Direct Measurement of Room-Temperature Nondiffusive Thermal Transport Over Micron Distances in a Silicon Membrane

The “textbook” phonon mean free path of heat carrying phonons in silicon at room temperature is $\sim 40\mathrm{nm}$. However, a large contribution to the thermal conductivity comes from low-frequency phonons with much longer mean free paths. We present a simple experiment demonstrating that room-temperature thermal transport in Si significantly deviates from the diffusion model already at micron distances. Absorption of crossed laser pulses in a freestanding silicon membrane sets up a sinusoidal temperature profile that is monitored via diffraction of a probe laser beam. By changing the period of the thermal grating we vary the heat transport distance within the range $\sim 1–10\mu \mathrm{m}$. At small distances, we observe a reduction in the effective thermal conductivity indicating a transition from the diffusive to the ballistic transport regime for the low-frequency part of the phonon spectrum.

Figure 1

Schematics of the sample and the experiment. (a) Freestanding Si membranes are fabricated from SOI wafers by backside etching. (b) Pump pulses are crossed in the silicon membrane, generating the transient thermal grating monitored via diffraction of the probe beam. Diffracted probe light is combined with a reference beam and directed to a fast detector.

Figure 2

Experimental data from membrane 1. (a) Thermal decay traces for transient grating periods ranging from 3.2 to $18\mu \mathrm{m}$. The decay time increases with the grating period. The inset shows the complete trace for the $7.5\mu \mathrm{m}$ period. (b) Thermal grating decay rate versus the grating wave vector squared showing the departure from diffusive behavior. The dashed line representing the diffusion model was obtained by fitting the low-wave-vector data in the range $L=15–25\mu \mathrm{m}$.

Figure 3

(a) The normalized effective thermal conductivity versus transient grating period compared with theory. (b) The calculated effective thermal conductivity as a function of the grating period and the membrane thickness.