Dispersion in ferroelectric switching performance of polycrystalline Hf0

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Functional Inorganic Materials and Devices

Dispersion in ferroelectric switching performance of polycrystalline Hf0.5Zr0.5O2 thin films Seung Dam Hyun, Hyeon Woo Park, Yu Jin Kim, Min Hyuk Park, Young Hwan Lee, Han Joon Kim, Young Jae Kwon, Taehwan Moon, Keum Do Kim, Yong Bin Lee, Beak Su Kim, and Cheol Seong Hwang ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b13173 • Publication Date (Web): 24 Sep 2018 Downloaded from http://pubs.acs.org on September 27, 2018

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ACS Applied Materials & Interfaces

Dispersion in ferroelectric switching performance of polycrystalline Hf0.5Zr0.5O2 thin films Seung Dam Hyun,† Hyeon Woo Park,† Yu Jin Kim,† Min Hyuk Park,‡ Young Hwan Lee,† Han Joon Kim,† Young Jae Kwon,† Taehwan Moon,† Keum Do Kim,† Yong Bin Lee,† Beak Su Kim† and Cheol Seong Hwang†* † Department of Materials Science and Engineering and Inter-University Semiconductor Research Center, Seoul National University, Seoul 151-744, Korea ‡ School of Materials Science and Engineering, Pusan National University, 2, Busandaehak-ro 63beon-gil, Geumjeong-gu, Busan, 46241, Korea. KEYWORDS Hf0.5Zr0.5O2 film; Ferroelectric switching kinetics; Inhomogeneous switching; Statistical distribution; Activation field

ABSTRACT

Interests in nanoscale integrated ferroelectric devices using doped HfO2-based thin films are actively reviving in academia and industry. Main driving force for the formation of the metastable non-centrosymmetric ferroelectric phase is considered to be the interface/grain boundary

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energy effect of the small grains in polycrystalline configuration. These small grains, however, can invoke unfavorable material properties, such as non-uniform switching performance. This study provides an in-depth understanding of such aspects of this material through careful measurement and modeling of the ferroelectric switching kinetics. Various previous switching models developed for conventional ferroelectric thin film capacitors cannot fully account for the observed time- and voltage-dependent switching current evolution. The accurate fitting of the experimental results required careful consideration of the inhomogeneous field distribution across the electrode area, which could be acquired by an appropriate mathematical formulation of polarization as a function of electric field and time. Compared with the conventional polycrystalline Pb(Zr,Ti)O3 film, the statistical distribution of the local field was found to be three times wider. The activation field and characteristic time for domain switching were larger by more than one order of magnitude. It indicates that doped HfO2 is inhomogeneous and “hard” ferroelectric material compared with conventional perovskite-based ferroelectrics.

1. INTRODUCTION

Ferroelectric (FE) thin film possesses inherent bi-stable and switchable polarization, which could be a critical asset for digital information processing and data storage in the computer. Ferroelectric random access memory (FRAM) and ferroelectric field effect transistor (FEFET) have, therefore, been actively researched during the past two-three decades, but their commercialization has been accomplished only for a niche market, where a state-of-the-art integration density is not required.1-4 The main problem of the conventional FE thin films, such as perovskite-structured Pb(Zr, Ti)O3 (PZT) is the difficulty related to the scaling and


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unavailability of process techniques that can guarantee the conformal deposition of the PZT film over a three-dimensional capacitor structure.5 In 2011, the high ferroelectric functionality of doped-HfO2 film was first reported due to the emergence of unexpected orthorhombic-phase (ophase, space group: Pca21).6 O-phase is the meta- (or unstable-) phase in the fluorite structured material under the normal thin film processing conditions, where the monoclinic-phase (mphase, space group: P21/c) is the thermodynamically stable phase from the bulk free energy point of view.7-8 While the precise origin of such phenomenon is still under extensive research, it is quite clear that the surface or interface/grain boundary energy effect,9-10 as well as the defectrelated energy effect11, mainly contribute to the FE o-phase formation. Since then, many works reported effects from the different dopants,12-19,42 film thickness,10,20-21 composition,10,12-19 electrode material,6,12-13,22-23 and process conditions.20-21,23-25 Another notable finding was made from the HfO2-ZrO2 (HZO) solid solution system, where the two end members show a typical dielectric behavior, which is well known to the community. However, the middle compositions show highly intriguing ferroelectric and anti-ferroelectric (AFE) properties, depending on the thickness and composition.10,26 While these diverse performances of the films make it viable to apply the film to various areas, including semiconductor memory, solid-state energy-storage devices, and electrocaloric devices, they also incur complications in understanding the underlying nature of the material’s FE behavior.27-32,44,63-66 Especially, the FE switching kinetics constitute the fundamental cornerstones for a deeper understanding of this material. However, the detailed switching kinetics study of the HfO2- or HZO-based FE films have rarely been reported. Therefore, this work reports an in-depth study on the switching kinetics of 8.5-, 8.9- and 11.3-nm-thick Hf0.5Zr0.5O2 FE film grown by an atomic


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layer deposition (ALD) technique with TiN bottom and top electrodes through measuring the switching current – time characteristics for different pulse voltage heights. Salahuddin and Datta reported another eye-catching work in the field of FE thin film research in 2008,33 where they suggested that the FE thin film can show a negative capacitance (NC) effect when the materials remained near the depoled state (FE polarization ~ 0) based on the LandauDevonshire phenomenological internal energy theory. Because the polarized states in the FE materials coincide with the ground state, they suggested stacking an appropriate dielectric (DE) layer to the FE layer to induce sufficient depolarization field which would depolarize the FE film. While this was an intriguing idea, no conclusive experimental proof on the presence of the static NC effect has been made, due mainly to the formation of ferroelectric domains at the depolarized state both in the epitaxial and polycrystalline FE thin films. Equal portions of up and down domains can show macroscopically depoled state, but the material has no reason to show the NC effect. Therefore, the more recent focus has been shifted to confirm the transient NC effect, which might be induced by the mismatch between the switched polarization bound charge of the FE crystal and flow-in compensating charge through external circuits during the FE switching. In this regard, Khan et al. reported a voltage drop (V-drop) effect in a single epitaxial FE PZT thin film while the positive charges were flowing in through a serially connected resistor.34 They claimed that such effect is a fingerprint-proof of the involvement of the (transient) NC effect during the FE switching. Such argument fundamentally assumes a uniform polarization switching from one direction to the other, according to the Landau-Khalatnikov (LK) formalism. However, this assertion is in contradiction to the well-established FE switching model based on the reverse domain nucleation and growth. Therefore, the authors’ group recently reported that the identical V-drop effect experimentally observed in an epitaxial BaTiO3


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thin film can be much more precisely reproduced when the reverse domain nucleation and growth model is adopted to simulate the voltage-time transient behavior.35 From the simulation results, it was revealed that the involvement of the retardation (or incubation) time of the reverse domain nucleation plays a critical role in the emergence of the V-drop effect. Therefore, the Vdrop effect cannot be the direct proof for the emergence of the (transient) NC effect; rather it could be better explained by the well-established domain-mediated switching mechanism for the epitaxial FE films. Another intriguing work on the V-drop effect of the FE Si-doped HfO2 film, even more closely related to the topic of the present work, was reported by Hoffmann et al.36 They also used the L-K formalism to explain the observed V-drop effect in the polycrystalline FE film. However, due to the involvement of multiple grains, it may not be very reasonable to assume a spatially uniform switching, and thus, they asserted that the polycrystalline film has a distribution in their Landau parameters up to 30 %, of which distribution follows a Gaussian form. They could fit the experimental data to the modified L-K model and concluded that the observed V-drop effect from the polycrystalline FE film could also be attributed to the transient NC effect. However, the assertion that the Landau parameters have such a Gaussian variation lacks formal justification, because those are intrinsic material parameters, and in fact, they are not well known for the HfO2-based FE thin films. Therefore, an alternative interpretation of the observed V-drop effect should be considered for the epitaxial film mentioned above. In fact, the involvement of numerous nucleation sites for the reverse domain in polycrystalline film greatly enhances the chance for the FE switching proceed via the conventional reverse domain nucleation and growth. Nevertheless, this also invokes complications in simulating the observed time-transient FE switching behaviors via the conventional nucleation and growth model, such as Kolmogorov-Avrami-Ishibashi (KAI) model, which has been feasibly used for the previous


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epitaxial film case35. This is because of the possible involvement of various non-uniformities in the physical and chemical parameters of much thinner polycrystalline FE film as discussed later. Therefore, before exploring the V-drop or NC effect in thin films, it is impending to examine which FE switching model can precisely explain the observed polarization switching behavior. In this study, it was found that the previously well-established switching models, such as nucleation-limited switching (NLS),38-39 and more recent current-limited-switching (CLS),40-41 cannot appropriately explain the observed switching behaviors of HZO film. (Since the HZO thin film is polycrystalline, the KAI model37 which is well known to explain the switching of single crystal FE thin films was not considered in this paper.) These difficulties arose from the inevitable involvement of the parasitic circuit components, such as series resistance, which could be incurred by the relatively high resistance of the TiN electrode, compared with the conventional noble metal (Pt or Au) in PZT capacitors. Furthermore, even more significant problems are the non-uniform material properties of the HZO film due to its much smaller thickness (~10 nm) compared with the PZT (~100nm) and random orientation of the grains in the polycrystalline material. For example, 1-nm-thickness non-uniformity corresponds to 10 % variation of local film thickness for 10-nm-thick HZO film, whereas the same thickness nonuniformity corresponds to only 1 % change of local film thickness for 100-nm-thick PZT film. Also, the grain orientations of FE HZO films are reported to be almost random, implying that the relative correlation of polarization direction of o-phase (c-axis) and electric field direction is random among different grains.20 These are, in fact, quite disadvantageous toward achieving the optimum FE performance of the HZO films; the theoretically expected remanent polarization (Pr) is as high as 50 – 55 µC cm-2 9,43 but experimentally reported values are typically limited to be 10 – 30 µC cm-2. These factors not only are undesirable for device application, but also invoke a


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difficulty in understanding the switching kinetics as shown in detail below. In this regard, the recent model of inhomogeneous field mechanism (IFM) suggested by Zhukov et al.44 has high relevance to the experimental results of this work. IFM model encompasses the inhomogeneous distribution of the electric field across the electrode area, and could describe the various structural non-uniformity of the HZO film. Therefore, this new model is combined with the appropriate circuit model that precisely represents the actual test circuit. The pulse number or time-dependent switching effect must also be carefully considered. In HZO- and HfO2-based FE films, the wakeup (and its competition with fatigue) is another extensively reported unique behavior.41,45 It appears that the domain pinning/depinning by several factors is more significant within HfO2 or HZO based thin films compared with the conventional FE thin films. Therefore, such transient effect must also be carefully taken care of during the switching kinetics study. This work fully considers all these parametric variations across the electrode area and cycling transient variations of the FE performances by setting up an appropriate mathematical model, encompassing the statistical variations of the device parameters and circuit effects. The established model precisely reproduced the experimental observations and derived material parameters were calculated to be largely different from those of the conventional FE thin films. The possible origins of such significant difference and their physical implications on the device application were also discussed in detail in conjunction with other physical/chemical analysis.

2. EXPERIMENTAL PROCEDURE


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50nm TiN substrate which also is used as the bottom electrode for electrical tests was deposited on SiO2/Si via direct current (DC) sputtering. (ENDURA 5500, Applied Materials) 8.5-, 8.9 and 11.3-nm-thick HZO films were then prepared by thermal atomic layer deposition (ALD) at a substrate temperature of 280oC using Hf[N(C2H5)CH3]4 (TEMA-Hf), Zr[N(C2H5)CH3]4 (TEMAZr) and ozone as the Hf-precursor, Zr-precursor, and oxygen source, respectively. Since HfO2 and ZrO2 have almost identical ALD growth rate, the Hf0.5Zr0.5O2 films were deposited with 1:1 ALD cycle ratio. The composition and the film thickness of the HZO films were examined via X-ray fluorescence analysis (Quant'X, Thermo SCIENTIFIC) and spectroscopic ellipsometry (ESM-300, J. A. Woollam), respectively. For the electrical characterization, Pt(30 nm)/TiN(5 nm) top electrodes(TE) with the various areas were formed by DC sputtering through a shadow mask with 400 µm of hole diameter for 8.5nm, 11.3nm thick HZO films and lift-off lithography process for various TE size of 8.9 nm thick HZO films. All electrode areas were measured using the optical microscope. After the TE deposition, post-metallization-annealing was conducted at the 30s at 500 oC under N2 ambient condition pressure with 100 torrs using rapid thermal annealing for the film crystallization. The crystal structure of the HZO films was analyzed using an X-ray diffractometer (X’pert Pro, Panalytical) via grazing-angle incidence X-ray diffraction. For the pulse switching measurements, rectangular positive or negative pulses with a rising/falling time of 2 ns with various pulse widths were supplied by a pulse generator (81110A, Agilent) with an internal resistance of 50 Ω. The switching current response from the HZO film was monitored using an oscilloscope (TDS684Dm Tektronix) with an internal resistance of 50 Ω


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3. RESULTS AND DISCUSSION 3.1 Ferroelectric switching models and inhomogeneous thin film 3.1.1 Precautions for pulse switching test and inaccuracy of previous models Ferroelectric switching kinetics is studied by measuring the amount of switched polarization upon applying voltage pulses with different heights and lengths to a 50-nm-thick Pt/5-nm-thick TiN/8.5-, 8.9-, or 11.3-nm-thick HZO/50-nm-thick TiN ferroelectric thin film capacitor with various electrode areas. All electrode areas were measured using the optical microscope. Details for the sample fabrication and test methods are included in the experimental section. To avoid the interference from the wakeup effect, the FE capacitor was pre-cycled for 105 times with alternating negative and positive electric field pulses of 4 MV cm-1 height and 10µs length. Before the detailed discussions on the analysis of the switching kinetics of the FE HZO thin films, several precautions should be taken not to cause the adverse influence of the imprint effect, which could be induced by the repeated voltage pulse application. Among the several methods to avoid such adverse effect, cycling the sample with four consecutive positive-negative pulses with 10µs was effective. After settling the appropriate testing sequence, the conventional NLS, and CLS models were applied to the experimental polarization – time or switching current – time curves, with different bias voltages and electrode areas. However, none of the previous models can precisely simulate the experimental results. All these preliminary test results and detailed discussions on the possible reasons for the failure of the attempted simulations are included in online Supporting Information (SI). 3.1.2 New ferroelectric switching model considering inhomogeneous material parameters


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The electrical representation of the test circuit when the voltage is applied to the ferroelectric capacitor is shown in Figure 1. Ferroelectric capacitor effectively consists of the parasitic capacitor (Cp) which includes background ferroelectric capacitance and circuit parasitic components from the pulse generator, oscilloscope, and wires, and a component that acts as a variable resistor when FE switching occurs. This FE component induces the switching current flow (if) to compensate for polarization during switching. Resistor (Rs), which includes contact resistance, the internal resistance of the pulse generator and oscilloscope, is connected serially. When the voltage V0 is applied, the parasitic capacitor is charged before switching. Under this circumstance, mere dielectric charging current (iP) occurs and current through Rs (iR) which is observed in oscilloscope decreases with time according to Equation 1, = =

−

(1)

As for the switching starts, an if is generated, which can be represented as Equation 2, =

,

(2)

, where A is the area of the FE capacitor. From the Kirchhoff’s law, = + =

=

+

,

(3)

The time-dependent VF can be calculated by solving these differential equations, and from iR = (V0 -VF)/Rs, iR can be obtained. In order to solve the Equation 3, time and voltage-dependent polarization P(t, VF) should be determined. This term reflects the material properties of the thin film. In this work, the IFM


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model is used for P(t, VF).44 Fundamental concept of this model is that when the external field (EF) is applied to a thin film, the different field (E) is applied in each region of the thin film due to the inhomogeneous thickness, grain size, interface quality between the film and electrode, and other possible reasons. Therefore, each grain of the polycrystalline HZO thin film has various switching time (τ). The correlation between the E and the τ is well known as Merz's law46-47 and is expressed as Equation 4. τE = !" $ %& # #

(4)

, where τ0 is the characteristic time and Ea is the activation field. These two parameters are proportional constants of the relationship between switching time and external field. If these values are large, the switching occurs slowly under a given electric field. In IFM model, the distribution of the normalized field, E/EF, is assumed as Gaussian distribution. In this case, total polarization reversal (∆P), which depends on t and EF, is represented by Equation 5, ∆P)* , + = ,- ./0 1

2$ 5 7 2 34 6

8√:

;

(5)

, where erfc (x) is a complementary error function, σ the standard deviation of E/EF, and t the observation time. τ represents the switching completion time and has different values for each grain because of the effective field distribution. Therefore, the switching of the grains which have τ smaller than t is completed at observation time t. Since each grain switches very quickly, their switching process is assumed to have a step function form. Detailed processes for the formalism derivation were reported previously44 and also included in on-line SI. Since grain


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boundary prevents domain wall propagation over the grain size, this model more adequately reflects the switching characteristics of HZO thin films with a small grain size of ~10 nm. Equation 5 is substituted to Equation 3, and the differential equation was solved. In this way, switching kinetics was analyzed by considering circuit equation and material property of the HZO. 3.2 Application of the new model to HZO capacitor and Discussion 3.2.1 Analysis of switching kinetics of HZO with the new model. In order to apply the IFM model described above to switching kinetics, it is necessary to determine the involved parameters in Equation 1 ~ 5: σ, Cp, Rs, A, Pr, Ea, and τ0. Therefore, the fitting of experimental data (current – time curves) with such model is quite complicated due to the involvement of many variables. Nonetheless, with the reasonable and systematic fitting procedures, the appropriate fitting can be accomplished as shown below. Figure 2a shows the voltage dependence of polarization reversal from the 8.5-nm-thick HZO film with an A value of ~102300µm2. It was pre-cycled for 105 times with alternating negative and positive rectangular electric field pulses of 4 MV cm-1 height and 10 µs length. The derivative, ∂∆P(V,t)/∂V, can be calculated from Figure 2a and normalized by dividing it by its maximum value, ∂∆P(V,t)/∂V|max. The voltage is also normalized by dividing it by the Vdm, where ∂∆P(V,t)/∂V has the maximum. Figure 2b shows the plot of the normalized ∂∆P(V,t)/∂V versus V/Vdm. In IFM model, these normalized values have the relation as Equation 644. ,?/

,?/|B$C

= DE F1 − DE − H 7

7

7DE DE

I

(6)


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, where ξ = V/Vdm and γ = 2/L√1 + 8N : − 1O. Since Equation 6 has a single parameter, γ,

which depends only on σ, γ can be obtained by fitting Equation 6 to the experimental results. The fitting is represented by a solid red line in Figure 2b, and the estimated σ value was 0.32. This value is higher than that estimated from the polycrystalline 1 mm-thick PZT film (0.11) with Ag electrodes,44 implying more non-uniform switching domains in HZO film of the present work, which has been already discussed in the Introductory section. This σ value is processdependent, and it may not be improbable to grow ferroelectric HZO film having a σ value which is even lower than that of the specific PZT by the process optimization of the HZO film. In addition, it is reported that the ferroelectric phase and the non-ferroelectric phase are mixed in HZO film, which also complicates the electric field distribution in the thin film. The dielectric constant of a ferroelectric phase (~29 9) and a non-ferroelectric phase (~49 for tetragonal-phase (t-phase) and ~24 for m-phase9) are quite different. Moreover, the uncompensated polarization of the ferroelectric phase at the boundary between the ferroelectric and non-ferroelectric phase should induce inhomogeneity in field distribution. If the amount of non-ferroelectric phase remaining after wakeup is unevenly distributed across the film area, the electric field applied to the ferroelectric phase may be varied for each grain. Furthermore, it is known that when TEMAHf or TEMA-Zr is used as the metal precursor, a considerable amount of residual C, H, N or their compounds can be present in the deposited thin films.48-50 Oxygen vacancy is another potential impurity in the HZO thin films, which were reported to significantly affect the electrical properties of HfO2 or HZO based thin films. Especially, the wakeup process is known to be strongly related to the redistribution of oxygen vacancies during repetitive field cycling. The inhomogeneous spatial distribution of the aforementioned defects is believed to influence the inhomogeneous distribution of electric field in this study.


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Cp and Rs can be estimated from the voltage-dependent charging and discharging behavior of the capacitor. Discharging current generated by the applied voltage was integrated over time to obtain the amount of discharging charges. Then, Cp was obtained from the applied voltage and charge relation. In addition, Rs was calculated from the RC constant. As a result, Cp and Rs values were measured to be 3.77nF and 135Ω, respectively. The 2Pr value was determined to be 40µC cm-2 from Figure 2a. Therefore, iR can be simulated as a function of time using Equation 3 with the predetermined measured values of σ, Pr, Rs, Cp, and A values while adjusting Ea and τ0 values. Figure 2c shows the result of fitting the switching current – time curves for the voltage pulses from 1.6 to 3.4V. The entire curves can be precisely fitted with the model (red lines), and the estimated Ea and τ0 values were 8.94 MV cm-1 and 1.0 x 10-10 s, respectively. The estimated Ea and τ0 values are larger than those of PZT (0.25MV cm-1 and 10-11 s44) by more than one order of magnitude, suggesting that the FE switching in HZO requires higher energy and is more timeconsuming. This is consistent with the much higher coercive field (0.8 - 2 MVcm-1) of these materials compared with that of the PZT (~0.1MV cm-1). (It should be noted that the coercive field extracted from the P-E curves is generally overestimated since the electric field divided to other circuit parameters are not well considered.40-41 From the pulse measurement, the coercive field of ~0.6 MV cm-1 was estimated.) Such observation was further confirmed by the FE capacitors with different areas as shown in Figure 2d. In these additional experiments, the 8.9nm-thick HZO capacitors with the electrode areas of ~24700, ~42600, and ~67400µm2 were used. The Cp value was varied to be 0.94nF, 1.62nF, and 2.57nF, and Rs and 2Pr values of 160Ω and 26µC cm-2, respectively, were used to calculate iR. It should be noted that a different process was adopted to form top electrodes with different size. Pt(30 nm)/TiN(5 nm) top electrodes(TE) with the various areas were formed by DC sputtering through a shadow mask with 400 µm of


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hole diameter for 8.5nm thick HZO films, whereas lift-off lithography process was conducted for various top electrode size for 8.9 nm thick HZO films. The much smaller Pr values of the 8.9 nmthick HZO film compared with that of the 8.5 nm-thick HZO film is due to the involvement of the damaging process effect incurred during the top electrode fabrication. For the 8.9 nm-thick HZO film case, a lift-off process was used, which appears to damage a certain portion of the grains or domains, whereas the 8.5 nm-thick HZO film was processed using the shadow-mask process. In fact, these two films intentionally selected to show the general applicability of the method to the cases where the film thickness is almost identical but have largely different Pr values. Despite the largely different Pr values, the estimated material parameters, such as Ea and τ0, did not show any critical differences. This finding implies that the non-ferroelectric region (damaged region) does not contribute to the switching process, and the switching region shows similar ferroelectric performances irrespective of the presence of nearby (parallel) nonferroelectric regions. In addition, the results here are useful for examining the effect of electrode area on switching parameters. The accurate fitting in FE switching region results (red lines) with identical Ea, τ0 and σ indicate that the model is applicable irrespective of different electrode areas. It should be noted that the fitting is inaccurate in the very low voltage region. This deviation could be interpreted as an indication of the presence of a tiny portion of grains or domains having distinctively smaller coercive voltage from the assumed single Gaussian distribution. This deviation also affects the RC charging in the low voltage range, which also causes a deviation in fitting at the beginning of the current-time fitting. However, its contribution to overall switching performance is negligible especially at higher voltages where majority of domains responds to the applied voltage. Therefore, this small portion is disregarded in this work.


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Chouprik et al. recently observed the switching behavior of TiN / Hf0.5Zr0.5O2 (10nm) / TiN capacitor by a piezoresponse force microscopy, where a gradual growth of switched area with the increasing field strength was observed.51 When the field is applied, and the effective field distribution is caused by the inhomogeneity of the thin film, the grain where the highest field is applied will nucleate a reverse domain first. Subsequently, the regions or grains where the slightly lower effective field is applied, which may most probably locate near the previously switched grains, will be switched. Such progressive switching mechanism may render that the ferroelectric switching in the inhomogeneous film occurs across the neighboring grains although the domain wall itself might be difficult to pass through grain boundaries. 3.2.2 Effect of the film thickness In Introduction, a much smaller film thickness of the HZO film than that of the PZT films was suggested to be a potential cause for an inhomogeneous distribution of electric field. As previously mentioned, a rather small non-uniformity in film thickness can induce quite large distribution in electric field distribution. Park et al. examined the surface morphology of the HZO thin films, and the root-mean-square roughness was smaller than 1 nm,52 suggesting that the effect of non-uniform thickness might be only a few % level in the HZO thin films. On the other hand, it is well known that the non-ferroelectric m-phase fraction in HZO film increases with increasing film thickness due to the decrease in interface (or grain boundary)-to-volume ratio.9-10 According to the interface/grain boundary energy model, m-phase is expected to form within grains with sufficiently large size. To examine the effect of film thickness on the inhomogeneous field distribution, the same model was further applied to the FE capacitors with slightly thicker HZO film (11.3 nm, A = ~98100µm2) to see if there are any notable changes in the critical material parameters. From GIXRD, it could be confirmed that the 11.3-nm-thick


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HZO film has a certain portion of m-phase which could not be observed in 8.5-nm-thick HZO film. The GIXRD patterns of 8.5 and 11.3-nm-thick HZO films are included in Figure S4 of SI. The thickness difference of 2.8 nm is insufficient to cause a significant difference in RMS roughness. Thus, by comparing the switching kinetics of these two films, the effect of the mphase fraction can be examined. Figure 3a~b shows the voltage dependence of polarization reversal and the normalized ∂∆P(V,t)/∂V vs. V/Vdm plot of this sample (green dots). For a fair comparison, this sample was also wakeup cycled for 105 times. In Figure 3b, data from Figure 2b are also appended for comparison (black circles). Both datasets can be fitted with the same simulation parameters (red line), suggesting that the σ value (0.32) stays constant for such film thickness change range. Figure 3c shows the fitting results with voltage pulses ranging from 2.12 to 3.8V. The values of σ, 2Pr, Cp, and Rs, were measured by the same method as above and were 0.32, 30 µC cm-2, 2.45 nF, and 152 Ω respectively. The Ea and τ0 values determined by the precise fitting were 8.85 MV cm-1 and 1.1 x 10-10 s. The important finding is that the most critical material parameters, Ea and τ0, were remained almost unaltered even with the thickness change and accompanying Pr variation. This result suggests that the field distribution in HZO films was not strongly affected by the existence of non-ferroelectric m-phase. Since the dielectric constant of the o-phase (29) and the m-phase (24) are quite different, the existence of the m-phase is expected to influence the field distribution. Thus, the result seems contradictory with the model in this study. However, this discrepancy can be understood when the spatial distribution of non-ferroelectric phase is considered. As previously mentioned, the formation of the m-phase is strongly affected by the


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lateral grain size based on the interface/grain boundary energy model. The sufficiently larger grains might crystallize into the m-phase, while others crystallize into the o-phase or the t-phase. This means that the non-ferroelectric m-phase is expected to exist laterally adjacent to the ferroelectric o-phase, and this cannot influence the inhomogeneous distribution of the electric field along the normal direction to the film surface. Consequently, the fitting parameters including σ is dominantly governed by the o-phase fraction of HZO film, so the differences in the fitting parameters can be negligible. The variation in the coercive field (Ec) of ferroelectric materials was examined by Kay and Dunn (Kay-Dunn law), where the Ec of triglycine sulphate (TGS) showed a dependency of Ec ~ d-2/3 (d is the ferroelectric crystal thickness).53 This law was later applied to the thin films of PVDF, PZT, and KNbO3 by Chandra et al., where the normalized Ec of the three materials can be described by a single functional form of Ec ~ Cd-2/3 (C is a constant depending on the types of the ferroelectric layer).54 Such a dependency was derived from the phase transition theory involving the critical dimension of stable nuclei of reverse domains at one electrode interface. However, the law fundamentally assumes the uniform and homogeneous material properties across the entire film thickness range as in the TGS single crystal in the original work of Kay and Dunn, which can hardly be the case in HZO of the present work. As described previously, the main driving force for the formation of the meta-stable ferroelectric o-phase in HZO is the subtle balance between the grain boundary/interface energy and bulk free energy. Therefore, film thickness itself is a critical experimental variable that influences the phase stability and phase purity. (Kim et al.55 reported that the Ec of the HZO thin film was hardly changed in the thickness range of 10 nm to 30 nm, which is in a stark contradiction to the expectation from the conventional Kay-Dunn law. However, the Pr decreased significantly because of the increase of the monoclinic phase, which


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is a non-ferroelectric phase.) Chandra et al. reported that the involvement of depolarization field due to the finite screening of metal electrode of the polarization charge (electrode polarization) in the cases of ultra-thin PVDF film.54 They reported decreasing Ec with the decreasing film thickness when the film was thinner than 2-3nm. However, the films with slightly larger thickness (> ~5nm) still follow the conventional Kay-Dunn law. Therefore, their model for the decreasing Ec with decreasing film thickness can hardly be applied to the present work. Rigorous discussion on the variation of Ec with the film thickness needs careful consideration of the phase evolution with film thickness, which is over the scope of the present work. Nonetheless, the estimated Ea and τ0 are independent of such variations, which can be understood from the fact that those parameters represent the properties of only the ferroelectric o-phase irrespective of the possible involvement of non-ferroelectric phases. 3.2.3 Wake up effect One of the characteristic features of the ferroelectric HZO thin film is the wakeup effect. The origin of such effect has been suggested by Pesic et al., where they used a high-angle annular dark field scanning transmission electron microscopy to prove that the effect can be mainly attributed to the phase transition from t-phase to o-phase at the electrode interface.45 Such transition was also accompanied by the migration of oxygen vacancies, which could be formed mainly near the TiN electrode interface due to the chemical reaction between the HZO and TiN layers, from the interfaces to bulk region of the HZO film. The adopted IFM model and fitting procedure to extract the various material and circuit parameters can be useful to elucidate further the physical change occurring during the wakeup.


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Therefore, the sample used in Figure 2 was taken and the pulse switching experiments were performed for the different wake up cycle numbers of 103, 5 x 103, 104, and 105, with the pulse voltages ranging from 1.6 to 3.4 V, as shown in Figure 4. It should be noted that the measurement process itself should not affect the extent of the wake up. In pristine HZO, it is known that wake up occurs rapidly only by a few field cycling.45 The very early stage of the wakeup process (< 103) of the HZO film could be largely affected by the small variations in analysis procedure and result in unreliable results. Thus, the evolution of polarization switching behavior after the wake up cycle of more than 103 times was examined. The data for 105 cycles are reproduced from Figure 2 for the sake of easy comparison. The experimental data were fitted to the IFM according to the previously described method. Figure 4a shows that the 2Pr value increases with increasing the wake up cycles, which is consistent with the previous report.41 Figure 4b shows that the σ value decreases with increasing wake up cycles and the higher level of coincidence between the experimental data and fitting results in Figures 4c ~ f (red lines) implies that the IFM model is feasibly applicable for different numbers of wake up cycles. The critical kinetic parameters can be extracted accordingly, and the results are summarized in Table 1. Rs did not show any notable changes, which seems reasonable because its value should mainly represent the spreading resistance of the electrode, which has no reason to vary with the field cycling. The minute decrease in Rs for 105 cycles could be attributed to the possible decrease in contact resistance between the electrode and HZO film. Cp decreased with the increasing cycle, which is consistent with the finding of increasing Pr. Increased Pr coincides with the increased ophase fraction, and the dielectric constant of o-phase (~29) is lower than that of t-phase (space


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group: P42/nmc, ~49). Therefore, the Cp decrease is consistent with the finding of tetragonal-toorthorhombic phase transition with the increasing cycle number as suggested by Pesic et al.45 However, there are several notable findings. First, σ value was as high as 0.53 after the 103 cycles but decreased to 0.32 after the 105 cycles. This implies that the uniformity of the field on FE domains improves as the cycling proceeds. Secondly, the obvious decreases in Ea and τ0 could also be observed. In section 3.2, the increase in the m-phase fraction (by the film thickness increase) did not affect the Ea and τ0 values, since it was governed by the o-phase fraction in HZO films. Thus, the changes in Ea and τ0 implies that there might be some physical/chemical changes even in the o-phase fraction. The evolution of the σ value with increasing number of wakeup field cycling can be understood based on two reasons: 1) the migration of oxygen vacancies and 2) the phase transition at the HZO/TiN interfaces. It is generally accepted that the oxygen vacancies exist in +2 effective charge state in HfO2-ZrO2 thin films56-57. According to Pesic et al.’s previous work, most of the oxygen vacancies are expected to exist at the interfacial region, implying that the electric field across the bulk and interfacial region can be quite different.45 In that report, the oxygen vacancies migrate during the wakeup cycling process, and they are homogeneously distributed in the sufficiently woken-up state. This means that the inhomogeneity in spatial distribution of electric field should also decrease with increasing number of electric field cycling, which should refer to the decrease in σ value of IFM model. Moreover, the oxygen vacancies are expected to influence the domain switching in the o-phase. Thus, the observed changes in Ea and τ0 can also be attributed to the redistribution of oxygen vacancies during wake-up process. Therefore, the changes in Ea and τ0 are consistent with the change in σ with the cycling number in this model.


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Another critical factor is the phase transition during wakeup process. According to the previous studies on the wakeup effect, the existence of the t-phase at the interfacial region can induce inhomogeneity in the electric field distribution. Different from the m-phase formation discussed in section 3.2, the interfacial t-phase can affect the distribution of the film-normal electric field. Materlik et al. reported that the dielectric constant of each phase of HZO varies considerably according to the crystallographic axis.9 In particular, for the t-phase, the difference between the dielectric constant along the shorter two axes (~60 for a and b axes) and the longest one (~24 for c axis) is significant9 although the differences in the lattice parameters (a vs. c) of the t-phase is less than 2 % 58. Given the fact that the various crystallographic orientation combinations can be present in HZO bulk and interfaces, a large inhomogeneity in the distribution of the electric field is expected in the pristine or insufficiently woken-up HZO films. It should be noted that the oxygen vacancy redistribution and the interfacial phase transition cause the evolution of ferroelectric performance during wakeup field cycling. However, the woken up sample after 105 times field cycling still has a quite large σ value, suggesting that strong inhomogeneity in the distribution of the electric field still remains. Such inhomogeneous electric field in woken- up HZO film might result from the factors other than the oxygen vacancies redistribution and the interfacial phase transition, such as chemical impurities from the ligands of metal-organic precursors.48-50 These impurities can affect the chemical bonding state and local dielectric response. Park et al. showed that the interfacial hydrogen could strongly affect the electric properties of HZO thin films59, and Kim et al. reported that the residual C and/or N could influence the electric properties of HZO thin films.48-49 There could also be (partially) uncompensated polarizations at the grain boundaries due to the random orientation of the grains. Lastly, even the sufficiently woken-up state might not represent a complete disappearance of the


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interfacial non-ferroelectric phase or inhomogeneous distribution of oxygen vacancies. In addition, the difficulty of aligning polarization orientations along with the external fields can be an important factor affecting large σ value of HZO films. Kratzer et al.60 observed that the polarization orientation of polycrystalline tetragonal PZT thin film is favorably aligned along the direction of the external field after poling using vector piezoresponse force microscopy. In the case of tetragonal PZT, six equivalent polarization directions are possible, which provides the material with a favorable route to align the polarization along the field direction. Also, the domain size is usually smaller than the grain size suggesting that the domain wall motion during the poling is hardly interfered by the grain boundaries. When the direction of polarization is aligned with the direction of the applied field, a uniform effective field is applied to each domain, which could induce the small σ value in PZT. In contrast, orthorhombic HZO can only have two polarization directions, which is a quite unfavorable condition to align all the domains to the direction of applied field during poling (wake up in this case) or subsequent switching. In addition, since it has a columnar grain size of 10 nm, the ferroelectric domain wall motion can be easily disturbed by the presence of numerous grain boundaries. In this case, the direction of the polarization in different grains or domains can easily deviate from the external field direction. Since the magnitude of this deviation is different for the different grains, the components of the field applied in parallel to the polarization direction are also different for the different grain (or domains). As a result, a wide distribution of the effective field distribution can be produced. When the effect of the polarization orientation distribution is a critical cause of the large σ of HZO, it would be more accurate to reflect the orientation distribution function in the field distribution. However, the various factors mentioned above also have a considerable influence on the field distribution. Therefore, it is difficult to adopt a certain distribution function with a specific physical implication. In this paper, the Gaussian function is used to simulate apparent field distribution for the convenience of calculation. It is, therefore, the limit of the adopted IFM model because it cannot determine which one of the above factors has the greatest effect on the field distribution.


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There have been several previous studies in which different polarization switching mechanisms were suggested for ferroelectric HfO2-based films. Mueller et al. first reported the polarization switching mechanism in their 10 nm-thick Si-doped HfO2 thin films 32. In this paper, they found a linear relation between logarithmic switching time and switched polarization, which is considered as a characteristic sign of NLS model. The similar linear relation could also be observed in this study, but it was found that the switching time of HZO is electrode area dependent, which is inconsistent with the NLS mechanism. The linear relation is not caused by the nucleation time distribution as it was the case for the NLS model, but rather by the switching time distribution from the uneven local field distribution and charge supply rate determined by the external resistance and parasitic capacitance. The details of this discussion can be found in the online SI. Zhou et al.61 examined the polarization switching kinetics in both medium (Ec

Dispersion in ferroelectric switching performance of polycrystalline Hf0

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