In response to the growing demand for intelligent thermal management in new-energy electric cars, I have focused my doctoral research on the improvement of positive temperature coefficient of resistance (PTCR) thermistors. PTCR thermistors are popular heating elements in electric cars because they can self-limit temperature, operate without complicated control systems, and convert electrical energy directly into heat. In electric cars, the heating module is not only used for cabin heating but also for warming the battery pack at low ambient temperature. My work addresses two urgent problems: the unwanted negative temperature coefficient (NTC) behavior that appears below the Curie temperature, and the limited voltage endurance when a high DC or AC voltage is applied. By using a two-step solid-state reaction route, I fabricated (Ba,Pb)TiO3-based PTCR ceramics and systematically modified the composition and sintering schedule. The goal was to produce reliable heating elements suitable for wide-temperature-range and wide-voltage-range electric-car applications.
Introduction and background
Modern electric cars require heating systems that operate reliably over a wide ambient temperature window. Unlike conventional vehicles that recover waste heat from internal combustion engines, electric cars must generate heat electrically. There are three primary thermal-management solutions for electric cars: heat pumps, PTC heaters, and hybrid heat-pump-plus-PTC systems. Heat pumps have high efficiency in moderate climates, but when the outdoor temperature falls below about -10 °C, their heating capacity deteriorates sharply. PTC heaters respond quickly, have a simple structure, and work over the full temperature range encountered by electric cars. Therefore, despite the energy consumption penalty, PTCR-based heating remains a core solution for electric cars, particularly in cold regions.
The essential component inside a PTC heater is the PTCR ceramic. For electric cars, the PTCR element must often operate from -40 °C to 120 °C and withstand working voltages from 220 V to 700 V. This wide electronic operational range is unusual for common household PTCR devices. A conventional BaTiO3-based PTCR thermistor has a resistivity-temperature curve with a characteristic drop in resistance when the temperature rises from very low temperature toward the Curie point. That negative-resistance-temperature region originates from different conduction mechanisms in the grain boundaries and grains. If this NTC region is strong, the cold-start resistance may be too high for the heater to draw enough power, and after the element is energised, the rapid resistance decrease can create a current surge large enough to destroy the component. Another equally important issue in electric cars is the requirement for high withstand voltage. High-voltage platforms in electric cars are beneficial for reducing cable mass and charging time, but they impose more severe electric-field stress on the ceramic. Therefore, I aimed at suppressing the NTC effect and strengthening the voltage endurance simultaneously.
The classical explanation for the PTCR effect is the grain-boundary barrier mechanism. In donor-doped BaTiO3, the grain boundaries contain acceptor states, and a double Schottky barrier is formed. Below the Curie temperature, the ferroelectric polarisation compensates part of the barrier, which contributes to the low resistance. Above the Curie temperature, the ferroelectric compensation disappears, and the dielectric constant falls rapidly. According to the Heywang model, the boundary resistance depends exponentially on the barrier height. The Poisson equation within the depletion layer can be written as
$$ \frac{d^2 \psi}{dx^2} = -\frac{eN_D}{\varepsilon_0 \varepsilon_{\text{eff}}}, $$
where $e$ is the elementary charge, $N_D$ is the effective donor concentration, $\varepsilon_0$ is the vacuum permittivity, and $\varepsilon_{\text{eff}}$ is the effective permittivity of the grain-boundary region. The resulting maximum barrier height $\Phi_s$ is
$$ \Phi_s = \frac{e^2N_s^2}{8\varepsilon_0 \varepsilon_{\text{eff}} N_D}, $$
where $N_s$ is the surface-state density at the grain boundary. Because the grain-boundary resistance is approximated by
$$ \rho = \rho_g + B\exp\left( \frac{\Phi_s}{k_BT} \right), $$
the sharp increase of resistance in the positive-temperature-coefficient region is linked to the collapse of $\varepsilon_{\text{eff}}$ according to the Curie-Weiss law,
$$ \varepsilon_{\text{eff}} = \frac{C}{T – T_C}, \;\;\; T > T_C. $$
At temperatures lower than $T_C$, the high dielectric constant keeps the barrier low, but the grain-boundary conductivity can still rise with temperature because small-polaron hopping or thermally activated carrier emission takes place. In electric cars, this low-temperature rise of resistance is not always observable from static $R$–$T$ scans if the room-temperature coefficient is large, but the NTC effect becomes serious when a cold heater is first connected to the battery voltage. Therefore, I quantified the NTC effect using the ratio $R_{25}/R_{\min}$.
Materials and methods used in my fabrication
I adopted a two-step solid-state synthesis route. The first step consisted of preparing separate precursor powders of BaTiO3 and PbTiO3. The reactions that occurred during calcination were
$$ \mathrm{BaCO_3 + TiO_2 \rightarrow BaTiO_3 + CO_2\uparrow}, $$
$$ \mathrm{Pb_3O_4 + 3TiO_2 \rightarrow 3PbTiO_3 + CO_2\uparrow}. $$
I deliberately used PbTiO3 instead of PbO and Pb3O4 in the second mixing stage. This reduced the loss of lead during high-temperature sintering and helped me maintain a high Curie temperature. The basic composition of the matrix was (Ba,Pb)TiO3. A small excess of TiO2 was fixed by the nominal formula (Ba,Pb)Ti1.01O3 because the Ti-rich stoichiometry is favourable for obtaining semiconducting ceramics with reproducible PTC behavior. Table 1 summaries the raw materials that I used in this work.
| Raw material | Function in the formulation |
|---|---|
| BaCO3 | Formation of BaTiO3 matrix |
| Pb3O4 | Formation of PbTiO3; raising $T_C$ |
| TiO2 | Matrix and stoichiometry adjuster |
| CaCO3 | Grain refinement; suppression of NTC effect |
| Nb2O5 | Donor dopant for semiconducting BaTiO3 |
| Mn(NO3)2 solution | Acceptor dopant for enhancing PTC jump |
| Al2O3 | Liquid-phase component; voltage-endurance enhancer |
| SiO2 | Liquid-phase component; liquid sintering aid |
| PVA binder | Granulation and green-body strength |
| Al paste/electrode | Ohmic contact formation |
The processing sequence included weighing, planetary ball milling with zirconia media, drying, calcination, binder addition, granulation through a 40-mesh sieve, uniaxial pressing, sintering in air, polishing, electrode printing and electrode firing. Sintering was performed in a bell-type furnace using a stepped heating profile. The maximum sintering temperature was varied from 1200 °C to 1320 °C to study its influence on the PTCR properties. I tested the electrical properties with a programmable resistance-temperature tester, a V-I characteristic apparatus, an I-t recording system, and an impedance analyser operating from 100 Hz to 10 MHz. The microstructure was observed by scanning electron microscopy, and phase formation was checked by X-ray diffraction.
Defect chemistry and its impact on the performance of electric-car PTCR ceramics
One of the most significant results of my work is that a moderately high Ca concentration is extremely effective for weakening the NTC effect below $T_C$. I first sintered two series of specimens, one at 1262 °C and another at 1240 °C, while increasing the Ca content from 3 mol% to 10 mol%. In the 1262 °C series, the room-temperature resistance $R_{25}$ initially increased from around 17 Ω at 3 mol% Ca to about 967 Ω at 6 mol% Ca, and then reached 4991 Ω at 8 mol% Ca. Interestingly, further Ca addition above 8 mol% reduced $R_{25}$, because excess Ca can enter both Ba and Ti sites and influence the compensation balance.
$$ 2\mathrm{CaO} \xrightarrow{\mathrm{BaTiO_3}} \mathrm{Ca}_{Ba}^{\times} + \mathrm{Ca}_{Ti}^{”} + 2O_O^{\times} + V_O^{\bullet\bullet} $$
The formation of oxygen vacancies is important in the defect chemistry. In the low-carbonate introduction range, Ca primarily occupies Ba sites and shrinks the lattice because Ca2+ has a smaller ionic radius than Ba2+. As the Ca content increases, some Ca2+ ions begin to occupy Ti sites. The acceptor-type defect $\mathrm{Ca}_{Ti}^{”}$ is compensated by oxygen vacancies. These oxygen vacancies can adsorb oxygen at grain boundaries. The adsorption reaction can be represented as
$$ V_O^{\bullet\bullet} + \frac{1}{2}O_2(g) \rightleftharpoons O_O^{\times} + 2h^{\bullet}. $$
The holes generated by this reaction act as traps for electrons, thus increasing the grain-boundary barrier. This explains why the room-temperature resistance increases with moderate Ca addition. However, when Nb donor doping is also present, the situation is more subtle. The Nb ion substituted on the Ti site is described by
$$ \mathrm{Nb}_2O_5 + 2Ti_{Ti}^{\times} + \frac{1}{2}O_2(g) \rightarrow 2\mathrm{Nb}_{Ti}^{\bullet} + 2e’ + 5O_O^{\times}. $$
There is a competitive compensation between the donor electrons of niobium and the acceptor-like holes or electron traps caused by calcium. When the amount of Ca that enters the Ti sites equals the amount of Nb on Ti sites, their effects partly cancel. Once Ca exceeds this matching amount, the acceptor-like role of $\mathrm{Ca}_{Ti}^{”}$ becomes dominant, and the material resistance and jump ratio increase again. In electric cars, this acceptor-like regulation is useful because it creates a high enough room-temperature resistance while maintaining a large PTC jump.
Effect of Ca doping on the R-T behavior
Table 2 gives the data of the 1262 °C-sintered series. The quantity $R_{25}/R_{\min}$ decreased from 2.35 at 3 mol% Ca to a minimum of 0.92 at 8 mol% Ca. A value below 1 means that the resistance does not decrease at any point when the sample is heated from -50 °C to above $T_C$. In other words, the NTC region has been completely eliminated.
| Ca content (mol%) | $R_{25}$ (Ω) | $R_{25}/R_{\min}$ | $\log_{10}(R_{\max}/R_{\min})$ | Breakdown voltage (V) |
|---|---|---|---|---|
| 3 | 17.0 | 2.35 | 0.67 | 528 |
| 5 | 58.8 | 2.21 | 0.55 | 633 |
| 6 | 967 | 3.65 | 0.54 | 727 |
| 7 | 875 | 1.35 | 0.44 | 775 |
| 8 | 4991 | 0.92 | 0.62 | 890 |
| 9 | 935 | 3.63 | 0.54 | 845 |
| 10 | 38.9 | 2.25 | 0.25 | 521 |
In the 1240 °C-sintered series, I observed a similar trend of decreasing $R_{25}/R_{\min}$ with increasing Ca content, and the minimum value again occurred at 8 mol% Ca. However, the sintering temperature of 1240 °C was not sufficient to produce dense, fully semiconducting ceramics when the Ca content was as high as 10 mol%. In that sample, the room-temperature resistance was too high for practical electric-car heaters because the amount of CaTiO3 formed was excessive. The comparison between the two sintering temperatures indicates that a homogeneous incorporation of Ca at Ti sites requires a sufficiently high sintering temperature.
From a defect-chemical viewpoint, the suppression of the NTC effect by Ca can be explained by the decrease of accessible Ti sites. Literature suggests that the low-temperature NTC effect in donor-doped BaTiO3 is associated with electron exchange between Ti3+ and Ti4+ ions. The hopping conductivity is often represented by
$$ \sigma_{\text{NTC}} \propto \frac{c(1-c)}{k_BT} \exp\left(-\frac{E_h}{k_BT}\right), $$
where $c$ is the fraction of Ti3+ and $E_h$ is the hopping activation energy. When divalent Ca replaces both Ba and Ti sites, the amount of titanium available for the Ti3+/Ti4+ hopping pairs is reduced. Consequently, the rise of grain-boundary conductivity with temperature in the warming process becomes much weaker. For electric cars, this leads to faster startup because the hot resistance remains high enough to avoid current runaway.
Microstructure and impedance evidence
Scanning electron microscopy revealed a clear dependence of grain size on Ca doping. Between 3 mol% and 7 mol% Ca, the grain size became smaller and more uniform. The addition of Ca restrained exaggerated grain growth, which is desirable for a large number of grain boundaries. However, when the Ca content exceeded about 8 mol%, the grain-size uniformity deteriorated. I observed bright non-conductive secondary phases at the grain boundaries. X-ray diffraction confirmed that a secondary phase $Ca_2SiO_4$ begins to appear when the Ca concentration is equal to or greater than 5 mol%. This silicate phase was more prominent in the sample containing 8 mol% Ca. The calcium silicate phase is rather insulating and resides at grain boundaries. It increases the grain-boundary resistance and also improves the resistance to voltage degradation.
Impedance spectroscopy is a powerful method for separating the bulk and grain-boundary contributions. In my measurement, I tested the samples at 100 Hz–10 MHz and at different temperatures. The impedance spectra consisted of almost a single arc, with a large intercept on the real axis. The fitted resistance of the grain boundary accounted for most of the total $R_{25}$. The grain-interior resistance was very small compared with the grain-boundary resistance. These observations confirm that the PTCR effect and the voltage endurance are controlled mainly by the grain boundary. In the sample with 8 mol% Ca, I also measured the impedance spectrum while cooling to -50 °C. The resistance change between -50 °C and room temperature was small, which was consistent with the $R_{25}/R_{\min}$ result. This is exactly the desired feature for a heater element inside an electric car, because it prevents the huge inrush current during cold motorway driving.
I-t characteristics of low-NTC PTCR elements
To further verify the benefit of low-NTC behavior, I carried out current-time tests by applying AC voltages of 220, 260 and 300 V to selected samples. I defined the current-rise time as the time required for the current to reach half of its peak current after energisation. Table 3 compares three elements: sample 1 had $R_{25}$ = 1781 Ω and a very small NTC region; sample 2 had $R_{25}$ = 1499 Ω and effectively no NTC region; sample 3 had $R_{25}$ = 1937 Ω but a stronger NTC region. The ratio of peak current to initial current is included in the table because this ratio is a crucial specification for electric-car PTC modules without additional soft-start controllers.
| Applied voltage (V) | Sample 1 rise time (ms) | Sample 2 rise time (ms) | Sample 3 rise time (ms) |
|---|---|---|---|
| 220 | 61 | 54 | 192 |
| 260 | 52 | 48 | 188 |
| 300 | 39 | 34 | 185 |
The low-NTC samples reached their operating state in less than roughly 60 ms, whereas the sample with a stronger NTC region required several times longer. The peak-to-initial-current ratio of the low-NTC samples remained smaller than 1.1, which satisfies the strict limit of about 2.5 proposed for electric-car PTC heaters without controllers. These I-t results illustrate that by eliminating the NTC effect, the thermistor itself can handle the startup transient safely without requiring an auxiliary pulse-width-modulated switching circuit.
Role of Al2O3 additives
After identifying 8 mol% as the optimum Ca content, I further modified the composition with Al2O3. The Al2O3 amount was varied from 2.0 mol% to 3.8 mol%. Al ions can influence both the grain growth and the barrier structure. Table 4 lists the room-temperature resistance, $R_{25}/R_{\min}$, and breakdown voltage obtained for this series.
| Al2O3 content (mol%) | $R_{25}$ (Ω) | $R_{25}/R_{\min}$ | Breakdown voltage (V) |
|---|---|---|---|
| 2.0 | 9313 | 1.01 | 804 |
| 2.6 | 4452 | 1.21 | 826 |
| 3.2 | 17471 | 1.38 | 841 |
| 3.8 | 12143 | 1.50 | 876 |
With the addition of Al2O3, the temperature coefficient $\alpha$ of the Ca-doped PTC ceramics exceeded 11%/°C, which is favorable for the rapid heating inside electric cars. Aluminum substitutes preferentially on Ti sites because the ionic radius of Al3+ is close to that of Ti4+. The defect reaction can be written as
$$ 2\mathrm{Al}_2O_3 + 2Ti_{Ti}^{\times} + O_2(g) \rightarrow 2\mathrm{Al}_{Ti}’ + 2\mathrm{Al}_{Ti}^{\bullet}? $$
In the more common acceptor form, the reaction is
$$ 2\mathrm{Al}_2O_3 + 2Ti_{Ti}^{\times} \xrightarrow{\mathrm{BaTiO_3}} 2\mathrm{Al}_{Ti}’ + 2V_O^{\bullet\bullet} + 2\mathrm{Al}_{Ba}^{\bullet}? $$
The exact site occupancy depends on the local stoichiometry and the concentration. Because Al is an amphoteric dopant, it can occupy Ba sites at high concentration, creating donor-like defects. This amphoteric behavior explains why the room-temperature resistance does not increase linearly with Al content. In my samples, the X-ray diffraction pattern of the higher-Al sample showed a small second phase that was identified as Ba3Al10TiO20. This liquid phase aided the densification and improved the voltage endurance. Scanning electron microscopy images showed that increasing Al2O3 from 2.0 to 3.8 mol% reduced porosity and promoted uniform grain growth. The liquid phase wrapped the grain boundaries, reduced defects and suppressed local field concentration. Therefore, I found that Al2O3 is beneficial for obtaining a high voltage-withstand capability, which is a critical requirement for electric cars on high-voltage platforms.
Role of SiO2 additives
Silicon oxide is a traditional liquid-forming additive that promotes liquid-phase sintering of PTCR ceramics. I added SiO2 in amounts from 1.4 mol% to 3.8 mol% to the formulation containing 8 mol% Ca and the Al-modified matrix. The sample with the lowest SiO2 content did not become semiconducting at all. With SiO2 equal to 2.0 mol%, the room-temperature resistance dropped to a practical level around 1200–2100 Ω. This result confirms that sufficient SiO2 is necessary for the formation of a eutectic liquid that promotes the incorporation of Nb donor ions.
| SiO2 content (mol%) | Room-temperature state | Approx. $R_{25}$ (Ω) | Breakdown voltage (V) |
|---|---|---|---|
| 1.4 | not semiconducting | very high | not measured |
| 2.0 | semiconducting | 1200–2140 | 770–802 |
| 2.6 | semiconducting | 3000 | 932–946 |
| 3.2 | semiconducting | 10040 | 528 |
| 3.8 | semiconducting | 53200 | 513 |
The X-ray diffraction patterns demonstrated that SiO2 reacts with the excess Ca and forms Ca2SiO4 at grain boundaries. This phase is visible when the SiO2 content is 2.6 mol% or larger. Although this secondary phase improves the breakdown voltage, too much SiO2 increases the intergranular resistance and reduces the heating power. For electric cars, the room-temperature resistance should stay in a moderate range, roughly 1000–5000 Ω for the designed electrode area. Thus, the optimal SiO2 content in my Ca-modified CAST system was around 2.0–2.6 mol%.
In the impedance spectra, the overall room-temperature resistance was again determined by the grain-boundary resistance. The addition of SiO2 increased the capacity of the material to store charge in the grain-boundary region, as evidenced by the stronger capacitive response in the Bode diagrams. The grain-interior resistance remained comparatively low. This implies that the superior voltage endurance of the Si-containing ceramics is related to the increased boundary barrier homogeneity and the reduction of conductive paths along pores.
Sintering temperature and heating-rate optimization for electric-car platforms
The electrical properties of PTCR ceramics depend strongly on thermal history. I varied the maximum sintering temperature for the composition containing 8 mol% Ca between 1240 and 1320 °C. When sintering was performed at 1200 °C, the sample could not become fully semiconducting, and its room-temperature resistance was more than 2.5 MΩ. At intermediate temperatures, 1250–1262 °C, the grain growth and oxygen incorporation were balanced. These samples displayed a large resistance jump of about four orders of magnitude. When the sintering temperature exceeded 1280 °C, the grain growth became exaggerated and the number of active grain boundaries decreased. This microstructure leads to a lower PTC jump and lower breakdown voltage.
The dependence of $R_{25}$ and the ratio $R_{25}/R_{\min}$ on sintering temperature was non-monotonic. At the lower-temperature side, Ca ions tend to segregate at the grain boundaries and produce strong acceptor states. At higher temperatures, more Ca enters the lattice, changing the width of the space-charge region. When the sintering temperature was too high, oxygen vacancies were also abundant, making it difficult to lower the residual resistance. Thus the optimum sintering temperature for the CAST-modified BPT ceramics was found to be approximately 1262 °C. This temperature was used for most subsequent experiments.
Influence of the heating rate
The heating rate above 1050 °C affected the color and the microstructure of sintered discs. A slow heating rate of about 7 °C/min produced dark blue-gray specimens with low room-temperature resistance and good PTC behavior. When I increased the heating rate to 8.5–14 °C/min, the color changed toward yellow and the resistance increased to the range of 56–300 kΩ, indicating incomplete semiconducting. The reason is that a too-rapid heating rate does not allow enough time for the liquid phase to distribute equally, and the chemical reactions inside the ceramic body lag behind the temperature ramp. The densification process is incomplete, leaving more pores. These pores create local field concentrations and lower the resistance against electrical breakdown. In electric cars, where the PTC heater must be cycled on and off frequently, such porosity is a serious weak point.
Electrode firing temperature
I also studied the influence of the aluminum electrode firing temperature on the final properties. Three electrode firing temperatures, 650 °C, 680 °C and 700 °C, were compared. The room-temperature resistance remained almost unchanged, which indicates that the ohmic contact is formed in all cases. However, the resistance jump and breakdown voltage were optimal when the electrode was fired at 650 °C. When the electrode firing temperature exceeded the melting point of aluminum, around 660 °C, the molten aluminum could penetrate into the ceramic and reduce the effective electrode thickness. This condition degraded the voltage endurance. Therefore, for the best electric-car PTC heater reliability, I recommend an electrode firing temperature of 650 °C for Al electrodes.
| Electrode firing temp. (°C) | Relative $R_{25}$ | Observed breakdown behavior |
|---|---|---|
| 650 | unchanged | breakdown voltage above 800 V, high PTC jump |
| 680 | unchanged | breakdown voltage reduced to about 710–760 V |
| 700 | unchanged | breakdown voltage reduced to about 370–470 V |
Integrated CAST strategy and final PTCR performance
Based on the individual studies of CaO, Al2O3 and SiO2, I developed a synergistic additive system that I refer to as CAST: Ca + Al + Si + Ti. The Ca component suppresses the NTC effect below $T_C$, the Al component increases the temperature coefficient and voltage endurance, and the Si component improves the liquid-phase sintering and breakdown resistance. This combination was applied to the composition (Ba,Pb,Ca)Ti1.01O3 with Nb as donor and Mn as a minor acceptor.
By carefully balancing the quantities of these additives and by sintering near 1262 °C, I obtained a batch of PTCR disks with the following properties:
| Property | Target for electric cars | Result obtained |
|---|---|---|
| Room-temperature resistance | 1000–5000 Ω | 1000–5000 Ω |
| $R_{25}/R_{\min}$ | less than 1.5 | 0.90–1.45 |
| Resistance jump ratio | more than $10^3$ | about $3\times10^3$ to $10^4$ |
| Breakdown voltage | higher than 800 V | 800–950 V |
| Peak-to-initial current ratio at 300 V | less than 2.5 | less than 1.1 for optimized samples |
These PTCR thermistors were designed for heating systems in electric cars. They operate with wide temperature margins from -40 °C to over 120 °C, and they withstand voltages that are substantially higher than the 350 V nominal voltage used by many current electric-car platforms. The low $R_{25}/R_{\min}$ ratio is advantageous because the element does not draw excessive inrush current when a cold battery bus voltage is applied. In fact, for the best samples, the startup current was almost equal to the initial current, so the heater can be connected to a power source without a separate pulse-width-modulated soft-start circuit.
Conclusion and future perspective
In this thesis, I systematically investigated the influence of CaCO3, Al2O3 and SiO2 on (Ba,Pb)TiO3-based PTCR thermistors and demonstrated the feasibility of building a CAST additive system for wide-temperature and wide-voltage applications in electric cars. The main conclusions are as follows:
First, calcium doping is the key to suppressing the NTC effect. When Ca is present in the range of 7–8 mol%, it occupies both Ba and Ti sites. The reduction of Ti content weakens the Ti3+/Ti4+ hopping contribution that normally causes negative resistance behavior below $T_C$. The optimized composition exhibited $R_{25}/R_{\min} <1.5$ or even <1, and therefore the startup current in electric-car heaters became highly stable.
Second, aluminum doping contributes to the temperature coefficient and voltage endurance. Although Al generally increases the NTC indicator slightly, the combination with Ca maintains the wide-temperature stability. The second phases that are formed at the grain boundaries, such as Ca2SiO4 and barium-aluminate-rich compounds, improve the resistance to high electric fields.
Third, silicon dioxide is necessary for liquid-phase sintering. Without sufficient SiO2, the PTCR ceramic is not semiconducting. With too much SiO2, the resistance becomes too high and the heating power is reduced. The optimum SiO2 content for my CAST-based BPT system is 2.0–2.6 mol%.
Fourth, sintering temperature and heating rate must be accurately controlled. I found that 1262 °C is the best maximum sintering temperature in my series; temperatures above approximately 1280 °C cause exaggerated grain growth and lower the PTC effect. A heating rate of about 7 °C/min is preferred. An electrode firing temperature of 650 °C also helps to preserve the high breakdown voltage.
The result of this work is a family of high-performance PTCR thermistors with a room-temperature resistance of 1000–5000 Ω, a low $R_{25}/R_{\min}$ of less than 1.5, and a breakdown voltage above 800 V. This technology is ready for integration into the thermal-management systems of electric cars. Future research should extend the CAST concept to other high-Curie-temperature materials and explore co-doping strategies that reduce lead content. One promising path is to replace part of the lead with other ions that shift $T_C$ while maintaining the low-NTC behavior. Another direction is to scale up the laboratory process to industrial tunnel sintering furnaces, where temperature gradients are larger. For practical electric-car applications, long-term reliability tests at high voltage and thermal cycling are still necessary. Nevertheless, the findings presented here provide a foundation for developing the next generation of wide-temperature and wide-voltage PTCR heating elements for electric cars.