SEMITIP V6, program Film2
This program computes the electrostatic potential between a metallic tip and a semiconducting
layer on top of another semiconductor, for a 3-dimensional geometry with azimuthal symmetry.
This is a special purpose program for handling a film on top of a substrate. The dielectric
constant of the film can be different than that of the substrate, and they also can have different
properties such as band gap, effective masses, doping, etc. Additionally, a distribution of
interface states between the film and the substrate (along with a distribution of states on the
surface of the film) can be specified.
For applying a voltage between the tip and sample, one must decide if the film or the substrate
is used as the sample "contact". Correspondingly, in the FORT.9 input file there is a parameter
that specifies which of the film or substrate Fermi levels (before a contact between them is
established) is used as the final film+substrate Fermi level throughout the sample. This choice has
First, this specification of which Fermi level to use will affect the "zero" of potential energy in
the problem. In the examples below, we have an undoped film with band gap of 2 eV adjoining an n-type
doped semiconductor that also has band gap of 2 eV. In the substrate, the Fermi level is close to
2 eV above its VB maximum, whereas in the film the Fermi level is 1 eV above its VB maximum. Consider
choosing the substrate Fermi level to serve throughout the film+substrate. In that case, everything is
fine deep in the substrate (i.e. its Fermi level is at the correct location). However, in the undoped
file, the Fermi level will adjust itself to match that in the substrate. That's no problem at all, since
the film is undoped anyway. Now consider
choosing the film Fermi level to serve throughout the film+substrate. In that case, the Fermi level in the
substrate is initially about 1 eV below where it should be, hence, there's very large charge density
in the substrate. The electrostatic solution will then produce a shift in the electrostatic potential
in the substrate by about -1 eV, such that the VB shifts so that the difference between Fermi level and
VB ends up being as it should be (for zero charge density in the material). This same electrostatic
potential energy of -1 eV will also appear in the film.
Second, this specification of which Fermi level to use will also affect how the applied sample-tip
bias appears in the problem. Let's say that the sample-tip bias is -1 V (tip Fermi level at -1 eV
below that of the sample), and there's zero contact-potential specified.
Consider the two situations just described. If we choose the substrate
Fermi level to serve throughout the film+substrate, then everything works out in a simple manner.
That is, there's zero potential throughout most of the substrate, with the potential then extending
downwards as we pass through both the undoped film and the vacuum, over to the tip (see Example 1 below).
choosing the film Fermi level to serve throughout the film+substrate. In that case, as just
described, an electrostatic potential energy of -1 eV is formed throughout the substrate
and the film. However, the tip is also at a potential energy of -1 eV. Thus, we end up with
no further band bending due to the tip, i.e. flat bands in the substrate and film, and zero
electric field in the vacuum (see Example 3 below).
Version 6.2; see top of
source code for prior version information.
A compiled version of the code, which should run on any Windows PC, is
available in the file Film2.exe.
Input for the executable code comes from the file FORT.9.
Download these two files, into filenames "Film2.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 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 voltage (V)
- contact potential (eV)
- Pot0 - the surface potential at the semiconductor surface (eV).
- FORT.11 - provides the potential (eV) along the central axis, as a
function of z-distance (output for IWRIT>=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); see
SEMITIP V6 documentation
for more details.
- FORT.16 - gives an exact copy of the output to the console
- FORT.20, FORT.21, ... - contour lines (nm) of the potential (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, the specification of a surface state density other than a uniform or Gaussian shaped one, and the specification of spatial arrangement of bulk or surface charge density. See
SEMITIP V6 Technical Manual
for additional information on these user-defined 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):
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.
routine for outputting contour plot.
general purpose Golden Section search routine, for dealing with nonlinear aspects of the problem.
routines for computing semiconductor charge densities, and multiple regions in the semiconductor (used in Film2 for handling both the substrate charge densities and the film charge densities).
performs the detailed finite element solution of Poisson's equation, for the special case of
a semiconducting film on top of a semiconducting substrate.
routines for handling surface charge densities for multiple semiconducting areas (used in Film2 for handling both the surface charge distributions and the interface charge distributions).
Illustrative Examples of Running the Code
semiconducting film on top of semiconducting substrate, contact to substrate, no interface states
semiconducting film on top of semiconducting substrate, contact to substrate, with interface states
semiconducting film on top of semiconducting substrate, contact to film, no interface states
semiconducting film on top of semiconducting substrate, contact to film, with interface states