快速計算的二維反轉層模擬器

Abstract

在N型金屬氧化物場效電晶體，非均勻的運算格子間距中，透過牛頓-里曼的疊帶法來解薛丁格和波松方程式自洽。這目的是為了在奈米元件中，模擬比三角位能井近似來的更真實的物理環境，而模擬顯示與Schred軟體的結果是非常相近的。然而在P型金屬氧化物場效電晶體中，六層的kp模型在過去已經常被用在計算電洞的能帶與遷移率，包括應力與不同的晶向的效應。在此篇論文的研究中，我們介紹了一種新的模擬方法，透過kp的哈密爾敦矩陣來快速得到電洞的能帶結構。而為了確保我們研究的準確性，所以我們也建立了一個在反轉層中的簡單的遷移率模型，再進行在不同溫度下此模擬結果與實驗值比較。在這模型中我們考慮的機制有:聲學聲子散射、光學聲子散射與表面粗糙度散射。至於因為摻入雜質所產生的庫倫散射不在我們討論中。此外，我們也透過有效質量的方法，來萃取量子化的等效質量，至於能態密度的等效質量也將會與低溫Shubnikov-de Haas震盪實驗的數據互相比較。

Self-consistent solving of Schrődinger and Poisson equations in n-channel MOSFETs (metal-oxide-semiconductor field-effect transistors) is obtained by using Newton-Raphson iteration technique with the non-uniform mesh arrangement. The method is applied to simulate more realistic physical environment than triangular potential well approximation in nano devices. The simulation results show excellent agreements with Schred’s. However, in p-channel MOSFETs, a six-band model has been used to calculate hole subband structure and mobility for different surface orientations and different strains. In this work, we introduce a new efficient model based on six-band Hamiltonian to rapidly obtain accurate hole properties. In order to ensure the validity of our work, we build an effective mobility model in the hole inversion layer and compare the results with the experimental data concerning the universal curves at different temperatures. The different scattering mechanisms are included in this study: acoustic phonon scattering, optical phonon scattering and surface roughness scattering. To focus on the high surface field region, Coulomb scattering due to ionized impurities will be ignored. In addition, with the use of an equivalent effective mass model, the extracted quantization effective mass and density of states effective mass will be compared with low temperature (2 K) Shubnikov-de Haas oscillation experiment results published in the literature.