Simplified feedback control system for scanning tunneling microscopy

Binnig et al. invented the Scanning Tunneling Microscope (STM) back in 1981.¹ The technique was soon extended to other probes based on a tip scanning a sample surface, revolutionizing the study and manipulation of materials at the nanoscale. The STM uses the quantum tunneling effect between an atomically sharp tip and a flat conducting sample through a vacuum barrier to sense the surface properties and the piezoelectric effect that provides precise subnanometric positioning of the tip over the sample. Usually, we measure the tunneling current between the tip and the sample and maintain its value constant using a feedback loop that acts on the piezo that controls the z-position of the tip. When scanning the tip in the x–y plane, the feedback signal provides the z-position of the tip. Thus, we can build two-dimensional (2D) maps of the surface at a constant tunneling current.

There are many different hardware designs to control scanning probe microscopes.^2–6 All STM designs are based on a kernel that includes a feedback mechanism that keeps a constant tunneling current during the scan. The feedback can be either analog^7–13 or digital.^14–18 It has been long thought that the digital feedback needs a real-time acquisition and control system using a digital signal processor (DSP) or a field programmable gate array (FPGA) that operates separately from the user computer. This indeed allows using a clock and taking data at fixed time intervals. However, the STM often requires measurement of a parameter as a function of the position, not as a function of time. Here, we show that one can successfully operate a STM using a simple universal serial bus (USB) based data acquisition on a computer running the Windows^® operating system. This eliminates the need for defining fixed time intervals for data acquisition. We also show that our setup allows for very low noise measurements. Addressing this problem usually requires careful filtering of the high frequency noise created at the control electronics.^5,19–26

Let us remind that Tersoff and Hamann applied Bardeen’s tunneling theory to the STM^27–29 and showed that under several simplifying assumptions and at zero temperature, the tunneling current vs bias voltage I(V_Bias) is given by

where z is the distance between the tip and the sample; $zϕ≡ℏ8mϕ$⁠, where ϕ is the average work function, m is the electron effective mass and N_s(E − eV) and N_t(E) are the energy dependent densities of states of the tip and the sample, respectively (E being the energy). The tip is atomically sharp, and its N_t(E) does not depend on the position of the tip over the sample. Thus, the 2D maps of the surface at a constant tunneling current provide maps of the local density of states N_s(x, y). The tunneling conductance $dIdV$ as a function of the bias voltage is often proportional to the energy dependent density N_s(E = eV, x, y). $dIdV$ can be recorded as a function of the position when scanning the tip on top of the surface. This leads to a set of 2D images, providing N_s(E = eV, x, y). Controlling the noise level is particularly important when there is a need to resolve sharp features in the tunneling conductance, $dIdV$⁠, caused by variations of N_s(E) in a small energy range. This is often the case in the cryogenic STM setups used to study materials with large variations in the electronic band structure at low energy scales.

The simplified control electronics described here helps achieving the goal of low noise measurements more easily. We show results obtained in relevant materials and in several different setups that use the device described here. The full schematic of the electronics and the software are available in Refs. 30 and 31, respectively.

We describe the hardware of our system in Fig. 1. The system has two 16 bit Digital-to-Analog Converter (DAC) chips (DAC8734), each with four analog output lines, which provide voltage signals from −10 to +10 V. These signals can be amplified by a factor of 14 using the high precision and ultralow noise amplifiers described in Ref. 26. Acquisition of analog voltage signals is carried out using a 16 bit Analog-to-Digital Converter (ADC) chip (ADC7606) with eight separate input channels.

To address the DAC and ADC systems, we use a USB 2.0 FIFO (first in first out) circuit (FTDI2232H), which addresses the serial peripheral interface (SPI). The USB is optocoupled to the board to avoid interference from the main computer. All SPI signals are filtered using one pole RC filters with a cutoff frequency slightly above the frequency of the clock required to address the DAC and ADC systems with the SPI (2 MHz). Outputs are carefully low pass filtered using analog one pole RC filters cutting at 10 kHz [Fig. 1(a)]. The digital part of the electronics [Fig. 1(d)] is mounted on a multilayer board, taking care of separating lines as far as possible, where the SPI bus runs from the signal input and output lines. Furthermore, it has a separate power supply and is mounted very close to the high voltage amplifiers to avoid picking up noise. Grounding is designed to avoid induction from digital signal lines by minimizing the impedance with large ground plates and a full connection to the metallic enclosure. In addition, microtransformers separate communication bus from signals to avoid interference. The noise of the output of the DAC is below 1 μV rms, and the ADC has an analog filter and a digital sampling averaging system, giving a high signal-to-noise ratio. The wiring between the electronics and the microscope is made by carefully mixing cables that hold the signals with ground cables, firmly attached to the electronics and the cryostat.

Five of the amplified output voltage signals are used to drive the scanner piezotube, four for the X and Y motion and one for the Z motion. The X and Y motion is performed using two DACs mounted in cascade, achieving thus μV resolution. This setup provides enough high voltage lines to operate a usual cryogenic microscope, as the ones discussed in Refs. 5 and 19–26. Another amplified voltage output line is used to drive the coarse approach motor. There are three further low voltage lines for the bias voltage and additional needs.

The electronics hardware is handy [Fig. 1(b)], and the whole system can be easily transported and connected to the USB port of a computer. Different systems can be used on the same computer by using separate USB ports.

We have written communication routines in Delphi.³¹ The feedback is made by reading the current and sending an output signal calculated using a PI (proportional integral) algorithm [Fig. 2(a)]. The latency of the USB port allows us to access the port with a bandwidth reaching a few kHz. This is below the typical resonance frequency of the STM, as required to avoid noise amplification and oscillations.⁴ We show an example of an obtained image on Co₃Sn₂S₂ using a Au tip in Figs. 2(b)–2(e). Further examples of similarly acquired images in other compounds and under different conditions are given below.

To have an optimized time base for execution, we use threaded timer and program its access in such a way that it is regularly called during time consuming operations such as loops for data saving.³² This provides smooth operation without interruptions.^33,34 We have followed data acquisition and PI operation for many hours, acquiring billions of points and observing random interruptions of the latency, which were significantly below 1 ms and just a few interruptions requiring up to 10 ms. None of these interruptions lead to a tip instability, as shown, for example, in Figs. 2(b)–2(e), which provide raw data (no corrected points). To better quantify the jitter in the latency, we have measured a signal as a function of time with a wanted time interval of 3.2 ms. In Fig. 2(f), we show the interval between two measurements. We see that we have a deviation of 0.2 ms from the wanted interval in less than 1% of the acquired points and deviations larger than 0.4 ms in far less than 0.1% of the acquired points. Thus, although the system is not a priori thought for real-time measurements, it can be used in measurements as a function of time where a constant time interval is not critical in the acquisition.

We show a block diagram of the components of the software (blue background) and how these are linked to the hardware (red and white backgrounds) in Fig. 3. The software interacts with the hardware through a main window (“WinSPM”). The main window includes two additional windows. One is used to make spectroscopy (“spectroscopy IV/IZ”) or any other operation that requires cutting the feedback loop, and the other (“STM topography”) is used to show and control the scanning process. The feedback (“digital feedback”) operates continuously in the background, reading the current value and acting on the Z electrode of the piezotube through the corresponding amplifier, whose value is also sent to the “STM topography” to monitor the Z as a function of the position of the tip during scanning. The main window handles the USB communication through the interface containing the DAC and ADC (“LHA-DigiMod”). One converter is used for setting the bias voltage, and others are amplified to set the x-, y-, and z-positions. The ADC is used, for instance, to read the current from the current to voltage transimpedance amplifier (“I/V converter”). In addition, another high voltage amplifier is used to drive the coarse approach motor. During imaging, we can stop at each point and perform IV or bias voltage vs conductance curves to obtain images of the current or the conductance as a function of the bias voltage (“scanning tunneling spectroscopy”).

We provide an example of screenshots during a typical experiment in Fig. 4. The experiment is made at 100 mK with a tip of Au and a sample of FeSe. In Fig. 4(a), we show the main working window, where we have pasted an image showing steps in FeSe. The large square shows an image of an area of several nm square, showing steps in FeSe, and another image taken around the central area, showing atomic resolution. The blue cross in the center of the square is the position of the STM tip. In Fig. 4(d), we show a typical scan (red line in the left panel) and the image being built up on the right panels. We can clearly see the profiles of Se atoms in the line scan and the square atomic Se lattice in the images. In Fig. 4(e), we show a current vs voltage curve (blue and red overlapped lines) obtained in FeSe under a magnetic field of 14.5 T. We see that the curve is slightly nonlinear due to the superconducting gap opening.

To obtain maps of IV or tunneling conductance vs bias voltage curves at each point of an image, we disconnect the feedback loop and perform the measurement at each point of the scan. We store separately the topography file with usual scanning information and the IV curves.

The file containing all IV (or tunneling conductance vs bias voltage) curves is actually a 3D matrix with an IV (or tunneling conductance) curve at each pixel of a 2D space that spans the real space image. We analyze these files using software based on the Matlab^® environment.³⁵ Related software based on Matlab can be found in Ref. 36. Our software includes numerous features required to analyze the STM images, such as Fourier transform spectroscopy, rotation and manipulation of images, plot of conductance maps at any bias voltage, and obtaining and analyzing tunneling conductance curves from anywhere in the images.

We show a block diagram of the data treatment software in Fig. 5. This includes a module for single curves, a reading module, and an image processing module.

The reading module needs two main inputs: the n by m dimensions of the topographic image and the corresponding binary file containing the associated spectroscopic curves and the starting point in the binary file. We then average data using adjacent points around an interval δ(V). Normalization with respect to the conductance value at a certain bias voltage range can be used to eliminate setpoint effects, as discussed in Ref. 37. Data can be saved into a structure object that stores all the variables needed for a further image processing analysis.

We show an example and screenshots in Fig. 6. In Fig. 6(a), we show the acquisition module, which we use to open files and set a few relevant parameters. In Fig. 6(b), we show the IV curve reader with an IV curve taken in β–Bi₂Pd at 100 mK and 0.1 T, shown as a blue line. We show the IV curve (left panel) and the tunneling conductance vs bias voltage (right panel). The red and blue vertical lines in the right panel show the voltage range that we use to normalize curves in this particular case. The resulting maps of the tunneling conductance are shown in Figs. 6(c) and 6(d), where we plot the zero bias conductance as a function of the position [Fig. 6(c)] and its Fourier transform [Fig. 6(d)]. The images show the superconducting vortex lattice of β–Bi₂Pd at 0.1 T and 100 mK.^38–40 We can visualize results at different bias voltages, identify vortices, or triangulate vortex lattices.^41–43 We can also use the same modules to visualize oscillations in the tunneling conductance due to impurity scattering, called quasiparticle interference. Quasiparticle interference measures the electronic band structure.^44–53 We can perform different operations of quasiparticle interference, such as rotations, symmetrization, filtering, or extraction of profiles. The module for single curves is shown in Fig. 6(d), with an example of an IV curve and the corresponding conductance obtained by using Al as the tip and the sample.

As an example of data treatment, we can discuss tunneling spectroscopy vs temperature measurements in Pb using a tip of Au, as shown in Fig. 7. The experimental curves obtained are shown as colored lines in Fig. 7(a). To understand these curves, we construct the density of states as a function of the energy N(E) [shown in Fig. 7(b), bottom light blue line]. N(E) closely follows the BCS expression [$N(E)=EE2−Δ2$⁠, where Δ is the superconducting gap], with the value of the superconducting gap expected for Pb (Δ = 1.37 meV), except that the divergence at eV = Δ is substituted by non-infinite quasiparticle peaks. This can be due to a combination of inelastic nonequilibrium quasiparticles, the anisotropy of the superconducting gap of Pb, and the finite energy resolution of our experiment.^{5,19–26,54,55} Using this N(E), we can then calculate the tunneling conductance for all temperatures by convoluting with the derivative of the Fermi function. The results are shown as black lines in Fig. 7(a). To obtain the tunneling conductance, we modify N(E) at each temperature until we reproduce the experiment. From the position of the quasiparticle peaks in N(E), we obtain Δ(T). We see that it follows the BCS superconducting gap dependence, Δ(T), as shown in Fig. 7(c).

We now operate in our laboratory several units of the system described here. In Fig. 8, we show results of topographic images at constant current in WTe₂, 2H–NbSe₂, Co₃Sn₂S₂, and FeSe. We see the one-dimensional Te chains that usually appear on the surface of WTe₂ [Fig. 8(a)]. We also see the typical atomic lattice and charge density wave that are characteristic of 2H–NbSe₂ [Fig. 8(b)]. The charge density wave is hexagonal and produces a charge modulation, which is nearly commensurate with a period three times the lattice constant. There are two vacancies visible in the surface lattice, which consists of a Se hexagonal lattice. In Co₃Sn₂S₂ [Fig. 8(c)], we observe an atomically resolved surface, consisting of two different atomic species. The continuous hexagonal layer is composed of Sn atoms. Notice their hexagonal shape. The upper incomplete layer is made of S atoms. There is a tendency to form rows, and the S atoms induce shadow-like features in the neighboring Sn atoms. In FeSe [Fig. 8(d)], we observe the square Se lattice. There are defects with an elongated in-plane shape characteristic of the nematic features of the electronic properties of this compound.

The images are provided raw, implying that, during their acquisition, which needed between half an hour and five hours, the data acquisition was fast enough so that there were no significant interruptions that influenced the stability of the PI algorithm controlling the tip z-position.

In summary, we have described a system where we successfully control a STM microscope using a simple USB based data acquisition. Details of hardware and software are available in Refs. 30 and 31, respectively.

Our approach builds on developments of the so-called soft real-time data acquisition, as opposed to data acquisition on an exactly periodic time basis.^33,34 Our results show that for the STM and probably for many other applications too, computers allow for an access latency for data acquisition in usual input and output ports that is enough for successful operation.

Care should be taken to use the method proposed here in combination with a PI algorithm. The system stability should be tested so as to make sure that random interruptions do not influence the PI stability. At least for the systems imaged here and probably for many other systems that require high resolution and thus slow data acquisition, the latency for accessing the port of a usual desktop computer is largely sufficient to maintain the stability of the PI. Furthermore, measurements as a function of time require obviously a stable time basis. This can be circumvented to some extent by measuring the time difference between acquisitions but leads to curves with random changes in the time base. Our results show that these changes are mostly below a ms and only rarely extend over more than a few ms.

There are commercially available choices for data acquisition using the USB port that include data processors.^56,57 Using appropriate filtering, a similar noise level as we obtain here could be achieved.¹⁵ However, we believe that its implementation is more difficult than using the simple solution proposed here. Furthermore, calculations required to acquire the actual data are made within the data acquisition systems. We believe instead that allowing the user to perform operations on the main controlling computer provides a significant improvement. Multiple core computers with different components running in parallel are becoming largely available. This will produce a shift toward integrating data acquisition within the running operational system environments. The results obtained here could then be applied to all kinds of scanning probe microscopes. The user will be able to considerably increase the possibilities for making complex operations during scanning.

We acknowledge discussions with Nicolás Agraït and Sebastián Vieira. This work was supported by the Spanish Research State Agency (Grant Nos. FIS2017-84 330-R, pPID2020-114071RB-100, CEX2018-000805-M, RYC-2014-15093, MAT2017-87134-C2-2-R, and MAT2017-88693-R), the Comunidad de Madrid through program NANOFRONTMAG-CM (Grant No. S2018/NMT-4321), and the European Research Council PNICTEYES through Grant Agreement No. 679080. We acknowledge collaborations through EU program Cost CA16218 (Nanocohybri). Work at Ames Laboratory was supported by the U.S. Department of Energy, Office of Basic Energy Science, Division of Materials Sciences and Engineering. Ames Laboratory is operated for the U.S. Department of Energy by Iowa State University under Contract No. DE-AC02-07CH11358. N.H.J. and J.S. were also supported by the Gordon and Betty Moore Foundation’s EPiQS Initiative through Grant No. GBMF4411.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.