Comunicación presentada en la COMSOL conference, celebrada en Rotterdam en noviembre de 2013.Peer reviewe

Borca Tasciuc, Diana-Andra

Borca Tasciuc, Theodorian

Martín-González, Marisol

Muñoz Rojo, Miguel

Ramos Vega, Daniel

Romero Fanego, Juan José

Digital.CSIC

Time dependent simulations of thermoelectric thin films and nanowires for direct determination of their efficiency with COMSOL Multi-physics®. Miguel Muñoz Rojo, Juan José Romero, Daniel Ramos,  Diana Borca-Tasciuc, Theodorian Borca-Tasciuc and  Marisol Martín Gonzalez. I. Introduction Thermoelectric materials transform heat into electricity, and vice-versa. I. Introduction. II. Modeling. III. Results. Cold side Hot side Thermoelectric pellets Nano-structuration increases efficiency of thermoelectric materials. • ZT determination: Measurement of individual properties. S = Seebeck coefficient. σ = Electrical conductivity. k = Thermal conductivity. I. Introduction. II. Modeling. III. Results. Harman technique Direct ZT determination t Vapplied t Ve VS V Vsample Vapplied t t Ve VS V Vsample Low frequency regime (fLF) High frequency regime (fHF) Traditional Modified II. COMSOL Model. I. Introduction. II. Modeling. III. Results. Thermoelectric equations Match equations with PDE of COMSOL module Convection effects with Heat Transfer COMSOL module Heat convective coefficient: h = 10-100 W/Km2 Box of air:  • Heat equation for fluids. • Effects of gravity for air. Constitutive equations Field equation ρ = density σ = electrical conductivity S = Seebeck coeficient [П]=T·S = Peltier coefficient ε = dielectric permitivity C = specific heat capacity T = absolute temperature φ = heat generation rate J = current density vector E = electric field vector Coupled-Field equation (Antonova et al., Finite elements for thermoelectric device analysis in ANSYS, ICT (2005)) II. COMSOL modeling • Geometry:           Thin Films                                           Nanowires I. Introduction. II. Modeling. III. Results. • Variable thickness. • With and without electrodes and electrical wire. • Variable diameter. • Length 20µm. Boundary conditions:  • Top side temperature and voltage evolve freely.  • Bottom side fixed at 293.15 K (heat sink) and grounded (V=0). • Material: p-type Bi2Te3 • S(T), σ(T) and k(T) Thermoelectric properties I. Introduction. II. Modeling. III. Results. Seifert, W., Ueltzen, M., Müller, E.; One Dimensional Modelling of Thermoelectric Cooling; phys.stat.sol. (a) 194, No.1, pp 277 – 290; 2002 T (K) S (µV/K) k (W/K·m) σ (mS·m) 100 75 2.5 185 150 125 2 142 200 170 1.55 100 250 200 1.35 72 300 218 1.28 60 350 225 1.35 55 400 218 1.75 70 100 150 200 250 300 350 40080120160200240  S (V/K)Temperature (K)100 150 200 250 300 350 4001.21.62.02.4  k (W/m·K)Temperature (K)100 150 200 250 300 350 4004080120160200   (mS·m)Temperature (K)III. Results: Films. I. Introduction. II. Modeling. III. Results. • Sample Temperature and voltage evolution during 10mV, 0.1 s, pulse. 10-310-210-110010101020301012141618 TT (K)Time (ms)  Total Voltage (mV) VoltagefLF fHF Example: 60µm film VS 1 10 100 100010-310-210-1100101102103104105106107108   fHF fLFFrequency (Hz)Thickness (m)I. Introduction. II. Modeling. III. Results. Ideal Conditions High (fHF) and low (fLF) frequencies needed for experimental Harman determination of ZT 0 50 100 150 200 250 30010-1100101102103104105106107108 f HF  f LF   Frequency (Hz)Radius (nm)fHF in nanowires is extremely high to be measured with typical experimental devices. Thin films Nanowires Dimension vs Frequency Vacuum and atmospheric conditions show similar results of ZT and fHF. I. Introduction. II. Modeling. III. Results. Influence of electrical contacts 20021022023024025010510610710810910100.00.10.20.30.40.50.6  fHF f HF (Hz)Electrical contact conductivity (S/m) ZT ZT fHF and ZT are modified depending on the electrical contact resistance and wire diameter Under the presence of contact resistances and electrical wire. 0 50 100 150 200 25002004006008000.40.50.60.7 fHFf HF(Hz)Wire Radius (m) ZT ZTWire radius 50µm Contact conductivity 108 S/m <25µm wire needed • Development of thermoelectric COMSOL module for time dependent simulations.  • Elucidation of experimental conditions to measure nanostructures with Harman technique.  I. Introduction. II. Modeling. III. Results. Conclusions 60µm Film Vacuum conditions Atmospheric conditions Vacuum Conditions and electrodes Atmospheric Conditions and electrodes Thank you for your attention! 

Time dependent simulations of thermoelectric thin films and nanowires for direct determination of their efficiency with COMSOL Multi-physics

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