ELECTRON TRANSPORT THEORY IN SEMICONDUCTOR SYSTEMS CONTAINING PERIODICALLY ARRANGED ASYMMETRIC POTENTIAL WELLS AND BARRIERS (Universal International Scientific Journal, 2026)
The transmission of electron wave functions in a material whose physical parametersvary along a specific spatial direction has been investigated from a rigorous theoretical perspective. Insuch systems, spatial inhomogeneity plays a crucial role in determining the quantum-mechanicalbehavior of charge carriers, since variations in potential energy, effective mass, or compositional profilesignificantly influence wave propagation. When an electron travels through a non-uniform medium, itswave function adapts to the changing environment, leading to reflection, transmission, and interferencephenomena that must be described consistently within the framework of quantum mechanics.The present analysis is based on the single-particle, time-independent Schrödinger equation,which provides a fundamental description of stationary states in quantum systems. This equation isformulated under the assumption of total energy conservation, meaning that the sum of kinetic andpotential energies remains constant throughout the motion of the particle. By applying appropriateboundary conditions at interfaces where material properties change, one can determine the amplitudesof reflected and transmitted waves, as well as calculate physically measurable quantities such astransmission and reflection coefficients.Within this formalism, elastic scattering processes of non-interacting, spinless particles areexamined in detail. Elastic scattering implies that the particle’s total energy is conserved duringinteraction with the potential landscape, although its momentum and direction of motion may change.Particular attention is given to quantum tunneling phenomena, in which particles penetrate potentialbarriers even when their kinetic energy is lower than the barrier height. Such processes arise purely fromthe wave nature of matter and have no classical analog. Altogether, the approach provides a unified,internally consistent framework for describing wave transmission, reflection, and tunneling in spatiallynon-uniform quantum systems.
Keywords: semiconductor structure; Schrödinger equation; elastic scattering