Paper Details

Name: Dr. Rajeev Kumar Sharma
Country: India

Year: 2025
Volume: Volume-12, Issue-2 (July-December)
Page Number: 624-633
DOI: https://doi.org/10.5281/zenodo.22896144

Low-dimensional electronic systems occupy the regime in which at least one device dimension approaches the carrier de Broglie wavelength or mean free path. In this regime, confinement changes the allowed energies, the density of available states and the way in which carriers acquire and lose momentum. This study develops a unified theoretical treatment of these effects and illustrates it with four reproducible calculations. A position-dependent effective-mass Hamiltonian is solved for a GaAs/Al₀.₃Ga₀.₇As finite quantum well; dimensional density-of-states functions are compared under common broadening; the transient drift response is evaluated in the relaxation-time approximation; and the thermal evolution of a one-dimensional conductance staircase is obtained from the Landauer formula. For a 0.245 eV conduction-band barrier, reducing the GaAs well width from 20 to 4 nm raises the ground electron subband from 10.10 to 95.39 meV and reduces the number of bound states from five to one. The density of states changes successively from a square-root continuum in three dimensions to steps in two dimensions, threshold singularities in one dimension and discrete peaks in zero dimensions. At an electric field of 1 kV cm⁻¹, relaxation times of 25-100 fs produce steady drift velocities of 6.56-26.25 km s⁻¹, while the corresponding response bandwidth decreases from 6.37 to 1.59 THz. Conductance plateaus remain sharply resolved at 4 K but are progressively rounded when thermal energy approaches the assumed 25 meV subband spacing. The results show that band engineering and carrier dynamics cannot be optimized independently: confinement controls both the spectrum that carriers occupy and the phase space through which they scatter and conduct.

Keywords: quantum confinement; semiconductor nanostructures; quantum wells; density of states; carrier relaxation; ballistic transport; Landauer conductance.