Organic materials can be printed into thermoelectric (TE) devices for low temperature energy harvesting applications. The output voltage of printed devices is often limited by (i) small temperature differences across the active materials attributed to small leg lengths and (ii) the lower Seebeck coefficient of organic materials compared to their inorganic counterparts. To increase the voltage, a large number of p- and n-type leg pairs is required for organic TEs; this, however, results in an increased interconnect resistance, which then limits the device output power. In this work, we discuss practical concepts to address this problem by positioning TE legs in a hexagonal closed-packed layout. This helps achieve higher fill factors (∼91%) than conventional inorganic devices (∼25%), which ultimately results in higher voltages and power densities due to lower interconnect resistances. In addition, wiring the legs following a Hilbert spacing-filling pattern allows for facile load matching to each application. This is made possible by leveraging the fractal nature of the Hilbert interconnect pattern, which results in identical sub-modules. Using the Hilbert design, sub-modules can better accommodate non-uniform temperature distributions because they naturally self-localize. These device design concepts open new avenues for roll-to-roll printing and custom TE module shapes, thereby enabling organic TE modules for self-powered sensors and wearable electronic applications.

Thermoelectric generators (TEGs) are solid-state devices that directly convert thermal energy into electrical energy. The operating principle for a TEG is based on the Seebeck effect, where a thermoelectric (TE) material generates a voltage under the application of a temperature difference. The magnitude of the generated voltage is proportional to the applied temperature difference, and the constant of proportionality is the Seebeck coefficient (S). Even for the best and most widely used TE materials based on inorganic semiconductors, the voltage from one TE leg is small (<200 μV/K); therefore, to augment the generated voltage, TEGs are fabricated by connecting many p- and n-type legs electrically in series and thermally in parallel, as shown in Fig. 1. TEGs are suitable for energy harvesting and power generation with a conversion efficiency that is proportional to the dimensionless material figure-of-merit (zT) given by zT = S2σT/k, where σ is the electrical conductivity, k is the thermal conductivity, and T is the absolute temperature. Due to the inherent correlation between S, σ, and k, obtaining a high zT material is challenging, and most research efforts are focused here.

FIG. 1.

(a) Schematic and (b) side view of a commercial inorganic TE device (Custom Thermoelectric, part # 12711–5L30–25CQ) showing p- and n-type legs connected electrically in series. The module consists of 127 p-n leg pairs (254 TE legs) sandwiched between ceramic plates. Device dimensions are provided for FF calculations.

FIG. 1.

(a) Schematic and (b) side view of a commercial inorganic TE device (Custom Thermoelectric, part # 12711–5L30–25CQ) showing p- and n-type legs connected electrically in series. The module consists of 127 p-n leg pairs (254 TE legs) sandwiched between ceramic plates. Device dimensions are provided for FF calculations.

Close modal

Thermoelectric power generation is based on inorganic semiconductors, due to their superior TE properties at high temperatures.1–3 However, for low grade (< 200 °C) energy recovery,4–7 inorganic TEs are unsuitable, since their higher thermal conductivity results in prohibitively high system costs, predominantly from the heat exchangers.8 An alternate class of materials for these lower temperature applications is organic TEs based on conducting polymers.9 Organic TEs have several advantages: (i) they have intrinsically low thermal conductivities, which help maintain the temperature difference across the device, (ii) the material costs are potentially lower, as no heavy or rare-earth elements are used,9–11 and (iii) they can be processed from solution, which allows for scalable, cost-effective and high-throughput module fabrication.9,12,13 Example applications for low grade energy recovery include self-powered sensors14–16 or Internet-of-Things devices17,18 powered by ubiquitous thermal sources (e.g., hot water pipes).7 Furthermore, since polymers can be fabricated as lightweight and flexible modules, they can be used in wearable body-heat harvesting devices as well.19–21 All the aforementioned applications require power sources on the order of μW–mW,19 which require well-designed modules to ensure that device resistance does not dominate and decrease the power output. Particularly, for wearable devices, thin-film TE modules are suitable power sources. However, in this thin-film limit, the electrical contact and interconnect resistances can become significant and can lower the overall module performance, necessitating careful consideration of module design.

While increasing zT for polymer TEs has been an active area of research,11,12,22 there have been only a few studies on device architectures and system-level optimization for improving the module performance for devices that use conducting polymers.7,23 In fact, polymer TEGs are fabricated using techniques developed for inorganic semiconductors, which do not leverage the inherent advantages of these materials. In this work, we show that by positioning the TE legs based on the hexagonal closed-packed layout and wiring them according to the Hilbert space filling curve, we can obtain larger fill factors (FFs), decreased interconnect resistances, better accommodation of non-uniform temperature distribution across the module, and facile load matching conditions; these are crucial attributes to improving the performance of organic TE modules for low grade energy harvesting applications.

The technology for fabricating organic TE modules is based on printing techniques, such as screen printing24–32 and inkjet printing.33–40 In screen printing, the material is directly cast onto a substrate that is covered by a pre-patterned mask. This technique has the potential to be used in continuous roll-to-roll (R2R) fabrication of square-meter TE devices.26 Higher precision fabrication with minimal material loss can be achieved by inkjet printing, which allows for non-contact deposition of small solution droplets (∼pL) on a substrate.41,42 Despite the differences in these printing techniques, the printed layer thickness is limited to tens of microns.26 This makes energy harvesting from a through-plane temperature difference challenging, because only a small portion of the imposed temperature difference occurs across the active TE material, and the majority occurs across the substrate.26 This drastically reduces the generated voltage from the TE device, resulting in low performance for organic prototypes. For this reason, most proposed designs for organic TEGs have used a lateral (in-plane) temperature gradient.7,19,33–39,43 However, for flexible TEGs and wearable devices, energy harvesting from a through-plane temperature difference is desirable.

Given that the voltage output depends on the temperature difference across the TE legs and the number of legs, two approaches can be envisioned to improve the performance of organic TEGs. The first approach is to make the TE legs longer (i.e., the active material thickness should be equal to or larger than substrate thickness), so that a higher portion of the imposed temperature difference is across the active material. The second approach is to increase the number of p-n leg pairs, so that even if the generated voltage per leg is small, many legs can provide the required output voltage.

Longer leg lengths from organic TE materials can be fabricated using molding44,45 and lithography.12,46 However, these techniques require modifications to the substrate, which consequently increase manufacturing costs. Longer leg lengths can also be achieved using 3D printing; this technology for printing organic TEs has not been fully demonstrated, although inorganic TEs47 and graphene48 have recently been 3D printed. Dispenser printing is another technique than can be utilized to fabricate longer TE leg lengths;33 this technique requires large amounts of material, and also requires modifications to the material properties to ensure that they are in the correct range for dispense printing.49 To make longer leg lengths and circumvent losses through the substrate, TE legs can also be printed on a porous substrate; this allows the TE material to diffuse into the substrate and make electrical connections from both the top and the bottom of the substrate.7,43 This way, the active material thickness is at least equal to the substrate thickness ensuring that most of the temperature drop occurs across the TE material. We have shown that there is an optimum leg length7,23 that maximizes the power output from a TEG device. For a typical polymer, this is approximately 250 μm (see supplementary material Note 1), which makes paper a candidate substrate for printing low cost organic TE devices.

Even if longer leg lengths can be fabricated by using any of the aforementioned techniques, due to the lower Seebeck coefficient of organic materials, the voltage output per p-n leg pair will still be lower than that of its inorganic counterpart. Therefore, one practical approach to augment the voltage from an organic TE module is to increase the number of legs per unit area. The voltage from the device is directly proportional to the number of TE legs, V = N.Spn.ΔT, where Spn is the Seebeck coefficient of one p-n leg pair (Spn = Sp - Sn), N is the number of p-n leg pairs in the module, and ΔT is the temperature difference across the TE legs. Assuming ΔT = 5 K (representing human touch for wearable electronics) and using the properties of de-doped PEDOT:PSS23 (S = 72 μV/K) as the p-type material and a fictitious material with identical properties except for the sign of the Seebeck coefficient as the n-type material, we can potentially generate a 2 V output with 3600 legs as shown in Fig. 2(a). It is worth noting here that increasing the number of legs does not necessarily lead to larger device sizes, as printing techniques (such as high resolution inkjet printing) allow for positioning many TE legs in a small area. Figure 2(b) illustrates this with 3600 red and blue circular dots, representing n- and p-type TE legs, respectively, that are printed using a desktop inkjet printer (EPSON XP-860) in an area of 31.2 mm by 36.0 mm. The substrate is a conventional copy paper that is used without further modification; better printing patterns can be obtained on paper treated with cellulose nanofibers to control substrate porosity and ink spreading. Such high packing densities for TE legs are impossible to achieve using the existing fabrication methods for inorganic TEGs that include dicing50 and pick-and-place techniques.51 

FIG. 2.

(a) Output voltage from a module as a function of number of TE legs using the properties of de-doped PEDOT:PSS. (b) 3600 legs are printed in an area of 36.0 mm by 31.2 mm on a conventional copy paper using a desktop inkjet printer (EPSON XP860) to show a large FF. Red and blue colors are regular printer inks that represent n- and p-type polymers, respectively, for illustration purposes alone.

FIG. 2.

(a) Output voltage from a module as a function of number of TE legs using the properties of de-doped PEDOT:PSS. (b) 3600 legs are printed in an area of 36.0 mm by 31.2 mm on a conventional copy paper using a desktop inkjet printer (EPSON XP860) to show a large FF. Red and blue colors are regular printer inks that represent n- and p-type polymers, respectively, for illustration purposes alone.

Close modal

While increasing the number of legs seems promising, it has one major drawback: the total interconnect length increases as the p- and n-type materials must be wired in series. This, along with operating in the thin-film limit, ultimately makes interconnects the dominant resistance in the system, and this has resulted in low power outputs for organic TE prototypes.26,34 Fabricating devices by inkjet printing the active material and interconnects is highly desirable for low cost energy harvesting applications. However, realization of such technology is currently limited by having access to (i) inkjet printable TE materials—this is an ongoing area of research49 and (ii) highly conductive inkjet printable interconnects—this is an area in need of further development, as has been our experience with commercial inkjet printable conducting inks. For a material to be inkjet printable, its rheological properties (e.g., surface tension, viscosity, and density) must be within operable ranges;35,52 this may require additives and binders, which decrease the electrical performance. Studies have shown that these property alterations can introduce additional resistances and make formulating highly conductive inkjet printable interconnects a challenging task.7,49 This is beyond the scope of what is reported here, as this work focuses on new design concepts for organic TE modules.

As a parallel approach to improving materials properties (i.e., zT) and printability, we explore redesigning the TE module by positioning the legs on a substrate following a different design and connecting them together in a new wiring pattern. Any possible improvements based on this approach can be readily realized in modules that are fabricated using existing TE polymers and interconnect materials.

The traditional leg placement and the interconnect pattern for a flat-plate Bi2Te3 thermoelectric module are shown in Fig. 3(a). Here, the legs are diced to have rectangular cross-sections, are positioned in a square lattice using a pick-and-place machine, and are wired in series using solder interconnects. Typical leg lengths for these modules are 2–5 mm, and these legs are sandwiched between ceramic plates that serve as the hot- and cold-side heat exchangers. Here, we define the FF of a module as the ratio of the area covered by the active TE material to the hot-side heat exchanger area (this is often the area of the ceramic plates). Based on the dimensions in Fig. 1(b), the FF for a flat-plate device can be calculated to be ∼25% (see supplementary material Note 2). For organic TE modules, printing-based fabrication techniques allow for a broader range of geometries and interconnect patterns. Particularly, using high resolution inkjet printing, legs with different cross-sections such as circular legs with smaller diameters can be printed much closer together. This results in a higher FF for the module, as shown in Fig. 3(b), which in turn results in a higher power density for energy harvesting applications. We can take this further and position the legs in a hexagonal closed-packed structure shown in Fig. 3(c), which can help achieve a maximum theoretical FF of π/23 ∼91% for circular junctions on a two-dimensional plane (see supplementary material Note 3). In addition to higher FFs, by placing TE legs closer together, the interconnect length also decreases, which in turn lowers the total resistance and results in a higher power output; this is crucial when the TE module includes a large number of legs (>2000 compared to the typical ∼250 legs for inorganic modules).

FIG. 3.

(a) Inorganic fabrication techniques typically produce square cross-section TE legs and use serpentine interconnect patterns. (b) Using high resolution printing, circular cross-sections can be fabricated with legs positioned much closer together, resulting in larger FFs. (c) Even larger FFs can be achieved by placing the legs in a closed-packed layout (hexagonal lattice) that reduces the interconnect length. The red and blue colors represent p- and n- type materials, respectively.

FIG. 3.

(a) Inorganic fabrication techniques typically produce square cross-section TE legs and use serpentine interconnect patterns. (b) Using high resolution printing, circular cross-sections can be fabricated with legs positioned much closer together, resulting in larger FFs. (c) Even larger FFs can be achieved by placing the legs in a closed-packed layout (hexagonal lattice) that reduces the interconnect length. The red and blue colors represent p- and n- type materials, respectively.

Close modal

To assess the increase in power density that can be obtained using this closed-packed layout of TE legs and obtain the optimum leg length, we have developed a numerical model that includes materials properties, device geometry and thermoelectric effects. As an illustration, we use the properties of de-doped PEDOT:PSS (S = 72 μV/K, σ = 890 S/cm, and k = 0.33) as the p-type material, and a fictitious n-type material with identical properties except for the sign of the Seebeck coefficient. We model flexible modules by using Kapton films instead of ceramic plates in traditional flat plate devices. For fixed hot- and cold-side temperatures of TH = 400 K and TC = 300 K (typical for low grade heat recovery), a system of coupled non-linear equations that includes the Peltier effect and Joule heating terms can be solved numerically.7,23 The leg length is a design variable that optimizes device geometry and performance. All assumptions and input parameters used in this model are listed in supplementary material Note 1. We observe that power density (normalized to the heat exchanger area) increases with leg length, reaches a maximum value called the optimum leg length, and then decreases. This is expected as the thermal and electrical resistances dominate at large leg lengths, thereby reducing the heat through the device and consequently, the power output. As was mentioned previously, the optimum leg length is found to be around 250 μm, and a power density of over 100 mW/cm2 is obtained at this optimized leg length. This is significantly higher than the existing organic TEG prototypes indicating that printing closed-packed devices could be very beneficial for achieving high performance. We note here that this is an upper limit on performance since the fill factor that is practically achievable is dictated by the resolution of the printer and the porosity or surface tension of the substrate. The printer resolution dictates how close the p- and n-legs can be positioned; if the legs are too close to each other and conducting inks spread across the substrate, it could result in a short-circuited device. We also point out that printing legs with a circular cross-section is easier, given that inkjet printers deposit droplets of ink onto a substrate, so sharp edges in a square cross-section may not be well-defined (i.e., rounded edges). This is in contrast to conventional inorganic modules where semiconductor ingots can be diced into square cross-sections, and although large FFs can be obtained with square legs, there is a practical limitation to how close the pick-and-place machine can position the legs.

We have shown that using printing techniques, organic TE legs can be positioned closer to each other and in a hexagonal layout to increase the power density. We can also print new patterns for interconnects between the legs. A group of patterns that can potentially be utilized as interconnects are fractal geometries with self-similarity characteristics that are referred to as space filling curves. Mathematically, space filling curves are defined as mapping functions from points on a unit interval of [0, 1] to the entire two-dimensional unit square. Hilbert curves and Peano curves are two examples of space filling curves. Recently, Fan et al.53 have shown that these curves provide ideal surface conformations for stretchable electronics. In this work, we choose Hilbert curves for wiring the module, as they not only allow for good surface conformation (which is beneficial for wearable devices),53 but also self-localize (which is beneficial for maintaining a uniform temperature across all the TE legs). A Hilbert curve of order n describes how 4n points are connected as shown in Fig. 4(a). To fabricate a TE module, legs can be positioned in place of these points, and they can be wired together based on the Hilbert pattern shown in Fig. 4(b). Moreover, a hexagonal layout for positioning TE legs can also accompany the Hilbert curve interconnects, thus allowing for much larger FFs, as shown in Fig. 4(c).

FIG. 4.

(a) From left to right—Hilbert curves of order one, two, three, and four, which have 4, 16, 64, and 256 legs, respectively. (b) Hilbert interconnect patterns (shown as black lines) can be used to connect TE legs electrically in series, where red and blue circles represent n- and p-type materials, respectively. (c) TE legs that are connected by the Hilbert curve can also be arranged in a hexagonal closed-packed layout, thus increasing the FFs.

FIG. 4.

(a) From left to right—Hilbert curves of order one, two, three, and four, which have 4, 16, 64, and 256 legs, respectively. (b) Hilbert interconnect patterns (shown as black lines) can be used to connect TE legs electrically in series, where red and blue circles represent n- and p-type materials, respectively. (c) TE legs that are connected by the Hilbert curve can also be arranged in a hexagonal closed-packed layout, thus increasing the FFs.

Close modal

One major benefit of using space filling curves for wiring interconnects in TE modules is that they allow the module to be divided into fractal geometries or sub-modules. Although, in theory, all space filling curves allow for dividing into sub-modules, the geometry of the resulting sub-modules differ and are dependent on the chosen curve. For instance, following the Hilbert pattern, we can divide the module into M groups of identical parts (i.e., sub-modules) connected in parallel, and each consisting of N legs wired in series (i.e., MxN total number of legs), as discussed below.

A module containing 1024 legs wired together by an order five Hilbert curve can be divided into eleven combinations of M and N (denoted by (M,N)), as (1,1024), (2,512), (4,256), (8,128), (16,64), (32,32), (64,16), (128,8), (256,4), (512,2), and (1024,1); four of these combinations are shown in Fig. 5. Following the concept of tessellating a device into sub-modules, an initial module can be printed such that all legs are connected in series [i.e. (1, MxN) combination], and then based on the end application, it can be divided into a desired number of sub-modules connected in parallel. For a specified voltage output, N legs can be wired in series and the power requirement can be met by connecting M such groups in parallel (to regulate the current) for either high voltage, low current devices or low voltage, high current devices. This opens up avenues to tailor the module such that it is electrically impedance matched or load matched to the end application; load matching7,23,54 is essential to obtain maximum power from the module. This is a significant advantage for printable TEs and a key outcome of this work, as these modules are no longer reliant on power conditioning circuits (e.g., DC-DC converters or boost converters) to match the impedance of the module to the application. This is particularly advantageous for wearable devices and sensors as external circuits add to the cost and complexity of the system since they are additional components.19–21 

FIG. 5.

The fractal nature of the Hilbert curve allows for tessellating a TE module into identical sub-modules (shown in green) that can be divided along lines of symmetry in series, parallel, or a combination thereof. A total of 1024 legs can be connected in eleven different configurations; four examples of these configurations for a hexagonal leg layout include (a) one module with all legs in series, (b) two sub-modules in parallel, each having 512 legs in series, (c) four sub-modules in parallel, each having 256 legs in series, and (d) sixteen sub-modules in parallel, each having 64 legs in series.

FIG. 5.

The fractal nature of the Hilbert curve allows for tessellating a TE module into identical sub-modules (shown in green) that can be divided along lines of symmetry in series, parallel, or a combination thereof. A total of 1024 legs can be connected in eleven different configurations; four examples of these configurations for a hexagonal leg layout include (a) one module with all legs in series, (b) two sub-modules in parallel, each having 512 legs in series, (c) four sub-modules in parallel, each having 256 legs in series, and (d) sixteen sub-modules in parallel, each having 64 legs in series.

Close modal

We extend these wiring rules and interconnect patterns for closed-packed configurations with a large number of legs, as would be the case for organic devices. For this, we define a cell based on a four-leg basis (two p-type legs and two n-type legs) rather than the traditional two-leg basis that is widely used for TE devices. Using this basis, there are four possible unique arrangements of these closed-packed legs, resulting in four types of cells as shown in Fig. 6(a). We restrict the total number of cells in a module to being a power of four, resulting in a total number of legs of 4n, where n is the order of the Hilbert curve (e.g., n = 1,2,3,…). This allows us to connect adjacent cells rather than individual legs using a Hilbert curve. From a macroscopic perspective, the leg placement pattern appears more random than the traditional serpentine alternating p-n placement used widely, but it does contain a deeper order. As an illustration in Fig. 6(b), we use a Hilbert curve of order 2 to connect 16 cells comprising 64 TE legs, in total. The voltage output from this configuration is V = N(2SpnT using the four-leg basis. For a larger number of legs, we can tessellate the module into N cells connected in series and M groups connected in parallel for load matching, as we discussed previously. Figure 6(c) shows this module configuration for an electrically impedance matched device for various combinations of M and N achieving the requisite load matching. The key idea here is that the current and the voltage can be tuned to obtain the same power—as we increase M, the output voltage decreases, but the output current increases, since MxN is a constant. As stated previously, this load matching by the TEG is advantageous since it eliminates the need for external circuits to trade off current and voltage.

FIG. 6.

(a) A four-leg basis consisting of two n-type and two p-type legs in a hexagonal closed-packed layout to form a cell, and the four resulting unique cell configurations, (b) a Hilbert curve of order two connecting eight cells in series to form a TE module, and (c) various combinations of N cells in series and M groups in parallel for load matching to a range of end applications. Current and voltage are traded-off with each other to maintain the same power output in all these cases. MxN combination ID#s from 1 to 11 refer to the following (M,N) designators, respectively: (1,1024), (2,512), (4,256), (8,128), (16,64), (32,32), (64,16), (128,8), (256,4), (512,2), and (1024,1).

FIG. 6.

(a) A four-leg basis consisting of two n-type and two p-type legs in a hexagonal closed-packed layout to form a cell, and the four resulting unique cell configurations, (b) a Hilbert curve of order two connecting eight cells in series to form a TE module, and (c) various combinations of N cells in series and M groups in parallel for load matching to a range of end applications. Current and voltage are traded-off with each other to maintain the same power output in all these cases. MxN combination ID#s from 1 to 11 refer to the following (M,N) designators, respectively: (1,1024), (2,512), (4,256), (8,128), (16,64), (32,32), (64,16), (128,8), (256,4), (512,2), and (1024,1).

Close modal

Another advantage of using Hilbert patterns over Peano or other space-filling curves (e.g., serpentine curves) arises from wearable and flexible applications, where the applied temperature difference may not be uniformly distributed across all the TE legs (i.e., all legs may not be thermally in parallel). This can lead to a lower device performance as some legs are inactive. In this regard, among all the space-filling curves, the sub-module geometries that are obtained from Hilbert curves result in better utilization of heat because the mapping is localized, i.e., Hilbert curves ensure that the closely-spaced points in 1D stay closer together in 2D as well (i.e., they preserve the locality of points).55 Figure 7 illustrates this concept by graphically comparing two TE modules that have equal FFs and closed-packed positioning of p-n leg pairs, but have different interconnect patterns—one based on the Hilbert curve and the other based on the Peano curve. The number of TE legs that can be connected using a Hilbert curve of order n and a Peano curve of order m is 4n and 3m+1, respectively. Therefore, to have a similar number of legs for the modules, a Hilbert curve of order 5 is compared to a Peano curve of order 5, which have 1024 and 729 legs, respectively. Following the cutting lines in Fig. 7, we obtain four sub-modules (each having 256 legs) using the Hilbert curve and three sub-modules (each having 243 legs) using the Peano curve. Although the number of legs in the Hilbert sub-module is larger, its geometry provides a better localization for the connected legs by keeping them closer together [see the mapping in Fig. 7(a)]. This ensures that all the legs in the sub-module remain thermally in parallel, which is beneficial for device performance. This is another key outcome of this work, and to our knowledge, this is the first time, these concepts are presented for TE devices.

FIG. 7.

A comparison of (a) a sub-module based on the Hilbert curve that results in better localization of connected TE legs and (b) a sub-module based on a Peano curve. The two depicted TE modules have equal FFs, and legs are positioned in a hexagonal closed-packed layout. Both Hilbert and Peano curves are of order five, resulting in a total of 1024 and 729 TE legs, respectively. The highlighted region (shown in green) represents a sub-module in each system based on the mathematical mapping, showing that Hilbert mapping preserves the locality better.

FIG. 7.

A comparison of (a) a sub-module based on the Hilbert curve that results in better localization of connected TE legs and (b) a sub-module based on a Peano curve. The two depicted TE modules have equal FFs, and legs are positioned in a hexagonal closed-packed layout. Both Hilbert and Peano curves are of order five, resulting in a total of 1024 and 729 TE legs, respectively. The highlighted region (shown in green) represents a sub-module in each system based on the mathematical mapping, showing that Hilbert mapping preserves the locality better.

Close modal

In the last decade, the organic TE community has largely focused on developing new materials and improving the TE properties of polymers.9,56,57 Despite having zT values comparable to inorganics for low grade energy harvesting, the demonstrated device prototypes have shown low performance. This indicates that device design and module engineering also play a crucial role in realizing practical devices. Given the solution processability of organic materials, we are not restricted to utilizing fabrication techniques developed for inorganic semiconductors, and we can instead leverage the unique properties of organic materials to design high performance modules. In this work, we suggest that by positioning n- and p-type legs in a closed-packed hexagonal layout and wiring them based on a Hilbert space-filling curve pattern a better module performance can be achieved. The closed-packed layout increases the fill factor, and the fractal nature of the Hilbert curve pattern allows for tessellation into sub-modules for load-matching to a variety of end applications. Furthermore, the tessellations are naturally more tolerant to non-uniform temperature distributions as sub-modules are localized in a Hilbert mapping, which is beneficial for wearable electronics. These concepts can be readily implemented in devices that are based on the existing organic TE materials via R2R printing techniques for large-scale deployment at a low cost for energy harvesting applications. Although the discussions were mainly directed toward printable organic TE modules, it should be noted that the hexagonal packing and the Hilbert interconnect wiring extend to printable inorganic TE modules as well.28,33,35,58

See supplementary material for calculations of the (i) power density and optimum leg length, (ii) FF for a flat plate commercial TE module, and (iii) FF for a 2D hexagonal closed-packed structure.

This work was partially supported by PepsiCo, Inc. and the AFOSR under Award No. FA9550–15-1–0145. A. K. Menon would like to acknowledge support from the Qatar Science Leadership Program fellowship. The authors would like to thank Professor Bryan Boudouris and Edward Tomlinson at Purdue University for insightful conversations.

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Supplementary Material