The main aim of this work is to optimize a Quantum Drift Diffusion model (QDD) (V. Romano, M. Torrisi, and R. Tracinà, “Approximate solutions to the quantum drift-diffusion model of semiconductors,” J. Math. Phys., vol. 48, p. 023501, 2007; A. El Ayyadi and A. Jüngel, “Semiconductor simulations using a coupled quantum drift-diffusion schrödinger-Poisson model,” SIAM J. Appl. Math., vol. 66, no. 2, pp. 554–572, 2005; L. Barletti and C. Cintolesi, “Derivation of isothermal quantum fluid equations with Fermi-Dirac and bose-einstein statistics,” J. Stat. Phys., vol. 148, pp. 353–386, 2012) by comparing it with the Boltzmann-Wigner Transport Equation (BWTE) (O. Muscato, “Wigner ensemble Monte Carlo simulation without splitting error of a GaAs resonant tunneling diode,” J. Comput. Electron., vol. 20, pp. 2062–2069, 2021) solved using a signed Monte Carlo method (M. Nedjalkov, H. Kosina, S. Selberherr, C. Ringhofer, and D. K. Ferry, “Unified particle approach to Wigner-Boltzmann transport in small semiconductor devices,” Phys. Rev. B, vol. 70, pp. 115–319, 2004). A situation of high non equilibrium regime is investigated: electron transport in a Resonant Tunneling Diode (RTD) made of GaAs with two potential barriers in GaAlAs. The range of the suitable voltage bias applied to the RTD is analyzed. We find an acceptable agreement between QDD model and BWTE when the applied bias is low or moderate with a threshold of about 0.225 V over a length of 150 nm; it is found out that the use of a field dependent mobility is crucial for getting a good description of the negative differential conductivity in such a range. At higher bias voltages, we expect that QDD model loses accuracy.

中文翻译：

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谐振隧道二极管的优化量子漂移扩散模型

这项工作的主要目的是优化量子漂移扩散模型 (QDD)（V. Romano、M. Torrisi 和 R. Tracinà，“半导体量子漂移扩散模型的近似解决方案”，J.马斯。物理。，卷。48，p。023501, 2007; A. El Ayyadi 和 A. Jüngel，“使用耦合量子漂移扩散薛定谔-泊松模型进行半导体模拟”暹罗 J. 应用程序。数学。，卷。66，没有。2，第 554-572 页，2005 年；L. Barletti 和 C. Cintolesi，“利用费米-狄拉克和玻色-爱因斯坦统计推导等温量子流体方程”，J. 统计。物理。，卷。148，第 353–386 页，2012 年），将其与玻尔兹曼-维格纳传输方程 (BWTE) 进行比较（O. Muscato，“没有 GaAs 谐振隧道二极管分裂误差的维格纳系综蒙特卡洛模拟”，J. 计算机。电子.，卷。20，第 2062–2069 页，2021 年）使用带符号的蒙特卡洛方法求解（M. Nedjalkov、H. Kosina、S. Selberherr、C. Ringhofer 和 DK Ferry，“小型半导体中维格纳-玻尔兹曼输运的统一粒子方法”）设备，”物理。修订版B，卷。70，第 115-319 页，2004 年）。研究了高度非平衡状态的情况：由 GaAs 制成的谐振隧道二极管 (RTD) 中的电子传输，其中有两个 GaAlAs 势垒。分析了施加到 RTD 的合适偏压范围。我们发现，当所施加的偏压较低或中等且在 150 nm 长度上阈值约为 0.225 V 时，QDD 模型和 BWTE 之间存在可接受的一致性；结果发现，使用场相关迁移率对于获得这种范围内的负微分电导率的良好描述至关重要。在较高的偏置电压下，我们预计 QDD 模型会失去准确性。