The Einstein Relation in Inversion Layers of Compound Semiconductors

It is well known that the electrons in bulk semiconductors in general, have three dimensional freedom of motion. When these electrons are confined in a one dimensional potential well whose width is of the order of the carrier wavelength, the motion in that particular direction gets quantized while that along the other two directions remains as free. Thus, the energy spectrum appears in the shape of discrete levels for the one dimensional quantization, each of which has a continuum for the two dimensional free motion. The transport phenomena of such one dimensional confined carriers have recently been studied with great interest. For the metal-oxide-semiconductor (MOS) structures, the work functions of the metal and the semiconductor substrate are different and the application of an external voltage at the metal-gate causes the change in the charge density at the oxide semiconductor interface leading to a bending of the energy bands of the semiconductor near the surface. As a result, a one dimensional potential well is formed at the semiconductor interface. The spatial variation of the potential profile is so sharp that for considerable large values of the electric field, the width of the potential well becomes of the order of the de Broglie wavelength of the carriers. The Fermi energy, which is near the edge of the conduction band in the bulk, becomes nearer to the edge of the valance band at the surface creating inversion layers. The energy levels of the carriers bound within the potential well get quantized and form electric subbands. Each of the subband corresponds to a quantized level in a plane perpendicular to the surface leading to a quasi two dimensional electron gas. Thus, the extreme band bending at low temperature allows us to observe the quantum effects at the surface.

In Sect. 7.2.1, of the theoretical background, the Einstein relation in n-channel inversion layers of tetragonal materials has been investigated for both weak and strong electric field limits. Section 7.2.2 contains the results for n-channel inversion layers of III – V, ternary and quaternary compounds for both the electric field limits whose bulk electrons obey the three and the two band models of Kane together with parabolic energy bands and they form the special cases of Sect. 7.2.1. Section 7.2.3 contains the study of the DMR for p-channel inversion layers of II – VI materials. Sections 7.2.4 and 7.2.5 contain the study of the DMR in p-channel inversion layers of IV – VI and stressed semiconductors for both the limits respectively. Section 7.3 contains the results and discussion of this chapter.