Figure 2.17. Temperature dependencies of the intrinsic carrier (tensity of the semiconductors Ge, Si, and GaAs. Note the lack of linearity at the lower temperatures arising from the T3'2 factor in Eq. (2.15). (From G. Burns, Solid State Physics, Academic Press, Boston, 1985, p. 315.)

depicted in Fig. 2.14. The Brillouin zone has eight such faces, with each point L shared by two zones, so the zone actually contains only four of these points proper to it, and we say that the valley degeneracy for Ge is 4. The semiconductor Si has its lowest conduction band minimum along the A or (001) direction about 85% of the way to the A' point, as shown in Fig. 2.16. The compound GaP, not shown, also has its corresponding valley along A about 92% of the way to X. We see from Fig. 2.14 that there are six such A lines in the Brillouin zone, so this valley degeneracy is 6. Associated with each of the valleys that we have been discussing, at point L for Ge and along direction A for Si, there is a three-dimensional constant-energy surface in the shape of an ellipsoid that encloses the conduction electrons in the corresponding valleys, and these ellipsoids are sketched in Figs. 2.19a and 2.19b for Ge and Si, respectively.

Some interesting experiments such as cyclotron resonance have been carried out to map the configuration of these ellipsoid-type constant-energy surfaces. In a cyclotron resonance experiment conduction electrons are induced to move along constant energy surfaces at a velocity that always remains perpendicular to an applied magnetic field direction. By utilizing various orientations of applied magnetic fields relative to the ellipsoid the electrons at the surface execute a variety of orbits, and by measuring the trajectories of these orbits the shape of the energy surface can be delineated.

Table B.6 lists values of the energy gap Eg for the type IU-V and II-VI semiconductors at room temperature (left-hand value) and in several cases it also lists the value at absolute zero temperature (right-hand value). Table B.7 gives the temperature and pressure dependencies, dEJdT and dEJdP, respectively, of the gap at room temperature.

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