Tip-enhanced bulk photovoltaic effect

Using the conventional macroscopic description of the bulk photovoltaic effect we analyze the light-induced currents and electric fields arising in the optical configuration with a continuous bottom electrode and a small circular top electrode. This scheme is relevant to recent experiments on the tip-enhanced photovoltaic effect in ferroelectrics. It is shown that a light-induced electric field remains nonzero inside the sample even in the short-circuit regime. Moreover, it is enhanced compared to the photovoltaic field in a large area and strongly enhanced near the top electrode. A field-assisted collection of charge carriers from the illuminated area produces a strong local enhancement of the current density near the top electrode. The tip-enhanced electric field is typically parallel to the photovoltaic current. It is sufficient to repolarize the crystal near the top electrode. The effect of the tip enhancement on the light-current transformation efficiency is considered, and predictions for the tip radius and sample thickness dependencies of the total light-induced current are made.

Figure 1

Two geometrical schemes for PVE experiments: (a) continuous bottom and top electrodes and (b) a continuous bottom electrode and a circular top electrode of radius $a$. The horizontal and vertical distances from the top electrode are $r$ and $z$. The bottom electrodes are transparent and $\mathit{e}\perp {\mathit{n}}_z$.

Figure 2

Closed circuit regime, $V=0$: Stream lines of the total current density $\mathit{j}$ (a) and of the field $\mathit{E}$ (b) in the $xz$ plane near the top electrode. For the field we set $d/a=100$. The roundish solid line in (b) separates the regions with $E_z<0$ and $E_z>0$. The negative value $E_z(x,0)=-E_{\mathrm{pv}}$ for $\left|x\right|>a$ ensures zero current through the nonelectroded part of the sample.

Figure 3

The function $f(r/d)$ as defined by Eq. (7).

Figure 4

Geometry of the electrostatic problem and the image charges. The PM boundary conditions must be fulfilled at the vertical planes $z=\pm d$.