SEMITIP V6, program UniIntSC2
Introduction
This program computes the electrostatic potential and the resulting tunnel current between a metallic tip and a uniform (homogeneous) semiconducting sample, for a 3dimensional geometry with azimuthal symmetry. The tunnel current is computed by integrating the Schrödinger equation along the central axis of the problem (i.e. as appropriate for a planar geometry, but an approximation for a nonplanar geometry). A selfconsistent solution between the wavefunctions and potential is obtained (important for situations of accumulation or inversion).
Version information
Version 6.6; see top of
UniIntSC26.6.f
source code for prior version information.
Usage
A compiled version of the code, which should run on any Windows PC, is
available in the file UniIntSC2.exe.
Input for the executable code comes from the file FORT.9.
Download these two files, into filenames "UniIntSC2.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. See
SEMITIP V6 Technical Manual
for additional comments on the meaning of the parameters.
Output
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)
 tipsample separation (nm)
 sampletip bias voltage (V)
 contact potential (eV)
 Pot0  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 zdistance (output for IWRIT>=1). Also, the electrostatic potential plus the
vacuum barrier energy is output to FORT.95, and the energy of the valence and conduction
band edges (as used in computing the tunnel current) are output to FORT.96 and FORT.97, respectively.
 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); see
VERSION 6 Technical Manual
for more details.
 FORT.14  provides the current (A/nm^2) (column 2) as a function of sample voltage (V) (column 1). Also, columns 3 and 4 provide the contributions to the current of extended states and
localized states, respectively. Separate contributions from the valence band and conduction band
go in to FORT.91 and FORT.92, respectively.
 FORT.15  provides the conductance dI/dV (A/(V nm^2)) (column 2) as a function of sample voltage (V) (column 1). Also, columns 3 and 4 provide the contributions to the conductance of extended states and
localized states, respectively. Separate contributions from the valence band and conduction band
go in to FORT.93 and FORT.94, respectively.
 FORT.16  gives an exact copy of the output to the console
 FORT.17  provides the charge densities on the central axis (column 2) as a function of zdistance along the central axis (column 1). Also, columns 3 and 4 provide the contributions to the charge densities of extended states and localized states, respectively.
 FORT.18  provides the surface charge densities (column 2) as a function of radial distance away from the central axis (column 1). Also, columns 3 and 4 provide the contributions to the charge densities of extended states and localized states, respectively.
 FORT.19  provides the surface charge density (column 2) at the point opposite the tip apex (i.e. on the central axis), as a function of bias voltage. Also, columns 3 and 4 provide the contributions to the charge densities of extended states and localized states, respectively.
 FORT.20, FORT.21, ...  contour lines (nm) of the potential (output for IWRIT>=2)
 FORT.30,FORT.40,FORT.50,FORT.60  listing of voltage (column 1), principal quantum number (column 2), energy of localized state (column 3), and the difference in electron occupation between sample and tip at that energy (column 4), for the lighthole, heavyhole, splitoff and conduction bands, respectively
 FORT.31,FORT.41,FORT.51,FORT.61  wavefunctions of localized states, as a function of distance along central axis, for individual bands as above. Only listed at final bias voltage in the problem (output for IWRIT>=7).
 FORT.32,FORT.42,FORT.52,FORT.62  charge densities of localized states, as a function of distance along central axis, for individual bands as above. Only listed at final bias voltage in the problem (output for IWRIT>=7).
 FORT.33,FORT.43,FORT.53,FORT.63  wavefunctions of extended states for zero parallel wavevector, as a function of distance along central axis, for individual bands as above. Only listed at final bias voltage in the problem (output for IWRIT>=9). CAUTION: these files could be large!
 FORT.81, FORT.82,...  listing of surface charge density (column 2) vs. Fermi energy (column 1), for various areas (output for IWRITE>=3)
 img1.PGM, img2.PGM, and img3.PGM provide images (PGM format) of the charge densities due to the localized, extended and total charge densities, respectively. The extent of these images is limited by the parameters that limit the region over which the quantum charge densities are computed, lines 47 and 48 of FORT.9. By construction, the number of pixels in the images is expanded (using linear interpolation) by 3x in each dimension from the number of grid points, and the images are placed on a 512x512 background. Parameters for the grayscale plotting of the images can be modified in the program code. Interpretation of these images is discussed in example 2 below.
All of the parameters in the program can be varied using the input file FORT.9, with the exception of the array sizes, the specification of a surface state density other than a uniform or Gaussian shaped one, and the specification of spatial arrangement of bulk charge density. See
SEMITIP V6 Technical Manual
for additional information on these userdefined functions. Modification of those functions
can be accomplished by changing the source code of the program. The source code is available, in the following files (version numbers follow the dash in the names):

UniIntSC26.6.f 
main program.

contr26.0.f 
routine for outputting contour plot.

gsect6.0.f 
general purpose Golden Section search routine, for dealing with nonlinear aspects of the problem.

intcurr6.1.f 
performs numerical integration of Schrödinger equation, on a potential curve supplied by potexpand2.

PlotGray6.0.o 
make gray scale plots of 2D functions (the charge densities).

potcut26.0.f 
takes a cut along the the central axis (r=0) of the potential from semitip2.

potexpand6.0.f 
expands the cut of the potential from potcut2, to a resolution suitable for numerical integration.

semirho6.0.f 
routines for computing semiconductor charge densities.

semitip26.1.f 
performs the detailed finite element solution of Poisson's equation.

surfrho6.2.f 
routines for handling surface charge densities.
All routines are written in Fortran. The source code can be downloaded
directly from the above locations, and it can be compiled and linked
on any platform. Sample input and output from the program is shown in the examples below.
Illustrative Examples of Running the Code

ntype GaAs(110), with no surface states.

ntype GaAs(110), viewing charge density images.

ntype Si surface, plotting energies of inversion states.