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
I. Introduction.
II. Modeling.
III. Results.
Thermoelectric materials transform heat into electricity, and vice-versa.
Cold side
Thermoelectric
pellets
Nano-structuration increases
efficiency of thermoelectric
materials.
Hot side
• ZT determination: Measurement of individual properties.
S = Seebeck coefficient.
σ = Electrical conductivity.
k = Thermal conductivity.
I. Introduction.
II. Modeling.
III. Results.
Harman technique
Traditional
Direct ZT determination
Vapplied
Low frequency
regime (fLF)
V
Vsample
Modified
Vapplied
High frequency
regime (fHF)
t
t
V
Vsample
Ve
Ve
VS
VS
t
t
I. Introduction.
II. Modeling.
III. Results.
II. COMSOL Model.
Thermoelectric 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
Constitutive equations
Coupled-Field equation
(Antonova et al., Finite elements for thermoelectric device analysis in ANSYS, ICT (2005))
Convection effects
with Heat Transfer
COMSOL module
Match equations
with PDE of
COMSOL module
Heat convective coefficient: h = 10-100 W/Km2
Box of air:
• Heat equation for fluids.
• Effects of gravity for air.
II. COMSOL modeling
• Geometry:
Thin Films
I. Introduction.
II. Modeling.
III. Results.
Nanowires
Boundary conditions:
• Top side temperature and
voltage evolve freely.
• Bottom side fixed at
293.15 K (heat sink)
and grounded (V=0).
• Variable thickness.
• With and without electrodes
and electrical wire.
• Variable diameter.
• Length 20µm.
I. Introduction.
II. Modeling.
III. Results.
Thermoelectric properties
• Material: p-type Bi2Te3
• S(T), σ(T) and k(T)
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
240
200
2.4
160
160
120
2.0
 (mS·m)
k (W/m·K)
S (V/K)
200
1.6
120
80
80
1.2
100
150
200
250
300
Temperature (K)
350
400
100
150
200
250
300
Temperature (K)
350
400
40
100
150
200
250
300
350
Temperature (K)
Seifert, W., Ueltzen, M., Müller, E.; One Dimensional Modelling of Thermoelectric Cooling; phys.stat.sol. (a)
194, No.1, pp 277 – 290; 2002
400
I. Introduction.
II. Modeling.
III. Results.
III. Results: Films.
• Sample Temperature and voltage evolution during 10mV, 0.1 s, pulse.
18
fLF
30
T
Voltage
T (K)
20
14
VS
10
12
0
10
-3
10
Example: 60µm film
fHF
-2
10
-1
10
Time (ms)
0
10
1
10
Total Voltage (mV)
16
I. Introduction.
II. Modeling.
III. Results.
Ideal Conditions
Dimension vs Frequency
Nanowires
Thin films
fHF in nanowires is extremely high to be
measured with typical experimental devices.
High (fHF) and low (fLF) frequencies needed for
experimental Harman determination of ZT
8
10
8
10
7
10
7
10
6
10
6
10
5
4
fHF
3
fLF
10
10
2
10
1
10
0
10
5
Frequency (Hz)
Frequency (Hz)
10
10
4
10
2
10
1
-1
10
-2
10
10
0
10
-3
10
f HF
f LF
3
10
-1
1
10
100
Thickness (m)
1000
10
0
50
100
150
200
Radius (nm)
Vacuum and atmospheric conditions show similar results of ZT and fHF.
250
300
I. Introduction.
II. Modeling.
III. Results.
Influence of electrical contacts
250
Under the presence of contact
resistances and electrical wire.
0.6
240
fHF (Hz)
230
220
ZT
0.4
fHF
0.3
Wire radius 50µm
ZT
0.5
0.2
210
0.1
0.0
200
5
10
6
10
7
10
8
10
9
10
10
10
Electrical contact conductivity (S/m)
800
Contact conductivity
108 S/m
fHF and ZT are modified depending
on the electrical contact resistance
and wire diameter
0.7
fHF
<25µm wire
needed
400
0.6
0.5
200
0
0
50
100
150
Wire Radius (m)
200
250
0.4
ZT
fHF(Hz)
600
ZT
Conclusions
I. Introduction.
II. Modeling.
III. Results.
• Development of thermoelectric COMSOL
module for time dependent simulations.
• Elucidation of experimental conditions to
measure nanostructures with Harman
technique.
60µm Film
Vacuum
conditions
Atmospheric
conditions
Vacuum
Conditions
and
electrodes
Atmospheric
Conditions
and
electrodes
Thank you for your attention!