On thermodynamic consistency of a Scharfetter–Gummel scheme based on a modified thermal voltage for drift-diffusion equations with diffusion enhancement
On thermodynamic consistency of a Scharfetter–Gummel scheme based on a modified thermal voltage for drift-diffusion equations with diffusion enhancement
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DOI：
10.1007/s11082-014-0050-9
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发表时间：
2014-09
影响因子：
3
通讯作者：
T. Koprucki;N. Rotundo;P. Farrell;D. Doan;J. Fuhrmann
中科院分区：
文献类型：
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作者：
T. Koprucki;N. Rotundo;P. Farrell;D. Doan;J. Fuhrmann
在有机半导体等应用的推动下，基于具有任意统计分布函数的漂移扩散模型的数值模拟越来越受到关注。这需要数值方案，保持定性性质的解决方案，如积极的密度，耗散性和热力学平衡的一致性。研究了Scharfetter-Gummel方案的一个扩展，保证了与热力学平衡的一致性。它是通过用平均扩散增强代替热电压导出的，为此我们提供了一个新的显式公式。这种方法避免了求解昂贵的局部非线性方程定义的电流广义Scharfetter-Gummel计划。
Driven by applications like organic semiconductors there is an increased interest in numerical simulations based on drift-diffusion models with arbitrary statistical distribution functions. This requires numerical schemes that preserve qualitative properties of the solutions, such as positivity of densities, dissipativity and consistency with thermodynamic equilibrium. An extension of the Scharfetter–Gummel scheme guaranteeing consistency with thermodynamic equilibrium is studied. It is derived by replacing the thermal voltage with an averaged diffusion enhancement for which we provide a new explicit formula. This approach avoids solving the costly local nonlinear equations defining the current for generalized Scharfetter–Gummel schemes.