Subjective Type

Pure silicon at room temperature has an electron number density in the conduction band of about $$5 \times 10^{15}m^{-3}$$ and an equal density of holes in the valence band. Suppose that one of every $$10^7$$ silicon atoms is replaced by a phosphorus atom. $$(a)$$ Which type will the doped semiconductor be, $$n$$ or $$p?$$ $$(b)$$ What charge carrier number density will the phosphorus add? $$(c)$$ What is the ratio of the charge carrier number density (electrons in the conduction band and holes in the valence band) in the doped silicon to that in pure silicon?

Solution

$$(a)$$ The semiconductor is $$n-type$$, since each phosphorus atom has one more valence
electron than a silicon atom.
$$(b)$$ The added charge carrier density is
$$n_P=10^{-7}n_{Si}=10^{-7}(5\times 10^{28}m^{-3})=5\times 10^{21}m^{-3}$$
$$(c)$$ The ratio is
$$(5\times 10^{21}m^{-3})/\left [ 2(5\times 10^{15}m^{-3}) \right ]=5\times 10^5$$
Here the factor of $$2$$ in the denominator reflects the contribution to the charge carrier
density from both the electrons in the conduction band and the holes in the valence band.

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