SEMITIP, VERSION 3, Electrostatic Computations for a Probe Tip near a Semiconductor

R. M. Feenstra
Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213

This program computes the electrostatic potential resulting from a metallic probe tip near a semiconductor. This program is an updated version of the prior VERSION 2, described here, and VERSION 1, described here. Basic usage is described below, and additional details are available in the SEMITIP V3 Technical Information describing changes relative to VERSION 2. A preprint of a paper describing the modifications made to the theory for VERSION 3 is available here, and this paper appeared in J. Appl. Phys. 103, 073704 (2008). The major change in VERSION 3 relative to VERSION 2 is the use of a modified coordinate system in the vacuum, which improves convergence for certain types of problems.

Some background information on the methods used in the program is contained in:

• Surface Charge arising from a distribution of Surface States
• Contact Potential
• Coordinate System with accompanying Diagram

A compiled version of the code, which should run on any Windows PC, is available in the file semitip_v3.exe. Input for the executable code comes from the file FORT.9. Download these two files, into filenames "semitip_v3.exe" and "fort.9". Then, run the code just by double clicking on it. Using a text editor, the input parameters in FORT.9 can be changed to whatever values are desired. In addition to the parameter values, this file also contains comments as to the meaning of each parameter.

Output from the program is contained in the following files (output depends on the value of the output parameter IWRIT as specified in the input file FORT.9):

• FORT.10 - gives the numerical results for the following quantities:
  • tip radius of curvature (nm)
  • tip-sample separation (nm)
  • sample-tip bias (V)
  • opening angle of tip shank
  • PHI0 - the surface potential at a point directly opposite the tip apex (eV)
• FORT.11 - provides the potential (eV) along the central axis, as a function of z-distance (output for IWRIT>=1) (the third column gives auxiliary output which are the potential values for all grid points at the maximal radial value in the problem, although the z-values for these points are not output and in particular do not correspond to the values in column 1).
• FORT.12 - provides the potential (eV) along the surface, as a function of the radial distance from the central axis (output for IWRIT>=1)
• FORT.13 - gives the entire array of potential values (eV) (output for IWRIT>=3)
• FORT.16 - gives an exact copy of the output to the console
• FORT.20, FORT.21, ... - contour lines of the potential (nm) (output for IWRIT>=2)

All of the parameters in the program can be varied using the input file FORT.9, with the exception of the array sizes (NRDIM, NVDIM, NSDIM, and NE), the specification of an auxiliary function other than a hemisphere which defines a protrusion on the end of the probe tip, and the specification of a surface state density other than a uniform one. Modification of those parameters can be accomplished by changing the source code of the program. The source code is also available, in the files:

• SEMITIP_V3.F - main routine.
• SEMISTIP2.F - performs the detailed finite element solution of Poisson's equation.
• SEMIRHO.F - auxiliary routines for computing semiconductor charge densities.
• SURFRHO.F - auxiliary routines for handling surface charge densities.
• CONTR.F - plots contour lines of the computed potential.