Semiconductors — Question 5

Question 5

Steady optical generation raises both carrier populations

Uniform illumination creates electron-hole pairs at rate $G=3.00\times10^{21}\,\mathrm{m^{-3}s^{-1}}$. Use a linear excess-carrier model $d\Delta n/dt=G-\Delta n/\tau$, with $\Delta p=\Delta n$ and $\tau=2.00\,\mu\mathrm s$. Let $\mu_n+\mu_p=.200\,\mathrm{m^2/(V\,s)}$ and $e=1.60\times10^{-19}\,\mathrm C$.

1. Find the steady excess density and photoconductivity.

2. If illumination begins at t=0 with zero excess carriers, find the time to reach 90 percent of the steady photoconductivity.

Question 5 - Solution

Steady optical generation raises both carrier populations

(a) Method and calculation

$$0=G-\Delta n_{\mathrm{ss}}/\tau\Rightarrow\boxed{\Delta n_{\mathrm{ss}}=G\tau=6.00\times10^{15}\,\mathrm{m^{-3}}}.$$$$\boxed{\Delta\sigma=e(\mu_n+\mu_p)\Delta n_{\mathrm{ss}}=1.92\times10^{-4}\,\mathrm{S/m}}.$$

(b) Interpretation and further calculation

$$\Delta n(t)=G\tau(1-e^{-t/\tau})\Rightarrow e^{-t_{90}/\tau}=.10.$$$$\boxed{t_{90}=\tau\ln10=4.605\,\mu\mathrm s}.$$

Physical check

Each generated pair supplies one electron and one hole. The stated linear lifetime model assumes recombination kinetics that remain valid over the chosen excess-density range.