Entropy, Electric Field and Heavily Doped Nanowires

Abstract

In this paper an attempt is made to study, the entropy in the presence of intense electric field in nanowires (NWs) of heavily doped (HD) III–V and optoelectronic materials on the basis of newly formulated electron dispersion relations within the frame work of k → ⋅ p → formalism. It is found taking HD NWs of InSb, InAs, Hg(1– x) Cd (x)Te and In(1– x) Ga( x) As( y) P(1– y) lattice matched to InP as examples III–V, ternary and quaternary compounds that the entropy increases with increasing electron concentration per unit length and decreasing film thickness in different spiky manners, since the coincidence of Fermi energy with the sub-band energy leads to the step functional dependence of the density state function and this fact is being reflected in the quantized variations of the entropy with the said variables. The entropy increases with increasing electric field and decreasing alloy composition respectively. The numerical values of entropy with all the physical variables are totally band structure dependent for all the cases. The most striking features are that the presence of poles in the dispersion relation of the materials in the absence of band tails creates the complex energy spectra in the corresponding opto-electronic HD NWs and the effective electron mass exists within the band gap which is impossible without the concept of band tailing. The well-known classical result of entropy for non-degenerate bulk semiconductors having parabolic energy bands has been obtained as a special case of our generalized formulation and thus confirming the compatibility test. The content of this paper finds four important applications in the field of quantum effect devices of nanoscience and nanotechnology.