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Assessing the quality of the excess chemical potential flux scheme for degenerate semiconductor device simulation

机译：评估退化半导体器件模拟的过量化学潜能通量方案的质量

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摘要

The van Roosbroeck system models current flows in (non-)degenerate semiconductor devices. Focusing on the stationary model, we compare the excess chemical potential discretization scheme, a flux approximation which is based on a modification of the drift term in the current densities, with another state-of-the-art Scharfetter-Gummel scheme, namely the diffusion-enhanced scheme. Physically, the diffusion-enhanced scheme can be interpreted as a flux approximation which modifies the thermal voltage. As a reference solution we consider an implicitly defined integral flux, using Blakemore statistics. The integral flux refers to the exact solution of a local two point boundary value problem for the continuous current density and can be interpreted as a generalized Scharfetter-Gummel scheme. All numerical discretization schemes can be used within a Voronoi finite volume method to simulate charge transport in (non-)degenerate semiconductor devices. The investigation includes the analysis of Taylor expansions, a derivation of error estimates and a visualization of errors in local flux approximations to extend previous discussions. Additionally, drift-diffusion simulations of a p-i-n device are performed.
机译：Van Roosbroeck系统模型电流流入（非）退化半导体器件。专注于静止模型，我们比较过量的化学电位离散化方案，一种磁通近似，基于当前密度的漂移项的改变，以及另一种最新的Scharfetter-Gummul方案，即扩散 - 营业计划。物理地，扩散增强方案可以解释为改变热电压的磁通近似。作为参考解决方案，我们考虑使用Blakemore统计数据来考虑隐式定义的积分通量。积分通量是指连续电流密度的局部两个点边值问题的精确解决方案，并且可以解释为广义的Scharfetter-Gummul方案。所有数值离散化方案都可以在Voronoi有限音量方法中使用，以模拟（非）退化半导体器件中的电荷传输。调查包括对泰勒扩展的分析，误差估计的推导和局部通量近似值的误差可视化以扩展以前的讨论。另外，执行P-I-N设备的漂移扩散模拟。

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