Letter pubs.acs.org/NanoLett
Voltage-Controlled Ferroelastic Switching in Pb(Zr0.2Ti0.8)O3 Thin Films Asif Islam Khan,*,† Xavier Marti,‡,⊥ Claudy Serrao,†,‡ Ramamoorthy Ramesh,‡,§,∥ and Sayeef Salahuddin*,†,∥ †
Department of Electrical Engineering and Computer Sciences, ‡Department of Materials Science and Engineering, and §Department of Physics, University of California, Berkeley, California 94720, United States ∥ Material Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States ⊥ Institute of Physics ASCR, v.v.i., Cukrovarnická 10, 162 53 Praha 6, Czech Republic S Supporting Information *
ABSTRACT: We report a voltage controlled reversible creation and annihilation of a-axis oriented ∼10 nm wide ferroelastic nanodomains without a concurrent ferroelectric 180° switching of the surrounding c-domain matrix in archetypal ferroelectric Pb(Zr0.2Ti0.8)O3 thin films by using the piezoresponse force microscopy technique. In previous studies, the coupled nature of ferroelectric switching and ferroelastic rotation has made it difficult to differentiate the underlying physics of ferroelastic domain wall movement. Our observation of distinct thresholds for ferroelectric and ferroelastic switching allows us investigate the ferroelastic switching cleanly and demonstrate a new degree of nanoscale control over the ferroelastic domains. KEYWORDS: Nanodomains, ferroelastic switching, ferroelectricity, Pb(Zr0.2Ti0.8)O3, thin film
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nanoscale phenomena such as formation of topological features (for example, flux-closure vortex structures14,15 and ferroelastic pair structures16) and ferroelastic vertex−vertex interactions over hundreds of nanometers17 have been reported recently. The emerging paradigm of domain wall nanoelectronics aims at the controlled manipulation of these nanoscale features and nanodomains in ferroelectric films.18 Thus, a proper understanding of ferroelectric and ferroelastic switching mechanisms is fundamentally important. A certain degree of control has been reported in regard to manipulation of ferroelastic nanodomains in ferroelectric thin films.5,7,14,16,19−31 Yet, this topic has remained a challenging and controversial one. The nature of electric field induced mobility of ferroelastic domain walls is elusive due to multiple reasons. Firstly, in previous studies, the creation of ferroelastic adomains was observed only when there is a concurrent ferroelectric 180° switching of the surrounding c-domain. For example, Nagarajan et al. showed that movement of otherwise immobile ferroelastic domains in epitaxial Pb(Zr0.2Ti0.8)O3 films can be obtained through coupled ferroelastic−ferroelectric switching by patterning the thin films into discrete islands of high aspect ratio.7 Afterward, Chen et al. reported coupled ferroelastic−ferroelectric switching in continuous PZT thin
erroic materials are characterized by the spontaneous emergence of order in properties, such as polarization, magnetization, and strain, which can be switched between multistable states by conjugated external stimuli: electric field for ferroelectrics, magnetic field for ferromagnets, and mechanical stress for ferroelastics. Often these materials form ferroic domains in which the corresponding order parameter is oriented along one of the symmetry permitted directions.1−3 In ferroelectric films, domains can be extremely thin, spanning only a couple of nanometers.4−6 Due to the lattice-polarization coupling, ferroelectric materials are also ferroelastic. Of the wide range of domain types observed in ferroelectric films, many are categorized as ferroelastic domains. The movement of the ferroelastic domains can lead to a strain that is of the order of lattice tetragonality and a piezoelectric response significantly larger than that obtained in single domain crystals can be achieved in ferroelastically twinned ferroelectrics.7 Ferroelastic domains play an important role in the coupling between the electric field and the magnetization in magneto-electric multiferroic materials, such as BiFeO3,8 and heterostructures such as CoFe−BaTiO3,9 which offer a promising route for ultralow power voltage controlled magnetic switching for spintronic applications. The domain walls that separate the adjacent domain also exhibit a wide range of exotic nanoscale phenomena exemplified by electronic conductivity of domain walls embedded into insulating parent materials,5,10−12 and generation of large photovoltage in domain walls.13 Interesting © 2015 American Chemical Society
Received: October 3, 2014 Revised: January 30, 2015 Published: March 3, 2015 2229
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Nano Letters
Figure 1. Decoupling of ferroelastic switching from a concurrent ferroelectric switching. (a) The out-of-plane and in-plane PFM images of a 1.3 μm × 1.3 μm area of PZT film grown on GSO substrate in the as-grown state. The stripe-like features are the a-domains. (b) Cross-sectional TEM image of a 40 nm PZT film grown on GSO substrate. The polarization directions in c- and a-domains are indicated using arrows. (c) Comparison of the out-of-plane PFM snapshots of the same 2 μm × 2 μm area of the 40 nm PZT film in the as-grown state and after the subsequent application of −2 V and −2.5 V on the entire region. The regions where ferroelastic a-domain are created are indicated by arrows. Close up out-of-plane PFM images of two regions corresponding to the boxes {A1, A2} and {B1, B2} are also shown in part c.
films.23 By now, similar switching has been reported by multiple groups.5,7,19,32 In single-crystal like epitaxial Pb(Zr0.2Ti0.8)O3 films, Li et al. showed that the pre-existing a-domains split into fine patterns of a- and c-domain stripes during the ferroelectric 180° switching of the c-domains.20 Nonetheless, the coupled nature of ferroelastic and ferroelectric switching adds complexity to the process of ferroelastic a-domain creation in terms of understanding. Secondly, a coupled ferroelastic switching mechanism is not reversible. For example, Le Rhun et al. showed that after the rearrangement of the ferroelastic domain pattern in PZT films by a ferroelectric 180° switching of the asgrown c-domain polarization state by a negative voltage pulse, the application of a subsequent positive voltage pulse such that the c-domain polarization switches back to the as-grown direction does not bring back the initial domain configuration; rather the system stabilizes in a completely different ferroelastic domain pattern.19 Ivry et al. reported that the striped patterns of alternate a- and c-domains in polycrystalline Pb(Zr0.3Ti0.7)O3 thin films are irreversibly reoriented through coupled ferroelectric−ferroelastic switching when subsequent positive and negative voltages, which are larger than the coercivity of the average out-of-plane polarization, are applied.25 Similar observations were also made in tensile strained PZT thin films33 and in polycrystalline bilayer heterostructures of Pb(Zr0.3Ti0.7)O3−Pb(Zr0.7Ti0.3)O3.27 In this paper, we report a new degree of nanoscale control of the ferroelastic switching process toward the reversible creation and annihilation of a-axis oriented ferroelastic ∼10 nm wide
nanodomains in archetypal ferroelectric Pb(Zr0.2Ti0.8)O3 (PZT) thin films by using the piezo-response force microscopy (PFM) technique. We show for the first time that a voltage controlled ferroelastic c→ a switching can be achieved without a concurrent ferroelectric 180° switching of the surrounding cdomain matrix in PZT films, which are epitaxially strain tuned by (110) oriented GdScO3 (GSO) substrates. By decoupling ferroelastic c → a switching from a simultaneous ferroelectric switching, we further show that it is possible to erase a newly formed a-domain by the application of a voltage of opposite polarity leading to the demonstration of a reversible creation and annihilation of ferroelastic a-domains. In contrast to the previous reports where only coupled and irreversible ferroelastic−ferroelectric switching was observed, the observation of the decoupling of these two mechanisms in this work allows us to develop an understanding of the ferroelastic switching process based on a simple phenomenological energy barrier type model. Based on this model, we also estimate the barrier heights for the ferroelastic c→ a and a→ c switching processes. We grew PZT films on 12 nm SrRuO3 (SRO) buffered GSO (110) substrates using the pulsed laser deposition technique. The GSO pseudocubic template (apc ≈ bpc = 3.968 Å)34 imposes a +0.96% tensile misfit strain on PZT films. This tensile strain stabilizes a distinct ferroelastic c/a type domain structures, where a dense square network of crossed narrow adomains is embedded into a ferroelectric matrix with the tetragonal c-axis oriented perpendicular to the substrate. Figure 2230
DOI: 10.1021/nl503806p Nano Lett. 2015, 15, 2229−2234
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Nano Letters 1a shows the in-plane and the out-of-plane PFM images of a 40 nm PZT film grown on SrRuO3 buffered GSO substrate. A similar domain structure has previously been observed in PZT, but only for much thicker films.7,21,35−39 The cross-sectional TEM image in Figure 1b shows that the a-domains have a wedge-like shape, which is tapered at the PZT−SRO interface. To investigate the response of the ferroelastic domain to an out-of-plane electric field, we applied different DC voltages on the same area of the films via a conducting scanning atomic force microscopy (AFM) tip. The surface topography, the inplane and out-of-plane piezoresponse were recorded after each voltage. Figure 1c compares the domain configuration of the same 2 μm × 2 μm region in the as-grown state and after −2 V and −2.5 V were applied on the entire region. A new ferroelastic a-domain forms at −2 V and −2.5 V in the regions corresponding to the dashed boxes {A1, A2} and {B1, B2} and the arrows in Figure 1c. Note that the ferroelectric polarization in the c-domains in the as-grown state points toward the PZT− SRO interface.The out-of-plane component of the electric field due to the application of the negative voltage at the conducting AFM tip is aligned antiparallel with the c-domain polarization. The coercive voltage for ferroelectric 180° switching varies from point to point on the surface of the sample. In some regions, the c-domain polarization switches by 180° at −2 V and −2.5 V (noted by ⊙ in Figure 1c). However, no reversal of c-domain polarization is observed in the region, where new adomains formed. The critical voltage for creation of a new adomain Vc→a is ∼−2 V (see Supplementary Figure S2 for the PFM sequence). Similar ferroelastic c→ a switching decoupled from a ferroelectric switching of the surrounding c-domains is also observed in a 90 nm PZT film grown on 12 nm SRO buffered GSO substrate (shown in the Supplementary Figure S8). To eliminate the possibility that a 180° switching occurs in the surrounding region of the new a-domain upon the application of the negative DC bias followed by a rapid ferroelectric back switching after the removal of the DC voltage, we imaged a region while applying a negative DC voltage on which an AC voltage was superimposed (see Supplementary Figures S5 and S6). No 180° switching is observed in the region where new a-domains form when the negative DC bias was being applied. These observations reveal that the reversal of c-domain polarization is not necessary for an electric field induced ferroelastic c→ a switching. The new a-domains created thusly can be annihilated by applying a positive DC bias such that the resulting out-of-plane electric field is aligned with the as-grown c-domain polarization. Figure 2a compares the out-of-plane PFM images of the same 2 μm × 2 μm region in the as-grown state and after the successive application of −2 V and +4.5 V. In Figure 2a, we observe that some of the new a-domains formed at −2 V (enclosed by dashed boxes) are annihilated at +4.5 V. The critical voltage for ferroelastic a→ c switching Va→c is ∼+3.5 V (see Supplementary Figure S3 for the PFM sequence). In Figure 2b, we show PFM snapshots of a 300 nm × 200 nm region, where an a-domain is reversibly created and annihilated twice by applying a voltage sequence −2 V→ +4 V → −2 V→ +4 V locally. This indicates that, although the a-domains form at apparently random places, once created some of these domains can be reversibly annihilated and created by applying positive and negative DC voltages respectively at the conducting AFM tip. On the other hand, when the c-domains are ferroelectrically switched by applying a voltage larger than their coercivity, some of the pre-existing a-domains gets erased, and some new a-
Figure 2. Reversible creation and annihilation of ferroelastic adomains. (a) Comparison of the out-of-plane PFM snapshots of the same 2 μm × 2 μm area of the 40 nm PZT film in the as-grown state and after an AFM tip has applied −2 V and subsequently +4.5 V on the entire region. The regions where ferroelastic a-domain are created or annihilated are indicated by dashed boxes. (b) PFM snapshots of a 300 nm × 200 nm region, where an a-domain is reversibly created and annihilated by applying a voltage sequence −2 V→ +4 V → −2 V→ +4 V locally.
domains are created, resulting in a complete reconstruction of the ferroelastic domain pattern. Figure 3 shows the topography and the out-of-plane piezo-response of the same 1.5 μm × 1.5 μm region in the as-grown state and after −4 V, +4 V, and −4 V were successively applied on the same region of the 40 nm PZT sample. We note in Figure 3 that a dramatic reconstruction of the domain pattern occurs after each 180° switching. Most importantly, after the c-domain polarization is switched back to the as-grown direction by the voltage sequence −4 V→ +4 V, the ferroelastic domain pattern does not come back to as-grown pattern. We also studied the stability of the newly formed a-domains over the span of 16 h and found that these domains are stable with this time period (see Supplementary Figure S9). In principle, ferroelastically twinned c- and a-domains correspond to two metastable energy states separated by an energy barrier. This is true, at least, in the regions where reversible c→ a and a→ c switching is observed. Figure 4a schematically illustrates the free energy landscape in those regions. A similar energy landscape description was used to explain ferroelastic 71° and ferroelectric 180° switching in BiFeO3.29 We note in Figure 4 that the energy barrier between the as-grown c-domain state and a-domain state, ΔFc→a, is 2231
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Figure 3. Coupled ferroelastic-ferroelectric switching. Topography and the out-of-plane piezo-response of the same 1.5 μm × 1.5 μm region of the 40 nm PZT film in the as-grown state and after −4 V, +4 V, and −4 V were successively applied on the entire region.
Figure 4. Energy barrier model of the ferroelastic switching. (a) Schematic illustration of the energy barrier model of ferroelastic twins which are separated by an activation barrier. The states A, B, and C correspond to the as-grown c-domain state with the polarization pointing toward the PZT− SRO interface, and the c-domain state with the polarization aligned antiparrallel to that of state A and the a-domain state, respectively. The free energy of the state A is taken as the reference for energies. The barrier height for ferroelastic switching with respect to state A is ΔFc→a. (b,c) Free energy landscapes during ferroelastic c→ a (b) and a→ c (c) switching. For a ferroelastic c→ a switching, the c-domain free energy has to increase by an amount of ΔFc→a (b). Similarly, for a ferroelastic a→ c switching, the a-domain energy needs to increase by ΔFa→c (c).
Figure 5. Calculation of ΔFc→a and ΔFa→c. (a) Different energies of the c- and the a-domain as functions of the voltage V. (b,c) Free energy of the cand the a-domain as functions of the voltage. Part c shows the zoomed-in version of part b.
smaller than that between the oppositely polarized c-domain states, ΔF180°. This allows for the decoupling of ferroelastic and ferroelectric switching. The energy landscapes at the critical voltages for c→ a and a→ c switching (Vc→a and Va→c, respectively) are depicted in Figure 4b and c, respectively.
Upon the application of a voltage, the increase in the es es electrostatic energy of the i-th domain ΔUes i = Ui (V) − Ui (V ⃗
E = 0) is given by −∫ P⃗ i·dE⃗ ≈ −P⃗i·E⃗ , where P⃗i is the polarization 0 of the ith domain and E⃗ is the electric field. Hence, for a cdomain with the polarization along the as-grown direction,
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Nano Letters ΔUes c (V) = −PcV/d. The voltage also changes the elastic energy of the domains due to the piezoelectric effect. We assume that, in the presence of the ferroelastic domain formation, the lattice parameters of c- and a-domains are relaxed to the bulk values. Based on the piezoelectric matrix for a tetragonal ferroelectric (crystal class: P4mm), the c-domain in-plane normal strain components {εxx,c and εyy,c} and the out-of-plane strain εzz,c change in magnitude by the amounts |d31V/d| and |d33V/d|, respectively, upon the application of a voltage V (see Supplementary Section 3 for the details of the calculations). Here, d33 and d31 are the piezoelectric coefficients, and d is the thickness of the PZT film. Assuming that there is no residual macroscopic stress in the domains, the elastic energy of the cdomain at a voltage V is given by Uelc = V2 × Y(2d231 + d233(1 − ν) + 4νd31d33)/((1 − ν)d2), where Y is theYoung’s modulus and ν is the Poisson’s ratio. On the other hand, the shear strain component of the a-domain εzx,a changes by an amount |d24V/ d|, d24 being a piezoelectric coefficient. The resulting elastic energy of the a-domain is Uela = V2 × Yd224/(4(1 + ν)d2). The evolution of elastic energies of c- and a-domains and the electrostatic energy of the c-domain with V is plotted in Figure 5a. In the calculations, we assumed Pc = 80 μC/cm2,40 Y = 148 GPa,41 ν = 0.3,41 d33 = 50 pm/V,7 d31 = 30 pm/V,41 and d24 = 90 pm/V.42 Free energy density of the c-domain Fc(V) (= Uelc (V) + ΔUes c (V)) is plotted in Figure 5b as a function of V. Getting back to the conceptual pictures shown in Figure 4a and b, we note that, at V = Vc→a, Fc equals the energy of barrier ΔFc→a. Hence, ΔFc→a = Fc(V = Vc→a = −2 V) = ∼4.06 × 107 J/m3. Given that the average coercive voltage for ferroelectric switching of the as-grown c-domain, V180°, is ∼2.5 V, the average barrier height between the oppositely polarized ferroelectric c-domain states, ΔF180° is PcV180° ≈ 5 × 107 J/ m3. As noted in Figure 4a, ΔF180° > ΔFc→a. The strain gradient at the interface between a c- and an adomain contributes to the free energy density of the a-domain, which can be phenomenologically taken into account by an energy term in the form of a domain wall energy per unit volume, 2UDW/W, W being the width of the a-domain. Hence, the free energy density of the a-domain at a voltage V is Fa(V) = Uela (V) + ΔUes a (V) + 2UDW/W. The width of the a-domain in the free surface is ∼15 nm (see Figure 2b). Given the tapered shape of the a-domain, the average width of the a-domain W is taken as 15 nm/2 = 7.5 nm. We note in Figure 4a and c that Fa = ΔFc→a at V = Va→c. By setting the value of Fa(V) at the experimental critical voltage for ferroelastic a→ c switching, Va→c = +3.5 V, equal to ΔFc→a, UDW = (ΔFa→c − Uela (V = Va→c = +3.5 V))W/2 is calculated to be ∼150 mJ/m2. Based on this, ΔFa→c(= (ΔFa→c − Fa(V = 0))) is estimated to be ∼1.84 × 106 J/m3. The calculated values of ΔFc→a and ΔFa→c are conservative estimates and valid for the regions where reversible c → a and a → c switching is observed (for examples, the indicated regions shown in Figure 2a and b). In the surrounding regions, the barrier for ferroelastic switching is larger than that for ferroelectric switching, for which only a ferroelectric switching is observed. Nonetheless, microstructures, defects, dislocations, etc. play important roles in lowering the barrier for ferroelastic switching. A study of this model system using direct imaging techniques15,24,35 combined with a detailed phase-field modeling43,44 can help to elucidate the role of microstructure formations, nonuniform electric, and elastic fields as well as the epitaxial strain on the ferroelastic switching process.
In summary, we have shown voltage-controlled reversible creation and annihilation of nanoscale ferroelastic a-domains without a concurrent ferroelectric 180° switching of the surrounding c-domain matrix in thin films of archetypal ferroelectric like PZT. In many prior studies,5,7,19,23,25,27,32,33 the simultaneous occurrence of ferroelectric switching and ferroelastic rotation has made it difficult to differentiate the underlying physics. Our observation of distinct thresholds for ferroelectric and ferroelastic switching in tensile strained PZT grown on GSO substrates allows us investigate the ferroelastic switching cleanly and demonstrate a new degree of control over the ferroelastic nanodomains.
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ASSOCIATED CONTENT
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AUTHOR INFORMATION
S Supporting Information *
Growth of the Pb(Zr0.2Ti0.8)O3 thin films, the piezo-response force microscopy experiments, and the model for voltage controlled decoupled ferroelastic switching. This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Authors
*E-mail: [email protected]. *E-mail: [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported in part by the Office of Naval Research (ONR), the Center for Low Energy Systems Technology (LEAST), one of the six SRC STARnet Centers, sponsored by MARCO and DARPA and the NSF E3S Center at Berkeley. A.I.K. acknowledges the Qualcomm Innovation Fellowship 2012-13. The authors thank B. Huey, P. Alpay, J. X. Zhang, J. Clarkson, P. Yu, M. Trassin, K. Ashraf, L. You, and S. Smith for fruitful discussions.
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REFERENCES
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Voltage-Controlled Ferroelastic Switching in Pb(Zr0.2Ti0.8)O3 Thin Films Asif Islam Khan,*,† Xavier Marti,‡,⊥ Claudy Serrao,†,‡ Ramamoorthy Ramesh,‡,§,∥ and Sayeef Salahuddin*,†,∥ †
Department of Electrical Engineering and Computer Sciences, ‡Department of Materials Science and Engineering, and §Department of Physics, University of California, Berkeley, California 94720, United States ∥ Material Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States ⊥ Institute of Physics ASCR, v.v.i., Cukrovarnická 10, 162 53 Praha 6, Czech Republic S Supporting Information *
ABSTRACT: We report a voltage controlled reversible creation and annihilation of a-axis oriented ∼10 nm wide ferroelastic nanodomains without a concurrent ferroelectric 180° switching of the surrounding c-domain matrix in archetypal ferroelectric Pb(Zr0.2Ti0.8)O3 thin films by using the piezoresponse force microscopy technique. In previous studies, the coupled nature of ferroelectric switching and ferroelastic rotation has made it difficult to differentiate the underlying physics of ferroelastic domain wall movement. Our observation of distinct thresholds for ferroelectric and ferroelastic switching allows us investigate the ferroelastic switching cleanly and demonstrate a new degree of nanoscale control over the ferroelastic domains. KEYWORDS: Nanodomains, ferroelastic switching, ferroelectricity, Pb(Zr0.2Ti0.8)O3, thin film
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nanoscale phenomena such as formation of topological features (for example, flux-closure vortex structures14,15 and ferroelastic pair structures16) and ferroelastic vertex−vertex interactions over hundreds of nanometers17 have been reported recently. The emerging paradigm of domain wall nanoelectronics aims at the controlled manipulation of these nanoscale features and nanodomains in ferroelectric films.18 Thus, a proper understanding of ferroelectric and ferroelastic switching mechanisms is fundamentally important. A certain degree of control has been reported in regard to manipulation of ferroelastic nanodomains in ferroelectric thin films.5,7,14,16,19−31 Yet, this topic has remained a challenging and controversial one. The nature of electric field induced mobility of ferroelastic domain walls is elusive due to multiple reasons. Firstly, in previous studies, the creation of ferroelastic adomains was observed only when there is a concurrent ferroelectric 180° switching of the surrounding c-domain. For example, Nagarajan et al. showed that movement of otherwise immobile ferroelastic domains in epitaxial Pb(Zr0.2Ti0.8)O3 films can be obtained through coupled ferroelastic−ferroelectric switching by patterning the thin films into discrete islands of high aspect ratio.7 Afterward, Chen et al. reported coupled ferroelastic−ferroelectric switching in continuous PZT thin
erroic materials are characterized by the spontaneous emergence of order in properties, such as polarization, magnetization, and strain, which can be switched between multistable states by conjugated external stimuli: electric field for ferroelectrics, magnetic field for ferromagnets, and mechanical stress for ferroelastics. Often these materials form ferroic domains in which the corresponding order parameter is oriented along one of the symmetry permitted directions.1−3 In ferroelectric films, domains can be extremely thin, spanning only a couple of nanometers.4−6 Due to the lattice-polarization coupling, ferroelectric materials are also ferroelastic. Of the wide range of domain types observed in ferroelectric films, many are categorized as ferroelastic domains. The movement of the ferroelastic domains can lead to a strain that is of the order of lattice tetragonality and a piezoelectric response significantly larger than that obtained in single domain crystals can be achieved in ferroelastically twinned ferroelectrics.7 Ferroelastic domains play an important role in the coupling between the electric field and the magnetization in magneto-electric multiferroic materials, such as BiFeO3,8 and heterostructures such as CoFe−BaTiO3,9 which offer a promising route for ultralow power voltage controlled magnetic switching for spintronic applications. The domain walls that separate the adjacent domain also exhibit a wide range of exotic nanoscale phenomena exemplified by electronic conductivity of domain walls embedded into insulating parent materials,5,10−12 and generation of large photovoltage in domain walls.13 Interesting © 2015 American Chemical Society
Received: October 3, 2014 Revised: January 30, 2015 Published: March 3, 2015 2229
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Figure 1. Decoupling of ferroelastic switching from a concurrent ferroelectric switching. (a) The out-of-plane and in-plane PFM images of a 1.3 μm × 1.3 μm area of PZT film grown on GSO substrate in the as-grown state. The stripe-like features are the a-domains. (b) Cross-sectional TEM image of a 40 nm PZT film grown on GSO substrate. The polarization directions in c- and a-domains are indicated using arrows. (c) Comparison of the out-of-plane PFM snapshots of the same 2 μm × 2 μm area of the 40 nm PZT film in the as-grown state and after the subsequent application of −2 V and −2.5 V on the entire region. The regions where ferroelastic a-domain are created are indicated by arrows. Close up out-of-plane PFM images of two regions corresponding to the boxes {A1, A2} and {B1, B2} are also shown in part c.
films.23 By now, similar switching has been reported by multiple groups.5,7,19,32 In single-crystal like epitaxial Pb(Zr0.2Ti0.8)O3 films, Li et al. showed that the pre-existing a-domains split into fine patterns of a- and c-domain stripes during the ferroelectric 180° switching of the c-domains.20 Nonetheless, the coupled nature of ferroelastic and ferroelectric switching adds complexity to the process of ferroelastic a-domain creation in terms of understanding. Secondly, a coupled ferroelastic switching mechanism is not reversible. For example, Le Rhun et al. showed that after the rearrangement of the ferroelastic domain pattern in PZT films by a ferroelectric 180° switching of the asgrown c-domain polarization state by a negative voltage pulse, the application of a subsequent positive voltage pulse such that the c-domain polarization switches back to the as-grown direction does not bring back the initial domain configuration; rather the system stabilizes in a completely different ferroelastic domain pattern.19 Ivry et al. reported that the striped patterns of alternate a- and c-domains in polycrystalline Pb(Zr0.3Ti0.7)O3 thin films are irreversibly reoriented through coupled ferroelectric−ferroelastic switching when subsequent positive and negative voltages, which are larger than the coercivity of the average out-of-plane polarization, are applied.25 Similar observations were also made in tensile strained PZT thin films33 and in polycrystalline bilayer heterostructures of Pb(Zr0.3Ti0.7)O3−Pb(Zr0.7Ti0.3)O3.27 In this paper, we report a new degree of nanoscale control of the ferroelastic switching process toward the reversible creation and annihilation of a-axis oriented ferroelastic ∼10 nm wide
nanodomains in archetypal ferroelectric Pb(Zr0.2Ti0.8)O3 (PZT) thin films by using the piezo-response force microscopy (PFM) technique. We show for the first time that a voltage controlled ferroelastic c→ a switching can be achieved without a concurrent ferroelectric 180° switching of the surrounding cdomain matrix in PZT films, which are epitaxially strain tuned by (110) oriented GdScO3 (GSO) substrates. By decoupling ferroelastic c → a switching from a simultaneous ferroelectric switching, we further show that it is possible to erase a newly formed a-domain by the application of a voltage of opposite polarity leading to the demonstration of a reversible creation and annihilation of ferroelastic a-domains. In contrast to the previous reports where only coupled and irreversible ferroelastic−ferroelectric switching was observed, the observation of the decoupling of these two mechanisms in this work allows us to develop an understanding of the ferroelastic switching process based on a simple phenomenological energy barrier type model. Based on this model, we also estimate the barrier heights for the ferroelastic c→ a and a→ c switching processes. We grew PZT films on 12 nm SrRuO3 (SRO) buffered GSO (110) substrates using the pulsed laser deposition technique. The GSO pseudocubic template (apc ≈ bpc = 3.968 Å)34 imposes a +0.96% tensile misfit strain on PZT films. This tensile strain stabilizes a distinct ferroelastic c/a type domain structures, where a dense square network of crossed narrow adomains is embedded into a ferroelectric matrix with the tetragonal c-axis oriented perpendicular to the substrate. Figure 2230
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Nano Letters 1a shows the in-plane and the out-of-plane PFM images of a 40 nm PZT film grown on SrRuO3 buffered GSO substrate. A similar domain structure has previously been observed in PZT, but only for much thicker films.7,21,35−39 The cross-sectional TEM image in Figure 1b shows that the a-domains have a wedge-like shape, which is tapered at the PZT−SRO interface. To investigate the response of the ferroelastic domain to an out-of-plane electric field, we applied different DC voltages on the same area of the films via a conducting scanning atomic force microscopy (AFM) tip. The surface topography, the inplane and out-of-plane piezoresponse were recorded after each voltage. Figure 1c compares the domain configuration of the same 2 μm × 2 μm region in the as-grown state and after −2 V and −2.5 V were applied on the entire region. A new ferroelastic a-domain forms at −2 V and −2.5 V in the regions corresponding to the dashed boxes {A1, A2} and {B1, B2} and the arrows in Figure 1c. Note that the ferroelectric polarization in the c-domains in the as-grown state points toward the PZT− SRO interface.The out-of-plane component of the electric field due to the application of the negative voltage at the conducting AFM tip is aligned antiparallel with the c-domain polarization. The coercive voltage for ferroelectric 180° switching varies from point to point on the surface of the sample. In some regions, the c-domain polarization switches by 180° at −2 V and −2.5 V (noted by ⊙ in Figure 1c). However, no reversal of c-domain polarization is observed in the region, where new adomains formed. The critical voltage for creation of a new adomain Vc→a is ∼−2 V (see Supplementary Figure S2 for the PFM sequence). Similar ferroelastic c→ a switching decoupled from a ferroelectric switching of the surrounding c-domains is also observed in a 90 nm PZT film grown on 12 nm SRO buffered GSO substrate (shown in the Supplementary Figure S8). To eliminate the possibility that a 180° switching occurs in the surrounding region of the new a-domain upon the application of the negative DC bias followed by a rapid ferroelectric back switching after the removal of the DC voltage, we imaged a region while applying a negative DC voltage on which an AC voltage was superimposed (see Supplementary Figures S5 and S6). No 180° switching is observed in the region where new a-domains form when the negative DC bias was being applied. These observations reveal that the reversal of c-domain polarization is not necessary for an electric field induced ferroelastic c→ a switching. The new a-domains created thusly can be annihilated by applying a positive DC bias such that the resulting out-of-plane electric field is aligned with the as-grown c-domain polarization. Figure 2a compares the out-of-plane PFM images of the same 2 μm × 2 μm region in the as-grown state and after the successive application of −2 V and +4.5 V. In Figure 2a, we observe that some of the new a-domains formed at −2 V (enclosed by dashed boxes) are annihilated at +4.5 V. The critical voltage for ferroelastic a→ c switching Va→c is ∼+3.5 V (see Supplementary Figure S3 for the PFM sequence). In Figure 2b, we show PFM snapshots of a 300 nm × 200 nm region, where an a-domain is reversibly created and annihilated twice by applying a voltage sequence −2 V→ +4 V → −2 V→ +4 V locally. This indicates that, although the a-domains form at apparently random places, once created some of these domains can be reversibly annihilated and created by applying positive and negative DC voltages respectively at the conducting AFM tip. On the other hand, when the c-domains are ferroelectrically switched by applying a voltage larger than their coercivity, some of the pre-existing a-domains gets erased, and some new a-
Figure 2. Reversible creation and annihilation of ferroelastic adomains. (a) Comparison of the out-of-plane PFM snapshots of the same 2 μm × 2 μm area of the 40 nm PZT film in the as-grown state and after an AFM tip has applied −2 V and subsequently +4.5 V on the entire region. The regions where ferroelastic a-domain are created or annihilated are indicated by dashed boxes. (b) PFM snapshots of a 300 nm × 200 nm region, where an a-domain is reversibly created and annihilated by applying a voltage sequence −2 V→ +4 V → −2 V→ +4 V locally.
domains are created, resulting in a complete reconstruction of the ferroelastic domain pattern. Figure 3 shows the topography and the out-of-plane piezo-response of the same 1.5 μm × 1.5 μm region in the as-grown state and after −4 V, +4 V, and −4 V were successively applied on the same region of the 40 nm PZT sample. We note in Figure 3 that a dramatic reconstruction of the domain pattern occurs after each 180° switching. Most importantly, after the c-domain polarization is switched back to the as-grown direction by the voltage sequence −4 V→ +4 V, the ferroelastic domain pattern does not come back to as-grown pattern. We also studied the stability of the newly formed a-domains over the span of 16 h and found that these domains are stable with this time period (see Supplementary Figure S9). In principle, ferroelastically twinned c- and a-domains correspond to two metastable energy states separated by an energy barrier. This is true, at least, in the regions where reversible c→ a and a→ c switching is observed. Figure 4a schematically illustrates the free energy landscape in those regions. A similar energy landscape description was used to explain ferroelastic 71° and ferroelectric 180° switching in BiFeO3.29 We note in Figure 4 that the energy barrier between the as-grown c-domain state and a-domain state, ΔFc→a, is 2231
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Figure 3. Coupled ferroelastic-ferroelectric switching. Topography and the out-of-plane piezo-response of the same 1.5 μm × 1.5 μm region of the 40 nm PZT film in the as-grown state and after −4 V, +4 V, and −4 V were successively applied on the entire region.
Figure 4. Energy barrier model of the ferroelastic switching. (a) Schematic illustration of the energy barrier model of ferroelastic twins which are separated by an activation barrier. The states A, B, and C correspond to the as-grown c-domain state with the polarization pointing toward the PZT− SRO interface, and the c-domain state with the polarization aligned antiparrallel to that of state A and the a-domain state, respectively. The free energy of the state A is taken as the reference for energies. The barrier height for ferroelastic switching with respect to state A is ΔFc→a. (b,c) Free energy landscapes during ferroelastic c→ a (b) and a→ c (c) switching. For a ferroelastic c→ a switching, the c-domain free energy has to increase by an amount of ΔFc→a (b). Similarly, for a ferroelastic a→ c switching, the a-domain energy needs to increase by ΔFa→c (c).
Figure 5. Calculation of ΔFc→a and ΔFa→c. (a) Different energies of the c- and the a-domain as functions of the voltage V. (b,c) Free energy of the cand the a-domain as functions of the voltage. Part c shows the zoomed-in version of part b.
smaller than that between the oppositely polarized c-domain states, ΔF180°. This allows for the decoupling of ferroelastic and ferroelectric switching. The energy landscapes at the critical voltages for c→ a and a→ c switching (Vc→a and Va→c, respectively) are depicted in Figure 4b and c, respectively.
Upon the application of a voltage, the increase in the es es electrostatic energy of the i-th domain ΔUes i = Ui (V) − Ui (V ⃗
E = 0) is given by −∫ P⃗ i·dE⃗ ≈ −P⃗i·E⃗ , where P⃗i is the polarization 0 of the ith domain and E⃗ is the electric field. Hence, for a cdomain with the polarization along the as-grown direction,
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Nano Letters ΔUes c (V) = −PcV/d. The voltage also changes the elastic energy of the domains due to the piezoelectric effect. We assume that, in the presence of the ferroelastic domain formation, the lattice parameters of c- and a-domains are relaxed to the bulk values. Based on the piezoelectric matrix for a tetragonal ferroelectric (crystal class: P4mm), the c-domain in-plane normal strain components {εxx,c and εyy,c} and the out-of-plane strain εzz,c change in magnitude by the amounts |d31V/d| and |d33V/d|, respectively, upon the application of a voltage V (see Supplementary Section 3 for the details of the calculations). Here, d33 and d31 are the piezoelectric coefficients, and d is the thickness of the PZT film. Assuming that there is no residual macroscopic stress in the domains, the elastic energy of the cdomain at a voltage V is given by Uelc = V2 × Y(2d231 + d233(1 − ν) + 4νd31d33)/((1 − ν)d2), where Y is theYoung’s modulus and ν is the Poisson’s ratio. On the other hand, the shear strain component of the a-domain εzx,a changes by an amount |d24V/ d|, d24 being a piezoelectric coefficient. The resulting elastic energy of the a-domain is Uela = V2 × Yd224/(4(1 + ν)d2). The evolution of elastic energies of c- and a-domains and the electrostatic energy of the c-domain with V is plotted in Figure 5a. In the calculations, we assumed Pc = 80 μC/cm2,40 Y = 148 GPa,41 ν = 0.3,41 d33 = 50 pm/V,7 d31 = 30 pm/V,41 and d24 = 90 pm/V.42 Free energy density of the c-domain Fc(V) (= Uelc (V) + ΔUes c (V)) is plotted in Figure 5b as a function of V. Getting back to the conceptual pictures shown in Figure 4a and b, we note that, at V = Vc→a, Fc equals the energy of barrier ΔFc→a. Hence, ΔFc→a = Fc(V = Vc→a = −2 V) = ∼4.06 × 107 J/m3. Given that the average coercive voltage for ferroelectric switching of the as-grown c-domain, V180°, is ∼2.5 V, the average barrier height between the oppositely polarized ferroelectric c-domain states, ΔF180° is PcV180° ≈ 5 × 107 J/ m3. As noted in Figure 4a, ΔF180° > ΔFc→a. The strain gradient at the interface between a c- and an adomain contributes to the free energy density of the a-domain, which can be phenomenologically taken into account by an energy term in the form of a domain wall energy per unit volume, 2UDW/W, W being the width of the a-domain. Hence, the free energy density of the a-domain at a voltage V is Fa(V) = Uela (V) + ΔUes a (V) + 2UDW/W. The width of the a-domain in the free surface is ∼15 nm (see Figure 2b). Given the tapered shape of the a-domain, the average width of the a-domain W is taken as 15 nm/2 = 7.5 nm. We note in Figure 4a and c that Fa = ΔFc→a at V = Va→c. By setting the value of Fa(V) at the experimental critical voltage for ferroelastic a→ c switching, Va→c = +3.5 V, equal to ΔFc→a, UDW = (ΔFa→c − Uela (V = Va→c = +3.5 V))W/2 is calculated to be ∼150 mJ/m2. Based on this, ΔFa→c(= (ΔFa→c − Fa(V = 0))) is estimated to be ∼1.84 × 106 J/m3. The calculated values of ΔFc→a and ΔFa→c are conservative estimates and valid for the regions where reversible c → a and a → c switching is observed (for examples, the indicated regions shown in Figure 2a and b). In the surrounding regions, the barrier for ferroelastic switching is larger than that for ferroelectric switching, for which only a ferroelectric switching is observed. Nonetheless, microstructures, defects, dislocations, etc. play important roles in lowering the barrier for ferroelastic switching. A study of this model system using direct imaging techniques15,24,35 combined with a detailed phase-field modeling43,44 can help to elucidate the role of microstructure formations, nonuniform electric, and elastic fields as well as the epitaxial strain on the ferroelastic switching process.
In summary, we have shown voltage-controlled reversible creation and annihilation of nanoscale ferroelastic a-domains without a concurrent ferroelectric 180° switching of the surrounding c-domain matrix in thin films of archetypal ferroelectric like PZT. In many prior studies,5,7,19,23,25,27,32,33 the simultaneous occurrence of ferroelectric switching and ferroelastic rotation has made it difficult to differentiate the underlying physics. Our observation of distinct thresholds for ferroelectric and ferroelastic switching in tensile strained PZT grown on GSO substrates allows us investigate the ferroelastic switching cleanly and demonstrate a new degree of control over the ferroelastic nanodomains.
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ASSOCIATED CONTENT
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AUTHOR INFORMATION
S Supporting Information *
Growth of the Pb(Zr0.2Ti0.8)O3 thin films, the piezo-response force microscopy experiments, and the model for voltage controlled decoupled ferroelastic switching. This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Authors
*E-mail: [email protected]. *E-mail: [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported in part by the Office of Naval Research (ONR), the Center for Low Energy Systems Technology (LEAST), one of the six SRC STARnet Centers, sponsored by MARCO and DARPA and the NSF E3S Center at Berkeley. A.I.K. acknowledges the Qualcomm Innovation Fellowship 2012-13. The authors thank B. Huey, P. Alpay, J. X. Zhang, J. Clarkson, P. Yu, M. Trassin, K. Ashraf, L. You, and S. Smith for fruitful discussions.
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REFERENCES
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