Discontinuous Finite Volume Method For Semiconductor Devices

In this article, the mathematical model of semiconductor devices we researchedis widely used in the theoretical design of solar cells, photoelectric detector, photodi-ode, laser diode and other semiconductor. The numerical simulation technique is anemerging technology for designing semiconductor devices. Numerical methods playan important role in the numerical simulation. In actual production, people hopeto obtain solution of ψ, e, p accurately to guide the design of the semiconductor.It has been found that the electronic potential is not appear in the concentrationequation directly, while its gradient appear in the concentration equation. We canapproximate potential gradient by choosing a high precision method to improve theconcentration approximation results. According to the convection-dominate prop-erties of concentration equation, we introduce the characteristic line to handle theconvection term.The purpose of this article is to establish a high-precision scheme named dis-continuous mixed volume method and characteristic discontinuous volume methodfor the following mathematical model of semiconductor devi ces.(a)△ψ=α(p e+N(x)),(x, t)∈×J,This scheme can approximate the potential, feld intensity, electron concentration and hole concentration simultaneously. Our argument shows that the method in-herits the advantages of discontinuous fnite element volume method, which is highorder accuracy, parallelizability, stability and simplicity of space construction. Inaddition, we can better approximate concentration through high precision compu-tation of the feld intensity and avoid the numerical dispersion of the front at thesame time.Through the theoretical analysis of the scheme which we have proposed, wecan obtain L2-error estimate of ψ, H(div)-error estimate ofâ†'u, L2-error estimateof e and L2-error estimate of p.