Virtual Scanning Tunneling Microscope Materials and Methods

Modeling of non-ideal phenomena . To our knowledge this is the first STM simulator to include the effects of noise in the tunneling current, noise in the voltages controlling the x -, y -, and z -motions of the piezoelectric actuator, and stochastic slow-drift in the vertical position of the tip electrode, which would be caused by vibration and temper- ature changes.

Figure 2 : Stable region for the two coeffi cients controlling PI feedback of the tunneling current.

demonstrate their product for imaging with an STM [ 3 ]. We have developed a LabVIEW Virtual Instrument (VI), which simulates the full operation of an STM that may be downloaded from our company website for permanent use without registration, cost, or time limits [ 4 ]. A 24-page description documenting the software and a video showing typical operation of the new simulator VI are also available at the website. The documentation includes figures, equations, and definitions of the terminology. We hope that this simulator VI will be useful in educational and training purposes. The STM simulator VI was compiled using LabVIEW Application Builder, which allows stand-alone applications to be bundled with the LabVIEW Run-Time Engine as an installer without requiring LabVIEW or other software. Our application was compiled to run on a Windows operating system; if requested, we will modify the STM simulator VI for use on Mac operating systems. Figure 1 shows the main display screen of the STM simulator VI when imaging silicon (100) unreconstructed. This article briefly describes the operation of the simulator and some of its features.

The effects of a series resistance, such as the spreading resistance in the sample at the tunneling junction, are also included. Bounds for these non-ideal behaviors may be set by the user to determine their effects on measurements and imaging. The software is written in a modular format to facilitate upgrading different parts to better meet our needs and also to follow the suggestions from those who have downloaded this simulator VI. For example, we could model the resonances, nonlinearities, and hysteresis in the response of the piezoelectric actuator, which is used for fine-positioning of the tip electrode and may also provide different approximations to calculate the tunneling current including expressions for semiconductor samples. Four methods for feedback control . Feedback control is used to adjust the tip-sample distance in an STM when initiating quantum tunneling and then to minimize the error in the tunneling current, which is given by e(t) = I(t) – I SP , where I(t) is the current at time t and I SP is the chosen value for the set-point current. Simply making a change in the voltage Δ V to the piezoelectric actuator that is proportional to the error is insufficient because this would cause the tunneling current to oscillate about the set-point value.

PI (Proportion + Integral) feedback control, where the change in the voltage that is applied to the piezoelectric actuator is proportional to the sum of the error and the integral of the error, as shown in Eq. (1), is frequently used in scanning tunneling microscopy.

Simulations made with the STM simulator VI show that PI feedback control is only stable over a specific range for the two coefficients K P and K I (see Figure 2 ). The size and location of the stable region for these two coeffi - cients depends on the properties of the tip and the tip-sample distance. Large oscillations in the tunneling current, including the possibility of tip-crash failure or loss of tunneling, occur when one (or both) of these coeffi cients is outside of the region for stability. It is inconvenient to have to estimate the value for both coeffi cients before the measurements. T e included algorithms are: (1)

Figure 3 : Graph of the simulated tunneling current vs. time showing the noise in the tunneling current. 20

Unmodifi ed PI as previously described, (2) D.A.S. (Digitally Adapted Steps), which adjusts the sizes of the steps of • 2018 May

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