Local polarization dynamics in ferroelectric materials

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Rep. Prog. Phys. 73 (2010) 056502 S V Kalinin et al Response, a.u. 1.0 0.5 0.0 -0.5 -1.0 (a) -10 -5 0 5 10 Bias, V dc Work of switching, a.u. V (b) 15 10 5 0 0 2 4 6 8 10 Modulation voltage, V ac 1.5 1.0 0.5 0.0 Switchable response, a.u. Figure 38. The driving bias effect on the hysteresis loop shape. (a) Hysteresis loops for PZT thin film for ( ) 1.5 V pp ,() 4V pp ,()6V pp and (•) 8V pp driving amplitudes. (b) Driving bias dependence of effective work of switching and saturation response. Reprinted from [329]. Copyright 2006, American Institute of Physics. These parameters provide a measure of the switching properties of the material. 4.1.1. Effect of imaging conditions on hysteresis loops. As in any spectroscopic method, PFS and SS-PFM are highly susceptible to a large number of external and internal factors that affect the veracity of spectroscopic data acquisition. The detailed analysis of instrumental factors is reported in [329]. Below, we discuss the effect of measurement parameters on PFS. 4.1.2.1. Probing bias and the bias window. One important consideration in PFM and SS-PFM is the choice of driving voltage, V ac , and bias window of measurements, V dc ∈ (V min ,V max ). Ideally the measurements are performed in the low signal limit, V ac ≪ (V + + V − ). However, practical considerations such as maximizing the signal strength often necessitate the use of high driving voltages, in particular for materials with relatively low piezoelectric coupling. The effect of a finite probing bias on the loop shape strongly depends on the fundamental hysteresis loop formation mechanism and bias frequency, and cannot be explained by a simple model. Here, we summarize the experimental studies of the driving bias effect. Shown in figure 37(a) are experimentally observed hysteresis loops obtained on a pulsed-laser deposition grown PZT thin film (70 nm) for different probing biases. The loops are normalized by bias amplitude to ensure similar units. Note that for V ac below the coercive bias, the loop shape remains largely unchanged—the loops slightly narrow indicating the onset of switching, but the variation in relevant parameters is relatively small (figure 37(b)). Conversely, modulation amplitudes greater than the coercive bias effectively result in a collapse of the loop to a straight line. The changes in the effective work of switching and switchable response as a function of V ac are shown in figure 38(b). The small variation in relevant characteristics for small biases is presumably due to a relatively larger noise level. Note that the behavior in figure 38 is reproducible and the shape is regained when small biases are used demonstrating that the collapse in the loop shape cannot be attributed to the damage to the conductive tip coating or the surface. Thus, for certain materials, voltages at ∼2/3 of the coercive bias level can be used to yield high-quality loops. At the same time, for materials with small coercive bias, e.g. ferroelectric nanodots, ultrathin films, etc, imaged at large modulation voltages, the absence of hysteresis loops can be erroneously interpreted as evidence for non-ferroelectric state. The dependence of the loop parameters on the bias window is illustrated in figure 39. The hysteresis loops become saturated when the bias windows exceed 20 V (figure 49(a)). The origins of the slight downward trend are unclear but can possibly be attributed to reverse switching induced by charge injection at the surface [304]. The bias window dependence of switchable polarization is illustrated in figure 39(b). Note the good agreement between the values obtained from fitting and those measured directly from the loop. Figure 39(c) illustrates the dependence of the positive and negative nucleation biases on the bias window. Despite the relatively large error in the determination of nucleation bias, the values are nearly biaswindow independent, suggesting that the loop formation is controlled by the nucleation process. Finally, figure 39(d) illustrates the bias window dependence of the effective work of switching as determined from functional fitting and the direct integration of the area below the curve. The values obtained are in good agreement and also illustrate that the leveling-off of hysteresis parameters at large voltages are indicative of loop saturation. 4.1.2.2. Ambient effects. One of the well-known factors affecting SPM measurements under ambient conditions is the presence of wetting water layers and associated capillary tip– surface forces as described in section 3.2.5. Here, we present experimental evidence illustrating the possible role of ambient conditions on hysteresis measurements by PFM. Shown in figure 40(a) is the PFM hysteresis loop obtained on a freshly prepared (buffered HF etch followed by O 2 annealing) atomically flat STO (1 0 0) surface. Shown are the average values and error bars corresponding to standard deviations determined from 64 hysteresis loops acquired on an 8×8 mesh of points separated by 100 nm. Note that clear hysteretic behavior can be seen despite the fact that the surface is (nominally) non-ferroelectric. We attribute 39
Rep. Prog. Phys. 73 (2010) 056502 S V Kalinin et al Response, a.u. 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 (a) Switchable polarization, a.u. 1.5 1.0 0.5 0.0 -40 -20 0 20 40 0 10 20 30 40 50 Bias, V dc (b) Bias window, V dc Nucleation bias, V (c) 8 6 4 2 0 0 10 20 30 40 50 Bias window, V dc Work of switching, a.u. (d) 80 70 60 50 40 30 20 10 0 0 10 20 30 40 50 Bias window, Vdc Figure 39. (a) Evolution of PFM hysteresis loops on an epitaxial PZT film as a function of bias. (b) Bias window dependence of switchable polarization. (c) Bias dependence of () positive and () negative nucleation bias. (d) Bias window dependence of effective work of switching. Shown in (b) and (d) are values determined from the functional fit ( ) and by direct integration of the area below the loop (⊓⊔). Reprinted from [329]. Copyright 2006, American Institute of Physics. Response, a.u. 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 -10 -5 0 5 10 (a) Bias, V dc Response, a.u. (b) 0.00 -0.05 -0.10 -0.15 -0.20 -10 -5 0 0 Bias, V dc Figure 40. The effect of ambient conditions on the hysteresis loop shape. (a) Hysteresis loops for a clean insulting STO surface. (b) Hysteresis loop for conductive SrRuO 3 /STO thin film. Reprinted from [329]. Copyright 2006, American Institute of Physics. this behavior to the electrocapillary condensation of water layers at the tip–surface junction [330, 331], resulting in an ‘unsaturated’ electromechanical hysteresis loop. For comparison, figure 40(b) shows hysteresis loops obtained on a conductive SrRuO 3 /STO surface. This surface is extremely stable in air and conductive (i.e. low energy electron diffraction pattern can be observed after air exposure) [332] and no hysteresis loops are measured, thus confirming that the behavior observed on the STO (1 0 0) surface is not an instrumental artifact. While this observation is not necessarily universal, it does illustrate that spurious hysteretic contributions to electromechanical measurements can exist when operating under ambient conditions. 4.2. Phenomenological theory of domain loop formation The progress in experimental methods has stimulated parallel development of theoretical models to relate PFM hysteresis loop parameters and materials properties. A number of such models are based on the interpretation of phenomenological 40
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