E4 Fermi-Dirac Statistics and Fermi Level

Topic

At a given temperature, the Fermi-Dirac distribution for this semiconductor material determines the occupancy probability for each available energy state within the material; this distribution drops—smoothly rather than abruptly—from an occupancy probability near one for energy states well below the Fermi level to an occupancy probability near zero for states well above that level. Consequently, a higher temperature causes the Fermi-Dirac distribution to drop more gradually around the Fermi level, rather than falling almost abruptly as it would at a much lower temperature.

Doping the semiconductor—according to the specific doping scheme established in another model within this set—shifts the Fermi level relative to the intrinsic Fermi level the material would possess if undoped (which lies near the middle of the bandgap). A higher concentration of ionized donor impurities (resulting from the doping) shifts the Fermi level upward, bringing it closer to the conduction band, whereas a higher concentration of ionized acceptor impurities shifts it downward, bringing it closer to the valence band. A doping level that introduces an even higher concentration of ionized donor impurities causes the Fermi level to shift even closer to the conduction band, moving it further away from the intrinsic Fermi level. Consequently, in this model—characterized by the Fermi-Dirac distribution and a Fermi level shifted by doping—that very Fermi level determines the free-electron and hole concentrations of the semiconductor material within the non-degenerate regime (where the Fermi level remains sufficiently far from both bands). In this regime, the model recovers the same law of mass action established by the Fermi-Dirac distribution: the closer the Fermi level is to the conduction band, the higher the free-electron concentration in the semiconductor material. Furthermore, since the Fermi level—shifted by doping—determines the occupancy of deep levels (described in greater detail by another model in this set), its position relative to those deep levels dictates whether they remain predominantly occupied or predominantly empty within the semiconductor material.

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