Solid State Physics by David S. Schmool

Author:David S. Schmool [David S. Schmool]
Language: eng
Format: epub, mobi
ISBN: 978-1-942270-77-5
Publisher: Mercury Learning and Information LLC
Published: 2017-02-09T05:00:00+00:00

FIGURE 9.5: Carrier concentration temperature dependence illustrating the various concentration regimes. Shown are the variations for different doping concentrations for both donors and acceptors. For the behavior is that of an n-type semiconductor. As the NA concentration increases, the saturation level reduces proportionally until ND = NA, where the semiconductor has an intrinsic like behavior. Actually this is called the compensated state, where the donor excess electrons are matched by the acceptor excess holes. (Figure adapted from source: www.nextnano.de/nextnano3/tutorial/1Dtutorial doped semiconductors.htm.)

It is instructive to equate expression (9.24) and (9.10), where we can solve for the Fermi energy, to obtain:

(9.27)

In the low temperature range, where we have: this simplifies to:

(9.28)

The variation of the Fermi level with temperature can thus be understood as a function of temperature and impurity concentration, see Figure 9.6.

At zero temperature (0K), the Fermi level starts at a position between the conduction band edge and the impurity (donor) level. With an increase of temperature there will be a small increase in EF, but with a further increase of temperature the impurity levels become denuded and excitation of electrons between the valence and conduction bands occurs and the Fermi level approaches the intrinsic value,

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