8.1 Drift diffusion model

Developing Comsol model

In the following text is summarized the implementation of a model 1D silicon diodes in the program COMSOL Multiphysics in version 3.5. The basic knowledge of working with the program is assumed, so we set out images of important dialogues that define the model. This model is a 1D structure of the doping profile of an identical as in fig. 8.1B.1. Are implemented equation (8.1B.31) and boundary conditions for ohmic contact (8.1A.37) and (8.1A.41). SRH recombination model and table the value of mobility carriers at 300K is used. To work with this model read the instructions in the layer C.

The diode consist of a line with the coordinates x1 = 0 and x2 = L = 8 μm. Definition of the necessary constants and expressions is given in fig. 8.1D.1, fig. 8.1D.2 and fig. 8.1D.3.

Obr. 8.1D.1 Setting of constants

Obr. 8.1D.2 Setting of expressions

Obr. 8.1D.3 Setting of integration variables

Module Poisson equation

In this section is described the electrostatic module. In fig. 8.1D.4 is depicted the settings of preset formula over the diode domain, where the tab Init is set to psi_init.

Obr. 8.1D.4 Setting of Poisson equation coefficients

The fig. 8.1D.5 shows the set of boundary conditions at points x₁ and x₂.

a)

b)

Obr. 8.1D.5 Setting of boundary conditions of the electrostatic module

Module convention and diffusion of electrons

In fig. 8.1D.6 is depicted the preset formula over the diode domain, where the tab Init is set to n_init.

Obr. 8.1D.6 Setting of convention and diffusion equations for electrons

The fig. 8.1D.7 shows identical set of boundary conditions of points x₁ and x₂.

Obr. 8.1D.7 Set of boundary conditions for convention and diffusion module of electrons

Module convention and diffusion of holes

In fig. 8.1D.8 is depicted the preset formula over the diode domain, where the tab Init is set to p_init.

Obr. 8.1D.8 Setting of convention and diffusion equations for holes

The fig. 8.1D.9 shows identical set of boundary conditions of points x₁ and x₂.

Obr. 8.1D.9 Setting of boundary conditions for convention and diffusion module of holes

Other settings

Setting of discretization mesh is shown in fig. 8.1D.10 and settings of solver in fig. 8.1D.11.

Obr. 8.1D.10 Setting of the density discretization mesh

Obr. 8.1D.11 Setting of solver parameters