Defect depletion

The impurity depletion is a term from solid state physics or semiconductor electronics . In the case of impurity conduction (a conduction mechanism for electrical current in semiconductors), it characterizes the temperature range in which all impurities are ionized, i.e. either their electron is released into the conduction band (in the case of donor impurities) or an electron is taken up from the valence band (acceptor impurity) to have. The area follows on from the so-called impurity reserve , in which the energy levels caused by impurities in the energy gap of semiconductors are still partially occupied.

description

Conduction mechanisms in doped and undoped semiconductors as a function of temperature

Conduction mechanisms in the Arrhenius graph with log (n) to T ⁻¹

The introduction of foreign atoms into a semiconductor crystal ( doping ) causes the formation of so-called impurity levels in the area of ​​the energy gap , that is, in the energy range between the valence and conduction band, which in the undoped semiconductor could not be occupied by electrons for quantum mechanical reasons. For donor defects (defects that give off electrons , e.g. by doping silicon with phosphorus ), this means that electrons can be more easily excited into the conduction band than with high-purity semiconductors. The reason for this lies in the significantly smaller energy gap to the conduction band, so that less energy (for example through the supply of heat) is required for this process.

With the usual doping concentrations of most semiconductors, the area of ​​the impurity depletion begins below the operating temperature (usually room temperature). In this case, the impurity conduction is the main mechanism for providing free charge carriers, and the charge carrier concentration essentially only depends on the original doping concentration of the semiconductor.

As already mentioned, with the impurity depletion (in contrast to the impurity reserve) all impurity levels are ionized , that is, the electrons occupy higher energy levels in the conduction band (n-doping) or the acceptor level itself (p-doping). The charge carrier concentration no longer increases with increasing energy, because the energy supplied is not yet sufficient to excite electrons directly from the valence band to the conduction band. The charge carrier concentrations are now only determined by the original doping concentration. The following applies to the electron density in the conduction band: ${\displaystyle n}$

${\displaystyle n\approx {N_{\mathrm {D} }}^{+}\approx N_{\mathrm {D} }}$.

where is the number density of ionized donors and the number density of donor impurities. ${\displaystyle {N_{\mathrm {D} }}^{+}}$ ${\displaystyle N_{\mathrm {D} }}$

The statement for the hole density in the valence band can be made analogously : ${\displaystyle p}$

${\displaystyle p\approx {N_{\mathrm {A} }}^{-}\approx N_{\mathrm {A} }}$.

where is the number density of ionized acceptors and the number density of acceptor defects. ${\displaystyle {N_{\mathrm {A} }}^{-}}$ ${\displaystyle N_{\mathrm {A} }}$

literature

• Frank Thuselt: Physics of Semiconductor Components: Introductory textbook for engineers and physicists . Springer, Berlin, 2004, ISBN 3-540-22316-9 .

Web links

• Defect depletion. In: Lexicon of Physics. Spectrum of Science, 1998. 
• Peter Böni: Solid State Physics 2002/03. (pdf) Physics Department, TU Munich, May 16, 2003, accessed on March 3, 2018 . 
• Othmar Marti, Alfred Plettl: Charge carrier densities in doped semiconductors. In: Lecture notes for physical electronics and measurement technology. Ulm University, August 14, 2007, accessed on March 29, 2009 . 
• Rudolf Gross, Achim Marx: Solid State Physics . de Gruyter, Munich 2014, ISBN 978-3-486-71294-0 , p. 493, Fig. 10.11 ( google.es ).