The conductivity of a semiconductor increases with increase in temperature because ______.

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The conductivity of a semiconductor increases with increase in temperature because number density of current carriers increases, relaxation time decreases but effect of decrease in relaxation time is much less than increase in number density. Explanation: The conductivity of Semiconductor: (1) In intrinsic semiconductors ne = nh. Both electrons and holes contribute to current conduction. (2) When some potential difference is applied across a piece of intrinsic semiconductor current flows in it due to both electrons and holes, i.e. i = i_e + i_h $\Rightarrow$ eA[n_ev_e + n_hv_h] (3) As we know σ = J/E = i/(AE). Hence conductivity of semiconductor is σ = e[n_eu_e + n_hu_h]; where v_e = drift velocity of electron, v_h = drift velocity of holes, E = Applied electric field, mu_e = v_e/E = mobility of electron and mu_h = v_h/E = mobility of holes. (4) Motion of electrons in the conduction band and of holes in the valence band under the action of electric field is shown below: (5) At absolute zero temperature (0 K) conduction band of the semiconductor is completely empty, i.e., σ > 0. Hence the semiconductor behaves as an insulator. We know that σ = (n e^2τ)/m, So, σ ∝ nτ Where n = number density and τ = relaxation time In semiconductors, conductivity increases with increase in temperature, because the number density of current carries increases, relaxation time decreases but effect of decrease in relaxation is much less than increase in number density. [Solution diagram: 329415_solution_1.png] [Solution diagram: 329415_solution_2.png]

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