Relating the Experimental Ionization Coefficients in Semiconductors to the Nonlocal Ionization Coefficients

The experimentally determined impact ionization coefficients, α'(β'), include intrinsically the presence of a dead-space, where carriers cannot impact ionize as they do not have sufficient energy. These, therefore, cannot be used by nonlocal ionization models, which require the enabled ionization coefficients, α*(β*), which describe the ionization probability after the dead-space. A relatively simple relationship is shown to exist between α'(β') and α*(β*), which requires only the knowledge of the carrier threshold energies. This allows α'(β'), conventionally limited to the local model framework, to be used to give a very good prediction of the avalanche multiplication and excess noise for a wide range of device widths down to 0.05 μm, where the dead-space effect is significant. Parameterized values of α'(β') and the carrier threshold energies are listed for a range of commonly used III-V semiconductors lattice matched to GaAs and InP substrates, as well as Si and SiC.