Semiconductors — Question 1

Question 1

Equal electron and hole populations need not carry equal currents

Use $e=1.602176634\times10^{-19}$ C, exact. An intrinsic semiconductor has $n=p=n_i=2.00\times10^{16}\,\mathrm{m^{-3}}$, electron mobility $\mu_n=.140$ and hole mobility $\mu_p=.0500$ m$^2$/(V s). Use $\sigma=e(n\mu_n+p\mu_p)$.

1. Find conductivity and the electron fraction of the current.

2. For length 1.00 mm and area 2.00 mm$^2$, find resistance and current at 5.00 V, neglecting contacts and heating.

Question 1 - Solution

Equal electron and hole populations need not carry equal currents

(a) Method and calculation

$$\sigma=en_i(\mu_n+\mu_p)=6.08827\times10^{-4}\,\mathrm{S/m}.$$$$I_n/I=\mu_n/(\mu_n+\mu_p)=14/19=.736842.$$

(b) Interpretation and further calculation

$$R=L/(\sigma A)=8.21251\times10^5\,\Omega.$$$$I=V/R=6.08827\,\mathrm{\mu A}.$$

Physical check

The two species are equal in number but their different mobilities weight their current contributions.