An All-Digital Cantilever Controller for MRFM and Scanned Probe Microscopy Using a Combined DSP/FPGA Design

An all-digital cantilever controller for magnetic resonance force microscopy (MRFM) was developed through a close collaboration between SC Solutions (Sunnyvale, CA), Cornell University (Ithaca, NY), and the U.S. Army Research Laboratory (Adelphi, MD). The advantage of an all-digital controller is its absence of thermal drift as well as its great tuning flexibility. The versatile controller comprises a field-programmable gate array (FPGA) connected via a low-latency interface to an analog input, an analog output, and a digital signal processor (DSP) with additional analog outputs. Performance of the controller was demonstrated in experiments employing ultrasensitive silicon microcantilevers fabricated at Cornell University’s Nanoscale Science and Technology Facility.

The scientific questions we can ask are largely determined by the quality of characterization technology available. In the 1980s, the scanning tunneling microscope (STM) generated tremendous excitement because it enabled one to “see” and manipulate individual atoms and molecules at a surface for the first time, opening the door to resolving long-standing questions about surface bonding, reactivity, and catalysis at metal and semiconductor surfaces. The invention of the atomic force microscope (AFM) (and related scanned probe microscopes) brought nonconductive surfaces into view.1 The resulting ability to generate nanometer-resolution surface maps of chemical forces, magnetization, and charge has revolutionized materials science.

The invention of the magnetic resonance force microscope by John Sidles in 1991 offered scanned probe microscopy two exciting new analytical capabilities: imaging subsurface features and imaging with unambiguous isotopic chemical contrast.2–4 Pushed to its limit, MRFM has the potential to obtain the full three-dimensional structure of any single molecule. Such progress would be a revolutionary advance, if it can be realized.

Imagine the scientific puzzles that could be addressed with a “molecular microscope” capable of nondestructively imaging the coordinates of all the protons in any single molecule. Such an instrument would allow us to form a three-dimensional picture of any single protein, in situ, with all of its post-translational modifications in place.

  • It would enable us to obtain the full structure of any membrane protein and we could look at any cell’s outer membrane with all the proteins and lipids frozen in action together
  • It would allow us to focus study on just the reactive part of a molecule or a suspected binding site in a protein. Such an instrument would open the door to studying impure samples, samples that can be isolated in only small quantities, and transient complexes
  • It would permit us to study the conformational heterogeneity among an ensemble of proteins in situ.

The magnetic resonance force microscope is a sensitive new technique for detecting nuclear magnetic moments (and unpaired electrons).5,6 MRFM is providing researchers the unprecedented ability to acquire, nondestructively, a three-dimensional image of subsurface nanoscale features with isotopic selectivity. The instrument will be invaluable to researchers and product developers in the semiconductor, materials, and biotechnology industries. The goal of the research reported here was to develop an all-digital cantilever controller for a prototype magnetic resonance force microscope capable of ultimately detecting the nuclear magnetic resonance signal from one proton. The paucity of tools for imaging materials with nanoscale resolution is presently a significant barrier to the development of such technologies. The research summarized here represents a significant step toward development and commercialization of a magnetic resonance force microscope for studying organic material at the nanoscale.

Cantilever control

Within scanned probe microscopy (SPM), active control of the cantilever is needed for several reasons:

  • Fast damping of the cantilever is needed to increase imaging speed in AFM. Cantilevers with a high quality factor have lengthy ring-down time (many tens of seconds) that slows imaging
  • AFM imaging with constant frequency and/or imaging with constant amplitude will provide different images. Both types of imaging require feedback control
  • In MRFM mode, the cantilever thermomechanical oscillations can be many nanometers. These random oscillations must be damped to below 0.1 nm rms if atomic-scale imaging resolution is to be achieved
  • As the cantilever approaches a surface, its natural frequency can change significantly. For many applications, it is favorable or required to track and measure the cantilever frequency continuously.

To accommodate these requirements, a generic cantilever controller was proposed, as shown in Figure 1.

Figure 1 - Schematic of generic cantilever controller, including low-level motion controllers, as well as high-level characterization and detection algorithms.

Current analog cantilever controllers suffer from significant thermal drift and are not easily tunable.7–10 To overcome this, an all-digital cantilever was developed that combines frequency shift measurements, phase shifting and amplitude control, as well as positive feedback control for driving the cantilever at resonance frequency.11–13 The versatile controller comprises a field-programmable gate array connected via a low-latency interface to an analog input, an analog output, and a digital signal processor with additional analog outputs.

Hardware design

For the feedback controller, a C6711 DSP-based system (Texas Instruments, Dallas, TX) tightly coupled to a Virtex-II FPGA (Xilinx, San Jose, CA) was chosen. The FPGA communicates directly through digital data lines to a fast (80-MHz) analog-to-digital converter (ADC) and digital-to-analog converter (DAC).

Figure 2 - Block diagram of cantilever controller. The scanned probe microscope provides a cantilever position signal, digitized at 80 MHz by the ADC, which passes it to the FPGA. The FPGA sends a phase-shifted AC signal to a fast DAC, which is used to drive the cantilever at its resonance frequency, thus closing the control loop. A DSP is used to set registers in the FPGA as well as control slow DACs.

As can be seen in Figure 2, the signal path is SPM—ADC—FPGA—DAC—SPM. The scanned probe microscope system provides a signal that is proportional to a cantilever position. The ADC digitizes this signal at 80 MHz and passes it to the FPGA. The FPGA computes an estimate of the cantilever’s frequency, amplitude, and phase. It also sends a phase-shifted AC signal to a fast DAC, which is used to drive the cantilever at its resonance frequency, thus closing the control loop. By using the FPGA to perform all the calculations in the critical path of the control loop, the overall system latency is reduced by eliminating the need to pass data to and from the DSP over its input/output bus.

Figure 3 - Photograph of controller hardware installed at Cornell University. The stacked FPGA/DSP cards can be seen slightly right from the center.

The DSP controls the FPGA by setting the values of several registers in the FPGA that determine the characteristics of the control loop. The DSP also sets the values in three slow (1-MHz) DACs. The slow DACs will be used for other aspects of the scanned probe microscope. One is used to produce a voltage proportional to the cantilever frequency, and another controls RF power levels. This leaves the third DAC free to control, for example, the height of the cantilever.

The 10-MHz clock reference for the ADC/DAC is externally provided from a stable, low-phase-noise crystal. The FPGA multiplies the 10 MHz up to 80 MHz using a digitally locked loop (DLL), and this 80-MHz signal becomes the clock for the ADC/DAC. The authors chose to provide the 10 MHz from an external source instead of using a DSP-generated clock reference to guarantee that the reference had low-phase noise. To obtain the rated accuracy of the ADC/DAC, low-phase-noise clocks must be used. A photograph of the completed all-digital cantilever controller hardware is shown in Figure 3.

Figure 4 - Screenshot of the LabVIEW user interface (National Instruments, Austin, TX), which controls the hardware by setting control registers in the FPGA. The software also monitors the estimated frequency shift of the resonating cantilever.

Software interface

Figure 4 shows the main user interface. Key features are the selection of the mode of operation, the display of relevant data, e.g., the current estimate of the cantilever frequency and/or frequency shift, as well as the magnitude of the cantilever signal. Another feature is setting up the connection with the target.

Figure 5 - Apparatus used to test the cantilever controller. a) Photograph of the scanned probe microscope head, b) schematic showing the cantilever approaching the surface in a perpendicular orientation to avoid snap-in to contact, and c) SEM of the cantilever. The scale bar is 10 μm.

Experimental setup

The experimental setup is shown in Figure 5. A custom-fabricated silicon cantilever with resonance frequency of roughly 7 kHz was brought within a distance d of approximately 5 μm of a gold surface. This is far enough away from the surface that the cantilever is not affected by van der Waals forces or friction, but close enough so that the cantilever frequency can be shifted by applying a voltage Vtip between the cantilever and the gold substrate. In the following experiments, the voltage Vtip was stepped up to induce a frequency shift that mimics an MRFM signal from nuclear or electron spins below the sample surface. In this way, we can fully demonstrate the performance of the digital cantilever controller by detecting small frequency shifts without having to set up a full MRFM experiment. The cantilever parameters were spring constant—k = 7.4 × 104 N/m, resonance frequency: f = 7373 Hz, and quality factor: Q = 2.8 × 104. The operating conditions were—temperature: T = 300 K, pressure: P ~ 1 × 106 Torr, rms cantilever drive amplitude: zrms = 55 nm, and detection bandwidth: b = 5 Hz. Under these operating conditions, the minimum detectable force is calculated to be:

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