Barium calcium zirconium titanate thin film-based capacitive thermoelectric converter for low-grade waste heat

TL;DR

This paper introduces a new capacitive thermoelectric device using barium calcium zirconium titanate thin films to convert low-grade heat into electricity.

Contribution

The novelty lies in using specific barium calcium zirconium titanate thin films to improve the efficiency of capacitive thermoelectric converters.

Findings

The device achieved power outputs of 0.06 mW to 0.3 mW with temperature differences of 5–20°C.

It performed under a dynamic workload of an Intel E5-2630 microprocessor.

The material shows potential for low-grade waste heat conversion.

Abstract

A capacitive thermoelectric device can harvest thermal energy and convert it to electrical energy by employing a temperature-dependent dielectric material whose permittivity sharply changes with temperature. Electricity can be generated by fluctuating the temperature of the capacitor. Currently, capacitive thermoelectric devices are not broadly used, which can be attributed to the low efficiency of the existing solutions, the lack of dielectric materials with suitable temperature non-linearity of the dielectric permittivity, and the complexity of modulating heat flux on the dielectric material. Here, we propose a device based on (Ba0.85Ca0.15)(Ti0.92Zr0.08)O3 and (Ba0.73Ca0.27)(Ti0.98Zr0.02)O3 thin films. It demonstrates power outputs of 0.06 mW to 0.3 mW across ΔT = 5–20 °C at 15 V bias, and a dynamic workload of an Intel E5-2630 microprocessor. These results highlight the potential of barium calcium zirconium titanate thin films to be used for a capacitive thermoelectric converter.

Figures

Schematic diagram of a capacitive thermoelectric convertor which consists of a capacitor with a temperature non-linear dielectric material, an external charging source (ECS) and an external circuit (e.g., load resistor R_L_). Its operational principle is based on the Clingman thermodynamic cycle. Initially, at point 1, starting at a temperature T_1,_ the capacitor is charged using an external source. After that, the switch is opened at point 2, and the system is gradually heated to reach temperature T_2,_, while the electric charge remains constant. At the same time, the temperature-dependent

XPS spectra fitting results of Ba, Ca, Zr and Ti atoms of Ba0.73 thin film. (a) Ba3d XPS spectra region, b) Ca2p XPS spectra region, c) Zr3d spectra region and d)Ti2p XPS spectra region.

XPS spectra fitting results of Ba, Ca, Zr and Ti atoms of Ba0.73 thin film. (a) Ba3d XPS spectra region, b) Ca2p XPS spectra region, c) Zr3d spectra region and d)Ti2p XPS spectra region.

Capacitance as a function of temperature at various frequencies for samples a) Ba0.73, b)Ba0.85 and at various DC bias voltages for samples (c) Ba0.73, d) Ba0.85. Both samples show similar Curie temperatures and a capacitance that sharply changes with temperature.

The estimated output power of a thermoelectric converter operating with a ΔT = 5, 10 and 20, as a function of applied bias voltage for samples (a) Ba0.73, and (b) Ba0.85.

Temperature of an Intel E5-2630 microprocessor as a function of the power consumption. The numbers in the graphs represent (a) the workload in % and (b) the number of active cores.

Full text

Introduction

Waste heat is classified into high, medium, and low grades based on the temperature range (see Table 1). 50% of the total waste heat falls in the low-grade category, which is the most challenging to recover compared to medium-grade or high-grade heat^1–4^. The heat emitted from electronic devices is considered low-grade waste heat. For example, a typical cell phone gives off around 0.2 W of heat when idle and closer to 1 W while making calls or running processor-intensive applications^5^. The heat generated by a tablet or laptop is much higher. Almost all of this heat is never recovered; therefore, focusing on the thermal characteristics of smaller mobile devices is a promising future development, especially since the number of mobile devices is expected to reach 18.22 billion worldwide by 2025, an increase of 4.2 billion devices compared to 2020 levels^6^.

Table 1. Emitted heat sources classification.GradeTemperature rangeTypical SourceHigh> 650 °CDirectly combustion processMedium230–650 °CExhaust of combustion unitsLow< 230 °Cproducts and the equipment of process units

At present, the solid-state devices used for capturing low-grade waste heat rely on the inherent properties of the materials employed. These materials can generate electricity from heat through thermoelectric (Seebeck effect), pyroelectric (spontaneous polarisation), or capacitive (dielectric permittivity) processes. However, the main obstacle arises from the fact that low-grade heat harvesting happens with very low efficiency. One potential solution is instead of enhancing the conversion efficiency, to increase the conversion rate by employing thin film-based devices.

A thermoelectric generator (TEG) is a solid-state device that directly converts temperature gradient into electricity through the Seebeck or thermoelectric effect. A thermoelectric device consists of two dissimilar thermoelectric materials joined at their respective ends by an n-type and a p-type semiconductor. The two thermoelectric materials must be thermally parallel and in electrical series^7,8^.

The conversion efficiency of a thermoelectric device mainly depends on the materials’ figure of merit^9,10^.

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:ZT=\frac{{S}^{2}\sigma\:\:T}{\kappa\:}$$\end{document}

Where S, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\:\sigma\:$$\end{document} , T and κ are Seebeck coefficient, electrical conductivity, absolute temperature, and thermal conductivity, respectively. The left side of the equation, ZT, represents the dimensionless thermoelectric figure of merit—a key parameter to evaluate a material’s intrinsic efficiency in thermoelectric energy conversion. It combines essential transport properties into one comprehensive, unitless measure of a material’s capacity to convert thermal energy into electrical energy (and vice versa). A higher ZT indicates better thermoelectric performance, making the material more suitable for practical uses like power generation and solid-state cooling. Because ZT is dimensionless, it allows for straightforward comparison of thermoelectric efficiency between different materials and temperature ranges. Generally, materials with ZT below 1 have limited efficiency, while those with ZT above 2 are considered highly promising for advanced thermoelectric applications. Simultaneously attaining good electrical properties and low thermal conductivity will lead to a high zT value. Most of the impressive advancements in zT have been achieved by effectively decreasing thermal conductivity through the enhancement of phonon scattering in material structures. This includes mechanisms such as dislocations, grain boundaries and interfaces^1,11–13^.

Yang et al.^14^ conducted a study in which a thin-film thermoelectric generator was created using Sb_2_Te_3_. They grew the thin film on 1 mm thick Pb(Zr_0.54_Ti_0.46_)O_3_ ceramic sheets using magnetron sputtering. Their thermoelectric generator achieved output power and output power density of 342.12 nW and 2.22 mW/cm^2^, respectively at ΔT = 42 K. In the work of Karthikeyan et al.^15^ 100 nm of both p-type tin telluride(SnTe) and n-type lead telluride (PbTe) thin films were fabricated using thermal evaporation grown onto a flexible polyimide substrate. The thermoelectric generator is based on SnTe–PbTe, consisting of 4 p-n pairs interconnected by a 50 nm thick aluminium film. Their results showed that the fabricated TEG produced 8.5 mW/cm^2^ at a temperature difference of ΔT = 120 °C. Ren et al.^16^ utilised a thermal evaporation process to create 14 thermoelectric (TE) chips on a polyimide film. Each thermoelectric chip was constructed by alternately depositing 4 pairs of thin films of Bi_0.5_Sb_1.5_Te_3_ (*p-*type) and Bi_2_Te_2.8_Se_0.3_ (*n-*type) onto the polyimide film using thermal evaporation. The results showed that for a 93 °C temperature gradient, the fabricated thermoelectric chips generated an output power of 18.625 µW/cm^2^.

Pyroelectric and capacitive thermoelectric devices can both convert heat fluctuation to electrical energy. They use dielectric materials with specific crystal structures that exhibit a unique axis of symmetry and lack a centre of symmetry; these are referred to as “polar” materials^17–21^. These materials show a temperature and electrical field dependence on the spontaneous polarisation and the dielectric permittivity.

A pyroelectric device operation is based on the material’s spontaneous polarisation caused by temperature change, which leads to variations in its surface charge density. The pyroelectric coefficient, denoted as p(T), represents the rate of change of spontaneous polarisation in the material with respect to temperature without the influence of an applied electric field or stress^22,23^.

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p(T)=d PS/dT$$\end{document}

The electric current ip generated during the heat fluctuation ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\frac{dT}{dt}$$\end{document} ) of a pyroelectric device connected to an external circuit with electrode surface area A can be written as follows:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{i}_{p}=A\:p\left(T\right)\frac{dT}{dt}\:$$\end{document}

Ashwath Aravindhan reported lead scandium tantalate, Pb(Sc_1/2_Ta_1/2_)O_3_ (PST) thin film for pyroelectric energy conversion^24^, where it is phase transition temperature is around room temperature. The fabricated thin film with a thickness of 165 nm was grown on a c-sapphire substrate using a chemical solution deposition. The maximum energy density achieved is 9.1 J/cm^3^ per cycle when there is a temperature change (ΔT) of 150 K. Bhatia^25^ fabricated a 200 nm thick BaTiO_3_ thin-film capacitor fabricated using pulsed laser deposition with top and bottom epitaxial SrRuO_3_ electrodes, grown on a GdScO_3_ (110) single crystal substrate. They have achieved a maximum power density of 3.0 W/cm^3^ working at a temperature range of 20–120 °C.

Pandya^26^ fabricated 150 nm 0.68Pb(Mg_1/3_Nb_2/3_)O_3_–0.32PbTiO_3_ (PMN–PT)/20 nm Ba_0.5_Sr_0.5_RuO_3_ heterostructures by pulsed laser deposition grown on (110)-oriented, single-crystalline NdScO_3_ substrate. Their results showed a maximum energy density of 1.06 J/cm^3^ at a temperature difference of ΔT = 10 K.

For a capacitive thermoelectric device, the value of the polar dielectric material’s permittivity changes with temperature. This will vary the capacitance value and, as a result, the electrical energy stored in the capacitor^27–30^. The fundamental concept behind converting thermal to electric energy (W) stored in a capacitor with capacitance (C) for a capacitive thermoelectric device is as follows:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:W=\frac{{Q}^{2}}{2C}$$\end{document}

Where Q is the electrical charge in the capacitor, which increases because of thermal energy when the capacitance value decreases, assuming the charge of the capacitor stays constant. The operational principle of capacitive converters based on the Clingman thermodynamic cycle is illustrated in Figure 1. Initially, at point 1, starting at a temperature T_1,_ the capacitor is charged using an external source. After that, the switch is opened at point 2, and the system is gradually heated to reach temperature T_2,, while the electric charge remains constant. At the same time, the temperature-dependent permittivity of the dielectric material changes, which causes an increase in the potential in the capacitor from V_1 to V_2_. When the switch is moved to position 3, the voltage built in the capacitor pushes the electrical charges through the external circuit (e.g., the load resistor).

Fig. 1. Schematic diagram of a capacitive thermoelectric convertor which consists of a capacitor with a temperature non-linear dielectric material, an external charging source (ECS) and an external circuit (e.g., load resistor R_L_). Its operational principle is based on the Clingman thermodynamic cycle. Initially, at point 1, starting at a temperature T_1,_ the capacitor is charged using an external source. After that, the switch is opened at point 2, and the system is gradually heated to reach temperature T_2,, while the electric charge remains constant. At the same time, the temperature-dependent permittivity of the dielectric material changes, which causes an increase in the potential in the capacitor from V_1 to V_2_. When the switch is moved to position 3, the voltage built in the capacitor pushes the electrical charges through the external circuit (e.g., the load resistor).

After the capacitor has been discharged, the system undergoes a cooling process to reach temperature T_1_, when the capacitor is charged again, and the cycle is repeated. Although pyroelectric devices and capacitive thermoelectric converters share similarities, the distinction lies in the way the change of temperature is utilised. In a pyroelectric device, the temperature change is used to generate electrical charges (Olsen thermodynamic cycle), while in a capacitive TE converter, it is used to push the charges stored in the capacitor (Clingman thermodynamic cycle). Further details about Clingman and Olsen thermodynamic cycles can be found elsewhere^31^.

The first mention of utilising the non-linear dielectric behaviour with temperature to convert energy was in 1961^27^. W. H. Clingman and R.G. Moore, Jr. proposed a design for a ferroelectric converter circuit based on barium titanate. They have found that power output can be increased by adjusting the temperature difference and electrical field strength. Their findings suggest that these converters can be used in applications that require lightweight devices with a periodic heat source for operation, such as a spinning space vehicle that undergoes repeated cycles of heating and cooling as a result of regular exposure to solar radiation, providing an optimistic vision for the potential of energy conversion in the years to come.

A year later, Childress^28^ estimated a power-generating capacity of 0.1 cm thick barium titanate with a 30 °C temperature difference. They calculated a power-generating capacity of roughly 32 W/lb (70.6 W/kg) per temperature cycle, per sec. In their analysis, the periodic heat transfer of the dielectric layer is a serious limitation for converting thermal energy. It is worth mentioning that a capacitive thermoelectrical device is electrically identical to a dielectric bolometer, which converts thermal to electrical energy for IR sensing^32,33^.

Both of these early studies on barium titanate ceramics showed that achieving fast heating-cooling cycling of such a device is challenging. However, using a material with non-linear temperature dependence in thin film form will significantly increase the speed of the heating-cooling cycle and generate a useful amount of power based on the increased conversion rate rather than efficiency.

Nevertheless, currently, the widespread application of capacitive thermoelectric devices is limited by the lack of dielectric materials in thin film form with sufficiently strong temperature-dependent permittivity. Moreover, generating a high frequency modulated heat flux suitable for application to these materials remains a considerable technical challenge.

To the best of our knowledge, the available data in the literature regarding thin-film-based capacitive TE converters is based on modelling. V.A. Volpyas et al.^29^ made a thermodynamic analysis of a capacitive thermoelectric converter based on barium strontium titanate ferroelectric film incorporated into a metal–insulator–metal (MIM) structure. Their device comprises a heat flux modulator, heater, and thin film capacitor on a cooled substrate surface. They have further evaluated the generated electrical power as the permittivity of the MIM changes under periodic heating and cooling cycles. This study has found that the electrical power generated is governed by the steepness of permittivity dependence on the temperature and the thermocycling frequency. Ferroelectric materials exhibit spontaneous electric polarisation that can be reversed by applying an external electric field within a temperature range.

These materials have a phase transition temperature from the ferroelectric phase (with the presence of spontaneous polarisation) to the paraelectric phase (absence of spontaneous polarisation). The phase transition temperature is known as the Curie temperature. Ferroelectric materials having a first-order phase transition show a sharp change of permittivity with temperature, where the maximum permittivity value is at the Curie temperature. Also, dielectric loss in the paraelectric phase is lower in comparison to the dielectric loss in the ferroelectric phase, where the stress-strain resulting from extrusions in the domain walls will convert electrical energy into heat^34,35^. Choosing a ferroelectric material with a sharp change of permittivity with a temperature operating at the paraelectric phase will increase the harvested energy and optimise the heating-cooling cycle.

The research result achieved by Liu et al. on the lead-free barium calcium zirconium titanate (BCZT) ferroelectric system is quite attractive since it offers an alternative to PZT-based systems. According to their findings, this new system exhibits a remarkably high piezoelectric coefficient and dielectric constant, which could benefit various applications^36^. Their method for achieving a high piezoelectric coefficient and a non-linear dielectric behaviour with temperature involves balancing the materials’ stoichiometry near a composition-induced phase transition between two ferroelectric phases. This transition is referred to as the ‘morphotropic phase boundary’ or MPB^36^.

Ferroelectric compositions near morphotropic phase boundaries (MPBs) exhibit exceptional properties that surpass those found in compositions situated farther from these boundaries. Additionally, the ferro-para transition induced by composition at MPBs can destabilise polarisation states, allowing for easy rotation of polarisation direction through external stress or electric field^37^. Consequently, it will result in high piezoelectricity and permittivity^38^. This resulted in a rise of investigations of BCZT in thin film form for applications in piezoelectric^39^, optical-thermal sensors^40^, and magneto-dielectric devices^41^. Nevertheless, the temperature-dependent non-linear dielectric properties of thin film materials near the MPB have not yet been investigated for use in capacitive thermoelectric devices.

Almost all of today’s electronic devices are built using semiconductor materials, which has been the case since the middle of the 20th century^42^.

Although the variety of materials keeps widening, silicon-based technologies remain by far the dominating choice for current and future electronic devices. At present, the most important application domains include Internet-of-things edge (IoTe) devices, cyber-physical systems, smartphones, personal augmentation devices, large-scale computers, and distributed systems^43^.

Normally, silicon-based semiconductor components are designed as low-power electronic devices with supply voltage ranging from 0.6 V to less than 20 V. For example, one of the most popular current solutions – the Field-Effect Transistor (FET) technology – operates with a voltage of 0.7 V at the device level, projected to trend down slowly to 0.6 V over the next decade^44^.

By contrast, the supply voltage for the traditional Complementary Metal Oxide Semiconductor (CMOS) technology is the only one that goes beyond 6 V, covering the range from 3 to 18 V. However, operation above 15 V is not recommended because of high dynamic power consumption and the risk of noise spikes on the power supply exceeding the breakdown voltage of around 20 V^45^. Therefore, the supply voltage range for our analysis was selected between 0.5 V and 15 V.

In this paper, we have estimated the power output of a capacitive thermoelectric device based on thin films with stoichiometry located near the phase boundary (Ba_0.73_Ca_0.27_)(Ti_0.98_Zr_0.02_)O_3_, referred further as Ba_0.73_ and (Ba_0.85_Ca_0.15_)(Ti_0.92_Zr_0.08_)O_3_, referred further as Ba_0.85_ and have assessed their suitability to be used to harvest low-grade waste heat.

Results and discussion

Fig. 2. XRD pattern of (a) Ba0.73 and (b) Ba0.85 thin films, respectively. They confirm that both thin films are grown on STO substrate epitaxially with sole (00I) orientation.

Figures 2 (a) and (b) show the XRD pattern of thin films Ba_0.73_ and Ba_0.85_; respectively. They confirm that both thin films are grown on STO substrate epitaxially with sole (00I) orientation. Table 2 lists the lattice parameters and residual strain in each thin film. Both films show relatively low residual strain, which is a result of the deposition condition and the low lattice misfit.

Table 2. The Lattice parameters and residual strain (in-plane and out-of-plane) in the epitaxially grown thin films.CompositionLattice parameters (A °)Residual Strainacin-plane a%out-of-plane c%Ba_0.73_3.9604.008−0.650.72Ba_0.85_3.9904.040−0.190.69

Fig. 3XPS spectra fitting results of Ba, Ca, Zr and Ti atoms of Ba0.73 thin film. (a) Ba3d XPS spectra region, b) Ca2p XPS spectra region, c) Zr3d spectra region and d)Ti2p XPS spectra region.

X-ray photoelectron spectroscopy (XPS) was used to characterise the BCZT thin films and confirm their stoichiometry. Figures 3 and 4 show peaks corresponding to photoemissions from the core-level of XPS spectra for Ba 3 d, Ti 2p, Ca 2p, and Zr 3d. These peaks are referenced in the literature to validate the chemical composition of BCZT thin films^46–48^. Based on the XPS spectra, the atomic concentrations were calculated and the results relevant to Ba, Ca, Zr and Ti are presented in Tables 3 and 4 for both thin films. Also, the XPS spectra were used to calculate the cationic site occupancy ratio (B/A site) for the perovskite ABO3-type BCZT unit cell. It was found to be (Ti + Zr/Ba + Ca) = 0.97 for Ba_0.73_ thin film and 0.98 for Ba_0.85_ thin film. These results for both thin films confirm that the chemical composition is as expected.

Fig. 4XPS spectra fitting results of Ba, Ca, Zr and Ti atoms of Ba0.73 thin film. (a) Ba3d XPS spectra region, b) Ca2p XPS spectra region, c) Zr3d spectra region and d)Ti2p XPS spectra region.

Table 3. Elemental composition (Atomic %) of the sample Ba0.73.ElementExpectedMeasuredBa0.730.74Ca0.270.28Zr0.020.03Ti0.980.96

Table 4. Elemental composition (Atomic %) of the sample Ba0.85.ElementExpectedMeasuredBa0.850.84Ca0.150.18Zr0.080.09Ti0.920.91

Fig. 5. Capacitance as a function of temperature at various frequencies for samples a) Ba0.73, b)Ba0.85 and at various DC bias voltages for samples (c) Ba0.73, d) Ba0.85. Both samples show similar Curie temperatures and a capacitance that sharply changes with temperature.

Figure 5 (a) and (b) show the capacitance as a function of the temperature applying AC voltage while, Fig. 6 (c) and (d) show the DC bias voltage measured for samples made using both types of thin films. They both show a capacitance that sharply changes with the temperature, with a maximum (corresponding to the Curie temperature of the ferroelectric material) at similar temperatures. This is a typical behaviour for ferroelectric thin films, corresponding to the ferroelectric–paraelectric phase transition. Beyond this temperature, the capacitance decreases sharply, reflecting the loss of spontaneous polarisation.

The capacitance values for samples Ba_0.73_ and Ba_0.85_ change around four and seven folds, respectively. These results indicate that these films are good candidates for thin film-based capacitive thermoelectric converters.

Fig. 6. The estimated output power of a thermoelectric converter operating with a ΔT = 5, 10 and 20, as a function of applied bias voltage for samples (a) Ba0.73, and (b) Ba0.85.

The power generated by a capacitive TE converter can be estimated as follows^30^:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\:\:\:\:P=0.5\cdot\:\left(k-1\right)\cdot\:{C}_{max}{\cdot\:V}^{2}\cdot\:f$$\end{document}

Where C is the capacitance, Cmax is the maximum capacitance value, C_min_ is the minimum capacitance value, k = Cmax/Cmin, V is bias voltage, and f is the frequency of temperature cycling.

Figure 6 displays the calculated power output of the Ba_0.73_ and Ba_0.85_ thin film-based devices, operating with a frequency of temperature cycling of 2 kHz, 15 V bias and various temperature changes (ΔT). By increasing the range of tunability, we anticipate achieving a significantly higher estimated power output in the proximity of T_C_. The amount of power output of the MPB structure Ba_0.85_ is higher than Ba_0.73_ at all ΔT and frequency of heating and cooling. Also, it is worth noting that the amount of converted energy can be increased by operating in a wider temperature range and/or by increasing the bias voltage. Taking an average microprocessor, such as the Intel E5-2630, and its widespread application in real-world systems makes it an ideal candidate for assessing thermal management techniques under typical operating conditions. One can observe the thermal characteristics (shown in Fig. 7) depending on the artificially generated workload by the Firestarter software^49^.

Fig. 7. Temperature of an Intel E5-2630 microprocessor as a function of the power consumption. The numbers in the graphs represent (a) the workload in % and (b) the number of active cores.

This software is specially designed to stress a processor to its fullest and provides opportunities to select partial or full workloads while using certain numbers of cores with its ‘stress code’ utility.

The results presented in Fig. 7 show that a deviation in temperature in the range of 15 °C is possible for higher workloads. However, this requires a longer period, while a deviation in temperature in the range of 5 °C is much faster at the beginning of the thermal rise or fall due to the exponential change of the thermal energy^50^.

Conclusion

Thus, two barium calcium zirconium titanate-based thin films were considered for the development of a capacitive TE converter. The estimated power output of a device operating at a bias voltage of 15 V with a ΔT = 5 °C and ΔT = 10 °C 5.62 × 10^− 5^ W and 1.76 × 10^− 4^ W, respectively. Also, at the same bias voltage of a device operating with a ΔT = 20 °C, range from 0.1 mW (the equivalent of 0.5 mW/mm^2^) to 0.3 mW (the equivalent of 1.5 mW/mm^2^), which is significantly higher for that temperature range compared to the previously reported values^14–16,24–26^. An Intel E5-2630 microprocessor with a dynamic workload was considered as a heat-modulated source. The possibility of achieving a suitable thermoelectric conversion was demonstrated, given an intelligent control of the processor’s workload, which does not compromise its performance.

It is also worth noting the double benefit of the proposed thermoelectric converter. In addition to the harvested energy, it will contribute substantially to the cooling of the electronic devices, hence reducing the demand of external energy required for their active cooling. In the future, the suitability of these materials for applications such as self-powered electronic circuits—including wearable health monitors, mobile phone sensors, flexible displays, smart earbuds, and other low-power portable or wearable devices—could be explored, particularly for workloads in the micro- to milliwatt range that require minimal or no external power.

Methods

Thin films design and preparations

The thin films were deposited via the pulsed laser deposition (PLD) method using in-house sintered ceramic pucks with the desired stoichiometry. Two types of films with a thickness of 300 nm were deposited onto strontium titanate (STO) substrates (Crystal 1STO 105E, 5 × 5 mm^2^, (100) oriented, one side polished). The substrates were secured by silver paste on a stainless resistive heater. The optimised deposition conditions for Ba_0.73_ thin film fabricated at 730 °C,100mTorr oxygen partial pressure, and laser fluence 2 J/cm^2^. Ba_0.85_ thin film was fabricated at 780 °C, 300mTorr oxygen partial pressure and laser fluence 2 J/cm^2^. The thickness of both films was measured using a (KLA) Tencor D-600 profiler. The crystal orientation of the film was analysed using X-ray diffraction (XRD) (Empyrean multipurpose diffractometer, Malvern Panalytical). A Thermo-Scientific K-alpha + X-ray photoelectron spectrometer investigated the stoichiometry of the thin films.

To facilitate electrical measurement on thin films, electrode layers of Au buffered with TiO_x_ were deposited by magnetron sputtering (HEX, Korvus Technology). After the electrode deposition, the samples were subjected to photolithography using an OAI model 200 mask aligner and ion milling using the scia Mill 150 system. The patterned capacitor structures had electrodes with a length and width of 450 μm and a 10 μm gap between them. Thin film dielectric properties were measured using an LCR meter (Hewlett Packard 4263B) attached to a probe station (Janis Inc.) in a temperature range 298–450 K at frequencies of 100 Hz, 1 kHz, 10 kHz and 1 MHz under DC bias ranging from 0 V up to 15 V.

Electronic device selection as a modulated heat source

In our work, the Intel E5-2630 microprocessor was considered as the source of modulated heat flux with varied workloads. This microprocessor is a mid-range homogeneous multi-core Intel Haswell device with 8 cores, which provide dedicated resources for the execution of individual threads. In contrast, the remaining microprocessor components are shared between all threads, and therefore, the workload depends on the balance between the number of active cores and the shared components. In summary, the Intel E5-2630 microprocessor is very well positioned as a representative of a wider range of electronic microprocessors and provides typical thermal characteristics which brings further confidence in our experimental results.