Virtual Scanning Tunneling Microscope
Figure 4 : 3D plot of a simulated image of silicon (100) surface unreconstructed.
the piezoelectric actuator based on the tunneling current, (3) Modified Proportion, in which the proportion coefficient is adjusted based on the tunneling current, and (4) Proportion + Average, which is similar to PI control, but instead of integrating it takes the mean of the last few values of the error. Each of these algorithms is described in detail on our website. T e STM simulator VI may be used to compare the stability, response time, and ease of use for feedback control of the current when using the four diff erent algorithms with various values for their parameters.
Stepper motor and piezoelectric actuator . To obtain atomic resolution in imaging, the piezoelectric actuator must have a small range of motion (typically 60 nm). T us, it is necessary to add a precision digital stepper motor for coarser positioning of the tip electrode in order to provide a greater range of motion in the system. T e piezoelectric actuator is automatically decremented each time before the digital stepper motor is incremented to avoid missing specifi c tip-sample distances, which would be caused by the eff ects of the fi nite precision of the step motor.
Simulation of crystal lattice sufaces in real time . Once the simulation shows that stable quantum tunneling has been achieved, it is possible to generate an image of highly ordered pyrolytic graphite (HOPG), graphene, silicon (100) unreconstructed, or the reconstructed surface of silicon after it has been cleaved. The surfaces of these four materials were modeled by approximating the contours for the local density of states of electrons in the atoms as spheres with appropriate sizes. The images of the surfaces are created by scanning over the simulated surfaces while calculating the tunneling current based on the distance from the surface to the tip. Figure 1 shows the main display screen when simulating the
2018 May •
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imaging of silicon (100) unreconstructed. The graph at the lower left corner of this figure shows the relative height of the tip, which is calculated from the voltage that is applied to the piezoelectric actuator. Oscillations in the height, which are seen in this graph, are caused by the tip electrode passing over several of the silicon atoms in the lattice. At the upper left corner of Figure 1 there is a sketch of the STM scan-head with an animated diagram showing the vertical tip electrode above the horizontal sample. If the value calculated for the tip position is below the surface of the sample, indicating a tip-crash has occurred, this cartoon shows that the tip is bent and the simulation has stopped. However, with an actual STM it may not be obvious that a tip-crash has occurred because images with high resolution are still possible. Thus, this feature enables the user to determine the optimum parameters to prevent tip-crash. Later we will incorporate an algorithm to determine if a tip-crash has occurred without relying on the simulated height of the tip. For example, a small increment in the voltage to the piezoelectric actuator would not change the current when the tip is in contact with the sample. This change would be necessary before the STM simulator VI software could be implemented in an actual STM. In the constant current mode, feedback control of the tunneling current is enabled during scanning. In the constant height mode, feedback control is disabled during scanning so that the tip is moved in a plane above the surface of the sample. T is mode is prone to loss of tunneling or tip-crash unless it is used to image small areas or with samples having relatively fl at surfaces.
Results
Figure 3 shows a graph of the simulated tunneling current over a specific time interval, which is incremented throughout each session. This figure shows the effects of the noise in the tunneling current. A separate plot that is made over a much longer time interval is used to monitor the effects of feedback control on the tunneling current as well as the response to the simulated stochastic slow-drift. Aſt er at least one line of a scan has been completed, a 3D image of the sample may be generated as the data are collected for an image. Figure 4 shows an example of a completed 3D simulated image of silicon (100) unreconstructed.
Discussion T e virtual instrument described in this article is our fi rst step in developing a prototype instrument, which is based on laser-assisted scanning tunneling microscopy. T is work is funded by the National Science Foundation as part of a project to develop a new means for carrier profi ling to meet the needs of the semiconductor industry at the new sub-22 nm lithography nodes [ 5 ]. T is project is based on an earlier project funded by the U.S. Department of Energy in which a microwave frequency comb, with hundreds of harmonics at integer multiples of the laser pulse-repetition frequency, was fi rst generated by laser-assisted tunneling [ 6 ]. Our next step in this project is to prepare a second LabVIEW VI to simulate our procedure for carrier profi ling, which will also be placed on the company website as a free-download.
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