以金屬有機化學氣相沈積法成長長波長面射型雷射

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(1)國立交通大學光電工程研究所博士論文. 以金屬有機化學氣相沈積法成長長波長面射型雷射 Long Wavelength Vertical Cavity Surface Emitting Laser Grown by Metal Organic Chemical Vapor Deposition. 研究生: 盧廷昌指導教授: 王興宗. Student: Tien-chang Lu Advisor: Shing-chung Wang. 中華民國九十三年六月.

(2) 以金屬有機化學氣相沈積法成長長波長面射型雷射 Long Wavelength Vertical Cavity Surface Emitting Laser Grown by Metal Organic Chemical Vapor Deposition 研究生: 盧廷昌指導教授: 王興宗. Student: Tien-chang Lu Advisor: Shing-chung Wang. 國立交通大學光電工程研究所博士論文. A dissertation Submitted to Institute of Electro-Optical Engineering College of Electrical Engineering and Computer Science National Chiao Tung University In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy In Electro-Optical Engineering June 2004 Hsin-chu, Taiwan, Repubic of China 中華民國九十三年六月.

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(5) 以金屬有機化學氣相沈積法成長長波長面射型雷射. 研究生：盧廷昌. 指導教授：王興宗教授. 國立交通大學光電工程研究所摘要本論文在研究以金屬有機氣相化學沉積法 (Metalorganic chemical vapor deposition, MOCVD)製作長波長面射型雷射。波長範圍在 1.3 到 1.5 微米的面射型雷射，因其具有圓形光束輸出、低製作成本、單一縱膜操作、以及整合二維陣列的潛在特性，因此在光纖通信及中、短距數據通信上，成為極具潛力的發光源。但因在傳統製作長波長雷射的材料中，不容易找到具有折射率差異大的材料組合以製作高反射率的布拉格反射鏡，加上傳統長波長雷射的主動層材料，其高溫特性不佳，使得長波長面射型雷射的發展遲緩。因此，在本研究中，我們從最基本的設計與模擬出發，先找出適合長波長雷射主動層的材料，然後將主動層材料應用在傳統邊射型雷射上，變化各種參數，我們發現量子井中的應力參數、多量子井的應力補償、以及參雜條件的多寡皆會影響雷射特性，我們優化各項參數，得到最好的臨界電流密度為 1.4 kA/cm2。另一方面，我們使用 MOCVD 成長磷化銦系列的布拉格反射鏡，以優化過的磊晶參數成功製作出高反射率的布拉格反射鏡，並研究其光學及電氣特性。同時，我們也嘗試製作以磷化銦搭配空氣，在只有三對組合下成功得到高反射率的布拉格反射鏡。為了要製作出擁有良好溫度效應的長波長面射型雷射，我們也發展了晶圓融合的技術將長波長雷射主動層的材料和砷化鎵系列的布拉格反射鏡結合成長波長面射型雷射，我們成功的製作出以光激發的方式操作的融合型長波長面射型雷射，其等效的臨界電流密度為 4 kA/cm2。最佳的等效臨界電流密度值是以磷化銦系列的布拉格反射鏡，加上週期性增益之共振腔，再加上以介電材料製成的布拉格反射鏡組合而成的長波長面射型雷射，以連續光激發的方式操作，其等效的臨界電流密度為 2 kA/cm2，雷射波長為 1562 奈米。我們最終的目的是要製作出電激發式的長波長面射型雷射，雖然在本研究中尚未達成這個目標，但為發展製作電激發式的長波長面射型雷射的過程中，我們發展了磊晶再成長技術、埋藏式穿透接面元件等技術，成功應用在長波長發光二極體，另外，我們同時也遇到了量子井相互擴散的情況、觀察到在傳統氧化侷限面射型雷射中的雙模態情形，這些研究都提供了良好的基礎朝向製作出電激發式的長波長面射型雷射。. i.

(6) Long Wavelength Vertical Cavity Surface Emitting Laser Grown by Metal Organic Chemical Vapor Deposition Student: Tien-chang Lu. Advisor: Dr. Shing-Chung Wang. Institute of Electro-Optical Engineering National Chiao Tung University. Abstract In this study, we have developed the process for fabrication of long wavelength vertical cavity surface emitting lasers (LW-VCSELs) by metal organic chemical vapor deposition (MOCVD). LW-VCSELs with emission wavelength ranging from 1.3 µm to 1.5 µm featuring circular-beam output, low production-cost, single longitudinal-mode operation, and possible integration of two-dimensional array are potentially suitable for light sources in fiber communication systems and in medium and short distance data transmission systems. However, the absence of high refractive index contrast in InP-lattice-matched materials impeded the development of 1.3-1.5 µm VCSELs. In addition, active layers with insufficient gain at elevated temperature, absence of natural oxidized current aperture and poor heat conductance in material systems for long wavelength range are problems in making LW-VCSELs.. Therefore, we started this study from design and simulation to obtain appropriate gain materials for LW-VCSELs. We have determined InGaAlAs as the gain material and applied it into the conventional edge emitting lasers to find out the optimized conditions of the active layers. The amount of compressively strain in quantum wells, the net amount of strain in multiple quantum wells (MQWs) with more pairs, and the ii.

(7) impurity concentration strongly influenced the performance of edge emitting lasers. The overall optimization of these factors makes us obtaining low threshold current density of 1.4 kA/cm2. On the other hand, we have fabricated InP/InGaAlAs-based distributed Bragg reflectors (DBRs) with excellent electrical and optical properties using MOCVD and the growth interruption technique. Meanwhile, we have successfully fabricated, and demonstrated a rigid InP/airgap structure with high reflectivity at 1.54 µm using InGaAs as the sacrificial layer. The 3-pair InP/airgap DBR structure has a peak reflectivity at 1.54 µm with a stop-band width of about 200 nm.. In addition, we have developed wafer-fusion technique to combine the conventional InP-based active layers with GaAs-based DBRs in order to simultaneously have the superior gain performance of InP-based active layers and the high reflectivity, high thermal conductivity and capability of oxidized layers of the GaAs-based DBRs. We demonstrated the optically pumped VCSEL structure with the fused bottom 30 pairs GaAs/AlAs DBR, InGaAlAs MQW and the fused top 25 pairs GaAs/AlAs DBR. The equivalent threshold current density is calculated to be 4 kA/cm2. The lowest threshold was obtained in InP-based LW-VCSELs. We successfully demonstrated the optically pumped InP-based VCSELs with the 35 pairs InP/InGaAlAs DBRs and 10 pairs SiO2/TiO2 top dielectric mirrors and a 2λ thick cavity composed of periodic strain compensated MQWs to fully utilize the gain in every quantum well. The optically pumped VCSELs operated at room temperature with equivalent threshold current density calculated to be 2 kA/cm2. The wavelength of the output beam is 1562 nm.. iii.

(8) Although our goal to fabricate electrically driven continuous wave LW-VCSELs with single mode operation has yet to be fulfilled, this process has led to many other developments. For example, we have developed the MOCVD regrowth technique to fabricate buried tunnel junction devices and have applied this technique to fabricate long wavelength light emitting diodes with buried tunnel junction. At the same time, we have studied the quantum well inter-mixing effect, and the coexisting two-cavity configuration in conventional oxide confined VCSELs. All in all, basic physical phenomenon and material issues observed in this study will turn into useful information in making electrically driven LW-VCSELs in the future.. iv.

(9) CONTENTS Abstract (in Chinese) Abstract Acknowledgement Contents List of tables List of figures. CHAPTER 1 1-1 1-2 1-3. CHAPTER 2 2-1. 2-2. 2-3. 2-4 2-5. CHAPTER 3 3-1. 3-2 3-3. i ii v vi ix x. Introduction Background Development of LW-VCSELs Overview of this Thesis References. 1 3 5 8. Principal Issues in Design of Long Wavelength Vertical Cavity Surface Emitting Lasers General Characteristics in Semiconductor Lasers Semiconductor Laser Oscillation Conditions General Characteristics of VCSELs Transverse Modes in VCSELs Modeling the Gain Mediums Optical Gain in Semiconductors Optical Gain in Quantum Well Structures Nonradiative Transitions Optical Gain in Strained Quantum Wells Characteristics of Distributed Bragg Reflectors Transfer Matrix Method Reflection Delay and Penetration Depth of DBRs Analysis of the Heat Flow LW-VCSEL Designs References. 19 19 23 25 27 27 30 32 33 35 35 38 40 42 45. Fabrication of Long Wavelength Vertical Cavity Surface Emitting Lasers Metal Organic Chemical Vapor Deposition System Reaction Equations Gas Blending Systems Reactor Chamber Uniformity Issue In-situ Monitoring Epitaxial Regrowth Techniques Wafer Fusion Techniques Introduction to Fusion Methods Key Issues in Wafer Fusion Process Wafer Fusion System Experiments for Fusion System Test vi. 73 73 74 75 76 77 78 79 80 81 81 82.

(10) References. CHAPTER 4 4-1. 4-2. CHAPTER 5 5-1. 5-2. CHAPTER 6 6-1. 6-2. CHAPTER 7 7-1. 7-2. 84. Optimization of the Active Layers Comparisons between Gain Materials in Long Wavelength Range GaAs-Based Gain Materials InP-Based Gain Materials Characterization and Optimization of the Active Layers Fabrication of Long Wavelength FP EELs The Effect of Strain The Effect of QW number The Effect of P-type Doping Amount References. 99 99 101 102 102 104 105 107 108. Fabrication of the Distributed Bragg Reflectors Comparisons of InP/InGaAlAs and InAlAs/InGaAlAs Distributed Bragg Reflectors Introduction Experimental Procedure Results and Discussion Distributed Bragg Reflectors for Long Wavelength VCSELs using InP/Air-gap Design and Fabrication Optical Characterization Thermal Analysis of LW-VCSELs with Air-gap Reflectors References. 121 121 123 124 128 128 131 131 135. Optically Pumped LW-VCSELs Structures and Characteristics of Optically Pumped LW-VCSELs Based on InP/InGaAlAs DBRs The Structure of LW-VCSEL The Results of Optical Pumping Structures and Characteristics of Optically Pumped LW-VCSELs with Wafer-fused GaAs/AlAs DBRs Influence of Distance between Fusion Interface and Active Region Comparisons of Spectra before and after Wafer Fusion Process Optical Pumping of VCSEL Structure with Double-fused DBRs References. 153 153 154 155 156 157 158 160. Electrically Driven LW-VCSELs Fabrication of LW-VCSELs by Ion-implantations The Structure of LW-VCSEL Results and Discussion Long Wavelength Light Emitting Diodes with Buried vii. 173 173 174.

(11) 7-2. CHAPTER 8. Tunnel Junctions Introduction The Structure of Long Wavelength LEDs with Buried Tunnel Junctions Results and Discussion Fabrication of LW-VCSELs by Wafer Fusion Techniques Quantum Well Inter-mixing The Structure of LW-VCSELs by Wafer Fusion Techniques Results and Discussion References. 175 175 176 177 177 177 178 179 180. Conclusions and Future Works Conclusions Future Works. 191 193. APPENDIXES A-1. Introduction to Laser Simulation Software References. viii. 197 199.

(12) List of tables Table 1-1 Comparison of features for EEL vs VCSEL. 11. Table 2-1 Comparison of threshold conditions for EEL vs VCSEL.. 47. Table 2-2 Magnitude of |M|2 for various material systems.. 48. Table 2-3 Magnitude of |MT|2/|M|2 for different transitions and polarizations.. 49. Table 2-4 Various material combinations for making high reflectivity DBRs. 50. ix.

(13) List of figures Chapter 1 Figure 1-1 Spectral loss profile of a typical single-mode silica fiber.. 13. Figure 1-2 Typical wavelength dependence of the dispersion parameter.. 14. Figure 1-3 Progress in lightwave communication technology over the period 1974-1996.. 15. Figure 1-4 Bandgap versus lattice constant for III-V compound semiconductors used in LW-VCSELs.. 16. Figure 1-5 Three LW-VCSEL structures:. 17. Chapter 2 Figure 2-1 Schematics of edge emitting lasers.. 51. Figure 2-2 Typical semiconductor laser output power vs. injection current relation (L-I curve).. 52. Figure 2-3 The gain, optical mode and power spectrum for a Fabry-Perot laser.. 53. Figure 2-4 Operation of a Fabry-Perot laser.. 54. Figure 2-5 General schematics of VCSELs.. 55. Figure 2-6 The gain and optical mode spectrum for a VCSEL.. 56. Figure 2-7 Schematics of alignment between gain and cavity mode peak at different temperature.. 57. Figure 2-8 Schematics of optical waveguide for oxide VCSEL.. 58. Figure 2-9 The spectrum and near field spontaneous emission patterns of the oxide-confined VCSEL with a 6x6 µm square aperture operated at 0.9 Ith (~1 mA).. 59. Figure 2-10 The relationship between energy and k-space and illustration of k-selected transition in parabolic shape band structure.. 60. Figure 2-11 Illustration of an incident light gaining its power after passing through a portion of gain medium. 61. Figure 2-12 Allowed and forbidden transitions in a quantum well.. 62. Figure 2-13 Valence band structures of unstrained bulk semiconductor such as GaAs. 63. x.

(14) Figure 2-14 Three major types of nonradiative recombination paths. 64. Figure 2-15 Illustration of thin epilayer of lattice constant ac grown under biaxial compression and tension on substrate with lattice constant as.. 65. Figure 2-16 Qualitative band energy shift of the conduction band and three valence bands for biaxial compressive and tensile strain.. 66. Figure 2-17 Band-edge profiles in real space with different strain.. 67. Figure 2-18 Schematics of plane wave incident on thin films on a substrate.. 68. Figure 2-19 The simulated results for a stack of InGaAlAs/InAlAs DBRs with 10, 20, 30, and 40 pairs.. 69. Figure 2-20 The illustration of the penetration depth concept.. 70. Figure 2-21 The simulated electric field in 40 pairs InGaAlAs/InAlAs DBRs.. 71. Figure 2-22 The main categories of considerations in designing the LW-VCSELs.. 72. Chapter 3 Figure 3-1 Major components of a low pressure MOCVD system.. 87. Figure 3-2 Components of a low pressure MOCVD system. 88. Figure 3-3 Schematics of gas blending system in MOCVD.. 89. Figure 3-4 Schematics of reactor design in MOCVD system.. 90. Figure 3-5 The reflectivity mapping of the AlAs/GaAs DBRs grown with various alkyl inject mass flow controller settings.. 91. Figure 3-6 Schematic of in-situ monitoring configuration and the measured reflectivity of calibration layers and DBR layers.. 92. Figure 3-7 Procedure for fabrication of buried heterojunction laser diodes.. 93. Figure 3-8 The bird’s view of the surface after the regrowth process and the cross-section of the buried ridge taken by the SEM.. 94. Figure 3-9 The schematic drawing of the fusion fixture.. 95. Figure 3-10 The apparatus of wafer fusion system.. 96. Figure 3-11 Optical microscope picture and SEM image of GaAs/InP. 97. xi.

(15) interface.. Chapter 4 Figure 4-1 The simulated gain-wavelength and gain-carrier relationships for InGaAlAs and InGaAsP strained compensating quantum wells.. 109. Figure 4-2 The simulated band diagrams under forward bias for InGaAlAs and InGaAsP multiple quantum wells.. 110. Figure 4-3 The epitaxial structure for 1550 nm FP lasers and the schematic of band diagram.. 111. Figure 4-4 The schematics of process flow for simple ridge FP lasers.. 112. Figure 4-5 The SEM cross-sectional image of the 1550 nm laser ridge.. 113. Figure 4-6 The temperature dependence of the threshold current for both 1310 nm and 1550 nm FP lasers.. 114. Figure 4-7 The dependence of the laser threshold current density on the amount of compressive strain in quantum wells.. 115. Figure 4-8 The X-ray diffraction patterns of different strain-compensated MQWs.. 116. Figure 4-9 The simulated valence band structure for 2.0% strain and 0.7% strain in quantum wells.. 117. Figure 4-10 The effect of quantum well numbers on the laser threshold current and confinement factor.. 118. Figure 4-11 The effect of the flow rate of p-type dopant on the laser threshold current.. 119. Chapter 5 Figure 5-1 The pit density of 10 pairs InP/InGaAlAs DBRs grown with different interruption time tp. and the cross section the InP/InGaAlAs DBRs grown with 0.1-minute interruption time investigated by SEM.. 137. Figure 5-2 The reflectivity curves of 10 pairs InP/InGaAlAs DBRs grown with different interruption time tp.. 138. Figure 5-3 The X-ray diffraction patterns of 10 pairs InP/InGaAlAs DBRs grown with different interruption time tp.. 139. Figure 5-4 The SIMS results of InP/InGaAlAs DBRs grown with tp. 140. xii.

(16) = 0.2 minute. Figure 5-5 The interface conditions of InP/InGaAlAs DBRs examined by TEM with different growth interruption time.. 141. Figure 5-6 The I-V curves of InP/InGaAlAs DBRs and InAlAs/InGaAlAs DBRs and the simulation of the equilibrium band diagrams.. 142. Figure 5-7 The reflectivity curves of 35 pairs InP/InGaAlAs and InAlAs/InGaAlAs DBRs measured by spectrometer.. 143. Figure 5-8 The reflectivity of three-pair of InP/airgap DBR structure with a fixed λ/4 InGaAs layer and different InP layer.. 144. Figure 5-9 Schematic diagram of the fabrication procedure of the InP/airgap DBRs.. 145. Figure 5-10 The cross section of the stable suspended InP/airgap DBRs captured by SEM.. 146. Figure 5-11 The calculated and measured reflectivity curves of the InP/airgap DBRs.. 147. Figure 5-12 The schematic cross section of LW-VCSEL with air-gap and dielectric reflectors.. 148. Figure 5-13 The temperature distribution and the heat flow pattern simulated by FEA tool based on the heat-transferred modal.. 149. Figure 5-14 The influences of the radius of undercut, thickness of InP spacer, thickness of n-InP spacer, and thickness of metal contact, on the values of the thermal resistance.. 150. Figure 5-15 The threshold gain versus the thickness of the n-InP and p-InP spacer layers.. 151. Chapter 6 Figure 6-1 Schematic cross section of VCSELs.. 161. Figure 6-2 Reflectance and PL spectrum VCSEL structure.. 162. Figure 6-3 Schematic setup of optical pumping.. 163. Figure 6-4 The VCSEL output power versus input laser pumping power characteristics at room temperature and the VCSEL emission spectrum at the pumping power above the threshold.. 164. Figure 6-5 Process for fused-MQW for quality experiment.. 165. Figure 6-6 Dependence of the PL peak intensity on the distance. 166. xiii.

(17) from the fusion interface. Figure 6-7 Flowchart of MQW/DBR fusion process.. 167. Figure 6-8 PL spectra of MQW before and after wafer fusion.. 168. Figure 6-9 The DBR reflectivity spectra before and after fusion.. 169. Figure 6-10 Process flow chart of double fused VCSEL.. 170. Figure 6-11 The refractive index distribution of the wafer-fused VCSELs and the simulation of the electric field inside the VCSEL structure.. 171. Figure 6-12 The double fused VCSEL output power versus input pumping laser power density characteristics at room temperature.. 172. Chapter 7 Figure 7-1 Schematics of LW-VCSEL with Si-implanted current aperture.. 181. Figure 7-2 The voltage and emission light output versus driving current characteristics for InP-based LW-VCSELs with Si-implantation.. 182. Figure 7-3 The reflectivity and PL curves of the LW-VCSEL with Si-implantation.. 183. Figure 7-4 Detailed descriptions of epitaxial structure for long wavelength LED with tunnel junction.. 184. Figure 7-5 Schematics of long wavelength LED structure with buried tunnel junction and the top view of the long wavelength LED before and after electrical operations.. 185. Figure 7-6 The voltage and emission light output versus driving current characteristics for the long wavelength LED with buried tunnel junction.. 186. Figure 7-7 Effect of quantum well inter-mixing.. 187. Figure 7-8 Schematics of double fused LW-VCSEL with pronton-implanted current aperture.. 188. Figure 7-9 The top emission image and the EL spectrum measured from the top surface of the LW-VCSEL with pronton-implanted current aperture.. 189. xiv.

(18) CHAPTER 1 Introduction. 1-1 Background In nowadays, the worldwide interconnections via the digital information streams have deeply influenced people’s life in many aspects, such as the rapid economic development, the knowledge share and flow, the way of learning and even the way of thinking. The basic infrastructures for the modern worldwide interconnections rely on the optical communication systems. Dated back to the 70’s, two breakthroughs had made great advances in optical communication systems. One is the successful continuous-wave (CW) operation of the semiconductor laser at the room temperature [1]. The semiconductor lasers can be directly modulated with information and provide compact and reliable light sources for optical communication systems. The other breakthrough is the improved fabrication technique of the optical fibers leading to the reduced transmission loss from 150 dB/km to 20 dB/km. The subsequent investigation in optical fibers shows a low transmission loss window in the wavelength range near the infrared band. Figure 1-1 shows that intrinsic material absorption for silica fiber is less than 0.03d B/km in the 1.3- to 1.6-µm wavelength window. In addition to the fiber loss, chromatic dispersion limits the performance of lightwave systems. For standard single mode fiber, the typical wavelength dependence of the dispersion parameter is shown in Figure 1-2. The zero dispersion wavelength locates at 1.3 µm. To further utilize the lowest loss band of fibers in 1.55 µm, dispersion flattened and dispersion shifted fibers with specialized structures have been introduced. Figure 1-3 shows that these advances accompanied with developments of semiconductor lasers and detectors demonstrate superior 1.

(19) performance in the long wavelength range from 1.3 to 1.6 µm than in the short wavelength at around 0.8 µm. Since the first successful CW double-heterojunction (DH) semiconductor laser had been demonstrated, commercial applications of edge-emitting lasers (EEL) have become practical. For this type of design, the optical gain was provided by electron-hole recombination in the active region, and cleaved facets perpendicular to the junction plane provided the optical feedback. The subsequent progress, such as improvement of epitaxial techniques, better material quality, utilization of the quantum wells (QW) active region, and the invention of distributed feedback (DFB) lasers, fulfill the stringent requirements in optical communication systems. In the late 70s, Iga et al. [3] had proposed a semiconductor laser oscillating perpendicular to the device surface plane, which is termed vertical cavity surface emitting laser (VCSEL) in contrast to EELs. VCSELs have demonstrated many advantages over EELs. First, the monolithic fabrication process and wafer-scale probe testing as per the silicon semiconductor industry substantially reduces the manufacturing cost because only known good devices are kept for further packaging [4]. Second, a densely packed two-dimensional laser array can be fabricated because the device occupies no larger of an area than a commonly used electronic device [5]. Third, the microcavity length allows inherently single longitudinal cavity mode operation due to its large mode spacing. Temperature-insensitive devices can therefore be fabricated with an offset between the wavelength of the cavity mode and the active gain peak [6]. Finally, the device can be designed with a low numerical aperture and a circular output beam to match the optical mode of an optical fiber, thereby permitting efficient coupling without additional optics [7]. Some additional advantages of VCSELs with respect to EELs are listed in Table 1-1.. 2.

(20) As the nearly completion of long haul interconnection in optical communication system around the world, how to further increase the bit rate and how to access through “the last mile” become demanding. The optical amplification for increasing the repeater spacing and the wavelength-division multiplexing (WDM) can further boost the bit rate. In the metropolitan connections or local area network (LAN) applications for gigabit ethernet and fiber to the home (FTTH), a high speed, low threshold, low cost long wavelength vertical cavity surface emitting lasers (LW-VCSEL) is much anticipated. Because of the larger distance-bandwidth product achievable in silica-based fiber at 1.3 µm, the maximum data-transmission rate and point-to-point distance in these links is expected to increase more than two times with the introduction of multimode 1.3 µm VCSELs. Single-mode VCSELs operating at both 1.3 and 1.55 µm can also be candidates for light sources in telecommunications and WDM applications due to the expected low cost of VCSELs, the possibility of fabricating arrays, and the integrability of the VCSEL structure.. 1-2 Development of LW-VCSELs GaAs-based VCSELs operating in the short wavelength range (0.78-0.98 µm) have exhibited tremendous progress in their performance over the past few years. Although the first VCSEL operated at 1.3 µm [3], the development of long wavelength VCSELs (operated at 1.3-1.5 µm) have been slower over the past years in comparison to GaAs-based VCSELs owing to several difficulties. The key issues have been the difficult realization of high reflectivity mirrors in the long wavelength range and of active layers with sufficient gain at elevated temperature. The corresponding problems are absence of natural oxidized current aperture and poor heat conductance in material systems for long wavelength range. As shown in Figure 1-4, appropriate 3.

(21) material systems used for long wavelength range lattice-match to InP. Unfortunately, the InGaAsP material systems lattice-matched to InP for gain medium have pronounced low characteristic temperature due to serious auger recombination and inter-valence band absorption in active region. The problem with the conventional InP-lattice-matched InP/InGaAsP and InAlAs/InGaAlAs is the small refractive index contrast (∆n = 0.27 for InP/InGaAsP and ∆n = 0.3 for InAlAs/InGaAlAs) resulting in a larger number of distributed Bragg reflector (DBR) pairs required to obtain high reflectivity. In addition, using the conventional DBRs, not only the penetration depth will increase causing more absorption, but the heat dissipation is also a problem. Therefore, efforts like developing active layers with high gain, fabricating DBRs with higher reflectivity, and designing device structures with higher thermal conductance have been studied for the past years. The device structures investigated for LW-VCSELs can be divided into three groups [9]. The simplified schematics of these device structures are shown in Figure 1-5: (1) Etched-well VCSEL structure that use amorphous-dielectric mirrors on both-sides of active layer [10] as shown in Figure 1-5(a), (2) VCSEL structures with one semiconductor and one amorphous-dielectric mirror that utilize ring contacts [11] as shown in Figure 1-5(b). (3) All-epitaxial devices that mimic the single-grown GaAs-based VCSEL structure [12] as shown in Figure 1-5(c). Recently, long wavelength VCSELs have been successfully demonstrated with several different approaches in all three device structures. First, wafer fusion technique, that integrated the InP-based active layers and GaAs-based DBRs together, had been successfully realized for high performance long wavelength VCSELs [13, 14]. Second, the InGaNAs 1.3 µm VCSELs grown on GaAs substrates have been demonstrated with excellent characteristics [15, 16], but to extend the InGaNAs gain 4.

(22) peak to beyond 1.5 µm is rather difficult. Monolithically grown DBRs lattice-matched to InP continued to attract interests due to the well existing highly efficient InGaAsP and InGaAlAs gain materials covered the wavelength window from 1.3 to 1.8 µm. Metamorphic GaAs/AlAs DBRs lattice-matched to InP substrate have been applied to realize the long wavelength VCSELs [17, 18] but the inherent dislocations in metamorphic layers have impacts on the reliability of the devices. The Sb-based DBRs have large refractive index contrasts ∆n ranging from 0.43 to 0.44 and have been successfully applied in the VCSEL structures [19, 20]. However, these DBRs have drawbacks such as the low thermal conductivity and relatively high growth complexity.. 1-3 Overview of this Thesis This study has focused on the design of active layers, the growth of the DBRs, the process of the LW-VCSEL structures. Two different material systems have been studied. The monolithically InP-based VCSELs are chosen since the potential of single epitaxial growth ensures the practical devices for mass production. Although the capability of mass production for wafer fused VCSELs is still questionable, the excellent thermal and optical properties of GaAs/AlAs DBRs as well as the capability of the oxidation process make the wafer fused VCSELs worth of studying. Chapter 2 reviews fundamentals in semiconductor lasers at beginning. The origin of differences between EELs and VCSELs will be discussed. Then, general operation principles of VCSELs including light-current characteristics, the relationship between gain and current, the gain peak and cavity mode alignment, the characteristics of DBRs, the analysis of the heat flow will be introduced and characterized with the use of simulation software. With specific conditions in. 5.

(23) requirement of LW-VCSELs, the fundamental issues in design of LW-VCSELs will be discussed at the end of the chapter. Chapter 3 mainly describes the fabrication method for LW-VCSELs. Metal organic chemical vapor deposition (MOCVD) systems have been used for growing all the epitaxial structures in this study. Since the epitaxial equipment and process determine most of the characteristics of LW-VCSELs, detailed descriptions and specific functions of this MOCVD system are given. The growth process, regrowth process and in-situ monitoring will also be addressed. Wafer fusion technique, which is the other special and important process step in fabrication of LW-VCSELs, will also be introduced. The characteristics of gain medium suitable for LW-VCSEL have been discussed at the beginning of chapter 4. By considering material quality and limitations of process equipment, the InGaAlAs system lattice-matched to InP has been chosen as the active layers in this study. The optimized layer structures have been determined by investigating performance of EELs with InGaAlAs multiple quantum wells (MQW) as the active layers. Chapter 5 reports several different fabrication methods for DBRs used in long wavelength range. The optical and electrical properties of different DBRs will also be studied. Followed by the comparisons of novel InP/InGaAlAs and conventional InAlAs/InGaAlAs DBRs, the extremely high reflectivity mirror made by InP/Air-gap DBRs will be discussed. The feasibility of the active layers and DBRs is first examined by the performance of optically pumped LW-VCSELs. Chapter 6 reports the structures of LW-VCSELs for optical pumping, including the InP-lattice-matched and wafer-fused structures. Chapter 7 reports several different approaches to make electrically driven 6.

(24) LW-VCSELs, including monolithically InP-based and wafer-fusion type devices. The ion-implantation or buried tunnel junction were used to make current apertures in devices. Although the goal to make electrically driven devices has not yet accomplished, efforts resulted from this study have led to develop other interesting devices. In addition, basic physical phenomenon and material issues observed in this study will turn into useful information in making electrically driven LW-VCSELs. Chapter 8 is the summary of this thesis.. 7.

(25) References [1] I Hayashi, M. B. Panish, P. W. Foy, and S. Sumuski, Appl. Phys. Lett., v17, p10, 1970. [2] G. P. Agrawal, Fiber-optic communication systems. 2nd ed. John Wiley & Sons, Inc., N. Y., 1997. [3] H. Soda, K. Iga, C. Kitahara, and Y. Suematsu, Jpn. J. Appl. Phys., v18, p2329, 1979 [4] K. Iga, F. Koyama, and S. Kinoshita, IEEE J. Quantum Electron., QE-24, p1845, 1988. [5] M. Orenstein, A. C. Von Lehmen, C. Chang-Hasnain, N. G. Stoffel, J. P. Harbison, and L. T. Florez, Electron. Lett., v27, p437, 1991 [6] D. B. Young, J. W. Scott., F. H. Peters, B. J. Thibeault, S. W. Corzine, M. G. Peters, S. L. Lee, and L. A. Coldren, IEEE Photon. Tech. Lett., v5, p129, 1993 [7] K. Tai, G. Hasnain, J. D. Wynn, R. J. Fischer, Y. H. Wang, B. Weir, J. Gamelin, and A. Y. Cho, Electron. Lett., v26, p1628, 1990 [8] C. DeCusatis, Handbook of Fiber Optic Data Communication, 2nd ed. Academic Press, 2002. [9] C. W. Wilmsen, H. Temkin, and L. A. Coldren, “Long-wavelength vertical-cavity lasers,” in Vertical-Cavity Surface-Emitting Lasers: Design, Fabrication, Characterization, and Applications, Cambridge University Press, 1999. [10] K. Iga and F. Koyama, “Vertical-cavity surface-emitting lasers and arrays,” in Surface-Emitting Semiconductor Lasers and Arrays, G. A. Evans and J. M. Hammer, eds., Academic Press, San Diego, 1993. [11] T. Tadokoro, T., H. Okamoto, Y. Kohama, T. Kawakami, and T. Kurokawa, IEEE Photon. Technol. Lett., v4, no.5, p409, 1992. [12] D. I. Babic, K. Streubel, R. P. Mirin, N. M. Margalit, J. E. Bowers, E. L. Hu, D. E. Mars, L. Yang, and K. Carey, IEEE Photon. Technol. Lett., v7, no.11, p1025, 1995. [13] D. I. Babic, J. Piprek, K. Streubel, R. P. Mirin, N. M. Margalit, D. E. Mars, J. E. Bowers and E. L. Hu, IEEE J. Quantum Electron., v33, no.8, p1369, 1997 [14] Y. Ohiso, C. Amano, Y. Itoh, H. Takenouchi and T. Kurokawa, IEEE J. Quantum Electron., v34, no.10, p1904, 1998) [15] S. Sato, N. Nishiyama, T. Miyamoto, T. Takahashi, N. Jikutani, M. Arai, A 8.

(26) Matsutani, F. Koyama and K. Iga, Electron. Lett., v36, no.24, p2018, 2000) [16] G. Steinle, F. Mederer, M. Kicherer, R. Michalzik, G. Kristen, A. Y. Egorov, H. Riechert, H. D. Wolf and K.J. Ebeling, Electron. Lett., v37, no.10, p632, 2001) [17] J. Boucart, C. Starck, F. Gaborit, A. Plais, N. Bouche, E. Derouin, J. C. Remy, J. Bonnet-Gamard, L. Goldstein, C. Fortin, D. Carpentier, P. Salet, F. Brillouet and J. Jacquet, IEEE J. Sel. Topics Quantum Electron., v5, no.3, p520, 1999 [18] W. Yuen, G.S. Li, R.F. Nabiev, J. Boucart, P. Kner, R.J. Stone, D. Zhang, M. Beaudoin, T. Zheng, C. He, K. Yu, M. Jansen, D.P. Worland and C.J. Chang-Hasnain, Electron. Lett., v36, no.13, p1121, 2000 [19] E. Hall, H. Kroemer and L.A. Coldren, Electron. Lett., v35, no.5, p425, 1999 [20] E. Hall, S. Nakagawa, G. Almuneau, J.K. Kim and L.A. Coldren, Electron. Lett., v36, no.17, p1465, 2000. 9.

(27) Table 1-1 Comparison of features for EEL vs VCSEL [8] Feature. EEL. VCSEL. Spectral bandwidth. Very narrow. Narrow. Size of active area. Typically 0.5-1×2-10 µm. Variable, 5-50 µm in diameter. Beam geometry. Strong elliptic. Circular. Beam divergence. High, up to 60°×20°. Low, 5°. Number of modes. Typically 1 or few. 1 or even up to many 10s. Coupling to fiber. Difficult and sensitive. Easy. Coupling efficiency. Moderate. High. Threshold current. Approximately 10 mA. Some mA. Direct modulation. High, up to 10 Gbit/s. High, up to 10 Gbit/s. bandwidth Temperature drift of Pop Fairly high. Tendentially low. Environmental. Extremely high. Moderate. Processing of chip. Very specific. Similar to LED. Final processing. Single bar. On wafer. Burn-in and functional. Single on heatsink. On wafer. sensitivity. test. 11.

(28) CHAPTER 2 Principal Issues in Design of Long Wavelength Vertical Cavity Surface Emitting Lasers This chapter reviews fundamentals in semiconductor lasers at beginning. The origin of differences between edge emitting lasers (EELs) and vertical cavity surface emitting lasers (VCSELs) will be discussed. Then, general operation principals of VCSELs including light-current characteristics, the relationship between gain and current, the gain peak and cavity mode alignment, the characteristics of distributed Bragg reflectors (DBRs), the analysis of the heat flow will be introduced and characterized with the use of simulation software. With specific conditions in requirement of long wavelength vertical cavity surface emitting lasers (LW-VCSELs), the fundamental issues in design of LW-VCSELs will be discussed at the end of the chapter.. 2-1 General Characteristics in Semiconductor Lasers Semiconductor Laser Oscillation Conditions The typical EELs shown in Figure 2-1(a) are Fabry-Perot (FP) lasers with double-heterojunction (DH) structures. The EELs, with small enough cross-section, may be initially modeled by considering a resonator, which contains plane optical waves travelling back and forth along the length of the lasers. The natural cleaved facets provide optical feedback for the laser cavity associated with the refractive index of the active layers. If the refractive index of the active layer is nr, for the normal incident light, the reflectivity of the cleaved facet is. r2 = R =(. nr − 1 2 ) nr + 1. 19. (2-1).

(29) Assumed an electromagnetic wave travelling back and forth in the laser cavity as shown in Figure 2-1(c), the amplitude decays or grows with distance because the wave suffers scattering and other fixed losses αi per unit length, but also experiences a material optical gain γ per unit length provided by the electrons and holes recombining at a rate which increases with the injected carrier density. The laser cavity length is L and the wave field at point (1) can be expressed as: I 1 = I o e jkzo. (2-2). After the wave travels through point (2), (3), (4) and backs to point (1), the wave field cab be expressed as: I 4 = R1 R2 I o e 2 (γ −α i ) L e jk ( zo + 2 L ). (2-3). The equilibrium wave field after one round trip must achieve for the occurrence of laser oscillation. Two oscillation conditions are obtained when I1 equals to I4. One is the amplitude condition: R1 R2 I o e 2 (γ −α i ) L = I o. (2-4). The other one is phase condition: e jk ( zo + 2 L ) = e jkzo k ⋅ 2 L = q ⋅ 2π. (2-5) (2-6). where q is an integer. From the amplitude condition (2-4), the threshold condition can be obtained:. γ th = α i +. 1 1 ln 2 L R1 R2. (2-7). which explains that the threshold gain is the summation of the internal loss and the mirror loss. However, the optical wave travelling in the laser cavity does not passes all the gain region, the confinement factor, Γ, has to added to modified the threshold condition:. 20.

(30) Γγ th = α i +. 1 1 =α i + α m ln 2 L R1 R2. (2-8). If a linear gain approximation is assumed, the relationship between gain and carrier density can be expressed as:. γ th ≡ a(nth − ntr ). (2-9). where a is the differential gain, ntr is the transparent current density. Assumed that thickness of the active layer is d, the threshold condition becomes: 1 Γ. γ th = (α i + J th = b≡. J τ J τ 1 1 ln ) = a( th n − tr n ) ed ed 2 L R1 R2. 1 d 1 (α i + ln ) + dJ o 2 L R1 R2 bΓ. (2-10). aτ n J , J o ≡ tr e d. where τn is the carrier lifetime, Jtr is the transparent current density. If the internal quantum efficiency is smaller than 1, the equation (2-10) should be modified as: J th =. dJ d 1 1 (α i + ln )+ o 2 L R1 R2 η i bΓ ηi. (2-11). To further explain the characteristics of laser output, the analytical rate equations have been used. Assumed the photon density in the laser cavity is nph, and the effective refractive index of the waveguide is nr, the rate equations for carrier density, n, and the photon density, nph, can be expressed as:. dn η i J n = − − g ⋅ n ph dt ed τ n dn ph dt. = Γ ⋅ g ⋅ n ph −. and g ≡γ ⋅ (. n ph. τp. (2-12) +Γ⋅β ⋅. c c ) = a ⋅ ( ) ⋅ (n − ntr ) nr nr. n. τn. (2-13). (2-14). where c is the speed of light, τp is the photon lifetime, and β is the spontaneous emission factor. Spontaneous emission factor represents the ratio that spontaneous 21.

(31) emission modes contribute to the stimulated emission modes. The value of β is very small that the last term of the equation (2-13) can be neglect. At the steady state, from equation (2-13), 1 g. τ p =( )=. nr ⋅ c. 1. αi +. 1 1 ln( ) 2 L R1 R2. (2-15). When the operation condition approaches threshold, the photon density still can be seen as zero, the equation (2-13) becomes: J th nth = ed τ n. (2-16). which is identical to equation (2-11). When the operation condition is above the threshold, the carrier density pins at nth, and the equation (2-13) becomes: J − J th (2-17) τp ed If the laser active volume is V, which is the product of the cross-section area A and n ph. =. thickness of active layer d. Let equation (2-17) time V at both sides of equation. Then, the power generated by stimulated emission inside the laser cavity can be expressed as: Ps = (. n ph ⋅ V. τp. ) ⋅ hν = η i ⋅. hν ⋅ ( I − I th ) e. (2-18). Since the laser power out of the laser cavity is termed as the mirror loss, the output power can be expressed as: 1 1 ln( ) 2 L R1 R2 hν ) ⋅ ( I − I th ) ⋅ ( Po =η i ⋅ 1 1 e ln( ) αi + 2 L R1 R2. (2-19). As shown in Figure (2-2), the slope efficiency defined as the ratio between output power over injected current is expressed as:. η s = Po /( I − I th ) = (. hν ) ⋅η d e. (2-20). where ηd is the differential quantum efficiency, which is the ratio between number of. 22.

(32) the increased photons over number of the injected electrons. From the phase condition (2-4), the threshold condition can be obtained: k ⋅ 2 L = q ⋅ 2π L=q⋅(. λo 2n r. ). (2-21). Equation (2-21) shows that the laser oscillation wavelength is determined by cavity length. For a typical EEL, the line width of the gain spectrum is larger than the mode spacing as shown in Figure 2-3. The allowed laser modes, or longitudinal modes can be several. The mode spacing between longitudinal modes derived from equation (2-21) can be expressed as: ∆λ =. λ2 λ ∂n 2nr L(1 − ( r )) nr ∂λ. (2-22). Figure 2-4 shows schematic of standing waves inside the laser cavity. Also shown in Figure 2-4 also shows that the laser output beam exhibits an elliptic shape due to the waveguide structure inside the laser cavity. The waveguide structure defines not only the optical confinement but also the carrier confinement. The optical confinement factor can be taken apart into three directions: Γ = Γx ⋅ Γy ⋅ Γz. (2-23). For typical EELs, Γz and Γy approaches unity and Γx ranges from 3% to 15%. Due to different confinement effect and field size in the transverse plane, the output beam shows different divergence angles in x and y direction. General Characteristics of VCSELs. The operation of a VCSEL, like above descriptions, can be understood by analyzing the flow of carriers into active regions, the generation of photons due to the recombination of some of these carriers, and the transmission of some of these photons out of the laser cavity. Consider a generic VCSEL illustrated in Figure 2-5. 23.

(33) with an active layer radius of a and active and effective cavity lengths of La and L, respectively. The threshold condition can be written as:. 1 1 1 g th = α a + α p ( − 1) + ln( ) +αd R1 R2 Γ Γ ⋅ La. (2-24). where αa and αp are the absorption loss in the active and passive layers, respectively, R1 and R2 are the reflectivities of two mirrors, and αd is the diffraction loss. The confinement factor is expressed as the product of the longitudinal confinement factor. Γz and the transverse factor Γxy, which is nearly unity for VCSELs. The longitudinal confinement factor Γz is expressed as: L Γz = a ⋅ ξ L. (2-25). The last factor, ξ, is referred to as the axial enhancement factor, because it enhances the normally expected fill factor La/L in the axial confinement factor. When the field is approximated as a sinusoid enveloped by a decaying exponential in the DBRs, ξ reduces to [1, 2]. ξ = e−z. DBR. / LDBR. (1 + cos(2β z s ) ⋅. sin β La ) β La. (2-26). where β = 2πnr/λ is the axial propagation constant, zs is the shift between the active layer center and the standing-wave peak, and the exponential pre-factor accounts for placement of the active region within the DBR mirror. In this, zDBR is the distance to the active material measured from the cavity-DBR interface and LDBR is the penetration depth of optical energy into the DBR. If the active region is placed between the mirrors, zDBR is zero, and the pre-factor is unity. If a thin active layer is centered on the standing-wave peak in the cavity, ξ can be as large as 2. If the active layer is thick enough, ξ is unity. If a thin active layer is placed at a null (2βzs = π), ξ can be near zero. Table 2-1 lists the calculations of equation (2-8) and (2-24) for EEL and VCSEL threshold conditions, respectively. For VCSEL operations, the reflectivity, R, has to 24.

(34) be greater than 99.8% to reach threshold gain of 0.1 µm-1. In order to reduce the threshold gain, it’s better to have smaller absorption in the passive layers. In addition, reducing the thickness of cladding layers and the penetration depths of DBRs are effective ways to lower the chance of absorption. Typically, the cavity length of VCSELs is on the order of half operating wavelength. In such a short cavity device, the width of mode spacing is larger than the line-width of a typical semiconductor gain medium as shown in Figure 2-6. As a result, VCSEL operates with a single longitudinal mode. Since there’s only one longitudinal mode within gain curve, the alignment between gain peak and cavity mode needs to be paid attention. Typically, the gain peak will red-shift as the temperature increases due to the band-gap shrinkage. At the same time, the cavity mode will also red-shift as the temperature increases due to the effective increase of the refractive index with the slower movement speed. Device engineers need to take into account the operation temperature to decide the best gain peak offset. Typically, for a commercial 850 VCSEL, the gain peal offset is set to be zero to few nanometers to assure proper operation during –10 to 85 degree Celsius. Transverse Modes in VCSELs. Although VCSELs operate with single longitudinal mode, several transverse modes existed in VCSELs for typical aperture size ranging from 5 µm to 30 µm in diameter. Take a VCSEL with oxidized aperture for example shown in Figure 2-8. Due to the complex 3-D structure for oxide VCSEL, the analysis of transverse mode can be assumed an optical waveguide using effective index model [3]. The effective refractive index of core region can be calculated as n1, while that of outer region is n2. The simplest rule for single transverse mode operation is: Vn =. 2π. λo. ⋅ a ⋅ 2 ⋅ ∆n ⋅ n1 < 2.405 25. (2-27).

(35) where ∆n ∆λo = λo n1. (2-28). n1 − n 2 (2-29) n1 and λo is the operating wavelength and Vn is the normalized frequency. The index ∆n =. difference of oxide VCSEL originates from the built-in oxidized layer with lower refractive index in comparison to periphery semiconductor materials. Due to the accurate position of oxidized aperture, tightly defining the injected carriers into the active regions and the built-in index guiding provided by the oxidized layer, the oxide-confined VCSELs have shown superior threshold current, efficiency and modulation speed in comparison to the proton implanted VCSELs [4]. However, the good transverse optical confinement results in multimode emission even in small aperture devices. Furthermore, the presence of the oxidized aperture and the inherent three-dimensional structure of the VCSEL have become a great challenge for researchers attempting to analyze and simulate the oxide-confine VCSELs [5]. Numerous works have been done in the study of the transverse emission mode patterns of the oxide-confined VCSELs to determine the mechanism of the transverse mode formation and evolution [6-12]. We report the investigation of the spontaneous emission patterns of oxide-confined VCSELs at the subthreshold condition using spectrally resolved near-field microscopy [13]. Figure 2-9 shows the example of transverse modes in oxide VCSELs. Not only the spontaneous emission patterns with similar mode structures as the stimulated emission patterns are observed, but also the high order Hermite-Gaussian and Laguerre-Gaussian modes are easily seen. We’ve also observed coexistence of two sets of identical lower order Hermite-Gaussian modes with different spot sizes, implying two cavity configurations in oxide-confined VCSELs and complex mechanism responsible for formation of laser modes in 26.

(36) oxide-confined VCSELs.. 2-2 Modeling the Gain Mediums Optical Gain in Semiconductors. As shown in Figure 2-10, parabolic band structure approximation is used for conduction and valence band E-K relationship. The density of states for the combined system involving transition between E2 and E1 can be written as: 2m * 1 N r ( E ) = ( 2 ) ⋅ ( 2 r ) 3 / 2 ⋅ (hν − E g )1 / 2 2π h where the reduced effective mass is: 1 1 1 = *+ * * m r m c mv. (2-30). (2-31). mc* and mv* is the effective mass for electron and hole, respectively, and hν is the. emission photon energy. Assumed: (1) The Einstein coefficient, B, is the same for semiconductor, (2) Photon energy density is ρ (ν )dν = n p ⋅ hν ,where np is the photon density, (3) Density of states is expressed as Nr(ν), The transition rate between E2 and E1 can be written as: Stimulated absorption: R1−> 2 = B12 ρ (ν )dν ⋅ N r (ν ) ⋅ [ f v ( E1 )(1 − f c ( E 2 ))]. (2-32). R2 −>1 = B21 ρ (ν )dν ⋅ N r (ν ) ⋅ [ f c ( E 2 )(1 − f v ( E1 ))]. (2-33). Stimulated emission:. The net stimulated emission rate is: Rst = R2 − >1 − R1−>2 = Bρ (ν )dν ⋅ ( f 2 − f 1 ). (2-34). where f2 =. 1. = f c ( E 2 ),. f1 =. 1. (2-35) = f v ( E1 ) e e +1 +1 If f2 - f1 > 0 or < 0, the stimulated emission or absorption occurs. If f2 - f1 equals to ( E 2 − E fc ) / kT. ( E 2 − E fv ) / kT. zero, the transparent condition occurs. Thus, the condition for net stimulated emission 27.

(37) is:. E g ≤ E 2 − E1 < E fc − E fv. (2-36). The gain is defined as the ratio of net power emitted per unit volume over the power crossing per unit area. As shown in Figure 2-11,.an incident light pass the distance of dz and gains the amount of power ∆I. The speed of light is vg, where dz = vg*∆t. The power of light can be express as: I(ν) = [ρ(ν)dν]*vg. The optical gain coefficient is written as:. γ (ν ) =. Rst ⋅ hν ρ (ν )dν ⋅ v g. = B( = B(. hν ) N r (ν )( f 2 − f 1 ) vg. hν )hN r ( E )( f 2 − f 1 ) (cm −1 ) vg. (2-37). After the introduction to the concept of gain in a relative macroscopic point of view, the detail behavior and interaction between light and atomic system require quantum mechanical analysis. If we consider an atom with two-level energy system, the electron under light interaction has the Hamiltonian expressed by: H=. 1 (p + eA) 2 + V (r ) 2m. (2-38). where A is the vector potential. The above equation can be expanded as: e e2 2 p2 H= + [p ⋅ A + A ⋅ P] + A + V (r ) 2m 2 m 2m e ∧ p2 ={ + V (r )} + { [ A e⋅ P]} 2m m = Ho + H'. (2-39). The term, H’, can be viewed as a time-dependent perturbation to the original Hamiltonian, Ho. This perturbation term is the driving force for transitions between the conduction and valence bands. From solutions of time-dependent Schrodinger’s 28.

(38) equation, the transition rate for semiconductors can be obtained as:. R21 =. 2π 2 H ' 21 N r ( E 21 )δ ( E 21 − hw) h. (2-40). where. H ' 21 = ∫ ϕ 2* H 'ϕ1* d 3 r = < 2 | H ' | 1 >. (2-41). Equation (2-40) is known as Fermi’s Golden Rules. Compared with equation (2-33) and (2-40), and substituted Einstein coefficient, B, with matrix element, |H’21|, the gain expression can be rewritten as: 2π 1 2 γ (ν ) = ⋅ H ' 21 ⋅ ( ) ⋅ N r ( E ) ⋅ ( f 2 − f1 ) h v g n ph. (2-42). The matrix element, |H’21|, determines the strength of interaction between two states. In semiconductors, ϕ2 and ϕ1 in equation (2-41) are expressed as:. ϕ1 = F1(r)*uv(r). for valence band,. (2-43). ϕ2 = F2(r)*uc(r). for conduction band,. (2-44). where: (1) uv(r) and uc(r) are Bloch functions of parabolic potential with atomic scale, (2) F1(r) and F2(r) are envelope functions of macroscopic potential, satisfying Schrodinger’s equation in such as quantum wells, quantum dots. The bulk, quantum-well, and quantum-wire envelope functions take the following form:. F (r ) = F (r ) = F (r ) =. 1 V 1 A 1 L. ⋅ e jk ⋅r. (bulk). (2-45). jk ⋅r||. (quantum well). (2-46). ⋅ e jk z ⋅ z. (quantum wire). (2-47). ⋅e. If we define: ∧ 1 A = e [| Ao (r ) | e jk ⋅r + | Ao (r ) |* e − jk ⋅r ] 2. 29. (2-48).

(39) The H’ can be written as: H' =. eAo ∧ (e⋅ P) 2 mo. (2-49). Then, H ' 21 = ∫ ϕ 2* H 'ϕ1 d 3 r =. ∧ e * e A ⋅ p)ϕ1 d 3 r ϕ ( o 2 ∫ 2m o. =. ∧ e * * F u A e ⋅ p) F1u v d 3 r ( c o 2 ∫ 2m o. =. ∧ e [ ∫ F2*u c*u v ( Ao e⋅ p) F1 d 3 r 2m o. ⇒ (u c*u v = 0),. ∧. + ∫ [ F2* ( Ao ) F1 ][u c* (e⋅ p)u v ]d 3 r ] =. ∧ eAo [ F2* F1 ][u c* (e⋅ p)u v ]d 3 r ∫ 2m o. =. ∧ eAo eA < u c | e⋅ p|u v >< F2 | F1 > ≡ ( o ) | M T | 2m o 2mo. Overlap of Bloch function. (2-50). Envelope function overlap integral. where |MT| is known as transition matrix element. Since photon energy density is nph*hν , and electromagnetic wave energy density = 1/2*nr2ξo|E|2, the Ao can be derived as: E = − jwAo ; | E | 2 = w 2 | Ao | 2 ; 1 n ph ⋅ hν = nr2 ⋅ ε o ⋅ w 2 | Ao | 2 ; 2 2h | Ao | 2 = ( 2 ) ⋅ n ph nr ε o w. (2-51). And the equation (2-42) can be rewritten as:. γ (ν ) = (. e2h )⋅ | M T | ⋅N r ( E ) ⋅ ( f 2 − f 1 ) 2ε o nr cmo2 hν. = γ max ⋅ ( f 2 − f 1 ). (2-52). Optical Gain in Quantum Well Structures. We specially pay attention to the optical gain for quantum well structures, since. 30.

(40) the active mediums for all the devices in this study have quantum wells (QW). If we assume the potential confinement is along the z direction, the envelope function overlap integral can be expressed as: < F2 | F1 > =. 1 jk ⋅r − jk ⋅r F2* ( z )e 2 || F1 ( z )e 1 || d 3 r ; ∫ A. for k 2 = k1 ; < F2 | F1 > =. 1 F2* ( z ) ⋅ F1 ( z )dz ∫ A. (2-53). Due to orthogonality between the quantum-well wave-function solutions, the overlap integral in equation (2-53) reduces to the following rule for sub-band transitions:. |< F2 | F1 >| 2 ≅ δ nc ,nv. (2-54). This means that transitions can only occur between quantum-well sub-bands which have the same quantum number, nc = nv. These are referred to as allowed transitions. Transitions between sub-bands with dissimilar quantum numbers are forbidden transitions. Both are illustrated in Figure 2-12. Except for the envelope function overlap integral; the other term in transition matrix element is the overlap of Bloch function, which is also known as momentum matrix element |M|2:. | M T | 2 = | M | 2 ⋅ |< F2 | F1 >| 2. (2-55). The momentum matrix element, which is polarization dependent, determines the transition probability between conduction band and valence band. To further define the Bloch functions of the various energy bands, the corresponding atomic orbitals have to be taken into account. The Bloch function, us, corresponding to the isotropic s atomic orbital in conduction band remains the same. However, the Bloch functions ux, uy and uz corresponding to three p atomic orbitals for valence bands: px, py and pz, interact with each other along with the spin up and down. Using the kp theory, the modified valence bands are shown in Figure 2-13. The three valence bands are. 31.

(41) commonly known as the heavy-hole (HH), light-hole (LH), and split-off hole (SO) bands. Since the constant |M|2 can be determined experimentally, Table 2-2 has listed the reported values for several important materials. Table 2-3 summaries the results for bulk and quantum-well materials for either transverse electric (TE: electric field in the quantum-well plane) or transverse magnetic (TM: electric field perpendicular to quantum-well plane) polarizations. Nonradiative Transitions. Nonradiative transition is relatively important when considering the overall carrier recombination process. Three major types of nonradiative transitions are depicted in Figure 2-14. The first type of nonradiative recombination happens when existing an energy level in the middle of the gap, which serves to trap an electron from the conduction band temporarily before releasing it to the valence band. Defects in the lattice structure are one source of traps. The recombination rate, also referred as Schockley-Read-Hall recombination, takes the form: NP − N i2 Rd = ( N * + N )τ h + ( P * + P)τ e. (2-56). where Ni is the intrinsic carrier concentration, τe is the time required to capture an electron from the conduction band assuming all traps are empty, τh is the time required to capture a hole from the valence band assuming all traps are full, and N* and P* are the electron and hole densities that would exist if the Fermi level was aligned with the energy level of the trap. For the laser applications, equation (2-56) can be simplified with the high-level injection regime: N Rd = τ h +τ e. (2-57). The second type of nonradiative recombination in Figure 2-13 depicts electrons recombining via surface states of the crystal. The surface recombination rate under. Rs =. as vs N V. 32.

(42) high level injection in the active region can be expressed as: (2-58) where as is the exposed surface area, V is the volume of the active region, and vs is the surface recombination velocity. Surface recombination is most damaging when the exposed surface-to-volume ratio is large. In addition, devices when make use of regrowth technique can suffer from poor interfaces and hence high interface recombination. Surface recombination is also material dependent. The recombination velocity of short-wavelength GaAs system is one order greater than that of long-wavelength quaternary InGaAsP system. The last type of nonradiative recombination depicted in Figure 2-14 is basically a collision between two electrons, which knocks one electron down to the valence band and the other to a higher energy state in the conduction band. An analogous collision can occur between two holes in the HH band and either SO or LH band. The above three types of collision are refereed to as Auger processed. In laser applications with high injection level, the Auger recombination rate can be expressed as: R A = CN 3. (2-59). where C is a generic experimentally determined Auger coefficient. In long wavelength InGaAsP materials, the Auger coefficient is one order lager than GaAs systems since the smaller band-gap in InGaAsP materials enhances the probability of momentum conservation. The reduced material dimensionality, such as quantum well, appears to reduce the Auger process due to the modification of band structures. Another possible method of minimizing Auger recombination is to use strained materials in active layers. Optical Gain in Strained Quantum Wells. Strained QWs use a material, which has different native lattice constant than the. 33.

(43) surrounding lattice constant. As shown in Figure 2-15, if the QWs native lattice constant is larger than the surrounding lattice constant, the QW lattice compress in the plane, and the lattice is said to be under compressive strain. If the opposite is true, the QW is under tensile strain. However, in any lattice-mismatched system, it is important to realize that there is a critical thickness beyond which the strained lattice will begin to revert back to its native state, causing high densities of lattice defects. For typical applications, this critical thickness is on the order of a few hundred angstroms, thus limiting the number of strained QWs in active layers. Because the energy gap of a semiconductor is related to its lattice spacing, distortions in the crystal lattice should lead to alterations in the bandgap of the strained layer. There are two types of modifications. The first effect produces an upward shift in the conduction band as well as a downward shift in both valence bands, increasing the overall bandgap by an amount, H (which is positive for compressive strain and negative for tensile strain). The H indicates that this shift originate from the hydrostatic component of the strain. The second important effect separates the HH and LH bands, each being pushed in opposite directions from the center by an amount, S. The S indicates that this shift originates from the shear component of the strain. Figure 2-16 illustrates the energy shifts of the bands for biaxial strains. No only the energy shift, the band curvatures will be modified due to the strain effect. For a quantum-structure such as an In1-xGaxAs layer sandwiched between InP barriers, the band structures are shown in Figure 2-17 for (a) a compressive strain (x < 0.468), (b) no strain (x = 0.468), and (c) a tensile strain (x > 0.468) [18]. The left-hand side shows the quantum-well band structures in real space vs. position along the growth (z) direction. The right-hand side shows the quantized subband dispersions in momentum space along the parallel (kx) direction in the plane. 34.

(44) of the layer. These dispersion curves show the modification of the effective masses or the densities of states due to both the quantization and strain effects. The above characteristics provide some advantages in using strained materials over unstrained materials. First, the bandgap can be adjusted to obtain certain emission wavelength. Next, the reduction in hole masses leads to lower threshold lasing and lower Auger recombination rate. Then, the applied strain can allow laser emission with tailored polarization. Finally, the built-in strain may suppress defect migration into the active region. More detailed demonstrations of the strain effect will be given in chapter 4.. 2-3 Characteristics of Distributed Bragg Reflectors From the discussions in chapter 1, the high-reflectivity DBRs are extremely important components in VCSELs. In this section, we’d like to discuss the characteristics of DBRs. We start this section with the transfer matrix method in stacks of thin films. We construct a computational simulation program for the transfer matrix. Then, based on the simulation, we’ll discuss the reflectance, transmittance, absorption, phase delay, and penetration depth for the DBRs. Transfer Matrix Method. A thin film is shown in Figure 2-18(a) [19]. The direction of the incident wave is denoted by the symbol + (that is, positive-going) and waves in the opposite direction is – (that is, negative-going). Since there is no negative-going wave in the substrate and the waves in the film can be summed into one resultant positive-going wave and one resultant negative-going wave. At this interface b, then, the tangential components of E and H are: Eb = E1+b + E1−b. (2-60). H b = η1 E − η1 E + 1b. − 1b. 35.

(45) (2-61) where η is the optical admittance of the film. Different polarizations have different forms: for s-polarization (TE):. η s = n cosθ ε o / µ o. (2-62). for p-polarization (TM):. η s = n ε o / µ o / cosθ. (2-63). Hence 1 (2-64) E1+b = ( H b / η1 + Eb ) 2 1 (2-65) E1−b = (− H b / η1 + Eb ) 2 1 (2-66) H 1+b = η1 E1+b = ( H b + η1 Eb ) 2 1 (2-67) H 1−b = − η1 E1−b = ( H b − η1 Eb ) 2 The field at the other interface a at the same instant and at a point with identical x and. y coordinates can be determined by altering the phase factors of the waves to allow for a shift in the z coordinate from 0 to –d. The phase factor of the positive-going wave will be multiplied by exp(iδ) where. δ = 2πn1 d cosθ 1 / λ. (2-68). and θ1 may be complex, while the negative-going phase factor will be multiplied by exp(-iδ). There the values of E and H at the interface are: 1 E1+a = E1+b e iδ = ( H b / η1 + Eb )e iδ 2 1 E1−b = E1−b e −iδ = (− H b / η1 + Eb )e −iδ 2 1 H 1+b = H 1+b e iδ = ( H b + η1 Eb )e iδ 2 1 H 1−b = H 1−b e −iδ = ( H b − η1 Eb )e −iδ 2. So that E a = E1+a + E1−a = Eb cos δ + H b. i sin δ. η1. H a = H + H = Eb iη1 sin δ + H b cos δ + 1a. − 136 a.

(46) This can be written in matrix notation as:.  Ea  H  =  a.  cos δ iη sin δ  1. (i sin δ ) / η1   Eb  cos δ   H b . (2-69). The 2×2 matrix on the right-hand side of equation (2-69) is known as the characteristic matrix of the thin film. Let another thin film be added to the single film so that the final interface is now denoted by c, as shown in Figure 2-18(b). The characteristic matrix of the film nearest the substrate is:.  cos δ 2 iη sin δ 2  2. (i sin δ 2 ) / η 2  cos δ 2 . And from equation (2-69):.  Eb  H  =  b.  cos δ 2 iη sin δ 2  2. (i sin δ 2 ) / η 2   E c  cos δ 2   H c . and.  Ea  H  =  a.  cos δ 1 iη sin δ 1  1. (i sin δ 1 ) / η1   cos δ 2 cos δ 1  iη 2 sin δ 2. (i sin δ 2 ) / η 2   E c  cos δ 2   H c . If we define a characteristic matrix of the assembly, the above equation becomes:. B C  =  .  cos δ 1 iη sin δ 1  1. (i sin δ 1 ) / η1   cos δ 2 cos δ 1  iη 2 sin δ 2. (i sin δ 2 ) / η 2   1  cos δ 2  η 3 . This result can be immediately extended to the general case of an assembly of q layers, when the characteristic matrix is simply the product of the individual matrices taken in the correct order, i.e. B q  cos δ r C  = ( ∏r =1 iη sin δ   r  r. (i sin δ r ) / η r   1  ) cos δ r  η m  37.

(47) (2-70) where we have now used the suffix m to denote the substrate or exit medium. If θo, the angle of incidence, is given, the values of θr can be found from Snell’s law. So the reflectance, transmittance and absorptance can be expressed as [19]:. ηo B − C ηo B − C * )( ) ηo B + C ηo B + C 4η o Re(η m ) T= (η o B + C )(η o B + C ) * R= (. 4η o Re( BC * − η m ) A= (η o B + C )(η o B + C ) *. (2-71) (2-72) (2-73). The phase change on reflection can be expressed as:  iη (CB * − BC * )   φ = tan −1  o2 * *   iη o ( BB − BC ) . (2-74). Reflection Delay and Penetration Depth of DBRs Since we are interesting in Bragg mirrors (quarter-wave mirrors) with incident light normal to the interfaces, the above equations can be much simplified. Due to the distributed nature of quarter-wave stack, these mirrors exhibit phase dispersion and a finite delay upon reflection [20]. The dispersion is responsible for pulse broadening and distortion [21], whereas the reflection delay adds to the laser cavity round-trip time. The storage of electromagnetic energy in a distributed reflector is also a factor of interest in the case of small-cavity structures where the cavity volume and the cavity round-trip time are of comparable magnitude as the mirror storage and the reflection delay. It has been common practice [22] to account for both the reflection delay time and the energy storage in distributed laser mirrors by defining a quantity called penetration depth as the depth inside the mirror at which the optical pulse appears to reflect, or the energy falls off to 1/e of its initial value. The sum of the. 38.

(48) physical cavity length and the mirror penetration depth gives the effective cavity length. Figure 2-19 shows the simulation results of InGaAlAs/InAlAs DBRs with center wavelength at 1550 nm for 10, 20, 30 and 40 pairs. Figure 2-19(a), (b) and (c) demonstrate the reflectivity, phase and delay time, respectively. Figure 2-20 illustrates the interpretation of penetration depth: a wave is incident from a medium with refractive index n onto a DBR with linear phase. Its reflection is delayed by τ and scaled by the value of the reflectivity. The equivalent model for the DBR is realized by extending the incident medium beyond the reference plane and by placing a fixed-phase mirror at depth LDBR. To the observer placed to the left of the reference plane, the mirrors will appear equivalent if the reflectivity and the phase characteristics of the two cases are equal. The effective length and phase can be expressed as: LDBR = where the reflection delay is:. τ =−. cτ 2n. θ o = ω oτ. ∂φ (ω ) ∂ω. (2-74). (2-75). and LDBR is the penetration depth. Figure 2-21 shows the simulated electric field in a 40 pairs InGaAlAs/InAlAs DBRs. The intensity of the electric field decreases from the incident plane. The distance from the incident plane to 1/e of the magnitude of the incident intensity represents the penetration depth. This depth needs to be considered in the determination of cavity mode wavelength in FP lasers and longitudinal confinement factor in VCSELs. The confinement factor is given by the ratio of electromagnetic energy in the active region of length La and the total energy present in the cavity: ΓL =. LFP. La + 2 LDBR. (2-76). 39.

(49) From equation (2-76), the longer penetration depth will lower the confinement factor. If the absorption is taken into account, the longer traveling path will increase more loss. Table 2-4 lists various kinds of material combination for making DBRs with center wavelength at 1550 nm. The larger refractive index difference between the DBR layers leads to a smaller number of pairs to reach 99.9% reflectivity and a shorter penetration depth.. 2-4 Analysis of the Heat Flow It is well known that the heating effect is very important for semiconductor lasers in almost all applications. For VCSELs with relatively small device volume, the heat dissipation is one of the major limitations for continuous-wave (CW) operations. Long wavelength VCSELs especially suffer from the temperature effect due to the insufficient gain at high temperature. We’d like to develop a thermal model by using finite element analysis (FEA) software to simulate the heat flow in VCSELs. Typically, the VCSEL structure is cylindrical symmetry. The coordinates in thermal model can be transformed to longitudinal, z, and axial, r, directions. The input parameters for the thermal model include the geometry, the thermal conductivity k(T, r, z) of the materials, and the heat source distribution P(r, z). The heat sources mainly originate from the Joule heat in conducting materials, nonradiative recombination and absorptions in active layers. The heat-transferred modal for the cylindrical symmetry can be expressed as: ∂ ∂T 1 ∂T ∂ ∂T ∂P + kr + kz =− (r , z ) kr ∂r ∂r r ∂r ∂z ∂z ∂V. (2-77). where T is temperature and ∂P/∂V is the heat power density. If we assumed anisotropic thermal conductivity in DBR layers, then: kr =. d 1 k1 + d 2 k 2 d1 + d 2. and k z = 40. d1 + d 2 d 1 / k1 + d 2 / k 2.

(50) (2-78) where k1 and k2 are thermal conductivities for bulk materials and d1 and d2 are the DBR layer thicknesses. The partial differential equation (2-77) can be easily solved by FEA software [23]. The visualized outputs contain the temperature distribution and heat flow. The thermal resistance can be calculated from the temperature distribution T(r, z) with uniform heat source in the active region: Rth = ∆Tmax / Pheat. (2-79). Although heat flow in a VCSEL can be solved with the FEA software, the average device temperature can be easily evaluated. The power dissipated in the laser is PD = Pin − PO = Pin (1 − η ). (2-80). where η is the wall-plug efficiency, which is the ratio between the emitted optical power over the injected electrical power. Then, the temperature rise is: ∆T = PD Z T. (2-81). where ZT is the thermal impedance. For small VCSELs on a relatively thick substrate, a simple analytic expression for ZT is useful [24]: ZT =. 1 4kT aeff. (2-82). where kT is the thermal conductivity of the substrate beneath the heat generating disk, and aeff is the effective device radius. In the uncovered etched-mesa case, aeff is approximately equal to the radius of active region; in other cases it tends to be somewhat larger due to heat spreading in either surrounding epitaxial material or deposited heat spreaders. In contrast, if the VCSEL is flip-chip bonded to a heat sink, a quasi-one-dimensional heat flow results, and then ZT =. h kT A. (2-83). 41.

(51) where A is the effective area of the heat flow, h is the distance to the heat sink and kT is the thermal conductivity of the material between the source and heat sink.. 2-5 LW-VCSEL Designs The fundamental issues in designing LW-VCSELs fall into four main categories: optical, gain, electrical and thermal considerations. First, in considerations of optical elements in LW-VCSEL, how to fabricate both mirrors with high reflectivity, large stop-band width and short penetration depth is important. The choices of materials for DBRs will influence the structure and the fabrication methods of VCSELs. In order to fabricate an efficient device, the optical confinement in transverse plane is necessary. In GaAs-based VCSELs, the oxidized high Al-contained aperture has been successfully applied to provide not only the optical confinement in transverse plane but also the precision current path to the active region, which makes good overlapping between optical field and carrier distributions. Unless the LW-VCSELs are made by wafer-fusion, in which the AlGaAs DBRs can be integrated with InP-based active region, other kinds of mechanisms for optical confinement in transverse plane have to be figured out. Buried tunnel junction [25] and under-cut active layer [26] have been successfully demonstrated. Second, due to the stringent requirement in fiber communication, the LW-VCSELs have to be operated at 85°C with high-modulated speed. To improve the high temperature characteristics, it is effective using the materials in active region with large conduction-band offset, which can reduce the probability of hot electrons jumping over the barrier potential. The strained materials discussed above are also effective for increasing the high temperature characteristics since the reduction of threshold current and probability of Auger recombination. Strained multiple quantum 42.