The hafnium oxide material class is characterized by the coexistence of several polymorphs between which phase transitions are induced by means of composition and external electric fields. Pyroelectric materials, which convert heat into electrical energy, exhibit the largest response at such morphotropic or field-induced phase transitions. The hafnium oxide material system is of special interest for pyroelectric applications since it allows for scalable and semiconductor-compatible fabrication. Here, we report large pyroelectric coefficients at the morphotropic transition from the ferroelectric orthorhombic to the centrosymmetric tetragonal phase. The electric field-induced transition between these two phases in doped HfO2 is found to yield large pyroelectric coefficients of up to −142 µCm−2 K−1, a value that is 20 times larger compared to AlN.

The class of hafnium oxide (HfO2) based ferroelectrics has spurred renewed interest in polar thin films due to its remarkable scalability down to 1 nm1 and compatibility with semiconductor fabrication processes.2 HfO2 exhibits some unique properties such as scale-free nano-ferroelectricity without a superparaelectric limit,3 sizable piezoelectric and pyroelectric coefficients,4,5 and a high coercive field in the order of 1 MV cm−1. It receives extensive research interest due to its huge application potential in non-volatile memories6,7 and neuromorphic computing,8 to name a few. Nevertheless, applications based on the pyroelectric and piezoelectric properties remain relatively understudied.

While HfO2 occurs in the monoclinic P21/c phase as a bulk ceramic under ambient conditions, other polymorphs may be stabilized in thin films, namely, tetragonal (P42/nmc), cubic (Fm3̄m), and polar orthorhombic (Pca21) phases. The latter exhibits ferroelectric behavior and is stabilized by means of doping,9 film thickness,10 interface engineering,11 and others. Recently, a further rhombohedral polymorph was stabilized in thin epitaxial films.12 

The pyroelectric effect describes the change in dielectric polarization with respect to temperature in the field-free case. Analyzing the phenomenon is essential: First, the HfO2 material system has the potential to evolve pyroelectric applications toward scalable, mass-market solutions for infrared sensors,13 energy harvesters,14 and electrocaloric refrigeration devices.15 Second, since the polar behavior forms the basis of ferroelectricity, investigation of the pyroelectric effect equally helps in understanding the material properties.

In this work, we examine the physical origin of enhanced pyroelectricity in HfO2-based thin films. First, we discuss how the response can be maximized by tuning the films at the morphotropic phase boundary (MPB) between the polar orthorhombic and the non-polar tetragonal phase. Then, we examine how field-induced phase transitions in antiferroelectric (AFE)-like HfO2 add significant contribution to the pyroelectric effect.

Pure HfO2 thin films crystallize in the centrosymmetric monoclinic phase. It has been established that an increasing doping, e.g., with Si, La, Al, Zr, or other elements, stabilizes the ferroelectric orthorhombic phase. Even higher doping levels will stabilize the centrosymmetric tetragonal phase, which is associated with an AFE-like behavior.9,16 The opportunity of an enhanced dielectric response between the orthorhombic and the tetragonal polymorphs has been suggested for applications such as dynamic random access memory17 or field effect transistor gate dielectrics.18 However, the enhancement of the pyroelectric and piezoelectric properties by tuning the phase composition of HfO2-based films toward the morphotropic transition point has not been examined yet.

In other material systems, such as Pb(Mg1/3Nb2/3)O3–PbTiO3 (PMN-PT) or PbZrxTi1−xO3 (PZT), the largest pyroelectric response is obtained close to the morphotropic phase boundary.19,20 Liu et al. assessed the pyroelectric response of HfO2 by molecular dynamics simulations,21 which predict a large pyroelectric response associated with the orthorhombic to tetragonal phase transition. By introducing Si cations, the authors report an enhancement of this response as well as a lowering of the phase transition temperature.

For a comprehensive analysis of the pyroelectric response, Si-doped HfO2 thin films with a range of dopant concentrations are manufactured. In Fig. 1(a), the evolution of the dielectric permittivity is depicted for successive electric field cycling at 3 MV cm−1. While the zero-field permittivity decreases during the wake-up process, the distinct ferroelectric peaks emerge at the coercive fields and the characteristic transforms toward a typical butterfly-like shape. The loss tangent in Fig. 1(b) evolves similarly, with switching peaks emerging at the coercive field. The loss at 0 MV cm−1 is 0.018 at a measurement frequency of 1 kHz and a small-signal amplitude of 50 mV. The permittivity exhibits a pronounced dependence on the Si doping content, which is shown in Fig. 1(c) for all samples. The largest value of 45 is registered for the 3.5 cat. % Si-doped sample. For the lowest Si concentration values, the dielectric constant approaches that of monoclinic HfO2 at 16.22 

FIG. 1.

(a) Wake-up effect of the dielectric permittivity for 3.5 cat. % Si-doped HfO2 in the initial state and for 103 and 104 electric field cycles. (b) Corresponding evolution of the loss tangent. (c) Stoichiometry dependence of the dielectric permittivity after 104 field cycles.

FIG. 1.

(a) Wake-up effect of the dielectric permittivity for 3.5 cat. % Si-doped HfO2 in the initial state and for 103 and 104 electric field cycles. (b) Corresponding evolution of the loss tangent. (c) Stoichiometry dependence of the dielectric permittivity after 104 field cycles.

Close modal

Ferroelectric polarization–field (PE) measurements are shown exemplarily in Fig. 2(a) for two samples with different Si contents. The films initially exhibit a reduced ferroelectric polarization. These films are then subjected to 104 electric field cycles, whereby the remanent polarization increases, which is referred to as the “wake-up” effect.5,23 Further electrical characteristics of the examined samples have been described in a prior publication.24 While the 2.1 cat. % Si-doped sample exhibits a distinct ferroelectric hysteresis shape, a higher dopant content of 3.5 cat. % leads to a less steep PE characteristic, with a reduced remanent value Pr. The latter possess an increased amount of tetragonal grains in the polycrystalline film, which are connected to an antiferroelectric-like behavior and pinching of the PE graphs.9 

FIG. 2.

(a) Polarization-field hysteresis graphs for two Si-doped HfO2 thin films. (b) Pyroelectric current induced by sinusoidal heating. Notably, the pyroelectric current is higher for the sample with the lower remanent polarization (blue lines). In the bottom graph, the virtually identical respective temperature waveforms of the pyroelectric measurements are shown. (c) Pyroelectric coefficients vs remanent polarization of Si-doped HfO2. The dopant content is shown next to the data points. Lines are guides for the eye.

FIG. 2.

(a) Polarization-field hysteresis graphs for two Si-doped HfO2 thin films. (b) Pyroelectric current induced by sinusoidal heating. Notably, the pyroelectric current is higher for the sample with the lower remanent polarization (blue lines). In the bottom graph, the virtually identical respective temperature waveforms of the pyroelectric measurements are shown. (c) Pyroelectric coefficients vs remanent polarization of Si-doped HfO2. The dopant content is shown next to the data points. Lines are guides for the eye.

Close modal

Pyroelectric properties are assessed by the Sharp–Garn method, where a sinusoidally varying temperature with an amplitude of 2 K is applied to the sample. The resulting pyroelectric short-circuit current between electrodes is registered, as shown in Fig. 2(b). The phase shifts between the temperature waveforms and the current are 99° and 97° for the 2.1 and 3.5 cat. % Si-doped samples, respectively. This is close to the value of 90°, which is expected for an ideal pyroelectric material. Here, the film with a higher Si concentration exhibits a larger pyroelectric response at −95 µCm−2 K−1, as compared to −50 µCm−2 K−1 for the 2.1 cat. % Si-doped film. It is evident that the zero-field polarization Pr is not proportional to the pyroelectric coefficients p.

The plot of the pyroelectric coefficients p of all manufactured samples vs Pr is depicted in Fig. 2(c), where the arrow indicates an increasing dopant content. It is evident that a counter-clockwise-directed trajectory exists, which is suspected to arise from the phase evolution from monoclinic, undoped HfO2 toward the polar orthorhombic phase with maximal Pr and finally to the non-polar tetragonal or cubic phase with increasing dopant concentration. It is noted that cubic and tetragonal polymorphs are difficult to distinguish due to their similar crystal structure.

To correlate the observed pyroelectric coefficients with structural properties, the phase composition of Si-doped HfO2 is analyzed. The phase fraction of the respective monoclinic, orthorhombic, and tetragonal/cubic polymorphs is extracted by means of Rietveld refinement25 with the respective diffraction data. Phase fractions of the tetragonal and cubic polymorphs are difficult to distinguish and are therefore combined. Further details of the refinement process are discussed in Ref. 24. In Fig. 3(a), the pyroelectric coefficients are visualized with respect to the film composition. It is evident that the pyroelectric effect is most pronounced in the transition region between the polar orthorhombic and the centrosymmetric tetragonal phases. The largest response is found for a composition ratio of ∼2:1 for the orthorhombic vs tetragonal/cubic phase fraction. It is noted that the very small film thickness could lead to uncertainties in the quantitative phase analysis; however, the qualitative trend of an enhanced pyroelectric response in the transitional region is clearly confirmed by the deconvolution results. Furthermore, we conclude that the presence of the monoclinic phase leads to a strong inhibition of the pyroelectric response. For applications, our results confirm that pyroelectric devices will generally require higher doping of the HfO2 films than ferroelectric field effect transistors or tunnel junctions.

FIG. 3.

(a) Pyroelectric coefficients vs phase composition of Si-doped HfO2 films, which is extracted by deconvolution of grazing-incidence x-ray diffraction (GI-XRD) data with the Rietveld method. An increasing Si content from 1.4 cat. % to 5.3 cat. % is indicated by an arrow, and tetragonal and cubic phases are combined due to their structural similarity. Lines are guides for the eye. (b) Curie constants calculated from the Si-doped HfO2 vs dopant cation ratio, where the morphotropic phase boundary (MPB) is marked.

FIG. 3.

(a) Pyroelectric coefficients vs phase composition of Si-doped HfO2 films, which is extracted by deconvolution of grazing-incidence x-ray diffraction (GI-XRD) data with the Rietveld method. An increasing Si content from 1.4 cat. % to 5.3 cat. % is indicated by an arrow, and tetragonal and cubic phases are combined due to their structural similarity. Lines are guides for the eye. (b) Curie constants calculated from the Si-doped HfO2 vs dopant cation ratio, where the morphotropic phase boundary (MPB) is marked.

Close modal

We speculate that a similar mechanism may be valid for the optimization of the piezoelectric response in HfO2-based films. The observed effect could be more pronounced in epitaxial films,12 where the transition temperature between the orthorhombic and the tetragonal phase is not broadened by grain size effects.26 

According to the Landau–Devonshire theory, the pyroelectric coefficients and the remanent polarization are linked by the dielectric permittivity and the Curie constant Cc = −εrPr/p. The plot of the calculated values of Cc vs Si dopant content is displayed in Fig. 3(b). Two regimes are observed: At a low Si content <2 cat. %, a Curie constant of 1.4 × 105 K is measured, while at an increased Si content >4 cat. %, the value decreases to 0.7 × 105 K. The increased uncertainty for the 5.3 cat. % Si-doped sample is caused by the minute pyroelectric response of this sample. The two ranges in Fig. 3(b) are attributed to the monoclinic/orthorhombic and orthorhombic/tetragonal and cubic phase mixtures. Physically, the observed behavior of Cc could be explained by the fact that the less-doped films are below the orthorhombic to tetragonal transition point, while highly doped HfO2 already satisfies the condition T > Tc at room temperature. In a recent report, a Curie constant of 0.62 × 105 K is reported at a Si content of 4.0 cat. %, which is compatible with our results, as shown by the orange symbol in Fig. 3(b).27,28

The extracted Curie constants are comparable to those of lithium tantalate, where values of 1.6 × 105 K and 0.7 × 105 K are extracted below and above the transition temperature, respectively. Landau coefficients with magnitudes on the order of 105 K are typical for many displacive ferroelectrics, while order–disorder transitions tend to yield much lower values of Cc.29,30

In the Landau–Devonshire theory of ferroelectrics, the Curie temperature is inversely proportional to the coefficient a0 in the free energy ansatz27 so that a0 = (Ccε0)−1. Coefficients in the range of 0.8 × 106 mF−1 K−1 to 1.64 × 106 mF−1 K−1 are calculated for Si concentrations below and above the phase transition, respectively. Hoffmann et al. recently extracted an absolute Landau parameter a = a0(T0T) with a value of −4.6 × 108 mF−1 for Hf0.5Zr0.5O2.

The AFE-like behavior in HfO2 films with a tetragonal phase fraction provides an opportunity to further enhance the pyroelectric response with an electric field bias. Several explanations for the effect are discussed in the literature, with the most prominent one being a field-induced phase transition from the centrosymmetric tetragonal toward the polar orthorhombic phase.16 Several groups have theoretically reproduced the effect in HfO2 using computational methods.3,31,32 These studies show that the energy barrier between the tetragonal and orthorhombic phase is lowered by doping, allowing for a field-induced transition. The effect also explains the large displacement that is observed in double-beam laser interferometry (DBLI) measurements of AFE-like HfO2 films.33 Field-, temperature-, and stress-induced phase transitions have been observed in relaxor ferroelectrics,34 which lead to a field-enhancement of the pyroelectric coefficient in such materials.35–39 However, other explanations such as depolarization fields40 or Kittel-type AFE behavior due to the scale-free nature of domains in HfO23 are discussed for the HfO2 material class as well.

In lead- and barium-based materials, pyroelectricity was found to be modulated by a transition from the ferroelectric to the AFE-like phase.41,42 AFE films exhibit a strong enhancement of the pyroelectric coefficient by means of an applied electric field. Pandya et al. have recently shown a more than fivefold increase in the pyroelectric response in PMN-PT relaxor ferroelectric films with an applied electric field, while suppressing the dielectric response at the same time.39 This is explained by the combined effect of field- and temperature-induced changes in the polarization magnitude and direction. Furthermore, an electric field contributes to the pyroelectric effect via the temperature dependence of the dielectric permittivity. In a crystallographic view, such field-induced pyroelectricity is plausible since an electric field breaks the centrosymmetry of any crystal lattice.

For pyroelectric measurements at a bias field, a second set of samples with a higher film thickness is used to minimize the leakage current density. A total film thickness of 20 nm is achieved by a nano-laminate of two Si-doped HfO2 layers, which are separated by an ∼0.5 nm thick Al2O3 layer. A transmission electron microscope (TEM) image of the manufactured pyroelectric nano-laminate is shown in Fig. 4(a). Energy-filtered transmission electron microscopy (EFTEM) is employed to distinguish the substrate, electrodes, and pyroelectric film, which are highlighted in blue, red, and green, respectively. In the magnified view in Fig. 4(b), the disruption of the crystal growth in the doped HfO2 is visible. The Al2O3 layer thereby creates an artificial grain boundary that reduces the charge transport through the film. Thereby, the leakage current with an applied electric field is low enough to ensure accurate pyroelectric measurements. The current density in Fig. 4(c) indicates that pyroelectric applications are feasible up to an electric field of ∼±1 MV cm−1 to keep the direct current flow below 5 nA cm−2. In this electric field range, the current density is slightly higher for the antiferroelectric-like films (red symbols), which is probably caused by the smaller grain size of the latter.

FIG. 4.

(a) Transmission electron micrograph of two 10 nm thick Si-doped HfO2 layers separated by an ∼0.5 nm thick Al2O3 interlayer. In the EFTEM micrograph, the Si (blue), Ti (red), and Hf (green) signals correspond to the substrate, electrodes, and pyroelectric film, respectively. (b) In the magnified view, the disruption of grain orientation in the nano-laminate is visible. (c) Leakage current density for two Si doping concentrations corresponding to ferroelectric and antiferroelectric-like films.

FIG. 4.

(a) Transmission electron micrograph of two 10 nm thick Si-doped HfO2 layers separated by an ∼0.5 nm thick Al2O3 interlayer. In the EFTEM micrograph, the Si (blue), Ti (red), and Hf (green) signals correspond to the substrate, electrodes, and pyroelectric film, respectively. (b) In the magnified view, the disruption of grain orientation in the nano-laminate is visible. (c) Leakage current density for two Si doping concentrations corresponding to ferroelectric and antiferroelectric-like films.

Close modal

Results of ferroelectric and pyroelectric measurements are shown in Fig. 5 for HfO2 thin films doped at two different Si concentrations. In the first column of Fig. 5, PE characteristics are shown for pristine samples (red lines) and after applying 104 electric field cycles at 3 MV cm−1 (blue lines). Both graphs exhibit pinched, AFE-like hysteresis loops in the as-deposited state (red lines). Upon electric field cycling, the pE characteristic of 3.8 cat. % Si-doped material in Fig. 5(a) shows a clear wake-up effect. A ferroelectric hysteresis loop with a remanent polarization of 12.4 µCm−2 K−1 and an almost symmetric coercive field of ±0.9 MV cm−1 is obtained (blue line). In contrast, the 4.8 cat. % Si-doped layer in Fig. 5(d) exhibits only a small wake-up effect. The stabilization of an AFE-like behavior with higher Si concentrations has been described in the literature43 and has been proposed for energy storage applications.44,45

FIG. 5.

Polarization–voltage characteristics, pyroelectric current density, and pyroelectric coefficients of 20 nm thick Si-doped HfO2 thin films with the dopant content of (a)–(c) 3.8 cat. % and (d)–(f) 4.8 cat. % Si-doped HfO2 for as-deposited and field-cycled states.

FIG. 5.

Polarization–voltage characteristics, pyroelectric current density, and pyroelectric coefficients of 20 nm thick Si-doped HfO2 thin films with the dopant content of (a)–(c) 3.8 cat. % and (d)–(f) 4.8 cat. % Si-doped HfO2 for as-deposited and field-cycled states.

Close modal

For pyroelectric measurements, the applied electric field is limited to 1.3 MV cm−1 to prevent degradation of the doped HfO2 and reduce contributions from leakage currents as discussed before. The registered short-circuit current amplitude is shown in the second column of Fig. 5. For both analyzed films, the pyroelectric current increases significantly upon electric field cycling. Qualitatively, pyroelectric coefficients bear some similarity to the hysteresis graphs in Fig. 5(a). Coercive fields determined from pyroelectric measurements in Fig. 5(b) are 0.65 and −0.85 MV cm−1, which are slightly lower than the values determined in ferroelectric hysteresis measurements. This is expected since the acquisition time for a full voltage sweep is orders of magnitude longer in Sharp–Garn measurements as compared to the ferroelectric hysteresis characterization at 1 kHz.

Similarly, for the pyroelectric current response of the AFE-like, 4.8 cat. % Si-doped film in Fig. 5(e), coercive fields of ±0.5 MV cm−1 are obtained for both ferroelectric polarization and pyroelectric coefficients after wake-up. Interestingly, the field-induced pyroelectric behavior of the AFE-like film exhibits a pronounced evolution upon application of electric field cycling as well. The wake-up effect has been associated with the re-distribution of charged defects. In the case of AFE-like HfO2, it is speculated that the re-distribution of charged defects enhances the susceptibility of a field-induced phase change in the temperature. This is supported by the fact that the electric field for which the largest opening of the AFE-like hysteresis is observed reduces upon field cycling.

In Fig. 5(c), the pyroelectric coefficients of 3.8 cat. % Si-doped HfO2 are depicted for the as-deposited (red squares) and the field-cycled state (blue circles). In the calculation, the phase of the total registered current is considered as a factor sin(φ). In the pristine state, the values at 0 MV cm−1 are 11 and −39 µCm−2 K−1 for negative and positive film polarizations, respectively. Pyroelectric coefficients increase significantly with an applied voltage in the pristine state, reaching 47 and −89 µCm−2 K−1 at ±1.3 MV cm−1. Upon electric field cycling, the pE graphs evolve toward a more symmetric behavior. After 104 cycles, values of 77 and −90 µCm−2 K−1 are registered at 0 MV cm−1. Toward the electric field maximum, pyroelectric coefficients decrease slightly for woken-up films. Electric field cycling leads to a transformation from field-induced pyroelectricity in the pristine state toward an intrinsic pyroelectric effect in the woken-up state for the 3.8 cat. % Si-doped films.

The AFE-like film in Fig. 5(f) exhibits remarkably high pyroelectric coefficients. After 105 cycles, a large field-induced pyroelectric response is observed, reading values of −142 µCm−2 K−1 at 0.8 MV cm−1. The maximal field-induced pyroelectric response coincides with the largest opening of the AFE hysteresis graph in Fig. 5(d). These values exceed the previously reported ones of 70 µCm−2 K−1 for Hf0.5Zr0.5O227 and 84 µCm−2 K−1 for Si-doped HfO2 by a factor of two.5 

The asymmetry of the pyroelectric coefficients with respect to the electric field bias indicates that there exists a preferred polarization orientation or that the pyroelectric effect is counteracted by metastable charges in the negative polarization direction, which is also referred to as electret effect. This is plausible since the deposition process of the pyroelectric capacitor structures is inherently asymmetric: The HfO2 atomic layer deposition (ALD) process partially oxidizes the lower electrode interface, forming a titanium oxynitride. Furthermore, the top electrode deposition will introduce chlorine species into the film. The different electrode interface chemistry might also lead to asymmetric screening effects, which might degrade the pyroelectric response. The asymmetry of the pyroelectric coefficients in comparison with the PU measurements in Figs. 5(a) and 5(d) is notably higher. This is ascribed to the ability of pyroelectric measurements to capture static effects such as metastable charges directly. Additionally, the comparably slow bias sweeping may cause an asymmetric imprint effect (i.e., defect migration) during pyroelectric measurements.

The pyroelectric coefficients do not resemble an archetypical response of a AFE material, such as that reported for lead-based materials before.46 The pE characteristic rather resembles a mixture of ferroelectric and field-induced, AFE-like behavior. The phase of the total current at the optimized electric field of 0.8 MV cm−1 is determined at 101°, which deviates slightly from the ideal value of 90°. Non-pyroelectric, in-phase currents correspond to 19% of the detected current amplitude. They originate from the thermally induced de-trapping of defect charges5 and the temperature modulation of the leakage current flow in the case of an applied electric field bias. Here, the latter effect is dominant as determined from the field-dependence of the phase. At electric field biases exceeding 1 MV cm−1, the phase of the pyroelectric current begins to deviate further from the ideal value, causing pyroelectric coefficients to ultimately diminish. This is also visible in the pyroelectric current graphs in Fig. 5(e), where the data points with the highest electric field bias deviate from the hysteretical behavior. The operation at a bias voltage may also reduce de-polarization effects (aging),47 which reduce the accuracy of pyroelectric sensors. To assess the stability of the field-induced pyroelectric coefficients, we sweep the electric field three times, whereby a value of (−146 ± 16) μCm−2 K−1 is determined. The observed uncertainty is attributed to the imprint effects of the prolonged application of an electric field bias.

The field-induced pyroelectricity of AFE-like films in combination with their relatively low permittivity leads to a strongly increased potential for sensor applications. Furthermore, the HfO2 material class possesses favorable parameters for energy harvesting. At the same time, the wide layer thickness scalability enables low-voltage operation with fields in the range of 1 MV cm−1. Since the HfO2-based materials are ubiquitous in semiconductor fabrication processes, the material class opens up the possibility of on-chip energy harvesting solutions.

In summary, we propose a semiconductor-manufacturing compatible pyroelectric material whose current response has been optimized by two pathways: First, the enhancement of the pyroelectric response at the morphotropic phase boundary in doped HfO2 is explored. Second, we exploit the field-induced phase change between tetragonal and orthorhombic polymorphs. Practically, this work provides a guideline for optimizing the stoichiometry of HfO2-based pyroelectrics, which are tuned toward the MPB between orthorhombic and tetragonal polymorphs. Furthermore, pyroelectric applications should be enhanced by operating at a bias voltage, which could also reduce aging phenomena. The increased response of up to −142 µCm−2 K−1 opens up new possibilities for integrated infrared sensor and energy harvesting applications, the exploration of which have already begun.48 A similar enhancement of the piezoelectric response of HfO2 remains to be confirmed experimentally and would benefit the development of future nano-electromechanical systems.

10 nm thick TiN top and bottom electrodes are fabricated by CVD and ALD, respectively. HfO2 films are formed by ALD in a Jusung Eureka warm-wall reaction chamber. Details of the deposition process are discussed elsewhere.24 For the Al2O3 interlayer deposition, five ALD cycles with trimethylaluminium/ozone precursors are employed. Finally, 100 nm Ni is deposited by electron beam evaporation through a shadow mask. The exposed TiN is removed in a subsequent wet etching step, thereby defining structures for polarization and pyroelectric measurements.

Electrical capacitance measurements are carried out with an Agilent E4980 LCR meter at an amplitude of 50 mV and a frequency of 1 kHz. Polarization-voltage measurements are performed with an Aixacct TF 3000 ferroelectric analyzer at a frequency of 1 kHz.

The phase-sensitive, small-signal Sharp–Garn method49,50 is used to accurately extract pyroelectric coefficients. A sinusoidal temperature variation is applied to the sample by means of a Peltier element and a source measurement unit (Agilent B2900) and monitored by a platinum temperature sensor and a Keithley 2000 multimeter. The pyroelectric current is registered by a picoammeter (Agilent B2981A). To study the effect of a bias voltage on the pyroelectric response, we modify the Sharp–Garn method used in previous sections by introducing a voltage source (Agilent technologies, model 33250A) in series with the picoammeter and pyroelectric capacitor.

Measurements are performed in an FEI Tecnai F20 device. For EFTEM, a Gatan imaging filter is used. Analyzer pass energies of 99, 456, and 1662 eV are set for Si, Ti and Hf species, respectively.

This work was funded via a subcontract from Globalfoundries Dresden Module One within the framework Important Project of Common European Interest (IPCEI) by the Federal Ministry for Economics and Energy and the State of Saxony.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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