Interfacial thermal conductance across metal-insulator/semiconductor interfaces due to surface states

We point out that the effective channel for the interfacial thermal conductance, the inverse of Kapitza resistance, of metal-insulator/semiconductor interfaces is governed by the electron-phonon interaction mediated by the surface states allowed in a thin region near the interface. Our detailed calculations demonstrate that the interfacial thermal conductance across Pb/Pt/Al/Au-diamond interfaces are only slightly different among these metals, and reproduce well the experimental results of the interfacial thermal conductance across metal-diamond interfaces observed by Stoner et al. [Phys. Rev. Lett. 68, 1563 (1992)] and most recently by Hohensee et al. [Nat. Commun. 6, 6578 (2015)].

Figure 1

(a) Band alignment of a metal-diamond interface along the $z$ direction. The SS only exists in a thin interfacial region, as shown. (b) Schematic of phonon emission due to the SS-phonon interaction. $\left({\mathbf{q}}_{\left|\right|},q_z\right)$ denotes the wave vector of the phonon, where ${\mathbf{q}}_{\left|\right|}$ is in the $x-y$ plane and $q_z$ is in the $z$ direction. $\left({\mathbf{k}}_{\left|\right|},\kappa \right)$ and $\left({\mathbf{k}}_{\parallel }^{\prime },{\kappa }^{\prime }\right)$ are the wave vectors of the initial and final electron states of SS, respectively. $\left({\mathbf{k}}_{\left|\right|},k_z\right)$ and $\left({\mathbf{k}}_{\parallel }^{\prime },{k^{\prime }}_z\right)$ are the related wave vectors of electrons in metal.

Figure 2

Calculated ITC across Pb/Pt/Al/Au-diamond interfaces for (a) free phonon modes and (b) localized phonon modes as a function of $E_{\mathrm{F}}-E_0$ for two different values of $D_{1}K$ when $T_p=293$ K. The realistic $E_{\mathrm{F}}-E_0$ listed in Table 1 are marked with vertical lines and the corresponding ITC are shown in Table 2.

Figure 3

Temperature dependence of ITC across Pb/Pt/Al/Au-diamond interfaces with $D_{1}K=3.09\times {10}^9\mathrm{eV}/\mathrm{cm}$. (a) When $T_p=293\mathrm{K},h_{\mathrm{K}}$ increases with $T_e$ because of more participating electron states at higher temperatures. (b) $h_{\mathrm{K}}$ dependence on $T_p$ for small $\mathrm{\Delta }T$. The increased phonon population at higher $T_p$ leads to more energy transfer.

Figure 4

(a) Spatial variations of normalized modular square of the SS for different energy $\xi$. $|{\psi }_{{\mathbf{k}}_{\left|\right|},\kappa }\left(\mathbf{r}\right){|}^2$ decays more significantly when the energy is at the middle of the band gap than that with the energy near the band edge. (b) Modular square of form factor $|I\left(0,0,{\kappa }^{\prime },\kappa ,0\right){|}^2$ as a function of $\xi$ and ${\xi }^{\prime }$. Changes in $|I\left(0,0,{\kappa }^{\prime },\kappa ,0\right){|}^2$ are significant when $|{\xi }^{\prime }|\sim |V_0|$ and $\left|\xi \right|\sim |V_0|$ while they are slight when $|{\xi }^{\prime }|\ll |V_0|$ and $\left|\xi \right|\ll |V_0|$.