Multi-ion scattering of charged carriers by ionized impurities in heavily doped semiconductors: From bulk to nanowires

Analytical expressions for the low-field mobility in heavily doped 3D, 2D, and 1D semiconductor structures are obtained using the quantum-kinetic approach. The study takes into account the multi-ion (M-ion) scattering of charge carriers by ionized impurities. The calculated dependences of the carrier mobility on doping concentration are compared with experiment in the heavily doped bulk materials (3D) Si, InP, GaAs, n-In0.49Ga0.51P, in heavily doped In0.15Ga0.85As quantum wells and InN nanowires, respectively. When calculating mobility in n-Si, the anisotropic effective masses of electrons in the valleys are taken into account. We explain the difference in the electron mobility of n-Si bulk crystals heavily doped by phosphorus and arsenic in the framework of the M-ion scattering model, which considers the scattering of electrons by interaction potentials with two characteristic lengths: the screening length and the effective radius of the doping ion. The number of ions M participating in the scattering process depends on the effective masses of charge carriers. For the light carriers with effective masses m<0.1m0 (m0 is the free electron mass), the two-ion (M = 2) scattering is more probable. For carriers with higher effective masses, three- and four-ion scattering is relevant.