We report on the diffusive-ballistic thermal conductance of multi-modedsingle-crystal silicon beams measured below 1 K. It is shown that the phononmean-free-path $\ell$ is a strong function of the surface roughnesscharacteristics of the beams. This effect is enhanced in diffuse beams withlengths much larger than $\ell$, even when the surface is fairly smooth, 5-10nm rms, and the peak thermal wavelength is 0.6 $\mu$m. Resonant phononscattering has been observed in beams with a pitted surface morphology andcharacteristic pit depth of 30 nm. Hence, if the surface roughness is notadequately controlled, the thermal conductance can vary significantly fordiffuse beams fabricated across a wafer. In contrast, when the beam length isof order $\ell$, the conductance is dominated by ballistic transport and iseffectively set by the beam area. We have demonstrated a uniformity of $\pm$8%in fractional deviation for ballistic beams, and this deviation is largely setby the thermal conductance of diffuse beams that support themicro-electro-mechanical device and electrical leads. In addition, we havefound no evidence for excess specific heat in single-crystal silicon membranes.This allows for the precise control of the device heat capacity with normalmetal films. We discuss the results in the context of the design andfabrication of large-format arrays of far-infrared and millimeter wavelengthcryogenic detectors.
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