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Question
The conductivity of a semiconductor increases with increase in temperature because ______.
Options
number density of free current carriers increases.
relaxation time increases.
both number density of carriers and relaxation time increase.
number density of current carriers increases, relaxation time decreases but effect of decrease in relaxation time is much less than increase in number density.
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Solution
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` ⇒ `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.
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