Magnetic Resonance Force Microscopy
Under this Army-sponsored Small Business Technology Transfer Research (STTR) Phase II project, a unique combination of technical expertise developed at Cornell University, SC Solutions, and CryoIndustries of America are being capitalized to produce a powerful new type of scanned probe microscope.
The Magnetic Resonance Force Microscope (MRFM) is a sensitive new technique for detecting nuclear magnetic moments (and unpaired electrons). In this program we developed the prototype of a variable-temperature MRFM capable of detecting and imaging at a sensitivity of a few thousand protons. Our microscope gives researchers the unprecedented ability to non-destructively acquire a three-dimensional image of subsurface nanoscale features with isotopic, and potentially chemical, selectivity. This unique instrument potentially has wide application for researchers and product developers in the semiconductor, materials, and biotechnology industries.
In MRFM and other Scanned Force Microscopes (SFM), interaction forces acting between a scanned probe tip and a sample are exploited for imaging purposes, similar to the tunneling current in STM. Other examples of SFM are atomic force microscopy (AFM) and electric force microscopy (EFM).
The key component in SFM is a tip on a cantilever, which acts as a force sensor. When the tip is brought close to the surface of the sample under investigation, the interaction force between the tip and the sample causes a deflection of the cantilever, which behaves as a soft spring. It can be shown that the force gradients acting on the cantilever, in effect, change the cantilever’s spring constant, and hence its resonance frequency.
Within SFM, 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 10’s 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 thermo-mechanical 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.
All-in-one Digital Cantilever Controller
To accommodate these requirements, SC Solutions has developed a generic all-in-one digital cantilever controller, a schematic of which is shown in Figure 1.
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| 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. To overcome this, an all-in-one-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 its resonance frequency. This versatile controller is comprised of 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.
Hardware & Software
The cantilever controller hardware consists of a Texas Instruments (TI) C6711 DSP based system tightly coupled to a Xilinx Virtex-II FPGA. The FPGA communicates directly through digital data lines to a high speed (80 MHz) ADC (Analog-to-Digital-Converter) and DAC (Digital-to-Analog-Converter). As can be seen in Figure 2, the signal path is SPM—ADC—FPGA—DAC—SPM.
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| Figure 2. Block diagram of the cantilever controller. The Scanned Probe Microscope provides a cantilever position signal, digitized at 80MHz 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. |
The Scanned Probe Microscope (SPM) system provides a signal which 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.
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 DAC’s 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 an 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. We 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 photo of the completed all-digital cantilever controller hardware is shown in Figure 3.
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| Figure 3. Photo of controller hardware installed at Cornell University. The stacked FPGA/DSP cards can be seen slightly right from the center. |
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| Figure 4. Screenshot of the LabView User Interface, which controls the hardware by setting control registers in the FPGA. This software also monitors the estimated frequency shift of the resonating cantilever. |
Figure 4 shows the main user interface. A key feature is the selection of the mode of operation. Another common feature is 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 common feature is setting up the connection with the target.
Experimental Results
A prototype controller has been tested on one of Cornell’s ultra-sensitive cantilevers. The all-digital cantilever controller quickly locked into the cantilever’s resonance frequency, see Figure 5. The controller successfully measured 5 to 10 millihertz shifts in a 5 Hz detection bandwidth in the resonance frequency of these ultra-sensitive microcantilevers on a millisecond timescale. Independently, a noise floor of 40 microhertz in one second was measured for this controller.
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| Figure 5. Frequency shift detection result. The three columns show the results of a 100 mHz, a 20 mHz, and a 5 to 10 mHz shift, respectively. The first row shows the step in tip voltage applied to induce a frequency shift in the cantilever. The second row shows the frequency shift estimated by the FPGA algorithm, without any filtering. The third row shows the same frequency shift estimate, but now post-processed using a moving average filter with a 10 Hz frequency gate and 1 Hz frequency gate. |