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A pure Si crystal has 5 xx 10^22 atoms m...

A pure Si crystal has `5 xx 10^22` atoms `m^(-3)`. It is doped by 1 ppm concentration of pentavalent As. The number of holes is `(n_i^2=n_p n_e)`
(Take `n_i = 1.5 xx 10^16 m^(-3)`)

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Note that thermally generated electrons `(n_i ~ 10^(16) m^(-3) )` are negligibly small as compared to those produced by doping.
Therefore, `n_e ~~ N_D `. Since `n_e n_h = n_(i)^(2)`
`n_e = ( 5 xx 10^(28))/( 10^6 ) = 5 xx 10^(22) `The number of holes
`n_h = ( 2.25 xx 10^(32)) // ( 5 xx 10^(22))~4.5 xx 10^9 m^(-3)`
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