Calculate the photoconductor gain of a silicon photoconductor.
Consider an n-type silicon photoconductor with a length L=100 \mu \mathrm{m}, cross-sectional area A=10^{-7} \mathrm{~cm}^{2}, and minority carrier lifetime \tau_{p}=10^{-6} \mathrm{~s} . Let the applied voltage be V=10 volts.
The electron transit time is determined as
t_{n}=\frac{L}{\mu_{n} \mathrm{E}}=\frac{L^{2}}{\mu_{n} V}=\frac{\left(100 \times 10^{-4}\right)^{2}}{(1350)(10)}=7.41 \times 10^{-9} \mathrm{~s}
The photoconductor gain is then
\Gamma_{\mathrm{ph}}=\frac{\tau_{p}}{t_{n}}\left(1+\frac{\mu_{p}}{\mu_{n}}\right)=\frac{10^{-6}}{7.41 \times 10^{-9}}\left(1+\frac{480}{1350}\right)=1.83 \times 10^{2}
Comment
The fact that a photoconductor—a bar of semiconductor material—has a gain may be surprising.