Predict the effect on the electrical properties of a silicon at room temperature if every millionth silicon atom is replaced by an atom of indium. Given: Concentration of silicon atoms are 5 x 1028 /m3, intrinsic conductivity of silicon is 4.4 x 10-4…

Given: \(N_{Si}=5\times10^{28}\) m\(^{-3}\), \(\sigma_i=4.4\times10^{-4}\) (Ω m)\(^{-1}\), \(\mu_h=0.048\) m²/V s.

Indium is trivalent, so it acts as an acceptor. Replacing one Si atom in \(10^6\):

\[ N_A=\frac{5\times10^{28}}{10^6}=5\times10^{22}\ \text{m}^{-3} \]

At room temperature all acceptors are ionised, so \(p\approx N_A=5\times10^{22}\) m\(^{-3}\). This is far greater than the intrinsic carrier concentration (about \(10^{16}\) m\(^{-3}\)), so the electron contribution is negligible.

Formula: \(\sigma_p=p\,e\,\mu_h\)

\(\sigma_p=5\times10^{22}\times1.6\times10^{-19}\times0.048=384\) (Ω m)\(^{-1}\)

\(\dfrac{\sigma_p}{\sigma_i}=\dfrac{384}{4.4\times10^{-4}}=8.73\times10^5\)

Effect:

• Silicon becomes a p-type extrinsic semiconductor, with holes as the majority carriers.
• Its conductivity rises from \(4.4\times10^{-4}\) to 384 (Ω m)\(^{-1}\), about \(8.7\times10^5\) times larger.
• Its resistivity falls to \(\rho=1/384\approx2.6\times10^{-3}\) Ω m.
• The Fermi level shifts down towards the valence band.