量子修正模式在奈米級金屬氧化物半導體元件特性模擬之研究

Abstract

隨著半導體產業的發展，積體電路要求速度快、低功率、小面積，許多新元件結構用來替代單閘極金氧半場效電晶體 (Single-Gate MOSFET)，本論文中介紹了常見的兩種新結構元件：雙閘極金氧半場效電晶體 (Double-Gate MOSFET)、全閘極金氧半電晶體 (Gate-All-Around MOSFET或稱Surrounding-Gate MOSFET)，並將此兩種結構和絕緣式矽單閘極金氧半場效電晶體 (Single-Gate MOSFET Silicon-on-Insulator) 做物理特性和電特性的比較。當金氧半電晶體氧化層厚度低於三奈米 (3nm) 以下時，在氧化層和半導體接面處會有明顯量子化效應的產生，古典的模式用來計算電子特性已經失真，必須加入量子化修正模式來表現真實電子在半導體中運動行為和電位在整個半導體結構中的分佈。 水丁格-泊松 (Schrödinger-Poisson) 方程式包含了波動和粒子的二元性，可以真實描述半導體中電子的物理特性，進一步的可以探討電子分佈的機率和位置及電子濃度的分佈和大小。利用數值方法離散物理方程式寫入電腦程式疊代計算收斂出答案，更能有效率且準確的得到所要的結果。然而在計算二維 (Two-Dimensional) 和三維 (Three-Dimensional) 水丁格-泊松方程式時太過費時，我們引用了其他不同種的量子化修正模式來近似真實結果。其中密度梯度 (Density Gradient) 不僅迅速容易收斂，和水丁格-泊松方程式的真實描述比較也非常準確，吾人用此法做二維電性特性分析與不同半導體元件特性之比較。 經過程式模擬和特性分析，對於次二十奈米 (Sub-20nm) 全閘極金氧半電晶體在相同特性條件下和其他兩種奈米元件相比較物理特性，有較好的閘極控制通道能力、較大的電子遷移率、較高的電子濃度，較低的功率消耗。在電性特性比較方面，全閘極金氧半電晶體有較好的開/關電流比 (On/Off Current Ratio)，受比較小的汲極電壓所造成之能障降低效應 (Drain Induced Channel Barrier Height Lowing)，較低的次臨界震盪 (Subthreshold Swing)，及較小的臨界電壓 (Threshold Voltage) 變化。

Diverse device structures have been recently proposed explored, and found better characteristics than that of conventional used single-gate (SG) metal-oxide-semiconductor field-effect-transistors (MOSFETs). Among them, the double-gate (DG) MOSFETs and gate-all-around MOSFETs (GAA) have been paid of great interest in recent years. Comparing with the SG silicon-on-insulator (SOI), these structures suppress short channel effects, have high transconductance, and sustain subthreshold swing. They have a superior ability in channel control that drain induced channel barrier height lowing (DIBL), threshold voltage roll off, and off state leakage are greatly improved. We compare the electrical characteristics for the three structures by using the quantum-mechanical (QM) simulation. In this comparison, the different gate voltage, various oxide thickness, and different channel doping concentration are designed. A comprehensive comparison leads to a conclusion that MOSFETs with a gate oxide thinner than 3nm should be carefully corrected with QM model when modeling their physical transport phenomena. The three nanoscale structures SG, DG, and GAA are explored numerically with various theoretical approaches that have been considered to study the quantum confinement effects. Those are full quantum mechanical model (e.g. nonequilibrium Green’s function) and quantum corrections to the Boltzmann transport and classical drift-diffusion (DD) and hydrodynamic (HD) transport models. In the beginning of this work, a set of Schrödinger-Poisson equations has been applied to study the quantum effect in the inversion layers, but it is a time-consuming task in the application to realistic device two-dimensional (2D) and three-dimensional (3D) simulations. In considering with the computational efficiency and simplicity, other quantum correction models are more attractive and greatly used in industrial application. In comparison, the different quantum correction models such as the Hänsch, the modified local density approximation (MLDA), the density gradient (DG), and the effective potential (EP) model are introduced and studied. Comparing of the 2D electrical characteristics for the three structures, we use the DG method to calculate them. It is easy to converge and can be demonstrated good accuracy in physical characteristics. Finally, we get GAA has the best quality, high mobility, low threshold voltage, superior channel controllability.