Thermal conductance of metal-metal interfaces

The thermal conductance of interfaces between Al and Cu is measured in the temperature range $78<T<298\mathrm{K}$ using time-domain thermoreflectance. The samples are prepared by magnetron sputter deposition of a $100\mathrm{nm}$ thick film of Al on top of layers of Cu on sapphire substrates. The chemical abruptness of the Al-Cu interface is systematically varied by ion-beam mixing using $1\mathrm{MeV}$ Kr ions. The thermal conductance of the as-deposited Al-Cu interface is $4\mathrm{GW}{\mathrm{m}}^{-2}{\mathrm{K}}^{-1}$ at room temperature, an order-of-magnitude larger than the phonon-mediated thermal conductance of typical metal-dielectric interfaces. The magnitude and the linear temperature dependence of the conductance are described well by a diffuse-mismatch model for electron transport at interfaces.

Figure 1

Ratio of the in-phase and out-of-phase changes in the intensity of the probe beam plotted as a function of the time delay between the pump and probe optical pulses. Each curve is labeled by the thickness of the Cu layer. The dashed lines are fits to the thermal model used to determine the thermal conductance of the Al-Cu and $\mathrm{Cu}\text{−}{\mathrm{Al}}_2{\mathrm{O}}_3$ interfaces.

Figure 2

The sensitivity of $V_{\mathrm{in}}∕V_{\mathrm{out}}$ to changes in selected parameters in the thermal model as calculated by Eq. (1). (a) Sensitivities at room temperature for the “thin Cu” sample, and (b) sensitivities at room temperature for the “thick Cu” sample. $G_1$ and $G_2$ are the Al-Cu and $\mathrm{Cu}\text{−}{\mathrm{Al}}_2{\mathrm{O}}_3$ interface conductances; $w_0$ is the spot size, and ${\Lambda }_{\mathrm{Al}}$ and ${\Lambda }_{\mathrm{Cu}}$ are the thermal conductivities of the Al and Cu layers.

Figure 3

Thermal conductance of the Al-Cu (open symbols) and $\mathrm{Cu}\text{−}{\mathrm{Al}}_2{\mathrm{O}}_3$ (filled symbols) interfaces as a function of the measurement temperature. The data are obtained by the combination of measurements on the two samples with different Cu layer thickness. The solid line shows the predictions for the conductance of the Al-Cu interface using the diffuse-mismatch model for electron transport described by Eq. (4).

Figure 4

Thermal conductance of Al-Cu interfaces as a function of ion dose. Each curved is labeled by the measurement temperature in degrees Kelvin. The dashed lines are fits to the data to determine the value of the parameter $\beta$ in Eq. (6); $\beta$ is given in units of $\mathrm{GW}{\mathrm{m}}^{-2}{\mathrm{cm}}^{-1}{\mathrm{K}}^{-1}$.