Absence of elastic clamping in quantitative piezoelectric force microscopy measurements of nanostructures

We establish that clamping effects, which limit accurate determination of piezoelectric responses in bulk materials and films using piezoelectric force microscopy (PFM), are not present when measuring discrete nanostructures with radii less than five times the tip radius. This conclusion is established by comparing the piezoelectric response in ZnO rods using two electrode configurations: one with the conducting atomic force microscopy tip acting as the top electrode and the other using a uniform metal top electrode. The distributions of piezoelectric coefficients measured with these two types of electrode configurations are the same. Hence, clamping issues do not play a role in the piezoelectric property measurement of nanomaterials using PFM. The role of conduction electrons on the piezoelectric measurement in both cases is also discussed.