New Laser Technologies Analysis of Quantum Dot and Lithographic Laser Diodes

University of Central Florida STARS

Electronic Theses and Dissertations, 2004-2019

2010

New Laser Technologies Analysis Of Quantum Dot And Lithographic Laser Diodes

Abdullah Demir University of Central Florida

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STARS Citation Demir, Abdullah, "New Laser Technologies Analysis Of Quantum Dot And Lithographic Laser Diodes" (2010). Electronic Theses and Dissertations, 2004-2019. 1561. https://stars.library.ucf.edu/etd/1561 NEW LASER TECHNOLOGIES: ANALYSIS OF QUANTUM DOT AND LITHOGRAPHIC LASER DIODES

ABDULLAH DEMIR B.S. and M.Sc. Koc University 2002, 2005 M.Sc. University of Central Florida 2009

A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the College of Optics and Photonics at the University of Central Florida Orlando, Florida

Summer Term 2010

Major Professor: Dennis G. Deppe

ABSTRACT

The first part of this dissertation presents a comprehensive study of quantum dot (QD)

lasers threshold characteristics. The threshold temperature dependence of a QD laser diode is

studied in different limits of p-doping, hole level spacing and inhomogeneous broadening.

Theoretical analysis shows that the threshold current of a QD laser in the limit of uniform QDs is not temperature independent and actually more temperature sensitive than the quantum well laser. The results also explain the experimental trends of negative characteristic temperature observed in QD lasers and clarify how the carrier distribution mechanisms inside and among the

QDs affect the threshold temperature dependence of a QD laser diode.

The second part is on the experimental demonstration of lithographic lasers. Today’s vertical-cavity surface-emitting lasers (VCSELs) based on oxide-aperture suffer from serious problems such as heat dissipation, internal strain, reliability, uniformity and size scaling. The lithographic laser provides solutions to all these problems. The transverse mode and cavity are defined using only lithography and epitaxial crystal growth providing simultaneous mode- and current-confinement. Eliminating the oxide aperture is shown to reduce the thermal resistance of the device and leading to increased power density in smaller lasers. When it is combined with better mode matching to gain for smaller devices, high output power density of 58 kW/cm2 is

possible for a 3 μm VCSEL with threshold current of 260 μA. These VCSELs also have grating-

free single-mode single-polarization emission. The demonstration of lithographic laser diodes

with good scaling properties is therefore an important step toward producing ultra-small size

laser diodes with high output power density, high speed, high manufacturability and high iii reliability. Lithographic VCSELs ability to control size lithographically in a strain-free, high efficiency device is a major milestone in VCSEL technology.

To my nieces Fatma and Derya

TABLE OF CONTENTS

LIST OF FIGURES...... viii

LIST OF TABLES...... x

LIST OF ACRONYMS/ABBREVIATIONS...... xi

CHAPTER 1: INTRODUCTION AND OUTLINE ...... 1

CHAPTER 2: QUANTUM DOT LASER MODEL...... 4 2.1 Introduction...... 4 2.2 Analysis of the Temperature Dependence of Threshold...... 7 2.3 Non-Equilibrium Rate Equation Model...... 10 2.4 Threshold Temperature Dependence for a QD Laser...... 13 2.5 Summary...... 16

CHAPTER 3: MODEL IN THE LIMIT OF UNIFORM QUANTUM DOTS ...... 18 3.1 Introduction...... 18 3.2 Uniform QDs with Energetically Isolated Ground State Transitions ...... 21 3.3 Uniform QDs with Multiple Discerete Levels...... 25 3.4 Summary...... 30

CHAPTER 4: DESIGN PRINCIPLES OF LITHOGRAPHIC LASER...... 32 4.1 Introduction...... 32 4.2 Oxide-VCSEL Issues and Limitations...... 34 4.3 Optical Mode Confinement...... 37 4.4 Current Confinement ...... 40 4.5 Summary...... 44

CHAPTER 5: EXPERIMENTAL RESULTS ON LITHOGRAPHIC VCSEL ...... 45 5.1 Introduction...... 45 5.2 Device Structure...... 45

5.3 Results...... 48 5.3.1 Lasing Characteristics...... 48 5.3.2 Low Thermal Resistance of Lithographic Structure...... 50 5.3.3 High Output Power Density of Small Devices...... 52 5.3.4 Single-Mode and Single-Polarization Lasing...... 53 5.3.5 Reliability ...... 57 5.4 Summary...... 59

CHAPTER 6: SUMMARY...... 60

LIST OF REFERENCES ...... 62

vii

LIST OF FIGURES

Figure 2-1: Atomic force microscope photograph of crystal surface right after QD formation...... 4

Figure 2-2: Schematic illustration of the energy structure and Fermi levels of two different QDs. Non-equilibrium distribution of electrons is created due to finite carrier relaxation from the barrier and carrier transport between the QDs through wetting layer...... 5

Figure 2-3: The effect of inhomogeneous broadening on threshold temperature dependence for undoped (squares) and p-doped (circles) QD laser with (a) uniform QDs and (b) inhomogeneously broadened QDs...... 15

Figure 3-1: Temperature dependence of dephasing rate. The inset shows the calculated homogeneous broadening at T = −40 °C and T = 40 °C...... 20

Figure 3-2: Characteristic temperature versus threshold population inversion of p-doped and undoped QD lasers. The inset shows the schematic of QD energy levels with single electron and hole states with acceptor doping...... 22

Figure 3-3: Temperature dependence of normalized threshold current for p-doped planar quantum well and QD lasers...... 24

Figure 3-4: Temperature dependence of threshold current for a multistate undoped QD laser at the 300 K transparency and threshold population inversions of 0.042, 0.113 and 0.182. The T0’s are calculated for 20 °C ≤ T ≤ 80 °C. The inset shows the schematic of energy levels in a multistate QD laser...... 26

Figure 3-5: Temperature dependence of threshold current for a multistate undoped QD laser at the 300 K transparency and threshold population inversions of 0.042, 0.113 and 0.182. The T0’s are calculated for 20 °C ≤ T ≤ 80 °C. The inset shows the schematic of energy levels in a multistate QD laser...... 28

Figure 3-6: The effect of wetting layer on the characteristic temperatures for undoped QD lasers at different threshold population inversions...... 29

Figure 4-1: Typical layout of a VCSEL []...... 34

Figure 4-2: Illustration of oxide-VCSEL limitations and drawbacks: Oxidation introducing point defects, heat barrier effect of oxide and size variation of oxide-aperture...... 36

Figure 4-3: The schematic of cavity with phase-shifting mesa where region “0” supports lasing mode and region “1” has only waveguide modes...... 37

Figure 4-4: Energy band diagram of upper DBR showing Fermi level pinning on Al0.3Ga0.7As surface []...... 42

viii

Figure 4-5: The device structure for current-confinement based on Fermi level pinning []...... 42

Figure 4-6: Current versus voltage characteristics of on-mesa and off-mesa region for a region of 70x110 μm, showing turn-on voltage difference for required for current blocking...... 43

Figure 5-1: Growth and fabrication process cycle of lithographic VCSELs showing an as-grown wafer, mesa formation for regrowth, after regrowth and after fabrication...... 46

Figure 5-2: (a) The schematic of lithographic VCSEL and (b) microscope image of the 8-μm diameter device and the contact pad...... 47

Figure 5-3: Output power and voltage versus current characteristics of 8 μm diameter VCSEL device...... 49

Figure 5-4: Emission spectra of 8 μm diameter device for various current levels below (0.5 mA) and above threshold (1, 12 and 18 mA)...... 49

Figure 5-5: (a) Lasing wavelength shift versus dissipated power for 8 μm diameter device, (b) Thermal resistance versus device diameter of current results with lithographic VCSEL and its comparison to oxide-confined VCSELs...... 51

Figure 5-6: Output power density versus injection current density showing that output power density is the highest for the smallest device size tested...... 53

Figure 5-7: AFM image of 3 μm (on the left) and 8 μm (on the right) lithographic VCSEL showing anisotropic formation of the device after regrowth...... 54

Figure 5-8: Above threshold emission spectra of 3 μm diameter lithographic VCSEL at I = 0.5, 1, 1.5 and 2.0 mA, showing single mode emission with more than 20 dB SMSR...... 55

Figure 5-9: The SMSR of 3 μm VCSEL showing single-mode single-polarization emission...... 56

Figure 5-10: Reliability of 3 μm lithographic VCSEL showing constant output power of 3.65 mW at an injection current level of I= 6.0 mA...... 58

LIST OF TABLES

Table 2-1: QD laser parameters used for the calculations...... 14

LIST OF ACRONYMS/ABBREVIATIONS

AFM Atomic Force Microscopy

EEL Edge-Emitting Laser

DBR Distributed Bragg Reflector

MBE Molecular Beam Epitaxy

MOCVD Metal-Oxide Chemical Vapor Deposition

QD Quantum Dot

QW Quantum Well

SMSR Side-mode Suppression Ratio

VCSEL Vertical-Cavity Surface-Emitting Laser

WL Wetting Layer

WPE Wall-Plug Efficiency

CHAPTER 1: INTRODUCTION AND OUTLINE

The gain region of semiconductor laser diodes evolved from bulk p-n junctions to today’s

quantum confined structures such as quantum well (QW) and quantum dot (QD) lasers. QD lasers showed rapid development with unique laser characteristics compared to QW lasers [1].

Three-dimensional quantum confinement of the gain material causes dramatic changes in the

device characteristics of semiconductor lasers. The change in the laser physics due to QD gain

medium lead to important device capabilities such as low threshold current and more

temperature stable laser operation. Two breakthroughs based on the self-organized epitaxial

growth have been the demonstration that the self-organized growth can be used to fabricate

GaAs-based 1.3 µm QD laser diodes [2], and the demonstration that acceptor doping (p-doping)

could counter gain saturation and increase the QD laser characteristic temperature (T0) [3, 4, 5] to values well beyond that so far possible with InP-based lasers.

In terms of the geometry of the optical cavity, semiconductor laser diodes fall into two categories: edge-emitting lasers (EEL) and vertical-cavity surface emitting lasers (VCSEL). In both types, the current is injected vertically from the top surface and the substrate while the difference between the two types of laser stems from the direction of the optical cavity. The first type of semiconductor diode lasers called EELs due to the light emission from the cleaved edges forming mirrors for laser oscillation. Alternatively, optical cavity can be formed by vertically stacked high reflective mirror pairs as in the case of the VCSELs. This difference in the cavity direction has dramatic effects on the optics, applications and manufacturing of these laser diodes.

Short cavity length of VCSELs allows single longitudinal mode operation and they can be made 1

very small with sub-miliampere threshold currents. Circular aperture VCSELs enable easy

coupling of output to fibers compared to elliptical emission of EELs requiring optics for fiber

optic integration.

The research reported in this dissertation presents the underlying physics observed in QD lasers unusual threshold characteristics. In Chapter 2, non-equilibrium rate equation model is described considering the inhomogeneous broadening of QD ensemble [6]. The transfer of

carriers between the QDs through the wetting layer (WL) is considered by carrier diffusion

process causing non-equilibrium electron distribution. It is found that the hole Fermi levels are in

equilibrium with the corresponding wetting layer due to close hole level spacing and high density

of carriers in the wetting layer. The temperature dependence of device characteristics is

investigated. It is demonstrated that although the negative T0 at low temperatures is due to hole

escape out of ground state to higher hole states, non-equilibrium carrier distribution due to

inhomogeneous broadening cause negative T0 around room temperature.

Chapter 3 presents the analysis of threshold temperature dependence of QD laser diode

for the case of active region with uniform QDs [6]. Even though it is a simplified case, it takes

into account the fundamental physics of carrier-phonon interaction and closely spaced energy

levels. This work reveals important results and shows that ideal QD laser has higher temperature

sensitivity than a QW laser. This chapter also shows why the threshold temperature sensitivity decreases and the T0 is optimized for a range of p-doping levels between 10 to 20 acceptors per

QD. The results have good agreement with the experimental work shown in the literature and

explain the underlying mechanisms.

Chapter 4 discusses a novel current and optical mode confinement technology that can be used for both for EEL and VCSEL with a QW or QD gain region. The fundamental problems of today’s most commonly used oxide-confinement method are described. The basic principles of lithographic laser to get optical mode and electrical injection confinement are given in this part.

Chapter 5 presents the experimental results of lithographic laser technology applied to

VCSELs [7]. In this early stage of the technology, device characteristics demonstrate that the lithographic VCSELs have better heat spreading than oxide-VCSEL showing much lower thermal resistance and therefore higher power densities. Single-mode lasing by grating-free polarization control is demonstrated with high polarization suppression ratios. Initial device lifetime tests were also performed confirming more reliable operation of lithographic VCSELs due to its oxide-free structure.

CHAPTER 2: QUANTUM DOT LASER MODEL

2.1 Introduction

Experimentally so far, size variations in the epitaxial self-organized QDs of laser diode

gain ensemble have produced inhomogeneous broadening that is much larger than the homogeneous broadening. Size variations can be determined indirectly by photoluminescence or

electroluminescence measurement and related to the spectral linewidth of the emission, which is

in the range of 20 to 50 nm for 1.3 μm QDs. Figure 2-1 shows an atomic force microscope

(AFM) image of the 1 μm x 1 μm area epitaxial surface right after self-organized growth of

nanometer-scale InGaAs QD islands on GaAs. As-grown QDs have an average size of ~30 nm

with density of 2x1010 dots/cm2.

Figure 2-1: Atomic force microscope photograph of crystal surface right after QD formation.

Figure 2-2 presents a schematic of the band diagram of QD active region. Carrier transfer

and capture processes of QDs are illustrated in a basic picture of two QDs of different size. The

carriers are injected from the barrier to the wetting layer of individual QDs. Due to small confinement energies of valence band, the hole states of different size dots are in quasi- equilibrium and therefore they all have a common Fermi level. On the other hand, the electron

quantum states of different dots are not in quasi-equilibrium and each QD has its own Fermi

level set by capture from the barrier and carrier transport through the wetting layer among QDs

of different sizes. Here 2D wetting layer is of fundamental importance for carrier capture and

carrier transfer among inhomogeneously broadened QDs.

One of the most studied characteristics of QD laser diodes has been QD laser diode’s T0 for the GaAs-based 1.3 µm QD laser. The QD laser T0 is characterized by the empirical relation

T / T0 Ith (T ) = Ith (T = 0)e , used generally to describe the temperature dependence of threshold for

semiconductor lasers. While the T0 parameter continues to be used for QD lasers, its empirical relation to an exponential severely breaks down because of the change in optical gain physics with a QD active region. This breakdown leads to negative T0 values over certain temperature

ranges [8].

While many processes can influence the T0 of a laser diode, these generally depend on the

temperature dependent nonradiative and radiative recombination rates needed to establish the

electron-hole occupation in the quantum states of the gain region for lasing threshold. For QD

lasers, the quantum states include the discrete states for confinement in the 3-D QD wells, and

the wetting layer continuum states that make up the energy bands at energies greater than the QD

ground and discrete levels. The wetting layer is known to produce charge trapping with sufficiently slow escape times to cause non-equilibrium charge distributions in the QD ensemble if inhomogeneous broadening is present.

Nonradiative recombination due to defects has also been shown to strongly influence T0

[9, 10, 11], including recombination from the wetting layer. In general, longer wavelength QD

lasers have shown the best temperature performance in threshold, especially for high

temperatures. This is in large part because the longer wavelength QD lasers have deeper

confinement potentials, and the deeper confinement can reduce the electron-hole population in

the wetting layer that usually leads to nonradiative recombination. In fact, it is now demonstrated 6

experimentally that recombination from the wetting layer continuum states can be effectively

eliminated from contributing to the QD laser diode threshold at room temperature [12, 13, 14].

The analysis is based on QDs that contain a discrete electronic level structure of multiple electron and hole levels consistent with InAs QDs on GaAs with homogeneous broadening but with size nonuniformity that adds inhomogeneous broadening. The analysis of QD laser with inhomogeneous broadening requires non-equilibrium rate equation model and the model and results are presented. The inhomogeneous broadening is believed to produce the negative T0 found experimentally [8]. Here we show that the negative T0 produced by the transparency

current provides a good description of the negative T0 behavior found experimentally in

inhomogeneously broadened QD lasers for temperatures between 150 K to 250 K, for both

undoped and p-doped QD lasers, and that inhomogeneous broadening mechanism proposed by

Zhukov et al. [8] can cause an additional negative T0 at slightly higher temperatures.

2.2 Analysis of the Temperature Dependence of Threshold

The optical gain for a given photon energy E of a semiconductor laser can be expressed

∞ hγ H (T ) g(E,T ) ∝ dE′ρred (E′)[Pe (E′,T ) − Ph (E′,T )] , (2.1) ∫−∞ 2 2 (E − E′) + [hγ H (T )]

where ρred (E′) is the reduced density of optical transitions for a photon energy E′ , Pe (E′,T ) is

the temperature dependent electron occupation of electron state taking part in the optical

7 transition for photon energy E′ , Ph (E′,T) is the temperature dependent electron occupation of

the hole state taking part in the optical transition for photon energy E′ , γ H (T) is the temperature dependent homogeneous linewidth of the optical transition, and h is Planck’s constant.

For a semiconductor laser with QD gain region, density of states is quantized in 3D and size variation of QD ensemble is characterized by a Gaussian distribution centered at an energy

level of E0 with full-width at half-maximum value of ΔEInh. . Then, the optical gain of the QD laser is given as

N −4⋅ln(2)⋅(E 2 −E 2 ) / ΔE 2 QD e 0 1l Inh. γ (T ) g(E,T ) ∝ [ f (T ) − f (T )] h H (2.2) ∑∑ ΔE e,ml h,ml (E − E )2 +[ γ (T )]2 lm=1 l Inh. ml h H where l labels the different QDs of the ensemble, E is the energy level of the state mof QD ml

l , and the summation over l runs over all the QDs, N QD , of the gain ensemble, and the

summation over ml runs over all quantum states of the QD gain region starting from ground state m = 1 , including wetting layer states. f (T ) and f (T ) is the temperature dependent e,ml h,ml

Fermi occupation probability of quantum state in level m associated with QD l in electron and hole states, respectively.

The charge neutrality is given by

N QD N QD s f (T ) − s [1− f (T )] + N = 0, (2.3) ∑∑ ml e,ml ∑∑ ml h,ml A l =1 ml l =1 ml

8 where s is the degeneracy of quantum state m , N is the number of acceptors per QD for p- ml l A doping used to generate a built-in equilibrium hole population.

In the presence of inhomogeneous broadening, the recombination current from the QD gain ensemble must account for all QDs and the wetting layer, and the spontaneous emission current is given by

NQD I (T ) ∝ s f (T )[1− f (T )] , (2.4) sp ∑∑ ml e,ml h,ml lm=1 l

where the summation over ml runs over all radiatively coupled quantum states of the QD gain region, including wetting layer states. More details of the role of the wetting layer states can be found in [15, 16, 17].

In the calculations presented below the wetting layer contributes little to the recombination current that sets threshold. However electron transport through the wetting layer plays an important role in establishing some of the details of the T0 in the presence of inhomogeneous broadening. Rapid relaxation of electrons and holes in the self-organized QDs

[18] creates quasi-equilibrium charge distributions within a given QD for spontaneous recombination times, with spontaneous emission establishing the current needed to reach lasing threshold.

2.3 Non-Equilibrium Rate Equation Model

A non-equilibrium treatment of the electron or hole relaxation within the QD discrete levels has already been given [17]. Using this, we have analyzed the non-equilibrium distributions of electrons and holes within the QDs based on their electronic structure of InAs

QDs. We find in all cases for temperatures greater than ~100 K that electrons and holes quasi- equilibrate and can be described by quasi-Fermi levels associated with a given QD. The reason is that the time constant for spontaneous emission is always much longer by more than an order of magnitude than for electron or hole relaxation time within their own discrete levels. Note that, at low temperature, non-radiative recombination can be neglected, while for higher temperatures we expect the faster relaxation stimulated by phonons to still cause quasi-equilibration in the separate QDs. Therefore the quasi-equilibrium approximation holds up to threshold for the electron-hole distribution within the discrete levels of the QD laser. We have also found that including transport through the wetting layer as in [16] and below, quasi-equilibrium is also maintained for all hole states in the QD ensemble for temperatures greater than ~100 K, and the

InAs QD electronic structure. The reason is that the wetting layer valence band confinement energies for holes are small, so that holes easily move between different QDs even at low temperature. However, the electron confinement is much larger, and distributions between different QDs are not in quasi-equilibrium, as discussed much earlier [8]. Therefore each QD must be considered to have its own quasi-Fermi energy for electrons, with different QD electron populations established by transport between the QDs. The model is illustrated in Figure 2-2 showing the carrier relaxation and transport processes.

The electron capture from the barrier to the wetting layer of QDs is described by a rate equation where the current is first injected into the barrier and then carriers spontaneously relax to the wetting layer of each QD. The rate equation is given by

NQD dfe,B I fe,B − fe,WL N s (T ) = − γ s s [ f (1 − f ) + l ] (2.5) QD B B B WL ∑ e,B e,WLl ( EB −EWL ) /(kT ) dt q l=1 e −1 where summation over l runs over all the QDs, N , of the gain ensemble, f is the electron QD e,WLl

wetting layer occupation of QD l , f e,B is the electron occupation probability in the barrier state

of the wetting layer, sWL is the degeneracy of the wetting layer, sB is degeneracy of electron

states in the wetting layer barrier, γ B is the spontaneous electron relaxation rate from the barrier

state to the wetting layer, EB − EWL is the energy difference between the barrier and the wetting layer in the conduction band.

The coupling between the quasi-Fermi populations in different QDs is described by a transport equation for electrons moving through the wetting layer and relaxing into different

QDs. The rate equation describing these couplings is given by [16]

df f − f e,WLl e,B e,WLl sWL = γ B sB sWL[ fe,B (1− fe,WL ) + ] l dt l e(EB −EWL ) /(kT ) −1

df − s [ e,ml + γ f (1− f )] ∑ ml sp e,ml h,ml ml dt

kT + μ n s ( f − f ) , (2.6) q WL QD WL e,WLave e,WLl

where stimulated emission has been neglected for threshold, γ sp is the spontaneous radiative

emission rate, and nQD is the QD density in a layer given by NQD divided by the active area of

the QD ensemble, and μWL is the electron mobility in the wetting layer. The driving term,

f − f , is given by e,WLave e,WLl

1 N QD f = f , (2.7) e,WLave ∑ e,WLl NQD l =1 and results in net electron transport into or out of those QDs l with f ≠ f . e,WLl e,WLave

The Fermi level of each QD is set by the carrier relaxation from the barrier to wetting layer, carrier transport between the dots through wetting layer and spontaneous emission current of that QD and given by the steady state solution of equation (2.6) as

1 kT γ s s f [1+ ] + μ n s f −γ s f (1− f ) B B WL e,B ( E −E ) /(kT ) WL QD WL e,WLave sp ∑ ml e,ml h,ml e B WL −1 q f = ml (2.8) e,WLl 1 kT γ B sB sWL [ f e,B + ] + μWLnQD sWL e( EB −EWL ) /(kT ) −1 q

In the limit of high mobility of electrons through the wetting layer, the relation reduces to

f = f , then every QD has the same population on its wetting layer states and quasi- e,WLl e,WLave equilibrium is established between the QDs.

For the case of very high relaxation rate from the barrier to the wetting layer of QDs, the carrier transport becomes negligible. The occupation probabilities of the wetting layer states are set by the barrier population and constant separation of barrier and wetting layer energy levels.

The wetting layer occupation probability is then given by

1 f [1+ ] e,B (EB −EWL ) /(kT ) f = e −1 (2.9) e,WLl 1 [ fe,B + ] e(EB −EWL ) /(kT ) −1 which is equal for all QDs and therefore creates quasi-equilibrium distribution of carriers.

Even though these two mechanisms are different in a way to set the wetting layer population of each QD, they both bring the QDs into quasi-equilibrium. The interplay between the carrier relaxation from the barrier and diffusion of carriers on the wetting layer creates non- equilibrium distribution of carriers among the QDs. It is also important to note that the analysis is carried out for below threshold operation of QD laser and fast recombination due to stimulated emission is not included, which will also be critical for above threshold analysis and have a fundamental effect due to finite carrier transport and relaxation rate of carriers.

2.4 Threshold Temperature Dependence for a QD Laser

In this section, threshold temperature dependence is analyzed for a QD laser with inhomogeneously broadened QDs and multiple discrete levels. Table I shows the parameters used for the structure with parameters taken to agree with the most heavily studied InAs QD

Table 2-1: QD laser parameters used for the calculations.

laser diodes grown on GaAs that operate near 1.3 µm. Figure 2-3 shows calculated results both for (a) hΔωIH = 0 (uniform QDs), and (b) hΔωIH = 80 meV. The 80 meV inhomogeneous broadening is characteristic of many of the experimental InAs QD laser diodes. Calculated plots of the relative threshold vs. temperature are given for the limiting case of a threshold

inversion fe,0 − f h,0 = 0, and fe,0 − f h,0 = 0.08, and for either undoped or p-doped. The trends in

Figure 2-3(b) agree closely with the experimental data. An excellent comparison can be made between the experimental data shown in figure 1 of [30], and the calculated curves presented here shown for the inhomogeneously broadened QD gain region in Figure 2-3(b).

Figure 2-3: The effect of inhomogeneous broadening on threshold temperature dependence for undoped (squares) and p-doped (circles) QD laser with (a) uniform QDs and (b) inhomogeneously broadened QDs.

There is also what may be surprising agreement between the trends shown by the curves in Figure 2-3(a) for uniform QDs, and (b) for a QD ensemble with size variation for which the inhomogeneous broadening is large ( hΔωIH = 80 meV). Especially in the undoped cases in 15

Figure 2-3(a) or (b), the negative T0 between 100 K and 250 K is due to the influence of the transparency current discussed in more detail in the next chapter, and is not related to inhomogeneous broadening. The abrupt increase in threshold current for temperatures in the range of 300 K to 350 K is due to gain saturation that increases the electron-hole populations in higher energy levels [3, 4, 5].

Negative T0 caused by inhomogeneous broadening [8] can be seen in either the undoped or p-doped calculated curves in Figure 2-3(b). For the undoped case with NA = 0 and

fe,0 (T) − fh,0 (T) = 0, a negative T0 can be seen with its minimum at 250 K (lowest dotted curve in (b)). This negative T0 due to inhomogeneous broadening comes in addition to that caused by the transparency current density, which can be seen in the undoped case in Figure 2-3 (b) for

fe,0 (T) − fh,0 (T) = 0.08 (solid curve with solid squares), with its minimum at 200 K. For the p- doped case the negative T0 due to inhomogeneous broadening, Figure 2-3 (b) solid and open circles, can be seen more clearly around 300 K. Therefore both transport between the QDs in the case of inhomogeneous broadening, and the hole population changes within a given QD with changes in temperature, must be included to fully describe the T0 behavior found experimentally

[3-5], [22-24], [30], and to predict the T0 for future designs.

2.5 Summary

Non-equilibrium rate equation model of inhomogeneously broadened QDs is shown to be capable of including the effects of electron transport and carrier relaxation from the barrier. The model is presented to analyze the expressions for optical gain, threshold current and threshold 16 temperature dependence of QD laser diode. The threshold temperature dependencies of QD lasers in different limits of p-doping and inhomogeneous broadening have been presented. It is found that the thermal broadening of holes is important and can create negative T0, especially in the lower temperature regime between 100 K and 250 K. Negative T0 due to inhomogeneous broadening is found at higher temperatures close to 300 K, especially for p-doped QD ensembles.

CHAPTER 3: MODEL IN THE LIMIT OF UNIFORM QUANTUM DOTS

3.1 Introduction

Here we present an analysis of the QD laser T0 that includes the temperature dependence of the transparency current, which is the current to get positive population inversion. The analysis is based on various QD electronic structures that include: (i) Truly isolated ground state energy levels based on fully uniform QDs that have only homogeneous gain broadening; (ii)

QDs that contain a discrete electronic level structure of multiple discrete electron and hole levels consistent with InAs QDs on GaAs, but with uniform QDs that have only homogeneous gain broadening. In each case we study the influence of built-in equilibrium hole concentrations. We show in each case that optimally populating QD discrete states with equilibrium hole charge is required to reach high T0. For case (ii), when the holes are energetically close with respect to the thermal energy, the transparency current exhibits a negative T0 that depends strongly on p-doping level.

For the limiting case of uniform QDs, ρred (E′) becomes a series of delta function optical transitions without Gaussian size variation of QD ensemble. The gain expression given in equation (2.2) now reduces to

sm gm (T) ∝ [ fe,m (T) − fh,m (T)], (3.1) hγ H (T)

18 where m labels a given discrete optical transition, sm is the degeneracy of the transition, and the occupation probabilities reflect quasi-equilibrium electron-hole distributions for discrete optical transitions. The charge neutrality equation given in equation (2.3) is simplified as

∑ sm fe,m (T ) − ∑ sm[1− fh,m (T )] + N A = 0, (3.2) m m

where N A is the number of acceptors per QD for p-doping used to generate a built-in equilibrium hole population. The levels in (3.4) run over all levels of interest, including the continuum states of a wetting layer. The current density due to spontaneous emission needed to reach threshold expressed by equation (2.4) is then given by

I sp (T ) ∝ ∑ sm fe,m (T )[1− fh,m (T )] . (3.3) m

In this form the change in current required to maintain a corresponding threshold gain value of

(3.1) can be found from (3.3). The homogeneous linewidth [19, 20, 21] approximately follows the Bose distribution due to thermal occupation of phonons, and can be described by the form

1 γ (T ) = γ + a ⋅T + b ⋅ , (3.4) H 0 ⎛ E ⎞ exp⎜ a ⎟ −1 ⎝ kT ⎠

9 −1 8 −1 13 −1 where γ 0 = 1.0×10 s , a = 7.5×10 (s·K) , b = 1.4×10 s and Ea = 29 meV, are taken from

[21]. Equation (3.4) includes contributions due to zero-temperature lattice motion, acoustic phonons, and optical phonons.

Figure 3-1: Temperature dependence of dephasing rate. The inset shows the calculated homogeneous broadening at T = −40 °C and T = 40 °C.

As shown in Figure 3-1, the dephasing rate from equation (3.4) approximately follows

kT with a linear dependence at high temperature. The inset in Figure 3-1 shows the Lorentzian linewidth and change in peak value for the temperatures of −40 °C and 40 °C. At 40 °C the peak value of the Lorentzian linewidth decreases by a factor of ~1.7 compared to the value at −40 °C.

To maintain a constant gain value in the QD for this broadening, the population inversion must be increased if possible by the same value. If the QD gain ensemble is inhomogeneously broadened, a change in homogeneous linewidth may have little effect on the ensemble peak gain value, as long as the inhomogeneous broadening significantly exceeds the homogeneous 20 broadening. In the limit of uniform QDs, however, the temperature dependence of the homogeneous broadening will significantly impact the QD laser’s T0. Therefore a complete model of either case must include the homogeneous broadening. In this chapter we consider uniform QD ensembles.

In the calculations presented below, the wetting layer contributes little to the recombination current that sets threshold. However electron transport through the wetting layer plays an important role in establishing some of the details of the T0 in the presence of inhomogeneous broadening treated in chapter 2.

3.2 Uniform QDs with Energetically Isolated Ground State Transitions

Figure 3-2 shows the threshold temperature dependence calculated for an ideal case of a

QD laser diode that has both uniform QDs in the gain region, and thermally isolated electron and hole ground states, with and without p-doping. Perhaps the most interesting aspect for this ideal case is the impact of p-doping, which decreases the QD laser T0 as compared to the undoped case. This is different than reported experimentally [3, 4, 5, 22, 23, 24], and points to the role of the closely space hole energy levels in the QD lasers that have so far been demonstrated experimentally, and homogeneous broadening.

The threshold current density from (3.3) is related to the electron and hole Fermi

occupations simply as Ith (T ) ∝ fe,0 (T )[1− fh,0 (T )] , and includes contributions that come from the transparency current density, and the additional current needed to provide that gain beyond

transparency to overcome the cavity losses. The threshold gain is related to the same Fermi

−1 occupations as gth ∝ γ H (T ) [ fe,0 (T ) − fh,0 (T )], and homogeneous broadening does not influence

−1 the transparency current in this case. However one can see from gth ∝ γ H (T ) [ fe,0 (T ) − fh,0 (T )]

that the increase in γ H (T ) with temperature will require an increase in [ fe,0 (T ) − fh,0 (T )] to

reach the same gain value if [ fe,0 (T ) − f h,0 (T )] is greater than zero.

The transparency current plays an important role in stabilizing the laser diode threshold

(assuming a Fabry-Perot laser cavity) against temperature changes because it can be temperature 22 insensitive in the ideal case of a thermally isolated ground state transition. When only a small population inversion is required to reach threshold, the transparency current makes up a significant fraction of the threshold current, and decreases the threshold current dependence on temperature.

As shown in Figure 3-2, and consistent with this, the T0 for the undoped ideal QD laser diode obtains its highest value at low values of gain inversion required for threshold, since for low gain inversion the contribution of the transparency current density to threshold is larger. As the gain inversion required for lasing increases, the T0 decreases, since the additional current that must be added to the transparency current to reach threshold depends on the temperature dependent homogeneous linewidth.

The lower curve in Figure 3-2 shows the dramatic decrease in T0 that occurs when p- doping is added to the ideal QD laser diode if the transparency current is forced to zero with a built-in equilibrium hole population. The built-in hole concentration may even reduce the threshold current density, depending on required gain value for threshold. However, the T0 characterizes a relative change in threshold current with change in temperature, as opposed to the absolute value of the threshold current. Therefore the reduction or elimination of the contribution of the transparency current by p-doping decreases the T0, because it reduces that component of the threshold current that is temperature independent. While the T0 of the undoped ideal QD laser diode may reach over 2000 K for a very low loss laser cavity design, the T0 of the p-doped QD laser diode is much lower at 157 K and nearly independent of the threshold gain value.

Figure 3-3 shows the calculated plots of this ideal case for a QD laser diode, and a planar quantum well laser diode threshold temperature dependence under the Lasher and Stern conditions [25, 26]. Figure 3-3 shows that the ideal QD laser diode, originally considered by

Arakawa and Sakaki [25], actually produces a smaller T0 of 157 K than the planar quantum well with a T0 of 278 K. The calculated plot for the planar quantum well also includes the contribution of homogeneous broadening due to dipole dephasing. However, homogeneous broadening makes little contribution to the planar quantum well laser’s T0, since the homogeneous broadening in this case is less than the gain broadening due to Fermi occupation of the quantum well states.

Therefore, the analysis of Lasher and Stern that neglects the homogeneous linewidth [26] proves

Figure 3-3: Temperature dependence of normalized threshold current for p-doped planar quantum well and QD lasers.

24 valid for bulk or quantum well lasers, since the gain broadening is dominated by the electron occupation of the continuum of states in bulk semiconductors that follows a Fermi occupation.

As we show below, the transparency current density continues to play an important role in T0 for the case of closely spaced hole levels and in the presence of inhomogeneous broadening, and is the source of much of the T0 behavior for different p-doping levels.

3.3 Uniform QDs with Multiple Discerete Levels

Figure 3-4 and Figure 3-5 show temperature dependent threshold and T0 behavior for QD lasers with multiple electron levels and multiple closely spaced (in energy) hole levels (see

Figure 3-4 inset) that can be thermally excited for the temperatures of interest. We have already shown that the value of the energy level separations can significantly influence T0 [27]. The calculated results in this section use energy level separations and degeneracy values characteristic of the most heavily studied InAs QD laser diodes grown on GaAs that operate near

1.3 µm, and can be compared with the calculations on p-doped QD lasers [28, 29, 15]. The electron energy levels are taken as 70 meV separation, while the hole levels are taken as 10 meV

separation. The lower level degeneracies are taken as s0 = 2 , s1 = 4 , s2 = 8 , s3 =12 and s4 =18

[28]. The T0 behavior changes dramatically when closely spaced hole levels can become thermally excited in the QD laser. The thermalization of the holes in this limit can lead to strong gain saturation with increasing temperature, especially for temperatures above room temperature

[3, 4, 5, 15, 29]. In Figure 3-4 the T0 decreases from 325 K at the limiting population inversion

threshold value approaching transparency, fe,0 − f h,0 = 0, to T0 = 81 K at the threshold population

25 inversion of fe,0 − f h,0 = 0.18. For the specific conditions considered for Figure 3-4, if the

required population inversion for lasing exceeds the value of fe,0 − f h,0 = 0.18, ground state lasing can no longer be obtained over the entire temperature range of interest, due to the temperature dependent gain saturation that comes from thermal excitation of holes from the ground state. This low value of gain saturation in the population inversion is close to that found experimentally for InAs QD lasers [15] and calculated previously [29], and emphasizes the important role of the hole energy level spacing in setting T0.

Figure 3-4: Temperature dependence of threshold current for a multistate undoped QD laser at the 300 K transparency and threshold population inversions of 0.042, 0.113 and 0.182.

The T0’s are calculated for 20 °C ≤ T ≤ 80 °C. The inset shows the schematic of energy levels in a multistate QD laser.

However, for lower temperatures and with p-doping, the transparency current can exhibit a negative T0 when multiple levels are present. Note the transparency current corresponds to the limiting case of lasing threshold for a very low loss laser cavity or with many QD gain layers.

The source of the negative T0 at these lower temperatures and with p-doping is that as the temperature is increased, holes are thermally excited out of the ground state transition and can decrease the current needed to maintain a given gain value. If we look for example at the

spontaneous current needed to maintain f e,0 (T ) = 1− f h,0 (T ) = 1/ 2 which gives

f e,0 (T ) − f h,0 (T ) = 0 , the spontaneous current is set by f e,0 (T )[1− f h,0 (T )] = 1/ 4. However the

values f e,0 (T ) = 1 and f h,0 (T ) = 1 also produce f e,0 (T ) − f h,0 (T ) = 0 , but f e,0 (T )[1− f h,0 (T )] = 0 and requires zero spontaneous current. This would be the case for an ideal case of n-doping.

Similarly, f e,0 (T ) = 0 and f h,0 (T ) = 0 also produces f e,0 (T )[1− f h,0 (T )] = 0 , and corresponds to an ideal case of p-doping. However n-doping produces severe gain saturation with increasing temperature, while p-doping can counter gain saturation [29, 15]. As long as the required gain for threshold is low, increasing the temperature can lead to depopulation of the hole from the QD ground state, and cause negative T0 over some temperature range.

Figure 3-5 shows a plot of the calculated T0 for various acceptor levels that generate a built-in equilibrium hole charge within the QDs. The inset shows the negative T0 that occurs from −40 °C to approximately 0 °C, for NA = 5. This built-in equilibrium hole population has also been shown to reduce the influence of gain saturation at higher temperatures, again depending strongly on the actual threshold gain value. Operating closer to a threshold gain of zero, for example with 10 QD stacks [24], will require only a small population inversion value to 27

Figure 3-5: Temperature dependence of threshold current for a multistate undoped QD laser at the 300 K transparency and threshold population inversions of 0.042, 0.113 and 0.182.

The T0’s are calculated for 20 °C ≤ T ≤ 80 °C. The inset shows the schematic of energy levels in a multistate QD laser.

reach threshold. Optimized p-doping values can be obtained for each of the threshold populations of interest, and for the temperature at which the maximum T0 is achieved.

Finally in this section, we also consider the influence of the wetting layer states, given uniform QDs. The effects of the wetting layer on the QD laser performance, and especially threshold, can be separated into transport effects that electronically couple the different QDs and establish the charge populations in different QDs [30, 31, 32, 33, 34, 35, 16], and radiative and nonradiative recombination that can come from its large density of continuum states [9, 10, 11].

Figure 3-6: The effect of wetting layer on the characteristic temperatures for undoped QD lasers at different threshold population inversions.

For uniform QDs the transport effects between the QDs no longer impact lasing threshold, which is set by the recombination from thermal populations of electrons and holes that exist in the wetting layer. The wetting layer separation from the ground state is taken as in Table 2-1. For the threshold dependence on temperature, our calculations shown in Figure 3-6 indicate that radiative recombination from the wetting layer in well designed InAs QDs on GaAs has negligible contribution to the threshold temperature of the QD laser. Figure 3-6 shows that this remains true for threshold inversion populations that remain sufficiently low to avoid ground state gain saturation. Only small changes in the T0 are found if the 2-D continuum corresponding to the density of the wetting layer states is included. Note that Figure 3-6 does not imply that the 29 wetting layer does not play any role in setting T0 for all QD laser diodes. If high material quality is not achieved, nonradiative recombination from the wetting layer can become quite large and can dramatically reduce the T0 [9, 10, 11, 28]. In addition, if the QDs have shallow energy potentials relative to the wetting layer, the wetting layer population will increase and can dramatically decrease T0. However our own experimental results provide strong evidence that both radiative and nonradiative recombination from the wetting layer recombination can be effectively eliminated, with the result being very low room temperature CW threshold currents of

< 9 A/cm2 with transparency currents as low as 6 A/cm2 [12, 13]. These threshold and transparency values are fully consistent with transitions due only to discrete electron-hole transitions within the QDs, and because of the demonstrations of high power [13], also point to the promise of QD lasers for a range of applications beyond telecom.

3.4 Summary

The threshold temperature dependencies of QD lasers in different limits of p-doping and hole level spacing have been analyzed. In the limit of zero inhomogeneous broadening and isolated ground state transitions, the transparency current is shown to play an important role in establishing T0. In addition, an ideal QD laser with thermally isolated ground state transitions, free of inhomogeneous broadening, and Lasher and Stern condition, is found to have a lower T0 than for an ideal planar quantum well under similar conditions. The planar quantum well suffers less relative change in its gain broadening due to quasi-Fermi occupation of its continuum of quantum states. In this case, whether or not the T0 is large can be less important than other advantages of QD laser diodes with uniform QD gain ensembles. It is found that the thermal 30 broadening of holes is important for QDs with closely spaced hole levels and degrade T0 for undoped QDs. P-doping of these QDs suppreses the hole escape and T0 is calculated to be maximized by using 10-20 acceptor/QD depending on the required population inversion level, which agrees well with the experimental trends in literature.

CHAPTER 4: DESIGN PRINCIPLES OF LITHOGRAPHIC LASER

4.1 Introduction

Oxide-confined EEL [36, 37, 38] and VCSELs [39, 40] have been heavily studied using conversion of buried AlAs layer to native oxide of AlxOy by selective oxidation [41, 42].

Oxide-confined quantum-dot edge emitting laser was shown to reach low threshold current densities [38]. Oxide-confinement brought important advantages in terms of device performance but the problems imposed by oxidation and oxide-aperture also put important limitations for further developments. This chapter describes a novel method of lithographic laser technology providing electrical and optical mode confinement for both EELs and VCSELs. Since lithographic laser method is applied to VCSELs in this work, this chapter particularly discusses the properties and issues for VCSELs.

VCSEL is a semiconductor laser that emits light vertically from the wafer and has significant advantageous compared to edge emitting laser devices that are vastly used in fiber optic communications. The active region is placed between the mirrors of high reflectivity of generally higher than 99%. The current semiconductor manufacturing technology allows VCSEL to be integrated with other components on the same wafer. They are favorable to be used for optical interconnects due to their low current requirements and ability to be integrated on a chip scale. Because of their near circular and small divergence output beams, it requires minimum need for optics for most of the applications which allows efficient coupling of light to optical fibers. Another key advantage of VCSELs is that they can be tested on a wafer without cleaving

32 and this enables higher yields than edge emitting lasers. They also offer higher data rates to be transmitted owing to their higher relaxation oscillation frequencies [43].

The first demonstration of VCSEL dates back to 1979 pioneered by Soda et. al.[44]. The first device had metallic mirrors and operated at liquid nitrogen temperatures at very high currents (900 mA, 44 kA/cm2) of pulse operation. Room temperature operation was shown with

GaAs active region in 1984 under pulsed current [45] and continuous wave room temperature

VCSEL was demonstrated in 1989 [46]. MBE and MOCVD technology and using distributed

Bragg reflector (DBR) mirrors made low threshold currents possible by current- and mode- confinement methods that were shown in 1990s.

Typical structure of a VCSEL shown in Figure 4-1 consists of an optical cavity of a multiple half wavelength thick with quantum well or quantum dot active region and high reflectivity DBR mirrors surrounding the optical cavity for longitudinal light confinement. DBR mirrors consist of alternating pairs of quarter wavelength thick high and low refractive index layers. The electric current is injected through ohmic contacts on top epitaxial surface and substrate. Different methods have been employed to confine the current to a predefined device area. Due to short cavity length, the longitudinal mode spacing is usually larger than the gain bandwidth of the gain medium and VCSELs have principally single longitudinal mode. On the other hand, short cavity length imposes low single pass gain for each cavity round trip and it requires high reflectivity mirrors of more than 99%. Most commonly used material system of intrinsically lattice matched GaAs/AlAs offers a large refractive index difference among other material systems, which has a refractive index of 3.5 for GaAs and 2.95 for AlAs at a wavelength

Figure 4-1: Typical layout of a VCSEL [47].

of 980 nm. This allows relatively low mirror pairs to get more than 99% reflectivity, typically between 15 and 30 mirror pairs are used. For lossless bottom mirrors, it requires more than 25

DBR mirror pairs to get more than 99.9% reflectivity. The large number of mirror pairs requires a few microns of epitaxial growth for each bottom and top mirror.

4.2 Oxide-VCSEL Issues and Limitations

The improvements of VCSEL performance have been remarkable due to the introduction of mode- and current-confinement through oxide-aperture. The low threshold and low power consumption have produced high speed modulation and high efficiency VCSELs [40, 48].

However, some problems are introduced by the oxide-aperture incorporation such as dislocation

34 formation after oxidation, strain, low thermal conductivity of oxide and size variation, all illustrated in Figure 4-2. The associated issues of oxide have drawbacks that cause early device failure for smaller lasers and it also limits the manufacturability and yield of VCSELs.

The oxide produced by conversion of AlAs is not in crystalline form and the oxidation process generates dislocations and forms point defects at the interface between the oxide and the semiconductor. These point defects can easily migrate towards the active region as non-radiative recombination centers causing device failure and these defects sources even earlier failure for smaller apertures. Since the oxidation is performed around 400 oC, the oxide shrinkage creates strain because of the difference in thermal expansion coefficient of the oxide and semiconductor and degrades the reliability of the VCSELs. The strain field increases the effect of point defects even further by driving them toward the active region.

Another trouble stems from oxide being heat barrier and increasing the thermal resistance of the device. For smaller devices, the heat dissipation becomes even more challenging since the resistance increases generating more heat and smaller aperture leaves less room for upward heat dissipation. Very low thermal conductivity of AlxOy (0.7 W/m·K) compared to GaAs and AlAs

(~ 50 W/m·K) [49] makes the heat spreading a fundamental issue limiting the output power and modulation bandwidth. Reducing the thermal resistance of oxide-confined VCSELs by applying effective heatsinking methods were demonstrated to increase the device performance by increasing the modulation bandwidth and output power [50]. Since lithographic VCSEL has an oxide-free structure, it should have much lower thermal resistance; hence it inherently promises better performance.

While oxide has the above mentioned drawbacks, it also has limitations in terms of manufacturability and yield due to its intrinsic difficulty in size control. The oxidation is a timed diffusion process resulting in variation in device size throughout a wafer and also variation from one wafer to another. Even using very strict control of the oxidation process, the absolute variation can not be lower than 1 μm. Smaller devices suffer more since the fractional variation becomes higher as the oxide aperture size gets smaller. The reproducibility of oxide-aperture size is very critical since most of the device performance characteristics have strong dependence on its size. This variation of oxide therefore decreases the yield and introduces manufacturing issues. The decreased uniformity along with high thermal resistance of oxide is a major problem for VCSEL arrays leading non-uniform heating and threshold variation.

Figure 4-2: Illustration of oxide-VCSEL limitations and drawbacks: Oxidation introducing point defects, heat barrier effect of oxide and size variation of oxide-aperture.

4.3 Optical Mode Confinement

Optical mode confinement in a lithographic VCSEL is provided by intracavity phase- shifting mesa. Fabry Perot cavity is created by high reflective mirrors and the cavity is divided into two regions of different cavity lengths of L0 and L1 as shown in Figure 4-3. The on mesa region “0” of width with r

“1” of r>W/2 laterally extending to infinity has the waveguide modes. The mode size can be different from the mesa width W. These regions have resonances tuned to different specific wavelengths. The vertical resonance shift is controlled by the mesa height ∆L=L0-L1 which also gives diffraction and scattering loss control. The mesa structure can be defined by lithography and lithographic processing of these VCSEL devices enables easy control of the lateral size and sub-micron size widths can be fabricated with high precision and uniformity.

Figure 4-3: The schematic of cavity with phase-shifting mesa where region “0” supports lasing mode and region “1” has only waveguide modes. 37

The standing wave normal to mirror is formed by the reflection from the mirrors and the tangential component of the electric field must vanish on the mirror. The wavevector of region

“0” in vertical direction is given by

π kz,0 = mz , (4.1) L0 ε and in region “1”

π kz,1 = mz , (4.2) L1 ε

where mz is a positive integer (mz=1, 2, 3...) and ε is the permittivity of the cavity regions. Using cylindrical coordinates and the relation between wavevector and frequency, one can write the total wavevector of the field as

ω k = k 2 + k 2 , (4.3) c ρ z

where k ρ is the wavevector in radial direction and c is the speed of light in vacuum. Because of the cylindrical structure of the mesa, the solution of the field profile is assumed to have the form of Bessel function of the first kind for the mesa cavity region “0”. Considering the lowest order eigenmode of the profile and overlap between the modes of region “0” and “1”, the relation between the wavevectors of on-mesa and off-mesa regions can be written as

2 ωo 4.81 2 2 2 = 2 + k z,0 = kρ,1 + k z,1 , (4.4) c εW0

38 where W0 is the optical mode size and kz,0 satisfies the resonance condition given in eq. (4.1).

The factor of 4.81 comes from the lowest order Bessel function solution of cylindrically symmetric mode profile. For the same mode number mz and L0>L1, eq.(4.1) and (4.2) leads to

2 2 kz,0 < kz,1 , (4.5)

2 showing that there is a range of possible mode sizes W0 for kρ,1 <0. This gives an imaginary kρ,1 value which is a decaying wave for off-mesa region while the lasing mode is confined in region

“0”. From eq. (4.5), it is found that the confinement mechanism works for mode sizes of

3.4 L W0 > (4.6) kz,0 ΔL and smaller mode sizes lose mode confinement and cause diffraction losses. Even though the diffraction loss is eliminated by introducing phase shift mesa, it causes scattering losses because of non-orthogonal longitudinal modes of on-mesa and off-mesa regions. The scattering losses are characterized by the normalized overlap of the resonant electric field of the regions given as

2 ∗ E0 (z)E1 (z)dz C 2 = ∫ (4.7) E (z)E ∗ (z)dz E (z)E ∗ (z)dz ∫ 0 0 ∫ 1 1 and C 2 = 1 gives minimum scattering loss when mesa height goes to zero. However, mode confinement would be lost in that limiting situation.

Oxide-confined VCSELs can be compared to lithographic mode confinement method through (4.7). It was shown that [51], oxide layer with a thickness 463 Å placed at the first node of upper mirror layer creates 40 Å resonance shift with a scattering parameter of C 2 = 0.990 .

For the same mode confinement condition with lithographic method, mesa height of 66 Å causes

40 Å resonance shift with a scattering parameter of C 2 = 0.994 . These results show that lithographic method results in lower loss mode-confinement compared to oxide-confinement approach. Mode confinement method described above has been demonstrated [51] to show strong mode-confinement to lithographically defined intracavity phase-shifting layer.

4.4 Current Confinement

Even though mode confinement to mesa is an important step to build high performance

VCSELs, current-confinement to the same mesa region is also essential to get high efficiency, low-threshold and stable VCSEL operation. Without current confinement or weak current- confining method, threshold current will be high and it will also cause heating and decrease the performance of the laser. As an example, a VCSEL device of 10 μm diameter with isolation mesa of 100 μm, the ratio of the areas is 100, which means the current blocking region needs to have resistance at least 1000 times higher than that of the mesa to get more than 90% current injection to mesa. The current blocking requirement becomes stricter for smaller mesa sizes since it is scaled by the square of the mesa radius. For a mesa size of 5 μm diameter, the required ratio of resistance increases to 4000 to get more than 90% current injection to mesa. Better current confinement becomes more critical for high efficiency operation of smaller devices. In this part,

40 selective Fermi level pinning method will be overviewed to get current blocking interfaces so that the current is confined to small areas.

The current passing through waveguide region “1” needs to be blocked. Fermi level pinning is based on the phenomenon known from metal-GaAs Schottky contact. When GaAs is exposed to air, oxygen in the air creates interface states in the bandgap of GaAs and Fermi level of the interface is pinned in the middle of the bandgap at any rate of doping. The same phenomenon occurs during the regrowth of GaAs on AlGaAs layer. Even though the oxide layer on GaAs is removed during prebake of the wafer under As4 ambient before regrowth, the native oxide on AlGaAs layer cannot be removed completely even at high temperatures. Therefore, the regrown interface on AlGaAs has some defect states that will work as Schottky barrier and the

Fermi level on this surface is pinned in the middle of the gap. For the lithographic VCSEL, the regrowth layer is part of the cavity and Figure 4-4 shows the energy band diagram of upper DBR with Fermi level pinning on Al0.3Ga0.7As surface. Fermi level is in the middle of energy band and it provides current blocking for low mobility holes. In general, utilizing surface states on the regrowth interface can be used to get current blocking. The intracavity phase shifting mesa gives mode-confinement and Fermi level pinning outside the mesa can be achieved simultaneously by an AlGaAs layer.

The schematic of the structure of the VCSEL is shown in Figure 4-5. The intracavity mesa has very thin layer of GaAs, around 200 Å. Outside the mesa is an AlGaAs selective interfacial Fermi-level pinning layer which is on top of the cavity and placed at the node of the optical field to minimize the scattering losses.

Figure 4-4: Energy band diagram of upper DBR showing Fermi level pinning on Al0.3Ga0.7As surface [52].

Figure 4-5: The device structure for current-confinement based on Fermi level pinning [53].

Figure 4-6 shows the current vs. voltage characteristics of one of the fabricated VCSELs.

The voltage measurement is done on planar phase-shifting mesa containing region and planar off-mesa region containing the same quantum well active layer as the VCSEL. The measurements show that the turn-on voltage increased from around 1 V for the mesa to 6 V for off-mesa region. The ratio of the on-mesa to off-mesa current density is very high showing that almost all the current is passing through the device mesa region. Even though this device does not have the optimum design yet, current blocking voltage is much better than the previously reported results [53, 54] and present very high current confinement to the device mesa. The current blocking performance shown Figure 4-6 enables efficient current confinement to very small size VCSEL devices.

Figure 4-6: Current versus voltage characteristics of on-mesa and off-mesa region for a region of 70x110 μm, showing turn-on voltage difference for required for current blocking.

4.5 Summary

The lithographic approach provides both mode- and current-confinement by an oxide-free

VCSEL formation and it enables easy scaling of the device and intracavity patterning for better mode matching to gain which will increase the efficiency of VCSELs. The fundamental issues of oxide-aperture lasers are described and the design principles of lithographic lasers are overviewed in this chapter. Lithographically defined mesa provides mode-confinement where the step height produces phase-shift. Selective interfacial Fermi-level pinning for outside the mesa region provides efficient current confinement to the mesa with turn-on voltage difference of around 5V that is sufficient to provide current confinement to even very small device areas.

CHAPTER 5: EXPERIMENTAL RESULTS ON LITHOGRAPHIC VCSEL

5.1 Introduction

In this chapter, we demonstrate lithographically-defined laser diodes in which the transverse mode and cavity are defined using only lithography and epitaxial crystal growth. We also show that eliminating the oxide aperture reduces the thermal resistance, with increased power density found in smaller lasers. A low thermal resistance can increase the output power saturation before thermal rollover. When it is combined with better mode matching to gain for smaller devices, high output power densities are possible from small devices. Lithographic processing gives the ability to reach small sizes that are difficult to achieve reproducibly for oxide-aperture lasers. The demonstration of lithographic laser diodes with good scaling properties could therefore be an important step toward producing ultra-small size laser diodes with high output power density, high manufacturability, and high reliability. Because modulation speed tracks stimulated emission rate, which in turn tracks power density, these high power density VCSELs are expected to be capable of high modulation speed. VCSEL devices of various sizes are fabricated and characterized to study the size effect on thermal resistance and output power density.

5.2 Device Structure

The devices are grown using solid source molecular beam epitaxy and they are defined lithographically as described in [53].Figure 5-1 illustrates the main processing steps of VCSEL

45 fabrication starting from mesa formation on as-grown wafer and then followed by p-mirror growth and metallization. Zn/Au and Ge/Au contacts are used for p- and n-metal, respectively.

The schematic of the VCSEL structure and microscope image of the device are shown in

Figure 5-2 with the mesa at the center of the p-metal contact pad. The device array of various sizes used in the fabrication ranges from 3 μm to 20 μm. The VCSEL consists of 21 n-type

AlAs/GaAs quarter-wave bottom mirror pairs with Al0.1Ga0.9As one-wavelength cavity spacer and three InGaAs/GaAs quantum wells placed at the center of the cavity and completed with p- type Al0.7Ga0.3As/GaAs mirror stack of 20 pairs.

Figure 5-1: Growth and fabrication process cycle of lithographic VCSELs showing an as- grown wafer, mesa formation for regrowth, after regrowth and after fabrication.

(a)

(b)

Figure 5-2: (a) The schematic of lithographic VCSEL and (b) microscope image of the 8-μm diameter device and the contact pad.

5.3 Results

The devices are isolated and tested on a wafer form without using any mounting or heatsinking process. Devices of the same size throughout the fabricated wafer are tested and they show good uniformity in terms of light output-current and current-voltage characteristics.

5.3.1 Lasing Characteristics

Figure 5-3 shows the light output versus current characteristics and the lasing spectrum at

1 mA for 8 μm diameter VCSEL. The device has sub-miliampere threshold current of 710 μA and lasing threshold voltage of 1.55 V. The slope efficiency of the device is 0.88 W/A corresponding to 70% differential quantum efficiency, which is comparable to the best results achieved by well-developed oxide-confined VCSELs [40]. The maximum power conversion efficiency of 26% is reached at four times the threshold with output power of 1.7 mW. The low threshold and linear trend of output power with injected current indicate stable operation of the laser.

Emission spectra of the laser are plotted in Figure 5-4 for sub-threshold (0.5mA) and above threshold currents including spectra at very high current level of 18 mA. Even though several modes are clearly observed at subthreshold current of 0.5 mA, only the fundamental mode of longest wavelength show lasing at above threshold current of 1 mA. At higher injection, higher-order transverse modes show up due to the large size of the confinement region and they show lasing initially at the longest wavelength. It is clear that the shift to longer wavelengths with increasing current is smaller compared to oxide-aperture VCSELs of same size. This

Figure 5-3: Output power and voltage versus current characteristics of 8 μm diameter VCSEL device.

Figure 5-4: Emission spectra of 8 μm diameter device for various current levels below (0.5 mA) and above threshold (1, 12 and 18 mA). 49 indicates that the temperature rise is not too high since all-epitaxial structure of lithographic laser allows better heat spreading compared to oxide-aperture VCSELs.

5.3.2 Low Thermal Resistance of Lithographic Structure

The performance of a semiconductor laser can be limited by losses in a waveguide or mirrors, injection efficiency, leakage current or non-radiative recombination. On the other hand, a VCSEL with a good design is limited mainly by heat dissipation. The heat generated in the active region reduces gain, differential gain and efficiency; therefore degrade speed, threshold and output power due to an increase in temperature. The heat is usually produced in the active

region due to dissipated electrical power, ΔPdiss. = Pelectrical − Poptical The thermal resistance of the device, Rth, is defined as the increase of temperature in the active region with an increase in dissipated power. As revealed by the spectral measurements in Figure 5-4, the emission shifts to longer wavelength with increase of input current due to temperature increase of the active region.

The thermal resistance of the device is then found by relating the wavelength shift with dissipated power to the wavelength shift by temperature,

ΔT Δλ ΔPdiss. Rth = = , (2.1) ΔPdiss. ΔT Δλ where ΔT is the temperature rise of the active region. Figure 5-5(a) demonstrates the redshift in wavelength with increasing dissipated power. Using 0.07 nm/K for the wavelength shift with temperature [40, 50], size dependent thermal resistance value is found to be 0.7 oC/mW for 8 μm diameter VCSEL.

Figure 5-5(b) demonstrates the thermal resistances of the VCSELs measured for device sizes ranging from 3 to 20 μm in diameter. It also compares our results on thermal resistance to the data in the literature obtained for oxide-confined VCSELs by various groups [40, 50, 55, 56].

Compared to the lowest thermal resistance oxide-confined VCSEL achieved by using copper plated heatsinks [50], our results without applying heatsinking demonstrate the significance of lithographic laser in terms of getting better heat spreading through the all-epitaxial structure. The demonstration reveals how low thermal conductivity of AlxOy (0.7 W/m·K) compared to GaAs and AlAs (~ 50 W/m·K) [57] makes the heat spreading easier and shows the potential of lithographic VCSELs for higher output power and modulation bandwidth.

5.3.3 High Output Power Density of Small Devices

Figure 5-6 demonstrates the output power density versus injected current for devices of 3,

4, 6, 8 and 10 μm diameter. It shows that the output power density is as high as 58 kW/cm2 for 3

μm diameter device. The output power density for 3 μm device is two times more than what is achievable by 8 μm diameter VCSEL. The increase of the output density with smaller sizes indicates that the overlap between the gain and optical mode is better for smaller sizes among the device sizes fabricated in this study. Because modulation speed tracks stimulated emission rate, which in turn tracks power density, these high power density VCSELs are expected to be capable of high modulation speed. High output power density of individual devices is also very promising to get high efficiency high power VCSEL arrays and closely packed arrays are possible when combined with better heat spreading characteristic of these devices.

Figure 5-6: Output power density versus injection current density showing that output power density is the highest for the smallest device size tested.

5.3.4 Single-Mode and Single-Polarization Lasing

VCSELs have single longitudinal mode due to their short cavity length. As depicted in

Figure 5-2(a), the cavity has a length of lambda and therefore the distance between the longitudinal modes is larger than the reflectivity bandwidth of the mirrors. However, the lateral size of the device defines the transverse modes that will be supported by the cavity. Larger size

VCSELs supports more number of transverse modes. The lateral size needs to be reduced so that the cavity supports only the fundamental mode and higher order modes are exposed to more losses leading to single transverse mode emission. Even though it is difficult to get reproducible device sizes for small devices, oxide-aperture VCSELs can be made small enough to get single- 53 mode emission. However, smaller oxide-aperture causes more stress due to reduced heat spreading through smaller apertures and degrades device reliability and lifetime as previously discussed in chapter 4.

VCSEL produces light with random polarization due to their symmetric structure but polarization must be fixed for high-speed modulation, long-haul fiber optic communication and for applications that incorporates polarization sensitive optical components. For polarization control, anisotropy needs to be introduced by making elliptical or rectangular structures.

However, it is difficult to get anisotropic geometries using oxide-apertures since it is hard to control wet-oxidation process. Another way to get single polarization is through patterning the output surface of the device but it introduces losses, decreases the efficiency and requires additional processing steps. Due to the anisotropy in regrowth of lithographic VCSELs, the circular structure becomes slightly elliptical as shown by AFM image in Figure 5-7.

Figure 5-7: AFM image of 3 μm (on the left) and 8 μm (on the right) lithographic VCSEL showing anisotropic formation of the device after regrowth. 54

The elliptical mesa formation shown in Figure 5-7 does not require additional patterning needed for single-mode single-polarization VCSELs. Lithographic approach can solve the difficulties in getting reliable devices to get single mode emission and provide grating-free polarization control. Elliptical devices can be patterned lithographically without further fabrication step to get polarization control. Here, the data is presented showing single-mode and single-polarization output. Emission spectra of our smallest device of 3 μm diameter are demonstrated in Figure 5-8. At the lowest current level of 0.5 mA, side-mode suppression-ratio

(SMSR) is more than 30 dB and decreases slowly down to 20 dB at 2.0 mA.

Figure 5-8: Above threshold emission spectra of 3 μm diameter lithographic VCSEL at I = 0.5, 1, 1.5 and 2.0 mA, showing single mode emission with more than 20 dB SMSR.

Figure 5-9: The SMSR of 3 μm VCSEL showing single-mode single-polarization emission..

As shown by the AFM image in Figure 5-7, the device has elliptical shape and therefore polarization locking along the longer axis of the VCSEL. Figure 5-9 shows the SMSR measured at different power levels for a 3 μm VCSEL. The polarization locking is obtained at all power levels and remains higher than 25 dB for power levels up to 1 mW. The SMSR goes lower for higher power levels since output of orthogonal polarization has an increasing fractional power with increasing current. Various devices of the small size VCSELs have been tested and they all show similar SMSR characteristics concluding high uniformity of the VCSELs due to lithographic process.

5.3.5 Reliability

The reliability performance of VCSELs is very critical for long operation lifetime of these devices and there have been reliability studies concerning the reliability of small size devices due to its importance to get low power operation and high speed modulation of VCSELs.

The reliability of oxide-aperture VCSELs has shown to be very dependent on device size with larger devices being better [58]. Even though there are various definitions of reliability and different ways to measure it, more reliable device always means a device of longer lifetime. A typical way to evaluate reliability is to measure the change in output power or modulation speed with time under various conditions such as output power levels, injection current or temperature.

In case of oxide-aperture VCSELs, oxide puts a fundamental limit for reliability because of the reasons explained in the chapter 4.2. The point defects and strain becomes stronger and more effective as the device size gets smaller and degrades the reliability of VCSELs. High thermal resistance of oxide-VCSEL builds up heat around active region and causes even more strain. In [58], Finisar researchers performed lifetime tests for VCSEL device sizes of 5, 14 and

17 μm diameter under various operation conditions. For the same settings of output power, current or temperature, smaller devices always performed for shorter periods of time. The smallest device size of 5 μm diameter oxide-VCSEL showed power degradation of more than 2 dB in 100 hours when driven at the output power level of 3 mW while 17 μm oxide-VCSEL can be run for more than one million hours under the same condition. The lifetime decreases dramatically for smaller devices.

The lithographic VCSELs oxide-free structure is expected to outperform oxide-VCSELs in terms of the reliability due to its strain-free, low thermal resistance nature without point defects. Since the reliability gets worse for smaller devices, we tested the smallest lithographic

VCSEL of 3 μm diameter fabricated in this study, which has a device area three times smaller compared to the smallest oxide-VCSEL of 5 μm tested in [58]. Lithographic 3 μm VCSEL is driven to put out 3.65 mW of output power at injection current level of 6.0 mA, which corresponds to very high injection current density of 85 kA/cm2. Figure 5-10 shows the reliability of the device showing that its output power is constant for the tested operation time of around 200 hours. While 5 μm oxide-VCSEL shows power decrease of 2 dB (37%) at 3 mW of output power in 100 hours, 3 μm lithographic VCSEL does not show degradation after 200 hours operation.

Figure 5-10: Reliability of 3 μm lithographic VCSEL showing constant output power of 3.65 mW at an injection current level of I= 6.0 mA. 58

This concludes that lithographic VCSELs are much more reliable even for very small device sizes due to its oxide- and strain-free structure.

5.4 Summary

We demonstrate an oxide-free, lithographically defined GaAs-based VCSEL that provides both mode- and current-confinement. The device solves problems of oxide-confined

VCSELs and provides size scaling to maximize the overlap between the optical gain and optical mode. The all-epitaxial oxide-free approach can extend the VCSEL technology to high reliability and fully planar VCSELs and dense VCSEL arrays can be produced. Low thermal resistance of lithographic VCSELs is demonstrated to be much better than oxide-confined VCSELs. The device characteristics of this first demonstration shows wall plug efficiencies of 26% and output power density of 58 kW/cm2 with 70% differential quantum efficiency that are comparable to the well-developed oxide-confined VCSEL technology. Single-mode and single-polarization is achieved with output power of 1 mW and SMSR of 25 dB. The lifetime tests have shown that the even smallest fabricated VCSELs operate for hundreds of hours without showing any degradation in output power. The reliable operation of small lasers opens the way to make ultra small and reliable single-mode single-polarization VCSELs for sensing applications and VCSEL arrays for high-speed data transfer and high power arrays.

CHAPTER 6: SUMMARY

The threshold temperature dependencies of QD lasers in different limits of p-doping, hole level spacings, and inhomogeneous broadening have been analyzed. In the limit of zero inhomogeneous broadening and isolated ground state transitions, the transparency current is shown to play an important role in establishing T0. An ideal QD laser with thermally isolated ground state transitions, free of inhomogeneous broadening, and Lasher and Stern condition, is found to have a lower T0 than for an ideal planar quantum well under similar conditions. When additional levels are sufficiently close in energy, the thermal broadening of holes is also important and can create negative T0, especially in the lower temperature regime between 100 K and 250 K. Non-equilibrium rate equation model incorporates inhomogeneous broadening, carrier transport between the QDs and carrier capture mechanisms. Negative T0 due to inhomogeneous broadening is found at high temperatures close to 300 K, especially for p-doped

QD ensembles.

The second part described in this dissertation demonstrated lithographic GaAs-based

VCSEL that can extend the VCSEL technology to high reliability and reproducibility. This is an important step toward producing lasers of ultra-small sizes with high speed and high output power density. The device characteristic of the lithographic laser showed power-conversion efficiency of 26% and the lowest thermal resistance for a VCSEL, which is essential for high- speed VCSELs. We also show that eliminating the oxide aperture reduces the thermal resistance, with increased power density found in smaller lasers since low thermal resistance increase the output power saturation before thermal rollover. In addition to scaling and uniformity advantage 60 of lithographic VCSELs compared to oxide-VCSELs, oxide-free lithographic VCSELs exhibited more reliable performance. The initial reliability tests showed that 3 μm lithographic VCSELs do not show any power degradation in long operation times in the lab while oxide-VCSELs shows decrease in output power even in a shorter time. In addition, grating-free single-mode single- polarization lasing and more reliable performance of these lasers shows that lithographic

VCSELs will be the VCSELs of next generation to be used in sensing, high power arrays and possibly high speed optical communication.

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