Quantum Wires for Temperature-Dependent Behaviour in Advanced Physical Electronics: MATLAB-Based Modelling of Ballistic-to-Diffusive Transition in GaAs Semiconductor Quantum Wires

This study investigates how temperature affects electron transport in GaAs quantum wires, tracing the shift from ballistic to diffusive behaviour between 1 K and 300 K. As semiconductor devices push deeper into the nanoscale, understanding quantum transport becomes vital for designing the next generation of electronics. A MATLAB model built on the Landauer–Büttiker framework forms the core of this work, combining quantum confinement, Fermi–Dirac statistics, and temperature-dependent scattering through Matthiessen's rule. The simulation focuses on a GaAs wire with cross-sectional dimensions of 50 nm × 50 nm and a length of 200 nm. Results show clear conductance quantisation at low temperatures, with near-ballistic transport yielding 5.7 G₀ at 1 K. As temperature rises, thermal broadening and acoustic phonon scattering gradually erode these quantised steps. By 300 K, conductance drops to just 0.25 G₀. The transition from ballistic to diffusive transport occurs around 50 K, where the electron mean free path becomes shorter than the wire length. Overall, the study demonstrates that GaAs quantum wires must operate below 50 K to maintain quantum transport, offering valuable insight for the design of quantum computing interconnects and nanoscale electronic devices.