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

Rivo Herivola Manjakamanana Ravelonjato; Ravo Tokiniaina Ranaivoson; Raoelina Andriambololona; Naivo Rabesiranana; Charles Oyverné Randriamaholisoa; Wilfrid Chrysante Solofoarisina; Malik Maaza

doi:10.25159/3005-2602/21936

Authors

Rivo Herivola Manjakamanana Ravelonjato National Institute of Nuclear Sciences and Techniques https://orcid.org/0009-0006-5658-6153
Ravo Tokiniaina Ranaivoson National Institute of Nuclear Sciences and Techniques
Raoelina Andriambololona National Institute of Nuclear Sciences and Techniques
Naivo Rabesiranana National Institute of Nuclear Sciences and Techniques
Charles Oyverné Randriamaholisoa University of Antananarivo
Wilfrid Chrysante Solofoarisina National Institute of Nuclear Sciences and Techniques
Malik Maaza University of South Africa

DOI:

https://doi.org/10.25159/3005-2602/21936

Keywords:

quantum phase space, anisotropic pressure, shape and size effects, nanoelectronics

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 B_u 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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