SEMITIP V6, program UniIntSC1

Introduction

This program computes the electrostatic potential and the resulting tunnel current between a metallic tip and a uniform (homogeneous) semiconducting sample. The tunnel current is computed by integrating the Schrödinger equation, as appropriate for a planar geometry. A self-consistent solution between the wavefunctions and potential is obtained (important for situations of accumulation or inversion).

Version information

Version 6.2; see top of UniIntSC1-6.2.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 UniIntSC1.exe. Input for the executable code comes from the file FORT.9. Download these two files, into filenames "UniIntSC1.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-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) 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.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 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.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 distance along central axis, 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 distance along central axis, 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 distance along central axis, 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):

UniIntSC1-6.2.f - main program.
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 potexpand2.
potcut1-6.0.f - takes a cut along the the central axis (r=0) of the potential from semitip2.
potexpand-6.0.f - expands the cut of the potential from potcut1, to a resolution suitable for numerical integration.
semirho-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

n-type GaAs(110), with no surface states.