Title: Precision control of thermal transport in cryogenic single-crystal silicon devices Show Chinese title

Title: 低温单晶硅器件中热传输的精度控制

Abstract: 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. Show Chinese abstract

Abstract: 我们报告了在低于1K的温度下测量的多模式单晶硅梁的扩散-弹性质热导率。研究表明，声子平均自由程$\ell$是梁表面粗糙度特性的强函数。 这种效应在长度远大于$\ell$的漫散射梁中得到增强，即使表面相对光滑（均方根5-10纳米），峰值热波长为0.6$\mu$米。在具有坑状表面形态且特征坑深为30纳米的梁中观察到了共振声子散射。 因此，如果表面粗糙度没有得到适当控制，对于在整个晶圆上制造的漫散射梁，热导率可能会显著变化。 相比之下，当梁的长度为$\ell$量级时，导热性由弹性质输运主导，并且实际上由梁面积决定。 我们展示了弹性质梁的均匀性在分数偏差方面为$\pm$8%，这一偏差主要由支持微机电装置和电引线的漫散射梁的热导率决定。 此外，我们未发现单晶硅膜中有过量的比热证据。 这使得可以使用正常金属薄膜精确控制器件的热容量。 我们在大型阵列的远红外和毫米波波长低温探测器的设计和制造背景下讨论了这些结果。