Kelvin probe force microscopy of semiconductor surface defects

We present a comprehensive three-dimensional analysis of Kelvin probe force microscopy of semiconductors. It is shown that high-resolution electronic defect imaging is strongly affected by free carrier electrostatic screening, and the finite size of the measuring tip. In measurements conducted under ambient conditions, defects that are not more then $2\text{nanometers}$ below the surface, and are at least $50\text{nanometers}$ apart can be imaged only if the tip-sample distance is not larger then $10\text{nanometers}$. Under ultrahigh vacuum conditions, when the tip-sample distance can be as small as $1\text{nanometer}$, it is shown that the tip-induced band bending is only around a few millivolts, and can be neglected for most practical purposes. Our model is compared to ultrahigh vacuum Kelvin probe force microscopy measurements of surface steps on GaP, and it is shown that it can be used to obtain local surface charge densities.