Carrier Concentration

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Silicon is doped with boron to a concentration of 4x10¹⁷  atoms per cubic centimeters (atoms/cm³). Assume the intrinsic carrier concentration of silicon to be 1.5x10¹⁰ per cubic centimeters (atoms/cm³) and the value of kT/q to be 25mV at 300K. Compared to undoped silicon , the Fermi level of doped silicon:

(a) goes sown by 0.13 eV

(b) goes up by 0.13eV

(c) goes down by 0.427 eV

(d) goes up by 0.427 eV

Answer is (c)

Concept

${N_A} = 4\times 10^{17}$

${n_i} =1.5\times 10^{10}$

${V_T} = \frac{kT}{q}$ $q \times {V_T} = kT$(q is charge of electron) $kT = 25meV$ $E_{F_P}$(Fermi Level of P-Type doped Si) $E_{F_i}$(Fermi Level of intrinsic Si) $E_{F_i} - E_{F_P} = kT\ln (\frac{N_A}{n_i})$ $E_{F_i} - E_{F_P} = 5\times10^{3}\ln(\frac{4\times10^{17}}{1.5\times10^{10}})$ $E_{F_i} - E_{F_P} = 0.457eV \therefore E_{F_P}$ moves down by 0.457eV