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What is the probability of an electron being thermally excited to conduction band in silicon at 20oC. The band gap energy is 1.12eV; Boltzmann constant is 1.38 x 10-23 JIk.
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f(EC)=11+exp[(ECEV)KT]

We know that,

K = Boltzman constant = 1.38×10-23 J/K

Boltzman constant can be expressed in eV as:

K=1.38×10231.6×1019=86.25×106eV

Also for an intrinsic semiconductor

ECEV=Eg2

ECEV=1.122=0.56eV

f(EC)=11+exp[0.5686.25×106×(20+273)]=11+exp0.5622.15956

(∴f(E_C )=\dfrac{1}{1+e^{0.0253} }=0.4936)

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