JEE Main 2020 · Physics · Semiconductors and Communication · medium

Pure silicon has an intrinsic carrier concentration ni = 1.5×10^16 m^-3 at room temperature. It is doped with phosphorus at 4.5×10^22 atoms m^-3, and…

Numerical answer

Pure silicon has an intrinsic carrier concentration

n_i = 1.5\times10^{16}\ \mathrm{m^{-3}}

at room temperature. It is doped with phosphorus at

4.5\times10^{22}\ \mathrm{atoms\,m^{-3}}

, and every donor atom is ionised. The hole concentration in the doped crystal, in units of

10^{9}\ \mathrm{m^{-3}}

, is

Show answer and solution

Answer: 5

Each ionised donor contributes one electron, and

4.5\times10^{22}\gg n_i

, so the electron concentration is

n \approx N_D = 4.5\times10^{22}\ \mathrm{m^{-3}}

. The mass-action law

n\,p = n_i^2

then gives

p = \dfrac{(1.5\times10^{16})^2}{4.5\times10^{22}} = \dfrac{2.25\times10^{32}}{4.5\times10^{22}} = 5\times10^{9}\ \mathrm{m^{-3}}

. The crystal is n-type, with holes as the minority carriers.

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