the anti
guide. In Figure 3-2, shown are the radiation losses as a function of lateral index step An
for the fundamental (7 = 0) and the first order (7=1) lateral modes with d = 5 fim, Xq =


4
07 07 07 07 07 07 07 07 07 07
Ef! Fermi level
Ec: Conduction band edge
Ev Valence band edge
Eg: Band-gap energy
'Ey
(a) zero bias: V = 0
-0
eeeeoeee
hv-E
g
Ev
(b) forward bias: V = Eg / q
Figure 1-1. Energy-band diagram of a p-n junction at (a) zero bias
and (b) forward bias


CHAPTER 5
FABRICATION OF MCTC ANTIGUIDED ARRAY LASERS
5.1 Introduction
The most crucial process in fabricating MCTC antiguided array lasers is the etching
process to obtain the precise interelement cap thickness required for in-phase operation.
As discussed in Chapter 4, process-windows for the interelement thickness to be pro
cessed are quite narrow for typical thin p-clad structures: 10-30 nm. Therefore, the
etching process for the required interelement thickness should be controlled with a preci
sion of less than 10 nm. There are quite a few etching techniques such as chemically
assisted ion beam etching (CAIBE) [61, 62], reactive ion etching (RIE) [63, 64], electron
cyclotron resonance (ECR) discharge etching [65, 66], and Ar(+) ion milling [67].
However, these techniques are not suitable for MCTC antiguided array devices because
the rms roughness values of the techniques are beyond the precision required for MCTC
devices. For fabrication of MCTC antiguided array lasers, the pulsed anodization tech
nique has been improved with developing a new electrolyte. The details of the pulsed
anodization etching technique are presented in Sec 5.2.
Since the p-clad thickness of thin p-clad structures is relatively small, the metal loss
of a thin p-clad device can be very high, depending on p-metallization. To minimize the
metal loss, a shiny gold contact is necessary and the electroplating technique is simple to
employ and good for the requirement. In Sec 5.3, the electroplating technique is dis
cussed. Finally, the fabrication sequence is presented in detail in Sec 5.4.
73


41
lateral coupling strength increases. In Figure 3-4, two near-field amplitude profiles of
resonant and non-resonant m = 3 in-phase array modes and the corresponding far-field
patterns of a 5 element antiguided arrayare compared. As shown in the figure, the
envelope function of the near-field profile of the resonant mode is uniform while that of
the non-resonant mode is cosine-shaped. This difference in the envelope function of the
near-field peaks mainly affects the FWHM of the far-field pattern and it does not strongly
(a)
(b)
A A A
111,
ill
MAMhi
IW n
A A
/ /'
i 11 li 11 111
Im
vv vy yy
Resonant in-phase mode
/ \
A / A
A 11 /
i i i /1
i i /
i
WAVIn III 1jf
I A
¡ I / \
I u /
w
Xl
la o.6
t/i
g 0.2
-0.2
c
3
X
c3
1.2
1
0.8
0.6
0.4
0.2
0
-0.2
.... 1 .... 1 ,
r
L
A
- Ml
: / 1 !
- 7 Uaw
FWHM = 1.39:

0j = 7.62 j
A
1 !\
\^J \ J
. 1 . . 1 . . 1 . .
.... i .... i .... i .... *
20 -15 -10 -5 C
5 10 15 20
Lateral angle ()
_ 1 1 I 1 1 1 1 I 1 1 1 1 I 1 1 1 1 I
FWHm'= 1.60:
^ j
1
- A
0, =7.59 j
1 A :
r ¡\ 1
J \ .
i/\ -
\ \ :
' i.... i
Non-resonant in-phase mode
-20 -15 -10 -5 0 5 10 15 20
Lateral angle ()
Figure 3-4. Near-field amplitude profiles of resonant (a) and non-resonant (b)
m = 3 in-phase array modes and their corresponding far-field patterns:
for the resonant mode, ne = 3.263 and n = 3.339; for the non-resonant mode
ne = 3.263 and n = 3.370.


CHAPTER 1
INTRODUCTION
1.1 Historical Perspective on Semiconductor Lasers
The first documented discussion of the possibility of light amplification by the use
of stimulated emission in a semiconductor was made in an unpublished manuscript written
by John von Neumann in 1953 [1]. He sent the manuscript to Edward Teller along with a
letter to ask some questions concerning specific points in the manuscript. In this paper,
von Neumann discussed using carrier injection across a p-n junction as one possible
means of achieving stimulated emission in semiconductors. During the late 1950s and
early 1960s, a number of theoretical and experimental papers were published on the
subject of the injection laser [2-4] prior to the actual demonstrations of injection laser
operation in 1962 [5,6]. Practical utility of these early devices was, however, limited
since a large value of the threshold current density (J^ > 50 kA/cm2) inhibited their con
tinuous operation at room temperature.
As early as 1963, it was suggested [7,8] that the threshold current density of semi
conductor lasers might be lowered significantly if a layer of one semiconductor material
was sandwiched between two cladding layers of another semiconductor material having
a relatively wider bandgap. Laser devices consisting of two dissimilar semiconductors
are commonly referred to as heterostructure lasers, in contrast to the single-semiconductor
devices which are labeled as homostructure lasers. Heterostructure lasers capable of con
tinuous wave (CW) operation at room temperature were first demonstrated in 1969 [9-11].
1


55
4.3 Modulated Cap Thin P-cIad (MCTC) Antiguided Array Lasers
A cross section of a typical MCTC antiguided array laser structure is shown in Fig
ure 4-3 (a). The cap layer for p-metal contact is highly p-doped GaAs and the structural
variation is etched into cap layer to induce the index modulation as shown in Figure 4-3
(b). The oxide layer in the interelement regions is used to confine carriers and hence
optical gain in the element regions. The thickness of the oxide is usually -100 nm. The
oxide is a GaAs native oxide and can be formed on the cap layer with pulsed anodization
technique which will be discussed in the next chapter. The metal contact can be different
in the element and interelement regions, but the metal contact in the element regions
should be shiny in order to reduce the optical loss due to mode overlap with the metal
layer [60]. The symbols, te and tj, are designated for cap layer thicknesses in element and
interelement regions, respectively. As used before, d and s are element and interelement
dimensions, respectively. For the p-clad thickness, the symbol t^ is used. The associ
ated lateral effective refractive-index variation (index step: An0) for a TE0 mode, to a first
approximation, is given by the difference in effective index between the TEg mode in each
region of the structure. In addition to the higher index, the mode loss of theTE0 mode in
the interelement regions is higher than that in the element regions as shown in Figure 4-3
(b). This is another merit of the thin p-clad structure since higher mode loss in the inter
element regions is required to discriminate against out-of-phase and adjacent modes as
discussed in Chapter 3. The interelement loss can be further increased by using a very
lossy metal with a thinner oxide layer for the metal contact in the interelement regions.
In this work, n0e and n0i are the effective refractive-indices for a TE0 mode in the element
and interelement regions, respectively and (Xqc and o^(- are the TEg mode losses in the ele
ment and interelement regions, respectively.