  Dimensional dependence of thermal conductance at low temperatures in
nanowires is studied using the nonequilibrium Green's function (NEGF) method.
Our calculation shows a smooth dimensional crossover of thermal conductance in
nanowire from one-dimensional to three-dimensional behavior with the increase
of diameters. The results are consistent with the experimental findings that
the temperature dependence of thermal conductance at low temperature for
diameters from tens to hundreds nanometers will be close to Debye law. The
calculation also suggests that universal thermal conductance is only observable
in nanowires with small diameters. We also find that the interfacial thermal
conductance across Si and Ge nanowire is much lower than the corresponding
value in bulk materials.
