Hee Seok
Kim
^{a},
Weishu
Liu
^{ab} and
Zhifeng
Ren
*^{a}
^{a}Department of Physics and The Texas Center for Superconductivity, University of Houston, Houston, Texas 77204, USA. E-mail: zren@uh.edu
^{b}Department of Materials Science and Engineering, Southern University of Science and Technology, ShenZhen, GuangDong 518005, China

Received
26th August 2016
, Accepted 17th November 2016

First published on 17th November 2016

While considerable efforts have been made to develop and improve thermoelectric materials, research on thermoelectric modules is at a relatively early stage because of the gap between material and device technologies. In this review, we discuss the cumulative temperature dependence model to reliably predict the thermoelectric performance of module devices and individual materials for an accurate evaluation of the p–n configuration compared to the conventional model used since the 1950s. In this model, the engineering figure of merit and engineering power factor are direct indicators, and they exhibit linear correlations to efficiency and output power density, respectively. To reconcile the strategy for high material performance and the thermomechanical reliability issue in devices, a new methodology is introduced by defining the engineering thermal conductivity. Beyond thermoelectric materials, the device point of view needs to be actively addressed before thermoelectric generators can be envisioned as power sources.

## Broader contextThermoelectric devices generate electricity directly from thermal energy, and they are composed of dissimilar layers, such as electrodes, insulators, and bonding interfaces, and thermoelectric materials. Because of the differences in their physical characteristics, fabricating thermomechanically reliable devices is challenging even though various thermoelectric materials have been developed over the last decades with enhanced figures-of-merit (ZT). To use thermoelectric generators as primary energy sources, the device technology needs to be balanced with the material fabrication technology. This review summarizes and discusses a reliable prediction model for thermoelectric efficiency and output power, direct thermoelectric indicators representing practical performance, and the methodology of how to improve a material's ZT and device reliability. This will provide important guidance to estimate the realistic performance of materials and devices, which will help in the development of thermomechanically robust and thermoelectrically high-performing power generators. |

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On the other hand, an analytical model for efficiency and output power prediction is simple and consistent. It also has less uncertainty depending on the various resources. The conventional analytical model was formulated in the 1950s based on the assumption that all physical properties are constant according to temperature, i.e., temperature independent, and the model has been commonly used. However, because of this assumption, the conventional model often overestimates or underestimates a material's efficiency, which may lead to the wrong design for thermoelectric module devices. Snyder et al.^{25} discussed the concept of a compatibility factor for a spatial temperature gradient when thermoelectric properties vary with temperature by matching the relationship between the heat flow and electrical current. Recently, to avoid a misunderstanding of the efficiency and output power, cumulative temperature dependence (CTD) models for thermoelectric materials^{26} and devices^{27} were developed and were based on an overall temperature dependence of the material properties at given temperature boundary conditions. The CTD models give rise to a reliable prediction of thermoelectric efficiency and output power compared with the conventional model. Additionally, the Thomson effect was ignored in the conventional model. Studies to account for the Thomson effect were reported under the condition of a constant Thomson coefficient,^{28–30} which is not practical in some cases, but the CTD model analytically takes into account the Thomson effect without any restrictions on the Thomson coefficient behavior. This provides practical fractions of Joule and Thomson heat returning to the hot end. It also shows direct indicators for thermoelectric efficiency with the engineering figure of merit (ZT)_{eng} and for output power with the engineering power factor (PF)_{eng}.

For the last decade, a reduction in thermal conductivity through nanostructure technology has been an effective route to improve ZT. This approach has shown dramatic ZT enhancement mainly due to reducing the lattice thermal conductivity κ_{lat} by intensive phonon scattering.^{31–36} Recently, high peak ZT values were reported in several materials, which were caused by a very low κ_{lat}, such as the peak ZT of 1.86 in Bi_{0.5}Sb_{1.5}Te_{3} with κ_{lat} = 0.3 W m^{−1} K^{−1},^{37} the peak ZT of 2.2 in PbTe:SrTe with κ_{lat} = 0.5 W m^{−1} K^{−1},^{38} the peak ZT of 2.3 in Cu_{2}Se with κ = 0.15 W m^{−1} K^{−1},^{39} and the peak ZT of 2.6 in SnSe with κ_{lat} = 0.23 W m^{−1} K^{−1}.^{40} Such low thermal conductivities lead to higher ZTs, but new challenges arise in designing thermoelectric generators at the device level. The reduced thermal conductivity allows for a higher thermal resistance in the thermoelectric material across the hot and cold side. This generates a larger temperature difference with a fixed length of the thermoelectric components or allows for a shorter length of the components corresponding to the given thermal boundary temperatures. A shorter length may lead to larger power generation when a cross-sectional area is fixed because of the reduced electrical resistance, and less consumption of materials leads to a larger specific power density, such as Watt per kg, Watt per volume, or Watt per dollar (cost). This is a superior design direction for thermoelectric devices. However, the shortened length because of the lowered thermal conductivity may cause a larger shear stress at the joining interfaces, a smaller thermal stress resistance, and a larger relative electrical or thermal contact resistance. Such thermomechanical vulnerability can cause position realignment of the thermoelectric components,^{41} cracks on the thermoelectric legs,^{42} degradation of the bonding strength between the thermoelectric component and metal electrodes,^{43}etc., which eventually result in a deterioration of the output power performance. To avoid such vulnerability, various approaches such as a device design with tapered thermoelectric legs,^{44} various leg geometries,^{45} a linear structure with a dovetail-shaped electrode,^{12} an angled linear structure,^{46} and optimized component dimensions^{47,48} were investigated. However, those approaches focused on an alternative design for thermoelectric devices without considering a thermoelectric material's tuning strategy. Kim et al. demonstrated a methodology for how to balance between the thermal conductivity reduction in thermoelectric materials and the thermomechanical reliability of fully assembled thermoelectric devices.^{49}

In this review, we summarize the analytical model for reliable prediction of thermoelectric efficiency and output power from the material to the device level based on the CTD model. In addition, the correlation of the efficiency vs. the engineering figure of merit (ZT)_{eng} and the output power density vs. the engineering power factor (PF)_{eng} are discussed. (ZT)_{eng} and (PF)_{eng} are direct thermoelectric indicators for efficiency and output power generation, respectively. We then review the methodology of how to reconcile the ZT improvement strategy by reducing the thermal conductivity and thermomechanical device reliability to create a thermoelectrically high-performance and thermomechanically stable system.

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Fig. 1
ZT vs. T for Ni-doped MgAgSb^{61} (a) and In_{4}Se_{3−x}^{57} (d), in which open symbols are measured data, and the black lines are fitted curves. The solid blue and dashed red lines are average ZTs by Z_{int}T_{avg} and Z_{Tavg}T_{avg}, respectively. Efficiencies at T_{c} = 25 °C from a numerical simulation (solid diamonds) and CPM using integration (solid blue line) and average temperature (dashed red line) for Z_{avg} of Ni-doped MgAgSb (b) and In_{4}Se_{3−x} (e). Z vs. T for Ni-doped MgAgSb (c) and In_{4}Se_{3−x} (f). Reproduced from ref. 26 with permission from the National Academy of Sciences. |

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Fig. 2a shows the efficiency prediction for K doped PbTe_{1−y}Se_{y}^{58} and SnSe^{40} with the temperature boundary condition that T_{h} increases while T_{c} is kept at 50 °C. Fig. 2b shows how relatively accurate the efficiency calculations by the CPM and CTD models are compared with the efficiency from the numerical simulation (solid line), η_{n}, which is the most accurate. The calculation by CPM (eqn (2)) overestimates the efficiency for K doped PbTe_{1−y}Se_{y} and SnSe compared with the numerical prediction, and the efficiency from the CTD model (eqn (3)) is close to the value from the numerical simulation. Fig. 2c shows the efficiencies for half-Heusler (HH: Hf_{x}(ZrTi)_{1−x}CoSb_{0.8}Sn_{0.2})^{18} and skutterudite (SKU: Ce_{0.45}Nd_{0.45}Fe_{3.5}Co_{0.5}Sb_{12}),^{54} and Fig. 2d shows their accuracy with respect to η_{n}. The calculated efficiencies for both materials from the CPM and CTD models are in good agreement with those from the numerical simulation. The small variations in HH and SKU compared to K doped PbTe_{1−y}Se_{y} and SnSe are because of the linear-like behavior of S, ρ, and κ in HH and SKU based on temperature.

Fig. 2 (a) Predicted efficiencies as a function of ΔT and (b) relative accuracy with respect to the numerical results of K-PbTeSe (blue circles) and SnSe (red squares). (c) Predicted efficiency and (d) relative accuracy of HH (blue circles) and SKU (red squares). Reproduced from ref. 26 with permission from the National Academy of Sciences. |

The accuracy is partially associated with the temperature dependent τ(T) representing the intensity of the Thomson heat (Fig. 3a). In order to examine the cumulative effect of the Thomson heat for a large temperature difference, the overall Thomson coefficient at a given thermal boundary condition is defined as , which is shown in Fig. 3b, and the positive values of τ_{ΔT} lead to an increased efficiency compared to that without the Thomson effect. Therefore, it is closer to the efficiency predicted by the numerical analysis. The reasons for the relative difference between the CTD model and numerical model are the linearized expression of dT/dx, and the different types of temperature dependence, i.e., a cumulative (or overall) effect in the CTD model and an instantaneous effect in the numerical model.

Fig. 3 (a) Calculated Thomson coefficient τ at each temperature and (b) the overall Thomson coefficient τ_{ΔT} as a function of ΔT at T_{c} = 50 °C. ΔT-Dependent weight factor of W_{J} for the Joule heat (c), and W_{T} for the Thomson heat (d), where T_{c} is fixed at 50 °C. Reproduced from ref. 26 with permission from the National Academy of Sciences. |

Fig. 3c and d shows ΔT-dependent weight factors for the Joule and Thomson heats, respectively, based on the CTD model. In Fig. 3c, the W_{J} above 1/2 indicates that a higher fraction of the Joule heating returns to the hot side than that calculated by CPM because of the increased trend of ρ(T). In Fig. 3d, the W_{T} below 1/2 means that the Thomson heat on the heat flux at the hot end is smaller than the simply lumped fraction from the CPM since the dS/dT decreases.^{18,54,58} The diverged W_{T} (inset in Fig. 3d) means τ_{ΔT} becomes zero (Fig. 3b), indicating that no overall effect of the Thomson heat at the temperature difference is considered even though the Thomson heat exists at each temperature.

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The units of (PF)_{eng} from the CTD model are different from that of the conventional PF. By this definition, PF gives the power density output for a given T, where the Seebeck coefficient S in PF is measured at a certain temperature T with a very small ΔT (a few degrees) compared to T (hundreds T). So, PF represents the potential for output power at a temperature, not ΔT, i.e., there is no ΔT information (T_{h} and T_{c}) in the conventional PF. The concept of (PF)_{eng} is the total amount of potential for output power at a given ΔT (T_{h} and T_{c}), which is imposed by the integral. That is why the units of (PF)_{eng} (W m^{−1} K^{−1}) are PF (W m^{−1} K^{−2}) times the temperature (K) that is the units of accumulation under ΔT condition.

Fig. 5 (a) ZT dependence on temperature and (b) (ZT)_{eng} dependence on the ΔT of selected n-type and p-type materials. For (ZT)_{eng}, a cold side temperature T_{c} is assumed to be 50 °C for all materials. p:BiTe, unpublished data; p:MgAgSb, ref. 69; p:BiCuSeO, ref. 70; p:half-Heusler, ref. 71; n:InSe, ref. 57; n:AlZnO, ref. 72; n:LAST, ref. 73; n:SiGe, ref. 74. |

p-Type | n-Type | ||||
---|---|---|---|---|---|

Material |
T
_{h,max} (°C) |
Ref. | Material |
T
_{h,max} (°C) |
Ref. |

a Unpublished data. | |||||

Bi_{0.4}Sb_{1.6}Te_{3} |
250 |
^{
} |
Bi_{2}Te_{2.7}Se_{0.3}S_{0.015} |
250 |
^{
} |

β-Zn_{4}Sb_{3} |
250 | 75 | Ba_{8}Ga_{14}Cu_{2}Sn_{30} |
275 | 76 |

Ba_{8}Ga_{15.75}Cu_{0.25}Sn_{30} |
275 | 76 | AgPb_{m}SbTe_{m+2} |
400 | 73 |

MgAgSb | 295 | 69 | In_{4}Se_{3−x} |
400 | 57 |

Pb_{0.98}Te_{0.75}Se_{0.25}K_{0.02} |
450 | 58 | Mg_{2}Sn_{0.75}Ge_{0.25} |
450 | 77 |

SnSe | 450 | 40 | Pb_{0.995}SeCr_{0.005} |
450 | 78 |

MnSi_{1.78} |
500 | 79 | Ba_{0.08}La_{0.05}Yb_{0.04}Co_{4}Sb_{12} |
550 | 80 |

Ce_{0.45}Nd_{0.45}Fe_{3.5}Co_{0.5}Sb_{12} |
550 | 54 | Mg_{2}Si-0.5 at% Sb/1.0 at% Zn |
550 | 81 |

Hf_{0.19}Zr_{0.76}Ti_{0.048}CoSb_{0.8}Sn_{0.2} |
650 | 18 | Hf_{0.25}Zr_{0.75}NiSn_{0.99}Sb_{0.01} |
650 | 82 |

Bi_{0.875}Ba_{0.125}CuSeO |
650 | 70 | ZnO-0.25 at% Al | 700 | 72 |

Si_{80}Ge_{20}B_{5} |
850 | 32 | Si_{80}Ge_{20}P_{2} |
850 | 74 |

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[η]_{CTD}* for a p-PbTe/n-PbSe paired module is shown in Fig. 8a, and the prediction by CPM underestimates the efficiency over the whole ΔT range. The CTD model efficiency prediction is accurate over the whole temperature range compared to the simulation result. For the p-SnSe/n-PbSe combination shown in Fig. 8b, the CTD model predicts efficiency by a 3% relative difference at ΔT = 400 °C from the numerical analysis while the prediction by the CPM is a 17% overestimation. In some cases, however, the CPM analysis is more accurate than the CTD model,^{27} but this is because the averaged material properties are accidentally close to each equivalent property. Thus, the analysis by the CPM is not reliable.

Fig. 8 The maximum efficiency as a function of ΔT for a p–n module of (a) p-PbTe/n-PbSe and (b) p-SnSe/n-PbSe. The maximum output power density as a function of ΔT for a p–n module of (c) p-PbTe/n-PbSe and (d) p-SnSe/n-PbSe. Reproduced from ref. 27 with permission from the American Institute of Physics. |

The [P_{d}]_{CPM}* prediction for p-PbTe/n-PbSe (Fig. 8c) and p-SnSe/n-PbSe (Fig. 8d) shows a large relative difference at ΔT = 400 °C compared to the simulation results. Because the prediction by the CPM is only reliable when thermoelectric properties have a weak temperature dependence, such as SKUs^{54,80} and HHs,^{18,82} the CTD model leads to a more accurate prediction through the whole ΔT range (Fig. 8c and d) compared to the numerical simulation. The differences between the CTD model and numerical analysis could result from the type of p–n pairs, type of temperature dependence of each material, integration, simulation conditions and the assumption of a linear temperature profile. The differences are also caused by the fact that the CTD model accounts for the path-independence of material properties according to the temperature while the numerical analysis incorporates the path-dependence along with the temperature.

Fig. 9 Comparison of [ZT]_{eng}* (larger symbols), (ZT)_{eng} of individual p- (solid lines) and n-type (dashed lines) materials, and their averaged (ZT)_{eng} (smaller symbols) in (a) p-SnSe/n-PbSe and (b) p-PbTe/n-PbSe. (c) The predicted efficiencies of the module devices by the CTD model as a function of (ZT)_{eng}. T_{c} is fixed at 50 °C. Reference materials are Bi_{2}Te_{3} of p-type,^{37} HH of p-type^{18} and n-type,^{82} p-type PbTe,^{58} n-type PbSe,^{78} p-type SnSe,^{40} SKU of p-type^{54} and n-type,^{80} SiGe of p-type^{32} and n-type,^{74} and n-type Bi_{2}Te_{3}. Reproduced from ref. 27 with permission from the American Institute of Physics. |

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L
_{min} is determined based on the half width (w) of a thermoelectric leg, the maximum thermal shear stress (τ_{max}), and critical criteria (τ_{Y}). The maximum shear stress τ_{max} is expressed based on the 1-pair thermoelectric assembly model (Fig. 11) by Suhir et al.^{83–85} as:

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5.3.1.
L
_{min} evaluation.
The ratio of τ_{Y} to τ_{∞} and the shear stress reduction factor χ_{r} of a Bi_{2}Te_{3} based module is shown in Fig. 13a as a function of L/L_{tot}, and the thickness of the ceramic plates, electrodes, and solder layers are 0.7, 0.5, and 0.07 mm, respectively, and f_{ce} = 2.86 (35% filling factor). The mechanical properties of each component are listed in Table 2. The τ_{Y} can be the yield strength of a solder layer ranging from 22.8 to 27.8 MPa at room temperature for various solder alloys applicable to the Bi_{2}Te_{3} based module assembly,^{91} the fracture strength of Bi_{2}Te_{3}, such as 34 MPa ultimate tensile strength at room temperature,^{92} or the bonding strength of the Ni metallization – Bi_{2}Te_{3} leg configuration, which was measured up to 30 MPa at room temperature.^{93} For a conservative design of the module, the yield strength (lower value of τ_{Y}) of the solder alloys leads to L_{min} of the thermoelectric leg with a cross sectional area of 1.6 × 1.6 mm^{2} (w = 0.8 mm),^{68} and L_{min} should be longer than 0.77 mm under the maximum ΔT = 150 °C at T_{c} = 50 °C when τ_{Y} = 25.7 MPa. The critical w–L_{min} relationship for the thermomechanical reliability is shown in Fig. 13b, where it is reliable when the selected w and L are placed in the upper zone of the border. If not, the interfacial structure in the module is vulnerable at the operating condition.

Fig. 13 (a) The τ_{Y}/τ_{∞} and reduction factor χ_{r} of the shear stress as a function of non-dimensional length, L/L_{tot}. The various yield strengths of solders (23–28 MPa) are shown as error bars. (b) The w vs. L/L_{tot} relationship to avoid the yield criteria of the solder. (c) The hot side temperature with L according to . The horizontal line indicates T_{h,max}. The solid and dashed curves indicate the numerical and analytical analyses, respectively, where _{1} = 1.13 and _{2} = 2.13 W m^{−1} K^{−1}. (d) The L_{max} associated with at a given thermal boundary. (e) The κ_{eng} at a steady state with L_{min}. (f) The κ_{eng} at a transient mode as a function of h. (A) h = 50 (forced convection by air), (B) h = 100 (natural convection by water), and (C) h = 6000 (forced convection by water) W m^{−2} K^{−1}. Reproduced from ref. 49 with permission from the Wiley-VCH. |

5.3.2.
L
_{max} evaluation.
To figure out the hot side temperature of the thermoelectric leg when the input heat flux q_{h} is given, a numerical simulation by a finite difference method was carried out based on a realistic assembly model accounting for the temperature dependence of the material properties. Fig. 13c shows the L-dependent hot side temperature of the Bi_{0.4}Sb_{1.6}Te_{3} leg according to the leg's average thermal conductivity where T_{h,max} = 200 °C. In Fig. 13d, L_{max} is 1.15 mm by the numerical analysis and 1.33 mm by eqn (13). If the thermal conductivity is further reduced from = 1.13 W m^{−1} K^{−1} to = 0.6 W m^{−1} K^{−1}, L_{max} becomes 0.68 mm and 0.95 mm by the numerical and analytical models, respectively, where q_{h} is assumed to be 20 W cm^{−2}, which is in a typical heat flux density range (up to 40 W cm^{−2}) for most thermoelectric applications.^{95} The L_{max} according to by the analytical model (eqn (13)) outweighs the L_{max} by the numerical analysis over the whole range. This is mainly because of the absence of the Thomson heat as well as the assumption of the temperature independence of S, ρ and κ in the analytical model. This leads to an underrated κ_{eng} in a steady-state mode by the analytical model as 0.4 W m^{−1} K^{−1} at L_{min} = 0.77 mm while the κ_{eng} evaluated by the numerical analysis is more conservative with a larger κ_{eng} (0.7 W m^{−1} K^{−1} at L_{min} = 0.77 mm) as shown in Fig. 13e. According to the L_{min} of 0.77 mm, its corresponding κ_{eng} in the transient mode was 0.08, 0.15, and 9 W m^{−1} K^{−1} by eqn (17) at h = 50, 100, and 6000 W m^{−2} K^{−1}, respectively (Fig. 13f).

5.3.3.
κ
_{eng} of Bi_{2}Te_{3} materials.
The thermal conductivities of some of state-of-the-art, p-type Bi_{2}Te_{3} materials have been reported as 0.5–1.7 W m^{−1} K^{−1} for ZT ∼ 1.8.^{31,37,96–98}Fig. 14 shows the for recent p-type Bi_{2}Te_{3}, and it is close to and/or below the κ_{eng} at steady state. This indicates that there is not much room for thermal conductivity reduction for ZT improvement. As discussed, the reduction of thermal conductivity may cause an immediate fracture of a material when it is below the transient κ_{eng}, and the failure of the interfacial structure or degradation of the output power occurs when the thermal conductivity is lower than the steady state κ_{eng}. Thus, the strategy of reducing thermal conductivity for ZT enhancement should be carefully addressed by considering the mechanical reliability issue.

Fig. 14 The averaged thermal conductivities of the state-of-the-art, p-type Bi_{2}Te_{3} compared with the κ_{eng} of the p-type Bi_{0.4}Sb_{1.6}Te_{3} for the steady state (solid line) and transient mode (dashed line). The measured property data of the reference materials are from ref. A,^{96} ref. B,^{97} ref. C,^{98} and ref. D.^{37} Reproduced from ref. 49 with permission from the Wiley-VCH. |

In general, regarding the approach to maximize the efficiency of a thermoelectric generator by maximizing the material ZT, the strategy depends on the system environment, target applications, generator design, etc. Assuming that no forced cooling is applied on the cold side, reducing the thermal conductivity can be the first priority for the material tuning process with larger ΔT (broad operating temperature) needs for a thermoelectric generator. Once a reasonably broad thermal boundary condition can be achieved, one can further reduce the thermal conductivity for more efficient systems. If the output power generation is more of a concern than the system efficiency, it is better to increase the power factor. For example:

(a) by reducing the electric resistivity: if a target area is limited or the thermoelectric materials are lightweight, a larger number of thermoelectric legs can be imbedded into a generator system, i.e., a higher filling factor is required or allowed. Such a design demands a high aspect ratio for leg length to width to avoid mechanical failure by trading off an optimum ratio and thermomechanical reliability even though the length and width are interrelated. In this design, the total resistance of a system should be minimized by decreasing the material's electric resistivity while an open circuit voltage is proportional to the number of thermoelectric legs.

(b) by increasing the Seebeck coefficient: if there is no limit on a target area or heavy thermoelectric materials are selected, a lower filling factor is allowed. Because a fewer number of legs are imbedded, the design decreases the device resistance, but requires a larger open circuit voltage because of the lack of legs, so an increase in the Seebeck coefficient is better to maximize ZT for a higher system efficiency.

As discussed in this section, if the thermal conductivity is saturated or below the κ_{eng} like Bi_{2}Te_{3}, increasing the power factor is a better material tuning strategy since the power factor does not affect the thermomechanical reliability. Additionally, tuning the temperature dependence of material properties is another concern in maximizing ZT according to the CTD model.

The device reliability of thermoelectric power generators depends on the yield or bonding strength of the interfacial structures as well as the thermal conductivity of the thermoelectric leg to ensure the mechanical stability and performance in a balanced way. Beyond the lower thermal conductivity of thermoelectric materials for higher efficiency and output power generation, the higher mechanical strength of interfacial structures and the study of mechanical characteristics in thermoelectric materials should be entailed. Besides the engineering thermal conductivity, the device reliability is also improved by the appropriate mechanical properties of each component. However, tuning the mechanical properties of a thermoelectric leg and/or interfacial structures without degrading the thermal and electrical properties is a challenge, and simultaneous achievement of a high bonding strength and low electric contact resistance at the metal/thermoelectric interface without deteriorating thermoelectric performance is key for balanced improvement of the reliability and output performance of a device.

For the last few decades, vast efforts have been devoted to developing new thermoelectric materials and improving the thermoelectric performance of the materials, but the research on design, fabrication, and demonstration of thermoelectric module devices is still in a relatively early stage compared to the material research. Such a gap in the technology between the material and device hinders the use of promising thermoelectric devices as primary power sources, especially in the intermediate and high temperature range. Beyond the performance improvement of thermoelectric materials, studies on the device point of view should be actively addressed to investigate the mechanical properties, electrode materials, thermal/electrical contact resistance, interface structures, and module packaging for a thermomechanically reliable and thermoelectrically high-performance design.

- G. J. Snyder and E. S. Toberer, Nat. Mater., 2008, 7, 105–114 CrossRef CAS PubMed.
- M. Zebarjadi, K. Esfarjani, M. S. Dresselhaus, Z. F. Ren and G. Chen, Energy Environ. Sci., 2012, 5, 5147–5162 Search PubMed.
- L. E. Bell, Science, 2008, 321, 1457–1461 CrossRef CAS PubMed.
- D. Kraemer, B. Poudel, H.-P. Feng, J. C. Caylor, B. Yu, X. Yan, Y. Ma, X. Wang, D. Wang, A. Muto, K. McEnaney, M. Chiesa, Z. F. Ren and G. Chen, Nat. Mater., 2011, 10, 532–538 CrossRef CAS PubMed.
- L. L. Baranowski, G. J. Snyder and E. S. Toberer, Energy Environ. Sci., 2012, 5, 9055–9067 Search PubMed.
- K. M. Saqr, M. K. Mansour and M. N. Musa, Int. J. Automot. Techn., 2008, 9, 155–160 CrossRef.
- C. Yu and K. T. Chau, Energy Convers. Manage., 2009, 50, 1506–1512 CrossRef CAS.
- D. Crane, J. LaGrandeur, V. Jovovic and M. Ranalli, J. Electron. Mater., 2013, 42, 1582–1591 CrossRef CAS.
- X. Liang, X. Sun, G. Shu, K. Sun and X. Wang, Energy Convers. Manage., 2013, 66, 304–311 CrossRef.
- J. Fleming, W. Ng and S. Ghamaty, J. Aircraft, 2004, 41, 674–676 CrossRef.
- J. P. Thomas, M. A. Qidwai and J. C. Kellogg, J. Power Sources, 2006, 159, 1494–1509 CrossRef CAS.
- H. S. Kim, T. Itoh, T. Iida, M. Taya and K. Kikuchi, Mater. Sci. Eng., B, 2014, 183, 61–68 CrossRef CAS.
- M. T. Johansson and M. Soderstrom, Energy Efficiency, 2014, 7, 203–215 CrossRef.
- K. Yazawa and A. Shakouri, Scr. Mater., 2016, 111, 58–63 CrossRef CAS.
- S. J. Kim, J. H. We and B. J. Cho, Energy Environ. Sci., 2014, 7, 1959–1965 Search PubMed.
- G. D. Mahan, J. Appl. Phys., 1991, 70, 4551–4554 CrossRef CAS.
- T. P. Hogan and T. Shih, Thermoelectrics Handbook: Macro to Nano, Taylor & Francis, 2005 Search PubMed.
- R. He, H. S. Kim, Y. C. Lan, D. Z. Wang, S. Chen and Z. F. Ren, RSC Adv., 2014, 4, 64711–64716 RSC.
- P. Ziolkowski, P. Poinas, J. Leszczynski, G. Karpinski and E. Mueller, J. Electron. Mater., 2010, 39, 1934–1943 CrossRef CAS.
- B. V. K. Reddy, M. Barry, J. Li and M. K. Chyu, Int. J. Therm. Sci., 2013, 67, 53–63 CrossRef.
- H. S. Kim, K. Kikuchi, T. Itoh, T. Iida and M. Taya, Mater. Sci. Eng., B, 2014, 185, 45–52 CrossRef CAS.
- E. Hazan, O. Ben Yehuda, N. Madar and Y. Gelbstein, Adv. Energy Mater., 2015, 5, 1500272 CrossRef.
- X. Hu, A. Yamamoto, M. Ohta and H. Nishiate, Rev. Sci. Instrum., 2015, 86, 045103 CrossRef PubMed.
- G. Skomedal, L. Holmgren, H. Middleton, I. S. Eremin, G. N. Isachenko, M. Jaegle, K. Tarantik, N. Vlachos, M. Manoli, T. Kyratsi, D. Berthebaud, N. Y. D. Truong and F. Gascoin, Energy Convers. Manage., 2016, 110, 13–21 CrossRef CAS.
- G. J. Snyder and T. Ursell, Phys. Rev. Lett., 2003, 91, 148301 CrossRef PubMed.
- H. S. Kim, W. S. Liu, G. Chen, C. W. Chu and Z. F. Ren, Proc. Natl. Acad. Sci. U. S. A., 2015, 112, 8205–8210 CrossRef CAS PubMed.
- H. S. Kim, W. Liu and Z. Ren, J. Appl. Phys., 2015, 118, 115103 CrossRef.
- J. E. Sunderland and N. T. Burak, Solid-State Electron., 1964, 7, 465–471 CrossRef.
- G. Min, D. M. Rowe and K. Kontostavlakis, J. Phys. D: Appl. Phys., 2004, 37, 1301–1304 CrossRef.
- E. J. Sandoz-Rosado, S. J. Weinstein and R. J. Stevens, Int. J. Therm. Sci., 2013, 66, 1–7 CrossRef.
- B. Poudel, Q. Hao, Y. Ma, Y. Lan, A. Minnich, B. Yu, X. Yan, D. Wang, A. Muto, D. Vashaee, X. Chen, J. Liu, M. S. Dresselhaus, G. Chen and Z. F. Ren, Science, 2008, 320, 634–638 CrossRef CAS PubMed.
- G. Joshi, H. Lee, Y. Lan, X. Wang, G. Zhu, D. Wang, R. W. Gould, D. C. Cuff, M. Y. Tang, M. S. Dresselhaus, G. Chen and Z. F. Ren, Nano Lett., 2008, 8, 4670–4674 CrossRef CAS PubMed.
- W. Liu, X. Yan, G. Chen and Z. F. Ren, Nano Energy, 2012, 1, 42–56 CrossRef CAS.
- X. Yan, G. Joshi, W. Liu, Y. Lan, H. Wang, S. Lee, J. W. Simonson, S. J. Poon, T. M. Tritt, G. Chen and Z. F. Ren, Nano Lett., 2011, 11, 556–560 CrossRef CAS PubMed.
- Q. Zhang, J. He, T. J. Zhu, S. N. Zhang, X. B. Zhao and T. M. Tritt, Appl. Phys. Lett., 2008, 93, 102109 CrossRef.
- W. Liu, Z. Ren and G. Chen, in Thermoelectric Nanomaterials, eds. K. Koumoto and T. Mori, Springer Berlin Heidelberg, 2013, pp. 255-286 Search PubMed.
- S. I. Kim, K. H. Lee, H. A. Mun, H. S. Kim, S. W. Hwang, J. W. Roh, D. J. Yang, W. H. Shin, X. S. Li, Y. H. Lee, G. J. Snyder and S. W. Kim, Science, 2015, 348, 109–114 CrossRef CAS PubMed.
- K. Biswas, J. He, I. D. Blum, C.-I. Wu, T. P. Hogan, D. N. Seidman, V. P. Dravid and M. G. Kanatzidis, Nature, 2012, 489, 414–418 CrossRef CAS PubMed.
- H. Liu, X. Yuan, P. Lu, X. Shi, F. Xu, Y. He, Y. Tang, S. Bai, W. Zhang, L. Chen, Y. Lin, L. Shi, H. Lin, X. Gao, X. Zhang, H. Chi and C. Uher, Adv. Mater., 2013, 25, 6607–6612 CrossRef CAS PubMed.
- L.-D. Zhao, S.-H. Lo, Y. Zhang, H. Sun, G. Tan, C. Uher, C. Wolverton, V. P. Dravid and M. G. Kanatzidis, Nature, 2014, 508, 373–377 CrossRef CAS PubMed.
- H.-S. Choi, W.-S. Seo and D.-K. Choi, Electron. Mater. Lett., 2011, 7, 271–275 CrossRef CAS.
- D. Zhao, X. Li, L. He, W. Jiang and L. Chen, Intermetallics, 2009, 17, 136–141 CrossRef CAS.
- Y. Hori, D. Kusano, T. Ito and K. Izumi, presented in part at the 18th International Conference on Thermoelectrics, Baltimore, MD, USA, 1999 Search PubMed.
- A. S. Al-Merbati, B. S. Yilbas and A. Z. Sahin, Appl. Therm. Eng., 2013, 50, 683–692 CrossRef.
- U. Erturun, K. Erermis and K. Mossi, Appl. Therm. Eng., 2014, 73, 126–139 CrossRef.
- T. Sakamoto, T. Iida, Y. Ohno, M. Ishikawa and Y. Kogo, J. Electron. Mater., 2014, 43, 1620–1629 CrossRef CAS.
- J.-L. Gao, Q.-G. Du, X.-D. Zhang and X.-Q. Jiang, J. Electron. Mater., 2011, 40, 884–888 CrossRef CAS.
- T. Clin, S. Turenne, D. Vasilevskiy and R. A. Masut, J. Electron. Mater., 2009, 38, 994–1001 CrossRef CAS.
- H. S. Kim, T. B. Wang, W. S. Liu and Z. F. Ren, Adv. Funct. Mater., 2016, 26, 3678–3686 CrossRef CAS.
- E. Altenkirck, Phys. Z., 1909, 10, 560–568 Search PubMed.
- A. F. Ioffe, Semiconductor Thermoelements and Thermoelectric Cooling, Infosearch, London, 1957 Search PubMed.
- H. J. Goldsmid, A. R. Sheard and D. A. Wright, Br. J. Appl. Phys., 1958, 9, 365–370 CrossRef CAS.
- Y. Lan, A. J. Minnich, G. Chen and Z. F. Ren, Adv. Funct. Mater., 2010, 20, 357–376 CrossRef CAS.
- Q. Jie, H. Wang, W. Liu, H. Wang, G. Chen and Z. F. Ren, Phys. Chem. Chem. Phys., 2013, 15, 6809–6816 RSC.
- J. Shuai, H. S. Kim, Y. Lan, S. Chen, Y. Liu, H. Zhao, J. Sui and Z. F. Ren, Nano Energy, 2015, 11, 640–646 CrossRef CAS.
- K. F. Hsu, S. Loo, F. Guo, W. Chen, J. S. Dyck, C. Uher, T. Hogan, E. K. Polychroniadis and M. G. Kanatzidis, Science, 2004, 303, 818–821 CrossRef CAS PubMed.
- J.-S. Rhyee, K. H. Lee, S. M. Lee, E. Cho, S. Il Kim, E. Lee, Y. S. Kwon, J. H. Shim and G. Kotliar, Nature, 2009, 459, 965–968 CrossRef CAS PubMed.
- Q. Zhang, F. Cao, W. Liu, K. Lukas, B. Yu, S. Chen, C. Opeil, D. Broido, G. Chen and Z. F. Ren, J. Am. Chem. Soc., 2012, 134, 10031–10038 CrossRef CAS PubMed.
- M. Koirala, H. Zhao, M. Pokharel, S. Chen, T. Dahal, C. Opeil, G. Chen and Z. F. Ren, Appl. Phys. Lett., 2013, 102, 213111 CrossRef.
- S. D. Bhame, D. Pravarthana, W. Prellier and J. G. Noudem, Appl. Phys. Lett., 2013, 102, 211901 CrossRef.
- D. Kraemer, J. Sui, K. McEnaney, H. Zhao, Q. Jie, Z. F. Ren and G. Chen, Energy Environ. Sci., 2015, 8, 1299–1308 Search PubMed.
- S. W. Angrist, Direct Energy Conversion, Allyn and Bacon, Boston, 1965 Search PubMed.
- W. Liu, Q. Jie, H. S. Kim and Z. F. Ren, Acta Mater., 2015, 87, 357–376 CrossRef CAS.
- H. J. Wu, L. D. Zhao, F. S. Zheng, D. Wu, Y. L. Pei, X. Tong, M. G. Kanatzidis and J. Q. He, Nat. Commun., 2014, 5, 4515 CAS.
- L.-D. Zhao, V. P. Dravid and M. G. Kanatzidis, Energy Environ. Sci., 2013, 7, 251–268 Search PubMed.
- A. A. Efremov and A. S. Pushkarsky, Energy Convers., 1971, 11, 101–104 CrossRef.
- E. Müller, K. Zabrocki, C. Goupil, G. Snyder and W. Seifert, in CRC Handbook of Thermoelectrics: Thermoelectrics and Its Energy Harvesting, ed. D. M. Rowe, Taylor & Francis, 2012, ch. 12, vol. 1 Search PubMed.
- A. Muto, D. Kraemer, Q. Hao, Z. F. Ren and G. Chen, Rev. Sci. Instrum., 2009, 80, 093901 CrossRef CAS PubMed.
- H. Zhao, J. Sui, Z. Tang, Y. Lan, Q. Jie, D. Kraemer, K. McEnaney, A. Guloy, G. Chen and Z. F. Ren, Nano Energy, 2014, 7, 97–103 CrossRef CAS.
- J. Sui, J. Li, J. He, Y. L. Pei, D. Berardan and H. Wu, Energy Environ. Sci., 2013, 6, 2916–2920 Search PubMed.
- C. Fu, S. Bai, Y. Liu, Y. Tang, L. Chen, X. Zhao and T. Zhu, Nat. Commun., 2015, 6, 8144 CrossRef PubMed.
- P. Jood, R. J. Mehta, Y. Zhang, G. Peleckis, X. Wang, R. W. Siegel, T. Borca-Tasciuc, S. X. Dou and G. Ramanath, Nano Lett., 2011, 11, 4337–4342 CrossRef CAS PubMed.
- M. Zhou, J.-F. Li and T. Kita, J. Am. Chem. Soc., 2008, 130, 4527–4532 CrossRef CAS PubMed.
- X. W. Wang, H. Lee, Y. C. Lan, G. H. Zhu, G. Joshi, D. Z. Wang, J. Yang, A. J. Muto, M. Y. Tang, J. Klatsky, S. Song, M. S. Dresselhaus, G. Chen and Z. F. Ren, Appl. Phys. Lett., 2008, 93, 193121 CrossRef.
- E. S. Toberer, P. Rauwel, S. Gariel, J. Tafto and G. J. Snyder, J. Mater. Chem., 2010, 20, 9877–9885 RSC.
- Y. Saiga, B. Du, S. K. Deng, K. Kajisa and T. Takabatake, J. Alloys Compd., 2012, 537, 303–307 CrossRef CAS.
- W. Liu, H. S. Kim, Q. Jie, B. Lv, M. Yao, Z. Ren, C. P. Opeil, S. Wilson, C. W. Chu and Z. F. Ren, Proc. Natl. Acad. Sci. U. S. A., 2015, 112, 3269–3274 CrossRef CAS PubMed.
- Q. Zhang, E. K. Chere, K. McEnaney, M. Yao, F. Cao, Y. Ni, S. Chen, C. Opeil, G. Chen and Z. F. Ren, Adv. Energy Mater., 2015, 5, 1401977 CrossRef.
- X. Chen, L. Shi, J. Zhou and J. B. Goodenough, J. Alloys Compd., 2015, 641, 30–36 CrossRef CAS.
- X. Shi, J. Yang, J. R. Salvador, M. Chi, J. Y. Cho, H. Wang, S. Bai, J. Yang, W. Zhang and L. Chen, J. Am. Chem. Soc., 2011, 133, 7837–7846 CrossRef CAS PubMed.
- Y. Oto, T. Iida, T. Sakamoto, R. Miyahara, A. Natsui, K. Nishio, Y. Kogo, N. Hirayama and Y. Takanashi, Phys. Status Solidi C, 2013, 10, 1857–1861 CrossRef CAS.
- S. Chen, K. C. Lukas, W. Liu, C. P. Opeil, G. Chen and Z. Ren, Adv. Energy Mater., 2013, 3, 1210–1214 CrossRef CAS.
- E. Suhir, J. Appl. Mech., 1986, 53, 657–660 CrossRef.
- E. Suhir and A. Shakouri, J. Appl. Mech., 2012, 79, 061010 CrossRef.
- E. Suhir and A. Shakouri, J. Appl. Mech., 2013, 80, 021012 CrossRef.
- M. Barth and K. Boriboonsomsin, ACCESS Magazine, 2009, 35, 2–9 Search PubMed.
- S. S. Manson, N.A.C.A. Tech. Note, 1953, 2933 Search PubMed.
- W. D. Kingery, J. Am. Ceram. Soc., 1955, 38, 3–15 CrossRef.
- D. P. H. Hasselman, Ceramurgia Int, 1978, 4, 147–150 CrossRef.
- E. Brochen, J. Poetschke and C. G. Aneziris, Int. J. Appl. Ceram. Tec., 2014, 11, 371–383 CrossRef CAS.
- T. Siewert, S. Liu, D. R. Smith and J. C. Madeni, Properties of Lead-free Solders NIST and Colorado School of Mines, 2002.
- D. Vasilevskiy, F. Roy, E. Renaud, R. A. Masut and S. Turenne, presented in part at the Proc 25th Int. Conf. on Thermoelectrics, Vienna, Austria, August 6–10, 2006.
- W. Liu, K. C. Lukas, K. McEnaney, S. Lee, Q. Zhang, C. P. Opeil, G. Chen and Z. F. Ren, Energy Environ. Sci., 2013, 6, 552–560 Search PubMed.
- G. Subhash and G. Ravichandran, J. Mater. Sci., 1998, 33, 1933–1939 CrossRef CAS.
- J.-P. Fleurial, JOM, 2009, 61, 79–85 CrossRef CAS.
- S. Jimenez, J. G. Perez, T. M. Tritt, S. Zhu, J. L. Sosa-Sanchez, J. Martinez-Juarez and O. Lopez, Energy Convers. Manage., 2014, 87, 868–873 CrossRef CAS.
- P.-Y. Lee, J. Hao, T.-Y. Chao, J.-Y. Huang, H.-L. Hsieh and H.-C. Hsu, J. Electron. Mater., 2014, 43, 1718–1725 CrossRef CAS.
- L.-P. Hu, T.-J. Zhu, Y.-G. Wang, H.-H. Xie, Z.-J. Xu and X.-B. Zhao, NPG Asia Mater., 2014, 6, e88 CrossRef CAS.
- X. Q. Shi, W. Zhou, H. L. J. Pang and Z. P. Wang, J. Electron. Packag., 1999, 121, 179–185 CrossRef.
- P. T. Vianco, J. A. Rejent and J. J. Martin, JOM, 2003, 55, 50–55 CrossRef CAS.
- W. S. Liu, H. Wang, L. Wang, X. Wang, G. Joshi, G. Chen and Z. F. Ren, J. Mater. Chem. A, 2013, 1, 13093–13100 RSC.
- T. Y. Lin, C. N. Liao and A. T. Wu, J. Electron. Mater., 2011, 41, 153–158 CrossRef.
- M. T. Barako, W. Park, A. M. Marconnet, M. Asheghi and K. E. Goodson, J. Electron. Mater., 2013, 42, 372–381 CrossRef CAS.

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