5.2 Synchrotron experiments
The presented results in this section were obtained at the MS-Surf-Diffr X04SA beamline at the Swiss Light Source in Zurich.
Figure 5.6: Result for a (9/4) 100-nm SL thick. (a) Schematic of the structure of the samples measured at PSI. The superlattice capacitors were etched down all the way to the bottom electrode to ensure that the diffracted signal strictly corresponds to the part of the sample that is under the electrode. Panel (b) shows the XRDθ−2θdiffractograms where the SL, the SRO and the substrate peaks are observed for different voltages. The resulting piezoelectric expansion of the SLc-axis is summarized in panel (c). (d) RSM of a (9/4) SL at RT. The four-fold symmetry of the satellites around the SL peak indicates that the domain walls are oriented along the crystallographic directions (a and b). The RC shown in red, which is a line-cut throughout the RSM shows satellite peaks up to third order.
Fig. 5.6(a) schematically shows the structure of the measured samples.
Columns were etched away to ensure that the diffracted signal from the SL strictly corresponds to the part of the sample that is under the electrode and at a given electric field. The SL thickness is 100 nm and the size of the measured electrodes is 200 by 200µm2. To help position the beam on the
sample, two methods were employed. At first the sample was scratched with a diamond pen between the electrodes. This way, a polycrystalline diffraction signal from the substrate could be observed and used to navi-gate on the sample in search of the desired electrode. Later we noticed that the dielectric loss measured simultaneously using the LCR meter increases when the X-ray beam hits the contacted electrode see Fig. 5.7; most prob-ably due to detrapping of charges by the X-rays or electrons being excited into the conduction band since the used energy of the X-rays is 9keV. In this way we were able to make sure the beam was accurately positioned on the contacted electrode.
Figure 5.7: C0 and C00 as a function of frequency at zero volt with and without the X-ray beam shining on the SL. A difference is observed, espe-cially in the imaginary part (loss).
Fig. 5.6(b) shows the XRDθ−2θdiffractograms where the SL, the SRO and the substrate peaks are observed for different voltages. Note that the SL Bragg peak broadens with increasing voltage. This is likely due to the imbalance in up/down domains. Domains anti-parallel to the electric field are wider with a largerc-axis (due to piezoelectric expansion) than the ones with opposite polarization state inducing an inhomogeneity in the c-axis which leads to a broadening of the peak. The effective piezoelectric
5.2 Synchrotron experiments
Figure 5.8: Result for a (9/3) 100-nm SL thick. The resulting piezoelectric expansion of the SLc-axis.
coefficient is defined by d33 = ∆V∆cN 3, with N the number of unit cells in the superlattice. The average piezoelectric expansion of a (9/4) SL is summarized in panel (c). The same measurements were taken for a (9/3) superlattice showing similar responses to the (9/4) SL. The results for the c-axis evolution as a function of the voltage for room temperature and 32 K are summarized in Fig. 5.8. Note that the observation of such a lattice expansion and the increase ind33with voltage indicates that domains of one polarization are becoming larger than those of opposite polarization.
Interestingly this implies that for both positive and negative voltages an increase in the lattice parameter is observed. The piezoelectric expansion of domains aligned with the field is counteracted by the contraction of domains aligned opposite to the field. However, since the domains aligned with the field expand with increasing field (approximately linearly with applied voltage), the overall response is dominated by domains aligned with the field and hence the sample expands for either polarity of the applied bias.
Fig. 5.6(d) shows an RSM of the (9/4) SL at RT. The four-fold symme-try of the satellites around the SL peak indicates that the domain walls are oriented along the crystallographic directions (a and b). The RC shown in red, which corresponds approximately to a horizontal line-cut through the RSM shows the first, second and third order domain satellites. This reflects the high crystalline quality of the samples with well-defined periodicities within each ferroelectric layer; all being under the same electrostatic
con-3We call it the effectived33since we are not at zero field.
Figure 5.9: (a) RC measured for different applied fields for a (9/4) SL at RT. The evolution of the intensity of each satellite peak versus voltage is displayed in (b).
ditions by construction. In addition to the delight of the observation of higher order satellite peaks, their presence offers a great opportunity to better understand the evolution of the domain structure under field. The RC evolution upon application of voltage is shown in Fig. 5.9 and the evo-lution of the intensity of each peak versus voltage is shown on the right hand side. With applied voltage, the first order peak (blue square) and the third one (red circle) decrease in intensity, whereas the second-order peak (green triangles) firstincreasesand then decreases. Data points were also taken with decreasing applied voltage and a hysteretical behavior was observed. This effect seems to have nothing to do with the ferroelectric nature of the sample but might be due to the fact that the data acquiring process took several hours for each voltage value. Therefore defects such as vacancies are most probably moving with time. This is corroborated by results in Fig. 5.10(a) and (b) showing that at around 5 Volts, the sample is becoming leaky irreversibly.
5.2 Synchrotron experiments
Figure 5.10: Result for a (9/4) superlattice taken during the measure-ments: C0 andC00 were recorded for different DC values. Panel (a) and (b) show the data from 0 to 5V and backwards.
In order to get a better understanding of what is being observed let us take one step back and model the system that is being measured. The 180◦ ferroelectric domains can be modeled using a step function. Such model-ing implies that the width of the domain walls is neglected. As shown in Ref. [40], the intensities of the satellites corresponding to this step func-tion strongly depend on the fracfunc-tion of up to down domains:
Im(a) Imax
=sin22maπ Λ
=sin2(mf π) (5.1) where 2a is the domain size of for instance the up ones,Λ is the do-main periodicity,f is the domain volume fraction defined as:f = 2aΛ and m the order of the satellite. For different m’s the expected intensity as a function of the volume fraction is displayed in Fig. 5.11. For a volume fraction of one half, only the first and the third peaks should be observed.
When the volume fraction changes, that is when some domains shrink and others expand, the intensities evolve and this is the evolution we are actu-ally tracking with the experiment. For the first order peak, the maximum intensity is expected atf = 0.5. For the second order, when starting in a configuration off = 0.5and going away from it by applying a voltage, the peak intensity should first increase up tof = 0.75and from then decrease.
For the m = 3, a maximum is observed at f = 0.5. The peak intensity should decrease up tof = 0.66where the intensity should eventually go
up again and so on.
Interestingly, the data in Fig. 5.9 shows the decrease of both the first and third order peaks, while the second one first increases and then de-creases. This is the key result which supports that the proposed domain wall breathing scenario indeed takes place.
Figure 5.11: (a) Shows the schematics of the idea behind the model of the domain wall breathing. (b) Simulation of the normalized intensity of each order satellite peak as a function of the volume fraction.
Note that Fig. 5.9 shows that a second order peak is observed even at zero applied bias when the domain fraction is expected to be 0.5. There are two possible explanations for this: 1) the net sample polarization is not exactly zero due to internal fields, 2) our simplified model is too crude to accurately describe a realistic domain structure with finite-width domain walls. The most probable answer is the second one. Indeed, it can be shown (for example by explicit simulation of a realistic domain wall pro-file) that a finite domain wall width leads to the appearance of even order peaks at half volume fraction. PE loops do not show significant imprints suggesting that internal fields are unlikely to be at the origin of the second order peak. Additionally, in case of the presence of an imprint, application of a field opposite to the built-in field should lead to a decrease in the sec-ond peak intensity and an increase in the intensity of the odd order peaks.
This is not something we have observed.
Further increase of voltage
In order to test the sample at larger voltages, we decided to measure an-other electrode on the same sample. We tested this new capacitor at room
5.2 Synchrotron experiments
Figure 5.12: Measurements for a (9/4) SL taken at 26 K. (a) RC measured for different applied fields. On the right side, the intensity evolution of each peak versus voltage is displayed. (b)θ-2θ scans for a SL sample to which the voltage has been ramped up to 8 V. A splitting of the SL Bragg peaks is observed. Within a doublet, the peak with the smallerc-axis cor-responds to the polydomain part of the sample, while the second one, with a largec-axis can be attributed to a monodomain response indicating that parts of the sample might have switched to a monodomain configuration.
Panel (c) shows the lattice evolution for the “polydomain” (squares) and the “monodomain” (circles) peak. After the sample has entered the new regime where a splitting of the Bragg SL peak is observed, the intensities of all the satellite peaks decrease when increasing voltage, meaning that the sample has been changed irreversibly.
temperature by doing a capacitance versus voltage between±5 V. Inter-estingly, as the field increases further, new features appear. For voltages above 5V the satellite intensities continue to decrease, while at the same time the SL Bragg peak splits into two as shown in Fig. 5.12(b) indicat-ing a strong structural change in the sample. Within a doublet, the peak with a smaller L value corresponds to a largerc-axis than the one with larger L value. Hence, the peak with a smallerc-axis corresponds to the as-grown state, namely polydomain and the second one, with a larger lat-tice parameter, could be a signal from regions of the sample that have turned monodomain. When the voltage is increased even more, a stronger piezoresponse is observed for the monodomain peak. In addition, their rel-ative intensities change: the “monodomain peak” gains more weight. On the RSM, (not shown here) domain satellites are still present around the
“polydomain” Bragg reflections only. Such an absence of satellites around the peak with a largec-axis corroborates the hypothesis that it is certainly due to parts of the sample that have become monodomain.
An important observation that complicates the above picture is the de-pendence of the sample behavior on its electrical history. Reversible do-main breathing is only observed when small voltages are applied to a vir-gin sample. Once the Bragg peak splitting occurs, however, the sample is irreversibly changed and the domain breathing is not observed when the field is reduced or applied in the opposite direction. Further irreversible changes are observed upon subsequent cycling; see Fig. 5.12. Note that in the work of Joet al.[68] the field is repeatedly pulsed and therefore the first evolution of the virgin sample is never probed.
Note about temperature dependence measurements
During the synchrotron measurements, we have tested the samples at dif-ferent temperatures (see Fig. 5.12) with a special focus on the (9/4) SL, where the PTO layers are considered to be electrostatically decoupled. The motivation for it was to see if any changes in domain sizes were observed.
The STO dielectric constant being largely temperature dependent, upon lowering the temperature, the increase of the dielectric constant makes the STO easier to polarize (namely the cost in energy is lower). The idea was the following: at low temperature, if the energy cost to polarize the STO is lower, a monodomain structure might be energetically more favor-able than the polydomain one. A structural change toward a monodomain structure would have implied that the satellites positions in the RC would have moved toward the main central peak and their relative intensities