A semiconductor is irradiated with light such that carriers are uniformly generated throughout its volume. The semiconductor is N-type with ND = 1019/cm3. If the excess electron concentration in the steady state is Δn = 1015/cm2 and if τp = 10 µs C minority carrier life time, then what is the generation rate due to irradiation ?
1020 e-h pairs/cm3/s
Under uniform optical generation the excess carriers are created in pairs, so the excess electron and excess hole concentrations are equal. In an N-type sample the holes are the minority carriers, and their lifetime \(\tau_p\) controls recombination of the excess pairs.
Step 1 — The continuity equation for uniform generation is \(\dfrac{d\,\Delta p}{dt} = G - \dfrac{\Delta p}{\tau_p}\). In the steady state the time derivative is zero, so \(G = \dfrac{\Delta p}{\tau_p} = \dfrac{\Delta n}{\tau_p}\).
Step 2 — Substitute \(\Delta n = 10^{15}\,\text{cm}^{-3}\) (a concentration, per unit volume) and \(\tau_p = 10\,\mu\text{s} = 10^{-5}\,\text{s}\).
Step 3 — \(G = \dfrac{10^{15}}{10^{-5}} = 10^{20}\,\text{pairs cm}^{-3}\,\text{s}^{-1}\). The donor density of 1019/cm3 only confirms low-level injection and does not enter the rate.
1014 and 1010 e-h pairs/cm3/s come from multiplying by the lifetime or misplacing the exponent, and 108 per cm2 per second has the wrong magnitude and the wrong unit for a volume generation rate.
1020 e-h pairs/cm3/s option is correct.
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