請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/16183完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 楊照彥 | |
| dc.contributor.author | Kuan-Ho Lao | en |
| dc.contributor.author | 勞冠豪 | zh_TW |
| dc.date.accessioned | 2021-06-07T18:04:09Z | - |
| dc.date.copyright | 2012-08-09 | |
| dc.date.issued | 2012 | |
| dc.date.submitted | 2012-07-27 | |
| dc.identifier.citation | [1] Abramowitz, M. & Stegun, I. A. (1964) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York, ninth dover printing, tenth gpo printing edition.
[2] Alekseenko, A. M., (2011) “Numerical properties of high order discrete velocity solutions to the BGK kinetic equation”, Applied Numerical Mathematics, 61, pp. 410–427. [3] Anile, M. A., Carrillo J. A., Gamba, I. M. & Shu, C. W., (2001) “Approximation of the BTE by a Relaxation-time Operator: Simulations for a 50 nm-channel Si Diode”, VLSI Design, 13, pp. 349-354. [4] Barenger, H. U. & Wilkins, J. W., (1987) “Ballistic structure in the electron distribution function of small semiconducting structures: General features and specific trends” Physical Review B, 36, pp. 1487-1502. [5] Bird, G. A., (1994) Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Clarendon Press Oxford. [6] Blotekjaer, K., (1970) “Transport equations for electrons in two-valley semiconductors”, IEEE Transactions on Electron Devices, 17, pp. 38-47. [7] Carrillo, J. A., Gamba, I. M. & Shu, C. W., (2000) “Computational macroscopic approximations to the 1-D relaxation-time kinetic system for semiconductors”, Physica D, 146, pp. 289–306. [8] Carrillo, J. A., Gamba, I. M., Majorana A. & Shu, C. W., (2003) “A WENO-solver for the transients of Boltzmann–Poisson system for semiconductor devices: performance and comparisons with Monte Carlo methods”, Journal of Computational Physics, 184, pp. 498–525. [9] Cercignani, C., Gamba, I.M., Jerome, J.W. & Shu, C. W., (2000) “Device benchmark comparisons via kinetic, hydrodynamic, and high-field models”, Computer Methods in Applied Mechanics and Engineering, 181, pp. 381-392. [10] Chen, D., Kan, E. C., Ravaioli, U., Shu, C. W. & Dutton, R. W., (1992) “An improved energy transport model including nonparabolicity and non-Maxwellian distribution effects”, IEEE Electron Device Letters, 13, pp. 26-28. [11] Chen, G., (2005) Nanoscale Energy Transport and Conversion, Oxford University Press. [12] Csontos, D. & Ulloa, S. E., (2004) “Modeling of Transport Through Submicron Semiconductor Structures:A Direct Solution to the Coupled Poisson-Boltzmann Equations”, Journal of Computational Electronics, 3, pp. 215-219. [13] Fatemi, E. & Odeh, F., (1993) “Upwind finite difference solution of Boltzmann equation applied to electron transport in semiconductor devices”, Journal of Computational Physics, 108, pp. 209. [14] Fischetti, M. V. & Laux, S. E., (1988) “Monte Carlo analysis of electron transport in small semiconductor devices including band-structure and space-charge effects”, Physical Review B, 38, 9721. [15] Gardner, C. L., (1991) “Numerical Simulation of a Steady-State Elctron Shock Wave in a Submicrometer Semiconductor Device”, IEEE Transactions on Electron Devices, 38, pp. 392–398. [16] Harten, A., Engquist, B., Osher, S. & Chakravarthy, S., (1987) “Uniformly high order essentially non-oscillatory schemes, III”, Journal of Computational Physics, 71, pp. 231-303. [17] Jerome, J. W., (1996) Analysis of Charge Transport; A Mathematical Study of Semiconductor Devices, Springer. [18] Liu, X. D., Osher, S. & Chan, T., (1994) “Weighted Essentially Nonoscillatory Schemes,” Journal of Computational Physics, 115, pp. 200-212. [19] Lundstrom, M., (2000) Fundamentals of Carrier Transport, Cambridge University Press. [20] Majorana, A. & Pidatella, R. M., (2001) “A finite difference scheme solving the Boltzmann-Poisson system for semiconductor devices”, Journal of Computational Physics, 174, pp. 649-668. [21] Masyukov, N. A., & Dmitriev, A. V., (2011) “A new numerical method for the solution of the Boltzmann equation in the semiconductor nonlinear electron transport problem”, Journal of Mathematical Sciences, 172, pp. 811-823. [22] Muljadi, B. P., Yang, J. Y. (2010) “A direct Boltzmann-BGK equation solver for arbitrary statistics using the conservation element/solution element and discrete ordinate method”, Kuzmin, A. (ed.) Computational Fluid Dynamics 2010, pp. 637–642. [23] Muljadi, B. P., Yang, J. Y. (2011) “Simulation of Shock Wave Diffraction over 90° Sharp Corner in Gases of Arbitrary Statistics”, Journal of Statistical Physics, 145, pp. 1674-1688. [24] Shi, Y. H., Huang, J. C. & Yang, J. Y., (2007) “High Resolution Kinetic Beam Schemes in Generalized Coordinates for Ideal Quantum Gas Dynamics”, Journal of Computational Physics, 222, pp. 573-591. [25] Shu, C. W., (1997) “Essential Non-Oscillatory and Weighted Essential Non-Oscillatory Schemes for Hyperbolic Conservation Laws”, ICASE Report, pp. 97-65. [26] Shu, C. W. & Osher, S., (1988) “Efficient Implementation of Nonoscillatory Shock Capturing Schemes”, Journal of Computational Physics, 77, pp. 439-471. [27] Shu, C. W. & Osher, S., (1989) “Efficient Implementation of Nonoscillatory Shock Capturing Schemes II”, Journal of Computational Physics, 83, pp. 32-78. [28] Uehling, E. A. & Uhlenbeck, G. E., (1933) “Transport phenomena in einstein-bose and Fermi-dirac gases, I”, Physical Review, 43, pp. 553-561. [29] van Leer, B., (1979) “Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov’s method ” Journal of Computational Physics, 32, pp. 101–136. [30] Yang, J. Y., Hsieh, T. Y. & Shi, Y. H., (2007a) “Kinetic Flux Splitting Schemes for Ideal Quantum Gas Dynamics” , SIAM Journal on Scientific Computing, 29, pp. 221-244. [31] Yang, J. Y., Hsieh, T. Y., Shi, Y. H. & Xu, K., (2007b) “High Order Kinetic Flux Vector Splitting Schemes in General Coordinates for Ideal Quantum Gas Dynamics”, Journal of Computational Physics, 227, pp. 967-982. [32] 謝澤揚 (2007) 聲子熱傳輸與理想量子氣體動力學之高解析算則，國立台灣大學工學院應用力學所博士論文，台北。 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/16183 | - |
| dc.description.abstract | 本文利用直接數值方法求解半古典的Boltzmann-BGK(Bhatnagar-Gross-Krook)方程與Poisson方程組成的系統以模擬電子在半導體裝置中的傳輸行為。數值方法方面，使用離散座標法(Discrete Ordinate Method)以及高解析算則如全變量消逝法(Total Variation Diminishing, TVD)和加權型基本不振盪(Weighted Essentially Non-Oscillatory, WENO)算則。算則將電子當作遵守Maxwell-Boltzmann統計以及Fermi-Dirac統計的粒子來模擬一維電子流動行為。本文使用不同的電子移動率(Mobility)假設來得到不同的鬆弛時間近似。最後再比較施加不同偏壓下的電子流動行為。 | zh_TW |
| dc.description.abstract | The electron transport in semiconductor devices is simulated by using direct algorithm for solving the semiclassical Boltzmann-BGK equation coupled with Poisson equation. The numerical method is based on the discrete ordinate method and high-resolution methods such as TVD (Total Variation Diminishing) method and WENO (Weighted Essentially Non-Oscillatory) method. The algorithm is implemented for solving one-dimensional electron flow that treats electron as particles obey the Maxwell-Boltzmann and Fermi-Dirac statistics. In this paper, using different mobility model to obtain different relaxation time approximation. Finally, simulating the electron flow under different voltage bias for comparison. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-07T18:04:09Z (GMT). No. of bitstreams: 1 ntu-101-R99543079-1.pdf: 3846346 bytes, checksum: bdc4415aa259f3614046edb39d2f226b (MD5) Previous issue date: 2012 | en |
| dc.description.tableofcontents | 誌謝 I
摘要 II ABSTRACT III 目錄 IV 附表目錄 VI 附圖目錄 VII 第一章 緒論 1 1.1 引言 1 1.2 金氧半場效電晶體簡介 2 1.3 文獻回顧 3 1.4 本文架構 4 第二章 BOLTZMANN 方程 7 2.1 氣體運動理論 7 2.2 LIOUVILLE 方程 9 2.3 BOLTZMANN 方程 10 2.4 鬆弛時間近似 12 2.5 連續體模型方程 13 2.6 電子傳輸方程 15 第三章 半古典BOLTZMANN方程 18 3.1 三種統計 18 3.2 半古典BOLTZMANN-BGK方程 19 3.3 半古典電子運動模型 21 第四章 數值方法 24 4.1 離散座標法 24 4.2 空間離散 26 4.2.1 中央差分法 26 4.2.2 迎風算則 27 4.2.3 高解析算則 28 4.3 時間離散 38 4.4 疊代法 39 4.5 初始和邊界條件 41 4.6 無因次化 43 第五章 數值模擬結果與討論 48 第六章 結論與展望 79 6.1 結論 79 6.2 展望 80 參考文獻 81 | |
| dc.language.iso | zh-TW | |
| dc.subject | 加權型基本不振盪算則 | zh_TW |
| dc.subject | 電子傳輸 | zh_TW |
| dc.subject | 半古典Boltzmann-BGK方程 | zh_TW |
| dc.subject | 離散座標法 | zh_TW |
| dc.subject | 全變量消逝法 | zh_TW |
| dc.subject | TVD method | en |
| dc.subject | WENO method | en |
| dc.subject | electron transport | en |
| dc.subject | semiclassical Boltzmann-BGK equation | en |
| dc.subject | discrete ordinate method | en |
| dc.title | 基於波茲曼-帕松方程之半導體電子傳輸數值模擬 | zh_TW |
| dc.title | Direct Simulation of Electron Transport in Semiconductors Based on Boltzmann-Poisson Equation | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 100-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 黃俊誠,陳旻宏,許長安,謝澤揚 | |
| dc.subject.keyword | 電子傳輸,半古典Boltzmann-BGK方程,離散座標法,全變量消逝法,加權型基本不振盪算則, | zh_TW |
| dc.subject.keyword | electron transport,semiclassical Boltzmann-BGK equation,discrete ordinate method,TVD method,WENO method, | en |
| dc.relation.page | 85 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2012-07-30 | |
| dc.contributor.author-college | 工學院 | zh_TW |
| dc.contributor.author-dept | 應用力學研究所 | zh_TW |
| 顯示於系所單位： | 應用力學研究所 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| ntu-101-1.pdf 未授權公開取用 | 3.76 MB | Adobe PDF |
系統中的文件，除了特別指名其著作權條款之外，均受到著作權保護，並且保留所有的權利。