超薄金氧半結構電容-電壓與電流-電壓特性之量子力學模型與驗證

A Comprehensive Quantum-Mechanical Model for C-V and I-V Characteristics in Ultrathin MOS Structure and Experiment Verification

李建緯(Chien-Wei Lee)

指導教授 ： 胡振國

國立臺灣大學/電機資訊學院/電子工程學研究所/碩士(2013年)

https://doi.org/10.6342/NTU.2013.00240

摘要

本研究分為兩大部分。在第一部分中，提出了一個新的統計物理模型，用於計算二維電子氣之態密度，並提出較精準的表面位能近似方法，用於計算金氧半結構在積累、強反型區的量子效應。本研究使用指數函數來近似表面位能並解得表面量子化能階，此外，採用了不準確原理和動量空間中的薛定鍔方程來估算在二維、三維過渡區的態密度。模擬的結果顯示出我們所提出的近似方法以及態密度理論可以有效的解決先前研究的兩大問題：因為使用線性函數來近似表面位能所造成不可忽略的誤差，以及由二維態密度過渡到三維態密度中所產生的態密度以及電荷濃度分佈的不一致性。
　　在第二部分，我們透過實驗量測出不同氧化層厚度的超薄金氧半結構的電容-電壓和電流-電壓特性曲線。超薄氧化層結構中的氧化層是由陽極氧化法生長，而厚度之測定是藉由對比量測所得的電容-電壓曲線與理論的電容-電壓特性曲線，其氧化層厚度介於1.8奈米到2.8奈米之間。而在另一方面，自撰程式模擬的電容-電壓與電流-電壓特性，主要是基於以下原則：1.應用本研究第一部分提出之理論 2.用修改過的Tsu-Esaki模型計算氧化層穿隧電流 3.計算出不同閘極偏壓時，準費米能階與熱平衡費米能階的能量差異，從而算出複合-產生電流 4.考慮閘極周圍的邊際電場效應。模擬的結果與實驗對照顯示出我們的理論模型成功的解釋了超薄金氧半結構的電容-電壓與電流-電壓特性曲線。這是世界上能第一個可以定性說明並量化模擬超薄金氧半結構的的深空乏電容-電壓關係與其特殊的電流-電壓特性曲線的研究。

關鍵字

金氧半結構 ； 表面量子化 ； 不準確原理 ； 穿隧電流

並列摘要

This research is divided into two parts. In the first part, we derive a new statistical physics model of two-dimensional electron gas (2DEG) and propose an accurate approximation method for calculating the quantum-mechanical effects of metal-oxide-semiconductor (MOS) structure in accumulation and strong inversion regions. We use an exponential surface potential approximation in solving the quantization energy levels and derive the function of density of states in 2D to 3D transition region by applying uncertainty principle and Schrodinger equation in k-space. The simulation results show that our approximation method and theory of density of states solve the two major problems of previous researches: the non-negligible error caused by the linear potential approximation and the inconsistency of density of states and carrier distribution in 2D to 3D transition region.
In the second part, we extracted the C-V and I-V data of the ultrathin MOS structures with different oxide thicknesses from experiments. The oxide layer of the ultrathin MOS capacitors are grown by anodic oxidation (ANO), and the physical thickness of the oxide layer is 1.8nm~2.8nm, which is estimated by fitting C-V curves with theoretical data of previous researches. On the other hand, the simulated C-V and I-V curves are obtained by: 1. applying the theories established in the first part, 2. calculating the tunneling current by a modified Tsu-Esaki model, 3. estimating the energy difference between electron quasi-Fermi level and hole quasi-Fermi level and the generation-recombination current, 4. considering the fringing field effect at the edge of the electrode. The results show that our model successfully explain the differences laid in MOS C-V and I-V characteristics with different doping types of substrates. This is the first research in the world which both qualitatively and quantitatively explains the deep-depletion C-V curves in leaky MOS cases and the unusual I-V characteristics of MOS(p) in reverse-biased region.

並列關鍵字

MOS structure ； Surface quantization ； Uncertainty principle ； Tunneling current

參考文獻

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