矽奈米元件量子修正理論暨模式應用比較之研究

Abstract

隨著摩爾定律的趨勢，快速省電的要求，積體電路上的晶片將逐年縮小，現今工業界所量產的65奈米製程技術所製作的金氧半場效電晶體其閘極長度已接近次45奈米世代的試產進程，其中閘極氧化層厚度趨近1奈米。因此不同程度的量子效應已變顯著，半導體傳輸模式必須考慮此問題，量子修正的研究有助於電晶體的分析。 本論文完整介紹隱形式與顯形式的量子修正模式，其中顯形式模式包含Van Dort’s、Hänsch’s、Li’s、修正的局部密度趨近與有效位勢模式；隱形式模式分析了密度梯度方程式、修正的密度梯度方程式與熱力學有效位勢模式。論文中從理論推演以及數值分析方面仔細比較這些模式的優劣之處。量子修正模式中電子有效質量通常視為可調的數學參數，找出在不同的外加條件下所需要代入的數值對於半導體工業應用非常有利，尤其是顯形式模式更於容易使用。在應用上來說，吾人利用量子修正模式研究一維金氧半結構的電容特性以及考慮二維效應所影響的電流電壓關係式。 總之，本論文已從理論暨數值方向分析不同量子修正方法論的物理模式暨在金氧半場效電晶體應用之準確性。

By the Moore's Law, chips manufactured on a wafer have approached sub-45 nm regime of gate length for metal-oxide-semiconductor-field-effect-transistors (MOSFETs). Quantum mechanics effects become significant and inevitable. Thus, the transport models used in semiconductors should be corrected by quantum correction models. In this thesis, explicit and implicit quantum correction models are introduced and reviewed completely. There are Van Dort's, Hänsch's, Li’s modified local density approximation (MLDA) and effective potential (EP) models in explicit forms; density-gradient (DG), modified density-gradient, thermodynamic effective potential models are in implicit forms. We compare these models with each other in terms of theoretical and numerical ways respectively. To find the relationship between the effective mass which is treated as fitting parameters in the models with varied physical settings is benefit for industry applications, especially the explicit models, they are simple to be implanted in the simulator. In application, C-V characteristics of a MOS structure and IV curves of a 20 nm double-gate MOSFET are numerically investigated in the work.