Semiconductors — Question 7

Question 7

Light-generated pairs produce a measurable conductivity transient

Uniform illumination creates electron-hole pairs at rate G per volume per time. Excess density obeys $d\Delta n/dt=G-\Delta n/\tau$ and $\Delta p=\Delta n$, starting from zero. Mobilities are constant.

1. Find the excess conductivity after the light is switched on.

2. For a bar of area A and length L held at voltage V, find the extra charge transported during illumination lasting T.

Question 7 - Solution

Light-generated pairs produce a measurable conductivity transient

(a) Method and calculation

$$\Delta n(t)=G\tau(1-e^{-t/\tau}),\quad\Delta p=\Delta n.$$$$\Delta\sigma=e(\mu_n+\mu_p)G\tau(1-e^{-t/\tau}).$$

(b) Interpretation and further calculation

$$\Delta I(t)=\frac{AV}{L}\Delta\sigma(t).$$$$\Delta Q=\frac{AV}{L}e(\mu_n+\mu_p)G\tau\left[T-\tau(1-e^{-T/\tau})\right].$$

Physical check

Both members of each pair contribute to conductivity; the transient depends on recombination as well as generation.