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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.
1 Answer
written 3.3 years ago by |
$f(E_C)=\dfrac{1}{1+exp\left[\dfrac{(E_C-E_V )}{KT}\right]}$
We know that,
K = Boltzman constant = 1.38×10-23 J/K
Boltzman constant can be expressed in eV as:
$K=\dfrac{1.38\times10^{-23}}{1.6\times10^{-19}}=86.25\times10^{-6}eV$
Also for an intrinsic semiconductor
$E_C-E_V=\dfrac{E_g}{2}$
$E_C-E_V=\dfrac{1.12}{2}=0.56 eV$
$f(E_C )=\dfrac{1}{1+exp\left[\dfrac{0.56}{86.25\times10^{-6}\times(20+273)}\right]}=\dfrac{1}{1+exp\dfrac{0.56}{22.15956}}$
(∴f(E_C )=\dfrac{1}{1+e^{0.0253} }=0.4936)