SEMITIP V6, program UniPlane3
Introduction
This program computes the electrostatic potential and the resulting tunnel current between a metallic tip and a uniform (homogeneous) semiconducting sample, for a fully 3dimensional geometry. The semiconductor is assumed to be uniform for the purpose of computing the electrostatic potential, but for the tunnel current a region with differing band edge positions can be defined (e.g. as would be encountered for a quantum dot at the surface). The tunnel current is computed using a plane wave expansion to solve Schrödinger equation, for a restricted spatial region centered around the point on the surface opposite the tip apex.
The plane wave basis is formed by matching plane waves in the semiconductor with decaying exponentials in the vacuum, as described in Ref. [1]. In the zdirection a periodic system is formed consisting of the semiconductor slab and a vacuum region, with the basis states having either odd or even parity relative to the center of the slab.
In the x and y directions a periodic system as also formed, with sine and cosine functions used for the basis in the semiconductor. The solution to Schrödinger's equation within planecurr3.f assumes a mirror plane lying along the xaxis (i.e. only cosine basis states in the y direction).
The most critical parameters in the plane wave solution to Schrödinger's equation are the number of plane waves (kpoints) used. This is set in the PARAMETER statement within planecurr3.f by the nkx, nky, and nkz parameters. A minimum value of 4 for these parameters will allow the program to run quickly, but with quite unreliable results. Values of 8 or 10 are much more reliable, but time consuming. To provide some reduction in computation time, the parameter on line 53 of the FORT.9 input file can be used. A setting of 1 for that parameter means that all the valence bands and the conduction band are evaluated for each voltage, whereas a setting of 0 means that only the valence bands are used for V<0 and the conduction band for V>=0. The latter restriction on the bands used is sufficient for many applications (unless accumulation or inversion occurs, in which case the plane wave method is not applicable anyway since it is not selfconsistent, as further discussed in the
SEMITIP V6 Technical Manual).
Larger values for the number of plane waves are very time consuming and require parallel processing for routine evaluation of the tunnel current.
The spatial size of the periodic supercell used in the solution to Schrödinger's equation is determined by the number of plane waves and by the energy limits for the plane waves as specified in the FORT.9 input file (with different limits used for each band due to their different effective masses). For number of kpoints NK, effective EFFM, and energy limit EMAX, the extent of the supercell is NK*2*PI/SQRT(C*EFFM*EMAX) where C equals 2m/hbar^2 where m is the free electron mass. Here, SQRT(C*EFFM*EMAX)/NK is the minimum nonzero wavevector, so the extent of the supercell (in each direction) is just the size corresponding to maximum wavelength of the problem. EMAX is generally kept fixed, corresponding to a scale on the order of 1 eV such that states of that energy (as needed for the voltage range of a spectrum) are included. Hence, increasing NK produces an increase in the size of the supercell. The sampling of spatial points within the supercell is set in the program to occur on a grid with 4*NK points in each dimension. For the maximum wavevector, which has NK wavelengths in the supercell, it will thus be sampled at 4 points along its wavelength.
Parameters internal to the planecurr3.f routine are:

IPOT  has value of 1 to include the computed potential from semitip3.f in the eigenvalue solution to Schrödinger's equation, or a value of 0 to not include it (this parameter is used mainly for debugging purpose). Default value is 1.

IVAC  has value of 1 to include the vacuum region in the potential used for the eigenvalue solution to Schrödinger's equation, or a value of 0 to not include it (without it, the problem solved consists only of a periodic semiconductor region, with sine and cosine functions used as basis states). Default value is 1.

Several parameters that affect the output of intermediate values such as wavefunction values or potential maps, as described in the Output section below.
Version information
Version 6.2; see top of
UniPlane36.2.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 UniPlane3.exe.
Input for the executable code comes from the file FORT.9.
Download these two files, into filenames "UniPlane3.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, for specified angle from xaxis, 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.20, FORT.21, ...  contour lines (nm) of the potential (output for IWRIT>=2), for specified angle from xaxis
 FORT.31, FORT.41 (odd and even parity, respectively)  z values (column 1) and band edge potential (column 2) (output for IWRIT>=5).
 FORT.32, FORT.42 (odd and even parity, respectively)  z values (column 1) and wavefunction values for the first five states (columns 27). The states that are output here can be changed by changing the values of IWF1, ... IWF5 in the program (output for IWRIT>=5).
 FORT.33, FORT.43 (odd and even parity, respectively)  x values (column 1) and band edge potential (column 2) (output for IWRIT>=5).
 FORT.34, FORT.44 (odd and even parity, respectively)  x values (column 1) and wavefunction values for the first five states (columns 27). The states that are output here can be changed by changing the values of IWF1, ... IWF5 in the program (output for IWRIT>=5).
 FORT.35, FORT.45 (odd and even parity, respectively)  eigenvalues of Hamiltonian matrix (output for IWRIT>=4).
 FORT.40  ordered list of eigenvalues (column 1), magnitude squared of wavefunction at surface (column 2), zderivative at surface of log of wavefunction (column 3), expectation value of parallel wavevector (column 4). The values in column 4 are used for computing the decay constant for states in the vacuum as detailed in Ref. [1] (output for IWRIT>=4).
 FORT.80, FORT.81 (odd and even parity, respectively)  energy eigenvalues (column 1) and local density of states at the point on the surface opposite the tip apex (column 2) (output for IWRIT>=6).
 img1.PGM, img2.PGM, img3.PGM, ..., img9.PGM provide images (PGM format) of the potential along planes located at zvalues of 0 (i.e. the surface), first zvalue, second zvalue, etc. For a setting of IPOT=0 in the program, these images provide a convenient means of examining a localized potential such as that produced by a quantum dot (i.e. to ensure that the code defining the quantum dot is correct). Parameters for the grayscale plotting of the images can be modified in the program code (output for IWRIT>=7).
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, the specification of spatial arrangement of bulk or surface charge density, and the specification of local variations in the band edge potential. The latter is accomplished with the routine DELVBEDGE and DELCBEDGE, which provide the change in band edge locations relative to the overall band gap defined in the FORT.9 input file. See
SEMITIP V6 Technical Manual
for additional information on 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):

UniPlane36.2.f 
main routine; includes DELVBEDGE and DELCBEDGE routines that define a small region
opposite the tip apex as would be encountered for a quantum dot. Input of parameters for this sort of computation is also included.

BoundWell3E6.0.f 
routine for forming plane wave basis states for conduction band (including extended states).

BoundWell3V6.0.f 
routine for forming plane wave basis states for valence band.

contr36.0.f 
routine for outputting contour plot.

dgsect6.0.f 
general purpose double precision Golden Section search routine, used in forming plane wave basis.

GetCurr6.0.f 
sums up states, to form the tunnel current.

gsect6.0.f 
general purpose Golden Section search routine, for handling nonlinear aspects of the electrostatic solution.

planecurr36.1.f 
performs the eigenvalue solution of Schrödinger's equation with a plane wave basis.

PlotGray6.0.f 
make gray scale plots of 2D functions (cuts of the potentials).

potcut36.0.f 
takes a cut along the the central axis (r=0) of the potential from semitip3, used to form the potential in the vacuum.

potperiod36.0.f 
expands the potential evaluated on the grid from semitip3.f into a finer grid with uniform spacing, as needed by planecurr3.f.

rseispackALL.f 
EISPACK routines for solving the eigenvalue problem of a real, symmetric, double precision matrix.

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

semitip36.1.f 
performs the detailed finite element solution of Poisson's equation.

surfrho6.1.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

undoped GaAs(110), with no quantum dot and no surface states.

InAs quantum dot in GaAs.

InAs quantum dot in GaAs, plotting wave functions.

InAs quantum dot in GaAs, showing dot outline.
References
1. S. Gaan, G. He, R. M. Feenstra, J. Walker, and E. Towe, Size, shape, composition, and electronic properties of InAs/GaAs quantum dots by scanning tunneling microscopy and spectroscopy, J. Appl. Phys. 108, 114315 (2010). For preprint, see
http://www.cmu.edu/physics/stm/publ/93/.