Arif Khan

Current density in generalized Fibonacci superlattices under a uniform electric field

We present an exhaustive study on tunneling and electrical conduction in an electrically biased GaAs-Al(y)Ga(1-y)As generalized Fibonacci superlattice. The study is based on transfer matrix formalism using an Airy function approach and provides an exact calculation of the current density in the case of quasi-periodic multibarrier systems. The results suggest the use of such quasi-periodic systems in perfect band-pass or band-eliminator (of extremely low width) circuitry. We have clearly demonstrated the resonance-type peaks and negative differential conductivity regimes in such systems. It has also been found that quasi-periodicity favors sharp negative differential conductivity peaks compared to those in periodic superlattices and thus have profound importance in device applications.

A study of Landauer resistance and related issues of the generalized Thue-Morse lattice

We have carried out an elaborate study of electrical conduction in the generalized Thue-Morse (GTM) lattice. We have studied (i) the Landauer resistance, trace map and localization length of GTM structures, and (ii) the effects of deviations of inter-barrier distances from ideal GTM structures on electrical conduction. Among other things, our results indicate clearly the conditions under which a GTM lattice is likely to be most akin to a periodic system.

Lifetime of resonant tunnelling states in multibarrier systems

Abstract We have studied the variation of the resonant tunnelling lifetime with resonant energies for multibarrier systems (MBS) consisting of rectangular barrier type potentials and going beyond the usual double barrier case. Among other things, this variation shows a special kind of minima for MBS with more than three barriers.

Relativistic impacts on tunnelling through multi-barrier systems

We have studied relativistic effects on the tunnelling of electrons through a multi-barrier system (MBS) consisting of rectangular barrier potentials, by deriving, for the purpose, relativistic formulae for the transmission coefficient and associated relativistic conditions for resonant tunnelling. Among other things, we have discussed critically the quantitative extents of relativistic impacts on tunnelling through MBSS, especially in the context of their measurability.

Correlation between trace map and Landauer resistance of Fibonacci lattice

Abstract We have studied the trace map and Landauer resistance (LR) of the Fibonacci lattice, and indicate how diverse features of the LR of this kind of system can be correlated in a meaningful way with the energy spectrum provided by the corresponding trace map. A study of this kind would facilitate the interpretation of the experimental results on the LR of the Fibonacci lattice.

Some features of resonant tunnelling

Abstract We show how the condition for resonant tunnelling in a system of two rectangular barriers can be interpreted in terms of the band structure and phase change of Bloch electrons in an infinite periodic system having a part of the two-barrier system as the periodicity.

LCAO approach to non-relativistic and relativistic Kronig-Penney models

We have reported a comparative study of dynamics of non-relativistic and relativistic electrons in Kronig-Penney models with the use of discretized Hamiltonians in the context of the linear combination of atomic orbitals approach. We have carried out general formulations of both non-relativistic and relativistic cases, by taking the atomic potentials appropriately as δ-function potentials; then, we have applied these general formulations to obtain significant results regarding relativistic impacts on certain important aspects of the electronic energy spectrum of periodic, quasiperiodic and disordered systems.

Carrier Concentrations in Degenerate Semiconductors Having Band Gap Narrowing

The density-of-states effective mass approximation and the conduction-band effective mass approximation are employed to formulate carrier concentrations and the diffusivity-mobility relationship (DMR) for heavily doped n-semiconductors exhibiting band gap narrowing. These are very suitable for the investigation of electrical transport also in heavily doped p-semiconductors. Numerical calculations indicate that the DMR depends on a host of parameters including the temperature, carrier degeneracy, and the non-parabolicity of the band structure.

Density of states of generalised Thue-Morse lattice and related issues

Abstract We have investigated the density of states (DOS) of the generalised Thue-Morse (GTM) lattice, and compared by that means the degrees of aperiodicity and relevant electronic states of various GTM lattices. Further, we have correlated the DOS of various GTM lattices with the corresponding energy spectrum. Among other things, we find that GTM lattices with higher ratios of relevant exponents are likely to be more periodic than other varieties of it.

Linkage between trace map and landauer resistance of thue-morse lattice

Abstract We have studied Landauer Resistance (LR) and “trace map” of Thue-Morse (TM) lattice, and we have indicated thereby how various features of LR of this kind of lattice can be clearly linked with the energy spectrum yielded by the corresponding trace map.