This simulation demonstrates charge transport in semiconductors. Blue particles represent electrons, and red particles represent holes. The crystal lattice is shown in the background, with doping impurities (donors or acceptors) indicated by green or purple circles.
You can adjust the temperature (affecting thermal velocity), electric field strength (directional drift), and doping type/concentration. The simulation includes realistic physics like thermal motion, field-induced drift, and scattering events from the lattice and impurities.
Thermal velocity distribution (Maxwell-Boltzmann):
Where \(v_p\) is the most probable speed, \(k_B\) is Boltzmann's constant, \(T\) is temperature, and \(m\) is the particle mass.
Drift velocity in an electric field:
Where \(v_d\) is drift velocity, \(\mu\) is carrier mobility, and \(E\) is electric field strength.
Carrier mobility relationship with temperature:
Mobility typically decreases as temperature increases due to increased lattice scattering.
Current density:
Where \(J\) is current density, \(\sigma\) is conductivity, \(n\) and \(p\) are electron and hole concentrations, and \(\mu_n\) and \(\mu_p\) are electron and hole mobilities.