**4. Heat exchanger**

The previous section highlights the importance of physically contacting the platform in order to improve heat extraction, and thus cooling it more efficiently. According to section 2.2 and the results shown in section 3.2, the need for a heat exchanger has been proven. In this section, we study the implementation of such component on the μTEG. This poses several problems from the technological point of view, especially considering the starting device architecture used to expose the thermoelectric material to a thermal gradient. The thermally isolated platform is a fragile structure and physically contacting it without caution might break it. A proper methodology with auxiliary components needs to be developed components to provide such contact safely.

The approach implies to have a thermally conductive piece contacting the platform and interfacing this part of the device with a heat exchanger of appropriate size. For this reason, such piece will be dubbed as 'adapter'. The contact needs to be compliant to absorb any excess vertical displacement with deformation. The compliant part of this contact will be a certain amount of silver paste. A rigid spacer (PMMA), sitting both on the silicon bulk rim and the platform, will also be necessary to limit the maximum excursion of the adapter over the platform so that pressure between the heat exchanger on top and the platform below can be applied in a safe way. Finally, the heat exchanger itself, a commercial one of similar footprint is assembled onto our chip. In this case, our chip is 7x7 mm2 and the smallest commercial heat exchanger found is 8x8 mm2 . A PCB with a through-hole, to insert a copper plate improving the thermal conductance from the hot surface to the bulk silicon rim, and a slightly larger partial etch to fit the chip and facilitate the wire bonding to auxiliary copper traces, are included in the assembly as shown in **Figure 10**.

#### **4.1 Modeling results**

The feasibility of the approach has been first tested building a physical model and solving finite element simulations (COMSOL) to evaluate the expected

## *Managing Heat Transfer Issues in Thermoelectric Microgenerators DOI: http://dx.doi.org/10.5772/intechopen.96246*

improvement on performance. The thermal and electrical properties of the materials used in the model are listed in **Table 1**.

The model boundary conditions include a constant hot temperature at the bottom (Thot = 100 °C) and natural convection on the vertical and horizontal walls of the heat exchanger through a heat exchange coefficient directly calculated in COMSOL for an air ambient temperature of 27 °C. When such element is not present, the heat exchange coefficient is applied directly on the platforms surface. **Figure 11** shows the temperature distribution for the whole model under such conditions. As it can be seen, even with a heat exchanger, the lowest temperature reached in the cold part is slightly below 70 °C although the ambient temperature is 27 °C. This is because the thermal resistance from the heat exchanger to the ambient is approximately one third of the total thermal resistance while the thermal resistance from the bottom of the PCB (actually most of this is from the silicon chip) to the heat exchanger is approximately two thirds of it.


*(1)Silicon NWs are modeled as a block, not individual nanowires, and the block material properties assume an occupation of only 5% of the total area with nanowires, while the remaining 95% has air material properties. (2)Tungsten electrical conductivity is different from the bulk literature values. The sheet resistance on a real device has been measured to obtain this value.*

#### **Table 1.**

In **Figure 9** the power curves obtained from the same device at a hot plate temperature of 250 °C with and without the cold finger are shown. It can be seen an important improvement in the performance of two orders of magnitude, from 1.3 to 142 nW, so proving the effectiveness of the cold finger approach as a proof of concept validating the further development of more effective heat exchanging

*Heat Transfer - Design, Experimentation and Applications*

The previous section highlights the importance of physically contacting the platform in order to improve heat extraction, and thus cooling it more efficiently. According to section 2.2 and the results shown in section 3.2, the need for a heat exchanger has been proven. In this section, we study the implementation of such component on the μTEG. This poses several problems from the technological point of view, especially considering the starting device architecture used to expose the thermoelectric material to a thermal gradient. The thermally isolated platform is a fragile structure and physically contacting it without caution might break it. A proper methodology with auxiliary components needs to be developed components

The approach implies to have a thermally conductive piece contacting the platform and interfacing this part of the device with a heat exchanger of appropriate size. For this reason, such piece will be dubbed as 'adapter'. The contact needs to be compliant to absorb any excess vertical displacement with deformation. The compliant part of this contact will be a certain amount of silver paste. A rigid spacer

(PMMA), sitting both on the silicon bulk rim and the platform, will also be necessary to limit the maximum excursion of the adapter over the platform so that pressure between the heat exchanger on top and the platform below can be applied in a safe way. Finally, the heat exchanger itself, a commercial one of similar footprint is assembled onto our chip. In this case, our chip is 7x7 mm2 and the smallest commer-

plate improving the thermal conductance from the hot surface to the bulk silicon rim, and a slightly larger partial etch to fit the chip and facilitate the wire bonding to auxiliary copper traces, are included in the assembly as shown in **Figure 10**.

The feasibility of the approach has been first tested building a physical model

*Isometric, cross section and detailed view of the proposed approach to safely contact the thin silicon platforms.*

and solving finite element simulations (COMSOL) to evaluate the expected

. A PCB with a through-hole, to insert a copper

structures.

**4. Heat exchanger**

to provide such contact safely.

cial heat exchanger found is 8x8 mm2

**4.1 Modeling results**

**Figure 10.**

**360**

*Thermal and electrical properties of the materials used in the model.*

**Figure 11.**

*Temperature distribution for the whole model with Thot = 100 °C.*

The internal temperature distribution for chips with four platforms with NW lengths of 10, 20, 30 and 40 μm (T1 to T4) has been analyzed for the cases with or without heat exchanger. The difference is significant as shown in **Figure 12**. The temperature difference across the NWs in the best case reaches about 25 °C of the total 73 °C externally available, when the heat exchanger is in place (right). This means the thermal resistance of the nanowires is approximately twice the thermal resistance from the platform to the ambient through the heat exchanger.

attained ΔT. However, when the presence of the heat exchanger secures most of ΔT, the positive effect of the lower thermal conductance of longer nanowires, which is still there, rapidly saturates and even reverse (see T4 vs. T3) because the detrimental impact of the increasing electrical resistance becomes dominant.

The significant increase in the generated power when applying a forced convection or a cold finger and the results from the simulations including a heat exchanger directed our efforts to the construction of the previously described heat exchanger

The preparation sequence of the required components is given in **Figure 14a**. A heat exchanger adapter is made from four Cu wires (one per on-chip a device), with diameter similar to the size of the suspended platform (which they will contact after the assembly) inserted in a square brass piece and machined to the appropriate length. The tips of the wires are dipped with thermal paste (**Figure 14b**) to fill the gap between the Cu wires and the suspended platforms to guarantee good thermal contact (**Figure 14c**). A PMMA spacer with a thickness appropriately matching the length of the protruding Cu wires is then assembled between the heat exchanger adapter and the μTEG, and finally, the aluminum heat exchanger is placed on top of adapter using a thermal paste (**Figure 14d**). Further details can be found in [27]

*(a) Steps of the construction of the heat sink adapter. Optical microscope images of (b) the Cu wire dipped in thermal paste and (c) the footprint left on the platform of the test device. (d) An image of the final assembly.*

**4.2 Manual assembly and impact on measurements**

*Managing Heat Transfer Issues in Thermoelectric Microgenerators*

assembly on our μTEGs (see **Figure 10**).

*DOI: http://dx.doi.org/10.5772/intechopen.96246*

from which **Figures 14**–**17** have been adapted.

**Figure 14.**

**363**

On the other hand, for the case without heat exchanger (left), the temperature differences across the nanowires do not reach beyond 2 °C. In this case, the thermal resistance to the ambient is much larger than the nanowires thermal resistance, and a very small temperature drop develops across the active thermoelectric material.

If the temperature solution from the finite element model is coupled to an electrical model through the Seebeck coefficient of the nanowires, the I-V curves and power output for each platform considering both scenarios can be obtained.

These results are shown in **Figure 13**, where the power output has been plotted as power density considering a device area of 2 mm<sup>2</sup> , large enough to contain the whole platform (approximately 1 mm<sup>2</sup> ) and space for additional contacts.

Clearly, a much larger power is obtained when the heat exchanger is in place due to the much higher ΔT perceived by the NWs. In addition, the behavior of the four platforms evolve differently. Without the heat exchanger, voltage and power scale with the length of nanowires since their thermal resistance is the dominant part of the total device thermal resistance and such length is directly determining the

#### **Figure 12.**

*Temperature distribution for each platform (from T1 to T4) without heat exchanger (left) and with heat exchanger (right).*

#### **Figure 13.**

*I-V curves (solid lines), and power output (dotted lines), versus current for T1-T4 devices, without (left) and with heat exchanger (right).*

*Managing Heat Transfer Issues in Thermoelectric Microgenerators DOI: http://dx.doi.org/10.5772/intechopen.96246*

The internal temperature distribution for chips with four platforms with NW lengths of 10, 20, 30 and 40 μm (T1 to T4) has been analyzed for the cases with or without heat exchanger. The difference is significant as shown in **Figure 12**. The temperature difference across the NWs in the best case reaches about 25 °C of the total 73 °C externally available, when the heat exchanger is in place (right). This means the thermal resistance of the nanowires is approximately twice the thermal

On the other hand, for the case without heat exchanger (left), the temperature differences across the nanowires do not reach beyond 2 °C. In this case, the thermal resistance to the ambient is much larger than the nanowires thermal resistance, and a very small temperature drop develops across the active thermoelectric material. If the temperature solution from the finite element model is coupled to an electrical model through the Seebeck coefficient of the nanowires, the I-V curves and power output for each platform considering both scenarios can be obtained. These results are shown in **Figure 13**, where the power output has been plotted

Clearly, a much larger power is obtained when the heat exchanger is in place due to the much higher ΔT perceived by the NWs. In addition, the behavior of the four platforms evolve differently. Without the heat exchanger, voltage and power scale with the length of nanowires since their thermal resistance is the dominant part of the total device thermal resistance and such length is directly determining the

*Temperature distribution for each platform (from T1 to T4) without heat exchanger (left) and with heat*

*I-V curves (solid lines), and power output (dotted lines), versus current for T1-T4 devices, without (left) and*

, large enough to contain the

) and space for additional contacts.

resistance from the platform to the ambient through the heat exchanger.

as power density considering a device area of 2 mm<sup>2</sup>

*Heat Transfer - Design, Experimentation and Applications*

whole platform (approximately 1 mm<sup>2</sup>

**Figure 12.**

**Figure 13.**

**362**

*with heat exchanger (right).*

*exchanger (right).*

attained ΔT. However, when the presence of the heat exchanger secures most of ΔT, the positive effect of the lower thermal conductance of longer nanowires, which is still there, rapidly saturates and even reverse (see T4 vs. T3) because the detrimental impact of the increasing electrical resistance becomes dominant.
