This video is taken from the CHARGE 100 course on Lumerical University.

## Transcript

The charge transport or CT solver is a physics-based simulation tool for electrical analysis of

semiconductor devices.

The solver self-consistently solves the system of equations describing the electrostatic

potential using the Poisson’s equation and density of free carriers through the drift-diffusion

equations.

In a semiconductor device, each carrier (electron or hole) moves under the influence of two

competing processes: drift due to the applied electric field, and diffusion due to the gradient

in the carrier density.

These processes are represented in the drift-diffusion equations as the sum of two terms.

To solve the drift-diffusion equations, the electric field must be known.

This can be determined by solving the Poisson's equation for the same device.

The charge transport solver discretizes and solves the drift-diffusion and Poisson’s

equations on a mesh grid in two or three dimensions.

The simulation region is partitioned into multiple domains along boundaries between

materials with unique physical descriptions.

The different materials used in the simulation may be categorized as insulators, semiconductors,

or conductors.

Each type of material has an associated model that describes its charge transport behavior.

Drift-diffusion equations are not solved inside domains containing insulators and conductors,

rather these domains provide boundary conditions for the semiconductor domains, also termed

as the active regions.

Poisson’s equation, however, is solved in all domains and the solution is transferred

to the drift-diffusion equations to find a self-consistent solution in the active regions.

The charge transport solver uses a finite-element mesh in the form of triangles in 2D and tetrahedra

in 3D, such as the one shown here.

The solution to the system of equations used to determine the physical quantities of interest

is estimated from the discrete formulation of those equations.

Fundamental simulation quantities such as material properties, geometry information,

temperature, and electrostatic potential are calculated at each mesh vertex.

A finer mesh (with shorter edge lengths and smaller elements) will better approximate

the exact solution to the system of equations, but at a substantial cost in simulation performance.

As the mesh features become smaller, the simulation time and memory requirements will increase.

DEVICE provides a number of tools, including the automatic and user-defined mesh refinement,

to take advantage of mesh refinements only in places where it’s needed, which allows

you to obtain accurate results, while minimizing computational effort.

Automatic mesh refinement is a feature that automatically uses a finer mesh for example

around the areas where there is a sudden change in properties such as doping and heat generation

to more accurately resolve these changes.

You can see an example of automatic mesh refinement here around the boundaries where a sudden

change in the value of an specific property is detected.

In the next unit, we will learn about different modes of simulation available in the CHARGE

solver.