發展自洽求解非平衡格林函數耦合泊松方程式之量子傳輸數值模擬軟體及在奈米元件的應用

Development of Self-Consistent NEGF-Poisson Quantum Transport Simulator and Application in Nanoscale Devices

蕭翰為(Han-Wei Hsiao)

指導教授 ： 吳育任

國立臺灣大學/電機資訊學院/光電工程學研究所/碩士(2018年)

https://doi.org/10.6342/NTU201801071

摘要

隨著金氧半場效電晶體的閘極長度來到了次10奈米節點的世代，量子效應開始顯著影響載子的傳輸行為，半古典波茲曼理論已不再適用。由於載子其波的物理性質逐漸開始扮演決定量子元件優劣的重要角色，以薛丁格方程式為基礎的非平衡格林函數方法提供了一套精確且有效率的理論架構來描述量子傳輸的現象。此研究中，我們透過耦合非平衡格林函數與泊松方程式自洽求解的數值模擬方法，成功地發展了一套能夠計算電子-聲子散射、摻雜離子散射與表面粗糙散射的三維量子傳輸模擬軟體，且將其運用於探討奈米尺度下電子元件的特性。藉由此模擬，我們能夠分析因非彈性散射所導致的電流分佈擴散其載子行為以及主要支配元件表現的散射機制。根據自洽求解的結果，不僅能得到臨界電壓、線性區和飽和區等典型金氧半場效電晶體的輸出特性，同時還能觀察到由源極至汲極穿隧效應所造成的漏電現象。此外，也將針對量子傳輸及半古典飄移-擴散兩種理論架構下所得的模擬結果其差異進行比較與討論。

關鍵字

非平衡格林函數 ； 泊松方程式 ； 自洽求解 ； 電子-聲子散射 ； 摻雜離子散射 ； 表面粗糙散射 ； 全包覆式奈米線場效電晶體 ； 鰭士場效電晶體 ； 穿隧效應

並列摘要

As the gate length of metal-oxide-semiconductor-field-effect transistors has been scaled down into the sub-10 nm regime, semi-classical Boltzmann transport theory can no longer accurately describe the behavior of electronic transport, since the quantum mechanical effects start to play a dominant role. Non-equilibrium Green's function formalism is a fully quantum mechanical approach which can take the wave nature of electrons into account, and it provides a framework for describing the incoherent and dissipative transport processes. In this work, we have successfully developed a three-dimensional quantum transport simulator based on solving the NEGF equation and Poisson equation self-consistently to investigate the characteristics of nanoscale devices in the presence of electron-phonon scattering, ionized impurity scattering, and surface roughness scattering. Our modeling can capture the phenomena of current spectrum broadening due to inelastic transition processes and the primary scattering mechanisms of current degradation. According to the self-consistent solutions obtained from the NEGF-Poisson cycle, we can simulate not only the typical electrical properties of output characteristic, such as threshold voltage, ohmic region, and saturation region but also the leakage current from source-to-drain tunneling. In addition, the results are also compared with the traditional drift-diffusion model.

並列關鍵字

NEGF Formalism ； Poisson Equation ； Self-Consistent ； Electron-Phonon Scattering ； Ionized Impurity Scattering ； Surface Roughness Scattering ； Gate-All-Around Nanowire Field-Effect Transistor ； Fin Field-Effect Transistor ； Tunneling Effect

參考文獻

[1] G.Moore,“Crammingmorecomponentsontointegratedcircuits,”Elec- tronics, vol. 38, p. 114, 1965.

[2] B. Doris, M. Ieong, and T. Kanarsky, “Extreme scaling with ultra-thin Si channel MOSFETs,” IEDM Tech, pp. 267–270, 2002.

[3] S.-H. Oh, D. Monroe, and J. M. Hergenrother, “Analytic description of short-channel effects in fully-depleted double-gate and cylindrical, surrounding-gate MOSFETs,” IEEE Electron Device Letters, vol. 21, no. 9, pp. 445–447, 2000.

[4] D. J. Frank, R. H. Dennard, E. Nowak, P. M. Solomon, Y. Taur, and H.-S. Philip Wong, “Device scaling limits of Si MOSFETs and their application dependencies,” Proceedings of the IEEE, vol. 89, pp. 259– 288, 2001.

[5] J. L. Hoyt, H. M. Nayfeh, S. Eguchi, I. Aberg, G. Xia, T. Drake, E. A. Fitzgerald, and D. A. Antoniadis, “Strained silicon MOSFET technol- ogy,” IEEE, pp. 23–26, 2002.