3. Impact of parasitic contact electrical resistances on ZT of the thermoelectric device

overlapping each other which makes impossible to distinguish them. One of the ways to model such a behavior in a simple model can be using in three series–parallel RC elements circuit. In Figure 10a, b, the solid line corresponds to the obtained fitting results. For clarity, such resistance results, as well as the effective thermoelectric figure of merit of the symmetrical and asymmetrical modules are shown in Table 1. Evidently, the thermoelectric figure of merit of the asymmetrical module is almost two-fold the thermoelectric figure of merit of the symmetrical module, such result confirms the enhanced thermoelectric performance of the asymmetrical module as a consequence of the larger temperature rise generated in the legs because of their asymmetry. Hence, harnessing of the Thomson coefficient via asymmetrical legs could be an important

On the other hand, it is worth to mention that the present experimental research is mainly focused on the development of devices for applications at room temperature (i.e. 300 K), in that case, it is not necessary to measure the temperature dependence of ZT. Besides, our devices are based on P and N-type Bi2Te3, it is well known that such materials present an optimal thermoelectric performance at around room temperature; hence, operation of such materials must be well below 100C, so an operation condition above this temperature will damage the device because by applying an excessive heat flux it could damage the device due to the melting of the weld joining the thermoelectric legs. In this sense, it is not possible to operate such device under a high-temperature rise away from room temperature would affect seri-

Figure 10. Experimental electrical impedance curves at room temperature for (a) symmetrical and (b) asymmetrical nine

Module Riso(mΩ) Rte(mΩ) Rad(mΩ) Rc(mΩ) Rw(mΩ) ZTc Symmetrical 137.25 16.81 154.06 98.2 18.3 0.43 Asymmetrical 231.01 48.09 279.10 165.4 18.3 0.73

Table 1. Experimental parameters of the symmetrical and asymmetrical leg thermoelectric modules.

strategy in order to accomplish thermoelectric devices with enhanced performance.

ously their performance.

114 Bringing Thermoelectricity into Reality

pairs of thermoelectric modules.

Thermoelectric device engineering involves the formation of several intrinsic parasitic resistances that affect the thermoelectric module performance. In this sense, the TLM has been applied to discard the parasitic resistances and demonstrate that the increase on ZT of the device is mainly due to asymmetric effect in thermoelectric legs and consequently the nonlinear Thomson effect that governs them.

Figure 11a shows different lengths in the symmetrical and asymmetric thermoelectric legs as well as their respective electrical resistances as a function of length. The total measured resistance consists of several components:

$$R\_T = R\_{W1} + R\_{C1} + R\_{p-TE} + R\_{C2} + R\_{n-TE} + R\_{C3} + R\_{W2} \tag{10}$$

Where RW1 y RW2 are wiring resistances, RC1 y RC3 are contact resistances due to metal contacts, RC2 is associated with the metallic contact between the junction of the P-type and Ntype thermoelectric legs, and RP-TE and RN-TE define the internal resistance of the P-type and N-type thermoelectric legs, respectively.

Figure 11. (a) Diagram of the variation of the length in thermoelectric couples and analysis of the electrical resistance, and (b) analogous electrical circuit of thermally coupled pairs with welding.

Therefore, the total parasitic electrical resistance Rp is given by the contact resistance Rc and the wiring resistance Rw, then Eq. (10) can be rewritten as:

$$R\_p = R\_w + R\_c \tag{11}$$

Where, Rc�<sup>P</sup> y Rc�<sup>N</sup> values are defined by slope interception with y-axes, as mentioned above. Such values are shown as inset table of Figure 12. This result is the total parasitic resistance of thermoelectric module with nine pairs that includes the wiring resistance of wire used during

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In addition, by way of the four-probe AC method, it is possible to measure the wiring resistance Rw, as shown in Figure 13. Where the value Rw is obtained by the intersection of the

Now, contact resistance Rc of the thermoelectric module with symmetrical legs is calculated as:

RC ¼ Rp�symmetric � RW

RC ¼ 115:29 mΩ � 18:38 mΩ

RC�symmetric ¼ 96:91 mΩ

By applying a similar procedure, it is possible to measure the parasitic resistance Rp using the TLM in the asymmetric device, in this case, the resistance as a function of the length is shown in Figure 14. The total parasitic resistance Rp of a thermoelectric module with nine couples of asymmetrical

Rp�asymmetric ¼ ð Þ Rc�<sup>P</sup> þ Rc�<sup>N</sup> ∗9

Rp�asymmetric ¼ ð Þ 17:84mΩ þ 3:59mΩ ∗9

Rp�asymmetric ¼ 191:97 mΩ

Figure 13. Wiring resistance of the wire used during thermoelectric characterization.

measurements as well as contact resistance.

legs (see Figure 7b) is calculated as:

adjustment with the y-axis as it is shown in the inset.

By way of the TLM, it is possible to measure the total parasitic electrical resistance Rp. In this sense, thermoelectric legs have been fabricated with 2, 3, and 4 mm in length. The TLM is a technique used to determine the contact resistance between a metal and a semiconductor. First, the electrical resistance is measured for each length and then each resistance is presented as a function of length as shown in Figure 12. In the limit of a zero-length resistor, the residual resistance would be just the contact resistance. Then can be found from the graph by extrapolating back to L = 0. Then, the parasitic resistance of the P-N junction is the sum of such interceptions; hence, the total parasitic resistance of the device is estimated by multiplying this value by the number of P-N junctions in the device (in this case, 9 P-N pairs).

The total parasitic resistance Rp of a thermoelectric module with nine couples of symmetrical legs (see Figure 7a) is calculated as:

$$R\_{p-symmetric} = (R\_{c-P} + R\_{c-N}) \* 9$$

$$R\_{p-symmetric} = (10.23 m\Omega + 2.22 m\Omega) \* 9$$

$$R\_{p-symmetric} = 115.29 \ m\Omega$$

Figure 12. Electrical resistance in symmetrical thermoelectric legs as the length is increased.

Where, Rc�<sup>P</sup> y Rc�<sup>N</sup> values are defined by slope interception with y-axes, as mentioned above. Such values are shown as inset table of Figure 12. This result is the total parasitic resistance of thermoelectric module with nine pairs that includes the wiring resistance of wire used during measurements as well as contact resistance.

Therefore, the total parasitic electrical resistance Rp is given by the contact resistance Rc and

By way of the TLM, it is possible to measure the total parasitic electrical resistance Rp. In this sense, thermoelectric legs have been fabricated with 2, 3, and 4 mm in length. The TLM is a technique used to determine the contact resistance between a metal and a semiconductor. First, the electrical resistance is measured for each length and then each resistance is presented as a function of length as shown in Figure 12. In the limit of a zero-length resistor, the residual resistance would be just the contact resistance. Then can be found from the graph by extrapolating back to L = 0. Then, the parasitic resistance of the P-N junction is the sum of such interceptions; hence, the total parasitic resistance of the device is estimated by multiplying this

The total parasitic resistance Rp of a thermoelectric module with nine couples of symmetrical

Rp�symmetric ¼ ð Þ Rc�<sup>P</sup> þ Rc�<sup>N</sup> ∗9

Rp�symmetric ¼ ð Þ 10:23mΩ þ 2:22mΩ ∗9

Rp�symmetric ¼ 115:29 mΩ

value by the number of P-N junctions in the device (in this case, 9 P-N pairs).

Figure 12. Electrical resistance in symmetrical thermoelectric legs as the length is increased.

Rp ¼ Rw þ Rc (11)

the wiring resistance Rw, then Eq. (10) can be rewritten as:

legs (see Figure 7a) is calculated as:

116 Bringing Thermoelectricity into Reality

In addition, by way of the four-probe AC method, it is possible to measure the wiring resistance Rw, as shown in Figure 13. Where the value Rw is obtained by the intersection of the adjustment with the y-axis as it is shown in the inset.

Now, contact resistance Rc of the thermoelectric module with symmetrical legs is calculated as:

$$R\_{\odot} = R\_{p-symmetric} - R\_W$$

$$R\_{\odot} = 115.29 \text{ } m\Omega - 18.38 \text{ } m\Omega$$

$$R\_{\odot -symmetric} = 96.91 \text{ } m\Omega$$

By applying a similar procedure, it is possible to measure the parasitic resistance Rp using the TLM in the asymmetric device, in this case, the resistance as a function of the length is shown in Figure 14.

The total parasitic resistance Rp of a thermoelectric module with nine couples of asymmetrical legs (see Figure 7b) is calculated as:

$$R\_{p-asymmetric} = (R\_{c-P} + R\_{c-N}) \* \Theta$$

$$R\_{p-asymmetric} = (17.84 m\Omega + 3.59 m\Omega) \* \Theta$$

$$R\_{p-asymmetric} = 191.97 \, m\Omega$$

Figure 13. Wiring resistance of the wire used during thermoelectric characterization.

demonstrated that clearly parasitic electric resistance plays an important role in the perfor-

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In the present chapter, it has been done an experimental demonstration of the influence of the device legs geometry as well as parasitic electrical contact resistance on ZT. Results prove that asymmetrical thermoelectric module shows to have almost twofold the thermoelectric figure of merit as compared to conventional one with a constant square cross-section. Thermal analysis of the device via analytical, as well as numerical modeling unveils an increment in the temperature gradient and Seebeck voltage across the device with asymmetrical thermoelectric legs. Such result confirms that the thermoelectric enhancement is due to the harnessing of Thompson effect which is normally neglected in rectangular legs devices. Additionally, the impact of parasitic electrical contact and wiring resistances on the thermoelectric module performance is shown. In this sense, a significant decrement on ZT due to parasitic effects is observed. Thereby, the general results of the present chapter experimentally prove that geometrical configuration of the device legs can improve significantly the thermoelectric performance of the device opening a new route to the development of enhanced performance thermoelectric modules via device engineering.

This work was supported by the National Council for Science and Technology-Conacyt Mexico, through the Grant for fundamental research No. 241597 and national issues No.1358. A.F. M. thanks to Conacyt Mexico for fellowship, as well as the thermoelectric laboratory at the

1 Centro de Investigación en Materiales Avanzados S. C. Unidad Monterrey, Apodaca,

2 Genes-Group of Embedded Nanomaterials for Energy Scavenging, CIMAV-Unidad

mance of the thermoelectric device.

4. Conclusion

Acknowledgements

Cardiff University for facilities.

Authors declare no conflicts of interest.

Monterrey, Apodaca, Nuevo León, México

Angel Fabian-Mijangos<sup>1</sup> and Jaime Alvarez-Quintana1,2\*

\*Address all correspondence to: jaime.alvarez@cimav.edu.mx

Conflict of interest

Author details

Nuevo León, México

Figure 14. Electrical resistance in asymmetrical thermoelectric legs as the length is increased.

Where, Rc�<sup>P</sup> y Rc�<sup>N</sup> values are defined by slope interception with y axes. Such values are shown as inset table of Figure 14. This result is the total parasitic resistance of thermoelectric module with nine pairs of asymmetrical legs that includes the wiring resistance of wire used during measurements as well as contact resistance.

Now, contact resistance Rc of the thermoelectric module with asymmetrical legs is calculated as:

$$R\_{\odot} = R\_{p-asymmetric} - R\_W$$

$$R\_{\odot} = 191.97 \, m\Omega - 18.38 \, m\Omega$$

$$R\_{\odot-asymmetric} = 174 \, m\Omega$$

In this particular case, Rp has been obtained around 116 mΩ y 183 mΩ for the symmetrical and asymmetrical device, respectively. Using this information, ZTp can be calculated as it is shown in Table 2. However, by correcting such parasitic effects the estimated values on ZT<sup>p</sup> are 0.79 and 1.02 for the symmetrical and asymmetrical thermoelectric modules, respectively. Thus, it is


Table 2. Effect of contact and parasitic resistances on ZT of thermoelectric modules with symmetrical and asymmetrical legs, respectively.

demonstrated that clearly parasitic electric resistance plays an important role in the performance of the thermoelectric device.
