Calculate the position of the intrinsic Fermi level with respect to the center of the bandgap in silicon at $T=300 \mathrm{~K}$ .

The density of states effective carrier masses in silicon are $m_{n}^{*}=1.08 m_{0}$ and $m_{p}^{*}=0.56 m_{0}$ .

Question

Calculate the position of the intrinsic Fermi level with respect to the center of the bandgap in silicon at [latex]T=300 \mathrm{~K}[/latex].

The density of states effective carrier masses in silicon are [latex]m_{n}^{*}=1.08 m_{0}[/latex] and [latex]m_{p}^{*}=0.56 m_{0}[/latex].

Accepted Answer

The intrinsic Fermi level with respect to the center of the bandgap is

[latex]E_{F i}-E_{ ext {midgap }}=\frac{3}{4} k T \ln \left(\frac{m_{p}^{*}}{m_{n}^{*}} ight)=\frac{3}{4}(0.0259) \ln \left(\frac{0.56}{1.08} ight)[/latex]

or

[latex]E_{F i}-E_{ ext {midgap }}=-0.0128 \mathrm{eV}=-12.8 \mathrm{meV}[/latex]

Comment

The intrinsic Fermi level in silicon is [latex]12.8 \mathrm{meV}[/latex] below the midgap energy. If we compare [latex]12.8 \mathrm{meV}[/latex] to [latex]560 \mathrm{meV}[/latex], which is one-half of the bandgap energy of silicon, we can, in many applications, simply approximate the intrinsic Fermi level to be in the center of the bandgap.

Question 4.4: Calculate the position of the intrinsic Fermi level with res...

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