First-principles calculations of thermal transport at metal/silicon interfaces: evidence of interfacial electron-phonon coupling

Abstract

With the increasing miniaturization of electronic components and the need to optimize thermal management, it has become essential to understand heat transport at metal/semiconductor interfaces. While it has been recognized decades ago that an electron phonon channel may take place at metal-semiconductor interfaces, its existence is still controversial. Here, we investigate thermal transport at metal-silicon interfaces using the combination of first principles calculations and nonequilibrium Green's function (NEGF). We explain how to correct NEGF formalism to account for the out of equilibrium nature of the energy carriers in the vicinity of the interface. The relative corrections to the equilibrium distribution are shown to arise from the spectral mean free paths of silicon and may reach 15 percents. Applying these corrections, we compare the predictions of NEGF to available experimental data for Au/Si, Pt/Si and Al/Si interfaces. Based on this comparison, we infer the value of the electron phonon interfacial thermal conductance by employing the two temperature model. We find that interfacial thermal transport at Au/Si interfaces is mainly driven by phonon phonon processes, and that electron phonon processes play a negligible role in this case. By contrast, for Al/Si interfaces, we show that phonon-phonon scattering alone can not explain the experimental values reported so far, and we estimate that the electron-phonon interfacial conductance accounts for one third of the total conductance. This work demonstrates the importance of the electron-phonon conductance at metal-silicon interfaces and calls for systematic experimental investigation of thermal transport at these interfaces at low temperatures. It paves the way for an accurate model to predict the conductance associated to the interfacial electron phonon channel.

Figures (18)

• Figure 1: Schematic representation of the metal/semiconductor interface. The system is divided in two contacts and a device. $D_1$, $D_2$ and $D_\mathrm{d}$ represent the dynamic matrices of the isolated contacts and device. $\tau_1$ and $\tau_2$ are the coupling matrices between the contacts and the device.
• Figure 2: Bulk phonon dispersion curves obtained by DFT calculations (lines) compared to experimental data (symbols). From top to bottom: Au, Pt, Al and Si. The experimental data are respectively taken from Refs. disp_Aldisp_Ptdisp_Audisp_Si_1disp_Si_2.
• Figure 3: Phonon-phonon transmission calculated within the Landauer formalism for the three systems considered.
• Figure 4: Interfacial phonon-phonon conductance as a function of temperature computed with the NEGF method for the three interfaces Au/Si, Pt/Si and Al/Si.
• Figure 5: Spectral phonon mean free paths $\Lambda_i$, smoothed out by the gaussian regressor gauss_ml, and calculated using the Grüneisen parameter and the $3$ phonon lifetimes calculations.