Terahertz Frequency, Heisenberg’s Uncertainty Principle, Einstein Relation, Dimensional Quantization, and Opto-Electronic Materials

In this chapter, the Einstein relation (ER) in quantum wells (QWs) and nano wires (NWs) of opto-electronic materials (taking QWs and NWs \(n - Hg_{1 - x} Cd_{x} Te and \, n - In_{1 - x} Ga_{x} As_{y} P_{1 - y}\) \(lattice \, matched \, to \, InP\) as examples) under terahertz frequency on the basis of Heisenberg’s Uncertainty Principle (HUP) has been investigated. It has been found that the ER exhibits quantum steps variations with electron statistics, film thickness, intensity, and wave length for all the cases. A relationship where the ER is inversely proportional to the thermo electric power in the presence of a strong magnetic field (\(L_{0}\)), which is an easily measurable experimental quantity, has been suggested in this context.