Phonon Conduction in Periodically Porous Silicon Nanobridges

Abstract

Thermal conduction in periodically porous nanostructures is strongly influenced by phonon boundary scattering, although the precise magnitude of this effect remains open to investigation. This work attempts to clarify the impact of phonon-boundary scattering at room temperature using electrothermal measurements and modeling. Silicon nanobeams, prepared using electron beam lithography, were coated with a thin palladium overlayer, which serves as both a heater and thermometer for the measurement. The thermal conductivity along the length of the silicon nanobeams was measured using a steady-state Joule heating technique. The thermal conductivities of the porous nanobeams were reduced to as low as 3% of the value for bulk silicon. A Callaway-Holland model for the thermal conductivity was adapted to investigate the relative impact of boundary scattering, pore scattering, and phonon bandgap effects. Both the experimental data and the modeling showed a reduction in thermal conductivity with increasing pore diameter, although the experimentally measured value was up to an order of magnitude lower than that predicted by the model.

Keywords:

• thermal conductivity
• porous silicon
• phononic crystals

Acknowledgments

The authors gratefully acknowledge financial support from MARCO Interconnect Focus Center, the National Science Foundation Graduate Research Fellowship program, and the Stanford Graduate Fellowship program.