Ultrafast thermal boundary conductance under large temperature discontinuities of ultrathin epitaxial Pb films on Si(111)

Abstract

Heat transfer is a critical aspect of modern electronics, and a deeper understanding of the underlying physics is essential for building faster, smaller, and more powerful devices with an improved performance and efficiency. In such nanoscale structures, the heat transfer between two materials is limited by the finite thermal boundary conductance across their interface. Using ultrafast electron diffraction under grazing incidence we investigated the heat transfer from ultrathin epitaxial Pb films to an Si(111) substrate under strong non-equilibrium conditions. Applying an intense femtosecond laser pulse, the 5-7 ML thin Pb film experiences a strong heat up by 10-120 K while the Si substrate remains cold at $\approx$ 10 K. At such large temperature discontinuities we observe a significantly faster cooling for stronger excited Pb films. The decrease of the corresponding cooling time constant is explained through the thermal boundary conductance in the framework of the diffuse mismatch model. The thermal boundary conductance is reduced by more than a factor of three in comparison with Pb films grown on H-terminated substrates, pointing out the importance of the morphology of substrate, heterofilm and their interface.

Figures (3)

• Figure 1: URHEED experiment: (a) Scheme of the laser pump - electron probe setup for the Pb/Si(111) heterosystem. (b) RHEED pattern at an electron energy of [30]keV taken from a [6]ML thin epitaxial Pb(111) film grown on Si(111). (c) Thickness calibration through layer-by-layer RHEED intensity oscillations of the (00) spot as function of Pb coverage during growth by MBE. The blue triangles indicate the positions where the shutter of the evaporator was opened and closed, i.e., at [1/3]ML Pb coverage (Si(111)-$\beta(\sqrt{3} {\times} \sqrt{3})\mathrm{R}30^\circ$-Pb wetting layer), and at 5, 6, and [7]ML Pb coverage, respectively.
• Figure 2: Lattice dynamics of ultrathin Pb films: (a) Excitation and recovery of the normalized intensity $I(\Delta t)/I(T_\mathrm{Si})$ of a [6]ML thin film using different absorbed energy densities $\Phi_\mathrm{abs}$. (b) Corresponding transient normalized temperature change $\Delta T(\Delta t)/\Delta T_\mathrm{max}$. (c) Fraction of recovery time constant $\tau_\mathrm{rec}$ and film thickness $d$ as function of temperature rise $\Delta T_\mathrm{max}$ from experiment (data points) and from DMM (black curve). The color of the symbols indicates the excitation strength, with blue corresponding to weak and orange to strong excitation. The shaded areas in (a,b) are the $1\sigma$ uncertainties of the fits.
• Figure 3: Thermal boundary conductance $G$ and structure of the wetting layer: (a) Experimental $G$ for film thicknesses of [5-7]ML and compared to DMM in Debye model with the sound velocities along the [111] direction (black curve). The color of the symbols indicates the excitation strength, with blue corresponding to weak and orange to strong excitation. Inset: Scattering mechanism for phonons in DMM. (b) STM image of the Si(111)-$\beta(\sqrt{3} {\times} \sqrt{3})\mathrm{R}30^\circ$-Pb wetting layer at room temperature taken at negative bias of [-1]V with a current of [810]pA, i.e., probing occupied states. Bright features correspond to Pb atoms while dark features indicate Si atoms in substitutional sites replacing the Pb atoms. The Pb coverage is reduced to [0.28]ML instead of [1/3]ML. (c) SPA-LEED pattern of the Si(111)-$\beta(\sqrt{3} {\times} \sqrt{3})\mathrm{R}30^\circ$-Pb wetting layer at [100]K taken at [130]eV. The formation of the Pb/Si surface alloy and increased disorder causes the honeycomb-shaped diffuse intensity at $(3 {\times} 3)$ positions.