On the Fowler-Nordheim Field Emission from Quantum-Confined Optoelectronic Materials in the Presence of Light Waves

Abstract

An attempt is made to present a simplified theoretical formulation of the Fowler-Nordheim field emission (FNFE) from quantum wires of optoelectronic materials, quantum wire effective mass Superlattices and quantum wire Superlattices (QWSLs) with graded interfaces on the basis of newly formulated electron dispersion laws within the framework of k.p formalism in the presence of strong light waves. The FNFE from the said structures under magnetic quantization has also been studied. It has been observed, taking quantum wires of n-InSb and QWSLs of GaAs/AlGaAs of the said types as examples that the FNFE increases with increasing concentration and after a critical value of degeneracy, the opposite behavior is being observed. The FNFE is a product of two functions inside the summation signs and both of them are functions of Fermi energy, effective mass and various system constants in a complex way. If the rate of increase of first function overcomes the rate of change of the second one, the FNFE will increase, whereas, for the opposite case, the FNFE will decrease. For 1D structure, the FNFE increases with increasing film thickness due to the existence van-Hove singularity and the magnitude of the quantum jumps are not of same height indicating the signature of the band structure of the material concerned. The appearance of the humps of the respective curves is due to the redistribution of the electrons among the quantized energy levels when the quantum numbers corresponding to the highest occupied level changes from one fixed value to the others. The FNFE increases with increasing electric field after a cut-off value and under magnetic quantization FNFE oscillates with magnetic field due to SdH effect for the said microstructures. In the presence of light waves, the FNFE increases to a very large extent in all the cases. Although the field current varies in various manners with all the variables in all the limiting cases as evident from all the curves, the rates of variations are totally band-structure dependent. Under certain limiting conditions, all the results as derived in this paper get transformed in to well known Fowler-Nordheim formula and thus confirming the compatibility test.