Quasiparticle relaxation times in clean Al films

Double tunnel junctions $S_1-S_2-S_3$ (Al-Al-Pb: Bi, mounted on sapphire substrates in vacuum) have been used to measure the inelastic (${\tau }_i$) and elastic (${\tau }_e$) scattering times in the center Al film ($T_c=1.28\mathrm{}$ K). The current peak at $V_{d1\mathrm{}}=\pm \mathrm{}\left[\right|\mathrm{}{V}_g|+\frac{({\Delta }_1-{\Delta }_3)}{e}]$ and the current step at $V_{d2\mathrm{}}=\pm \mathrm{}\left[\right|\mathrm{}{V}_g|-\frac{({\Delta }_1+{\Delta }_3)}{e}]$ provide complementary data on ${\tau }_i(E,T^{*})$ and ${\tau }_e(E,T^{*})$ in $S_2$ over the energy range $1.5\Delta \mathrm{}\left(0\right)<E<\mathrm{}5.5\mathrm{}\Delta \mathrm{}\left(0\right)\mathrm{}$ and the temperature range $0.6<\mathrm{}{T}^{*}<1.1\mathrm{}$ K; $e{V}_{d1\mathrm{}}$ and $e{V}_{d2\mathrm{}}$ yield ${\Delta }_1^{*}$ which through the BCS gap equation yields $T_1^{*}$. We assume $T_1^{*}=T_2^{*}=T^{*}$ and $T_3=T_s$ the substrate temperature which is measured directly. The measured generator junction power per unit area $P_g$, $T^{*}$, and $T_s$ yield $P_g=11(T^{*4\mathrm{}}-T_s^{*4\mathrm{}})$ mW ${\mathrm{cm}}^{-2\mathrm{}}$, in good agreement with the calculations by Kaplan for an Al-sapphire interface. A fit of our data for ${\tau }_i$ with theory gives a value of (1.0±0.14) × ${10}^{-7\mathrm{}}$ sec for ${\tau }_0$, the characteristic electric-phonon scattering time.