Physics

Physics

Problem

(Comparing two intrinsic semiconductors) Two intrinsic semiconductors P and Q at a certain temperature have charge-carrier concentrations nPn_{\mathrm P} and nQn_{\mathrm Q}, respectively. Their electrical conductivities satisfy σP=3σQ\sigma_{\mathrm P}=3\sigma_{\mathrm Q} while the carrier concentration of P is half that of Q. (i) Starting from fundamental definitions, derive an expression for the ratio of the mobilities μP/μQ\mu_{\mathrm P}/\mu_{\mathrm Q} in terms of the given conductivities and carrier concentrations. (ii) Using the given numerical factors, calculate μP/μQ\mu_{\mathrm P}/\mu_{\mathrm Q}. (iii) If the mobility in Q is 0.15 m2 V−1 s−10.15\,\text{m}^{2}\,\text{V}^{-1}\,\text{s}^{-1}, find the corresponding mobility in P. a. Starting from fundamental definitions, derive an expression for the ratio of the mobilities μP/μQ\mu_{\mathrm P}/\mu_{\mathrm Q} in terms of the given conductivities and carrier concentrations. b. Using the given numerical factors, calculate μP/μQ\mu_{\mathrm P}/\mu_{\mathrm Q}. c. If the mobility in Q is 0.15 m2 V−1 s−10.15\,\text{m}^{2}\,\text{V}^{-1}\,\text{s}^{-1}, find the corresponding mobility in P.
Intuitive explanation

Conductivity in a semiconductor depends on both how many charge carriers are available and how easily they move through the material. The key is to use the fundamental conductivity formula—which relates σ\sigma to carrier concentration nn and mobility μ\mu—and rearrange it to isolate mobility. Once you have mobility in terms of the quantities you know, you can use the given ratio constraints to find the numerical answer.

Intuitive explanation

Conductivity in a semiconductor depends on both how many charge carriers are available and how easily they move through the material. The key is to use the fundamental conductivity formula—which relates σ\sigma to carrier concentration nn and mobility μ\mu—and rearrange it to isolate mobility. Once you have mobility in terms of the quantities you know, you can use the given ratio constraints to find the numerical answer.

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