本书系统介绍半导体光电子器件设计中的物理模型和数值分析方法。全
书共12 章，主要分为三部分。第一部分为第2～5 章，涵盖光电子器件中描
述各相关物理过程的主导方程的推导和解释；第二部分为第6～9 章，介绍
第一部分所涉及的主导方程的数值求解技术，并讲解将其整合应用于器件仿
真中的方法；第三部分为第10～12 章，提供基于前述建模和求解技术的光
电子器件设计与仿真实例，包括半导体激光器、电吸收调制器、半导体光放
大器、超辐射发光二极管等，以及这些器件的单片集成。
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目录
- 目录
译者序前言
第 1章绪论················································································································1
1.1 器件的物理基础 ·····························································································1
1.2 建模和仿真方法 ·····························································································1
1.3 建模研究对象·································································································2
1.4 器件建模技术·································································································3
1.5 本书主要内容·································································································4
第 2章光学模型 ········································································································5
2.1 有源介质中的波动方程··················································································5
2.1.1 麦克斯韦方程组·······················································································5
2.1.2 波动方程·································································································6
2.2 时域内约化的波动方程··················································································8
2.3 空域内约化的波动方程··················································································9
2.4 时域与空域内同时约化的波动方程——行波光场模型······························ 10
2.4.1 完全限制结构中的波动方程 ···································································· 10
2.4.2 部分限制结构中的波动方程 ···································································· 15
2.4.3 周期性波纹结构中的波动方程 ································································· 18
2.5 宽带行波光场模型 ······················································································· 26
2.5.1 直接卷积模型 ························································································ 27
2.5.2 等效布洛赫方程模型 ·············································································· 29
2.5.3 波段分割模型 ························································································ 31
2.6 时空分离的驻波光场模型············································································ 34
2.7 光子速率方程和相位方程——光场行为模型 ············································· 40
2.8 自发辐射噪声的处理 ··················································································· 40 参考文献 ··············································································································· 44
第 3章材料模型 I：半导体能带结构 ······································································ 47
3.1 体材料半导体中的单电子能带 ···································································· 47
3.1.1 薛定谔方程和哈密顿算符········································································ 47
3.1.2 布洛赫定理和能带结构 ··········································································· 49 3.1.3 k = 0处的解—— Kane模型 ····································································· 57
3.1.4 k≠0处的解—— Luttinger-Kohn模型 ························································ 63
3.1.5 4×4哈密顿算符和轴向近似下的解·························································· 68
3.1.6 不同半导体材料的哈密顿算符 ································································· 71
3.2 半导体量子阱结构中的单电子能带 ···························································· 72
3.2.1 有效质量理论和约束方程········································································ 72
3.2.2 导带(无简并) ························································································ 75
3.2.3 价带(有简并) ························································································ 76
3.2.4 量子阱能带结构 ····················································································· 78
3.3 应变层结构中的单电子能带 ········································································ 82
3.3.1 一般性方法 ··························································································· 82
3.3.2 应变体材料半导体·················································································· 84
3.3.3 应变量子阱结构 ····················································································· 85
3.3.4 闪锌矿结构的半导体 ·············································································· 86
3.4 k-p理论总结 ································································································ 88 参考文献 ··············································································································· 89
第 4章材料模型 II：光学增益 ················································································ 92
4.1 考虑多体效应的综合模型············································································ 92
4.1.1 引言 ····································································································· 92
4.1.2 海森堡方程 ··························································································· 93
4.1.3 综合模型······························································································· 93
4.1.4 一般性约束方程 ····················································································· 98
4.2 自由载流子模型——零阶解 ······································································ 108
4.2.1 自由载流子模型 ··················································································· 108
4.2.2 载流子速率方程 ··················································································· 109
4.2.3 极化激元的速率方程 ············································································ 112
4.2.4 极化率 ································································································ 113
4.3 屏蔽的库仑相互作用模型——一阶解······················································· 113
4.3.1 屏蔽的库仑相互作用模型······································································ 113
4.3.2 屏蔽的库仑势 ······················································································ 115
4.3.3 零注入和激子吸收情形下的解 ······························································· 118
4.3.4 任意注入情形下的解 ············································································ 122
4.4 多体相关模型——二阶解·········································································· 125
4.4.1 多体相关模型 ······················································································ 125
4.4.2 半解析解····························································································· 125 4.4.3 全数值解····························································································· 127 参考文献 ············································································································· 131
第 5章载流子输运和热扩散模型 ········································································· 133
5.1 载流子输运模型 ························································································· 133
5.1.1 泊松方程和载流子连续性方程 ······························································· 133
5.1.2 非有源区的漂移和扩散模型 ·································································· 134
5.1.3 有源区的载流子输运模型······································································ 135
5.1.4 载流子输运模型的简化 ········································································· 139
5.1.5 自由载流子输运模型 ············································································ 141
5.1.6 复合速率····························································································· 142
5.2 载流子速率方程模型 ················································································· 144
5.3 热扩散模型································································································· 145
5.3.1 经典热扩散模型 ··················································································· 145
5.3.2 一维热扩散模型 ··················································································· 148 参考文献 ············································································································· 148
第 6章光学方程的求解方法 ················································································· 151
6.1 横截面上的光场模式 ················································································· 151
6.2 行波方程 ····································································································· 152
6.2.1 有限差分法 ························································································· 152
6.2.2 分步交替法 ························································································· 160
6.2.3 由数字滤波器实现的时域卷积 ······························································· 165
6.3 驻波方程 ····································································································· 167 参考文献 ············································································································· 173
第 7章材料增益方程的求解方法 ········································································· 176
7.1 单电子能带结构 ························································································· 176
7.2 材料增益计算····························································································· 176
7.2.1 自由载流子增益模型 ············································································ 176
7.2.2 屏蔽的库仑相互作用增益模型 ······························································· 181
7.2.3 多体增益模型 ······················································································ 181
7.3 材料模型的参量化 ····················································································· 186 参考文献 ············································································································· 187
第 8章载流子输运和热扩散方程的求解方法 ······················································ 189
8.1 静态载流子输运方程 ················································································· 189
8.1.1 尺度换算····························································································· 190 8.1.2 边界条件····························································································· 191
8.1.3 初始解 ································································································ 192
8.1.4 有限差分离散化 ··················································································· 193
8.1.5 非线性代数方程的求解 ········································································· 202
8.2 瞬时载流子输运方程 ················································································· 205
8.3 载流子速率方程 ························································································· 206
8.4 热扩散方程································································································· 206 参考文献 ············································································································· 208
第 9章器件性能的数值分析 ················································································· 210
9.1 一般方法 ····································································································· 210
9.1.1 材料增益的处理 ··················································································· 210
9.1.2 准三维处理 ························································································· 212
9.2 器件性能分析····························································································· 213
9.2.1 稳态分析····························································································· 213
9.2.2 小信号动态分析 ··················································································· 215
9.2.3 大信号动态分析 ··················································································· 217
9.3 模型的标定和验证 ····················································································· 218 参考文献 ············································································································· 221
第 10章半导体激光器的设计和模拟实例···························································· 223
10.1 增益优化的有源区结构设计和模拟························································· 223
10.1.1有源区材料························································································ 223
10.1.2有源区结构························································································ 227
10.2 光场和载流子限制优化的横截面结构设计和模拟·································· 230
10.2.1横截面叠层设计的一般考虑································································· 230
10.2.2脊波导结构························································································ 232
10.2.3掩埋异质结结构 ················································································· 235
10.2.4脊波导与掩埋异质结结构的比较 ·························································· 238
10.3 激射振荡优化的腔结构设计和模拟························································· 239
10.3.1 Fabry-Perot激光器·············································································· 239
10.3.2通过光栅设计实现不同耦合机制的分布反馈激光器································ 242
10.3.3多段结构激光器的设计 ······································································· 249 参考文献 ············································································································· 253
第 11章其他单一光电器件的设计和模拟实例 ···················································· 257
11.1 电吸收调制器 ··························································································· 257 11.1.1器件结构 ··························································································· 257
11.1.2材料特性和器件性能模拟 ···································································· 258
11.1.3高消光比和低插入损耗的设计 ····························································· 263
11.1.4偏振无关吸收的设计··········································································· 265
11.2 半导体光放大器 ······················································································· 267
11.2.1器件结构 ··························································································· 267
11.2.2性能模拟 ··························································································· 268
11.2.3提高性能的设计 ················································································· 272
11.3 超辐射发光二极管 ··················································································· 272
11.3.1器件结构 ··························································································· 272
11.3.2性能模拟 ··························································································· 273
11.3.3提高性能的设计 ················································································· 275 参考文献 ············································································································· 278
第 12章集成光电器件的设计与模拟实例···························································· 281
12.1 集成半导体分布反馈激光器与电吸收调制器 ········································· 281
12.1.1器件结构 ··························································································· 281
12.1.2集成界面 ··························································································· 283
12.1.3分布反馈激光器性能模拟 ···································································· 284
12.1.4电吸收调制器性能模拟 ······································································· 285
12.2 集成半导体分布反馈激光器与监测光探测器 ········································· 288
12.2.1器件结构 ··························································································· 288
12.2.2激光器性能模拟 ················································································· 291
12.2.3信道间串扰的模拟 ·············································································· 292 参考文献 ············································································································· 296
附录 A Lowdin重整化理论···················································································· 298
附录 B 多体增益模型中的积分·············································································· 300
附录 C 5阶 Runge-Kutta方法的 Cash-Karp实现 ·············································· 312
附录 D 稀疏线性方程的解法 ················································································· 313
D.1 直接法········································································································ 313
D.2 迭代法········································································································ 315 参考文献 ············································································································· 319
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