AI 中文总结
针对忆阻器的三物种漂移扩散模型，提出保持结构的全隐式Scharfetter-Gummel有限体积格式，重铸通量揭示隐藏信息分量，建立离散解存在性等，二维数值模拟证实格式特性及忆阻器细丝形成。
AI 中文摘要
本文提出并分析了一种用于半导体三物种漂移扩散模型的保持结构的全隐式Scharfetter-Gummel有限体积格式。这些方程描述了（有界）忆阻器器件中电子、空穴和氧空位密度的演化，并与电势的泊松方程耦合，具有混合型边界条件。以迎风形式重铸Scharfetter-Gummel通量，揭示了一个隐藏的Fisher信息分量。由于通量中出现的伯努利函数的退化，需要额外的沿边强制性估计，从而得到精细的局部和全局耗散估计。利用这些思想，建立了离散有限体积解的存在性、离散自由能不等式和数值格式的收敛性。二维空间的数值模拟证实了该格式的保持结构特性，并说明了忆阻器器件中的细丝形成。
英文摘要
A structure-preserving fully implicit Scharfetter-Gummel finite-volume scheme for a three-species drift-diffusion model for semiconductors is proposed and analyzed. The equations describe the evolution of the electron, hole, and oxygen vacancy densities in a (bounded) memristor device, coupled to the Poisson equation for the electric potential, with mixed-type boundary conditions. Recasting the Scharfetter-Gummel fluxes in an upwind form, a hidden Fisher information component is revealed. Owing to the degeneracy of the Bernoulli function appearing in the fluxes, additional edgewise coercivity estimates are required, leading to refined local and global dissipation estimates. Using these ideas, the existence of a discrete finite-volume solution, a discrete free energy inequality, and the convergence of the numerical scheme are established. Numerical simulations in two space dimensions confirm the structure-preserving properties of the scheme and illustrate the filament formation in a memristor device.
