Intrinsic Fermi level

The intrinsic Fermi level is the Fermi level of an intrinsic (non- impurity- containing, undoped ) semiconductor . ${\displaystyle W_{\mathrm {i} }}$

By equating the electron and hole density in thermodynamic equilibrium, it results :

${\displaystyle N_{\mathrm {c} }\cdot e^{-{\frac {W_{\mathrm {c} }-W_{\mathrm {i} }}{k_{\mathrm {B} }T}}}=N_{\mathrm {v} }\cdot e^{-{\frac {W_{\mathrm {i} }-W_{\mathrm {v} }}{k_{\mathrm {B} }T}}}}$

and subsequent conversion to the Fermi energy : ${\displaystyle W_{\mathrm {F} }}$

${\displaystyle \Leftrightarrow W_{\mathrm {i} }={\frac {W_{\mathrm {c} }+W_{\mathrm {v} }}{2}}+{\frac {1}{2}}\cdot k_{\mathrm {B} }T\cdot \ln \left({\frac {N_{\mathrm {v} }}{N_{\mathrm {c} }}}\right)=W_{\mathrm {F} }}$

With

• ${\displaystyle N_{\mathrm {c} }}$: effective density of states in the conduction band
• ${\displaystyle N_{\mathrm {v} }}$: effective density of states in the valence band
• ${\displaystyle W_{\mathrm {c} }}$: Energy of the conduction band edge in the band model
• ${\displaystyle W_{\mathrm {v} }}$: Energy of the valence band edge in the band model
• ${\displaystyle k_{\mathrm {B} }}$: Boltzmann constant
• ${\displaystyle T}$: Temperature on the Kelvin scale .

In the case of doped semiconductors, the Fermi level deviates from the intrinsic Fermi level.

The intrinsic Fermi level is always roughly in the middle of the band gap . In the case of self-conduction , this deviation is so small that it can be roughly said:

${\displaystyle W_{\mathrm {i} }\approx {\frac {W_{\mathrm {c} }+W_{\mathrm {v} }}{2}}\,.}$

literature

• J. Smoliner: Fundamentals of semiconductor physics . Springer-Verlag, 2018, ISBN 978-3-662-56629-9 ( limited preview in Google book search).