Effects of Quantum Confinement on Thermodynamic Properties of Ideal Fermion Gases at the Nanoscale

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Original abstract

Quantum confinement in nanoscale systems dramatically alters the thermodynamic behaviour of fermions, with direct implications for nanoelectronics, quantum materials and energy devices. Using a quantum phase space formalism, we derive exact analytical expressions for the thermodynamic properties of an ideal Fermi gas under arbitrary confinement. A central outcome is the introduction of a unified parameter Bu that explicitly links confinement geometry to quantum degeneracy, interpolating smoothly between classical and quantum regimes. This approach predicts an anisotropic pressure tensor, reflecting direction-dependent quantum forces, and a low-temperature heat capacity scaling linearly with temperature, ensuring compliance with the third law of thermodynamics. Classical isotropic behaviour is recovered at high temperatures or large system sizes. Numerical simulations for confined electrons (5 nm – 50 nm) at metallic densities confirm that quantum effects dominate at experimentally accessible temperatures. Our results provide a predictive framework for interpreting quantum-confinement phenomena in diverse systems, including 2D perovskites, silicene heterostructures, quantum dot solar cells, and superconducting monolayers, where geometric tuning controls electronic and thermal responses.

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