  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.
