電子穿越肖基障之一致化模擬

Abstract

在此論文中我們已經發展一個數值模擬程式來探討電子穿越金屬版導體接面的現象。能障的分布在半導體的表面被適當地分成幾個小區塊，能障位能可近似一連串的線性區塊或階梯狀區塊。藉由airy function來解薛晶格方程式可以產生一個轉移矩陣來表示每一小區塊裡的電子傳輸現象。電子穿越整個接面能障的穿越係數可以每一小區塊的轉移矩陣相乘而得，並與傳統的WKB近似法所求的穿越係數做比較。 不論電子能量大於或小於接面能障，電子傳輸係數都可以被計算出來，所以我們首次提出電子穿越半導體表面及金屬半導體介面電子熱傳輸之一致化模擬。傳輸係數是金屬至半導體電子移轉機率的方程式，而越過肖基障的熱傳導電流可由經由對傳輸係數的積分而得。而電子穿越肖基障的電流則可以轉成電子電動的合併及產生過程，此一過程與半導體的費米能階與未能分佈有關。這電子穿越過程與半導體中電流的傳輸能自發性前後一致地連結起來。 在不同傳輸模型及不同參雜濃度下的傳輸係數與電子能量的相關性及熱傳導電流與外加偏壓的關係也在此論文中加以討論。

A numerical simulation program has been developed in this work to investigate the transmission of electrons through the metal-semiconductor contacts. The semiconductor surface is discretized properly into a number of small intervals and the potential barrier is approximated as a series of piece-wise linear or step functions. The transfer matrix for electron transmission through or cross each interval of simple potential distribution can be obtained by solving the Schrödinger equation using Airy or exponential function. The transmission coefficient of electrons through or across the whole contact barrier is then derived from the cascaded transfer matrices. As a comparison, the conventional WKB approximation method has also been illustrated. Since the transmission coefficient can be calculated numerically for electron with energy below or above the contact barrier, we propose, for the first time, a unified simulation for electron tunneling through the semiconductor surface and thermionic-emission at the metal-semiconductor interface. The thermionic-emission current across the Schottky barrier is integrated from the transmission coefficient, which is a function of electron energy together with the transition probability of electron between metal and semiconductor. However, the tunneling current through the Schottky barrier is converted into a local generation or recombination process with local rate depending on the local Fermi-level and the potential distribution. The tunneling processes are self-consistently treated with all current transport in the semiconductor. The transmission coefficient is a function of electron energy as well as the tunneling and thermionic-emission currents as a function of applied voltage for different transmission models and various doping concentrations has been discussed in this paper.