Polarity-dependent nonlinear optics of nanowires under electric field

Polar materials display a series of interesting and widely exploited properties owing to the inherent coupling between their fixed electric dipole and any action that involves a change in their charge distribution. Among these properties are piezoelectricity, ferroelectricity, pyroelectricity, and the bulk photovoltaic effect. Here we report the observation of a related property in this series, where an external electric field applied parallel or anti-parallel to the polar axis of a crystal leads to an increase or decrease in its second-order nonlinear optical response, respectively. This property of electric-field-modulated second-harmonic generation (EFM-SHG) is observed here in nanowires of the polar crystal ZnO, and is exploited as an analytical tool to directly determine by optical means the absolute direction of their polarity, which in turn provides important information about their epitaxy and growth mechanism. EFM-SHG may be observed in any type of polar nanostructures and used to map the absolute polarity of materials at the nanoscale.


Nanowires growth scheme
The vapor liquid solid growth of surface-guided ZnO nanowires was done in a three-zone furnace in a quartz tube. ZnO powder (99.999% Alfa Aesar) was mixed with graphite powder (99.99% Aldrich) in a 1:1 mass ratio and held at 1050 °C while the substrate was held downstream at 850 °C. The growth was done in a constant flow of 500 sccm N2 (99.999% Gordon Gas) and a pressure of 400 mbar. In a typical synthesis, a substrate with catalyst was placed on a fused silica carrier plate and inserted to a 25 mm diameter quartz tube. The tube was inserted into a split oven and purged by 4 cycles of pumping to 5 mbar and purging with N2 at elevated temperature. After purging, N2 was streamed into the tube, and pressure was maintained at 400 mbar. Once the desired temperature (1050 o C) is achieved, the furnace was slide over the sample for one minute for preheating and then slide over the crucible for 20 min for the actual growth. At the end of the growth the furnace is turned off and moved away for the sample to cool down.      Table S1. Measured phase and growth direction of 18 different nanowires. * Outlier result.
Note that for all the nanowires, the measured phase is either close to 0 deg or to 180 deg within a range of less than  5 deg.

EFM-SHG of a parallel polar nanowire
In addition to performing EFM-SHG measurements on polar and nonpolar nanowires we examined the polar nanowires along its nonpolar axis. This was achieved by patterning the electrodes parallel to polar nanowires ( Figure S4b). Similar to the case of a nonpolar nanowire, the c-axis is perpendicular to the applied electric field. The difference between these two configurations is the geometric effect, influencing the ratio of SHG signal along different crystal axes. Here too, we expect SH response only at 2ω. However, we observe an additional 1ω component (

Fourier analysis details
Given here is a more thorough analytic description of the Fourier amplitudes discussed in Explicitly express the external field as a sine wave with amplitude 0 E : Express the oscillating terms in positive and negative frequencies: space is meaningless here; rather the difference between the two options (180 ) is of significance, as shown in figure 2 of the main text. The normalized amplitudes presented in figures 3b, 3c, and 4d of the main text are given by:  Figure S5. Examples of fits used to extract the ratio between the nonlinear coefficients.
The median of the fit results for r was used to present the estimated values in the main text.
The spread of the results (2.3 − 13 • 10 −9 ) is most likely due to difficulties in estimating the exact amplitude of the applied electric field. The small thickness of the gold electrodes (few 100s of nm) makes them different from an ideal capacitor, an effect we neglect in the calculations. Furthermore, the local environment may include features around the nanowire (metallic or dielectric) left over from the photolithography process that may affect the local electric field differently in each experiment. An error in the field amplitude would affect the ratio r' more than the ratio r due to their quadratic and linear dependence respectively.

Longitudinal analysis
We performed an EFM-SHG scan along a single polar nanowire. It appears that around the center of the nanowire there is a smaller modulation of the SHG signal. This is most likely due to the deviation of the electrodes from an ideal capacitor thus a non-uniform electric field is present along the nanowire.