Built-in voltage in thin ferroelectric PbTiO₃ films: the effect of electrostatic boundary conditions

On the series of samples without a top electrode layer, the built-in voltage was measured using switching spectroscopy piezoresponce force microscopy (SSPFM), as described in [19]. The set-up is represented in figure 2(a): a DC bias V_DC is applied to the AFM tip in addition to the AC probing voltage V_AC, and the bottom electrode is grounded. The PFM phase and amplitude are then recorded while the DC bias is ramped stepwise, going back to zero bias after each step, as schematically shown in figure 2(b). This produces two measurements: one as a function of the bias applied at the time of the acquisition ('on'), and one as a function of the bias applied just before the acquisition ('off'). To avoid effects of electrostatic interactions between tip and sample, only the results of the 'off' state are used. This produces the typical loop shape for the phase, and a butterfly shape for the amplitude as shown on figure 2(c) for a 50 nm PbTiO₃ film with a 2 nm top SrTiO₃ spacer and a 22 nm SrRuO₃ bottom electrode. To make our measurements more reliable, they were repeated a large number of times on a grid (typically at least 16 × 16 points evenly spaced on a 2 × 2 $\mu {{\rm{m}}}^{2}$ grid). The switching biases were then extracted as the points of lowest amplitude, and used to calculate the built-in voltage for each point, corresponding to the value of V_DC at the center of the loop¹ . An example of such a grid of values is shown in figure 2(d).

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The phase and amplitude loops are all systematically shifted towards positive bias, corresponding to a residual field in the ferroelectric layer pointing up, resulting in a preferred up polarization.

The measurements were performed using two different kind of tips: NSC18 Cr–Au coated silicon tips from MikroMasch and B-doped diamond tips from NaDiaProbes. It is worth noting that the values are different when the measurements are performed with different kind of tips. The additional AFM-tip/ferroelectric interface itself modifies the built-in bias, so that the values measured are for the whole system including the ferroelectric layer, the surrounding layers and the electrodes/tip. It is then possible to compare the values obtained for different samples under the same conditions when using the same tip.

The evolution of the built-in voltage has been studied as a function of the thickness of the SrTiO₃ layers, for two different series of samples, one with 50 nm thick PbTiO₃ layers, and one with 20 nm thick PbTiO₃ layers, and with two different kind of AFM tips, as reported in table 1.

Figure 3 shows the results for a series of four samples consisting of a 50 nm PbTiO₃ film with a top and/or bottom SrTiO₃ spacer of 2 nm (5 u.c.). The samples without a bottom spacer (A and D) are monodomain up, while those with a bottom spacer (B and C) are polydomain (up background with down nanodomains), independently of the top spacer, as shown in [12].

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A positive built-in voltage is observed for all the samples, consistent with the observed preferential direction of polarization. The built-in voltage correlates with the c-axis values measured via x-ray diffraction (see figure 3). Samples A and D are monodomain with a larger built-in voltage that results, under zero applied bias, in an increase in their polarization, associated with an increase of the c-axis due to polarization-strain coupling. On the other hand, samples B and C are polydomain, as a result of a stronger depolarization field that would be present in these samples if they were monodomain. In these samples, the built-in voltage is smaller, leading to a reduced piezoelectric distortion. Moreover, the domains with an up polarization would experience an increase in their c-axis, while the opposite domains would have their c-axis decrease. It is most certainly the presence of domain walls in the polydomain configuration that explains the observed reduced tetragonality, as domain walls are paraelectric and correspond therefore to a reduced distortion. As mentioned in [12], Takahashi et al [20] also observed such an increase of the c-axis lattice parameter for monodomain PbTiO₃ films grown directly on Nb-doped SrTiO₃ substrates compared to polydomain ones, upon using photochemical switching to induce the polydomain to monodomain transition.

The other series of samples is composed of a 20 nm PbTiO₃ film with symmetric SrTiO₃ spacers of different thicknesses, from 0 up to 10 unit cells (see schematic representation in figure 4). These samples were shown to be monodomain for the samples with 0 and 1 unit cell of SrTiO₃ and polydomain for thicker spacers [12]. Figure 4 shows the built-in voltage measured with two different tips, a B-doped diamond tip (black dots) and a Cr/Au coated silicon tip (red squares). The results obtained with both kinds of tips demonstrate that the built-in voltage decreases for the sample with the thickest SrTiO₃ spacers. This observation can be compared to the study by Lu et al [21]: in BaTiO₃ thin films with SrRuO₃ top and bottom electrodes, they also observed a reduction of the built-in field by adding 2 unit cells of SrTiO₃ between the film and the top electrode. This was attributed to the symmetrization of the chemical interface termination sequence. The RuO₂/BaO interface termination sequence occurring naturally at the top interface seems to be detrimental due to the presence of a pinned interface dipole arising from a mismatch between ionic radii. By adding the SrTiO₃ layer, the unfavorable interface termination is eliminated, leading to a stable and switchable ferroelectric polarization. The insertion of the SrTiO₃ also results in a further enhancement of the ferroelectric stability.

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Our measurements additionally show that the built-in voltage measured with a Cr/Au coated silicon tip is systematically lower than that measured with a B-doped diamond tip, demonstrating the effect of the tip itself. Note that in the sample with the thickest SrTiO₃ spacer, the built-in voltage measured with the Cr/Au coated silicon tip is actually negative. Here the tip directly plays the role of top electrode, and changing the tip material results in different electrical boundary conditions, therefore affecting the total built-in voltage. The measured built-in voltage is then the sum of the built-in voltage in the sample and the one due to the tip, and depending on the tip material, can actually be negative.

To study the effect of a top electrode layer, a sample similar to sample C in figure 3 (50 nm PbTiO₃ film with top and bottom 2 nm SrTiO₃ spacers and with 22 nm bottom SrRuO₃ electrode on SrTiO₃ substrate) was grown, with the addition of an 11 nm top SrRuO₃ electrode layer sputtered in situ and then patterned to form squares of different sizes (the one used here is 100 × 100 $\mu {{\rm{m}}}^{2}$).

PFM measurements were performed through the electrode, under different DC biases applied directly to the electrode, as described by Gruverman [22] and used by different groups (e.g., [23, 24]). In this case, we did not perform SSPFM measurements, as V_DC is applied to the whole electrode, so the whole area below switches at every cycle and each point in the grid will be affected by all the measurements performed before. Instead, the domain configuration underneath the electrode was monitored on 2 × 2 $\mu {{\rm{m}}}^{2}$ scans by recording the phase and amplitude PFM response to a small AC voltage V_AC while applying a DC voltage V_DC to the tip and the top electrode layer. Figure 5 (left) shows some of the phase images obtained on this sample with ${V}_{\mathrm{AC}}=1\;{\rm{V}}$. For ${V}_{\mathrm{DC}}=0\;{\rm{V}}$, the region below the electrode is mostly uniformly polarized, with the polarization oriented up (a). When increasing the voltage, down polarization domains appear (b)–(d), until the region is fully down polarized at ${V}_{\mathrm{DC}}=1.8\;{\rm{V}}$ (e). When V_DC is then progressively decreased, up polarized domains appear in the down polarized background (f). These up domains grow until they cover most of the region (g)–(i), with only a few down domains left, until finally the region is fully monodomain up at ${V}_{\mathrm{DC}}=-1\;{\rm{V}}$ (j). Note also the difference between (c) and (f), both taken for ${V}_{\mathrm{DC}}=1\;{\rm{V}}$, but one on increasing V_DC and the other on decreasing it.

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From each image, it is possible to extract the switched area proportion which is taken as the number of pixels with a polarization pointing down divided by the total number of pixels. This gives a value of 1 for a fully down polarized region, and 0 for up. When plotted as a function of the voltage applied to the tip and top electrode layer V_DC, this results in a hysteresis loop as shown in figure 5 (left; the values for the images (a)–(j) are reported directly on this graph, together with the values obtained for other scans not shown here). This hysteresis loop is shifted and shows a built-in voltage of 0.9 V. For comparison, the phase hysteresis loop and amplitude butterfly loops obtained on the same sample but without a top SrRuO₃ electrode are also shown in figure 5 (right). For this sample, the built-in voltage is close to 0 V, and the PFM phase image obtained with V_DC = 0 V has a switched area proportion close to 0.5. This demonstrates that the presence of a top SrRuO₃ electrode induces a built-in voltage in a sample that does not have any otherwise.

In the hysteresis in figure 5 (left), data points are displayed for different V_AC values. Even for very large V_AC (larger than the coercive voltage observed for this loop), the measurement does not seem to be affected. This can be explained by the fact that the PFM signals are recorded using the DART mode at a very high frequency (typically 370 kHz), so that the effective voltage applied to the ferroelectric layer is reduced by the RC time constant of the circuit. The signal period is shorter than the observed minimum switching time in similar systems (100 $\mu {\rm{s}}$ lower limit for one pulse switching in 270 nm thick PbZr_0.2Ti_0.8O₃ [25]). This agrees with the work of Ivry et al [26] where high-resolution PFM imaging is achieved by using a V_AC higher than the DC coercive voltage of the sample near the cantilever in-contact resonance frequency. Increasing the value of V_AC however can reduce the noise level in the PFM measurements.

In the series of samples with 50 nm PbTiO₃ films, the samples without a SrTiO₃ bottom spacer have a larger built-in voltage and are monodomain, while the two samples with a bottom SrTiO₃ spacers are polydomain with a reduced built-in voltage, as shown in figure 3. The built-in voltage results in a preferential polarization orientation that corresponds to the polarization direction of the monodomain samples, and to the direction of the polarization background for the polydomain samples.

In the series of samples with 20 nm PbTiO₃ films, the samples without SrTiO₃ spacers or with very thin (1 u.c.) ones are monodomain, while they become polydomain with SrTiO₃ spacer layers of 2 u.c. and more. The domains are more difficult to resolve in the polydomain samples in this series than in the 50 nm series. However, a gradual change of the phase can be seen as the SrTiO₃ spacer layer thickness increases (figure 6). To quantify this evolution, two reference regions were written by applying negative or positive DC bias to the tip, resulting in two square domains with well defined polarization oriented up or down. The mean phase in the as grown region can then be directly compared to that in the switched regions for this series of samples, as shown in figure 6. For the samples with thicker spacers, the mean phase of the as-grown region is significantly higher than ${0}^{\circ }$, meaning that more domains of opposite polarization are present in those samples, in agreement with the observations of a lower built-in voltage. However, none of the samples shows a mean phase in the as-grown region of more than 90°, corresponding to half up, half down. This is in line with our measurement of the built-in voltage, suggesting a preferred up polarization for all these samples.

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50 nm series

Figure 7 shows PFM measurements obtained on the 50 nm PbTiO₃ film with 2 nm top and bottom SrTiO₃ interlayers. PFM measurements on the same 1.2 × 1.2 μm² region and under the same conditions were repeated after the area was first scanned with a DC bias applied to the tip (from −2.5 V up to +2.5 V as indicated in the figure). After applying a negative tip bias, the down polarized domains (white) shrink in size, while they expand after applying a positive tip bias. The images were not taken in that specific order, and although there is some spatial drift from one image to the other, it is possible to recognize and follow specific domains in their size alteration. Moreover, a noticeable relaxation of the domain size was observed after the poling, as shown in figure 8, with a recovery of the initial configuration after a time of typically 3 h, showing that the position of the domain wall reproducibly relaxes back to its original position. These results demonstrate that it is possible to switch locally the polarization by applying a DC voltage between the AFM tip and the bottom electrode by moving the intrinsic domain walls, with a relaxation on a time scale suitable for measurements.

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Polarization back-switching was also studied in the series of samples with 20 nm PbTiO₃ films by using the same procedure as described above to follow the evolution of written regions as a function of time and are shown in [12]. Measurements of the retention time of the written polarization (up and down) regions show a rather different mechanism for different SrTiO₃ spacer thicknesses. Without any SrTiO₃ spacer, the domain wall of the written structure moves and deforms with time, reducing the extension of the written region, but keeping the full amplitude of the switched region bounded by the domain wall. This mechanism can be explained by the presence of a built-in-field pushing towards a preferential orientation state, with the back-switching occuring at the domain wall. On the other hand, with increasing thickness of the SrTiO₃ spacers, the back-switching mechanism is rather different with nano-domains appearing within the written region. This mechanism, changing a monodomain region towards a polydomain configuration, can be attributed to the depolarization field. For the sample with SrTiO₃ spacer layers of just 1 u.c., both effects can be seen: the roughening of the domain wall delimiting the written region as well as the appearance of opposite nano-domains inside, attesting that both mechanisms, i.e. the built-in voltage and the depolarization field, can play a role simultaneously.

When adding a top electrode layer to these samples, we noticed that not only the domain configuration is changed and the loop is more shifted, but also the back-switching is much faster. To emphasize how quickly the change in polarization configuration occurs on a sample composed of a 50 nm PbTiO₃ film with 2 nm top and bottom SrTiO₃ interlayers and top (11 nm) and bottom (22 nm) SrRuO₃ electrodes, PFM phase is measured continuously along the same line (2 μm length) (figure 9). While scanning, different DC voltages are applied to both the tip and top electrode layer. The horizontal scale is the measurement time, with a reading frequency of 1 Hz. The dotted red lines show the time at which the DC voltage is changed to the value indicated above. The domain configuration changes abruptly at each modification of the DC voltage, with almost no evolution as a function of time for a constant DC voltage. These measurements also show the uniform up polarization state for ${V}_{\mathrm{DC}}\lt 0\;{\rm{V}}$ and uniform down polarization state for ${V}_{\mathrm{DC}}\gt 1\;{\rm{V}}$. This is in line with the shifted loop shown in figure 5 for the same sample.

Note also that even upon complete switching, the opposite domains always start to nucleate at the same position, proving again the presence of strong nucleation sites, both for up and down domains. This is very much in line with the observations of Kim et al [23] or Jesse et al [28], who demonstrated the presence of preferential nucleation sites in Pb(Zr, Ti)O₃ capacitors using PFM measurements.