SEMITIP, VERSION 4, Electrostatics and Tunnel Current Computations for a Probe Tip near a Semiconductor

R. M. Feenstra
Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213

This program computes the electrostatic potential and resulting tunnel current produced by a metallic probe tip near a semiconductor. This program is an updated version of the prior VERSION 3, VERSION 2, and VERSION 1. Basic usage is described below, and additional details are available in the SEMITIP V4 Technical Documentation, describing changes relative to VERSION 3. The major change in VERSION 4 relative to VERSION 3 is the added capability to compute the tunneling current.

Some background information on the methods used in the program is contained in:

It is important to note that VERSION 4 of the program is not self-consistent, in the sense that the charge densities used in the electrostatics are computed semi-classically in the z-direction (normal to the surface) whereas the tunneling current is based on wavefunctions in this direction that are fully quantum mechanical. (In the lateral x- and y-directions, both the charge densities and the wavefunctions are semi-classical). For situations of semiconductor depletion, as commonly occurring in experiment, this lack of self-consistency is not significant (self-consistency is automatically ensured under depletion conditions). However, for accumulation or inversion, self-consistency will in general produce a noticable effect on the tunnel current. A version of the program that includes self-consistency (VERSION 5) is also available; the code for that version is, however, considerably more complicated than the present VERSION 4, so users are encouraged to get familiar with VERSION 4 before attempting use of VERSION 5. One additional factor that greatly affects accumulation in the case of n-type GaAs(110) is the occurrence of surface states. These act to constrain the Fermi-level thus preventing any substantial accumulation to occur, as described in Phys. Rev. B 80, 075320 (2009) which follows work of N. D. Jäger et al., Phys. Rev. B 67, 165327 (2003). Thus, even for accumulation conditions involving n-type GaAs, the present non-self-consistent version of the program is quite accurate, so long as one includes an appropriate surface charge density (see example 1 below).

A compiled version of the code, which should run on any Windows PC, is available in the file semitip_v4.exe. Input for the executable code comes from the file FORT.9. Download these two files, into filenames "semitip_v4.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.

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):

All of the parameters in the program can be varied using the input file FORT.9, with the exception of the array sizes (NRDIM,NVDIM,NSDIM, and NEDIM), the specification of an auxiliary function other than a hemisphere which defines a protrusion on the end of the probe tip, and the specification of a surface state density other than a uniform or Gaussian shaped one. Modification of those parameters can be accomplished by changing the source code of the program. The source code is available, in the files:

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

  1. n-type GaAs(110), with intrinsic surface states.
  2. n-type GaAs(110), with a positive contact potential between tip and sample.
  3. n-type GaAs(110), with extrinsic surface states.
  4. plotting wave-functions for localized states.
  5. plotting potential profiles and contours.