SEMITIP V6, program MultInt2

Introduction

This program computes the electrostatic potential and the resulting tunnel current between a metallic tip and a nonuniform (inhomogeneous) semiconducting sample, for a 3-dimensional 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).

Version information

Version 6.6; see top of MultInt2-6.6.f source code in example(s) below for prior version information.

Usage

Source code files for the program are available in the example(s) provided below. In order to specify the inhomogeneities in the semiconductor, it is necessary to modify the source code as follows:

The routine IGETREG (at the bottom of the source code) defines the various regions in the semiconductor. The input parameters R and S are the radial and z positions in the semiconductor, respectively. The routine should return an integer value giving the number of the region for the specified radial and z values (i.e. return a value of 1 to use the first set of parameters in the FORT.9 input file defining the semiconductor region, a value of 2 for the second set of parameters, etc.).
The maximum number of region types in the semiconductor is specified by the parameter NREGDIM and the maximum number of area types on the surface by the parameter NARDIM. The values of these parameters are set in the main programs and its associated routines by PARAMETER statements. By default these values are set to 2, but they can be increased by changing all of the PARAMETER statements.

Additional details of these source code modifications can be found in the SEMITIP V6 Technical Manual. With the appropriate modifications, the source code of the main program, together with the subroutines listed below, must by re-compiled and linked in order to produce the executable code. All input for the program (other than that modifications to the source code detailed above) comes from the file FORT.9, which is also included in the example(s) provided below.

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 the semiconductor surface (eV).
FORT.11 - provides the electrostatic potential energy (eV) along the z axis, as a function of 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, 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)
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):

MultInt2-6.6.f - main program, available in example(s) below.
contr2-6.0.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.
potcut2-6.0.f - takes a cut of the potential from semitip2.
potexpand-6.0.f - expands the cut of the potential from potcut2, to a resolution suitable for numerical integration.
semirhomult-6.0.f - routines for computing semiconductor charge densities.
semitip2-6.1.f - performs the detailed finite element solution of Poisson's equation.
surfrhomult-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

GaAs(110) with 10 nm diameter area having extrinsic states