摘要

這篇文章主要會討論有關半導体基本方程式且將其在SPICE3的架構下予以程式化。我們將會用一個簡單的PN接面二極体為例子，並研究其直流及暫態的特性。有了這技術，我們可以方便的來模擬各種半導体元件或是一電路包含此一半導体元件。

ABSTRACT
This thesis presents the equivalent circuit of basic semicondonductor equations, which are implemented as the device elements of circuit simulator: spice3. We use a simple example of a pn junction diode to study the DC and transient characteristics. Using this technique, it is easy to simulate the semiconductor device composed of the elements and to include the semiconductor device as a part of a circuit.

CONTENT

Ⅰ. Introduction 1-1

Ⅱ. Basic equations of semiconductor electrical and physical behavior
2.1 Carrier Continuity equations 2-1
2.2 Poisson Equation 2-1
2.3 Heat flow Equation 2-2

Ⅲ. Basic semiconductor equations with finite difference method
3.1 Carrier continuity equation 3-1
3.2 Poisson equation 3-3
3.2 Heat flow equation 3-4

Ⅳ. Device element in circuit simulator
4.1 Linear device elements
4.1.1 Simple example 4-1
4.1.2 Linear resistor 4-2
4.1.3 Current source 4-2
4.1.4 Voltage controlled voltage source 4-3
4.2 Non-linear device elements 4-3
4.3 Matrix in spice 4-6

Ⅴ. Linearized device elements base on the basic semiconductor equations
5.1 Electron current element 5-1
5.2 Hole current element 5-3
5.3 Recombination current element 5-5
5.4 Charge current element 5-6
5.5 Heat flow 5-8
5.6 circuit composition
5.6.1 Unit cell 5-9
5.6.2 Displacement current 5-10
5.6.3 Boundary conditions 5-11

Ⅵ. Examples 6-1

Ⅶ. Conclusion 7-1

Appendix A-1

Reference R-1

References

[1] C.T.SAH :“The Equivalent Circuit Model In Solid-State Electronics”, Solid-State Electronics, vol.13, pp.1547-1575, 1970.

[2] Siegfried Selberherr :“Analysis and Simulation of Semiconductor Devices”. Springer-Verlag Wien New York.

[3] Scharfetter, D.L.,Gummel, H.K.: “Large-Signal Analysis of a Silicon Read Doide Oscillator”. IEEE Trans. Electron Devices ED-16, p64-77, 1969.