标题: 使用平衡方程式的半导体元件模拟
Semiconductor Device Simulation Based on Balance Equation Method
作者: 林志芳
Chic-Von Lin
郭双发
Shung-Fa Guo
电子研究所
关键字: 半导体元件;平衡方程式;流体力学;抛射物二极体;semiconductor device;balance equation;hydrodynamic;ballistic diode
公开日期: 1999
摘要: 本研究从波兹曼方程式推导出平衡方程式,用来模拟半导体元件。吾人采用蒙地卡罗模拟方法所求出的弛懈率近似值,而此近似值考虑到非抛物线能带结构。这种流体力学模拟方法可用来描述次微米的抛射物二极体。我们是利用牛顿法来线性化这些耦合在一起的平衡方程式和帕森方程式,且用左上右下三角矩阵(LU)分解法求解线性系统。在平衡状态下和施予偏压的情况下,描述电位、载子浓度、速度和能量(温度)的暂态分布。并于数个不同的偏压下,观察这些变量在不同的偏压下在稳态的不同情况。这个流体力学的模型可以正确的预测载子在次微米元件中受热而增加温度和速度变化的情形,且速度的异常超射的情况并没有在我们的模拟结果中出现。
The balance equation method derived from Boltzmann transport equation is presented. The relaxation rate approximation is accounted to nonparabolic band structure by using Monte Carlo method. The hydrodynamic simulation of submicron ballistic diode is described. The coupled system of the balance equations and Poisson’s equation are linearized by Newton’s iteration and solved by LU decomposition method. The transient distributions of the variables such as electrostatic potential, carrier concentration, velocity, and energy under equilibrium and during voltage applied are illustrated. The distributions of all variables under steady state at various applied voltages are also shown. The hydrodynamic model can accurately predict the carrier heating phenomena in sub-micron device. However, the spurious velocity overshoot has not been observed in this work.
English Abstract ii
Acknowledges iii
Contents iv
Figure Captions v
Chapter 1 Introduction 1
Chapter 2 Fundamental Equations and Physical Models 4
2.1 Boltzmann Transport Equation 4
2.2 Derivation of Balance Equations 5
2.2.1 Carrier Balance Equation 5
2.2.2 Momentum Balance Equation 6
2.2.3 Energy Balance Equation 7
2.3 Collision Terms 9
2.4 Balance Equations for Silicon 11
2.5 Poisson’s Equation 11
2.6 Boundary Conditions 12
Chapter 3 Numerical Method and Solution 14
3.1 Normalization 14
3.2 Discretization 15
3.3 Linearization 18
3.4 Solution Procedure 21
Chapter 4 Results and Discussion 24
4.1 Transient Response at Thermal Equilibrium 24
4.2 Transient Response with Applied Voltage 32
4.3 Steady State Distribution under Various Applied
Voltages 38
4.4 The Current Density 45
4.5 The Effect of Mesh Size 49
Chapter 5 Conclusion and Future Work 53
References 54
URI: http://140.113.39.130/cdrfb3/record/nctu/#NT880428090
http://hdl.handle.net/11536/65731
显示于类别:Thesis