Large harvested energy with non-linear pyroelectric modules

Coming up with sustainable sources of electricity is one of the grand challenges of this century. The research field of materials for energy harvesting stems from this motivation, including thermoelectrics1, photovoltaics2 and thermophotovoltaics3. Pyroelectric materials, converting temperature periodic variations in electricity, have been considered as sensors4 and energy harvesters5–7, although we lack materials and devices able to harvest in the joule range. Here we develop a macroscopic thermal energy harvester made of 42 g of lead scandium tantalate in the form of multilayer capacitors that produces 11.2 J of electricity per thermodynamic cycle. Each pyroelectric module can generate up to 4.43 J cm−3 of electric energy density per cycle. We also show that two of these modules weighing 0.3 g are sufficient to sustainably supply an autonomous energy harvester embedding microcontrollers and temperature sensors. Finally, we show that for a 10 K temperature span these multilayer capacitors can reach 40% of Carnot efficiency. These performances stem from (1) a ferroelectric phase transition enabling large efficiency, (2) low leakage current preventing losses and (3) high breakdown voltage. These macroscopic, scalable and highly efficient pyroelectric energy harvesters enable the reconsideration of the production of electricity from heat.


Note 1. Multilayer capacitor inner structure
Here we show the characteristics of the 0.5 mm thick PST multilayer capacitor (MLC). More details are available in Nouchokgwe et al. [1] Characteristics of 1 mm thick PST-MLCs can be found in [2] .

Note 2. X-Ray Diffraction of PST MLC
The B-site cation order Ω plays an important role in PST electrocaloric properties. Its extraction is obtained by comparing the (111) and (200) X-Ray diffraction peaks collected in reflexion geometry. In our experiment, the 2θ range was 15°-60°. The step increment was 0.01° with a collection duration of 2s. To be relevant, the extraction of Ω requires that PST is randomly oriented, which was obtained by crushing one MLC in order to obtain a powder. Fig. S2 shows the peaks (111) and (200) of PST powder. After [3,4] , Ω is obtained by the following equation

Note 3. Calorimetric measurements of PST MLC
The specific heat Cp of one 0.5-mm thick MLC has been obtained with a Mettler Toledo 3 Differential Scanning Calorimeter. One MLC is too heavy to allow reliable Cp values. Therefore an 18 mg-piece of MLC has been collected to enable quantifiable measurements. We deployed the standard differential method using sapphire as a reference. The results are displayed in Fig. 3.1. We can clearly see the first-order phase transition occurring in PST at 20°C while heating.
There is a thermal hysteresis because the phase transition happens at 15°C while cooling. The associated latent heat is around 550 J kg -1 . The background value of Cp is 300 J kg -1 K -1 .
More details are available in Nouchokgwe et al. [1] Supplementary Figure 3.1 I Specific heat Cp of a 0.5mm thick PST-MLC obtained from Differential Scanning Calorimetry. Data collected while heating (orange) and cooling (purple).

Isofield measurements
Isofield measurements are heat flow measurements at constant applied field when sweeping in temperature. These measurements presented in Fig. S3.3a, were done at a heating rate of 5 K min -1 on a customized DSC from Mettler Toledo. To be able to apply an electric field, the entire PST-MLC (scheme in Fig. S1.1a) of approximately 300 mg was used for this investigation. The sample mass surpasses the maximum mass (~30 mg) required to observe a good and relevant signal in DSC. Therefore, the signal measured ( Fig. S3.3a) is quantitatively incorrect. However, the position of the peak is correct as we went sufficiently slow (5 K min -1 ) to get accurate values of the transition temperature. In a temperature range between 283 K and 323 K, constant electric fields were applied using a source meter (Keithley 2410). From isofield measurements, we constructed the ST diagram ( Fig. S3.3b) on heating of PST-MLC. Figure 3.2 I Isofield measurements in a PST-MLC of 300 mg. The red and blue curves are measured respectively on heating and cooling. Due to the mass of the sample which is an order of magnitude larger than the maximum required mass, the DSC signal is incorrect. Hence, no values are displayed on the y-axis in these plots. a Isofield measurements at different electric fields. At 0 kV cm -1 , we observe single peaks on heating and cooling as already seen in Fig. S3.1 showing heat flow measurements on an 18 mg piece of PST-MLC. Despite the difference in mass in both plots, one can see that the heat flow peaks at the same position at 0 kV cm -1 . Therefore, proving 5 K min -1 as a good heating rate to get accurate values of temperature in 300 mg of PST-MLC. The application of an electric field decouples the peak at 0 kV cm -1 into two peaks. As shown in Fig. S3.3a, one of these peaks shifts toward high temperatures with the increasing electric field. This peak (active) corresponds to the active area of the MLC where the electrodes overlap, therefore where the field is being applied (structure in Fig. S1.1a). The other peak (inactive) under applied electric field remains at the same position as the peak at 0 kV cm -1 . This represents the inactive region of the MLC which is unresponsive to the electric field. Moreover, the active peak sensitive to the electric field gets broader (second-order like) at higher electric fields. b S(T) diagram of PST-MLC on heating at different electric fields 0, 13, 26 kV cm -1 . This diagram was constructed from data in Fig. S3.3a using the equations described above. Under applied electric field we observed two jumps at two different temperatures. The lowtemperature jump is insensitive to the electric field (inactive region of MLC) as it occurs at the same temperature as at 0 kV cm -1 . The high-temperature jump corresponds to the active region. This jump is shifted towards high temperatures with the increasing electric field.

Note 4. Reproducibility of Olsen cycles
Here we show reproducibility of Olsen cycles by running several cycles under the same conditions consecutively.

Supplementary Fig. 4a
Charge q of one 1 mm PST-MLC as a function of the applied voltage V at 70°C (blue), first cycle at 5°C when the sample is not poled (light green) and second cycle at 5°C (dark green). b 20 cycles energy curve of 1 mm PST-MLC as a function of time with isofield legs at 0 and 80 kV cm -1 (300 V) and isothermal legs at 5°C and 70°C (time resets after each cycle). The inset shows the energy harvested at the end of each cycle.

Note 5. Olsen cycle giving 4.43 J cm -3
Here we show an Olsen cycle in a 0.5 mm thick PST-MLC showing the highest energy density harvested (4.43 J cm -3 ). The total energy harvested is 74.9 mJ (0.0749 J). The total active volume of PST is 16.9 mm 3 (0.0169 cm 3 ). Figure 5. Olsen cycle in a 0.5 mm thick PST-MLC. The applied voltage is 750 V and the isothermal legs 5 °C and 180 °C. The total energy harvested is 74.9 mJ, which corresponds to an energy density of 4.4 mJ cm -3 .

Note 6. Leakage current in PST-MLCs
We measured the leakage current of a 0.5 mm thick PST-MLC at constant field (195 kV cm -1 , 750 V) and different temperatures (Fig S6.1). The raw experimental data was fitted with Curievon Schweidler empirical law (Fig. S6.2) and finally the leakage current plotted as a function of temperature ( Fig. S6.3). Leakage current time evolution after fitting the experimental data with Curie-von Schweidler empirical law [5] . Theses graphs show that the leakage current of our PST-MLC sample is <10 -7 A at 750 V applied and temperatures lower than 180 °C. Note that for temperatures T<140 °C, the precision of our sourcemeter is not enough to capture the leakage current. The fluid circuit is divided into two circuits (yellow tube and white plug-in connectors), each with their own cold bath and fluid reservoir. The hot reservoir is shared by the two fluid circuits, with no fluid returning so that its temperature it is not altered. Two pinched valves select accordingly whether to pump from the cold bath (to cool down the PST-MLCs prototypes) or the hot reservoir (to heat them up). The 8 prototypes are connected electrically in parallel and are charged and discharged from a sourcemeter. Thermocouples are added at inlet and outlet of 2 prototypes to monitor temperature. Sourcemeter, valves, thermocouples and pump are governed and synchronized with a python script, so the system operates Olsen cycles. All 8 prototypes were operated simultaneously.

Supplementary Fig. 8.2
Energy of the Olsen cycle run in HAR 2 vs time. In cycle's step A, the PST-MLCs in HARV2 are charged to 500 V (E = 130 kV cm -1 ) at a current of 15 mA and temperature Ti = 11 °C. The energetic cost for that is 2.3 J. At B, the hot fluid starts circulating and heats up the PST-MLCs. As a result, some HARV2 starts harvesting some energy, reaching -6 J at C, when the PST-MLCs reach thermal equilibrium with the hot fluid at a temperature of 98°C. Right after, PST-MLCs are discharged, and the energy harvested value reaches 11.2 J (D). At this point, the cold fluid starts circulating, cooling down the temperature of the PST-MLCs so that another cycle can be started again.

Note 9. Olsen cycles in HARV3
Olsen cycle in one single 0.5 mm-thick PST-MLC inserted in one prototype, similarly to what is described for HARV1 and HARV 2. This specific small prototype has been fabricated to estimate how fast the heat exchange can happen with these MLCs and the dielectric fluid we have used all along this study.  Fig. 2b where 3.1 J were harvested in 57 s period using silicone oil as the heat exchange fluid and a parallel plate matrix of 7 columns and 4 rows. The blue square represents the corresponding values obtained with our FEM simulations with the same fluid and PST-MLC matrix. The green squares represent the corresponding values when using water as a heat exchange fluid and the same PST-MLC matrix. In the dark green triangles, water was used as a heat exchange fluid, but the PST-MLC matrix was reversed to 4 columns and 7 rows. In the dark green pluses, water was used as a heat exchange fluid, the PST-MLC matrix consisted of 4 columns and 7 rows and the time the fluid needs to travel from the reservoir to the harvester τw was neglected (τw = 0).

Note 11. Autonomous energy harvester
The main objective of this autonomous system is to spontaneously harvest energy by thermal cycling when the pyroelectric material reaches a pre-determined temperature. The energy harvested from the PST-MLCs is efficiently recovered and utilized for charging our system for the subsequent cycles. Figure S11.1 is the block diagram of our harvester.

Electronic components in the autonomous system
Two PST-MLCs (10.4 x 7.2 x 0.5 mm³ connected in parallel) act as the heat harvester that will experience a Stirling cycle. Two reed relays (S2-05EU / S2-03PU) act as load switches to control the flow of current in the circuit. To step down the voltage from the harvester that reaches hundreds of volts, we employ a low voltage converter made of two diodes (BYW56-TR), an inductor (1140-122K-RC) and a multilayer storage capacitor (FA22X7R1E226MRU06) in the system (described later in Fig. 11.3). In addition, we have a DC/DC converter (LTC 3588-1) to deliver a regulated DC output voltage at 3.3 V. The system also embeds a low power consuming microcontroller (ATtiny 45), a temperature probe (TMP36FSZ) and a boost converter (LT8410) to ensure the autonomous charging and discharging of the system as a function of temperature.
There is no battery in all this system.

Description of the autonomous pyroelectric energy harvesting system
For all this description, please refer to Figure 11.1. A Keithley 2400 is used to initially charge the storage capacitor (Ta capacitor storage element in Fig.11.1) at room temperature. This initial energy initiates the electronic components in the autonomous system. Once this initial energy is provided, the system runs autonomously.
The energy from the storage capacitor will tread through the LTC 3588-1 voltage regulator, which delivers a regulated DC voltage of 3.3 V. The output of LTC 3588-1 serves as the input for the ATtiny 45 microcontroller (MC). Note that the minimum operating voltage of the LTC is 4 V. Hence, the voltage in the storage capacitor must always be greater than 4 V for the functioning of the autonomous pyroelectric energy harvesting system. Hence, we can simultaneously execute the Stirling cycle and monitor the voltage in the system.
If the temperature of the material is above the set threshold temperature in the MC, the MC will spontaneously discharge PST-MLCs in the storage capacitors through the low voltage converter by closing the load switch S1 (reed relay S2-05EU / S2). Indeed, the voltage from PST-MLC (Vfinal) must be stepped down using a low voltage converter before storing the energy in the capacitor.
For this system to be sustainable, the energy harvested and stored in the capacitor must be greater than the energy required for running the autonomous system.

Low voltage converter
The low voltage converter steps down the voltage from the pyroelectric material and delivers a low voltage output. It consists of a reed relay, an inductor and two diodes (cf Fig. 11.3). A low voltage converter operates by storing the energy in the inductor in the form of a magnetic field.
The working mechanism of the low voltage converter is akin to the buck converter, which is a DC/DC step-down converter.

Supplementary Figure 11.3. Schematics of the low voltage converter.
When the switch S1 is closed, the current from PST-MLC passes through the diode D1 towards the inductor. The inductor opposes the changing current by creating a voltage drop across its terminals. The energy is stored in the inductor and then in the capacitor. All this time, the diode D2 is reverse biased, and thus prevents flow of current. When the switch S1 is opened, the polarity of the inductor reverses due to the collapsing field and the diode D2 becomes forward biased. In this way, the energy from the PST-MLC is efficiently stepped down and stored in the capacitor. The next step was to estimate the energy recovered in the storage capacitor after stepping down the voltage from PST-MLC using the low voltage converter. For this study, the Stirling cycle was executed for five different temperature spans. The input voltage and initial temperatures were 20 V and 5 °C respectively. One tantalum electrolytic capacitors (C = 10.5 μF and voltage rating of 16 V) was used as storage capacitor. The energy in the storage capacitor was calculated using Energy harvested from the PST-MLC (full blue squares) and energy stored in a Ta storage capacitor after transfer from the PST-MLC (empty blue squares) when Stirling cycle was executed for different temperature spans. The initial temperature is always 5 °C and the final temperatures of the Stirling cycle varies from 55°C to 95°C. Vin is the initial voltage applied to the PST-MLC at the beginning of the Stirling cycle (starting at low temperature). The right-hand Y-axis is the ratio between the harvested and stored energies, which corresponds to the percentage of energy collected after this low voltage conversion. The top X-axis is the final temperature of the Stirling cycle. And the bottom X-axis is the final voltage reached across the PST-MLC. Note that values as high as 550 V can be reached, while the initial voltage is only 20V.

Results of the autonomous energy harvester
A Stirling cycle of the entire autonomous energy harvester described in Fig. 11.1 was carried out for a temperature span of 90 °C, from -5 to 85° C. The threshold temperatures in the MC was programmed at 5°C and 60 °C. Only when the temperature is away from these limits, the boost and shutdown event occur spontaneously. In this study two PST-

Note 12. Efficiency of Olsen cycles in PST-MLCs
The figure of merit is defined as the ratio of harvested electrical energy density over input heat density where is calculated from integrating the area between two DE-loops at the two oscillating temperatures of a given Olsen cycle (Fig. S12.1). These DE-loops have been measured experimentally with a Keithley sourcemeter 2410. The electric displacement field D is calculated by numerical integration of the current supplied over time (electric charge) and dividing it by the active area (0.489 cm 2 ) and number of active layers (9) of a 0.5 mm thick PST-MLC (Table S5).
Supplementary Figure 12.1 Electric displacement field Delectric field E loops for a 0.5 mm thick PST-MLC at temperatures ranging from 5 to 100 °C.
The amount of heat absorbed by the material has two contributions: 1) the Olsen heating leg BC, in which the sample undergoes a temperature variation, namely ∆ , and 2) the entropy change associated to the removal of the electric field at the leg CD (electrocaloric effect). These can be expressed as with ′ being the specific heat background value, measured experimentally with Differential Scanning Calorimetry (DSC) (SM note 3). Unfortunately, 2 cannot be measured quantitatively in our DSC because the mass of the PST-MLCs is too large (~300 mg vs the maximum of 20 mg that can be placed in the DSC). Hence, we assume ℎ ∆ →0 ≅ ′∆ →0 , which is a very good approximation, as shown in [6] . Note that ∆ →0 is the electrocaloric (EC) effect under adiabatic conditions. Thus, becomes with ′ = 300 J kg -1 K -1 and = 8570 Kg m -3 (measured experimentally in our laboratory, SM note 3). To ensure an upper bond for , we take the highest value of ∆ at 750 V applied. This is ∆ = 3.10 ± 0.11 K (at = 30 °C, SM Fig. 12.2). Under these conditions, the sample is in the ferroelectric phase before it is discharged (V = 750 V), and it transitions to the paraelectric phase once it is discharged (V = 0 V). The term ′ ∆ →0 is thus 986 J kg -1 , notably larger than the latent heat associated to the phase transition when crossed with temperature (L = 572 J kg -1 ) because it includes the electric field contribution (dipolar entropy). We assume then ′ ∆ →0 = 986 J kg -1 constant to all points. This gives us an upper bond for , and thus a lower bond for efficiency. Note that the latent heat L = 572 J kg -1 does not vary with the electric field applied as our previous study on bulk PST has shown [6] . Instead, the effect of applying an electric field is to shift the transition temperature TC towards higher temperatures.
It is also interesting to consider the upper bound Carnot efficiency that reads Measuring conditions: Aixacct tool measuring capacitance versus temperature at 500 Hz. The temperature has been varied from -4°C to 120°C and then back to -4°C.
The capacitance versus temperature clearly shows the phase transition that occurs in PST around 20°C (TC). This observation is perfectly in line with the measurements performed with Differential Scanning Calorimetry in Supplementary Note 3. Below TC, PST is ferroelectric.
Beyond TC, PST is paraelectric. Below TC, there is a slight hysteresis between the data collected while heating and cooling, though the difference is barely visible.
Maximum harvested energy density Nd in J cm -3 of representative examples from the literature performed on actual Olsen cycles at a given electric field E, initial temperature Ti and temperature span ∆Tspan.

Supplementary Table 5
Properties and dimensions of 1 mm thick PST-MLCs, taken from [2] , and 0.5 mm ones, measured by us.