Suppose an intrinsic semi-conductor at room temperature has...

Suppose an intrinsic semi-conductor at room temperature has 1 billion free electrons at room temperature. If temperature changes to $75^{\circ} \mathrm{C}$, how many holes are there?
(A) Fewer than 1 billion
(B) 1 billion
(C) More than 1 billion
(D) Impossible to say

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Key Concepts

Thermal Generation of Carriers

Thermal energy in a semiconductor can excite electrons from the valence band to the conduction band, creating an electron-hole pair. This means that any process that increases the number of free electrons will correspondingly increase the number of holes, as both carriers are produced simultaneously.

Temperature Dependence of Carrier Concentration

While increasing the temperature of an intrinsic semiconductor boosts the overall concentration of charge carriers due to enhanced thermal generation, the key principle is that electrons and holes are generated in pairs. Therefore, any count of free electrons directly corresponds to an equal number of holes.

Intrinsic Semiconductor

In an intrinsic semiconductor, the material is pure without intentional doping, so the conduction electrons arise solely from thermal excitations. This thermal generation process creates electron-hole pairs in equal numbers, ensuring that the concentration of electrons is equal to the concentration of holes under equilibrium conditions.

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