SEMITIP V6, program UniInt3

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 3-dimensional geometry. 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).

Version information

Version 6.3; see top of UniInt3-6.3.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 UniInt3.exe. Input for the executable code comes from the file FORT.9. Download these two files, into filenames "UniInt3.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)
- tip-sample separation (nm)
- sample-tip 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 z-distance (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 x-axis, 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 z-distance 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), for specified angle from x-axis
FORT.81, FORT.82,... - listing of surface charge density (column 2) vs. Fermi energy (column 1), for various areas (output for IWRITE>=3)

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):

UniInt3-6.3.f - main routine.
contr3-6.0.f - routine for outputting contour plot.
gsect-6.0.f - general purpose Golden Section search routine, for dealing with nonlinear aspects of the problem.
intcurr-6.1.f - performs numerical integration of Schrödinger equation, on a potential curve supplied by potexpand.
potcut3-6.0.f - takes a cut along the the central axis (r=0) of the potential from semitip3.
potexpand-6.0.f - expands the cut of the potential from potcut3, to a resolution suitable for numerical integration.
semirho-6.0.f - routines for computing semiconductor charge densities.
semitip3-6.1.f - performs the detailed finite element solution of Poisson's equation.
surfrho-6.2.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

undoped GaAs(110), with no surface states.