場效電晶體量子效應之半解析研究｜國立清華大學博碩士論文庫

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研究生：	吳柄宣 Wu, Pin-Hsuan
論文名稱：	場效電晶體量子效應之半解析研究 A Semi-Analytical Study of Quantum Effect in FETs
指導教授：	吳玉書 Wu, Yu-Shu
口試委員:	陳峰梧 Chen, Feng-Wu 葉昭輝 Yeh, Chao-Hui
學位類別：	碩士 Master
系所名稱：	電機資訊學院 - 電子工程研究所 Institute of Electronics Engineering
論文出版年：	2024
畢業學年度：	112
語文別：	中文
論文頁數：	35
中文關鍵詞：	數值模擬、量子效應、場效電晶體
外文關鍵詞：	numerical simulation, quantum effect, FETs
相關次數：	點閱：42 下載：0
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隨著 IC 元件尺寸的縮減，元件中的量子效應逐漸明顯。在此研究中，我們將使用一個半解析模型來研究奈米尺寸下場效電晶體所展現的量子現象。在垂直於電子傳輸的方向上將採用數值計算的方式，從非量子的古典帕松方程式出發，擴展到自洽的薛丁格–帕松方程式，再用量子井模型進行簡化；另一方面，在電子傳輸的方向上，將採用飄移擴散模型的解析解。研究結果顯示，該模型與 TCAD 程序（Silvaco）的模擬結果具有一致性。通過這個研究，可以在簡化的模型內，提供電晶體中量子相關的物理特性，並有助於元件的設計。

As the IC fabrication scales down, the quantum effects within the device become increasingly apparent. In this work, a semi-compact model is introduced to investigate the quantum phenomena exhibited by the nanoscale field-effect transistors (FETs). A compact model is applied in the transport direction while the numerical procedure is
implemented in the transverse direction. We start with the classical Poisson equation, extend it to the self-consistent Schrodinger-Poisson equation, and then simplify the quantum confinement using the quantum well model. On the other hand, a compact drift-diffusion model is implemented in the transport direction. The model shows good consistency with the simulation result of TCAD program (Silvaco). Through this study, quantum-related physical properties within transistors can be understood within a limited model, aiding in the design of the devices.

摘要 ------------------------------------------------------- i

Abstract -------------------------------------------------- ii

Outline -------------------------------------------------- iii

Chapter 1: Introduction ------------------------------------ 1

Chapter 2: The Classical Approach -------------------------- 3

1 Theoretic background of semiconductor devices ---------- 3
1.1 Carrier concentration -------------------------------- 3
1.2 Carrier transport ------------------------------------ 4
1.3 The Poisson’s equation and the boundary condition ---- 6

2 Solving Poisson’s equation ----------------------------- 8
2.1 Finite difference method ----------------------------- 8
2.2 Newton-Raphson method ------------------------------- 10
2.3 The initial guess ----------------------------------- 13

3 Numerical result -------------------------------------- 14
3.1 Conduction band edge and electron density ----------- 14
3.2 Drain current versus drain voltage ------------------ 16
3.3 Realistic consideration ----------------------------- 17
3.4 Voltage drop in the source and drain region --------- 19

Chapter 3: Modeling with quantum effect ------------------- 21

1 Quantum effect on carrier density --------------------- 21
1.1 Electrons in 2D ------------------------------------- 21
1.2 Effective mass in silicon --------------------------- 22

2 The Schrödinger equation ------------------------------ 23
2.1 The self-consistent Schrödinger-Poisson system ------ 23
2.2 Numerical result ------------------------------------ 25
2.3 Classical vs quantum models ------------------------- 27

3 The quantum well approximation ------------------------ 28
3.1 The quantum well and the perturbation theory -------- 28
3.2 Numerical result ------------------------------------ 31
3.3 Realistic consideration ----------------------------- 32

Chapter 4: Conclusion ------------------------------------- 34

References ------------------------------------------------ 35

                                

[1] Mohan Vamsi Dunga, “Nanoscale CMOS Modeling.”
[2] H. C. Pao and C. T. Sah, “Effects of diffusion currents on characteristics of metaloxide (insulator)-semiconductor transistors.”
[3] Chenming-Hu, “Modern Semiconductor Devices for Integrated Circuits.”
[4] G. Baccarani and S. Reggiani, "A compact double-gate MOSFET model
comprising quantum-mechanical and nonstatic effects."
[5] D. Ruić and C. Jungemann, "A self-consistent solution of the Poisson, Schrödinger
and Boltzmann equations by a full Newton-Raphson approach for nanoscale
semiconductor devices."
[6] S. Birner et al, “Modeling of Semiconductor Nanostructures with nextnano.”

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