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The thermal conductivity of phononic-like membranes and their analogous nano-wires are computed with both Molecular Dynamics and Monte Carlo simulations. Using both methods, the thermal conductivity of the porous membranes with cylindrical pores is found to be lower than the nano-wire's one for the same scattering surface to volume. This work confirms experimental observations by Nomura et al [1] and Yu et al [2] for similar systems. The lower thermal conductivity of membranes is attributed to the different orientation of the scattering surfaces either at the pores or at free surfaces and not to coherent effects. The comparison between the porous membranes and nano-wires with periodic cylindrical modulations shows that thermal transport is hindered further when there are surfaces perpendicular to the heat flow. These results show that coherent effects have no impact on thermal transport in both kind of nano-structures at room temperature.

In this work we study the effects of disorder on the thermal conductivity of porous 100 nm thick silicon membranes, in which the size, shape and position of the pores were varied randomly. Measurements using two-laser Raman thermometry on both non-patterned and porous membranes revealed more than a 10-fold reduction of the thermal conductivity compared to that of bulk silicon and a six-fold reduction compared to non-patterned membranes for the sample with random pore shapes. Using Monte Carlo methods we solved the Boltzmann transport equation for phonons and 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 partially overlap. Up to a 15% reduction of the thermal conductivity with respect to the purely circular pores was predicted for a porous membrane with 37% filling fraction. The effect of the pore shape and distribution was further studied. Maps of temperature and heat flux distributions clearly showed that for particular pore placement heat transport can be efficiently blocked and hot spots can be found in narrow channels between pores. These findings have an impact on the fabrication of membrane-based thermoelectric devices, where low thermal conductivity is required. This work shows that for porous membranes with a given filling fraction the thermal conductivity can be further modified by introducing disorder in the shape and placement of the pores., The ICN2 is funded by the CERCA program/Generalitat de Catalunya. ICN2 is supported by the Severo Ochoa program from Spanish MINECO (Grant No. SEV-2017-0706). We acknowledge the financial support from the Spanish MINECO project PHENTOM (FIS2015-70862-P). We acknowledge the financial support from the French ANR with the project MESOPHON (ANR-15-CE30-0019). BG acknowledges the support from the Foundation for Polish Science (Homing/ 2016-1/2 and First Team POIR.04.04.00-00-5D1B/18-00) and ERC AdG SmartPhon (Grant No. 694977).