The calculation of the avalanche multiplication factor in silicon p—N junctions taking into account the carrier generation (thermal or optical) in the space-charge region

The influence of carrier generation within the space-charge regions of silicon p-n junctions upon their breakdown characteristics is analyzed. Universal plots for the calculation of the total multiplication in one-sided silicon junctions versus voltage and substrate concentration are given, which take into account both injection and generation of initiating carriers. It is shown that the multiplication factor
M
of practical (i.e., generation-dominated) silicon junctions differs from the pure hole-pure electron multiplication factors M
p
and M
n
and ranges between them, i.e.,
M_{p} < M < M_{n}
. Its calculated voltage dependence is well approximated by Miller's relationship with an exponent
n
between 4 and 7 for impurity concentrations in the substrate between 10
¹⁴
and 10
¹⁷
cm
^-3
.