馬西森定則在金氧半場效電晶體電子通用遷移率造成的誤差並其修正

Abstract

本篇論文主旨係分析利用馬西森定則計算使用平面場效電晶體量子模擬器模擬得到的電子通用遷移率與使用馬西森定則計算萃取的電子通用遷移率之間的誤差。此研究方法主要專注於高電場區域，通用的遷移率含有兩種不同的散射機制(1)聲子散射所造成的遷移率與(2)表面粗糙度散射所造成的遷移率。通過實驗驗證組成的自洽求解薛丁格方程式與卜松方程式以及通用遷移率的模擬程式的使用，我們嘗試修正使用馬西森定則來求得金氧半場效電晶體的遷移率所造成的實驗誤差。而此修正過的定則的核心在於物理的半經驗模型，並且可以使用最低能帶的佔有率與各個遷移率的組成來明確表示使用傳統馬西森定則所造成的誤差。此新的模型可以在實際的條件下成立(溫度高達400K)並且可應用在廣泛的基底摻雜濃度(1014 to 1018 cm-3)。另外，也可以延伸應用到500MPa單軸拉應力下。

An analysis of the errors caused by Matthiessen’s rule between the apparent universal mobility which is calculated by Matthiessen’s rule and the simulated universal mobility curves are presented in this thesis. To focus on the high surface field region, the universal mobility features two distinct scattering mechanisms: one of phonon alone and one of surface roughness alone. By means of the experimentally-validated simulation package consisting of a self-consistent solving of Schrődinger and Poisson’s equations and a universal mobility simulation program, we try to correct the experimental error of applying Matthiessen’s rule to MOSFET mobility universality. Thus, the aim of this work is to devise an error-free version of Matthiessen’s rule. The core of the new rule lies in a physically- based semi-empirical model, which explicitly expresses the errors due to the conventional use of Matthiessen’s rule as a function of both the lowest subband population and the relative strength of individual mobility components. The new model holds under practical conditions (with temperatures up to 400 K) and in a broad range of substrate doping concentrations (1014 to 1018 cm-3). Extension to the case of strain is also presented in terms of a uniaxial tensile stress of 500 MPa.