Innovating in-situ characterization: a comprehensive measurement system for measuring the ZT and the contact resistance of vertical thermolegs exploiting the vertical transfer length method

In order to optimize their system design and manufacturing processes, it is crucial to undertake a thorough electrical and thermal characterization of micro thermoelectric generators (µTEGs). To address this need, a highly advanced and fully integrated in-situ measurement system has been developed. The main objectives of this system are to (1) enable the measurement of ZT and thereby of all thermoelectric (TE) properties of thermolegs made from powder-based TE materials and (2) at the same time accurately measure the contact resistance between the TE material and the electrical contacts. The µTEG fabrication concept used in this study is based on copper-cladded printed circuit board (PCB) material as a substrate, using the Cu layers for easy contact formation. In a first step, an innovative measurement concept, based on a distinctive vertical rendition of the well-established transfer length method, has been realized, allowing for the in-situ measurement of contact resistance between the TE material and the copper conductors on the PCB substrate. This enables a comprehensive assessment of the impact exerted by the applied force and temperature during e.g. a hot-pressing step for compacting the powder-based thermolegs during the manufacturing process. In a second step, a comprehensive measurement platform, referred to as the ZT-Card, has been devised to facilitate the evaluation of all relevant TE material properties—Seebeck voltage, electrical conductivity and thermal conductivity (all measured in vertical cross-plane orientation)—inherent to a highly miniaturized thermoleg. Additionally, the ZT-Card also allows for the assessment of contact resistance between the copper contacts and the TE material. Successful testing of this measurement system inspires confidence in the capabilities of the platform and will aid in future µTEG development.

In order to optimize their system design and manufacturing processes, it is crucial to undertake a thorough electrical and thermal characterization of micro thermoelectric generators (µTEGs).To address this need, a highly advanced and fully integrated in-situ measurement system has been developed.The main objectives of this system are to (1) enable the measurement of ZT and thereby of all thermoelectric (TE) properties of thermolegs made from powder-based TE materials and (2) at the same time accurately measure the contact resistance between the TE material and the electrical contacts.The µTEG fabrication concept used in this study is based on copper-cladded printed circuit board (PCB) material as a substrate, using the Cu layers for easy contact formation.In a first step, an innovative measurement concept, based on a distinctive vertical rendition of the well-established transfer length method, has been realized, allowing for the in-situ measurement of contact resistance between the TE material and the copper conductors on the PCB substrate.This enables a comprehensive assessment of the impact exerted by the applied force and temperature during e.g. a hot-pressing step for compacting the powder-based thermolegs during the manufacturing process.In a second step, a comprehensive measurement platform, referred to as the ZT-Card, has been devised to facilitate the evaluation of all relevant TE material properties-Seebeck voltage, electrical conductivity and thermal

Introduction
Thermoelectric micro-generators (µTEGs), miniature counterparts of conventional thermoelectric generators (TEGs), hold immense potential in energizing the Internet of Things ecosystem.They possess unique advantages over other concepts of energy harvesting, like a robust design without the need of moving parts, the capability to tap small thermal energy reservoirs with temperature differences of a few Kelvin only, and a long lifetime of suitable thermoelectric (TE) materials within their envisaged operation conditions.They can therefore serve as reliable alternatives when other energy harvesting technologies face limitations, such as unfavourable weather conditions or simply darkness in the case of photovoltaic cells or harsh environments in the case of mechanical vibration harvesters.Also, µTEGs provide direct current electrical output, exhibiting consistent electrical properties even amidst fluctuating environmental conditions encountered when subjected to temperature gradients [1].
Among several planar designs, the vertical or cross-plane arrangement of thermolegs is a standard building concept for a majority of TEGs and µTEGs, as shown in figure 1.This is accomplished either by stacking pre-fabricated thermolegs between a top and bottom plate carrying pre-fabricated electrical contacts (figure 1(a)) for their connection, or by embedding thermolegs into a substrate material, with the electrical contacts realized afterwards on both sides of the same (figure 1(b)).The latter version opens the way for a costefficient and scalable mass fabrication of miniaturized TEGs or µTEGs, as TE material can be integrated into the substrate via cost-efficient techniques like ink dispensing or screen printing.The mechanical placement, mounting and soldering of thermolegs is avoided, together with the limitations on the number and size of thermolegs.
For an optimal device performance, it is crucial to conduct an electrical and thermal evaluation of µTEGs during fabrication.Therefore, the focus of this study is on the characterization of both the TE materials fabricated with an ink dispensing process as well as the thermolegs in µTEGs, specifically through the measurement of all relevant TE properties-Seebeck voltage, electrical conductivity and thermal conductivity.This is done on thermoleg level in its anticipated cross-plane orientation, taking all influences of the fabrication process and the device geometry into account.In addition, the contact resistance between the TE material and the Cu contacts of the substrate is determined, again under the influence of all process parameters.
In the scope of fabrication techniques, printing technology, particularly dispenser printing, is widely employed for producing TEGs and thermolegs [2].Leveraging this approach, the study applies dispenser printing to fabricate µTEGs based on a previously established fabrication concept for printed circuit board (PCB) base material [3].To assess the impact of applied force and temperature during the hot-pressing processes of powder-based thermolegs in µTEGs, an integrated setup was used, enabling measurements in the same PCB substrate as used as µTEG substrates.
This first setup enables an in-situ measurement of the contact resistance between the TE material and the Cu layers of the PCB substrate.The contact resistance is quantified using the transfer length technique (TLM) in an unconventional vertical arrangement along the sides of the thermolegs.The transfer length method (TLM) is the preferred technique for determining contact resistances in semiconductors [4].However, the unique vertical positioning of the µTEG legs within the PCB deviates from the conventional in-plane orientation of TLM structures, requiring a modification to the standard design (see figure 2).The in-plane TLM provides a straightforward approach to determine the sheet resistance of a thin layer of material.By employing a constant current and a digital voltage meter, a four-point measurement configuration can be established [4], where the current is applied and the voltage drop monitored between two adjacent contacts.The overall resistance can be determined and via measurements between each pair of contacts, a TLM graph can be constructed.To calculate the contact resistance the linear regression of the measured resistances is extrapolated to zero distance, which results in double the contact resistance.Additionally, the contact resistance associated with the specific contact region can be utilized to evaluate the contact resistivity.When considering vertical cylindrical samples, the electrical resistivity is determined by the dimensions of the sample and the resistivity of the material [5].In contrast to in-plane TLM, the vertical TLM measures the resistance through the plane.In vertical TLM the layer thickness L between the contacts takes the place of the contact distance in regular TLM (figure 2).Similarly, the radius of the cylindrical hole in vertical TLM corresponds to the layer thickness underneath the contacts for regular TLM.The increasing interest in nanoscale TE material [6] has motivated the development of measurement techniques and devices dedicated to not only determine the contact resistance, but also the figure of merit ZT = σS 2 T/λ with the electrical conductivity σ, the Seebeck coefficient S, the mean temperature T, and the thermal conductivity λ of the vertical or crossplane thermolegs.Although lots of studies exists for thin film or in-plane thermoelectric (TE) material characterization [7][8][9], vertical TE material characterization is crucial for precise evaluation of vertical thermolegs, as the direction of measurement can play an important role in vertically fabricated µTEGs [10].Several techniques are known in literature for vertical measurement of the Seebeck coefficient and the thermal conductivity, e.g. the 3ω method [11] and the heating method [12].For the setups discussed here, suitable technologies from literature have been selected and adapted to fit within the capabilities and instruments available in our lab.
In this light, the contact resistance measurement platform was developed into a comprehensive measuring platform called ZT-Card.The ZT-Card was implemented on a PCB substrate, similar to the one used for the complete µTEG [13] in order to access the µTEG properties in a realistic application scenario.It enables the evaluation of all TE parameters as well as a determination of the contact resistance.This paper describes the development of the ZT-Card with a focus on the assessment of materials quality in µTEGs based on nanoscale TE Bi 0.5 Sb 1.5 Te 3 (p-type) and Bi 2 Te 2.7 Se 0.3 (n-type) [13].Based on the vertical TLM method and the contact resistance platform, a four-point measurement setup and a temperature control system, the ZT-Card is designed, fabricated, tested and demonstrated to measure all TE properties for the vertical ZT calculation.

Contact resistance platform
In order to evaluate the performance of powder-based µTEG in PCB substrates, the contact resistance between the TE material and the copper contacts on the PCB can be monitored [13].Herby the impact of paste dispensing, hot pressing and thermal treatment on the electrical output of the µTEG can be assessed.A specialized PCB substrate incorporating integrated vertical TLM structures has been developed and previously published [13].This substrate seamlessly integrates into µTEG production process, facilitating an accurate and efficient evaluation of contact resistances and thereby µTEG performance.
The contact resistance measurements are conducted on a 10 × 10 mm 2 FR4-based four-layer PCB substrate.The vertical TLM structures are formed by the four layers of copper with a thickness of 110 µm each and three layers of FR4 with a thickness of 260 µm in between.The design features a cylindrical cavity, with diameters between 500 µm and 1000 µm and a height of 1 mm, located at the centre, which is filled with either p-type or n-type TE material in a process identical to the previously described µTEG fabrication [13].The contacts to the thermoleg consist of four copper ring connections in each of the layers [14].The top view of the contact resistance measurement platform is depicted in figure 3 [14].The measurement follows a modified TLM pattern as the distances between the contacts are fixed and therefore resistances have to be measured between different Cu layers in order to get an effect from changing contact distances.Figure 4 illustrates all the possible resistances that are evaluated within the vertical arrangement.The vertical distance between the contacts is plotted against the mean values of resistances (R 1 , R 2 , R 3 ), (R 4 , R 5 ) and R 6 , as demonstrated in figure 4.

ZT-Card
The ZT-Card was designed as a five-layer PCB substrate with dimensions of 55 × 25 mm 2 , as illustrated in figure 5.It serves as a comprehensive measurement platform for the TE characterization of both p-type and n-type TE materials in cross-plane orientation at the same time.The ZT-Card combines electrical contact resistance and conductivity measurement with a Seebeck measuring setup as well as a method for thermal conductivity measurement on one single substrate.
In the ZT-Card, the same four-layer TLM contacts used in the contact resistance platform for contact resistance measurement are integrated, but used additionally as a four-point measurement setup to determine the electrical conductivity.The copper pads on the top surface of the ZT-Card are connected to the copper ring contacts along the material-filled cylindrical cavity.For p-type and n-type materials, the ZT-Card has eight voltage and current measurement contacts separately to support up to eight layers of TLM measurement.
The Seebeck voltage of the p-and n-type thermoleg can be measured with the assistance of external thermocouples placed on top and bottom of the sample, as well as an on-board heating structure (coil shown in figure 5), to generate a temperature difference across the TE leg.
To measure the thermal conductivity of the TE material vertically, different method, like e.g. the 3ω method [11] or the heating method [12] can be used.Based on available technologies in our lab, the transient hot bridge (THB) system (Linseis, Germany) was used and for this purpose square chambers measuring 5 × 5 mm 2 were incorporated into the ZT-Card.The main element of the THB system is a strip-shaped electrical conductor, which works as both a Joule heat source and a resistance thermometer.Positioned between two halves of the sample, the strip is subjected to a consistent heating current throughout the measurement, heating up its immediate surrounding.The temperature rise over time serves as the metric for determining the thermal transport properties of the surrounding material.This way, the thermal conductivity of the TE material can be assessed in the same vertical direction as all the other parameters, ensuring consistency in this regard.The ZT-Card was treated throughout the whole µTEG fabrication process identical to all other µTEG samples, ensuring that the outcomes of material characterization can be directly correlated with process variables.

Contact resistance platform
In order to fill the central hole with TE material, the bottom of the hole was closed by soldering a 35 µm thick circular Cu foil to the bottom side.After that a dispensing process was used to deposit the powder paste TE material into the central hole, creating a single thermoleg.This process was identical to the one used when fabricating µTEGs [13].To compact the TE material within the thermolegs a hot-pressing step was used (for further details, refer to [13]).

ZT-Card
The copper-based microheater on the top PCB layer of the ZT-Card is necessary to provide the temperature gradient for the measurement of the TEG materials Seebeck coefficient.The COMSOL Multiphysics 6.1 simulation software was used to analyse and optimize its performance and to determine the impact of the supply current on the temperature profile over time.A tiny mesh-sized microheater model was used in a timedependent study utilizing Joule heating physics (coupled heat transfer in solids and electric currents module).For the TE material, the values reported previously [15] have been used.
In order to account for the radiative qualities of the gold coating used to construct the manufactured TEG [13] and the contact measurement platform, a surface emissivity of 0.033 [16] was employed to describe radiation heat transfer.Out of the various possible microheater topologies discussed in e.g [17], two circular heater geometries were selected for a consistent temperature distribution.Width (100 µm), thickness (35 µm) and minimal pitch (100 µm) of the Cu layer where chosen according to fabrication limitations by a commercial manufacturer (Multi-CB, Germany).The overall thickness of the multilayer PCB is 1200 µm.
For the simulation study, both circular geometries (meander design and spiral) where initially set to room temperature and a supply current was applied.Comparing the two structures, the spiral structure demonstrates approximately double the resistance of the meander structure with the same geometric parameters.
Based on the simulation results, the spiral microheater structure was selected for the ZT-Card design.To further increase the heater resistance to 92.2 mΩ, the number of spirals was increased in the final heater design.The modified spiral heater structure (figure 6) heats up to 318 K in 10 s using 500 mA supply current at 461 mV (230 mW power dissipation), with an assumed ambient temperature of 293 K.In figure 6, the simulated cross-section view of the thermoleg with a spiral heater design on top shows a temperature gradient of 1 K from the top to the bottom along the thermoleg.
To validate the simulation results, a micro heater prototype was fabricated in-house via laser PCB fabrication (LPKF Protolaser, Germany) on PCB material with a single 18 µm layer of Cu (figure 7(a)).
The prototype of the microheater had an electrical resistance of 1.03 Ω and showed the behaviour expected from simulation during testing (figure 7(b)), although the resistance was higher than the simulated value because of the lower copper thicknesses used.The temperature distribution was analysed using a thermal camera (Optris-PI 450) after coating  the microheater structure with black varnish (tetanal kameralack spray, 95% light absorption capability).The temperature rise and power dissipation correlated closely with the simulation data, inspiring confidence in the selected 6 mm diameter spiral heater for the final design of the ZT-Card.
A photograph of the final ZT-Card substrate is shown in figure 8.The card is separated into two halfs-one for p-and one for n-type material.Each central hole as well as the larger squares on both sides can be filled with the respective material.The squares are used for THB thermal conductivity measurement, whereas the central hole incorporates four layers of Cu contacts for contact resistance and electrical conductivity measurements.The fifth layer is structured with the microheater structure in order to create the temperature gradient for the Seebeck voltage measurement.The multiple contacts on both sides are connected to the different Cu-contacts in the lower layers and only used partially in the current four-layer setup.The system can be extended to handle up to 8 layers of contacts for both vertical TLM and electrical measurements as described in 2.2.
A platform to safely hold and contact the ZT-Card in the correct spots to perform TLM, four-point and Seebeck voltage measurements was designed using SolidWorks (Dassault Systems, France).
The setup is shown in figure 9.It consists of a ZT-Card/spring contacts housing to ensure repeatability and exact The housing platform was designed as a three-layer structure with the bottom part incorporating the PCB with the D-sub connectors.The middle structure houses spring contacts and thermocouples for the temperature measurement at one end of the thermoleg, and the top structure incorporates thermocouples for the temperature measurement at the other end.Since the TE material to be characterized is filled inside a 500 µm diameter cylindrical cavity, even a slight misalignment between the layers may result in the thermocouples hitting the substrate and producing an inaccurate measurement.Therefore, to prevent any parts from moving during the measurement process, the housing was rigidly constructed with all three layers guided by alignment structures.The entire assembly was fabricated using Rigid 4000 resin on a Formlabs Form 3 3D printer.
All electrical measurements where conducted using a Keithley 3706 switch/multimeter linked to a Keithley 2601A source meter, responsible for the current input.
The switching between the 16 measurement channels from the ZT-Card is achieved using a Keithley 3730 matrix card.For Seebeck coefficient measurement, two spring-loaded Ttype copper-constantan thermocouples are pressed against top and bottom of the thermolegs for simultaneous temperature and voltage measurement.
The in-house fabricated setup for the spring-loaded thermocouples is shown in figure 10.The thermocouple probes were fabricated by embedding very thin thermocouples (Type T, AWG 40, Omega Electronics, Germany) into a 3D printed holder with the help of two-component epoxy resin.The tip of the thermocouple was left exposed to allow electrical contact with the TE material.The automatic cold junction compensation of the Keithley 3721 switching module inside the 3706 multimeter allows direct temperature reading from the connected thermocouples.
The temperature of the onboard micro heating structure is controlled using a temperature control algorithm on a microcontroller and an external power supply unit.To maintain a stable temperature, the temperature controller software uses a relative change in the microheater resistance value as a function of temperature.By keeping the heater resistance value within a defined range, the microheater can be maintained within a ±1 • C temperature deviation.The continuous variation of the microheater temperature within the tolerance range does not affect the measurement as the temperature at the thermoleg is measured independently and at the same time as the Seebeck voltage.The electrical measurements are fully automated and controlled using a specifically designed Python program.A dedicated software application was developed in Python for the ZT-Card, focusing on data acquisition, control, and analysis during measurements.
The connection diagram of the measurement system is shown in figure 11.D-Sub 37 and D-Sub 9 connectors interface with the Keithley instrumentation and temperature controller unit.The matrix card's rows connect the current source and voltmeter, while the columns connect the measurement channels.Type-T thermocouples are connected to the Keithley 3706 multimeter through Omega Electronics' miniature thermocouple connectors.
This sub-section provides an overview of the measurement platform (figure 12).It combines the ZT-Card, microheater design, housing and hardware setup that have been described in the previous sub-sections.A GUI for ease of use was programmed.The step-by-step procedure of a measurement is as follows: (1) The ZT-Card is placed upside down in the sample holder with correct orientation of the p-and n-side, indicated by labels on the ZT-Card measurement platform and securely tightened with four screws.(2) After powering on all instruments (Keithley 3706A, Keithley 2601A, power supply, and temperature controller), the ZT-Card application software is launched.(3) The material type for analysis is selected.(4) For a four-point measurement, the specify current range, steps, layer thickness, and thermoleg diameter is entered  and the layers are chosen between which the resistance should be measured.( 5) For a TLM measurement, the same inputs as in the previous step are specified along with the number of layers and distance between them.(6) For a Seebeck measurement, the microheater is activated from the temperature controller application to create a controlled temperature gradient.The temperature controller settings are adjusted and real-time continuous Seebeck measurement in the ZT-Card application is started.(7) The Seebeck coefficient and resistivity values can either be entered manually or automatically through the 'Add to ZT Calculator' button in the GUI.(8) The thermal conductivity of the TE material is measured externally at the THB setup using the two squares on the ZT-Card and has to be entered manually.The ZT value can be calculated by a press of the respective button.

Contact resistance platform
In order to monitor the fabrication process for powder-based µTEGs, the contact resistance under various hot-pressing conditions was evaluated using the contact resistance platform described above.One of the resulting TLM graphs is shown in figure 13.In table 1 the results from multiple tests under various conditions are shown together with the respective contact resistance.The results, previously reported in [14], highlight the substantial influence of elevated temperature and applied  Reprinted, with permission, from [14].
force during the hot-pressing process.As the temperature and applied force increase, the contact resistance (RC) shows a decreasing trend.The one exception for the highest temperature and applied force combination (175 • C, 5 kN) can be attributed to the occurrence of fractures in the small copper contacts, resulting from a slight plasticity of the FR4 layer at high applied force and temperature.Table 1 also displays the specific contact resistivity, i.e. ρC = RC × A contact at the corresponding hot-pressing parameters.

ZT-Card
The Seebeck coefficient, the electrical conductivity, the thermal conductivity and contact resistivity were determined for 3 samples using the measurement methods described in the previous sections.The respective thermolegs had a diameter of 500 µm, a height of 1.1 mm and were constituted of n-and p-type TE material.
The results are shown in table 2, all values were taken at room temperature except for the Seebeck measurements, which required a temperature gradient.By adjusting the current through the heater at the top, the upper section of the thermoleg was heated to ∼46 • C, while the lower section reached temperatures of ∼41 • C by natural convection only, thereby generating a temperature gradient of 4-5 K.
The values in table 2 represent the mean values derived from a minimum of 200 measuring points for the Seebeck  The measured Seebeck coefficients for the n-type material ranged from −88.2 µV K −1 to −111 µV K −1 per thermoleg, while for the p-type material, measurements are within the range of 197-216 µV K −1 per thermoleg.The obtained Seebeck values for the p-type material corresponded well with other reported values for Bi 0.5 Sb 1.5 Te 3 (p-type) in [18], which were at 220 µV K −1 .In contrast, the Seebeck value for Bi 2 Te 2.7 Se 0.3 (n-type) was notably lower than the bulk value of −208 µV K −1 [18].
The lower value for the n-type material can potentially arise from composition changes during TE paste formation or a lower than desired final density after the hot processing step [18].The reduced value is further attributed to the polycrystalline powder in the TE material paste, opposed to the monocrystalline bulk material.
The electrical conductivity measurement results from three ZT-Cards are given in table 2. The considered thickness of TE materials for electrical conductivity measurement is 192 µm based on microscope analysis of the ZT-Card.The electrical conductivity for p-type materials is in the range of 15-22 Scm −1 , while for n-type materials is in the range of 17-29 Scm −1 .The electrical conductivity of both dispensed TE materials was less than 200 S cm −1 [18] and therefore needs considerable improvement.One reason for the lower electrical conductivity in the TE material can certainly be attributed to sub-optimal contact between the material and the copper ring of the ZT-Card.Additionally, insufficient compaction of the material would lead to the same result.Likely both effects play a role in the results shown and will be addressed in the future using the insights provided by the ZT-Card.The low magnitudes of electrical conductivity due to the abovementioned reason, results in a worse measurement precision, subsequently giving larger error bars (shown in figure 14).This can be explained by the sensitivity characteristics of the measurement system at lower electrical conductivity levels.
The thermal conductivity of both n-type and p-type materials was measured using the THB system.The obtained thermal conductivity values were in the range of 0.2-0.3W m −1 K −1 for p-type and 0.4-0.5 W m −1 K −1 for n-type material for the thickness of 1.1-1.2mm.The measured thermal conductivity for p-type and n-type materials are in the optimum range and show good agreement with the values of both types of material reported in [7,18,19].Even though there is precedence in literature the measured thermal conductivity values of both n-type and p-type materials are very low, approaching the theoretical limit [20].Therefore, the measurements were repeated for a new sample and the thermal conductivity measurement points for the n-type material were in the range of 0.4-0.9W m −1 K −1 and for the p-type material in the range of 0.2-0.4W m −1 K −1 .Although the higher measured values such as 0.9 W m −1 K −1 for the n-type and 0.4 W m −1 K −1 for the p-type were only observed at one measurement point, thus the averaged values were considered as the final thermal conductivity value.One speculative reason for a reduced thermal conductivity could be the formation of micro-cracks acting as 'voids' after the hot-pressing step and a press tool which is used in measurement setup for sandwich the hot point sensors and samples.No such cracks have been observed so far and the values are therefore reported as measured, but the issue is currently under investigation and will be published later.
To measure the contact resistance between the TE material and the copper contacts, vertical TLM measurements were conducted as described in sub-section 2.1.A current ranging from 1 mA to 10 mA was incrementally applied in 10 equal steps, and the corresponding voltage was measured at each step.This process was repeated for all the distances (d 1 = 171 µm, d 2 = 405 µm, d 3 = 624 µm), and the corresponding resistance was determined.The contact resistivity obtained from all three ZT-Card samples is summarized in table 2. The values are in the range of 7.8 × 10 −5 -6.3 × 10 −4 Ωcm 2 , which are similar to the values obtained from the previous measurement setup explained in section 2 and published values [13,21].
The ZT value, calculated using the equation ZT = σS 2 T/λ, is presented in table 2 as well.For the p-type and n-type materials, the highest ZT values achieved at room temperature were 0.13 and 0.016, respectively.In a study [18], the same p-type and n-type materials exhibited room-temperature ZT values of 0.65 and 0.81, respectively.Despite possessing lower thermal conductivity, the primary reason for the notably lower ZT values obtained in this study is the significantly diminished electrical conductivity observed in both types of materials.The exact reason for this is subject to current investigation using the ZT-Card.

Conclusions
This study presents a comprehensive in-situ measurement setup that integrates various techniques to measure TE properties of fabricated thermolegs in µTEGs and determine the contact resistance in PCB-based µTEGs at the same time.The performance of the fabricated µTEGs can be checked by analysing the contact resistance between the TE material and the copper contacts on the PCB substrate.This was shown with a specific focus on the impact of the paste dispensing and hotpressing processes on our fabrication.The results demonstrate that the contact resistance reaches its lowest value when the hot-pressing is performed at a temperature of 175 • C and an applied force of 2.5 kN.
Additionally, a complete measuring platform named ZT-Card was designed, which incorporates a circular spiral heater structure for generation of a temperature gradient between the top and bottom of a single thermoleg.With the ZT-Card, it becomes possible to assess all significant TE material parameters, as well as the contact resistance of miniaturized thermolegs, while correlating the measurements directly with changes in process parameters.Overall, the ZT-Card provides a robust framework for evaluating and understanding the TE properties of µTEGs fabricated in PCB-based substrate.The results obtained through this setup can contribute to the optimization and enhancement of TE material development and µTEG performance optimization by informing the design and fabrication processes.

Figure 1 .
Figure 1.Vertical or cross-plane TEGs (a) TEG fabricated by stacking thermolegs between a top and bottom plate carrying electrical contacts for their connection (b) TEG fabricated by embedding thermolegs into a substrate (thermoleg holder), with the electrical contacts realized on both sides of the substrate.

Figure 2 .
Figure 2. (a) Regular (in-plane) TLM (b) vertical TLM with the relevant contact dimension c as well as the distances d between the contacts.

Figure 5 .
Figure 5. 3D view of the ZT-Card design, which includes a contact resistance measuring unit and four larger square material samples for thermal characterization.The overall dimensions are 55 mm × 25 mm.

Figure 6 .
Figure 6.3D view of the spiral heater structure designed and simulated around the single thermoleg of the ZT-Card (top); cross-sectional view of the simulated temperature distribution in a single thermoleg of the ZT-Card (spiral heater design) unit with 5 surrounding Cu layers (bottom).

Figure 7 .
Figure 7. Final 6 mm diameter circular spiral heater design (a) microscope image and (b) IR-image after heating for 180 s with 500 mA of current, at an ambient temperature of 293 K.

Figure 9 .
Figure 9. Overview of the setup for the measurement platform which consists of thermocouples, thermocouple holders, spring contacts, D-Sub connectors and the ZT-Card.

Figure 10 .
Figure 10.Integration of the thermocouples into the measurement setup.

Figure 11 .
Figure 11.Connection diagram of the measurement system.

Figure 13 .
Figure 13.TLM graph for determination of contact resistance of a n-type TE material.Colours and point shapes reflect the outcomes of varying hot-pressing parameter combinations.© 2022 IEEE.Reprinted, with permission, from[14].

Figure 14 .
Figure 14.Standard deviation graphs of Seebeck coefficient, electrical conductivity, thermal conductivity and contact resistance of 3 samples each n-and p-type TE materials.

Table 1 .
Contact [14]stance values and contact resistivity for various hot-pressing conditions of a 500 µm diameter n-type thermoleg with a height of 1 mm.© 2022 IEEE.Reprinted, with permission, from[14].