Defect reserve

The impurity reserve 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 impurities still partially bind charge carriers (electrons), i.e. in which not all impurities ( electron donors or electron acceptors introduced by doping ) in the semiconductor crystal are ionized. If this reserve of possible charge carriers is used up by increasing temperature, the impurity depletion occurs .

Physical description

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

In the case of the impurity reserve, the Fermi level ( ) lies between the effective donor level ( ) and the conduction band ( ), with the effective donor level taking on the function of the valence band : ${\displaystyle E_{\mathrm {F} }}$ ${\displaystyle E_{\mathrm {D} }^{*}}$ ${\displaystyle E_{\mathrm {L} }}$

${\displaystyle {E_{\mathrm {D} }^{*}}\leq E_{\mathrm {F} }\leq E_{\mathrm {L} }}$.

For comparison, a comparison for the case of self-conduction

${\displaystyle n={\sqrt {N_{\mathrm {L} }N_{\mathrm {V} }}}\cdot \mathrm {e} ^{-{\frac {E_{g}}{2kT}}}}$

and the formula for the electrons in the conduction band at the impurity reserve:

${\displaystyle n={\sqrt {N_{\mathrm {L} }N_{\mathrm {D} }}}\cdot \mathrm {e} ^{-{\frac {E_{\mathrm {L} }-{E_{\mathrm {D} }^{*}}}{2kT}}}}$.

where the electron concentration in the conduction band, the effective density of states of the conduction band states (for silicon = 2.73 · 10 ¹⁹  cm ⁻³ ), or the concentration of donors or acceptors, the energy of the band gap , the energy of the lower conduction band edge, the (absolute ) Is the energy of the donor state, the Boltzmann constant and the temperature. ${\displaystyle n}$ ${\displaystyle N_{\mathrm {L} }}$ ${\displaystyle N_{\mathrm {L} }}$ ${\displaystyle N_{\mathrm {V} }}$ ${\displaystyle N_{\mathrm {D} }}$ ${\displaystyle E_{g}}$ ${\displaystyle E_{\mathrm {L} }}$ ${\displaystyle E_{\mathrm {D} }^{*}}$ ${\displaystyle k}$ ${\displaystyle T}$

meaning

As can be seen from the equations, the electron concentration in the conduction band in the area of ​​the impurity reserve is strongly dependent on the temperature. This makes the design of an electronic circuit much more complicated. The operating temperature of most semiconductor components is, however, at room temperature (and higher), so that one is in the area of impurity depletion , in which the electron concentration increases approximately linearly with the doping concentration.

literature

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

Web links

• Defect reserve. In: Lexicon of Physics. Spectrum of Science, 1998. 
• 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 . 
• Peter Böni: Solid State Physics 2002/03. (pdf) Physics Department, TU Munich, May 16, 2003 . 
• Rudolf Gross, Achim Marx: Solid State Physics . de Gruyter, Munich 2014, ISBN 978-3-486-71294-0 , p. 493, Fig. 10.11 ( google.es ).