Pure silicon at room temperature has an electron number density in the conductio

Question

Pure silicon at room temperature has an electron number density in the conduction band of
about 5 x 10^15 m2 and an equal density of holes in the valence band. There are about 5 x 10^28
silicon atoms per m3 , Suppose that one of every 107 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 doped silicon to that in pure silicon?

Explanation / Answer

(a) Phosphorus is a pentavalent impurity (Atomic number 15, electronic configuration 1s2 2s2 2p6 3s2 3p3)

Thus, when it is doped to a pure silicon sample, it provides with one excess electron, which is a free electron, per atom. Thus, the specimen is an n-type material.

(b) Phosporus will add n type carriers in excess. Since 1 of every 107 atoms is doped, and 5 x 10^28 atoms per unit volume are present, added impurity would add 4.67 x 10^26 free electrons.

(c)The correponding ratio, hence, would be approximately 10^28 : 10^15 = 10^13

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