Are you talking about the contact area between ZnO and Si? If it is yes, the answer is no since diode characteristics and rectification factor strongly depend on quality of the junction and interface.
There may not be any change in Turn-ON of the diode based on contact area. However, the contact area plays a major role when you plot graph in terms of Current density (mA/cm2) vs. Voltage. For normal I-V graph no need to consider about contacts area.
Ideally there should be no change. But if you have higher contact area, the possibilities of pin holes are more and hence performance can be affected. Also surface roughness may a major role and for higher contact area, more surface roughness (as it is hard to grow uniform file for higher area).