EUROTHERM SEMINAR 91 Microscale Heat Transfer III Poitiers France, August 2011 Kapitza resistance of rough superlattice interfaces, a molecular dynamics study K. Termentzidis 1, S. Merabia 2, and P. Chantrenne 1 Konstantinos TERMENTZIDIS 1 CETHIL UMR-5008, Université de Lyon, INSA de Lyon, CNRS, Université Lyon 1, Lyon F-69621, France 2 LPMCN UMR-5586, Université Lyon 1, F-69621, France 31 August 2011 Konstantinos TERMENTZIDIS EUROTHERM91 31 August 2011 1 / 9
COFISIS Project COFISIS: Collective Fabrication of Inexpensive Suppelattices in Silicon Collaboration between theoretical and experimental groups: ESIEE (Paris), CETHIL et MATEIS (INSA of Lyon) AIM: develop integrated silicon-based and low-cost superlattices for thermoelectric conversion Konstantinos TERMENTZIDIS EUROTHERM91 31 August 2011 2 / 9
COFISIS Low cost vertical superlattices Verical superlattices are obtained by: Patterning and then etching the silicon by DRIE (Deep Reactive Ion Etching) The trenches were filled using electrodeposition on a thin metallic seed layer (Cu) Excess copper was polished away using chemical-mechanical polishing NEED: prediction of thermal conductivity of layers and interfaces SEM images: a. two submicron trenches in a silicon wafer, b. copper filled 5-µm-wide trenches Konstantinos TERMENTZIDIS EUROTHERM91 31 August 2011 3 / 9
Computational Methods Prediction of Thermal Conductivity with Molecular Dynamics Comparison between NEMD - EMD NEMD: Non-Equilibrium MD Structure is coupled to a heat source and sink, and the TC is obtained extracting the heat flux and the temperature profile from MD steady state results method of choice for nanomaterials, adapted for inhomogeneous materials small uncertainties 10% several system sizes, extrapolation needed to get the TC for infinite size EMD: Equilibrium MD The conductivity vector related to the autocorrelation of the heat current vector J, through the Green-Kubo relation. method of choice for bulk materials - less severe size effects large uncertainties, migh be decreased with bigger statistics (different initial conditions). small system size: thus longwave length phonons might be filtered EMD results are 20% smaller than NEMD The difference between the two methods is less pronounced for high T PRB 77 (2008) 184302 and IJHMT 54 (2011) 2014 Konstantinos TERMENTZIDIS EUROTHERM91 31 August 2011 4 / 9
Computational Methods Modelling rough interfaces Modelling superlattices with rough interfaces Peridodic triangular interfaces Studied parameters: height of interfaces and superlattice s period Other shapes of interfaces: i. smooth, ii. periodic triangles, iii. superposition of smaller triangles on ii, iv. cosine like, v. random like, vi. periodic square PRB 79 (2009) 214307 and IJHMT 54 (2011) 2014 Konstantinos TERMENTZIDIS EUROTHERM91 31 August 2011 5 / 9
Results Prediction of Thermal Conductivity Thermal conductivity of superlattices with rough interfaces TC.vs. height interface roughness 2 SL s periods: 20a 0 and 40a 0 TC.vs. shape of interfaces constant roughness height R K plays significant role. PRB 79 (2009) 214307 and IJHMT 54 (2011) 2014 Konstantinos TERMENTZIDIS EUROTHERM91 31 August 2011 6 / 9
Results Prediction of Kapitza Resistance Kapitza resistance of superlattices with rough interfaces EMD vs NEMD NEMD: temperature jump across only a planar interface EMD: R K auto-correlation of the total flux across an interface 1 1 = R K Sk B T 2 0 q(t)q(0) dt = 1 R θ = 1 Sk B T 2 0 q θ (t)q θ (0) dt This angular Kapitza resistance quantifies the transmission of the heat flux in the direction making an angle θ with the normal of the interface. Nanoscale Reseach Letters 6 (2011), 288 Konstantinos TERMENTZIDIS EUROTHERM91 31 August 2011 7 / 9
Results Prediction of Kapitza Resistance Angular Kapitza resistance Cross-plane and in-plane directions of the SLs cross-plane orientation θ = 0, in-plane orientation θ = π 2 R 0 > R π 2 consistent with the observation that TC // > TC Heat transfer properties of SLs are explained by the phononic nature of the energy carriers the phonons feel less friction in the in-plane direction Konstantinos TERMENTZIDIS EUROTHERM91 31 August 2011 8 / 9
Coclusions- Discusion Coclusions- Discusion Nanostructured materials Interfaces and surfaces dominate the heat transfer in this scale TC of superlattices Reduction of the anisotropy in increasing the interface roughness To understand heat transfer in SLs The phononic nature of the energy carriers has to be taken into account, obliging the qualitative understanding of Kapitza resistance Directional Kapitza resistance first step towards a quantitative measurement of the transmission factor of phonons on their direction of propagation across an interface. EMD, NEMD give the same tendencies, one method can replace the other Konstantinos TERMENTZIDIS EUROTHERM91 31 August 2011 9 / 9