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.