Semiconductors — Question 10

Question 10

Surface recombination shortens the measured carrier lifetime

A thin semiconductor slab of thickness d has nearly uniform excess density $\Delta n$. Bulk recombination rate is $\Delta n/\tau_b$ per volume. Each of its two broad faces removes carriers at flux $S\Delta n$, where S is the surface recombination velocity; edge losses are negligible.

1. Derive the effective lifetime using a carrier balance.

2. For $d=100\,\mu\mathrm m$, $\tau_b=10.0\,\mu\mathrm s$, and $S=10.0\,\mathrm{m/s}$, evaluate the lifetime and the fraction of losses occurring at the surfaces.

Question 10 - Solution

Surface recombination shortens the measured carrier lifetime

(a) Method and calculation

$$Ad\frac{d\Delta n}{dt}=-Ad\frac{\Delta n}{\tau_b}-2AS\Delta n.$$$$\boxed{\tau_{\mathrm{eff}}^{-1}=\tau_b^{-1}+2S/d}.$$

(b) Interpretation and further calculation

$$\boxed{\tau_{\mathrm{eff}}=1/(10^5+2\times10^5)=3.333\,\mu\mathrm s}.$$$$\boxed{f_s=\frac{2S/d}{1/\tau_b+2S/d}=2/3}.$$

Physical check

The uniform-density approximation requires diffusion across the slab to be fast enough to prevent a strong depth gradient. Passivation increases lifetime by reducing S.