Intrinsic Semiconductors

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In a perfectly pure silicon crystal kept at room temperature, thermal vibrations alone create mobile charge carriers without any added impurity. How do the free electron and hole concentrations compare in this sample?

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An intrinsic semiconductor is a chemically pure crystal in which the only source of charge carriers is the thermal breaking of covalent bonds. Each time a bond breaks, one electron is freed into the conduction band and simultaneously leaves behind exactly one hole in the valence band, so carriers are always created in pairs. Because there is no donor or acceptor impurity to add carriers of one type preferentially, the electron density $n_e$ and hole density $n_h$ must be equal, both equalling the intrinsic carrier concentration $n_i$. The option claiming electrons far exceed holes describes an n-type extrinsic sample and is therefore wrong here. The option claiming holes dominate describes a p-type sample, again requiring doping that is absent. The option stating no free carriers exist is wrong because silicon has a moderate band gap of about 1.1 eV, so thermal energy at 300 K does liberate a small but non-zero carrier population. As a sanity check, charge neutrality of the isolated crystal demands equal positive and negative mobile charge, confirming $n_e = n_h = n_i$.

Intrinsic Semiconductors

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