Near-Field Radiative Heat Transfer Between Heavily Phosphorus-Doped Silicon Plates: Effects of Doping Concentration

To address the critical thermal challenges in high-performance computing and three-dimensional integrated circuits, the doping-tunable control of near-field thermal radiation using CMOS-compatible materials offers a highly promising non-contact cooling strategy. In this work, radiative heat transfer between two parallel heavily phosphorus-doped silicon plates separated by a vacuum gap is studied using fluctuational electrodynamics. A doping-dependent Drude model is employed to describe the dielectric response of doped silicon, including carrier concentration, ionization, and mobility effects. The influences of gap width and doping concentration on the total and spectral heat transfer are systematically analyzed. The results show that the heat transfer increases sharply as the gap decreases and is mainly governed by TM-polarized evanescent modes. Under symmetric doping, the spectral peak shifts to higher frequencies as the doping concentration increases from 1018 to 1021 cm−3, while the strongest transfer occurs at 1019 cm−3 because of favorable surface-plasmon-polariton coupling and impedance matching. These findings provide a theoretical foundation for chip-scale thermal management and on-chip radiative cooling in CMOS-compatible silicon platforms, although practical implementation would require dynamic tuning mechanisms and device-level engineering in future work.