Variation of E_F with Doping Concentration and Temperature

We may plot the position of the Fermi energy level as a function of the doping con centration. Figure 1.1 shows the Fermi energy level as a function of donor concentration (n type) and as a function of acceptor concentration (p type) for silicon at T = 300 K. As the doping levels increase, the Fermi energy level moves closer to the conduction band for the n-type material and closer to the valence band for the p-type material. Keep in mind that the equations for the Fermi energy level that we have derived assume that the Boltzmann approximation is valid.

Figure 1.1 Position of Fermi level as a function of donor concentration (n type) and acceptor concentration (p type).

The intrinsic carrier concentration n_i , is a strong function of temperature, so that E_F in a function of temperature also. Figure 1.2 shows the variation of the Fermi energy level in silicon with temperature for several donor and acceptor concentrations. As the temperature increases, n_i increases, and E_F moves closer to the intrinsic Fermi level. At high temperature, the semiconductor material begins to lose its extrinsic characteristics and begins to behave more like an intrinsic semiconductor. At the very low temperature, freeze-out occurs; the Boltzmann approximation is no longer valid and the equations we derived for the

Figure 1.2 Position of Fermi level as a function of temperature for various doping concentrations.

Fermi-level position no longer apply. At the low temperature where freeze-out occurs, the Fermi level goes above E_d for the n-type material and below E_a for the p-type material. At absolute zero degrees, all energy states below E_F are full and all energy states above E_F are empty.