Semiconductors — Question 3

Question 3

Equal carrier populations need not contribute equal currents

An intrinsic semiconductor has $n_i=2.00\times10^{16}\,\mathrm{m^{-3}}$, $\mu_n=.140\,\mathrm{m^2/(V\,s)}$, $\mu_p=.0500\,\mathrm{m^2/(V\,s)}$, and $e=1.60\times10^{-19}\,\mathrm C$. A bar has length .0100 m and area $1.00\,\mathrm{mm^2}$.

1. Find resistivity and bar resistance.

2. For a 2.00 V bias, find total current and the electron fraction of the conventional current.

Question 3 - Solution

Equal carrier populations need not contribute equal currents

(a) Method and calculation

$$\sigma=en_i(\mu_n+\mu_p)=6.08\times10^{-4}\,\mathrm{S/m}.$$$$\boxed{\rho=1.645\times10^3\,\Omega\,\mathrm m,\quad R=\rho L/A=1.645\times10^7\,\Omega}.$$

(b) Interpretation and further calculation

$$\boxed{I=V/R=1.216\times10^{-7}\,\mathrm A}.$$$$\boxed{I_n/I=\mu_n/(\mu_n+\mu_p)=.7368}.$$

Physical check

Electrons and holes drift in opposite directions, but their charge signs make their conventional currents add.