Prediction of the thermal conductivity of a multilayer nanowire Patrice Chantrenne, Séverine Gomés CETHIL UMR 5008 INSA/UCBL1/CNRS Arnaud Brioude, David Cornu LMI UMR 5615 UCBL1/CNRS Motivations Nanowire description Models Thanks to Laurent David, CETHIL Lyon Florian Lagrange, LCTS Bordeaux LAYOUT Jean-Louis Barrat LPMCN UMR 5586 UCBL1/CNRS

Microelectronic components - length scale lower than 30 nm - film thickness less than10 nm Motivations : applications Require temperature measurements in order to ensure the reliability of the microsystem

Nanostructured materials (nanoporous, nanosequences, nanolayered) Nanostructures (nanoparticles, nanotubes, nanowires, nanofilms…) Require experimental caracterisations limitation until now : almost one experimental device has been developped for each nanostructure Motivations : applications SiC/graphitelike C nanosequence matérial SiO2/SiC nanowire SiC/SiO2/BN nanowire

Temperature measurement Thermophysical properties measurement High spatial resolution below 100 nm Quantitative measurement lower the uncertainty and higher sensitivity Motivations : development of a new sensor The most popular commercial sensor actually used with an AFM Diameter : 5 µm Length : 200 µm Curvature radius : µm

Motivations : development of a new sensor Modèle de Lefèvre Modèle de David Thermal conductivity - low sensitivity at high thermal conductivity values - uncertainty of about 20 % at low thermal conductivity values S. Gomès & Dj. Ziane, 2003, Solid State Electronics 47 pp L. David Ph D, CETHIL S. Gomès et al., IEEE Transactions on Components and Packaging Technologies, 2006 Temperature measurement - qualitative values only - quantitative measurement require a calibration - spatial resolution limited by the tip geometry and surface roughness

Interfaces nanowire nanolayers Core : BN, SiC crystalline / periodic defect (mâcle) layers : metallic dielectric crystal (SiC)/amorphous (SiO2) The new sensor : a functionalised multilayer nanowire The sensor should exhibit a low thermal conductivity in order to a good temperature and thermal conductivity sensitivity The prediction of the thermal conductivity is essential to optimize the design of the sensor. Motivations : development of a new sensor nm eventually sharpened

Thermal conductivity versus thermal conductance/thermal resistance ? Length l Heat transfer across the nanowire depends on heat transfer - in the core (dielectric crystal) - in metallic nanolayer - in amorphous nanolayer - in dielectric nanolayer - across the interfacesforecoming studies Thicknesses e 1 e 2 e 3... Radius of the core r c Tip end Model : macroscopic approach Use the bulk value Prediction for nanowire Prediction for nanofilm

Atomic collective vibration modes of energy Model for dielectric crystals In dielectric crystaline material, heat carriers are Wave vector K, polarization p, dispersion curves number of phonon per vibration mode PHONON = Phonon liftime These vibration modes may be characterised by

The total thermal conductivity = sum of individual thermal conductivity of each vibration modes (K,p) The kinetic theory of gaz allow to write with Spécific heat Group velocity Model for dielectric crystals

Thermal conductivity calculation require the knowledge of - vibration modes - dispersion curves - relaxation time parameters main assumption of the model vibrational properties of a cristalline nanostructure = vibrational properties of the bulk crystal Validation of the model for Silicon... Model for dielectric crystals

Silicon structure in the real space diamond structure the elementary cell contains two atoms Model for dielectric crystals

x y z Vibration modes In the reciprocal space - K = linear combination of de b 1, b 2, b 3 - K belong to the first Brillouin ’s zone - nomber of wave vectors K : number of elementary cells - Number of polarisations p = 6 i j k Model for dielectric crystals

Dispersion curves B.N. Brockhouse, P.R.L. 2, 256 (1959) Linear fit of the experimental dispersion curves in the [1,0,0] direction S. Wei et M.Y. Chou, PRB, 50, 2221 (1994) The optical mode contribution to the thermal conductivity is negligible if T < 1000 K P. Flubacher et al., Philos. Mag, 4,273 (1959) LA TA Model for dielectric crystals

Relaxation time parameters determination M.G. Holland, PR, 132, 2461 (1963) Fit of the thermal conductivity of a Si crystal (L = 7,16 mm) function of the temperature Transverse mode A = B = 0  = 1  = 4 Longitudinal mode A = B = 0  = 2  = 1.5 F = 0.55 D = s -3 Model for dielectric crystals

D. Li, et al., A.P.L, 83, 2934 (2003) Excellent agreement except for the 22 nm wide nanowire Thermal conductivity of Si nanowires

M. Asheghi et al., ASME JHT, 120, 30 (1998) M.Z. Bazant, PRB, 56, 8542 (1997) Excellent agreement with the experimental resutls Thermal conductivity of Si nanofilms

Prediction of the thermal conductivity function of the heat transfer direction T= 300K Thermal conductivity of Si nanofilms

CONCLUSION Thermal conductivity of dielectric nanofilms and nanowires Thermal conductivity of metallics and amorphous nanofilms Thermal conctact resistance Confident to get a accurate value The bulk value overestimate the real value Still a Problem, several models may be used However, one need to evaluate the maximun value of the thermal conductivity