  Theoretical prediction of phonon transport in modern semiconductor
nanodevices requires atomic resolution of device features and quantum transport
models covering coherent and incoherent effects. The nonequilibrium Green's
function method (NEGF) is known to serve this purpose very well, but is
numerically very expensive. This work extends the very efficient B\"uttiker
probe concept to phonon NEGF and discusses all implications of this method.
B\"uttiker probe parameters are presented that reproduce within NEGF
experimental phonon conductances of Si and Ge between 10K and 1000K. Results of
this method in SiGe heterojunctions illustrate the impact of interface
relaxation on the device heat conductance and the importance of inelastic
scattering for the phonon distribution.
