A program for computing the electric potential around a probe tip in proximity to a semiconductor, with circular symmetry. Prolate spheroidal coordinates are used in the vacuum, and a carefully chosen updating scheme is used to ensure stability of the iterative solution. Includes capability for a user specified distribution of surface states.

Version 2.0 - written by R. M. Feenstra, Carnegie Mellon University, Oct 2004
Version 2.1 - posted Dec 2, 2004

All routines are written in standard FORTRAN.

A complete description of the background theory of this program is contained in Refs. 1 and 2. Also, a user should carefully study the documentation for VERSION 1 of the program. VERSION 2 incorporates the following modifications relative to VERSION 1:

  1. A new array, TIP(NR,NV) is used to denote locations within the vacuum grid that are occupied by the probe tip.
  2. In both VERSIONS 1 and 2, a lookup table of bulk charge densities is constructed. For VERSION 1 if an energy occurred outside of the range of this lookup table then an error resulted. In VERSION 2 this problem is overcome by explicitly evaluating all charge densities at energies outside the range of the lookup table.
  3. A variable size grid is employed, described in Ref. 2, to handle in particular cases with low semiconductor doping.
  4. The possibility of surface charge density due to surface states is included, as described here and in Ref. 2. By default a uniform distribution of states is used, but any user-specified distribution can be handled by changes to the program code.
  5. A slightly different ending criterion for the iterations is employed. (In VERSION 1 the iterations cease when the change is less than a specified value. In VERSION 2, the iterations cease when the present change is less than a specified value AND the prior change is less than twice the specified value.)
  6. The starting grid size chosen by the program is different than in VERSION 1.
  7. For solution of the boundary condition at the semiconductor surface, a third order scheme is used rather than the first order one of VERSION 1, producing substantially improved convergence.

1. R. M. Feenstra, Electrostatic Potential for a Hyperbolic Probe Tip near a Semiconductor, published in J. Vac. Sci. Technol. B 21, 2080 (2003). For preprint, see
2. R. M. Feenstra, S. Gaan, G. Meyer, and K. H. Rieder, Low-temperature tunneling spectroscopy of Ge(111)c(2x8) surfaces , published in Phys. Rev. B 71, 125316 (2005). For preprint, see