隨著這些年量子運算的快速發展，量子運算已經變成世界上熱門的研究主題。在包括工程、生物科技、財經科技、人工智慧、醫療科技等領域之中，量子運算和傳統電腦相比，有機會能以更有效率的方式解決日益複雜的數值、物理問題。

在不同的物理系統中，採用了先進的半導體技術之矽自旋量子位元（量子位元）成為最有潛力實現量子計算機的發展、增加量子位元數量的選項之一。為了在量子處理器核心上執行初始化，操作和讀取，成熟的CMOS技術已被視為控制器的最佳選項。因此在近年來對於低溫CMOS的元件和行為之研究已成為熱門的研究主題。

在這篇碩士論文之中，我們會使用以雙閘極電晶體(DGMOSFET)作為元件結構，並以Sentaurus TCAD simulator進行元件模擬。而由於在超低溫下會導致極端小的本質濃度，因此在計算上容易遭遇到嚴重的收斂問題。我們在此篇碩士論文中，會介紹包括低溫物理模型和用以強化收斂性的數學模型。在物理模型中，不同的載子傳輸方程式會被討論，包含飄移擴散模型(Drift-diffusion model)和流體力學模型(Hydrodynamic model)，並且我們會比對從常溫到超低溫下的電流電壓特性、晶格溫度、載子溫度等趨勢。在論文最後，晶格溫度和載子溫度分佈中的尖端飄移現象會被著重討論，這些結果將會成為超低溫下電性的物理基礎。

From the rapid improvement and progress of quantum computing in recent years, it has grown up to be a popular and important research topic. For many scientific research domains, e.g., engineering, biology, finance, artificial intelligence, and medical science, quantum computing may be favorable to solve computationally expensive problems in a relatively shorter time than classical computers.
Among various physical systems, thanks to sophisticated semiconductor technology, the silicon spin qubit (quantum bit) is one of the most promising candidates realizing the quantum computer with the potential to increase the number of qubits. To perform initialization, manipulation, and readout of individual qubits at the core of a quantum processor, mature CMOS technology has been recognized as the best electronic controller. Consequently, the study of the behavior of cryogenic CMOS, or cryo-CMOS has become a popular research topic in recent years.
In this master thesis, we use a two-dimensional double gate MOSFET (DGMOSFET) as the device structure and self-consistently calculate the electrical characteristics with the Sentaurus TCAD simulator. Because of the tiny values of intrinsic carrier concentration, numerical simulation at low temperature encounters serious convergence issues. We will introduce the cryogenic physical models, and math models employed in the simulation will be detailed as well, which are essential for solving convergence problems. For physical models, the different carrier transport models will be discussed, including the drift-diffusion model and the hydrodynamic model. We compare the current-voltage characteristics, lattice temperatures, and carrier temperature distribution from room temperature to cryogenic temperatures. Furthermore, the peak shift in lattice temperature and peak shift in carrier temperature would be discussed. These results will be evident in the cryogenic electrical property of the device and will pave the way towards future quantum computing study.

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Reference in chapter 3
[28] BAND-TO-BAND TUNNELING MODEL CALIBRATION AND DESIGN OPTIMIZATION OF GROUP IV TUNNEL-FETS, Frank Kao