# High Power Density Thermoelectric Generators with Skutterudites

Soufiane El Oualid, Iurii Kogut, Mohamed Benyahia, Eugen Geczi, Uwe Kruck, Francis Kosior, Philippe Masschelein, Christophe Candolfi, Anne Dauscher, Jan Dieter Koenig, et al.

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## To cite this version:

Soufiane El Oualid, Iurii Kogut, Mohamed Benyahia, Eugen Geczi, Uwe Kruck, et al. High Power Density Thermoelectric Generators with Skutterudites. Advanced Energy Materials, 2021, 11 (19), pp.2100580. 10.1002/aenm.202100580. hal-03969757v2

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https://hal.univ-lorraine.fr/hal-03969757v2

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Distributed under a Creative Commons Attribution 4.0 International License
# High Power Density Thermoelectric Generators with Skutterudites

Soufiane El Oualid, Iurii Kogut, Mohamed Benyahia, Eugen Geczi, Uwe Kruck, Francis Kosior, Philippe Masschelein, Christophe Candolfi, Anne Dauscher, Jan Dieter Koenig, Alexandre Jacquot, Thierry Caillat, Eric Alleno, and Bertrand Lenoir*

Thermoelectric generators (TEGs) offer a versatile solution to convert low-grade heat into useful electrical power. While reducing the length of the active thermoelectric legs provides an efficient strategy to increase the maximum output power density $p_{max}$, both the high electrical contact resistances and thermomechanical stresses are two central issues that have so far prevented a strong reduction in the volume of thermoelectric materials integrated. Here, it is demonstrated that these barriers can be lifted by using a nonconventional architecture of the legs which involves inserting thick metallic layers. Using skutterudites as a proof-of-principle, several single-couple and multi-couple TEGs with skutterudite layers of only 1 mm are fabricated, yielding record $p_{max}$ ranging from 3.4 up to 7.6 W cm$^{-2}$ under temperature differences varying between 450 and 630 K. The highest $p_{max}$ achieved corresponds to a 60-fold increase per unit volume of skutterudites compared to 1 cm long legs. This work establishes thick metallic layers as a robust strategy through which high power density TEGs may be developed.

## 1. Introduction

Thermoelectric materials have the ability to directly and reversibly convert a thermal gradient into electrical energy, offering an elegant and versatile way to recover energy from any heat source.[1–15] Thermoelectric generators (TEGs), consisting of n- and p-type legs composed of doped semiconductors, have been mostly used as

Dr. S. El Oualid, Dr. I. Kogut, Dr. F. Kosior, P. Masschelein, Dr. C. Candolfi, Dr. A. Dauscher, Prof. B. Lenoir
Institut Jean Lamour
UMR 7198 CNRS – Université de Lorraine
Campus ARTEM, 2 allée André Guinier, BP 50840, Nancy 54011, France
E-mail: bertrand.lenoir@univ-lorraine.fr
Dr. M. Benyahia, Dr. E. Alleno
ICMPE
UMR 7182
CNRS-Université Paris Est Creteil
2 rue Henri Dunant, Thiais 94320, France
E. Geczi, U. Kruck,[1] Prof. J. D. Koenig, Dr. A. Jacquot
Fraunhofer Institute for Physical Measurement Techniques IPM
79110 Freiburg, Germany
Dr. T. Caillat
Jet Propulsion Laboratory
California Institute of Technology
Pasadena, CA 91109, USA

The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/aenm.202100580.

[1] U.K. passed away in April 2020.

DOI: 10.1002/aenm.202100580

reliable power supplies for rovers and deep-space probes.[10,11] Despite being an attractive solid-state technology primarily due to its high reliability and absence of greenhouse gas emissions, the limited use of TEGs in terrestrial applications is tied to their output performances, still surpassed by other green energy-conversion technologies such as solar cells.

The last decades have witnessed the emergence of novel families of thermoelectric materials such as skutterudites, half-Heusler, or Zintl phases.[16–24] Their higher performances with respect to state-of-the art materials are captured through their dimensionless thermoelectric figure of merit $ZT = \alpha^2 T/\rho\kappa$ where $\alpha$ is the thermopower (or Seebeck coefficient), T is the absolute temperature, $\rho$ is the electrical resistivity, $\kappa$ is the total thermal conductivity,

and $\alpha^2/\rho$ is the power factor.[10] Because increased ZT values yield enhanced conversion efficiency $\eta$,[10] these important advances have stimulated the development of TEGs operating at moderate temperatures (500–800 K). Several designs, including segmented legs composed of two or three joint thermoelectric materials,[10] have been investigated yielding very encouraging results with $\eta$ values exceeding 10%.[8,25,26] While the optimization of $\eta$ is of prime importance for applications for which the heat source is limited or expensive, numerous waste-heat energy recovery applications do not require high TEG’s efficiency due to the availability of unlimited, cost-free heat sources. The ability to generate the electrical power required to energize autonomous electronic devices is then the primary concern, making the maximum output power $P_{max} = A p_{max}$ (where A is the cross-section area and $p_{max}$ is the output power density) the key parameter to be optimized.[10,27,28]

One of the most direct ways to increase $P_{max}$ is to optimize the geometry of the n- and p-type legs, as highlighted by its simplest form determined for a fixed temperature difference $\Delta T$, a matching of the electrical impedance and assuming temperature-independent transport properties of the thermoelectric materials[10,29–33]

$$P_{max} = \frac{(\alpha_p - \alpha_n)^2 \Delta T^2}{4R} = \frac{A(\alpha_p - \alpha_n)^2 \Delta T^2}{4L(\rho_n + \rho_p)} \quad (1)$$

where $\alpha_i$ and $\rho_i$ are the thermopower and electrical resistivity of the leg i = n, p, respectively, and $R = \frac{L(\rho_n + \rho_p)}{A}$ is the internal
resistance of the thermocouple, *L* being the length of the n- and p-type legs. In addition to n- and p-type materials possessing high power factors, Equation (1) shows that high $P_{max}$ can be achieved by considering large surface areas *A* of the thermoelectric legs. However, the volume of thermoelectric materials scales with *A*, thereby rapidly increasing the cost per Watt generated. For this reason, lowering the length *L* seems to provide a straightforward strategy to enhance $P_{max}$ and, meanwhile, reach cost-efficiency.

However, while seemingly simple, this strategy faces two major adverse effects, the control of which is then pivotal in achieving high $P_{max}$. The first effect is tied to the contribution of the electrical contact resistances $\rho_c$ to the internal resistance of the legs, which is of increasing importance as $L$ decreases. This effect limits $P_{max}$ due to the resistance term $R_c$ in the total internal resistance $R_{int}$, $R_{int} = R + R_c = \frac{L(\rho_n + \rho_p)}{A} + \frac{4\rho_c}{A}$ (assuming that the contact resistances are the same for the n- and p-type legs), which is no longer negligible.[31] Meanwhile, lowering $L$ results in a significant increase in the thermal gradient undergone by the thermoelectric materials, which generate high thermomechanical stress levels. Because thermoelectric materials are often mechanically fragile, this effect strongly limits the robustness of the legs and hence, the lifetime of the module. Moreover, a strong reduction in $L$ tends to detrimentally impact the conversion efficiency $\eta$ through a decrease in $\Delta T$ due to the interfacial thermal resistance (see the Supporting Information),[29–33] thus placing a lower bound below which this strategy will no longer be viable. Due to these difficulties, only few studies have so far attempted to exploit this strategy to optimize $P_{max}$, if we except the specific case of $\mu$-TEGs that integrate thin films with $L$ on the order of tens of $\mu$m or less.[34–42] While $\mu$-TEGs are currently being extensively investigated as a possible solution to power Internet-of-things autonomous devices such as wireless sensors or networking devices,[34,40,41] they only operate around room temperature with limited $P_{max}$ ranging from $\mu$W to mW. Both increasing this level of power and enlarging their operating temperature are of particular interest and would open up new avenues to harvest low-grade heat in many industrial sectors (ovens, steam lines, hot fluid, motors, heating...) or in domestic devices (cookers, stoves...), thereby widening the application landscape of TEGs.

Here, leveraging on prior achievements on the development of TEGs,[29–33] we demonstrate how these two issues can be successfully overcome using a nonconventional design of the thermoelectric legs that enables to reduce the length of the active thermoelectric layers to only 1 mm while concomitantly maintaining both $\eta$ and electrical contact resistances to state-of-the-art values.[14,15,43–56] The key design principle consists in inserting a thick layer of metallic composites, acting as a buffer, between the active thermoelectric materials sandwiched by the diffusion barrier and the metallic interconnections or electrodes. Among their advantages, these composites enable limiting the thermomechanical stresses undergone by the thermoelectric materials and easing the final brazing of the legs on the metallic interconnections. As a proof of principle, we used as thermoelectric materials n- and p-type skutterudites of chemical compositions $In_xCo_4Sb_{12}$ (0.16 $\le x \le 0.20$) and $Ce_{0.90}Fe_3CoSb_{12}$, respectively, in order to take full advantage of the good understanding

of their chemistry acquired over the last two decades and their high power factors.[10,16–18] The robustness and versatility of our approach is demonstrated by the fabrication of several single- and multi-couples TEGs with two distinct diffusion barriers (Ti or Ni) and compositions of the metallic composites (Ti/Cu or Ti/Ag), showing that both types of layers can be easily adapted to the integrated thermoelectric material. With conversion efficiencies ranging between 6.5% and 6.9% that are comparable to state-of-the-art values for nonsegmented skutterudite legs,[14,15,43–56] the measured output power density $p_{max}$ varying from 3.4 up to 7.6 $W cm^{-2}$ for applied $\Delta T$ between 450 and 630 K, are the highest achieved so far for skutterudite-based TEGs.

## 2. Results and Discussion

### 2.1. Design and Fabrication of the Thermoelectric Legs

The nonconventional design of the n- and p-type thermoelectric legs consists in (Ti/Cu)_{n,p} metallic composites placed on either side of the active skutterudites (Figure 1). A pure Ti layer of 25 $\mu$m is inserted between the skutterudites and the (Ti/Cu)_{n,p} composites that serves as a diffusion barrier, preventing diffusion of the skutterudite elements toward the metallic composites or Cu contacts at high temperatures. A central aspect of the assembly of both legs is the applied thermomechanical cycle using the spark plasma sintering (SPS) technique, which allows for the consolidation of the assembly (metallic composite/diffusion barrier/ skutterudite/diffusion barrier/metallic composite) in one single step (Figure S1 in the Supporting Information). Furthermore, the temperature-pressure cycle has been carefully optimized for each type of leg to achieve flat interfaces between the different layers and good electrical contacts (see below). Importantly, changing the nature or chemical composition of one of the three layers requires a re-optimization of the SPS cycle.

The key role played by these 1 mm thick metallic composites is demonstrated by their ability to limit the thermomechanical stresses undergone by the skutterudites due to the differences between the thermal expansion coefficients $\alpha_T$ of the skutterudites ($\alpha_T \sim 9.3 \times 10^{-6}$ and $11.3 \times 10^{-6}$ K$^{-1}$ at 300 K for the n- and p-type skutterudites, respectively) and those of the lower and upper metallic contacts made of Cu ($\alpha_T \sim 16.5 \times 10^{-6}$ K$^{-1}$ at 300 K) that is usually used to connect the thermoelectric legs. The $\alpha_T(T)$ curves of the n- and p-type skutterudites measured up to 773 K, shown in Figure 2, evidence a nearly linear behavior above 423 K with increasing temperature, reaching $12.5 \times 10^{-6}$ and $15.0 \times 10^{-6}$ K$^{-1}$ at 773 K for the n- and p-type skutterudites, respectively. Because of the mismatch in $\alpha_T$ between the n- and p-type skutterudites,[57] the chemical composition of the metallic composite has been specifically adapted and hence, differs between the n- and p-type legs. Due to the large difference in the $\alpha_T$ value of elemental Ti and Cu ($8.5 \times 10^{-6}$ and $16.0 \times 10^{-6}$ K$^{-1}$ at 300 K, respectively), the $\alpha_T$ values can be accommodated by adjusting the Ti-to-Cu volume ratio according to the Reuss model[58]

$$ \alpha_T^{\text{skutterudite}} = \alpha_T^{\text{composite}} = x\alpha_T^{\text{Cu}} + (1-x)\alpha_T^{\text{Ti}} \quad (2) $$

where *x* is the volume fraction of Cu. From the above-mentioned values of $\alpha_T$, volume fractions of *x* = 0.37 and *x* = 0.10
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Fabrication process of the skutterudite-based thermoelectric modules. a) Expanded view of an illustrative six-couple TEG made of n-type and p-type skutterudites connected electrically in series and thermally in parallel. b) Nonconventional design of the thermoelectric legs composed of the skutterudites sandwiched by Ni or Ti layers acting as diffusion barriers and Ti/Cu or Ti/Ag metallic composites that accommodate differences in the lattice thermal expansion between the skutterudites and the Cu metallic contacts and favor the brazing step. c–f) Steps of the assembly for an illustrative six-couple TEG. c) The InCuSil braze is applied on the lower Cu-Ni paths, deposited on an Al₂O₃ ceramic plate, to electrically connect the d) p- and e) n-type thermoelectric legs fabricated by spark plasma sintering. f) The second, upper ceramic plate is then brazed on the assembly.</figcaption></figure>

were used for the p- and n-type legs, respectively. The perti-
nence of this simple approach is confirmed by the α<sub>T</sub>(T) data
measured on each metallic composite (see Figure 2), which
demonstrates that the α<sub>T</sub> values are close to those of the respec-
tive skutterudites up to 523 K. A difference between both values
is solely observed for the p-type skutterudite at higher tempera-
tures, being at most 10% at 773 K. Of note, other combinations
of elements used in prior studies on skutterudite-based TEGs
may be also considered such as Mo/Cu or Al/Ti for instance.[31]
As a further demonstration of the versatility of the present
approach, a detailed characterization of n- and p-type thermo-
electric legs with (Ti/Ag)<sub>n,p</sub> composites and Ni acting as the
diffusion barrier are provided in the Supporting Information
(Figures S2–S9 in the Supporting Information). Although the
significant diffusion of Ni toward the skutterudites will prevent
its use due to the induced rapid deterioration of the thermo-
electric performances of the TEG, the large phase space for the
choice of the nature of these two layers is of particular impor-
tance for determining the most suitable combinations of ele-
ments to achieve long-term stability, as recently demonstrated
in skutterudite-based TEGs with Nb as the diffusion barrier.[15]
The results obtained herein show that the chemical composi-
tion of the composites and the diffusion barrier may be adapted
to the thermoelectric materials on a case-by-case basis.

The beneficial role of these metallic composites on the
mechanical stability of the TEGs is supported by 3D finite-ele-
ment analyses of the distribution of the equivalent Von-Mises
stresses, calculated for a single couple with an illustrative tem-
perature difference ΔT of 500 K and for skutterudite length L
varying between 1 and 3 mm (Figure 3). The boundary condi-
tions used in these calculations are described in the Supporting
Information. In the absence of metallic composites (Figure 3a),
the thermal expansion of the skutterudites, when subjected

to high temperature differences, induces the development of
tensile stresses, the level of which increases with decreasing
*L* due to the corresponding increase in the thermal gradient.
Upon decreasing *L* from 3 to only 1 mm, the maximum ten-
sile stress level undergone by the skutterudites may exceed
their tensile strength (see Supporting Information), resulting in
the breakage of the legs. Because of differences in α*<sub>T</sub>* between
the n- and p-type skutterudites, this limit is first reached in
the latter. In contrast, the addition of the metallic composites
on either side of the skutterudites maintains the maximum
tensile stress in the skutterudites to values well below their
tensile strength down to *L* = 1 mm (Figure 3b). Of note, this
beneficial effect does not originate from a decrease in the Δ*T*
undergone by the skutterudites due to the additional thermal
resistance induced by the composites (see below). Additional
calculations performed on this assembly with an increased
Δ*T* yielding a temperature difference of 500 K across the skut-
terudites confirm that the maximum stress level reached still
remains well below their tensile strength (see Table S1 in the
Supporting Information). The positive effect of these metallic
composites on the mechanical properties of the legs can be
qualitatively understood by taking into account their specific
mechanical characteristics. In the elastic regime (i.e., under low
strain), their Young's moduli are lower than those of the skut-
terudites (see Table S1, Supporting Information), which helps
to decrease the overall rigidity of the legs. Furthermore, their
plastic regime, characterized by a more or less flat plastic strain
rate, is also beneficial to decrease the stress level undergone by
the skutterudites at higher strain levels. For these reasons, the
metallic composites can be considered as acting as buffers from
a mechanical point of view. These results demonstrate that the
integrity of the skutterudite layers and hence, the mechanical
robustness of the TEG, can be maintained while decreasing the
<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /><figcaption>**Figure 2.** Thermal expansion $\Delta L/L_0$ of the a) p-type and b) n-type skutterudites as a function of temperature. The temperature dependence of the thermal expansion of the (Ti/Cu)$_n$ and (Ti/Cu)$_p$ metallic composites are also shown for comparison. For each material, the thermal expansion coefficients $\alpha_T = \frac{1}{L_0} \left(\frac{\partial \Delta L}{\partial T}\right)$ is indicated in the different temperature ranges highlighted by the vertical black lines.</figcaption></figure>

thickness of the skutterudite layer. Furthermore, increasing the number of couples will increase the total surface area of the legs and hence, will contribute to further reduction of the developed tensile stresses.

## 2.2. Characterization of the Thermoelectric Legs and Interfaces

Scanning electron microscopy (SEM) images combined with energy dispersive X-ray spectroscopy (EDS) elemental mapping were performed to assess the spatial distribution of the elements and determine the nature of the interfacial reaction layer between the skutterudite and the diffusion barrier for both the n- and p-type legs (Figure 4). A central aspect evidenced by these analyses is the absence of porosity and cracks in the skutterudite layers and the presence of an interfacial reaction layer between the skutterudites and the metallic composites that plays a key role in determining the electrical contact resistance of the legs.

The microstructure of the Ti/Cu composites is characterized by an overall two-phase mixture of homogenously distributed Cu and Ti regions of variable sizes spanning a range from few µm up to about 100 µm. The higher density of Cu regions observed in the p-type leg compared to the n-type leg naturally reflects the different Cu-to-Ti volume ratios considered. In agreement with the Cu-Ti binary phase diagram,[59] the EDS maps further show the formation of several Cu-Ti compounds at the interfaces between the Cu and Ti regions giving rise to a thin layer of ≈2 µm.

A closer inspection of the skutterudite/diffusion barrier interfaces shows that chemical reactions occurred during the consolidation process, giving rise to the presence of additional phases. These phases are confined to a layer of ≈6 µm located along the interface between the Ti diffusion barrier and the skutterudite (see Figure 4). For the n-type leg, chemical analyses further reveal the development of SbTi₂ at the Ti interface followed by TiSb₂ and CoTiSb. Another very thin layer of an In-rich phase is also observed, which may correspond

<figure><img src="image_6.png" /><figcaption>**Figure 3.** Distribution of the equivalent von Mises stresses calculated by 3D finite element analyses on a single couple of p- (left parallelepipeds) and n-type (right parallelepipeds) skutterudites for an illustrative $\Delta T = 500$ K and for $L = 1, 2, \text{ and } 3$ mm. These calculations were performed a) without and b) with (Ti/Cu)$_{n,p}$ metallic composites.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>**Figure 4.** BSE images and elemental X-ray maps of the thermoelectric legs composed of the p-type (panels a to h) and n-type (panels i to n) skutterudites sandwiched by the (Ti/Cu) metallic composites and the Ti diffusion barrier. p-type and n-type skutterudites are at the top and bottom of the images respectively. The panels (e), (h), and (l) correspond to overlaid images of several X-ray maps as indicated in the legend (left bottom). These analyses evidence the formation of several intermetallic compounds forming an interfacial reaction layer that prevents the migration of the elements. Note that the X-ray map of Ce is not shown due to the emission line of Ce being very close to that of Ti.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Figure 5.** Electrical contact resistance of the spark-plasma-sintered skutterudite legs. The electrical contact resistance $\rho_c$ of the a) n-type and b) p-type skutterudite legs highlights the excellent control of the interfaces achieved with no obvious significant drop at the interfaces (see Figure S12 in the Supporting Information for sketches of imperfect contacts), represented as vertical dotted lines, ongoing from the (Ti/Cu)_{n,p} metallic composites to the skutterudite through the Ti layer. The slopes of the three linear lines correspond to the electrical resistivity of the materials. The values inferred from these measurements are in very good agreement with those measured on each material separately.</figcaption></figure>

to the formation of indium oxide. For the p-type leg, similar analyses evidence the presence of a thin layer of ≈6 µm that originates from the reaction between Ti and the skutterudite. The additional phases formed are also Ti-Sb alloys as well as an Fe-containing ternary phase. EDS maps further show that the Ti diffusion barrier enables preventing a strong diffusion of the skutterudite elements, notably Fe and Sb. Overall, in agreement with prior studies, these results show that Ti possesses several advantages that notably include a high reaction activity during the consolidation process that ensures the formation of interfacial layers consisting in electrically and thermally conductive Ti-based alloys and hence, a good bonding strength between the skutterudites and the metallic composites.

The quality of the electrical contact resistance achieved for both legs can be appreciated by considering the evolution of the resistance $R$ measured at 300 K over the length of the legs $x$ (Figure 5). Both $R(x)$ profiles are characteristic of low electrical contact resistance $\rho_c$ (Figure S10 in the Supporting Information). The $\rho_c$ values are as low as 0.57 and 3.0 $\mu\Omega$ cm$^2$ at the top and bottom interfaces, respectively, between the thick metallic layer and the p-type skutterudite, and 8.7 and 9.9 $\mu\Omega$ cm$^2$ for the n-type skutterudite. The values measured for the n-type skutterudite compare very well with those reported in the literature and, in the case of the p-type skutterudite, are among the lowest achieved so far.[14,15,43–56] The room-temperature $\rho$ values of the skutterudites, inferred from the slope of the $R(x)$ curves, are in very good agreement with those measured on those materials separately (Figures S11–S13 in the Supporting Information). These results show that the possible detrimental influence of the increased number of interfaces on the electrical contact resistances has been successfully minimized through a careful optimization of the applied SPS cycle, yielding excellent electrical joints between the skutterudites and the metallic composites.

As a final step of the fabrication process of the TEGs, the n- and p-type legs were brazed on AlN or Al$_2$O$_3$ ceramic plates (see the Supporting Information), onto which either nickel-copper or copper paths of 0.30 mm in thickness were pre-deposited. This step is particularly critical due to the necessity to induce a strong bonding between the semiconducting thermoelectric

materials and the metallic interconnections in order to minimize the electrical contact resistances at their interface. However, the difficulty in brazing metals to semiconductors, or more generally to ceramics, is notably due to the insufficient wettability of most braze alloys on ceramics. In such a case, residual stresses often accumulate within the brazing layer once the process is completed, resulting in poor mechanical properties. For these reasons, the braze should possess a good wettability. In the present case, this issue is naturally overcome due to the metallic nature of the (Ti/Cu)_{n,p} composites that facilitates the brazing process. The excellent wettability of the In-Cu-Ag braze (InCuSil) used herein is evidenced by SEM images (Figure 6), showing an interlayer structure Cu/braze/(Ti/Cu)_{n,p} that spreads over a distance of about 20 µm. The resulting structure is typical of the eutectic Ag-Cu-In with an Ag-rich phase into which both In and Cu have dissolved (light gray areas) coexisting with a Cu-rich phase containing dissolved In and Ag (dark gray areas). Intermetallic phases as well as reaction layers at the submicron scale are also observed at the interfaces braze/Cu and braze/(Ti/Cu)_{n,p}. Near this last interface, a reaction layer of CuTi$_2$ of about 1 µm in thickness is clearly visible. The elemental X-ray maps further reveal the diffusion of In in Cu over a distance of about 10 µm, both toward the Cu interconnection and the metallic composite, and the presence of Ti in the brazing layer.

## 2.3. Thermoelectric Performances of the TEGs

In order to demonstrate the reproducibility and robustness of the present approach, both single- and multi-couple TEGs with length of the skutterudite layers varying between 0.5 and 3 mm have been fabricated and tested (Figure 7a). The shortening of the active skutterudite layers and the excellent control of the interfaces achieved concur to yield a $p_{max}$ of 2.8 W cm$^{-2}$ under a temperature difference $\Delta T$ of 450 K for a TEG consisting of one couple with 3 mm length skutterudite layers. Further lowering the length of the skutterudite layers to only 1 mm in a four-couple TEG increases $p_{max}$ to 3.3 W cm$^{-2}$ for a similar temperature difference (Figure 7b). These performances, obtained
<figure><img src="image_9.png" /><figcaption>**Figure 6.** SEM images and corresponding elemental X-ray maps of the interfaces between the metallic composites of the legs and the Cu-Ni interconnections after completion of the brazing process using InCuSil.</figcaption></figure>

using (Ti/Cu)ₙ,ₚ composites, have been further increased in a six-couple TEG with (Ti/Ag)ₙ,ₚ composites yielding 4.6 W cm⁻² that increases to 7.6 W cm⁻² under a ΔT of 630 K. The optimized geometry and technological choices made for the design of the legs concur to yield pₘₐₓ values that surpass those achieved so far for skutterudite-based TEGs with a pₘₐₓ of 2.1 W cm⁻² under a ΔT of 580 K obtained with skutterudite layers of 4 mm (Figure 7c).[¹⁴,¹⁵,⁴³⁻⁵⁶] Equivalently, the highest pₘₐₓ achieved corresponds to a 60-fold increase in the output power generated per unit volume of skutterudites, a prominent aspect to reach cost efficiency (Figure 7d). These significantly higher values stem from the strong reduction of the leg length while maintaining the internal electrical resistance of the module Rᵢₘt to low values, despite the presence of additional interfaces induced by the metallic composites. This last point further highlights the very good bonding achieved between the metallic composites and the skutterudites. The significant lowering of L down to 1 mm represents a nearly fourfold increase in pₘₐₓ compared to that expected for conventional, 1 cm long legs (Figure 7e).

Measurements performed over several heating/cooling cycles (Figure S14 in the Supporting Information) did not evidence

any degradation of the output performances, indicative of the good mechanical stability of the 1 mm length legs. Of particular relevance, this significant increase in pₘₐₓ is not realized at the expense of the conversion efficiency η, which remains to appreciable experimental values ranging between 6.5% and 6.9% (Figure 7f), comparing very well with those reported for nonsegmented skutterudite-based TEGs.[¹⁴,¹⁵,⁴³⁻⁵⁶] This result shows that the addition of thick metallic layers is a viable strategy to enhance the generated pₘₐₓ at nearly constant η. While the primary goal of this study was to increase pₘₐₓ, these results further evidence that this approach may be also beneficial for applications that necessitate high η, which may be then increased by using thermoelectric materials with higher ZT values than those of the present skutterudites.[¹⁴,¹⁵,¹⁶⁻²⁴] All these experimental values match with the theoretical predictions of 3D finite-element analyses (see Figure 7f and Supporting Information for details of the simulations), confirming the excellent control of the different steps of the fabrication process.

Additional results obtained on a TEG integrating 0.5 mm thick skutterudite layers show that further lowering the length below 1 mm is detrimental to pₘₐₓ, which contrasts with the
<figure><img src="image_10.png" /><figcaption>**Figure 7.** a) Photographs illustrating four TEGs integrating skutterudites, representative of the various TEGs fabricated and tested in this study: (upper left) a single-couple TEG with (Ti/Cu)~n,p~ metallic composite and Ti diffusion barrier with skutterudite layers of 1 mm, (upper right) a two-couple TEG with (Ti/Cu)~n,p~ metallic composite and Ti diffusion barrier with skutterudite layers of 3 mm, (bottom left) a two-couple TEG with (Ti/Cu)~n,p~ metallic composite and Ti diffusion barrier with skutterudite layers of 2 mm, (bottom right) and a six-couple TEG (Ti/Ag)~n,p~ metallic composite and Ni diffusion barrier with skutterudite layers of 1 mm. b) Maximum power density *p*<sub>max</sub> of various TEGs measured experimentally as a function of the applied temperature difference ΔT. For two of them, the measurements were collected up to ΔT = 630 K. c) Comparison of the maximum output power density *p*<sub>max</sub> expressed in W cm<sup>-2</sup> achieved in the present study with the literature data<sup>[14,15,43–56]</sup> as a function of the temperature difference ΔT applied. Red, blue, and green symbols correspond to the length of the legs varying between 1 and 3 mm, 4 and 10 mm, and above 10 mm, respectively. The results obtained in the present study are encircled in red. d) Comparison of the maximum output power density *p*<sub>max</sub> as a function of the applied temperature difference ΔT per unit volume of skutterudites, allowing for a straightforward comparison between devices integrating skutterudite legs of various lengths. Note the logarithmic scale of the y-axis. The results obtained in the present study are encircled in red. e) Prediction of the variations in the maximum output power density *p*<sub>max</sub> as a function of the length of the skutterudites *L* determined by finite-element analyses. The theoretical red dotted curve has been calculated using hot side *T*<sub>h</sub> = 483 K and cold side *T*<sub>c</sub> = 33 K temperatures, electrical contact resistances *ρ*<sub>c,p</sub> = 12.9 μΩ cm<sup>2</sup> and *ρ*<sub>c,n</sub> = 15.2 μΩ cm<sup>2</sup> of the p- and n-type legs, respectively, and an interface thermal resistance *R*<sub>th</sub> = 4 × 10<sup>-4</sup> K m<sup>-2</sup> W<sup>-1</sup> between the module and the reservoir. The experimental points measured on the various TEGs have been added. *p*<sub>max</sub> significantly increases upon shortening the length of the skutterudites. The maximum value, achieved around 1 mm, drops if the length is further reduced due to the detrimental influence of the thermal resistances of the metallic composite layers. f) Variations in the conversion efficiency as a function of the length of the skutterudites. The red dotted curve represents the predictions of finite-element analyses. The experimental points have been added.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>**Figure 8.** Evolution of the temperature on the p- and n-type skutterudite legs calculated by finite-element analyses. The temperature profiles on the a) p- and b) n-type legs induced by the temperature difference ΔT of 450 K imposed between the hot and cold reservoirs. For sake of clarity, the structures of the legs are overlaid. Due to differences in thermal conductances of the different materials (mainly the ceramic plates), the skutterudite layers are not subjected to the imposed ΔT but to a fraction of it, which amounts to around 64% and 61% for the p- and n-type legs, respectively. Except for the temperature drop due to the external contacts between the module and the hot and cold reservoirs (28% and 31% of ΔT for the p- and n-type legs, respectively), the main drops in temperature occur across the (Ti/Cu)_{n,p} metallic composites (around 8% of ΔT for both legs). Lowering these temperature drops would increase the temperature difference undergone by the skutterudite layers and hence, the maximum output power $p_{max}$ delivered by the thermoelectric generator.</figcaption></figure>

predictions of Equation (1) that does not take into account parasitic effects due to additional interfaces inevitably present in real devices. While the experimental $p_{max}$ of 4.2 W cm⁻² closely follows the theoretical predictions and remains well beyond the state-of-the-art values (see Figure 7c),[14,15,43-56] the lower $p_{max}$ achieved with a length of the legs of 0.5 mm reflects the increasing importance of thermal resistances at the interfaces, limiting $p_{max}$ below the optimum skutterudite length of 1 mm.

The modeling of the overall output performances of the TEGs by 3D finite-element analyses provides relevant insights into possible routes to further improving $p_{max}$. These calculations indicate that the active skutterudite layers are only subjected to around one half of the temperature difference applied on the module (Figure 8), due to the inevitable external contact thermal impedance between the TEG and the hot and cold reservoirs, and the thermal resistance induced by the (Ti/Cu)_{n,p} metallic composite and the ceramics. The influence of these layers on the temperature drops is further highlighted by calculations performed on TEGs with (Ti/Ag)_{n,p} metallic composites for 1 mm long and 0.5 mm long skutterudite layers (see Figure S9 in the Supporting Information). Increasing the thermal conductivity of these two components or reducing their thicknesses are two possible strategies that would increase the temperature difference applied on the skutterudites and hence, the maximum output power delivered by the TEG. However, the optimum height of the metallic composites should correspond to a compromise between the temperature drop and the maximum thermomechanical stress level undergone by the skutterudites. Finally, because the thermoelectric properties of the n- and p-type skutterudites used herein correspond to state-of-the-art values,[16-18] further increasing their power factors by manipulating their chemical compositions would also contribute to further enhancement of $p_{max}$.[16-18,60-64]

Beyond these possibilities of further enhancement and the record values obtained for the highest ΔT applied, it is important to note that the $p_{max}$ values of the present TEGs still remain higher than those reported in the literature when considering

lower ΔT. This can be appreciated in both Figures 7b and 7c where the results obtained on a TEG with skutterudite layers of 1 mm (brown square symbols) with an applied ΔT of 350 K are reported. The measured $p_{max}$ of 2.2 W cm⁻² is higher than the best results reported so far for ΔT of at least 550 K. The possibility to achieve high power densities despite the application of lower temperature difference is an appealing characteristic in terms of practicality and lifetime in real applications. In particular, applying lower ΔT values will significantly mitigate the sublimation of elements and the possible detrimental influence of interfacial phenomena over time, such as the growth of intermetallic layers due to the interdiffusion of elements or of the intermetallic compounds formed within the metallic composite layers. Meanwhile, lower ΔT values will be also beneficial to drastically decrease the thermomechanical stresses undergone by the skutterudites, further ensuring the mechanical robustness of the modules. Future detailed studies dedicated to the evolution of the interfacial phenomena and output performances over long-time periods will be important to determine the maximum operating temperature that can be safely undergone by these TEGs. Finally, achieving high power densities for relatively low ΔT thanks to the present architecture makes these modules the counterparts of high-cooling-capacity Peltier coolers using thin (<1 mm) Bi₂Te₃-based materials and hence, pave the way toward a new landscape for TE power generation.

### 3. Conclusion

We have successfully developed a robust strategy to reach high output power densities with TEGs, while strongly limiting the volume of the integrated thermoelectric materials, by means of the addition of thick metallic layers in the thermoelectric legs. As a proof-of-principle demonstration of this approach, several single- and multi-couple TEGs with skutterudites as the active thermoelectric materials have been fabricated. These TEGs are able to deliver output power densities of up to 3.4 and 7.6 W cm⁻² under temperature differences of 450 and 630 K,
respectively, which significantly surpass the values achieved so far for skutterudite-based TEGs. The advantages of this nonconventional design of the thermoelectric legs are manifold. First, the thick metallic layers act as absorbers of the thermomechanical stresses induced by the mismatch in the thermal expansion coefficients between the skutterudites and the metallic contacts, and thus, reduce the stresses undergone by the mechanically fragile skutterudites. Second, they ease the final, yet critical, brazing step of the legs onto the Cu-pre-deposited ceramic plates. Third, their presence helps to avoid the overflow of the braze on the thermoelectric elements due to their small length, which would induce an electrical short-circuit. Fourth, they enable achieving high power densities even for relatively low temperature differences, a key characteristic to mitigate various temperature-induced effects detrimental to the output performances over time. The versatility of our approach is demonstrated by the use of two distinct compositions of the metallic composites (Ti/Cu and Ti/Ag) and diffusion barrier (Ti and Ni), both leading to similar thermoelectric performances. These experimental results, in excellent agreement with the predictions of 3D finite-element analyses, show that our approach should be equally applicable to diverse highly efficient thermoelectric materials, thus enabling the development of cost-efficient, miniaturized TEGs with high $p_{max}$ that fill the gap between bulk and μ-TEGs. Further studies on the protection of these skutterudite-based high power density TEGs against oxidation as well as long-term stability tests are the necessary next steps to bring them closer to real applications.

## 4. Experimental Section

**Synthesis and Characterizations of the Skutterudites:** Polycrystalline samples of skutterudites of nominal compositions $In_xCo_4Sb_{12}$ with $0.16 \le x \le 0.20$ (n-type) and $Ce_yFe_3CoSb_{12}$ with $0.75 \le y \le 0.90$ (p-type) were prepared from high-purity elements. The n-type skutterudites were synthesized by direct reaction of the elements in evacuated-, carbon-coated-sealed silica tubes. The tubes were heated in a vertical furnace to 650 °C, dwelt at this temperature for 96 h before being quenched in room-temperature water. The chemical homogeneity of the obtained pellets was improved by annealing them at 650 °C for 96 h followed by a final quenching. For the p-type composition, Ce, Fe, and Co were first melted in an induction furnace. The ingot was crushed in an agate mortar and the resulting coarse-ground powders were reacted with Sb in a sealed, carbon-coated silica tube placed in a rocking furnace at 650 °C for 96 h. The mixture was ground by ball-milling into fine powders which were further pelleted and annealed again at 650 °C for 96 h. The annealed pellets were then ground into fine powders.

The crystal structure was verified by powder X-ray diffraction (PXRD) measurements and the lattice parameters, strongly sensitive to the In or Ce content, were determined from Rietveld refinements against the PXRD data using the FullProf software.[65] These analyses confirmed the successful insertion of In and Ce into the cages of the cubic crystal structure of skutterudites described in the *Im*₃* space group*. The inferred lattice parameters were consistent with literature data and corresponded to the expected values for nominal In and Ce contents of $0.16 \le x \le 0.20$ and $0.75 \le y \le 0.90$, respectively.

A part of the prepared powders was consolidated by spark plasma sintering (SPS, Dr Syntex 505) in order to assess their thermoelectric properties between 300 and 800 K. To this end, the powders were placed in a graphite die and consolidated at 620 °C for 5–10 min under a uniaxial pressure of 50 MPa. The geometrical density of the consolidated cylindrical pellet, determined from weight and dimensions of the

pellets, was found to be higher than 97% of the theoretical density. The consolidated pellets were subsequently cut with a diamond-wire saw into samples of appropriate shape and size for high-temperature transport properties measurements.

**Electrical and Thermal Transport Measurements and Dilatometry:** Thermal diffusivity *d* measurements were performed between 300 and 800 K using a laser flash instrument (LFA 457, Netzsch) on cylindrical-shaped samples of 10 mm in diameter and around 1 mm in thickness. Prior to these measurements, both sides of the samples were spray-coated with a thin layer of graphite. The thermal conductivity was calculated according to the relation $\kappa = dC_p\rho_V$ where $C_p$ is the isobaric specific heat and $\rho_V$ is the density. As a first approximation, $C_p$ was calculated using the Dulong-Petit law and was thus considered as temperature-independent. The temperature dependence of the density was neglected. Electrical resistivity and thermopower were measured in the same temperature range on bar-shaped samples of dimensions $2 \times 2 \times 8$ mm³ using a ZEM-3 instrument (Ulvac-Riko). The thermal expansion coefficient $\alpha_T$ of the n- and p-type skutterudites was determined from 300 up to 773 K on bar-shaped samples of dimensions $2.5 \times 2.5 \times 9$ mm³ using a dilatometer (DIL402, Netzsch). An alumina sample was used as a standard for these measurements.

**Preparation of the n- and p-Type Thermoelectric Legs:** The thermoelectric legs were prepared by considering two possible approaches. In the first approach, the diffusion barrier and the metallic composites were placed on either side of dense cylindrical pellets of n- or p-type skutterudites, and subsequently consolidated by SPS. As a second approach, the assembly of the n- and p-type legs was realized by cold-pressing the different layers in the sequence (Ti/Ag)ₙ,ₚ/Ni layer/(dense skutterudite)ₙ,ₚ/Ni layer/(Ti/Ag)ₙ,ₚ or (Ti/Cu)ₙ,ₚ/Ti layer/(powdered skutterudite)ₙ,ₚ/Ti layer/(Ti/Cu)ₙ,ₚ. The obtained structure was subsequently sintered within one single step using SPS. While both approaches led to similar results and thermoelectric performances of the final TEG, the second approach was found to improve reproducibility.

For both approaches, the Ni or Ti layers were cut from Ni or Ti foils of 25 µm in thickness into disks of 10 mm in diameter. Those disks were chemically washed in a hydrofluoric acid/nitric acid/water bath to remove any oxide layer. This chemical attack reduced the thickness of the disks by 15% to 20%. The Ti/Ag and Ti/Cu metallic composites were prepared by mechanically mixing Ag or Cu powders (100 µm according to the supplier) with Ti powders (44 µm according to the supplier). The mixed powders were cold-pressed into cylindrical pellets of 10 mm in diameter under a uniaxial pressure of 130 MPa yielding a thickness of around 1 mm with a density corresponding to about 80% of the theoretical density. In order to characterize their thermal and electrical properties, some pellets were consolidated by spark plasma sintering following the same cycle as that used for the preparation of the thermoelectric leg (see below) in order to acquire experimental data that correspond as close as possible to those of the final legs.

The thermal expansion coefficients of the (Ti/Ag)ₙ, (Ti/Ag)ₚ, (Ti/Cu)ₙ, and (Ti/Cu)ₚ compositions were measured under the same experimental conditions used for the skutterudites. Similarly, the electrical resistivity, thermopower, and thermal diffusivity were also measured.

**Module Fabrication and Characterization:** The consolidated sandwiches were polished and cut into rectangular-shaped bars of 1.5 or 4 mm in length (0.5 or 3 mm of skutterudite, respectively, and 1 mm of buffer layers) and $2 \times (2-2.5)$ mm² in surface area. All surfaces of the bars were carefully polished to ensure their flatness and parallelism and to obtain similar heights of the legs. The electrical connection between the thermoelectric legs was realized using AlN or Al₂O₃ plates of 0.63 mm in thickness onto which either nickel-copper or copper paths of 0.30 mm in thickness were deposited (C-Components and Curamik). The surface area of these plates was around 1 or 4 cm² depending on the size of the module. The thermoelectric legs were brazed on the Cu path using InCuSil or Al-Si based paste as the brazing alloy on home-made brazing setups.

The electrical contact resistance of the thermoelectric legs was measured at 300 K using a home-made set-up or a commercial set-up (Quick Home) which enabled probing the resistance over the length of
the legs with a resolution of 15 µm. Prior to measurements, gold was deposited on the faces of the polished legs.

The assembled TEGs with the (Ti/Ag)_{n,p} and Ni layers were characterized in a home-made set-up, the details of which can be found in ref. [50]. Briefly, the test station was consisted of a vacuum chamber cooled by water that housed the cold and hot reservoirs, between which the thermoelectric module was inserted. The maximum temperature of the hot reservoir was 973 K while the temperature of the cold reservoir could vary between 288 and 373 K. A uniaxial pressing force and grafoil (0.36 mm in thickness) were used to minimize the external contact thermal impedance between the module and the reservoirs. For each temperature difference applied on the module, the voltage-current characteristic curves were established by using a variable electrical load.

All the other TEGs composed of (Ti/Cu)_{n,p} and Ti layers were characterized with a commercial Mini-PEM apparatus (Ulvac-Riko). The measurements were realized under primary vacuum (<5 × 10⁻² Pa) up to 773 K. The TEG was placed onto a copper platform connected to a spring. The platform was cooled by circulating water. The hot source was provided by a resistive heater placed on the top side of the TEG. Thanks to the presence of the spring, a pressure between 0.1 and 1 MPa could be applied on the TEG to ensure a better thermal coupling. In order to further improve the coupling on the hot and cold side of the TEG, a thin layer of papyex (thickness of 0.1 mm), covered with thermal grease, was placed on the top and bottom side of the TEG. The hot-side temperature was varied between 350 and 773 K while the cold-side temperature was maintained to about 300 K. Both temperatures were monitored using two thermocouples anchored on the respective surfaces of the TEG. The Mini-PEM allowed to extract the output electrical power of the module through the voltage-current characteristic curves but also its efficiency by measuring the thermal power ($Q_{out}$, see the next paragraph), which was dissipated at the cold side.

**3D Finite-Element Analyses:** Thermoelectric effects (Seebeck, Peltier, and Thomson effects) are defined by the coupling of the heat ($\vec{q}$) and current density ($\vec{j}$) flows through a material. They can be modeled using the following coupled equations expressed, for an isotropic material, as[10,29,30]

$$ \vec{q} = \pi \vec{j} - \kappa \vec{\nabla} T \quad (3) $$

$$ \vec{j} = \sigma \vec{E} + \sigma \alpha \vec{\nabla} T \quad (4) $$

where $\vec{E}$ is the electric field that derives from the potential $V$ ($\vec{E} = -\vec{\nabla}V$), $\vec{\nabla}T$ is the temperature gradient, $\pi$ is the Peltier coefficient, $\kappa$ is the total thermal conductivity, $\sigma$ is the electrical conductivity, and $\alpha$ is the thermopower (or Seebeck coefficient).

In a stationary state, the local energy balance and charge conservation can be expressed by the two equations[10,29,30]

$$ \vec{\nabla} \cdot \vec{q} = \vec{E} \cdot \vec{j} \quad (5) $$

$$ \vec{\nabla} \cdot \vec{j} = 0 \quad (6) $$

This set of partial differential equations, combined with Equations (3) and (4), can be solved numerically by finite-element analyses to determine the temperature and electrical potential fields in the material. Herein, all the electrical and thermal characteristics of the modules were calculated using 3D finite-element analyses implemented in the software COMSOL Multiphysics. The thermoelectric effects in steady state were expressed by the above-mentioned set of differential equations with temperature and electrical potential as unknown parameters. The 3D distributions of these parameters, together with the electrical current density and heat flux, were solved using the boundary conditions of the experimental set-up (temperatures and thermal interface contact resistances) used to characterize the modules. These simulations were conducted on model thermoelectric modules of dimensions corresponding to the fabricated modules. The measured temperature dependences of the transport properties of the skutterudites and the

Ti/Ag or Ti/Cu composites were fitted using third-order polynomials, which were used as input parameters in these calculations. The output power $P$ reached its maximum value $P_{max}$ when the impedance matching condition was achieved, i.e., when the electrical load matched the internal resistance $R_{int}$ of the module. The conversion efficiency $\eta$ of the TEG was calculated using the following relation

$$ \eta(l) = \frac{P(l)}{P(l) + Q_{out}(l)} \quad (7) $$

where the current $I$ and output heat flow $Q_{out}$ were calculated using $\vec{j}$ and $\vec{q}$, respectively.

The derivation of the stress-strain state in the modules was performed using the software COMSOL Multiphysics by considering the boundary conditions (thermal, electrical, and mechanical) imposed by the Mini-Pem. For the mechanical aspects, a spring force at the bottom surface (initial pressure equaled to 0.5 MPa), a free displacement of the AlN cold plate, and a null displacement along the normal of the AlN hot side were applied. This load state was considered to be close to actual situations. Table S1 in the Supporting Information gathers the mechanical and thermal properties of the materials constituting the module used in the modeling. The Young modulus and the tensile strength (in compression) of skutterudites were extracted from nanoindentation measurements. The Poisson ratio of the skutterudites and metallic composites were experimentally determined using sound velocity measurements at 300 K. The other parameters were taken from references mentioned in the Supporting Information. The Young's moduli and the yield strength of the metallic composites were averaged according to the Voigt law as a first approximation.[66] A brittle linear elastic behavior for the n- and p-type skutterudites and ceramic (AlN) was assumed. An elastoplastic behavior was considered for the metallic composites and copper, for which the hardening was supposed to be linear. Moreover, the tensile strength of the skutterudites was considered to be the same as the tensile strength in compression. Moreover, except for the coefficient of thermal expansion (CTE) of skutterudites and composites, it was further assumed, as a first approximation, that the other mechanical parameters were temperature independent. From all these data and assumptions, the equivalent von-Mises tensile stresses were calculated in the modules made of a single couple of n- and p-type skutterudites.

## Supporting Information

Supporting Information is available from the Wiley Online Library or from the author.

## Acknowledgements

A.D. and A.J. acknowledge the financial support of the Agence Nationale de la Recherche (ANR) and the Deutsche Forschungsgemeinschaft (DFG) in the frame of the project WATTS ("Wafers-based thin thermoelectric systems development," ANR-11-PICF-0007). I.K. acknowledges the financial support of the ANR in the frame of the WATTS project. E.A., A.D., and B.L. acknowledge the financial support of the Agence Nationale de la Recherche (ANR) in the frame of the project NANOSKUT ("Nanostructured skutterudites for thermoelectric generation," ANR-12-PRGE-0008). M.B. acknowledges the financial support of the ANR in the frame of the NANOSKUT project. The authors acknowledge the financial support of the European project ENSO ("Energy for Smart Objects"; https://enso-ecsel.eu). This project has received funding within the Electronic Components and Systems for European Leadership Joint Undertaking (ECSEL JU) program under grant agreement n° 692482. This JU receives support from the European Union's H2020 research and innovation program and France, Netherlands, Denmark, Belgium, Germany, Czech Republic and Spain. S.O. thanks Benoît Denand for his help in the dilatometry measurements.
## Conflict of Interest

The authors declare no conflict of interest.

## Author Contributions

B.L., A.J., A.D., J.K., T.C., and E.A. supervised the project. M.B. prepared the n- and p-type skutterudite powders for (Ti/Cu) TEGs. P.M. and I.K. prepared the n- and p-type skutterudite powders, developed and synthesized the buffer materials, and optimized the densification process of the n- and p-type legs for the (Ti/Ag) TEG with active skutterudite layers of 0.5 mm. C.C. and B.L. performed the high-temperature transport property measurements on the various legs of the (Ti/Cu) and (Ti/Ag) modules. A.D. and S.O. carried out the SEM analyses of the different interfaces. S.O. and P.M. carried out the densification process of the n- and p-type legs for the (Ti/Cu) TEGs, characterized the legs, performed the brazing step, and characterized the performances of the modules. S.O. and F.K. performed the 3D finite-element analyses of the different modules. U.K. and E.G. carried out the densification process of the n- and p-type legs for the (Ti/Ag) TEG with active skutterudite layers of 1 mm. E.G. performed the measurements of the electrical contact resistances and assembled the (Ti/Ag) modules. E.G. and J.K. characterized the performances of the (Ti/Ag) modules. C.C. and B.L. wrote the manuscript with inputs from all co-authors (except U.K.).

## Data Availability Statement

Research data are not shared.

## Keywords

power generation, skutterudite, thermoelectric, thermoelectric modules

Received: February 19, 2021

Published online: April 1, 2021

[1] L. E. Bell, *Science* **2008**, *321*, 1457.

[2] G. J. Snyder, E. S. Toberer, *Nat. Mater.* **2008**, *7*, 105.

[3] D. Kraemer, Q. Jie, K. McEnaney, F. Cao, W. Liu, L. A. Weinstein, J. Loomis, Z. Ren, G. Chen, *Nat. Energy* **2016**, *1*, 16153.

[4] J. P. Heremans, M. S. Dresselhaus, L. E. Bell, D. T. Morelli, *Nat. Nanotechnol.* **2013**, *8*, 471.

[5] Y. Pei, X. Shi, A. LaLonde, H. Wang, L. Chen, G. J. Snyder, *Nature* **2011**, *473*, 66.

[6] X. Lu, D. T. Morelli, Y. Xia, F. Zhou, V. Ozolins, H. Chi, X. Zhou, C. Uher, *Adv. Energy Mater.* **2012**, *3*, 342.

[7] W.-D. Liu, D.-Z. Wang, Q. Liu, W. Zhou, Z. Shao, Z.-G. Chen, *Adv. Energy Mater.* **2020**, *10*, 2000367.

[8] J. Yu, Y. Xing, C. Hu, Z. Huang, Q. Qiu, C. Wang, K. Xia, Z. Wang, S. Bai, X. Zhao, L. Chen, T. Zhu, *Adv. Energy Mater.* **2020**, *10*, 2000888.

[9] T. J. Slade, T. P. Bailey, J. A. Grovgoui, X. Hua, X. Zhang, J. J. Kuo, I. Hadar, G. J. Snyder, C. Wolverton, V. P. Dravid, C. Uher, M. G. Kanatzidis, *Adv. Energy Mater.* **2019**, *9*, 1901377.

[10] D. M. Rowe, in *Thermoelectrics and its Energy Harvesting: Modules, Systems, and Applications in Thermoelectrics* (Ed: D. M. Rowe), CRC Press, Boca Raton, FL **2012**.

[11] N. Jaziri, A. Boughamoura, J. Müller, B. Mezghani, F. Tounsi, M. Ismail, *Energy Rep.* **2019**, *6*, 264.

[12] R. He, G. Schierning, K. Nielsch, *Adv. Mater. Technol.* **2018**, *3*, 1700256.

[13] F. Freer, A. V. Powell, *J. Mater. Chem. C* **2020**, *8*, 441.

[14] S. H. Park, Y. Jin, J. Cha, K. Hong, Y. Kim, H. Yoon, C.-Y. Yoo, I. Chung, *ACS Appl. Energy Mater.* **2018**, *1*, 1603.

[15] J. Chu, J. Huang, R. Liu, J. Liao, X. Xia, Q. Zhang, C. Wang, M. Gu, S. Bai, X. Shi, L. Chen, *Nat. Commun.* **2020**, *11*, 2723.

[16] B. C. Sales, D. Mandrus, R. K. Williams, *Science* **1996**, *272*, 1325.

[17] G. Rogl, P. Rogl, *Curr. Opin. Green Sustain. Chem.* **2017**, *4*, 50.

[18] C. Uher, in *Recent Trends in Thermoelectric Materials Research, Vol. 69* (Ed: T. M. Tritt), Academic Press, San Diego, CA **2001**, pp. 139–253.

[19] C. Fu, T. Zhu, Y. Pei, H. Xie, H. Wang, G. J. Snyder, Y. Liu, Y. Liu, X. Zhao, *Adv. Energy Mater.* **2014**, *4*, 1400600.

[20] S. Anand, K. Xia, T. Zhu, C. Wolverton, G. J. Snyder, *Adv. Energy Mater.* **2018**, *8*, 1801409.

[21] C. Fu, S. Bai, Y. Liu, Y. Tang, L. Chen, X. Zhao, T. Zhu, *Nat. Commun.* **2015**, *6*, 8144.

[22] S. R. Brown, S. M. Kauzlarich, F. Gascoin, G. J. Snyder, *Chem. Mater.* **2006**, *18*, 1873.

[23] J. Zhang, L. Song, K. A. Borup, M. R. Vogel Jorgensen, B. B. Iversen, *Adv. Energy Mater.* **2018**, *8*, 1702776.

[24] S. Ohno, U. Aydemir, M. Amsler, J.-H. Pöhls, S. Chanakian, A. Zevalkink, M. A. White, S. K. Bux, C. Wolverton, G. J. Snyder, *Adv. Funct. Mater.* **2017**, *27*, 1606361.

[25] A. Muto, J. Yiang, B. Poudel, Z. Ren, G. Chen, *Adv. Energy Mater.* **2013**, *3*, 245.

[26] M. Hong, K. Zheng, W. Lyv, M. Li, X. Qu, Q. Sun, S. Xu, J. Zou, Z.-G. Chen, *Energy Environ. Sci.* **2020**, *13*, 1856.

[27] S. LeBlanc, S. K. Yee, M. L. Scullin, C. Dames, *Renewable Sustainable Energy Rev.* **2014**, *32*, 313.

[28] G. Min, D. M. Rowe, *J. Power Sources* **1992**, *38*, 253.

[29] *Advanced Thermoelectrics: Materials, Contacts, Devices, and Systems* (Eds: Z. Ren, Y. Lan, Q. Zhang), CRC Press, Boca Raton, FL **2017**.

[30] R. R. Heikes, R. W. Ure, *Thermoelectricity: Science and Engineering*, Interscience Publishers, New York; London **1961**.

[31] Q. H. Zhang, X. Y. Huang, S. Q. Bai, X. Shi, C. Uher, L. D. Chen, *Adv. Eng. Mater.* **2016**, *18*, 194.

[32] D. Champier, *Energy Convers. Manage.* **2017**, *140*, 167.

[33] D. K. Aswal, R. Basu, A. Singh, *Energy Convers. Manage.* **2016**, *114*, 50.

[34] S. El Oualid, F. Kosior, A. Dauscher, C. Candolfi, G. Span, E. Mehmedovic, J. Paris, B. Lenoir, *Energy Environ. Sci.* **2020**, *13*, 3579.

[35] Q. Xu, S. Qu, C. Ming, P. Qiu, Q. Yao, C. Zhu, T.-R. Wei, J. He, X. Shi, L. Chen, *Energy Environ. Sci.* **2020**, *13*, 511.

[36] Y. Qi, M. C. McAlpine, *Energy Environ. Sci.* **2010**, *3*, 1275.

[37] M. He, J. Ge, Z. Lin, X. Feng, X. Wang, H. Lu, Y. Yang, F. Qiu, *Energy Environ. Sci.* **2012**, *5*, 8351.

[38] C. Wan, X. Gu, F. Dang, T. Itoh, Y. Wang, H. Sasaki, M. Kondo, K. Koga, K. Yabuki, G. J. Snyder, R. Yang, K. Koumoto, *Nat. Mater.* **2015**, *14*, 622.

[39] Y. Lu, Y. Qiu, K. Cai, Y. Ding, M. Wang, C. Jiang, Q. Yao, C. Huang, L. Chen, J. He, *Energy Environ. Sci.* **2020**, *13*, 1240.

[40] G. Hu, H. Edwards, M. Lee, *Nat. Electron.* **2019**, *2*, 300.

[41] R. Dhawan, P. Madusanka, G. Hu, J. Debord, T. Tran, K. Maggio, H. Edwards, M. Lee, *Nat. Commun.* **2020**, *11*, 4362.

[42] W. Zhou, Q. Fan, Q. Zhang, L. Cai, K. Li, X. Gu, F. Yang, N. Zhang, Y. Wang, H. Liu, W. Zhou, S. Xie, *Nat. Commun.* **2017**, *8*, 14886.

[43] M. S. El-Genk, H. H. Saber, T. Caillat, J. Sakamoto, *Energy Convers. Manage.* **2006**, *47*, 174.

[44] H. H. Saber, M. S. El-Genk, T. Caillat, *Energy Convers. Manage.* **2007**, *48*, 555.

[45] D. Zhao, C. Tian, S. Tang, Y. Liu, L. Jiang, L. Chen, *Mater. Sci. Semicond. Process.* **2010**, *13*, 221.

[46] S. M. Choi, K.-H. Kim, S.-M. Jeong, H.-S. Choi, Y. S. Lim, W.-S. Seo, I.-H. Kim, *J. Electron. Mater.* **2012**, *41*, 1004.
[47] J. Q. Guo, H. Y. Geng, T. Ochi, S. Suzuki, M. Kikuchi, Y. Yamaguchi, S. Ito, *J. Electron. Mater.* **2012**, *41*, 1036.

[48] J. Garcia-Canadas, A. V. Powell, A. Kaltzoglou, P. Vaqueiro, G. Min, *J. Electron. Mater.* **2013**, *42*, 1369.

[49] T. Ochi, G. Nie, S. Suzuki, M. Kikuchi, S. Ito, J. Q. Guo, *J. Electron. Mater.* **2014**, *43*, 2344.

[50] J. R. Salvador, J. Cho, Z. Ye, A. Thompson, J. Sharp, J. König, R. Maloney, T. Thompson, J. Sakamoto, H. Wang, A. A. Wereszczak, *Phys. Chem. Chem. Phys.* **2014**, *16*, 12510.

[51] E. Alleno, N. Lamquembe, R. Cardoso-Gil, M. Ikeda, F. Widder, O. Rouleau, C. Godart, Y. Grin, S. Paschen, *Phys. Status Solidi A* **2014**, *211*, 1293.

[52] G. Nie, S. Suzuki, T. Tomida, A. Sumiyoshi, T. Ochi, K. Mukaiyama, M. Kikuchi, J. Q. Guo, A. Yamamoto, H. Obara, *J. Electron. Mater.* **2017**, *46*, 2640.

[53] Q. Zhang, Z. Zhou, M. Dylla, M. T. Agne, Y. Pei, L. Wang, Y. Tang, J. Liao, J. Li, S. Bai, W. Jiang, L. Chen, G. J. Snyder, *Nano Energy* **2017**, *41*, 501.

[54] P. Zong, R. Hanus, M. Dylla, Y. Tang, J. Liao, Q. Zhang, G. J. Snyder, L. Chen, *Energy Environ. Sci.* **2017**, *10*, 183.

[55] J. Prado-Gonjal, M. Phillips, P. Vaqueiro, G. Min, A. V. Powell, *ACS Appl. Energy Mater.* **2018**, *1*, 6609.

[56] S. Katsuyama, W. Yamakawa, Y. Matsumara, R. Funahashi, *J. Electron. Mater.* **2019**, *48*, 5257.

[57] G. Rogl, L. Zhang, P. Rogl, A. Grytsiv, M. Falmbigl, D. Rajs, M. Kriegisch, H. Müller, E. Bauer, J. Koppensteiner, W. Schranz, M. Zehetbauer, Z. Henkie, M. B. Maple, *J. Appl. Phys.* **2010**, *107*, 043507.

[58] A. Reuss, Z. Angew. Math. Mech. **1929**, *9*, 49.

[59] P. Canale, C. Servant, Z. Metallkd. **2002**, *93*, 273.

[60] D. Qin, H. Wu, S. Cai, J. Zhu, B. Cui, L. Yin, H. Qin, W. Shi, Y. Zhang, Q. Zhang, W. Liu, J. Cao, S. J. Pennycook, W. Cai, J. Sui, *Adv. Energy Mater.* **2019**, *9*, 1902435.

[61] Y. Tang, Z. M. Gibbs, L. A. Agapito, G. Li, H.-S. Kim, M. B. Nardelli, S. Curtarolo, G. J. Snyder, *Nat. Mater.* **2015**, *14*, 1223.

[62] M. Puyet, B. Lenoir, A. Dauscher, C. Candolfi, J. Hejtmanek, *Appl. Phys. Lett.* **2012**, *101*, 222105.

[63] J. Leszczynski, V. Da Ros, B. Lenoir, A. Dauscher, C. Candolfi, P. Masschelein, J. Hejtmanek, K. Kutorasinski, J. Tobola, R. I. Smith, C. Stiewe, E. Müller, *J. Phys. D: Appl. Phys.* **2013**, *46*, 495106.

[64] M. Benyahia, V. Ohorodniichuk, E. Leroy, A. Dauscher, B. Lenoir, E. Alleno, *J. Alloys Compd.* **2018**, *735*, 1096.

[65] J. Rodriguez-Carvajal, *Phys. B* **1993**, *192*, 55.

[66] W. Voigt, *Ann. Phys.* **1889**, *274*, 573.