矽奈米元件模擬器之發展

Abstract

目前，半導體元件製程技術不斷的進步，當元件尺寸小到奈米等級時，如何對元件中的載子運動做數值上的分析就顯得十分重要。在奈米尺寸等級的元件中，載子的傳輸行為必然與目前被廣泛採用於Technology Computer-Aided Design (TCAD)中的漂移–擴散電流模型(drift-diffusion model)有很大的不同。我們的目標是建立一組可以適用於奈米元件的新的載子運動模型(不同於漂移–擴散電流模型)，來描述奈米元件中的載子運動行為。在這篇論文中，我們會先回顧在元件模擬領域中會使用到的物理模型及常被使用的數值分析方法。透過歷史的回顧，我們可以對於現今的元件模擬器是如何運作的以及對它們在使用上的限制有更深入的了解。接著我們會以奈米元件的觀點來探討目前所採用之分析方法的優劣。 在載子傳輸的模型裡面，波茲曼方程式(Boltzmann transport equation)是最為普遍的描述方程。但是由於它同時包含了連續項與不連續項，導致我們無法直接求得其解。於是在漂移–擴散電流模型中使用了平均場近似(mean-field approximation)的假設來消除不連續項。在此篇論文，我們先回顧了半導體物理中基本的物理模型，接著討論不同的數值分析方法，如：有限差分離散法、Scharfetter-Gummel離散法、牛頓迭代法及Gummel迭代法。此外，我們會探討目前半導體元件物理的優缺點，接著討論對於開發通用奈米元件模擬器(General-Purpose Nano Device Simulator)的關鍵因素。在我接續的博士論文中，則會持續的開發通用奈米元件模擬器。

The computational study of electron devices physics is becoming more important, as the device scaling is advanced to lift the curtain on nano-devices technologies. The carrier transport phenomenon in nano-meter scaled devices (nano-devices) must be quite different from the drift-diffusion model which has played a central role of the Technology Computer-Aided Design (TCAD). Our final goal is to establish new device physics (beyond the drift-diffusion model) for the fundamental study of the carrier transport in nano-devices. In this thesis, we will review the history of the basic formulation and the numerical approaches of the device physics so far, which is useful to foreknow the essential ability of today’s device modeling, and briefly survey the perspective of the future device modeling. In particularly, the Boltzmann transport equation (BTE) is the most general equation in the history of the carrier transport study. Since BTE involves the discontinuous term that causes the equation unsolvable, the drift-diffusion model is established within the mean-field approximation for successfully removing this discontinuity [1]. In this thesis, we will review the physical model and the numerical recipes, such as the finite difference discretization, Scharfetter-Gummel discretization [2], Newton’s method, and Gummel’s iteration method [3]. In addition, we will discuss about the advantages and disadvantages of today’s device physics, and then to reveal a key point for General-Purpose Nano Device Simulator. In the PhD dissertation to be continued from this Master thesis, we will develop General-Purpose Device Simulator.