Scattering Theory
Analytical descriptions of carrier transport in doped semiconductors use electrostatic potential formulations to calculate deflection rates. The brooks-herring model describes the scattering of charge carriers by ionized impurities in a semiconductor crystal. This model accounts for the shielding effect of free carriers by modifying the bare Coulomb potential with a screening length.
Mobility Calculation
The screening parameter determines the effective range of the impurity potential and depends on carrier density. Mobility calculations based on the brooks-herring model yield carrier behavior as a function of temperature and doping concentration. The calculation relies on the Born approximation to evaluate the scattering cross-section of the screened potential.
Higher temperatures increase carrier thermal velocity, reducing the interaction time with the impurities and yielding a higher calculated mobility.
Doping Constraint
Application of the model is restricted to cases where the impurity centers act independently. This assumption holds true for moderate doping levels where the distance between impurities exceeds the screening length. At high dopant concentrations, the potentials overlap and create localized band-tail states.
Physical Limitation
Compensated semiconductors present additional challenges for accurate mobility predictions. In these materials, the model underpredicts the scattering rate because it assumes a uniform distribution of charge. Heavy compensation yields spatial fluctuations in the potential energy that are better addressed using alternative formulations.
