We report measurements and Monte Carlo simulations of thermal conductivity of porous 100nm- thick silicon membranes, in which size, shape and position of the pores were varied randomly. Measurements using 2-laser Raman thermometry on both plain membrane and porous membranes revealed more than 10-fold reduction of thermal conductivity compared to bulk silicon and six-fold reduction compared to non-patterned membrane for the sample with 37% filling fraction. Using Monte Carlo solution of the Boltzmann transport equation for phonons we compared different possibilities of pore organization and its influence on the thermal conductivity of the samples. The simulations confirmed that the strongest reduction of thermal conductivity is achieved for a distribution of pores with arbitrary shapes that partly overlap. Up to 15% reduction of thermal conductivity with respect to the purely circular pores was predicted for a porous membrane with 37% filling fraction. The effect of pore shape, distribution and surface roughness is further discussed.
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