  We theoretically investigate the dependence of the enhancement of optical
near-fields at nanometric tips on the shape, size, and material of the tip. We
confirm a strong dependence of the field enhancement factor on the radius of
curvature. In addition, we find a surprisingly strong increase of field
enhancement with increasing opening angle of the nanotips. For gold and
tungsten nanotips in the experimentally relevant parameter range (radius of
curvature $\geq 5\,$nm at $800\,$nm laser wavelength), we obtain field
enhancement factors of up to ${\sim}35$ for Au and ${\sim}12$ for W for large
opening angles. We confirm this strong dependence on the opening angle for many
other materials featuring a wide variety in their dielectric response. For
dielectrics, the opening angle dependence is traced back to the electrostatic
force of the induced surface charge at the tip shank. For metals, the plasmonic
response strongly increases the field enhancement and shifts the maximum field
enhancement to smaller opening angles.
