Scanning Tunneling Microscope Simulator

This program simulates the working principle of the scanning tunneling
microscope. The program uses a real STM image as an example to illustrate
the physical principles on which an STM is based. The user begins with
analyzing the image in much the same way as a real STM would, by moving the
"probe tip" across the surface of the sample. The program displays a cross
section of the sample along the line of scan by the probe tip, by using the
intensity values of the pixels of the image that lie along the line.

Next the program numerically solves the Poisson's equation in the 2D space
in the vicinity of the sample's surface and determines the electric
potential distribution in space around the sample's surface. This
information is used to determine the electric field line emerging from the
probe tip and terminating at the sample's surface. The electric field line
is the nominal path taken by the electron as it tunnels from the sample's
surface to the probe tip, so the wave function of the electron is determined
by numerically solving the Schrodinger's equation along the field line using
the values of the electrical potential energy computed from the solution of
Poisson's equation in 2D space, which determine the potential energy diagram
for the electron.

Given the potential energy diagram, the user can change the total energy of
the electron and observe the wave function. The program also calculates the
tunneling probability of the electron and its variation with electron energy
and probe tip voltage. Having determined these various quantum mechanical
quantities related to the tunneling electron, the program enables the user
to relate these concepts to a more tangible effect - the tunneling current.

The I-V graph is displayed by the program for any given position of the
probe tip, and finally, the user can determine the current profile i.e. the
variation in the tunneling current as the probe tip is dragged above the
sample's surface, in either the constant elevation mode, where the variation
in tunneling current reflects changes in the surface relief; or the constant
current mode, where the current is kept constant and the movement of the
probe tip to ensure that determines the surface relief.

Future Enhancements: The user interface will be improved to avoid too many
overlapping windows.
