Enriched residual free bubbles for semiconductor device simulation

Abstract

This article outlines a method for stabilising the current continuity equations which are used for semiconductor device simulation. Residual-free bubble functions (RfBF) are incorporated into a finite element (FE) implementation that are able to prevent oscillations which are seen when using the conventional Bubnov-Galerkin FE implementation. In addition, it is shown that the RfBF are able to provide stabilisation with very distorted meshes and curved interface boundaries. Comparison with the commonly used SUPG scheme is made throughout, showing that in the case of 2D problems the RfBF allow faster convergence of the coupled semiconductor device equations, especially in the case of distorted meshes.

Influence of environmental temperature and device temperature difference on output parameters of c-Si solar cells

“…Based on the former Yee grid, Equations (A1)-(A10) can be discretized and solved by enriched residual free bubble method provided by R. N. Simpson et.al. [16]. Due to the fact that environmental temperature is the main factor influencing the temperature distribution of the cell and heat absorbed or released by different thermal mechanisms will only disturb the temperature distribution, equations (1)-(2) can be solved separately by finite difference method.…”

“…By introducing the charge source into the Poisson equation and temperature variable into the properties of c-Si material, the semiconductor device equations can be solved by enriched residual free bubble method proposed by R. N. Simpson et.al. [16]. Finally, the temperature distribution of the c-Si SC and the heat absorbed and released by different mechanisms can be obtained by [17],…”

“…where  is the thermal conductivity, C is the heat capacity per unit volume and Qthermal denotes the heat generated per unit volume, which can be rewritten as [16],…”

“…In order to decrease the numerical errors arising from the finite-difference approximations, we adopt Yee grid resolution in both X and Y directions as one twentieth of the minimum absorption wavelength (i.e.300nm for c-Si material). In our calculation, we assume that the substrate is a p-type c-Si wafer with a uniform doping concentration equal to 710 16 /cm 3 (=0.266.cm) and the lifetime of minority carriers is equal to 1ms; the PN junction with the junction depth equal to 0.358m is fabricated by traditional phosphorus diffusion process and the impurity profile follows Gaussian distribution with its surface concentration equal to 10 20 /cm 3 ; good ohmic contacts have been formed between the active layer and two electrodes. In our simulation, the relationships between temperature and the properties of c-Si material adopt the following equations [19][20][21]…”

The output parameter and temperature distribution characteristics of crystalline silicon solar cell varying with temperature

“…求 解 过 程 中 , ERFBM 的网格划分直接使用频域有限差分法划分的 网格结构, 欧姆电极区和非欧姆电极区的边界条件 分别采用 Dirichlet 和 Neumann 边界条件. 最后将求 解的电学参量带入(1)式中, 求解电池内部的温场分 布 [14] .…”