簡易檢索 / 詳目顯示

研究生: 張淵智
Chang, Yuan-Chih
論文名稱: 基於頂閘極二維材料電晶體物理建模驗證應用於電流電壓之特性分析
Physics-Based Modeling and Validation of Top-Gated 2D FETs for Analytical Current-Voltage Characteristics
指導教授: 葉昭輝
Yeh, Chao-Hui
口試委員: 吳玉書
呂寧遠
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: 72
中文關鍵詞: 二維材料物理模型二硫化鉬帕松方程飄移擴散方程
外文關鍵詞: 2D materials, physical model, Molybdenum disulfide, Poisson equation, drift diffusion equation
相關次數: 點閱:35下載:0
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報
  • 二維材料因結構與電性特殊,已經有諸多二維材料在電晶體相關的研究,本次研究目的在模擬以二硫化鉬(MoS2)作為通道材料的頂閘極電晶體,建立物理模型用於模擬電晶體的電流與電壓特性,過程使用Matlab 進行數值計算,利用牛頓–拉弗森法求解帕松方程以及飄移擴散模型,將此半經典模型與接面穿隧模型結合,來考慮蕭特基接觸對電流的影響,最後評估模型的合理性,再與我們實驗室的實驗數據進行對比分析。


    The unique structural and electrical properties of two-dimensional
    materials have led to extensive research on various two-dimensional materials transistors. The study aims to simulate a top-gate transistor using Molybdenum disulfide (MoS2) as the channel material and establish a physical model for simulating the current-voltage characteristics of the transistor. Numerical calculations were performed using Matlab, and the Newton-Raphson method was employed to solve the Poisson equation and drift-diffusion model. This semi-classical model was then combined with the junction tunneling model to account for the impact of Schottky contacts on the current. Finally, the reasonableness of the model was evaluated and compared with experimental data from our
    laboratory for analysis.

    摘要-----------------------------------i 目錄----------------------------------vi 表目錄--------------------------------vii 圖目錄---------------------------------x 1 導論---------------------------------1 1.1 電晶體發展--------------------------1 1.2 二維材料簡介------------------------2 1.2.1 石墨烯----------------------------3 1.2.2 過渡金屬二硫族化物-----------------5 1.3 二硫化鉬 vs 矽----------------------8 1.4 二維材料電晶體----------------------10 1.5 研究動機----------------------------12 2 電晶體之靜電位勢----------------------14 2.1 元件結構----------------------------14 2.2 帕松方程式--------------------------15 2.3 離散化帕松方程----------------------16 2.4 德拜長度 (LD)-----------------------18 2.5 載子濃度----------------------------19 2.6 邊界條件 (V )-----------------------20 3 載子飄移擴散模型-----------------------22 3.1 連續方程----------------------------22 3.2 愛因斯坦關係式-----------------------23 3.3 離散化飄移擴散方程-------------------24 3.4 散射機制----------------------------25 3.5 邊界條件 (ϕ)------------------------28 3.6 理想金屬接觸-------------------------30 4 蕭特基位障-----------------------------31 4.1 蕭特基接觸---------------------------31 4.2 費米能階釘扎-------------------------32 4.3 接面穿隧模型-------------------------34 4.4 量子穿隧機率-------------------------36 5 數值分析-------------------------------39 5.1 有限差分法---------------------------39 5.2 牛頓-拉弗森法------------------------40 6 結果討論-------------------------------43 6.1 元件設定-----------------------------43 6.2 分析---------------------------------45 6.2.1 理想接觸---------------------------45 6.2.2 蕭特基接觸--------------------------50 6.3 實驗對比-----------------------------56 7 總結與展望------------------------------59 附錄-------------------------------------60 A.1 特徵長度 (Scale length)---------------60 A.2 等效狀態密度--------------------------61 A.3 矩陣算符------------------------------62 A.3.1 二階微分算符------------------------62 A.3.2 狄利克雷----------------------------63 A.3.3 諾伊曼------------------------------63 A.4 波茲曼傳輸方程-------------------------64 A.5 收斂誤差------------------------------65 A.6 理查係數------------------------------65 參考文獻----------------------------------67

    [1] S.M. Sze. Semiconductor Devices: Physics and Technology. John Wiley & Sons Singapore Pte. Limited, 2012.
    [2] A. Onyia, H.I. Ikeri, and A. Nwobodo. Theoretical study of the quantum confinement effects on quantum dots using particle in a
    box model. Journal of Ovonic Research, 14:49–54, 01 2018.
    [3] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V.
    Dubonos, I.V. Grigorieva, and A.A. Firsov. Electric field effect in
    atomically thin carbon films. Science, 306(5696):666–9, 2004.
    [4] L. Banszerus, M. Schmitz, S. Engels, J. Dauber, M. Oellers, F. Haupt, K. Watanabe, T. Taniguchi, B. Beschoten, and C. Stampfer. Ultrahigh-mobility graphene devices from chemical vapor deposition on reusable copper. Science Advances, 1:e1500222, 2015.
    [5] D.C. Elias, R.V. Gorbachev, A.S. Mayorov, S.V. Morozov, A.A. Zhukov, P. Blake, L.A. Ponomarenko, I.V. Grigorieva, K.S. Novoselov, F. Guinea, and A.K. Geim. Dirac cones reshaped by interaction effects in suspended graphene. Nature Physics, 7(9):701– 704, July 2011.
    [6] A.V. Kolobov and J. Tominaga. Two-Dimensional Transition Metal Dichalcogenides. Springer Cham, 2016.
    [7] V.K. Sangwan and M.C. Hersam. Electronic transport in two- dimensional materials. In M. A. Johnson and T. J. Martinez, editors, Annual Review of Physical Chemistry, volume 69, pages 299–325. Annual Reviews, 2018.
    [8] R. Shankar. Principles of Quantum Mechanics. Springer, 1994.
    [9] J.W.G. van den Berg, S. Nadj-Perge, V.S. Pribiag, S.R. Plissard,
    E.P.A.M. Bakkers, S.M. Frolov, and L.P. Kouwenhoven. Fast spin-orbit qubit in an indium antimonide nanowire. Physical Review Letters,
    10(6), February 2013.
    [10] T.Y. Wei, Z.C. Han, X.Y. Zhong, Q.Y. Xiao, T. Liu, and D. Xiang.
    Two dimensional semiconducting materials for ultimately scaled transistors. Iscience, 25(10):27, 2022.
    [11] Y. Liu, X. Duan, H.J. Shin, S. Park, Y. Huang, and X. Duan. Promises and prospects of two-dimensional transistors. Nature, 591:43–53, 03 2021.
    [12] W.S. Li, X.S. Gong, Z.H. Yu, L. Ma, W.J. Sun, S. Gao, Ç Köroglu,
    W.F. Wang, L. Liu, T.T. Li, H.K. Ning, D.X. Fan, Y.F. Xu, X.C. Tu, T. Xu, L.T. Sun, W.H. Wang, J.P. Lu, Z.H. Ni, J. Li, X.D. Duan, P. Wang, Y.F. Nie, H. Qiu, Y. Shi, E. Pop, J.L. Wang, and X.R. Wang. Approaching the quantum limit in two-dimensional semiconductor contacts. Nature, 613(7943):274–279, 2023.
    [13] R.H. Yan, A. Ourmazd, and K.F. Lee. Scaling the si mosfet from bulk to soi to bulk. Ieee Transactions on Electron Devices, 39(7):1704–1710, 1992.
    [14] M.D. Siao, W.C. Shen, R.S. Chen, Z.W. Chang, M.C. Shih, Y.P. Chiu, and C.M. Cheng. Two-dimensional electronic transport and surface electron accumulation in mos2. Nature Communications, 9:1442, 2018.
    [15] J.R. Nagel. Numerical solutions to poisson equations using the
    finite-difference method. Ieee Antennas and Propagation Magazine, 56(4):209–224, 2014.
    [16] A.R. Bechhofer, A. Ueda, A. Nipane, and J.T. Teherani. The 2d
    debye length: An analytical study of weak charge screening in 2d semiconductors. Journal of Applied Physics, 129(2):10, 2021.
    [17] D.A. Neamen. Semiconductor Physics and Devices: Basic Principles. McGraw-Hill, 2012.
    [18] S. Selberher. Analysis and simulation of semiconductor devices. In Proceedings of the Conference Name, Year.
    [19] M. Lundstrom. Fundamentals of Carrier Transport. Cambridge University Press, 2 edition, 2000.
    [20] H. Beirão da Veiga. On the semiconductor drift diffusion equations.
    Differential and Integral Equations, 9, 1996.
    [21] X.W. Jia, H.B. An, Y. Hu, and Z.Y. Mo. A physics-based strategy for choosing initial iterate for solving drift-diffusion equations.
    Computers & Mathematics with Applications, 131:1–13, 2023.
    [22] H.M. Alan and A. David. A generalized einstein relation for semiconductors. Solid-State Electronics, 16(6):675–679, 1973.
    [23] J.M. Gonzalez-Medina, F.G. Ruiz, E.G. Marin, A. Godoy, and
    F. Gámiz. Simulation study of the electron mobility in few-layer
    mos2 metal-insulator-semiconductor field-effect transistors. Solidstate Electronics, 114:30–34, 2015.
    [24] K. Kaasbjerg, K.S. Thygesen, and K.W. Jacobsen. Phonon-limited
    mobility in n-type single-layer mos2 from first principles. Physical Review B, 85(11):16, 2012.
    [25] N. Ma and D. Jena. Charge scattering and mobility in atomically thin semiconductors. Physical Review X, 4(1):9, 2014.
    [26] D. Esseni, P. Palestri, and L. Selmi. Nanoscale MOS Transistors: Semi-Classical Transport and Applications. Cambridge University Press, 2011.
    [27] C. Kim, I. Moon, D. Lee, M.S. Choi, F. Ahmed, S. Nam, Y. Cho,
    H.J. Shin, S. Park, and W. Yoo. Fermi level pinning at electrical
    metal contacts of monolayer molybdenum dichalcogenides. ACS Nano, 11, 2017.
    [28] R. Islam, G. Shine, and K. Saraswat. Schottky barrier height reduction for holes by fermi level depinning using metal/nickel oxide/
    silicon contacts. Applied Physics Letters, 105:182103, 2014.
    [29] X. Liu, M.S. Choi, E. Hwang, W. Yoo, and J. Sun. Fermi level pinning dependent 2d semiconductor devices: Challenges and prospects. Advanced Materials, 34:2108425, 2022.
    [30] K. Sotthewes, R. van Bremen, E. Dollekamp, T. Boulogne, K. Nowakowski, D. Kas, H.J.W. Zandvliet, and P. Bampoulis. Universal fermi-level pinning in transition-metal dichalcogenides. Journal of Physical Chemistry C, 123(9):5411–5420, 2019.
    [31] M. Ieong, P.M. Solomon, S.E. Laux, H.S.P. Wong, and D. Chidambarrao. Comparison of raised and schottky source/drain MOSFETs using a novel tunneling contact model. In IEEE International Electron Devices Meeting (IEDM), pages 733–736. IEEE, 1998.
    [32] H. Fu, J.X. Wei, Z.X. Wei, S. Li, L. Zhang, S. Bai, R.H. Huang,
    X.L. Yang, S.Y. Liu, and W.F. Sun. Theory and design of novel power poly-si/sic heterojunction tunneling transistor structure. Ieee Transactions on Electron Devices, 70(11):6086–6092, 2023.
    [33] T.M. Abdolkader, A. Shaker, and A.N.M. Alahmadi. Numerical
    simulation of tunneling through arbitrary potential barriers applied
    on mim and miim rectenna diodes. European Journal of Physics, 39(4):24, 2018.
    [34] A. Sidi. Unified treatment of regula falsi, newton-raphson, secant, and steffensen methods for nonlinear equations. Some Journal
    Name, 10(2):1–13, 2006.
    [35] T. Cheiwchanchamnangij and W.R.L. Lambrecht. Quasiparticle band structure calculation of monolayer, bilayer, and bulk mos2. Physical Review B, 85(20):4, 2012.
    [36] U. Bhanu, M.R. Islam, L. Tetard, and S.I. Khondaker. Photoluminescence quenching in gold - mos2 hybrid nanoflakes. Scientific Reports, 4:5, 2014.
    [37] K.K.H. Smithe, C.D. English, S.V. Suryavanshi, and E. Pop. High- field transport and velocity saturation in synthetic monolayer mos2. Nano Letters, 18(7):4516–4522, 2018. PMID: 29927605.
    [38] K.S. Novoselov, D. Jiang, F. Schedin, T.J. Booth, V.V. Khotkevich,
    S.V. Morozov, and A.K. Geim. Two-dimensional atomic crystals. Proc Natl Acad Sci U S A, 102(30):10451–3, 2005.
    [39] S.S. Li. Semiconductor Physical Electronics. Springer New York,
    2007.
    [40] C.R. Crowell. The richardson constant for thermionic emission in
    schottky barrier diodes. Solid-state Electronics, 8:395–399, 1965.
    [41] R. Tsu and L. Esaki. Tunneling in a finite superlattice. Applied
    Physics Letters, 22(11):562–564, 06 1973.

    QR CODE