Diffusion stress

The diffusion voltage , seldom also called anti- diffusion voltage , is the potential difference ( electrical voltage ) across a space charge zone that counteracts the diffusion of charge carriers ( electrons and holes ) . It depends on the material and is ≈ 0.7  V for silicon and ≈ 0.3 V for germanium . ${\displaystyle U_{D}}$

Above: electron and hole concentration; Middle (top): charge carrier densities; Middle (bottom): electric field; Below: electrical potential

A semiconductor diode with a pn junction is considered : At the boundary between p- and n-doped semiconductors , the concentration gradient causes diffusion of charge carriers, i.e. H. Free electrons from the n-area migrate into the p-area ( diffusion current ), analogous to this the holes (defect electrons) migrate from the p- to the n-area.

This movement of charge carriers creates an opposing electric field between the space charges inside the crystal . This counteracts the further diffusion of mobile charge carriers, as it generates an opposite drift current .

The voltage generated by the counter electric field is called diffusion voltage (hence the name anti diffusion voltage ):

${\displaystyle U_{D}=U_{T}\cdot \ln {\frac {N_{A}\cdot N_{D}}{n_{i}^{2}}}}$

With

• the temperature stress ${\displaystyle U_{T}={\frac {k_{B}\cdot T}{q}}}$
  • the Boltzmann constant ${\displaystyle k_{B}}$
  • the absolute temperature ${\displaystyle T}$
  • the elementary charge ${\displaystyle q}$
• the number of acceptors ${\displaystyle N_{A}}$
• the number of donors ${\displaystyle N_{D}}$
• the intrinsic charge carrier density . ${\displaystyle n_{i}}$