有限差分法分析矽基底沉積製程的擴散現象

Abstract

擴散是一濃度因為化學梯度的變化而造成移動的過程。在半導體製程中，雜質濃度的多寡和擴散時間的長短是p-n接面形成的重要原因之一。在早期的電晶體和積體電路製造過程中，摻雜物的來源主要是來自於製造的材質上，但是，最近這幾年，離子佈植儼然成為半導體製程的主要方法之一。隨著元件製造越來越小，擴散和離子佈植也相對地複雜。因此，為了精確的控制，模擬製程的工具更是需要。 在這論文中，我們將會探討：(a)在半導體製程中相關的數學模型；(b)利用有限插分法來分析1-D的擴散方程，以及展示模擬的結果；(c)有限插分法分析2-D的擴散方程，以及展示模擬的結果。

Diffusion is the process by which a species moves as a result of the presence of a chemical gradient. The diffusion of controlled impurities or dopants into Si is the basis of p-n junction formation and device fabrication in semiconductor processing. In the early days of transistors and IC processing, dopants were supplied to the silicon by chemical sources. But more recently, ion implantation has become the major means for the semiconductor processing. As device features are continuously miniaturized, diffusion and implantation processes are increasingly complex. Consequently, simulation tools for the semiconductor process are more demanding. In this thesis, we will present: (a) the models which govern the mass transport phenomena of diffusion in semiconductor process; (b) FDM (Finite Difference Method) for 1-D diffusion equation (including processing algorithm and physical problem ); (c) FDM for 2-D diffusion equation (including processing algorithm and test models).