A micro Peltier cooler/heater module has been modelled. The module consists of n-type bismuth telluride and p-type antimony telluride thermoelectric materials. The commercial software package CFD-ACE+ has been used to implement and analyse the model. A two-dimensional coupled electrical and thermal simulation was performed. This software includes the possibility to incorporate the Peltier effect. The temperature, electric field intensity and wall heat flux distributions were simulated for different applied potentials. The variation in temperature difference with respect to the Seebeck coefficient of the material was calculated and analysed

Kalantar-Zadeh, K

Kandasamy, S

Rosengarten, G

Wlodarski, W

RMIT Research Repository

Modelling of a Thin Film Thermoelectric Micro-Peltier Module 
S. Kandasamy1, K. Kalantar-zadeh1, G. Rosengarten1,2, W. Wlodarski1
1School of Electrical and Computer Engineering, RMIT University, Melbourne, Australia 
2Department of Chemical and Biomolecular Engineering, University of Melbourne, Melbourne, 
Australia
 ABSTRACT 
A micro Peltier cooler/heater module has been 
modelled. The module consists of n-type bismuth telluride 
and p-type antimony telluride thermoelectric materials. 
The commercial software package CFD-ACE+ has been 
used to implement and analyse the model. A two-
dimensional coupled electrical and thermal simulation 
was performed. This software includes the possibility to 
incorporate the Peltier effect. The temperature, electric 
field intensity and wall heat flux distributions were 
simulated for different applied potentials. The variation in 
temperature difference with respect to the Seebeck 
coefficient of the material was calculated and analysed. 
1. INTRODUCTION 
Peltier thermoelectric modules are widely used in 
microelectronics for temperature control and 
stabilization [1]. There is an increasing demand in the 
applications of thermoelectrics for the semiconductor and 
optical communication industry [2] [3]. Microprocessors, 
micro–sensors, micro-controllers and lab-on-a-chip are 
among some of the devices, which require an efficient 
temperature control during their operation. A 
conventional thermoelectric cooler consists of a number 
of n- and p-type semiconductors, which are electrically in 
series but thermally in parallel. The functionality of such 
devices is based on the bulk property of the materials [4]. 
Thus these devices are incompatible with microelectronic 
fabrication processes. Thin film micro-thermoelectric 
modules offer higher efficiency than their bulk 
counterparts due to quantum and classical size effects of 
electrons and phonons [5]. However to date, such thin 
film thermoelectric Peltier modules have not been 
successfully used in commercial micro cooler/heater 
applications. The technological practicality of 
thermoelectric cooling is by and large constrained by the 
poor performance factor. This could be due to the large 
dependence on the properties of the materials used in 
these devices. The main benefit of using thin film 
technology is the dramatic increase in the cooling power 
density [6].  
Prospects of optimising the geometrical dimensions 
and the design parameters to achieve higher performance 
could be achieved through ?modelling of the specified 
device. The multi-physics simulation software from CFD 
? 0-7803-8560-8/04/$20.00©2004IEEE 
Research Corporation (http://www.cfdrc.com)
provides a useful tool for the design and simulation 
of the micro Peltier modules. This software is an 
advanced multi-physics package for modelling 
thermal and electrical effects in individual 
semiconductor devices, packages, boards, and 
complete electronic enclosures. The software has the 
ability to run parametric studies, which significantly 
help to achieve optimization of the device design. 
In this paper, we modelled a micro Peltier 
module consisting of one n-type and one p-type 
semiconductor. The modelled device has been 
investigated based on material properties and for 
different temperatures. Furthermore, the temperature, 
electric field intensity and wall heat flux distributions 
were studies. 
2. THEORY 
N-type semiconductor bismuth telluride 
(Bi2Te3) and p-type semiconductor antimony telluride 
(Sb2Te3) are widely used low operational temperature 
materials for the development of Peltier cooler/heater 
modules [4]. These materials have a high Seebeck 
coefficient, moderate electrical conductivity and low 
thermal conductivity. As a result, they have a high 
figure of merit, which is a significant factor for the 
improvement of efficiency of the micro Peltier 
modules.  
Figure of merit is defined as: 
npnp
np
np
S
Z
,,
2
,
, ??
?     (1) 
where Sp,n is the Seebeck coefficient of the material 
(μV/K),  ?p,n is the electrical resistivity (μ?m) and 
?p,n is the thermal conductivity (W/m-k).  
The suffix n & p denotes the respective 
material properties for the n- and p-type 
semiconductors employed.  ?p,n and ?p,n depend on the 
geometrical parameters of cross-sectional area (A)
and the length (L) of the semiconductor component. 
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Figure 1: Schematic diagram of a thermoelectric 
Peltier module 
The thermoelectric micro Peltier module used in 
the simulation is shown in Figure 1. It consists of the n- 
and p-type thermoelectric materials sandwiched between 
two electrical insulators. The cold end carries the heat 
load, thereby creating a temperature difference across the 
device. As a result of this temperature difference, a heat 
flux appears. The heat is transferred from the load (cold 
end) to the heat sink (hot end) via conduction, since the 
materials are in physical contact with each other. It takes 
place at the molecular level and involves the transfer of 
energy from the higher energetic molecules to those at a 
lower energy level [7].   
The change in temperature ?T can be expressed as 
a function of the material parameters [4], such as 
2
,
2
1
cnp TZT ??     (2) 
where Tc is the temperature in Kelvin at the cold surface. 
From equations 1 and 2, it is clear that the figure of 
merit Zp,n, the change in temperature ?T and the 
geometrical dimensions  (A and L) of the device are all 
inter dependent. Therefore to simplify the design 
parameters in the simulation of the micro Peltier module, 
the material properties and the dimensions of the device 
were kept constant. 
3. SIMULATION 
The coupled heat and electrical analysis was 
performed for a two dimensional micro Peltier module. 
The simulations provided a means to observe the variation 
in temperature across the device. The simulated model 
consists of a cross-sectional area (A) and leg length (L) of 
10 ?m2 and 1?m, respectively. Silicon Carbide (SiC) was 
used as the electrical insulator and heat sink element 
because of its high thermal conductivity. The thickness of 
SiC employed was 1 ?m. it was placed above the 
electrical connector and under the pads to provide 
efficient electrical isolation and higher rate of thermal 
transfer. A 0.25 ?m thick aluminium layers provide 
electric connection between the two semiconductors 
and the voltage source. The distance between the two 
semiconductors was 5 ?m. The material properties 
[8] are listed in Table 1. 
Table 1 Properties of the materials used in the 
simulation 
Material 
Properties 
Bi2Te3 Sb2Te3 Al SiC 
Density
(kg/m3)
7700 6500 2700 3210 
Specific Heat 
Capacity  
(J/kg-K) 
155 210 900 750 
Thermal 
Conductivity 
(W/m-K) 
1 1 240 120 
Electrical
Resistivity
(?m)
1x10-5 1x10-5 5x10-9 1x104
Seebeck 
coefficient
(μV/K)
-230 180 3.5 -10 
Figure 2 shows the structured mesh used in the 
simulation. Approximately 30,000 nodes were 
generated after meshing. Up to 4 nodes for a length 
of 0.25μm was used. The mesh has the same shape 
and size in al the components of the module. 
Figure 2: Two-dimensional mesh format for the 
micro Peltier module 
The geometrical parameters used in the 
simulation were assumed to be constant throughout 
the simulation. This assumption was carried out in 
order to study the effect of the material properties on 
the device performance as a function of change in 
temperature. The effect of change in Seebeck 
coefficient of the semiconductor materials for similar 
dimensions of both the n- and p-type materials was 
investigated.  The length of the semiconductor blocks 
were (L=Lp=Ln) 1μm each and the cross-sectional 
area (A=Ap=An) was 10 μm2. This model is based on 
the assumption that the heat transfer mechanism 
across the device is purely conduction. The boundary 
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condition on the sidewalls was assumed to be adiabatic. 
All the simulations were conducted with constant 
electrical current and the temperatures were fixed at both 
the hot and the cold end. Normally these are the reference 
conditions provided by the commercial manufacturers [9]. 
A number of simulations were performed, corresponding 
to different changes in temperature between the hot and 
the cold end. The deviation in the temperature difference 
was in the range of 1 to 10 K. A 38.5 mV voltage was 
applied across the Peltier module and the temperature, 
electric field intensity and wall heat flux distributions 
were simulated. They are shown in Figure 3. As can be 
seen, a heat flux is generated due to the Peltier effect. The 
module is capable of generating approximately 40K 
localized temperature difference.  A current of 0.1 A was 
passing through the module at this voltage. There was a 
quasi-linear electric field distribution in the two semi-
conductors. 
In order to observe the Peltier effect, a series of 
simulations were performed for different values of the 
Seebeck coefficient for Bi2Te3 while the coefficient was 
kept constat for Sb2Te3 at 180 ?V/K. They were changed 
in the range of –140 to –250 ?V/K and the temperature 
differences were calculated. Figure 4 shows comparison 
of change in temperature calculated from equation (2) to 
the simulated one based on the material properties of the 
semiconductors. The properties of the materials were 
found to largely influence the performance of the micro 
Peltier module. As can be seen for the average values of 
the Seebeck coefficients greater than 180?V/K only an 
appreciable temperature difference was observed. 
However the temperature difference obtained for the 
numerical calculations was found to be linear. 
Although the dimensions of the semiconductor 
components were the same, there are some discrepancies 
in the distribution of the of electric field intensity. This 
could be attributed due to the mismatch of the Seebeck 
coefficients of different materials in the thermoelectric 
micro Peltier module. Arenas et al [9] reported similar 
discrepancies. In addition the difference in the calculated 
and simulated values could be due to some of the 
assumptions related to heat transfer mechanisms. 
Figure 3 Distribution of A) temperature, 
B) electric field intensity and C) wall heat flux 
2.5
3.5
4.5
5.5
6.5
7.5
8.5
150 170 190 210 230
Average Seebeck Coefficient [μV/K]
Te
m
pe
ra
tu
re
 d
iff
e
re
n
ce
 [K
]
Calculated
Simulated
Figure 4: Temperature difference versus the 
average magnitude of the Seebeck coefficient of 
semiconductor materials
4. CONCLUSION 
A two- dimensional simulation for a single 
pair n- and p-type thermoelectric micro Peltier 
module has been performed.  The commercial 
software package CFD-ACE+ has been used. At 38.5 
mV, 0.1 A current was drawn by the module and a 
temperature change of 40.5K was observed.  The 
temperature, electric field intensity and wall heat flux 
distributions were analysed. Simulations for different 
Seebeck coefficients for the thermoelectric materials 
have been conducted. Significant variations in the 
performance of the device were observed. The 
simulation approach using the software package 
CFD-ACE+ offers an efficient solution for modelling 
A
B
C
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micro-Peltier modules. A 3D simulation is planned for the 
next modelling stage.  Additionally, the effect of variation 
of the semiconductor material thickness on the module 
performance will be investigated.  
5. ACKNOWLEDGEMENT 
The authors would like to thank CASS Foundation, 
Australia for providing financial support for this project. 
6. REFERENCES 
[1] F. Völklein, Gao Min and D. M. Rowe, “Modelling 
of a microelectromechanical thermoelectric cooler,” 
Sens. Actuators A, 75, 2, 1999, 95-101.  
[2] R. E. Simons., and R. C. Chu, “Application of 
thermoelectric cooling to electronic equipment: a 
review and analysis,” 16th Annual IEEE, 
Semiconductor Thermal Measurement and 
Management Symposium, 2000, 1-9. 
[3] Lance Rushing, Ali Shakouri, Patrick Abraham and 
John E. Bowers, “Micro Thermoelectric Coolers for 
Integrated Applications,” Proceedings of IEEE, 16th
International Conference on Thermoelectrics, 1997, 
646-649  
[4] D. M. Rowe, “CRC Book on Thermoelectrics,” CRC 
Press, 1995.  
[5] D. Y. Yao., C. J. Kim., and G. Chen, “Design of 
Thin-Film Thermoelectric Microcoolers,” 
Proceedings of the ASME Heat Transfer Division, 2, 
2000, 1-7.  
[6] J. W. Vandersande., and J. P. Fleurial., “Thermal 
Management of Power electronics Using Thermo-
electric Coolers,” Proceedings of the 15th 
International Conference on Thermoelectrics, 1996, 
252-255. 
[7] J. Esarte, G. Min, D. M. Rowe, “Modelling Heat 
Exchangers for Thermoelectric Generators,” Journal 
of Power Sources, 93, 2001, 72-76. 
[8] Luciana W. da Silva and Massoud Kaviany, “Micro-
thermoelectric cooler: Interfacial effects on thermal 
and electrical transport,” International Journal of 
Heat and Mass Transfer, 47, 10-11, 2004, 2417-2435.  
[9] Antonio Arenas, Jorge Vázquez, Rafael Palacios, 
“Bidimensional Analysis of a Thermoelectric Module 
using Finite Element Techniques”, Proceedings of the 
14th International Conference on Thermoelectrics, 
2000 
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Modelling of a thin film thermoelectric micro-Peltier module

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