Debye Length - Debye Length in Semiconductors

Debye Length in Semiconductors

The Debye length has become increasingly significant in the modeling of solid state devices as improvements in lithographic technologies have enabled smaller geometries.

The Debye length of semiconductors is given:

where

ε_Si is the dielectric constant,

k_B is the Boltzmann's constant,

T is the absolute temperature in kelvins,

q is the elementary charge, and

N_d is the density of dopants (either donors or acceptors).

When doping profiles exceed the Debye length, majority carriers no longer behave according to the distribution of the dopants. Instead, a measure of the profile of the doping gradients provides an “effective” profile that better matches the profile of the majority carrier density.

In the context of solids, the Debye length is also called the Thomas–Fermi screening length.