The Einstein Relation in Nipi Structures of Compound Semiconductors

With the advent of modern experimental techniques of fabricating nanomate-rials, it is possible to grow semiconductor superlattices (SLs) composed of alternative layers of two different degenerate layers with controlled thickness [1]. These structures have found wide applications in many new devices such as photodiodes [2], photoresistors [3], transistors [4], light emitters [5], tunneling devices [6], etc. [7–18]. The investigations of the physical properties of narrow gap SLs have increased extensively, as they are important for optoelectronic devices and also because the quality of heterostuctures involving narrow gap materials has been greatly improved. It may be noted that the nipi structures, also called the doping superlattices, are crystals with a periodic sequence of ultra-thin film layers [19, 20] of the same semiconductor with the intrinsic layer in between together with the opposite sign of doping. All the donors will be positively charged and all the acceptors negatively charged. This periodic space charge causes a periodic space charge potential which quantizes the motions of the carriers in the z-direction together with the formation of the subband energies. The electronic structures of the nipis differ radically from the corresponding bulk semiconductors as stated below:

• (a) Each band is split into mini-bands

• (b) The magnitude and the spacing of these mini-bands may be designed by the choice of the superlattices parameters and

• (c) The electron energy spectrum of the nipi crystal becomes two-dimensional leading to the step functional dependence of the density-of-states function.

In Sect. 8.2.1, of the theoretical background, the Einstein relation in nipi structures of tetragonal materials has been investigated. Section 8.2.2 contains the results for nipi structures of III—V, ternary and quaternary compounds, in accordance with the three and the two band models of Kane together with parabolic energy bands and they form the special cases of Sect. 8.2.1. Sections 8.2.3–8.2.5 contain the study of the DMR for nipis of II–VI, IV–VI, and stressed Kane type semiconductors, respectively. Section 8.3 contains the result and discussions of this chapter.