Signature of the Reduced Sound Velocity in Thin NbN Films

Here, we investigate thermal transport and phonon dynamics in the 30-nm thick NbN device. By measuring the thermal resistance
$Z_{\text{2}D}$
at temperatures beyond the critical temperature
$T_{c}$
and the resistance relaxation time
$\tau _{R}$
in the vicinity of
$T_{c}$
, we obtain thermal parameters that are consistent with the acoustic mismatch model. Using the acoustic mismatch model and the experimental values of
$Z_{\text{2}D}$
and
$\tau _{R}$
, we determine the phonon heat capacity, which also gives access to the sound velocity
$v_{s}$
in NbN. The obtained value of
$v_{s}$
is two times lower than the value in bulk NbN, and it corresponds to the velocity estimates obtained by other experimental methods. Our findings can be useful for modeling and improving the performance of low-temperature devices based on NbN films.