半導體元件暫態模擬之研究

Abstract

採用有限差分法而寫的元件模擬程式已經發展而成. 由此程式, 在穩態及 暫態條件下, 一維和二維PN接面二極體的電位和電流之數值計算已被求 得.本文中, 也將說明不同的系統方程組離散化的方法與解法.我們發現新 提出的剩餘誤差方法和共軛誤差方法,與原有的ICCG方法比較,明顯有著快 速的收斂速度與較少的記憶體需求之優點. 在暫態模擬中, 捕獲率方程式 已經引入傳統的半導體方程式中, 同時也和傳統的穩態複合率比較. 結果 得知, 方程式中之淨複合率項並沒有太大的影響於PN二極體上. 此外,加 入捕獲率方程式於半導體方程式中也導致較高的計算成本. 隨著積體電路 複雜度的快速進展, 本文提供給半導體元件在穩態和暫態情況下前後一致 的模擬方法而有助於元件特性的分析. A complete device simulation program based on the finite difference method is developed and the numerical calculations of potentials and currents in one- and two-dimensional pn junction under steady-state and transient conditions is performed. Various discretization and solution methods are described. It is found that the newly proposed methods, such as Residual Error and Conjugate Error, have the advantages of fast convergence speed and less memory requirement as compared with the original ICCG method. The trapping rate equation has been included and compari- son has been made with the conventional steady-state recombina- tion rate in the transient simulation. The net recombination term contributes very little effect on a pn diode. Moreover, the system of four equations results in more computational cost. With the advance of increasingly complex integrated circuits, this thesis provides a self- consistent simulation method for semicon- ductor devices under steady-state and transient conditions to benefit the characteristic analysis of devices.