SEMITIP, VERSION 3, DOCUMENTATION

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 3.0 - written by R. M. Feenstra, Carnegie Mellon University, Sept 2008

All routines are written in standard FORTRAN.

A complete description of the background theory of this program is contained in Ref. 1 and the Appendices of Refs. 2 and 3. Also, a user should carefully study the documentation for VERSION 1 and VERSION 2 of the program. VERSION 3 incorporates the following modifications relative to VERSION 2:

  1. A new coordinate system is used, that exactly matches the tip shape for all tips (rather than just matching the tip shape for tips with a particular shape). This change should be relatively transparent to the user, although for some problems the new coordinate system displays improved convergence. A schematic illustration of the coordinate system is given here, and a full description is given here.
  2. A minor change is made in the input, in that the user now specifies both the sample-tip bias voltage and the tip-sample contact potential. The sum of these values corresponds to the electrostatic potential of the tip relative to a point far inside the semiconductor (it is this latter value that was a specified input parameter in VERSIONS 1 and 2), as further discussed here.
  3. An additional input parameter (line 18 of FORT.9) is included to indicate whether or not the semiconductor will invert. For a given value, this parameter has the following effect:
    0 - no effect
    1 - does not allow any occupation of the valence band (VB) by holes
    2 - does not allow any occupation of the conduction band (CB) by electrons
    3 - does not allow occupation of the VB by holes nor of the CB by electrons
  4. The executable code for VERSIONS 3 and higher is compiled and linked using GNU Fortran, rather than the previous usage of Digital Fortran in VERSIONS 1 and 2. Hence, the internal storage of the variables is now different (it is compatible with C++), and the quantities output in binary form to FORT.13 have different format. Additionally, a few more variable values have been output to FORT.13. A complete list of the output variables in FORT.13 is as follows:
    nr - number of radial grid points (4 byte integer)
    nv - number of grid points into the vacuum (4 byte integer)
    ns - number of grid points into the semiconductor(4 byte integer)
    sep - tip-sample separation (nm) (4 byte real)
    rad - tip radius of curvature (nm) (4 byte real)
    rad2 - radius of small hemisphere on end of tip (nm) (4 byte real)
    slope - shank slope (4 byte real)
    bias - sample voltage relative to tip (V) (4 byte real)
    epsil - relative dielectric constant of semiconductor (4 byte real)
    ((vac(1,i,j),i=1,nr),j=1,nv) - potential in vacuum (eV) (4 byte reals)
    ((sem(1,i,j),i=1,nr),j=1,ns) - potential in semiconductor (eV) (4 byte reals)
    (vsint(1,i),i=1,nr) - potential on surface (eV) (4 byte reals)
    (r(i),i=1,nr) - radial values of grid points (nm) (4 byte reals)
    (s(j),j=1,ns) - z-values of semiconductor grid points (nm) (4 byte reals)
    (delv(i),i=1,nr) - z-values of vacuum grid points (nm) (4 byte reals)
  5. A couple of warning messages that were output previously but didn't really serve any useful purpose have been eliminated. A few other minor changes to the output were made.

References:
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 http://www.cmu.edu/physics/stm/publ/52/.
2. R. M. Feenstra, S. Gaan, G. Meyer, and K. H. Rieder, Low-temperature tunneling spectroscopy of Ge(111)c(2x8) surfaces , Phys. Rev. B 71, 125316 (2005). For preprint, see http://www.cmu.edu/physics/stm/publ/65/.
3. Y. Dong, R. M. Feenstra, M. P. Semtsiv and W. T. Masselink, Band Offsets of InGaP/GaAs Heterojunctions by Scanning Tunneling Spectroscopy, J. Appl. Phys. 103, 073704 (2008). For preprint, see http://www.cmu.edu/physics/stm/publ/79/.