Precision control of thermal transport in cryogenic single-crystal
  silicon devices
  We report on the diffusive-ballistic thermal conductance of multi-moded
single-crystal silicon beams measured below 1 K. It is shown that the phonon
mean-free-path $\ell$ is a strong function of the surface roughness
characteristics of the beams. This effect is enhanced in diffuse beams with
lengths much larger than $\ell$, even when the surface is fairly smooth, 5-10
nm rms, and the peak thermal wavelength is 0.6 $\mu$m. Resonant phonon
scattering has been observed in beams with a pitted surface morphology and
characteristic pit depth of 30 nm. Hence, if the surface roughness is not
adequately controlled, the thermal conductance can vary significantly for
diffuse beams fabricated across a wafer. In contrast, when the beam length is
of order $\ell$, the conductance is dominated by ballistic transport and is
effectively set by the beam area. We have demonstrated a uniformity of $\pm$8%
in fractional deviation for ballistic beams, and this deviation is largely set
by the thermal conductance of diffuse beams that support the
micro-electro-mechanical device and electrical leads. In addition, we have
found no evidence for excess specific heat in single-crystal silicon membranes.
This allows for the precise control of the device heat capacity with normal
metal films. We discuss the results in the context of the design and
fabrication of large-format arrays of far-infrared and millimeter wavelength
cryogenic detectors.
