Strain-gradient mediated local conduction in strained bismuth ferrite films

It has been recently shown that the strain gradient is able to separate the light-excited electron-hole pairs in semiconductors, but how it affects the photoelectric properties of the photo-active materials remains an open question. Here, we demonstrate the critical role of the strain gradient in mediating local photoelectric properties in the strained BiFeO3 thin films by systematically characterizing the local conduction with nanometre lateral resolution in both dark and illuminated conditions. Due to the giant strain gradient manifested at the morphotropic phase boundaries, the associated flexo-photovoltaic effect induces on one side an enhanced photoconduction in the R-phase, and on the other side a negative photoconductivity in the morphotropic \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T\prime$$\end{document}T′-phase. This work offers insight and implication of the strain gradient on the electronic properties in both optoelectronic and photovoltaic devices.


Supplementary Note 1: Conduction process of the conductive AFM measurement
The morphotropic and ′ -phases in the strained BiFeO 3 thin films combine epitaxially with each other in an alternating way with a tilting angle (see Supplementary Figure 1). As both morphotropic phases possess certain conduction, they will always get involved in the current conduction to certain extend regardless of whether the AFM tip contacts -phase or ′ -phase. Specifically, when the AFM tip contacts the middle of the less conductive -phase, the tip probes a low current (Supplementary Figure 1a); when the tip moves towards the ′ -phase, current would also flow in the conductive ′phase after passing the less conductive -phase, leading to an increased current magnitude (Supplementary Figure 1b); When the tip contact directly at the middle of ′ -phase, the dark current reach to its maximum value, thus forming the previously mentioned saw-like features. The plateaus in the scan profile would appear if one of the phases in completely insulating, thus blocking current injection from the AFM tip when the tip only contacts this phase. This occurs for example in the AFM scanning on the conductive domain walls embedded in the insulating domain matrix. 1 Furthermore, even in the case that the phase boundaries is more conductive than the morphotropic phases, the cAFM scan profile would also show the saw-like feature but with maxima appearing directly at the boundary locations. Clearly, this is not the case in our work. Thus, it is justified to conclude that the morphotropic ′ -phase possesses an enhanced dark conduction compared to that of the -phase.    Figure 5a). Due to the higher density of non-equilibrium carriers in the -phases, non-equilibrium carriers diffuse from the -phase to the ′ -phases, resulting in space charge of which field prevents further carrier diffusion (see Supplementary Figure 5b). Consequently, the density of non-equilibrium carriers in the ′ -phase is increased, resulting in

Supplementary
where is the density of non-equilibrium carriers. As the conduction is proportional to the density of carriers, this would give rise to the photoconduction contrast as Clearly, this is inconsistent with experimental observation presented in the manuscript wherein R−phase > T−phase > T ′ −phase . Thus, the light absorption contrast between morphotropic phases cannot account for the photoconduction contrast experimentally observed.
To further demonstrate the crucial role of the flexo-photovoltaic effect and especially, to exclude the effect of light absorption variation, we mapped spatial distribution of the photoconduction over Owing to the tilting of the ferroelectric polarization away from the surface normal direction (i.e. [001] pc ), both morphotropic phases (namely, -phase and ′ -phase) in principle possess certain light polarization dependent absorption. Although we have confirmed above that the light absorption difference between morphotropic phases do not account for the observed photoconduction contrast, the potential impact of its light-polarization dependence on local photoelectric properties deserves further exploration. To this end, we studied the light polarization dependent photoconduction of This is also consistent with previous report using out-of-plane capacitor geometry (see ref. 5).
In the case of morphotropic -phase in the mixed region, it is difficult to directly probe the intrinsic light polarization dependence of its photoelectric properties due to its small dimension and strong interaction with its surroundings. To circumvent this difficulty, we studied the less strained If it is the light polarization dependence of optical absorption that determines the local photoconduction variation while rotating the light polarization (see Figure 4 of the Manuscript), the photoconduction contrast between the -phase and the -phase should maximize when light polarization is parallel to the in-plane ferroelectric polarization of -phase (i.e. = 45°). Afterwards, it reaches a minimum value while light polarization equals to = 135°, as schematically illustrated in Supplementary Figure 7e. Apparently, this is inconsistent with experimental result shown in Figure   4 of the Manuscript. Therefore, we can conclude that the polarization dependent optical absorption also do not play a major role in the mediating local photoconduction. Instead, as demonstrated in the Manuscript, it is the flexo-photovoltaic manifested at the morphotropic phase boundaries that controls local photoelectric properties in the mixed phase region.

Supplementary Note 6: Domain structure of the morphotropic region
Owing to the ferroelectric nature of the morphotropic phases in the strained BiFeO 3 thin film, both R-phase and ′ -phase possess non-centrosymmetry and exhibit the bulk photovoltaic effect, which is also able to separate light-excited electron-hole pairs. The domain structure of a morphotropic phase region is characterized by piezoresponse force microscopy as shown in Supplementary Figure 8a-c. In the out-of-plane direction, the strained BiFeO 3 film shows a uniform polarization direction pointing towards the substrate. In the in-plane direction, the polarization is aligned toward the right side of the scanned area. As schematically shown in Supplementary Figure 8d, the "unidirectional polarization feature" refers to that each -phase matrix in a morphotropic phase region possess the same polarization distribution and the ′ -phase matrix also exhibits the same polarization features but different from that of -phase, which is consistent with previous reports. 4,5 In contrast to the simple domain patterns in the and ′ phase, domain configuration in the morphotropic phase boundaries  Moreover, if the depolarization field exists at the morphotropic phase boundaries due to the large polarization divergence ∇• , this polarization divergence would also induce charge accumulation at the phase boundaries, leading to an enhanced conduction at the boundaries, as in the case of ferroelectric domain walls. 8,9 However, the dark cAFM characterization shown in Figure 1 of the main manuscript did not show any conduction enhancement at phase boundaries. Therefore, it would be reasonable to claim that the polarization divergence and depolarization field is minimal at the morphotropic phase boundary. Thus, the existence and the manifestation of the depolarization field at the morphotropic phase boundaries is highly questionable and speculative and do not play a major role in mediating local photoelectric properties. and the matrix -phase shows sinusoidal dependence on the light polarization, which can be well fitted by Eq. 1 of the manuscript. The photoconduction ratio between ′ and matrix -phase also depends on the light polarization but with a 0° phase shift compared to that of ⁄ conductance ratio. This is also consistent with our proposed model. Note that the variation amplitude of the ′ ⁄ photocurrent ratio is much smaller than that of the ⁄ ratio. This is probably due to the entangled conduction path underneath the AFM tip. As illustrated in the inset of Supplementary Figure 10b