Multiplication in collector junctions of silicon n-p-n and p-n-p transistors

The values 1-1/
M
for both electrons and holes, where
M
is the multiplication factor, have been calculated in three different silicon p-n junctions. The logarithmic plot of 1 - 1/
M
versus the normalized voltage
V/V_{B}
is well approximated by a straight line for 0.1 > 1 -1/
M
> 0.005. This range corresponds to the useful range of α
0
for most bipolar transistors. An empirical expression has been obtained for the ratio
V_{CEO}/V_{CBO}
within this range.