Hot Carriers in Si and Ge Radiation Detectors

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Abstract
Characteristics of silicon and germanium radiation detectors are developed from an analysis of the energy‐loss mechanisms for hot carriers. The carrier behavior is described in terms of phonon and ionization scattering rates. A calculation of the probability of ionization vs primary electron energy in silicon, using Kane's characterization of the scattering rates, indicates an effective ionization threshold several times the band‐gap energy. Calculations of phonon losses and the carriers' residual kinetic energies are combined to give an average energy expended per created pair ε of 4.24 eV. Closer agreement with the experimental value of 3.67 eV is achieved by lowering the phonon to ionization scattering‐rate ratio. Temperature effects, which enter through changes in the band gap, are calculated to be ∂ε/∂Eg=1.73. The analysis also predicts a Fano factor of 0.059 for silicon. Discussion of the germanium situation is based on the premise of hot‐carrier behavior similar to that in silicon. Because germanium has a more complicated band structure, two sets of calculations are made using different effective band gaps. With ε=2.96 eV at 90 °K, very similar results are obtained in both cases and indicate ∂ε/∂Eg≈1.77 and F≈0.066.