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

100 150 200 250 300 350 400

80

120

160

200

240

S (V

/K)

Temperature (K)

100 150 200 250 300 350 400

1.2

1.6

2.0

2.4

k (

W/m

·K)

Temperature (K)

100 150 200 250 300 350 40040

80

120

160

200

(

mS

·m)

Temperature (K)

III. Results: Films. I. Introduction. II. Modeling. III. Results.

• Sample Temperature and voltage evolution during 10mV, 0.1 s, pulse.

10-3

10-2

10-1

100

101

0

10

20

30

10

12

14

16

18

T

T

(K

)

Time (ms)

Tota

l V

oltage (

mV

)

Voltage

fLF

fHF Example: 60µm film

VS

1 10 100 100010

-3

10-2

10-1

100

101

102

103

104

105

106

107

108

fHF

fLF

Fre

qu

en

cy (

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

-1

100

101

102

103

104

105

106

107

108

f HF

f LF

Fre

qu

en

cy (

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

200

210

220

230

240

250

105

106

107

108

109

1010

0.0

0.1

0.2

0.3

0.4

0.5

0.6

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 2500

200

400

600

800

0.4

0.5

0.6

0.7

fHF

f HF(H

z)

Wire Radius (m)

ZT

ZT

Wire 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!