Pure silicon at room temperature has an electron number density of about 5 x 10^

Question

Pure silicon at room temperature has an electron number density of about 5 x 10^15 m^-3 and an equal density of holes in the valence band. Suppose that one of every 106 silicon atoms is replaced by a phosphorus atom. (a) What charge carrier number density will the phosphorus add (in terms of nm^-3)? (b) 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? The density of silicon is 2.33 g/cm3 and its molar mass is 28.086 g/mol

Explanation / Answer

Here one of every 108 silicon atoms isreplaced by a phosphorus atom.

We know that number of atoms per unit volume in thesilicon is nsi= 5 *1028atoms/m3

a) We know that added charge carrier density is np=nsi/108=  (5 *1028atoms/m3)/108

                                                                            = 5 * 1020/m3

b) Now Pure silicon at room temperature has an electron number density ofabout 5 x 1015 m-3and an equaldensity of holes in the valence band.

Then ratio of ratio of the charge carrier number density(electrons in the conduction band and holes in the valence band) inthe doped silicon to that in pure silicon is

       np/2( 5 x1015 m-3) =  5 *1020/m3 / 2( 5 x1015 m-3) = 5*104.

Here the factor 2 in the denominator is due to contribution ofboth electrons and holes .

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