Temperature and Doping Level Effect on Silicon Thermal Conductivity

Heat transfer management is a crucial concern in various fields, such as in miniaturized integrated circuits. Gaining insight into the mechanisms of heat conduction in these systems requires investigating the underlying physical processes, particularly in relation to temperature and doping level in semiconductors. In this study, we examine the temperature dependence of silicon (Si) thermal conductivity as a function of doping level across a range of p- and n-type concentrations varying from 1014 cm-3 to 1019 cm-3 . Planar Si substrates, covered with a 200 nmthick silicon dioxide layer, are characterized by using the 3ω method [1] over temperatures ranging from 80 K to 303 K. Thermal conductivity of the Si samples is determined by comparing experimental results with a semi-analytical model [2]. While many studies addressed silicon thermal conductivity since the 1960s, the systematic interplay between doping and temperature was surprisingly not scrutinized experimentally. Furthermore, two different mechanisms have been suggested to explain the reduction of thermal conductivity at high doping - the scattering of phonons by the dopant atoms or by electrons/holes [3] – and it has not been possible to determine precisely which one is leading until now. Here, the obtained lattice thermal conductivity values are compared to an analytical model based on the Boltzmann transport equation and other published modelling and experimental results. The analytical model considers the distortion of the crystal lattice – and thus the creation of obstacles for phonon propagation – by the dopant atoms, based on their difference in mass, size, and chemical bonding with Si atoms. The results tend to show that the later parameters have a significant impact on phonon drag. Elsewhere, from density functional theory (DFT) calculations [3], which only consider electron/hole-phonon scattering, it is found that the presence of electrons/holes in the crystal would mainly disrupt the crystal lattice and thus contribute to the scattering of phonons by these charge carriers. In this work more complete DFT calculations were performed to clarify the contribution of the aforementioned mechanisms. We also provide an estimation of the critical doping at which thermal conductivity reduces as a function of temperature.

[1] D. G. Cahill, Rev. Sci. Instrum. 61, 802 (1990)
[2] T. Borca-Tasciuc, A. R. Kumar and G. Chen, Rev. Sci. Instrum. 72, 2139 (2001)
[3] B. Liao et al., Phys. Rev. Lett. 114, 115901 (2015)

We acknowledge the support of project EFICACE (ANR-20-CE09-0024).