本論文中，我們對氮化銦鎵/氮化鎵雷射二極體的活性區以及p型包覆層作理論性探討。在活性區方面，我們討論了溢出載子對臨界電流密度、增益頻譜以及自發性放射頻譜的影響，同時利用p型摻雜來降低溢出載子的負面效應。包覆區方面，我們分析氮化鋁鎵/氮化鎵超晶格的結構，找出造成高垂直阻抗的主要因素，並且提供最佳化的結構參數。
我們利用能量在量子井能障之上的綿密不連續次能帶來近似連續能帶，當載子溢出量子井時即佔據在這些能帶上。計算結果顯示，有沒有考慮這些連續能帶，對輻射電流密度以及增益頻譜都有顯著差異。我們進一步探討在改變量子井寬度或深度、共振腔損耗及溫度時，載子溢出效應對輻射電流密度、增益頻譜跟自發性放射頻譜所造成的影響。對較淺的量子井而言，這個效應特別明顯。它會使得自發性放射頻譜變寬，進而增加雷射二極體的臨界電流。較長的共振腔以及多層量子井可以有效的降低溢出載子所造成的負面效應。我們提供了在考慮溢出載子效應下最佳的量子井寬度以及層數。此外，為了更進一步降低臨界電流，我們探討活性區中引入n型與p型摻雜對雷射的影響。結果顯示，p型摻雜不但能有效降低因為溢出電子所造成的漏電流，而且可以讓增益頻譜變成更往峰值集中，能更有效率產生雷射光。而n型摻雜則恰恰產生相反的結果。我們進一步提出高p型摻雜的單量子井為最佳化結構，如果高p型摻雜在實作上不容易達成，則低濃度p型摻雜的雙量子井為最佳結構。
除了活性區，我們也對p型端的氮化鋁鎵/氮化鎵超晶格結構作最佳化。為了探討超晶格的垂直電阻，我們利用飄移擴散、穿隧以及熱放射電流方程式建立計算模型。我們發現造成高垂直電阻的主要因素是超晶格中能障的數量。即使這些能障能有效的提升p型雜質的解離率，它們本身卻形成電洞移動時主要的障礙。當這些能障夠窄，使得電洞在跨越能障時的散射效應可以忽略時，較寬的能障寬度反而能得到較小的垂直阻抗。我們的結果顯示，在能障的鋁濃度為20%且氮化鎵寬度固定2奈米時，當能障的寬度從2奈米增加到6奈米，垂直阻抗可以降低大概50%。

In this dissertation, the InGaN/GaN laser diode is theoretically studied. We have optimized its active region and the cladding layer composed of a p-type AlGaN/GaN superlattice by studying the spillover effect, the influence of dopants, and the key factor making the vertical resistance of the p-type superlattice large.
The effects of electron spillover from quantum wells on the optical property of InGaN/GaN laser diodes are theoretically studied in detail. Six-band model including strain effect is used to calculate valence band states. Continuous subbands are simulated deliberately by dense discretized subbands for the spillover electrons. The calculation results show obvious differences in the radiative current densities and the gain spectra between the cases with and without considering the spillover effect. We further investigate the spillover effect on the radiative current densities and the spontaneous emission spectra, with variations in the depth and the width of quantum wells, the total loss of the cavity, and the temperature. For shallow wells, the spillover effect is particularly important. It broadens both the gain and the spontaneous emission spectra and hence deteriorates the threshold of laser diodes. Such an effect can be alleviated by employing lasers with a long cavity and a multi-quantum-well active region. The concepts of the electron spillover studied in this work are not only applicable to the nitride lasers, but also to other kinds of quantum-well lasers.

The influences of the modulation-doping in InGaN/GaN laser diodes are also theoretically studied with the effects of electron spillover from quantum wells considered. The calculation results show that the threshold current can be significantly reduced by p-type modulation-doping around the wells but not by n-type doping, supposed that the layers are of a perfect quality and the impurity-induced defects are ignored. Also, the p-type modulation doping can make the threshold current more insensitive to the cavity loss compared with other cases. An optimized threshold current density can be achieved for single-quantum-well lasers by introducing p-type dopants. However, the dopant concentration is high and may be inaccessible. For double-quantum-well lasers an optimized low threshold current can be achieved with a slighter and practicable p-type doping level.

We also study the vertical transport of holes through p-type AlGaN/GaN superlattices with both Ga- and N-face polarities by drift-diffusion, tunneling, and thermionic emission models to find the key factors that dominantly influence the average vertical resistivity at different temperatures. It is shown that although the acceptors in the barriers are easily ionized to give a high spatially averaged density of holes, the barriers themselves are the main obstacle to the transport of holes through the superlattices. In our calculation results, the number of barriers in the superlattices dominantly affects the average vertical resistivity if the barriers are thin enough. So the resistivity can be reduced by decreasing the barrier number for a fixed total length of superlattices. Our results show that about 50% reduction in the resistivity can be excepted when the structure varies from Al0.11Ga0.8N(2 nm)/GaN(2 nm) to Al0.11Ga0.8N(6 nm)/GaN(2 nm).

ABSTRACT (Chinese) i
ABSTRACT (English) iii
ACKNOWLEDGMENTS vi
CONTENTS vii
TABLE CAPTIONS ix
FIGURE CAPTIONS x

CHAPTER 1 INTRODUCTION
1.1 Milestones of developing nitride-based optical devices 1
1.2 Motivation and background 12

CHAPTER 2 CALCULATION MEHTOD
2.1 Piezoelectric and spontaneous polarization 16
2.2 Band structure of quantized heterojunction 19
2.3 Calculation method for optical properties 26
2.4 Current transport in p-type layers 31
2.5 Numerical methods 34

CHAPTER 3 RADIATIVE LEAKAGE CURRENT
3.1 Some assumptions and definitions 41
3.2 Result and Discussion 43
3.3 Summary 71

CHAPTER 4 VERTICAL RESISTIVITY OF THE SUPERLATTICE
4.1 Some assumptions and definitions 73
4.2 Result and Discussion 74
4.3 Summary 83

CHAPTER 5 CONCLUSION AND SUGGESTION
5.1 Conclusion 84
5.2 Suggestion for Future Work 85

REFERENCE 87

VITA 94

PUBLICATION LIST 95

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