D.
Beretta
^{ab},
A.
Perego
^{ac},
G.
Lanzani
^{ab} and
M.
Caironi
*^{a}
^{a}Center for Nano Science and Technology@PoliMi, Istituto Italiano di Tecnologia, via Pascoli 70/3, 20133 Milano(MI), Italy. E-mail: mario.caironi@iit.it
^{b}Dipartimento di Fisica, Politecnico di Milano, P.zza Leonardo da Vinci 32, 20133 Milano(MI), Italy
^{c}Dipartimento di Energia, Politecnico di Milano, via Lambruschini 4, 20156 Milano(MI), Italy

Received
28th October 2016
, Accepted 21st December 2016

First published on 19th January 2017

Micro energy harvesting to power low energy electronics has been recognized to be of primary importance for today's society to pursue a sustainable supply of energy by the integration of networks of sensors and actuators into smart grids. In this context, sustainable exploitation of distributed renewable energy sources represents a key aspect. Among the variety of sustainable energy conversion technologies, thermoelectric technology is receiving increasing attention because of its capability to harvest energy at the microscale, in the dark, with no moving parts and thus with limited maintenance. In this framework, organic materials, due to their intrinsic electro-mechanical properties, are studied with the aim to realize flexible, battery competitive and/or complementary, thermoelectric generators, and thus to expand the potential of thermoelectrics to all those applications not viable with the present technology based on rigid architectures. In this work, the strengths and limitations of the organic technology are analyzed, identifying a set of novel and promising applications of flexible thermoelectric generators based on organic matter, clearly outlining minimum thermoelectric property requirements to be achieved and ultimately paving the way towards future applications. The study clearly identifies the closest opportunity in the adoption of organic micro-thermoelectric generators for powering distributed sensors in housing and industrial environments, while evidencing the requirement of advanced generator architectures and/or material thermoelectric property breakthroughs in order to realistically target wearable applications.

(1) |

(2) |

Thermoelectric generators have been designed and realized according to different architectures, among which the vertical geometry is the most adopted one.^{2} With the advent of thin film technology, planar architectures have been introduced, and folding techniques have recently been discussed in order to re-obtain vertical-like architectures starting from planar devices and thus to exploit thin film large area fabrication methods in thermoelectric module fabrication.^{14,15} Each architecture has its own pros and cons, among which the key variables are represented by (i) the density of thermocouples that can be accommodated, (ii) the thermal resistance of the thermocouples with respect to the whole generator, (iii) and the physical dimensions of the device, the latter strongly determining the applicability of the generator on the basis of space availability. Planar architectures suffer from low packing density and thus low output voltage under small temperature gradients. Folding techniques were implemented to circumvent this limit,^{15} obtaining however rather bulky modules that prevent their implementation for energy harvesting at the microscale and/or limit their use in applications requiring a high degree of flexibility, such as wearables. Vertical architectures, instead, allow for very high packing density (potentially up to thousands of thermocouples per cm^{2} depending on the fabrication technology) and thus relatively high output voltage even under small temperature differences, and they can be designed with a characteristic thickness in the interval 10–500 μm, definitely representing the optimal choice for energy harvesting at the microscale under small temperature differences, and also more easily lending themselves to applications requiring flexibility or, more simply, bendability. Note however that there is no definitive choice, because device architectures must be also chosen on the basis of the specific environmental conditions. Indeed the power generated and the efficiency of conversion strongly depend on other parameters besides the architecture, such as the thermal coupling with the environment, the latter addressing a desired length of generator thermocouples to maximize the fraction of temperature difference falling across the thermocouples, and thus to maximize the power generated.^{16}

With the increasing interest in waste heat harvesting under small temperature differences for IoT applications, models of thermoelectric generators working under such conditions have been proposed and compared.^{16–23} However, a study dedicated to flexible devices based on organic matter has to be addressed yet.

In this work, organic thermoelectric generators are investigated by means of an appositely derived non-linear thermoelectric model, and the corresponding linearized one, by considering only substrates and thermoelectric materials characterized by mechanical properties suited for flexible applications. The model, generally valid for generators with vertical or folded planar architectures, is used to capture key aspects of organic TEG engineering, and thus strategies to improve their performances, ultimately serving as a powerful tool to identify the most promising applications and to define a possible roadmap towards them. The present work mainly focuses on the investigation of organic TEG capability to satisfy fundamental electrical requirements posed by emerging technologies, and combined with studies on other fundamental properties such as device resistance to mechanical stresses and deformations, weight and ease of integration allows forecasting a potential future for applications of organic thermoelectrics.

p_{out} = v_{load}i | (3) |

(4) |

(5) |

The efficiency of thermoelectric conversion is defined as the ratio between the power delivered by the generator and the corresponding heat absorbed _{h}, namely

(6) |

Since the effective temperature difference T_{h} − T_{c} falling across the thermocouples is only a fraction of the external temperature difference T_{r,h} − T_{r,c}, and since it is a non-linear function involving the Joule and Peltier effects, a suitable model to estimate T_{h} − T_{c} has to be introduced.

(7) |

(8) |

The heat dissipated per unit area due to the Joule effect is given by = nR_{pn}i^{2}, in the formula

(9) |

(10) |

(11) |

(12) |

In the light of the given definitions, the non-linear system of thermoelectric equations is finally obtained:

(13) |

(14) |

Therefore, under small temperature differences, the error of the linearized model essentially coincides with the error committed by discarding the Peltier terms, the latter depending on the device design and material thermoelectric properties. Under linear approximation, no thermal losses within the device due to thermoelectric conversion are considered and the outgoing heat flux at the cold reservoir equals the absorbed one from the hot reservoir. Therefore, T_{h} − T_{c} is linearly related to the external temperature difference T_{r,h} − T_{r,c} by the following equation:

(15) |

(16) |

Co-optimization with respect to the thermocouple length and load resistance ratio is obtained for

(17) |

(18) |

(19) |

(20) |

Therefore, when the thermoelectric properties of the p- and n-type legs are equal, the generated power is maximized for symmetric thermocouples, namely for A_{p} = A_{n}, while, when the thermoelectric properties of the p- and n-type legs are different, the power is maximized by properly tuning their section ratio according to eqn (19).

Direct comparison between the linear and the non-linear model at load matching (m = 1) is shown in Fig. 3 for ΔT = 5 K and good thermal coupling with the environment (h_{eq.} = 10^{4} W m^{−2} K^{−1}). The architecture considered is made of 525 μm thick silicon substrates with nominal thermal conductivity κ_{Si} = 140 W m^{−1} K^{−1}, and vacuum insulation between thermocouples is supposed. Data are normalized with respect to the non-linear model and two different values of Z are considered, namely 3 × 10^{−3} K^{−1} and 2.5 × 10^{−4} K^{−1}. As shown, the linear model is found to overestimate the power generated by more than 10% at load and thermal matching for Z = 3 × 10^{−3} K^{−1}, but when thermocouples characterized by a smaller Z are considered, the differences between the models are rapidly smoothed out.

Although the linear model is shown to overestimate the performances of thermoelectric devices, it provides immediate and valuable information on device engineering and architecture designs from closed forms of power and efficiency. Nonetheless, the non-linear model should be preferred especially for high Z and when it is not computationally time consuming. In this work, the linear model will be first used to identify, from closed forms, requirements of the thermocouple figure of merit and device geometry needed to achieve a certain power output per unit area. Then, the non-linear model will be used to confirm predictions from the linear one for a series of different cases considering different families of potential applications.

In Fig. 5 the effect of increasing the heat transfer coefficient of the substrates by spanning their thickness over six orders of magnitude is shown for a representative case with κ_{pni} = 0.4 W m^{−1} K^{−1}. Two substrates characterized by two different thermal conductivities are considered, namely κ_{s} = 0.15 W m^{−1} K^{−1} and κ_{s} = 6.5 W m^{−1} K^{−1}, and distinction is made between good and poor thermal coupling with the environment. Data are normalized with respect to the case of good thermal coupling and high thermal conductivity. In the case of poor thermal coupling with the environment, no appreciable differences in the power output are observed when the substrate thickness goes below 1 mm. On the other hand, when the thermal coupling with the environment is good, the power generated becomes strongly sensitive to the heat transfer coefficient of the substrates, and thus to their thickness. In the light of this discussion, since the higher the equivalent heat transfer coefficient, the higher the power generated, and since thin substrates are necessary to push the equivalent heat transfer coefficient up to the ultimate limit represented by the thermal contact resistance, thin substrates, needed to ensure flexible properties to the final device, are in all cases either beneficial or not detrimental.

(21) |

Fig. 6 Thermoelectric efficiency factor calculated with the linear model and with FF = 0.5. According to eqn (22) and (25), tuning the fill fraction, the efficiency factor can be shifted by approximately one order of magnitude with respect to the value reported in the figure. The regions corresponding to liquid cooling, heat exchangers and flat surfaces are shown in order to identify the upper limit of h_{eq.} depending on the cooling mechanism adopted. |

(22) |

Therefore, the characteristic dimension of the thermocouple unit needed to generate the voltage Ṽ on a surface whose extension is A is given by . In Fig. 7 the thermoelectric characteristic dimension at load and thermal matching is shown as a function of the relative thermopower of the thermocouples and as a function of device area. For instance, by choosing , in order to generate 1.5 V from a device occupying a superficial area smaller than 5 cm^{2}, a relative thermopower higher than 100 μV K^{−1} is required. In contrast, if larger surfaces were available, smaller relative thermopower could satisfy the needs. Therefore, depending on fabrication technologies and thus thermoelectric unit resolution, and on the field of applications, more or less high relative thermopower is needed to target a desired voltage from a given surface. When considering air cooling from heat exchangers, the will of pursuing devices occupying the smallest surfaces is basically dictated by two reasons: the smaller the device, the larger the possibility of device implementation due to limited space needs; and the smaller the device, the smaller the heat exchangers required to dissipate the heat at the cold side. The latter aspect arises from considerations on module costs. It was in fact demonstrated that generators optimized with respect to cost per Watt are such that the overall fabrication costs are mainly due to heat exchangers.^{29,30} In the light of these observations, large flexible thermoelectric devices could suffer from much higher costs with respect to batteries when cooling is provided by heat exchangers. In contrast, exploitation of the heat source and sink by direct mechanical contact of both device substrates could represent a promising path for organic devices based on cost effective processing methods.

Fig. 8 Thermopower module versus electrical conductivity of representative materials belonging to different families of organic materials. |

Material |
σ (Ω^{−1} m^{−1}) |
α (μV K^{−1}) |
κ (W m^{−1} K^{−1}) |
Z (K^{−1}) |
---|---|---|---|---|

PEDOT:PSS^{41} |
3.6 × 10^{3} |
15 | 0.15 | 5.4 × 10^{−6} |

Ag | 6.3 × 10^{7} |
1.5 | 429 | 3.3 × 10^{−7} |

PDI^{37} |
50 | −167 | 0.2 | 7 × 10^{−6} |

N^{+} |
10^{4} |
−75 | 0.5 | 1.1 × 10^{−4} |

P^{+} |
10^{4} |
75 | 0.5 | 1.1 × 10^{−4} |

N^{++} |
10^{5} |
−180 | 0.3 | 10^{−2} |

P^{++} |
10^{5} |
180 | 0.3 | 10^{−2} |

SU-8 | 0.2 | |||

PEN | 0.15 |

The simulations distinguish between three cases (5.1)–(5.3), belonging to the wearables and the networks scenario, characterized by different conditions of thermal coupling with the environment, and thus being representative of a series of different potential applications. In detail:

In Fig. 9 and 10 the simulated power and voltage generated per unit area are shown as a function of the thermocouple thickness, which is allowed to span the interval 1 μm to 1 cm, according to the conditions established by the three cases discussed. While Fig. 9 represents the cases for actually available materials, namely PEDOT:PSS, Ag and PDI, Fig. 10 represents the cases for hypothetical thermocouples made of P^{+}, P^{++}, N^{+} and N^{++} hypothetical materials. Continuous and dashed lines are used for the symmetric and the optimized geometry respectively. In every case and for each choice of thermocouple, the power and the voltage generated are observed to be an increasing function of Z and FF, and the maximum power is obtained corresponding to the thermal matching conditions, the latter being a decreasing function of the thermal coupling with the environment, as expected. While in the two networks scenarios, by geometry optimization, thermal matching is achieved for relatively short thermocouples (<500 μm), in the wearables scenario, due to poor thermal coupling with the environment, thermal matching is always achieved for very long thermocouples (>1 cm) irrespective of the thermal conductivity of the thermocouple unit, and the power generated remains always largely below 1 μW per cm^{2}. This happens even in the case of hypothetical thermocouples characterized by Z = 10^{−2} K^{−1} (ZT = 3), namely a value approximately two times higher than that of the best thermocouple known so far for room temperature applications.^{59} In order to generate tens of μW per cm^{2} at thermocouple lengths compatible with micro architectures (<500 μm) and under the conditions of poor thermal coupling with the environment (h_{eq.} ∼ 10 W m^{−2} K^{−1}), according to eqn (17), κ_{pni} must be in the order of 10^{−3} W m^{−1} K^{−1}. Therefore, even considering the case of thermoelectric materials characterized by extremely low thermal conductivity κ_{p} = κ_{n} = 0.2 W m^{−1} K^{−1}, thermocouple insulation cannot be provided by solid state matter, and vacuum encapsulation must be considered (air is not enough since κ_{i} ≅ 0.02 W m^{−1} K^{−1} at 1 atmosphere). In fact, when κ_{i} = 0, κ_{pni} = κ_{pn}FF and for FF < 0.025 thermal matching is achieved in the micro region. However reducing the fill fraction also reduces the power generated, and thus the minimum Z required is shifted up by approximately one order of magnitude, namely Z > 10^{−1} K^{−1} (ZT > 30) and, even in the case of larger surfaces (i.e. 100 cm^{2}), the required figure of merit does not go below 10^{−3} K^{−1} (ZT = 0.3). This lays the emphasis on the need for more efficient coupling with the environment. In fact, unless a significant breakthrough in organic thermoelectric materials is obtained in the near future, or novel device architectures are proposed for the purpose,^{26,27} conventional architectures adopting organic materials will hardly find application in the wearables scenario. In contrast, novel architectures directly knitted into clothes could make use of the much thicker structures granted by cloth thickness (few mm) and could exploit the temperature gradient established by the clothes themselves. Novel methods of investigation and modeling of these architectures are required to estimate the potentiality of the technology in this framework. For instance, considering the temperature difference sustainable by trekking and diving suits, sport garments look like promising niches for the implementation of thermoelectric technology in wearable applications. In these cases, thermoelectrics could provide an effective way to power sensors dedicated to monitor the health of the user. In fact, despite the fact that issues concerning thermal coupling with the environment are not solved, thermal matching conditions are achieved for κ_{pni} ∼ 0.01, which can be obtained even by air insulation and appropriate fill fraction tuning. In this case, using larger devices, the inefficiency of thermal coupling can be well compensated and, with reference to Fig. 6, Z > 10^{−4} K^{−1} (ZT > 0.03) could be sufficient for many purposes. It is worth underlining that these are hypotheses which require practical assessment to be validated.

On the other hand, in the two networks scenarios, due to the better thermal coupling with the environment, micro architectures are more appropriate and power and voltage targets are much more easily achievable by proper geometrical tuning and material choice. With reference to Fig. 9b and c, it is interesting how geometrical optimization of the couple PEDOT:PSS/Ag leads to a shift of almost 6 orders of magnitude in the power generated per unit area, up to almost 1 μW per cm^{2} corresponding to the thermal matching conditions of the optimized structure. This is a consequence of the shifting of the thermal matching length towards shorter legs, and is ascribed to the significant increase of the sectional area of the PEDOT:PSS leg (the diameter shifts from 100 μm to 6.7 mm) with respect to the one of silver. However, consequently the number of thermocouples per cm^{2} is strongly reduced (to approximately 0.03 per cm^{2}), and so is the voltage delivered to the load, which drops down in the order of tens of pV per cm^{2}, namely values of no practical use.

With reference to Fig. 9e and f, the couple PEDOT:PSS/PDI is not affected by geometrical optimization as much as the previous one is. This follows from the smaller difference between the thermal and electrical conductivities of the constituent materials. However, while the voltage delivered to the load can be pushed up to 1 V per cm^{2} by tuning the fill fraction, the power generated never exceeds 1 μW per cm^{2}, even in the unrealistic case of FF = 0.99. Comparison between the couples PEDOT:PSS/Ag and PEDOT:PSS/PDI reveals how fundamental the improvement of the thermoelectric properties of both p- and n-type legs becomes in order to increase the power and voltage generated, and makes micro architectures suitable for the purpose.

Once the inadequacy of the present materials to address technological requirements has been assessed, with reference to Fig. 10b, c, e and f, the networks scenarios are studied under the hypothesis of thermocouples having Z > 10^{−4} K^{−1} (ZT > 0.03) and Z > 10^{−2} K^{−1} (ZT > 3) respectively, the former being the minimum figure of merit required for IoT applications according to the linear model. The simulations confirm that 10^{−4} K^{−1} (ZT > 0.03) is the minimum value for the figure of merit Z to be targeted for thermoelectric technology to be implemented in this sector.

Material thermoelectric properties were then discussed in direct relation with the equivalent heat transfer coefficient. By means of the thermoelectric efficiency factor, the minimum requirement of Z was estimated on the basis of the power to be generated per unit area, on the external temperature difference available, and on the mechanism of thermal coupling with the environment. Approximately, they were identified as Z > 10^{−4} K^{−1} (ZT > 0.03) and Z > 10^{−2} K^{−1} (ZT > 3) for the two scenarios of networks and wearables respectively.

The characteristic dimensions of the thermoelectric units were analyzed in direct relation with the voltage generated per unit area. The study unveiled the necessity of a high relative thermopower (>100 μV K^{−1}) and/or technological breakthrough to reduce the minimum size feature, in order to deliver, under nominal operative conditions, voltages competitive to the ones delivered by batteries (1.5 V) from devices occupying relatively small surfaces (<5 cm^{2}).

A series of simulations were then conducted, using the non-linear model, on a series of devices made of different thermocouples. Available materials were considered, and so were fictitious ones in order to assess forecasts from the linear model. The simulations confirmed the assumptions on material properties and thermal management needs. In particular, while for wearable devices Z > 10^{−2} K^{−1} (ZT > 3) was found to be necessary to generate tens of μW from 1 cm^{2}, less stringent demands were found necessary for IoT applications in the field of industrial and housing networks, namely Z > 10^{−4} K^{−1} (ZT > 0.03). However, these requirements of the figure of merit were found to be compatible with micro architectures only in the case of good thermal coupling with the environment. In the case of wearables, where the thermal coupling is poor, in order to generate tens of μW per cm^{2} from μTEGs based on conventional micro architectures, thermocouples with extraordinary thermoelectric properties (Z > 0.1 K^{−1} (ZT > 30)) are necessary. This requirement, being more than one order of magnitude far beyond the figure of merit of the best thermocouple for room temperature applications ever discovered,^{59} is unlikely to be achieved in the short term. However, increasing the extension of the surface up to 100 cm^{2} allows the reduction of the requirements of the figure of merit, which shifts down to approximately 10^{−3} K^{−1} (ZT = 0.3), a more likely value to be achieved in the near future. Novel and innovative architectures of TEGs directly knitted into clothes could even shift the requirements of the figure of merit down to 10^{−4} K^{−1} (ZT = 0.03) in order to generate few μW from a 100 cm^{2} surface. Considering the steady advances in the synthesis of more and more performing conjugated organic materials during the last two decades,^{31,33,60–70} this last requirement represents a more probable and promising target for future applications of organic thermoelectrics in this sector, addressing the needs for further studies of innovative architectures.

The results achieved within this work allow defining a potential roadmap towards future applications of organic thermoelectrics. The roadmap is shown in Fig. 11, where, given the characteristic equivalent heat transfer coefficient, the families of applications are shown as functions of the necessary thermocouple figure of merit. Target power was set equal to a few μW, and clouds surrounding each family were drawn to take into account for different fill fractions and/or device surface extension (in the interval 1–100 cm^{2}). The line of the present is established considering the couple PEDOT:PSS/PDI, namely the best thermocouple made of actual materials processable from solution. Despite the fact that no applications can be addressed by the present technology, slight improvements of solution processable thermoelectric materials could allow for practical applications in the field of industrial and housing devices, such as movement sensors for alarm systems, position sensors, temperature and humidity sensors, general industrial process sensors, actuators for self-regulating environments and battery chargers from waste heat energy conversion, to name a few. On the other hand, IoT applications in the field of wearables demand innovative architectures, such as the already discussed knitted ones, in order to concretely integrate the generators into clothes and exploit increased thickness and larger surfaces to reach power requirements under poor thermal coupling and plausible materials in the near future. If novel architectures demonstrate to be effective, among the variety of potential applications, those belonging to the biomedical sector will be among the most promising: smart clothes capable of health monitoring will become feasible and collection of signals among millions of users could make available a large set of data from which, by means of big data analysis, a deeper understanding of human disease causes will be possible, potentially leading towards a more effective disease prevention.

As a closing remark, it has to be noted that, so far, the cross-plane thermoelectric properties of organic materials have received far less attention than their in-plane ones. Since the direction of the thermal and electric transport depends on the architecture of the generator, and since anisotropic thermoelectric properties are not only possible but even likely in many organic systems, these anisotropies should be accurately investigated in the near future. This will allow forecasting, by modeling, more accurate performances and identifying, with a higher degree of confidence, potential fields of applicability of the thermoelectric technology based on flexible materials.

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## Footnote |

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6se00028b |

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