The current induced by the motion of the carriers (electrons-e, holes-h) in the electric field induces current in the electrodes connected to low impedance as given by equation

In order to simulated the induced current in the detector the knowledged of electric field and weigthing field in the detector is crucial. It is always assumed that magnetic field in the sensors is constant.

Both electric field and weigthing field can be calculated from

The partial differential equation is solved numericaly by using finite difference equation on the mesh (FEM approach). An example of the mesh in 2D is shown in figure below. The mesh can be defined in 3D with complex electrode arrangements/shapes (see examples). The mesh should be ortoghonal but doesn't have to be equidistant.

The differnial equation translates to solving the system of equations for

Any non-equilibrium free carrier distribution (e-h pairs) due to traversing minimum ionizing particle, laser light, alpha particle, photoelectic effect etc., is divided into charge buckets. Each bucket is considered as a point charge (with given number of e-h pairs) which is transported in the electric and magnetic field according to the Lorentz force and diffusion.

The transport is done in steps defined by the user, where step size is defined by the user. For each step drift and diffusion components are summed and corresponding induced charge, drift time, charge from impact ionization etc. are calculated.

The charge transport is finished when, charge reaches the electrodes or boundaries of the simulated volume. An example of the e-h pairs drift after mip particle traversing pixel detector perpendicularly is shown in figure below (blue electron, red holes).