4.2 Intrinsic Semiconductor

For an intrinsic semiconductor，the concentration of electrons in the conduction band is equal to the concentration of holes in the valence band. We may denote ni and pi as the electron and hole concentrations，respectively，in the intrinsic semiconductor. These parameters are usually referred to as the intrinsic electron concentration and intrinsic hole concentration. However，ni=pi，so normally we simply use the parameter ni as the intrinsic carrier concentration，which refers to either the intrinsic electron or hole concentration.

The Fermi energy level for the intrinsic semiconductor is called the intrinsic Fermi energy. For a given semiconductor material at a constant temperature，the value of ni is a constant，and independent of the Fermi energy.

The intrinsic carrier concentration for silicon at T=300K may be calculated by using the effective density of states function values from Tab.4.1. The value of ni calculated from Equation（4.8）for Eg=1.12eV is ni=6.95×109cm-3. The commonly accepted value of ni for silicon at T=300K is approximately 1.5×1010cm－3. This discrepancy may arise from several sources. First，the values of the effective masses are determined at a low temperature where the cyclotron resonance experimentsare performed. Since the effective mass is an experimentally determined parameter，and since the effective mass is a measure of how well a particle moves in a crystal，this parameter may be a slight function of temperature. Next，the density of states function for a semiconductor was obtained by generalizing the model of an electron in a three-dimensional infinite potential well. This theoretical function may also not agree exactly with experiment. However，the difference between the theoretical value and the experimental value of ni is approximately a factor of 2，which，in many cases，is not significant. Tab.4.2 lists the commonly accepted values of ni for silicon，gallium arsenide，and germanium at T=300K.

The intrinsic carrier concentration is a very strong function of temperature. Fig.4.2 is a plot of ni for silicon and gallium arsenide as a function of temperature. As seen in the figure，the value of ni for these semiconductors may easily vary over several orders of magnitude as the temperature changes over a reasonable range.

We have qualitatively argued that the Fermi energy level is located near the center of the forbidden bandgap for the intrinsic semiconductor. If the electron and hole effective masses are equal so that m*p=m*n，then the intrinsic Fermi level is exactly in the center of the bandgap. If m*p＞m*n，the intrinsic Fermi level is slightly above the center，and if m*p＜m*n，it is slightly below the center of the bandgap. The density of states function is directly related to the carrier effective mass，thus a larger effective mass means a larger density of states function. The intrinsic Fermi level must shift away from the band with the larger density of states in order to maintain equal numbers of electrons and holes.

Tab.4.2 Commonly accepted value of ni at T=300K

Fig.4.2 Intrinsic carrier concentration of Si，and GaAs as a function of temperature.