New Journal of Physics The open–access journal for physics
Capacitance tuning in antiferroelectric–ferroelectric PbZrO3−Pb(Zr0.8Ti0.2)O3 epitaxial multilayers Lucian Pintilie1,2,3 , Ksenia Boldyreva1 , Marin Alexe1 and Dietrich Hesse1 1 Max Planck Institute of Microstructure Physics, Weinberg 2, D-06120 Halle (Saale), Germany 2 NIMP, PO Box MG-7, 077125 Bucharest-Magurele, Romania E-mail:
[email protected] and
[email protected] New Journal of Physics 10 (2008) 013003 (12pp)
Received 25 July 2007 Published 14 January 2008 Online at http://www.njp.org/ doi:10.1088/1367-2630/10/1/013003
The capacitance of PbZrO3 –Pb(Zr0.8 Ti0.2 )O3 epitaxial multilayers is significantly enhanced as the number of interfaces increases at the same total thickness of the structure. A possible explanation for this enhancement can be the increase of the dielectric susceptibility due to the presence of some interfacial polarization related, for instance, to trapped charges at the multilayer interfaces. The presented results suggest that capacitance tuning is achievable in antiferroelectric–ferroelectric epitaxial multilayers.
Abstract.
Contents
1. Introduction 2. Experiment and results 3. Discussion 3.1. Interface polarization model . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Interface charge-based model . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Conclusions Acknowledgments References
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Author to whom any correspondence should be addressed.
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2 1. Introduction
Epitaxial multilayered ferroelectric (FE) heterostructures (superlattices) are the subject of increased interest due to their potential for artificial materials with enhanced properties. Twoand three-component superlattices were studied, using various combinations of FE materials with perovskite structure such as BaTiO3 –SrTiO3 , PbTiO3 –PbZrO3 , SrTiO3 –BaTiO3 –CaTiO3 , and others. Experimental and theoretical work has addressed the structural and dielectric/FE properties of superlattices [1]–[10]. Both experiment and theory have shown that it is possible to obtain enhanced FE and dielectric properties in case of superlattices compared to the single components. In particular, large values of the dielectric constant of superlattices were reported. It was experimentally shown that the value of the dielectric constant increases with decreasing periodicity (thickness of the bi-layer unit) of the component layers for the same total thickness [1, 2, 8], [11]–[13]. Generally, this result was explained by the increased contribution from strain as the periodicity decreases below the critical thickness for relaxation. Maxwell–Wagner relaxation (MWR) and the transverse Ising model with interfacial coupling were also considered [11, 12], [14]–[16]. However, the problem is far from being solved. The inherent interface charges related to structural imperfections and/or polarization discontinuities were not considered as a possible source for the increase of the dielectric constant in superlattices. In fact, the term ‘dielectric constant’ of a superlattice has to be used with caution as it refers to the global dielectric response of the superlattice (including the electrodes). This value might be dependent on the processing conditions of the superlattice. Recently, we have investigated the properties of epitaxial multilayered PbZrO3 – Pb(Zr0.8 Ti0.2 )O3 (PZO–PZT80/20) structures with equal volume fractions and different thicknesses of the bi-layer unit (periodicity). We have found that below a thickness of about 9–10 nm the PZO layer experiences a structural transformation reflected in the hysteresis loop of the multilayer, which changes from a mixed antiferroelectric–FE (AFE–FE) shape to a FE shape only [17]. This thickness-driven phase-transition-like transformation leads to an increase by about three times of the dielectric constant of the multilayer at zero voltage. Although the structural change experienced by the PZO layer was proven by x-ray diffraction reciprocal space mapping, the origin of this behavior was not fully understood. Also, the origin of the capacitance increase at thicknesses far from the phase-transition-like transformation is not very clear, as transmission electron microscopy (TEM) studies do not reveal any relaxation by the formation of misfit dislocations at the interfaces between PZO and PZT80/20 layers. Therefore, we may assume that the component layers in the structures are subjected to the same strain in the investigated thickness range and the strain does not play a significant role in the capacitance increase. In the present paper, we are proposing an interface-related phenomenological model for this increase. 2. Experiment and results
The PZT80/20 and PZO layers were prepared by pulsed laser deposition, using a KrF excimer laser (wavelength λ = 248 nm), on (100) oriented SrTiO3 (STO) substrates covered with an epitaxial SrRuO3 (SRO) layer as bottom electrode and a thin (4–6 nm) Pb(Zr0.2 Ti0.8 )O3 (PZT20/80) seed layer. The laser fluence was in the 0.9–1.5 J cm−2 range while the oxygen pressure was in the range of 0.1–0.2 mbar. The substrate temperature was 575 ◦ C for all layers. New Journal of Physics 10 (2008) 013003 (http://www.njp.org/)
3
Figure 1. Transmission electron micrograph of an epitaxial PZO–PZT80/20
multilayer. The epitaxial quality of the deposited multilayers was verified through TEM and electron diffraction (not shown). A TEM micrograph is shown in figure 1. Top Pt electrodes were sputtered through a shadow mask. Hysteresis loops were measured using a TF2000 analyzer. Capacitance–voltage (C–V) measurements were performed at room temperature and 100 kHz using a HP 4194A impedance and gain analyzer. Three series of samples were investigated, having a total thickness of 50, 100 and 150 nm, respectively. Examples of hysteresis loops are presented in figure 2 for multilayers containing 1 and 16 bi-layer units, respectively, with a total thickness of 150 nm. A change in shape, corresponding to a change from mixed AFE–FE behavior to only FE behavior, can be observed. We will not dwell on this aspect as it is detailed in [17]. The same behavior has been observed in the static hysteresis loops measured at 100 Hz with a relaxation time of 0.1 s. An example of the change in the shape of the hysteresis loop as the thickness of the individual layers is reduced is shown in figure 3. Typical C–V characteristics are presented in figure 4 for the samples with 100 nm total thickness. Similar results were obtained for the other two series of thicknesses. It can be seen that up to four bi-layer units the multilayer shows mixed AFE–FE behavior. This is not surprising as PZO is AFE while PZT80/20 is FE. However, a previous report on PbZrO3 –PbTiO3 (PZO–PTO) superlattices showed only FE behavior independent of the number of bi-layer units [18]. Returning to figure 4, it can be seen that the shape of the C–V characteristic for six bi-layer units changes towards a FE-like behavior. It can be presumed that up to four bi-layer units, corresponding to about 12.5 nm thickness of the individual layers, the overall coupling between the AFE and FE layers is weak and the layers behave more or less independently. New Journal of Physics 10 (2008) 013003 (http://www.njp.org/)
4
Polarization (µC cm–2)
60
1
40 20 0 –20
16
–40 –60 –10 –8
–6
–4
–2 0 2 Voltage (V)
4
6
8
10
Figure 2. Dynamic hysteresis loops at 1 kHz for multilayers comprising 1 and
16 bi-layer units, respectively. The total thickness is 150 nm in both cases. 8
Polarization (µC cm–2)
40
1 20 0 –20 –40 –6
–4
–2
0
2
4
6
Voltage (V)
Figure 3. Static hysteresis loops for multilayers comprising 1 and 8 bi-layer
units, respectively. The total thickness is 100 nm in both cases. At 6 bi-layer units, corresponding to about 9 nm thickness of the individual layers, the coupling may become significant. The PZO layer undergoes a structural transformation from orthorhombic to rhombohedral symmetry. This will lead to a drastic change in the properties of the multilayer, reflected in the change in shape for the C–V characteristics as well as for the hysteresis loops, as shown in figures 2 and 3, and in [17]. We may say that the structure changes its behavior from a weakly coupled multilayer of AFE and FE films to a strongly coupled AFE–FE superlattice. We draw attention to the fact that, up to the change of shape, the C–V characteristics show a constant increase of capacitance with the number of interfaces Ni . This increase is present at zero bias as well as at maximum applied bias, which corresponds to the saturation of the FE polarization. Similar results were obtained for the sample series with 50 and 150 nm total thickness. New Journal of Physics 10 (2008) 013003 (http://www.njp.org/)
5 Specific capacitance (F m–2)
6
0.05
4
0.04 2
0.03
1
0.02 0.01 –6
–4
–2
0
2
4
6
Voltage (V)
Figure 4. C–V characteristics of the PZO–PZT80/20 multilayers with total
thickness of 100 nm and with 1, 2, 4 and 6 bi-layer units. 130
6
120 110
Conductance (µS)
100 90 80 70 60 50
4
40 30
2
20 10 0
–6
1 –4
–2
0
2
4
6
Voltage (V)
Figure 5. The G–V characteristics (G = conductance) for structures containing
1, 2, 4 and 6 bi-layer units. The total thickness is 100 nm in all cases. The conductance, which is directly related to the loss tangent, shows similar behavior to the capacitance (see figure 5). It can be seen that the conductance at zero bias increases significantly as the number of bi-layer units increases resembling a phase-transition-type behavior. The results shown in figure 5 are in agreement with those presented in figures 2 and 3. On the other hand, the conductance in the high-voltage range, where the polarization is saturated, is almost the same for all the multilayers with thickness below the value corresponding to the structural change, whereas the capacitance shows a significant increase (see figure 4). An example of the frequency dependence of the capacitance and conductance is shown in figure 6. No major relaxation occurs up to the frequency of 100 kHz. The high frequency relaxation might be charged to serial resistance introduced by the thin SRO electrodes. Similar results were obtained for all multilayers under investigation. New Journal of Physics 10 (2008) 013003 (http://www.njp.org/)
6 700
0.002
500 400 0.001 300 200
Conductance (S)
Capacitance (pF)
600
100 0
1000
10 000 100 000 Frequency (Hz)
0.000 1000000
Figure 6. The frequency dependence of capacitance and corresponding
conductance at zero bias measured on a multilayer sample containing 4 bi-layer units with a total thickness of 150 nm. 500
Dielectric constant
450
Regime of multilayer with weak coupling
400 350 300 250
Regime of superlattice with strong coupling
200 150 100 –2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36
Number of interfaces (N i)
Figure 7. The dependence of the dielectric constant on the number of interfaces
for different total thicknesses of the multilayers. Figure 7 shows the dependence of the dielectric constant on the number of interfaces Ni , at voltage values corresponding to polarization saturation, for the three series of thicknesses. We have preferred to consider only the capacitance in the voltage range where the polarization is saturated because in this case the contribution of polarization switching to the dielectric constant is minimized. This is not the case at zero bias, where this contribution can be significant, as results from the hysteresis loops. Therefore, we consider only the linear response and its increase with the number of interfaces. The relation between the thickness tl of individual layers and the number of interfaces Ni for a constant total thickness t is tl = t/(Ni + 1). As can be seen from figure 7, the dependence of the dielectric constant on the number of interfaces is linear up to the thickness where the structural change occurs. The hatched part of New Journal of Physics 10 (2008) 013003 (http://www.njp.org/)
7 figure 7 marks the thickness range in which the structures behave as superlattices with a strong coupling between component layers. The strong coupling may induce structural changes in one of the components. The un-hatched part of figure 7 corresponds to the thickness range for which the structures behave as multilayers with weak, if not negligible, coupling between components. The following discussion will refer only to this thickness range, where the linear dependence on the number of interfaces is observed. Therefore, the points corresponding to the thickness domain where the structures behave as strongly coupled superlattices are not discussed here. TEM investigations showed no evidence of relaxation through the formation of misfit dislocations at the interface between the component AFE and FE layers, therefore we might assume that the strain conditions are the same for the considered thickness range. The strain–stress effects due to the lattice misfit between the component layers, which might have an impact on the dielectric constant, are hence considered to be negligible. The stress effects might be present at lower thickness, as suggested in previous studies [2, 19]. In fact a distinction should be made between the inter-layer strain and the substrateimposed strain. At thicknesses above 12.5 nm the first PZT80/20 layer grown on the STO–SRO–PZT20/80 substrate will certainly relax some of the large misfit strain imposed by the substrate, allowing the rest of the layers to grow only with small misfit strain between the PZO and PZT80/20 films, which is less than 1% and does not change with thickness. Below 10 nm it may be that all the layers grow under the compressive strain imposed by the substrate, triggering the structural transformation of the PZO from orthorhombic to rhombohedral symmetry and the AFE-to-FE phase transition. According to the above discussion we can presume that the observed increase in the dielectric constant with the number of interfaces, for thicknesses of the individual layers larger than 12.5 nm, is not an intrinsic effect due to the lattice misfit-induced stress but is an extrinsic effect related to some other interface phenomenon. 3. Discussion
The MWR mechanism can be considered as a possible candidate for the increase of the dielectric constant, as already suggested in previous works [11, 12]. The application of MWR in previous studies assumes the presence of an interface layer, of finite thickness and with different properties compared to the bulk [11, 20]. In fact, the model developed in [11] is based on the assumption that there is a difference of resistivity between an interface layer of constant thickness ti and the bulk of the component layers of thickness tb . The total thickness of an individual layer is t = ti + tb . Following the model it can be easily shown that the dielectric constant in the MWR hypothesis is directly dependent on the ti /t ratio. As the thickness of the interface layer ti is considered to be constant and equal to about 0.65 nm, it follows that the dielectric constant increases as the thickness t of the individual layers decreases. It was assumed that the low resistivity interface layer is a consequence of an accumulation of oxygen vacancies at the interfaces between the component layers and, because they act as donors, the resistivity of the interface layer will be reduced compared to the bulk. We have applied the MWR model to our data, assuming the same hypothesis as in [11]. Using comparable values for the quantities involved in the model (ti = 1 nm; ρi = 1000 m; ρb = 105 m; εi = εb = 150) we have obtained very low values for the equivalent dielectric constant, in the range 1–10, which are far from the experimental values. To obtain values New Journal of Physics 10 (2008) 013003 (http://www.njp.org/)
8 comparable with the experimental ones, the thickness of the interface layer should be around 40 nm or the resistivity of the interface layer should be about the same as the bulk value of 105 m. It has to be underlined that in our case the ti /t ratio is very small, even negligible, as the total thickness is larger than that of the interface layer, t ti . The MWR model in [11] was developed for values of the ti /t ratio which are comparable to unity. In fact TEM investigation does not prove the presence of any interfacial layer. We recall that the micrograph in figure 1 was made for a multilayer with a thickness of 12.5 nm of each individual layer. Therefore the presence of an interface layer of at least 1 nm thickness and of different conductive properties due to accumulation of oxygen vacancies should be visible [21]. Still we may presume that there is a difference between the resistivities of the two component layers, but the thickness ratio is constant and equal to unity for all structures. In this case, according to the MWR model, the dielectric constant should be independent of the thickness of the individual layers. We may conclude that the MWR model is not the appropriate one to explain the results presented in figure 7 and that the linear increase is produced by another interface-related phenomenon and not by the presence of an interface layer of different resistivity. For example, considering the semiconducting properties of lead zirconate titanate (PZT) [22, 23] we may assume that there is a certain density of trapped charges at each PZO–PZT interface, analogous to the charge trapped at the oxide–semiconductor interface in metal–oxide–semiconductor (MOS) structures [24, 25]. If this is the case, the trapped charge will produce a change in the polarization of the film leading to a change of the surface charge on the metal electrodes. In order to explain the presented experimental results we introduce two alternative models: 1. A simplified model which considers interfacial polarization. 2. A model based on a surface charge at each interface. 3.1. Interface polarization model The model considers an interfacial polarization that is added to the other polarization mechanisms existing in the multilayer [26]. Any interfacial polarization will bring a positive contribution to the dielectric susceptibility of the system. The model is developed on the assumption that the multilayer behaves as a homogeneous material with interfaces carrying an interfacial polarization Pin . Although it is a rough assumption, it is supported by the fact that the component layers have close compositions and the dielectric constants are not very much different [27, 28]. Therefore, the electric field will be considered to be uniform in the multilayer. An average dipolar polarization Pdip will be considered instead of separate values for the AFE and FE components. In analogy with previous texts the electric displacement D is given by [29, 30]: D = ε0 E + P = ε0 E + Plin + Pdip + Pin , (1) where ε0 is the vacuum permittivity, E is the electric field. The total polarization P is the sum of the different existing polarization mechanisms: Plin , the linear response of the system to an applied electric field, Pdip , the dipolar polarization and Pin , the interfacial polarization. Following the definition of the dielectric permittivity, the total dielectric constant εt of the multilayer can be calculated from [29]: ∂Plin ∂Pdip ∂Pin 1 ∂Pdip ∂Pin ∂D ε0 εt = = ε0 + + + = ε0 1 + χ l + + . (2) ∂E ∂E ∂E ∂E ε0 ∂E ∂E New Journal of Physics 10 (2008) 013003 (http://www.njp.org/)
9 It was considered that Plin = ε0 χl E, with χl being the electric susceptibility in the linear approximation [31]. In analogy to Pdip , the interfacial polarization Pin can be defined as [32]: Ni Ni Ni 1 X 1 X pi X j Pin = p = pi = 1 = Ni Pi , V j in V j V j j
(3)
where pin is an interfacial dipole associated to the jth interface and V is the sample volume, which remains constant as Ni increases. For simplicity it was assumed that the interfacial dipoles j are equal ( pin = pi ), although there might be some differences between them due to different growth sequence (PZO on PZT80/20 or PZT80/20 on PZO). Pi = pi /V defines the contribution of a single interface to the polarization. Simply speaking, the entire multilayer was reduced to a homogeneous FE in which two dipolar sub-lattices are present: one is formed by the normal FE dipoles giving Pdip , the other is formed by interface dipoles giving Pin . Using (3), equation (2) can be re-written as: ∂ Pi 1 ∂ Pdip + Ni . ε0 εt = ε0 1 + χl + (4) ε0 ∂ E ∂E The term in parenthesis in equation (4) is the dielectric constant of the multilayer in the absence of interface-related phenomena. The second term is due only to the interfaces and can be rewritten as ε0 Ni εit where εit is the ‘dielectric constant’ of one PZO–PZT80/20 interface. Equation (4) shows that the total dielectric constant can increase linearly with Ni , as shown in figure 7. Apparently, equation (4) is valid at any electric field and for any number of interfaces. However, according to figure 7 this is not true. The linear dependence of εt on Ni is valid only for a limited number of interfaces, considering that the thickness of the component layers should be larger than the thickness for which the FE-like behavior occurs (see figure 2). On the other hand, the ∂ Pdip /∂ E term, which is related to polarization switching, has a strong non-linear dependence on voltage. This dependence may differ from sample to sample as it is expected that the increased number of interfaces will affect the switching process. In some cases a linear dependence may occur even at zero bias. This is possible as long as the ∂ Pdip /∂ E term does not introduce large non-linearity in the dielectric constant defined by equation (4). In accordance with the data shown in figure 7 we will consider only the saturation regime, where ∂ Pdip /∂ E is zero. In this case, the intercept of the εt ≈ Ni representation should give the linear dielectric constant εl = ε0 (1 + χl ) of the structure in the absence of interfaces, while the slope will give an estimation of the ‘dielectric constant’ εit associated with one PZO–PZT80/20 interface. The results obtained for maximum voltage applied on the multilayer, when the FE polarization is assumed to be saturated, are: εl = 90 and εit = 22 for a total thickness of 50 nm; εl = 95 and εit = 9 for 100 nm; εl = 200 and εit = 18 for 150 nm. The equivalent dielectric constant of a PZO–PZT80/20 multilayer, calculated from the simple serial model of capacitance, should be εeq = 2ε1 ε2 /(ε1 + ε2 ) where ε1,2 are the dielectric constants of the two phases. Considering a value of about 150 for the dielectric constant of epitaxial PZT80/20 [33] and of about 200 for high quality PZO [34], the dielectric constant of the multilayer should be about 171. This is close to the value of 200 obtained for the multilayer of 150 nm total thickness. It may be that in this case the structure is not fully depleted and the calculation of the dielectric constant as for a parallel capacitor is not correct [35]. For the other two thicknesses the values are about the same, suggesting that in these cases the structures are fully depleted. The interface contribution is in the range of 10–20 in all cases. The fact that the dielectric constant of the multilayers increases with the number of interfaces when the quantity called New Journal of Physics 10 (2008) 013003 (http://www.njp.org/)
10 the ‘interface dielectric constant’ εit has such small values may look odd, especially in the case when the multilayer is regarded as a serial connection of capacitors. However, equation (4), from which the εit values were calculated, was deduced based on the fact that polarization mechanisms are additive [26]. 3.2. Interface charge-based model A more detailed model might be developed, based on the assumption that there is a surface charge σ at each interface. This charge may originate, for instance, from the carriers trapped on the interface states. We will show that such an interface charge can bring an additive contribution to the capacitance and, consequently, to the value of the equivalent dielectric constant. For the sake of simplicity we will make the calculations for a bi-layer, the generalization being rather straightforward. We start from two basic equations, which are the conservation of energy and the continuity of the electric displacement [36]: E 1l + E 2l = V,
D2 − D1 = σ,
(5)
Here, E 1,2 are the electric field in the two components of the bi-layer, D1,2 the dielectric displacements, and V is an applied voltage. Considering that D = ε0 εst E + P, where εst is the linear part of the dielectric constant and P is the FE polarization, the electric fields can be calculated and the charge on the electrode can be found by applying Gauss’ law [37]: V 2ε0 ε1 ε2 P1 ε2 + P2 ε1 ε1 σel = −D1 = ε0 ε1 E 1 + P1 = − + + σ. (6) 2l ε1 + ε2 ε1 + ε2 ε1 + ε2 Using the definition of the capacitance C = d(σel )/dV and taking into account that the derivative ∂ P1,2 /∂ E is zero when the FE polarization is saturated, the equivalent capacitance Ce is given by: 1 ε1 ε0 d d 1 Ce = σ =C+ σ . (7) (ε1 ε2 + ε2 ε1 ) + L ε1 + ε2 dV 2 dV ε1 + ε2 If the interface charge σ is zero, then equation (7) expresses the capacitance C of the bi-layer as a serial connection of two capacitors, which is a correct result. If the interface charge σ is not zero, then it brings an additive contribution to the capacitance. Without further comments we will just observe that equation (7) is similar to a parallel connection of capacitors. One is the equivalent capacitor C of the serial connection, the other is a ‘capacitor’ induced by the interface charge σ : Ce = C + Cint .
(8)
When the multilayer has Ni interfaces, each one carrying the charge σ , we can simplify the picture regarding the multilayer as a bi-layer with an interface carrying the charge σ Ni . The capacitance of the multilayer will be: Ce = C + Ni Cint .
(9)
Equation (9) is similar to equation (4), and both show that the capacitance increases with the number of interfaces. However, we underline that this increase is not indefinite. The model is valid only in the multilayer case and not in a superlattice case when there is a strong coupling New Journal of Physics 10 (2008) 013003 (http://www.njp.org/)
11 between the component layers. In our case, as the thickness of each layer drops below a certain value, the component layers experience structural changes and the above models become invalid. We should also note that the present model and the MWR model address different thickness regimes and might be complementary. 4. Conclusions
In summary, the capacitance of PZO–PZT80/20 multilayers was studied. The observed linear increase of the capacitance with the number of interfaces, in the polarization saturation regime, can be explained either by an increase of the total dielectric constant due to the presence of an interfacial polarization or by the increase of charges on electrodes induced by an interface charge σ . The models are valid as long as no major structural changes occur in the multilayer. In this case the total capacitance can be tuned through the number of interfaces. Acknowledgments
This work was supported by Volkswagen Stiftung under contract no. I/77738 and the German Science Foundation (DFG) via FOR 404. LP acknowledges the collaboration with the DINAFER-2-CEEX-06-11-44 project funded by the Ministry of Education and Research, Romania. We are thankful to Dr I B Misirlioglu for fruitful discussions. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24]
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