We report on the thermal resistances of thin films (20 nm) of hafnium zirconium oxide (Hf1–xZrxO2) with compositions ranging from 0 ≤ x 1. Measurements were made via time-domain thermoreflectance and analyzed to determine the effective thermal resistance of the films in addition to their associated thermal boundary resistances. We find effective thermal resistances ranging from 28.79 to 24.72 m2 K GW−1 for amorphous films, which decreased to 15.81 m2 K GW−1 upon crystallization. Furthermore, we analyze the heat capacity for two compositions, x =0.5 and x =0.7, of Hf1–xZrxO2 and find them to be 2.18 ± 0.56 and 2.64 ± 0.53 MJ m−3 K−1, respectively.

Due to their unique ferroelectric behavior, ease of manufacture, and inherent silicon compatibility, HfO2-based systems have recently begun to garner attention as potential candidates for non-volatile memory, negative differential capacitance transistors, and energy harvesting applications, among others.1–4 Since ferroelectric properties were first demonstrated in 2011,5 various factors have been shown to allow stability of the ferroelectric phase, including alloying with Zr,6 depositing onto a nitride electrode layer such as TaN,7 as well as tuning the grain size and film thickness.6,8,9 The ferroelectric response of HfO2-based films is attributed to the polar crystalline structure inherent to the orthorhombic Pca21 phase.1,7 When alloyed with ZrO2, ferroelectricity in Hf1–xZrxO2 systems can be tuned with a field-induced phase transition from the tetragonal to orthorhombic phase,10 which broadens the horizons for application in energy storage devices as well as electronic memory devices and architectures.1 

While ample studies have focused upon the electrical and structural properties of Hf1–xZrxO2 systems,1,5–11 there exists a gap in the literature in terms of their thermal properties, particularly in thin-film form. Even for pure hafnia or zirconia, the literature on thermal properties is limited, especially with regard to heat capacity.12 The preferred method of fabrication for Hf1–xZrxO2 films is atomic layer deposition (ALD),1,11 and though prior studies have reported measurements of the thermal conductivity of ALD grown HfO213–16 films, there have been no studies investigating their thermal properties when alloyed with ZrO2. Furthermore, given the potential for HfO2-based materials to impact infrared sensing and thermal energy harvesting applications, knowledge of the thermal properties is vital to CMOS integrated device development.17 

In this study, we measure the thermal resistance and effective thermal conductivity of Hf1–xZrxO2 films, grown between TaN and aluminum electrodes, for nominal Zr doping concentrations of x =0, 0.5, 0.7, and 1. As annealing enables crystallization into the ferroelectric phase in Hf1–xZrxO2, we report on the effective thermal conductivity values for both annealed and unannealed films. Furthermore, our use of time-domain thermoreflectance (TDTR) for thermal metrology allows for determination of the volumetric heat capacity of selected Hf1–xZrxO2 films when deposited on thermally insulating substrates. Thus, we also report on the measured volumetric heat capacity of films for nominal Zr concentrations of x =0.5 and x =0.7, a thermophysical parameter that is critical for further development of devices based on this material, for example, devices leveraging pyroelectric effects.17,18

Samples were fabricated by rf-magnetron sputtering a 10 nm thick TaN layer onto (001) silicon substrates. Thermal atomic layer deposition (ALD) was then used to deposit 20 nm thick films of Hf1–xZrxO2 for compositions ranging from 0 ≤ x 1. The precursors for the HfO2 and ZrO2 cycles included Tetrakis(dimethylamino) hafnium (TDMA Hf) and Tetrakis(dimethylamino)zirconium (TDMA Zr), respectively, at 75 °C, with H2O used as the oxidant for both. For HfO2 and ZrO2, the growth per cycle (GPC) was 0.1086 and 0.0968 nm, respectively, measured via ellipsometry. To control the composition of the Hf1–xZrxO2 films, the number of cycles for each precursor was adjusted relative to the other. For example, for x =0.5 (5:5 Hf:Zr), 20 “supercycles” of 5 ZrO2:5 HfO2 were utilized, and for x =0.7 (3:7 Hf:Zr), 20 “supercycles” of 7 ZrO2:3 HfO2 were utilized. This process yielded films with a nominal thickness of 20 nm with a variance of 0.068–1.72 nm, depending on the composition. Actual film compositions are Hf0.58Zr0.42O2 for the 5:5 Hf:Zr film and Hf0.36Zr0.64O2 for the 3:7 Hf:Zr film, as determined by x-ray photoelectron spectroscopy on identically prepared samples.11 To facilitate the thermal property analysis, control samples were also fabricated without a Hf1–xZrxO2 layer on both Si and SiO2 substrates. For further details of fabrication processes, we direct readers to a prior study.11 

Following fabrication, a subset of the samples were subjected to a 30 s anneal at 600 °C using a rapid thermal annealer in a nitrogen atmosphere. To analyze crystallinity, grazing incidence x-ray diffraction (GIXRD) was performed for samples of each composition. An ω angle of 2° was utilized, and measurements were taken over a range of 26°–33° of 2θ. We find that in the unannealed state, the films are amorphous, in agreement with prior findings for unannealed films.6 As shown in Fig. 1, after annealing, Hf1–xZrxO2 films crystallize into either monoclinic or mixed tetragonal/orthorhombic phases depending upon the concentration of zirconia. For films containing primarily hafnia, the 1¯11 and 111 reflections of the monoclinic phase are readily apparent at 28.4° and 31.6° in 2θ, respectively.5,6,11,19 For films with zirconia concentrations greater than or equal to 50%, the intensity of the monoclinic phase reflections is reduced, and 011 and 111 reflections associated with a mixture of the orthorhombic/tetragonal phase are intensified, which occur at approximately 30.4° in 2θ.1,11,19 Film phase fractions were quantified via the ratios of the integrated peak intensities20 for the monoclinic and tetragonal/orthorhombic phases. Intensities of the pure HfO2 (monoclinic) and ZrO2 (tetragonal) reflections and atomic scattering factor differences with composition were used in normalization to account for structural and compositional dependences of peak intensity, respectively. Volumetric phase fractions of 0.08 monoclinic and 0.92 tetragonal/orthorhombic were calculated for the 3:7 Hf:Zr film and 0.59 monoclinic and 0.41 tetragonal/orthorhombic were calculated for the 5:5 Hf:Zr film.

FIG. 1.

(a) GIXRD measurements of annealed samples for various compositions of Hf1–xZrxO2. (b)–(d) The polarization field responses for the annealed Hf1–xZrxO2 films with nominal concentrations of x =0, 0.5, and 0.7, respectively. The black, innermost curves display polarization field responses for an applied voltage of 1 V; the lighter shades, moving outward, display voltage increases in 1 V increments, ending with an applied voltage of 6 V (light orange) for the outermost curve.

FIG. 1.

(a) GIXRD measurements of annealed samples for various compositions of Hf1–xZrxO2. (b)–(d) The polarization field responses for the annealed Hf1–xZrxO2 films with nominal concentrations of x =0, 0.5, and 0.7, respectively. The black, innermost curves display polarization field responses for an applied voltage of 1 V; the lighter shades, moving outward, display voltage increases in 1 V increments, ending with an applied voltage of 6 V (light orange) for the outermost curve.

Close modal

To verify ferroelectric responses in the Hf1–xZrxO2 films, polarization electric field responses were measured for nominal compositions of x =0.5 and x =0.7 and contrasted against pure hafnia. To make these measurements, contacts were fabricated on the surface of the Hf1–xZrxO2 films: a 10 nm electrode layer of TaN was sputtered onto the surface followed by a 70 nm layer of platinum which was rf-magnetron sputtered through a shadow mask in order to create square contacts with side lengths of approximately 635 μm, separated by 2 mm in a two dimensional array. A reactive ion etch was then used to etch the TaN layer in between the platinum contacts leaving isolated electrodes atop the exposed Hf1–xZrxO2 layer. Polarization-field measurements were collected with voltage biases ranging from ±1 to ±6 V, as displayed in Figs. 1(b)–1(d). For all as-deposited Hf1–xZrxO2 films, we measure a linear dielectric response (not shown). For the annealed HfO2 sample, as shown in Fig. 1(b), the same linear response can be seen. For annealed samples of Hf0.58Zr0.42O2 and Hf0.36Zr0.64O2, hysteresis is displayed in the polarization-field response, confirming ferroelectric behavior in the films.8,11

Following an alcohol clean (five minute sonications in isopropanol, acetone, and methanol, respectively), the samples were then coated with an 80 nm aluminum layer via electron beam evaporation to prepare them for thermal property measurements via time-domain thermoreflectance (TDTR).21 We utilize a repetition rate of 80 MHz and a central wavelength of 800 nm (bandwidth of 10.5 nm) and spot sizes of 18 and 11 μm in diameter for the pump and probe beams, respectively. The thermal properties of the samples were measured by fitting the ratio of the in-phase to out-of-phase lock-in signals to a thermal model, the particulars of which have been thoroughly detailed in the literature.21–24 

Due to the thinness of the Hf1–xZrxO2 and TaN layers, we do not directly fit for the intrinsic thermal conductivity of the Hf1–xZrxO2 layer since we cannot explicitly separate the thermal conductivity of the layer from the interfaces using a single measurement on a single sample.13,26 Rather, we treat the two layers as an effective resistive interface between the aluminum transducer and the silicon substrate. As such, when modeling the TDTR data, we treat each sample as a two layer system and fit for the effective thermal boundary conductance. In order to quantify the thermal resistance associated with the Hf1–xZrxO2 layer (REff), we take the inverse of the measured thermal boundary conductance and subtract the thermal resistances measured from the sample without an Hf1–xZrxO2 layer (complete calculations are detailed in the supplementary material). The error in the measurement is attributed to measurement repeatability, uncertainty in aluminum thickness, and uncertainty in the interfacial resistance between aluminum and TaN, which has been taken from the literature.25 For the effective film thermal conductivity, κEff, we take the product of the film thickness and the inverse of the thermal resistance. An additional source of uncertainty is introduced here for film thickness variation in the ALD Hf1–xZrxO2 films. The results for REff and κEff are displayed in Figs. 2(a) and 2(b), respectively.

FIG. 2.

(a) The effective thermal resistance of the Hf1–xZrxO2 films as a function of ZrO2 concentration, x. (b) recasts this resistance as an effective thermal conductivity, κEff, which is the product of the film thickness and the inverse of its associated thermal resistance. In both panels, the unannealed samples are represented by solid blue squares, whereas the annealed samples are represented by open red circles.

FIG. 2.

(a) The effective thermal resistance of the Hf1–xZrxO2 films as a function of ZrO2 concentration, x. (b) recasts this resistance as an effective thermal conductivity, κEff, which is the product of the film thickness and the inverse of its associated thermal resistance. In both panels, the unannealed samples are represented by solid blue squares, whereas the annealed samples are represented by open red circles.

Close modal

In addition to thermal resistance, heat capacity is also of interest for thin Hf1–xZrxO2 systems. For nominal compositions of x =0.5 and x =0.7, a second set of samples were fabricated and annealed in the same manner as previously described, on top of a 400 nm layer of SiO2 on silicon in order to increase sensitivity to the volumetric heat capacity of the Hf1–xZrxO2 layer (sensitivity analysis in the supplementary material). To a first approximation, the thermal penetration depth, δ, can be estimated as δ=κ/(πCvf), where κ is the layer thermal conductivity, Cv is the volumetric heat capacity, and f is the modulation frequency of the pump.27,28 Setting κ = 1.35 W m−1 K−1 and Cv = 1.65 MJ m−3 K−1, the thermal penetration depth in SiO2 can be estimated as 228 nm for a pump modulation frequency, f, of 5 MHz. More rigorous formalisms provide higher degrees of accuracy for the actual thermal penetration depth;29–31 however, given that the thickness of the SiO2 films is 400 nm and all modulation frequencies were above 5 MHz, it is safe to assume that the thermal penetration depth is contained within the SiO2 layer. As such, we utilize a four-layer model for sensitivity calculations and when fitting for volumetric heat capacity; the four layers consist of an 80 nm aluminum transducer layer, followed by the 20 nm Hf1–xZrxO2 films, followed by 10 nm of TaN, on a SiO2 substrate.

For the four-layer model, we verify the aluminum thickness through profilometry and picosecond ultrasonics32–35 (80 ± 5 nm), calculate the thermal conductivity via the Wiedemann-Franz law from four-point probe resistivity measurements (110 W m−1 K−1), and assume a literature value of 2.43 MJ m−3 K−1 for the volumetric heat capacity at room temperature.36,37 For the SiO2 substrate, we apply a thermal conductivity of 1.35 W m−1 K−1 and assume a literature value of 1.65 MJ m−3 K−1 for the volumetric heat capacity of intrinsic silicon at 300 K.38 For the TaN layer, we sputter a 10 nm layer of TaN on top of SiO2 and verify thickness through profilometry (10 ± 1 nm). We measure the effective thermal conductivity in the same manner previously discussed, which is found to be 1.48 ± 0.21 W m−1 K−1. For reference, Bozorg-Grayeli et al. have reported values of 3.0 and 3.4 W m−1 K−1 as the intrinsic thermal conductivity of TaN films of 50 and 100 nm, respectively.25 We note that our measured effective thermal resistance of the TaN layer also includes the interfacial resistance between the aluminum transducer and the TaN layer; however, we proceed under the assumption that the resistance attributed to the TaN layer is the dominant resistance. For the lattice heat capacity of TaN, we apply a literature value of 2.94 MJ m−3 K−1.39 Given that the effective thermal conductivities of the Hf1–xZrxO2 films were determined from TDTR analyses of the Al/Hf1–xZrxO2/TaN/Si samples, the only unknown of these Al/Hf1–xZrxO2/TaN/SiO2 samples is the volumetric heat capacity of the Hf1–xZrxO2 film. To decrease the uncertainty in our reported values of heat capacity of the Hf1–xZrxO2 film, we analyze TDTR sensitivity calculations.40,41 In summary, we find an increase in sensitivity to the heat capacity of the Hf1–xZrxO2 layer when there is an SiO2 layer and also by analyzing the data from the in-phase signal. Therefore, we analyze the in-phase signal for samples of Hf1–xZrxO2 concentrations of x =0.5 and x =0.7, fitting only for the heat capacity of that layer. To enhance accuracy further, we analyze data for pump frequencies of 5.82, 8.4, and 12.2 MHz. Further details of the sensitivity analysis can be found within the supplementary material.

A few observable trends in the effective thermal conductivity and thermal resistance of the Hf1–xZrxO2 films emerge from Fig. 2. First, it is of note that the effective thermal conductivity is, in most cases, significantly higher when subjected to a 30 s anneal at 600 °C. We attribute this increase to an increase in crystallinity of the film, which was verified through GIXRD. A second, more subtle result, for the annealed samples, shown in Fig. 2, is a slight decrease in the mean effective thermal conductivity for alloys of HfO2 and ZrO2. While all effective thermal conductivity values are within error, no definitive claims can be made regarding trends in the data; however, it can be observed that the nominal effective thermal conductivity ranges from 5.8% to 25.7% higher for pure HfO2 or ZrO2 compared to alloys of the two. Similar results have been shown in a number of other alloyed material systems owing to alloy scattering of phonons.47–50 There are no signs of this trend for the unannealed samples. As the unannealed samples are amorphous and because the measured effective thermal conductivities of the pure hafnia and zirconia films are nearly identical, compositions of the two would yield a negligible change in thermal conductivity. We re-emphasize, however, that these observations are based upon the nominal values of the measurements, and overall trends within the two different datasets (as-deposited and annealed) cannot be concluded with high certainty due to the relatively large uncertainties in these effective thermal conductivities. However, our results do conclusively show that annealing the Hf1–xZrxO2 films increases the thermal conductivity, which we attribute to crystallization of the as-deposited amorphous film.

For the results of the heat capacity measurements in Table I, we note that, with their associated uncertainties, the measurements are within error of previously reported measurements for the heat capacity of pure hafnia or pure zirconia. For Hf0.58Zr0.42O2, we report a volumetric heat capacity of 2.18 ± 0.56 MJ m−3 K−1, which is slightly lower than prior measurements of pure HfO2, and 2.64 ± 0.53 for Hf0.36Zr0.64O2. Of the existing measurements for the room-temperature heat capacity measurements of HfO2, all are of the monoclinic phase.12,42–44 Because compositions of x 0.5 for Hf1–xZrxO2 have been shown to also include tetragonal and orthorhombic crystalline phases,1,11 it could serve to explain why we measure a slightly lower heat capacity. We also note relatively large error bars in our measurement of approximately 30% for the two measurements. While all the fits for the heat capacity have a low mean square error [as can be seen in Fig. 3(a)], we gain further insight into the accuracy of the TDTR data fit for heat capacity by generating a contour in Fig. 3(b), which illustrates uncertainty in the interplay between the effective thermal conductivity and heat capacity of a Hf1–xZrxO2 film. We utilize a similar uncertainty contour calculation as has been previously outlined in the literature,51–54 which calculates the sum of the standard deviation between the fitted thermal model and the measured data, according to the following equation:52 

σ=1ni=1n(Xm,iXd,iXd,i)2,
(1)

where Xm,i and Xd,i represent the in-phase values from the thermal model and the measured TDTR data, respectively, at time delay, i, and n is the total number of time delays in a particular TDTR scan. The best fit of the thermal model to the TDTR data provides the lowest value of σ, which we denote as σmin. Therefore, a contour with a constant value of 2σmin would correspond to a 95% confidence interval for combinations of thermal conductivity and heat capacity which produce a standard deviation less than or equal to 2σmin. As an example, we use Eq. (1) to calculate a σ contour plot for a Hf0.36Zr0.64O2 sample measured with TDTR at a modulation frequency of 8.4 MHz [shown in Fig. 3(b)]. The best fit to the data in this example provides a σmin of 5.05 × 10−5, and therefore, a 95% confidence interval can be generated by outlining a contour of σ values equal to 1.1 × 10−4. Therefore, for a given thermal conductivity of 1 W m−1 K−1, heat capacity values ranging from 2.1 to 2.5 MJ m−3 K−1 could be obtained within a 95% confidence interval. As the thermal conductivity of the Hf1–xZrxO2 layer is not the only parameter with uncertainty in the thermal model, we utilize propagation of error to take into account uncertainty in the thickness of all films in the stack (Al, Hf1–xZrxO2, and TaN), as well as uncertainty in the Hf1–xZrxO2 and TaN effective thermal conductivity to obtain the error displayed in Table I.

TABLE I.

Room temperature volumetric heat capacities for Hf1–xZrxO2. For reference, specific heat values are also provided for x =0 and x =1 and are displayed as volumetric capacities assuming the materials are fully dense.

Hf1–xZrxO2 (x)Cv (MJ m−3 K−1)References
2.63–2.77 12 and 42–44  
0.5 2.18 ± 0.56 This study 
0.7 2.64 ± 0.53 This study 
2.56–2.60 42, 43, 45, and 46  
Hf1–xZrxO2 (x)Cv (MJ m−3 K−1)References
2.63–2.77 12 and 42–44  
0.5 2.18 ± 0.56 This study 
0.7 2.64 ± 0.53 This study 
2.56–2.60 42, 43, 45, and 46  
FIG. 3.

(a) Representative TDTR data which have been fit for the heat capacity of the Hf0.36Zr0.64O2 film at frequencies of 5.82, 8.4, and 12.2 MHz. The open symbols display measured data, and the solid lines represent their associated fits. (b) A contour plot which displays the standard deviation, σ, between the thermal model and measured TDTR data for the Hf0.36Zr0.64O2 sample at a modulation frequency of 8.4 MHz. The black dashed contour provides a boundary outlining a 95% confidence interval, defined as 2σmin, for a given thermal conductivity.

FIG. 3.

(a) Representative TDTR data which have been fit for the heat capacity of the Hf0.36Zr0.64O2 film at frequencies of 5.82, 8.4, and 12.2 MHz. The open symbols display measured data, and the solid lines represent their associated fits. (b) A contour plot which displays the standard deviation, σ, between the thermal model and measured TDTR data for the Hf0.36Zr0.64O2 sample at a modulation frequency of 8.4 MHz. The black dashed contour provides a boundary outlining a 95% confidence interval, defined as 2σmin, for a given thermal conductivity.

Close modal

In summary, we report on the effective thermal resistance of thin films of Hf1–xZrxO2 for compositions ranging from 0 ≤ x 1, in addition to the heat capacity of two different film compositions. Ultimately, we find the effective conductivity of the films to be the highest for pure concentrations (in this case, hafnia and zirconia) and slightly decreased for alloys of the two. Furthermore, we note an increased thermal conductivity when films are subjected to a 30 s anneal at 600 °C, which is attributed to the formation of the monoclinic crystalline phase for films consisting primarily of hafnia and tetragonal/orthorhombic crystalline phases for samples alloyed with zirconia. Given the limited nature of literature regarding the thermodynamic properties of hafnia-zirconia systems, and the promise that Hf1–xZrxO2 has demonstrated as a ferroelectric material, characterization of its thermal properties in thin film form is critical for considerations in computing and pyroelectric applications.

See supplementary material for details of the thermal resistance calculations, tabulated data for the thermal measurements, and sensitivity analyses.

Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. DOE's National Nuclear Security Administration under Contract No. DE-NA-0003525. The views expressed in the article do not necessarily represent the views of the U.S. DOE or the United States Government. This material is based upon work supported by the Air Force Office of Scientific Research under Award No. FA9550-18-1-0352.

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