SEMITIP V6, program MultInt1

Introduction

This program computes the electrostatic potential and the resulting tunnel current between a metallic tip and a nonuniform (inhomogeneous) semiconducting sample, for a 1-dimensional geometry. The tunnel current is computed by integrating the Schrödinger, as appropriate for a planar geometry.

Version information

Version 6.2; see top of MultInt1-6.2.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 parameter S is the z position in the semiconductor, and the routine should return an integer value giving the number of the region for that z position (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 in the main programs and its associated routines by NREGDIM as set in the PARAMETER statements. By default this value is set to 2, but that 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-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.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 (column 2) as a function of z-distance (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), 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.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 light-hole, heavy-hole, split-off and conduction bands, respectively
FORT.31,FORT.41,FORT.51,FORT.61 - wavefunctions of localized states, as a function of z-distance, 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 z-distance, 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 z-distance, for individual bands as above. Only listed at final bias voltage in the problem (output for IWRIT>=9). CAUTION: these files could be large!

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 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):

MultInt1-6.2.f - main program, available in example(s) below.
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 potexpand1.
potcut1-6.0.f - takes a cut of the potential from semitip1.
potexpand-6.0.f - expands the cut of the potential from potcut1, to a resolution suitable for numerical integration.
semirhomult-6.0.f - routines for computing semiconductor charge densities.
semitip1-6.1.f - performs the detailed finite element solution of Poisson's equation.
surfrho-6.1.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

GaAs(110) with larger band gap film on top