Prediction of the thermal conductivity of a multilayer nanowire

1. 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 Jean-Louis Barrat LPMCN UMR 5586 UCBL1/CNRS Thanks to Laurent David, CETHIL Lyon Florian Lagrange, LCTS Bordeaux Motivations Nanowire description Models LAYOUT

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

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

4. Motivations : development of a new sensor High spatial resolution below 100 nm Quantitative measurement lower the uncertainty and higher sensitivity Temperature measurement Thermophysical properties measurement The most popular commercial sensor actually used with an AFM Diameter : 5 µm Length : 200 µm Curvature radius : 15-20 µm

5. Motivations : development of a new sensor Modèle de Lefèvre Modèle de David Temperature measurement - qualitative values only - quantitative measurement require a calibration - spatial resolution limited by the tip geometry and surface roughness L. David Ph D, CETHIL S. Gomès & Dj. Ziane, 2003, Solid State Electronics 47 pp 919-922 Thermal conductivity - low sensitivity at high thermal conductivity values - uncertainty of about 20 % at low thermal conductivity values S. Gomès et al., IEEE Transactions on Components and Packaging Technologies, 2006

6. Motivations : development of a new sensor Interfaces nanowire nanolayers The new sensor : a functionalised multilayer nanowire Core : BN, SiC crystalline / periodic defect (mâcle) layers : metallic dielectric crystal (SiC)/amorphous (SiO2) 10-50 nm eventually sharpened 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.

7. Model : macroscopic approach 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 Prediction for nanowire Use the bulk value Prediction for nanofilm Radius of the core rc Thermal conductivity versus thermal conductance/thermal resistance ? Length l Tip end Thicknesses e1 e2 e3 ...

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

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

10. 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...

11. Model for dielectric crystals a a 3 1 z y a 2 x a 0 a0 = 0.543 nm Silicon structure in the real space diamond structure the elementary cell contains two atoms

12. Model for dielectric crystals z y x Vibration modes In the reciprocal space - K = linear combination of de b1, b2, b3 - K belong to the first Brillouin ’s zone - nomber of wave vectors K : number of elementary cells - Number of polarisations p = 6 k j i

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

14. Model for dielectric crystals Relaxation time parameters determination Fit of the thermal conductivity of a Si crystal (L = 7,16 mm) function of the temperature Transverse mode A = 7 10-13 B = 0 c = 1 x = 4 Longitudinal mode A = 3 10-21 B = 0 c = 2 x = 1.5 F = 0.55 D = 1.32 10-45 s-3 M.G. Holland, PR, 132, 2461 (1963)

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

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

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

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