Pacific Nanotechnology Inc.
Feedback In SPM Instrumentation
Introduction
Mechanical profilers create a topographic representation of a surface by recording the motion of a sharpened probe as it traverses a surface. In a mechanical profiler, as first conceived in the early 20th century, the force of the probe on a surface varies as the probe is scanned across the surface. A dramatic improvement was made in profiler instrumentation with the addition of a feedback loop that maintained a fixed relationship between the probe and surface during a scan.
Figure 1: A feedback electronic circuit is used to establish a fixed relationship between a probe and a sample. The output from the force sensor is used to activate the Z piezoelectric ceramic. Adjusting the Zset voltage changes the force between the probe and surface.
Background
One of the first mechanical profilers to use a feedback loop to maintain a fixed relation- ship between a probe and a surface was the Topografiner(1). In the Topografiner, the field emission current between a probe and surface is used to establish feedback. Because a current between the probe and surface is required, the Topografiner required electrically conductive samples for operation.
Figure 2. Block diagram of the topografiner developed by R. Young in 1972. A current between the probe and surface is used for feedback. Piezoelectric ceramics scan the probe over the surface in the x,y and z axis. An image of the surface is obtained by measuring multiple line scans as the probe is raster scanned across a surface.
Figure 3 illustrates a mechanical profiling instrument having a constant probe-sample force that was capable of making profiles on electrically insulating surfaces. This profiling instrument, developed in 1979 by Schnell et.al.(2), used a piezoelectric bimorph for measuring the force between the probe and surface, and a feedback loop for keeping the force constant during scanning.
Figure 3: This illustration from U.S. Patent # 4,359,892 is of a mechanical profiler that uses a feedback electronic circuit to maintain a constant force between the probe and surface during a scan. The force between the probe and surface is adjusted using the set-point voltage, Us.
In their pioneering work on surface structures, Binnig and Rohrer(3) used a feedback loop in their Scanning Tunneling Microscope(STM). The STM monitors the tunneling current between a probe and surface to establish a fixed relationship while scanning. Later, in 1986, a feedback electronic circuit was used in the atomic force microscope(4). In the atomic force microscope, the forces between a probe and surface were established with a probe at the mounted at the end of a cantilever. Using the cantilever method permitted scanning with a force of less than a nanoNewton between the probe and surface.
PID Controller
Typically the feedback control circuits used in a scanning probe microscope use the widely excepted proportional, integral, derivative algorithem. Figure 4, shows the relationship between the controller input, and the controller output. The input to the PID controller is the error signal from the force sensor, and the controller output is used to actuated a Z piezoelectric ceramic that ultimately controls the relationship between the probe and surface.
Figure 4: The input to the PID controller is the error signal and the output of the controller is the voltage used to drive the Z piezoelectric ceramic. The responsiveness of the controller is set with the coefficients P,I and D in equation 1.
In the initial designs of scanning probe microscopes, analog circuits were used and the PID control parameters were set using knobs at the front of electronic boxes. Optimizing the PID parameters involved turning the knobs until the best images were obtained. With the advent of personal computers and high speed digital electronics there are many options for the design of feedback control circuits.
Analog versus Digital Feedback Controllers
PID feedback controllers used in scanning probe microscopes can be constructed from either analog or digital control circuits. There are advantages and disadvantages to each of the designs.
Analog:
The primary advantages of analog PID controllers are:
Low noise
Large bandwidth
Greater dynamic range(1 part in 100,000)
Greater resolution
Beginning in the late 1980's digital computers were used for setting the values of the PID parameters in scanning probe microscopes. Figure 5 illustrates the design used by the pioneering SPM Instrumentation company, Omicron. An advantage of this approach is that software is used for adjusting the PID parameters.
Figure 5: Design of digitally controlled analog feedback offered for sale in 1993. There are numerous advantages of this design listed in this Figure.
Digital
The primary advantage of digital control is that it is very flexible. The flexibility is a result of the fact that the digitized sensor output is processed with software algorithms. Changing feedback conditions such as response time, and probe motions are easily done with different software algorithms.
With the advent of Digital Signal Processing(DSP) chips digital feedback became a practical alternative to analog feedback methods. In the early 1980's, Texas Instruments, a pioneer in the development of DSP chips, suggested that all analog feedback circuits should be replace by digital control circuits. The primary advantage of digital feedback is that it is very flexible.
There are two early examples of the flexibility of digital feedback circuits. In the first, 1986, Hartoonian et.al. used digital feedback to control the motion of a NSOM probe as it was scanned across the surface, see Figure 6.
Figure 6: Digital feedback circuit used by Hartoonian et. Al. In this microscope, the probe was lowered to the surface until a tunneling current was measured, and then the probe was removed from the surface, moved horizontally, and then lowered to the surface. This jumping motion was repeated until an image of the surface could be constructed.
A second example demonstrating the flexibility of digital feedback was made by Bard et. Al. in 1987. Bard demonstrated that it was possible to use digital feedback to scan a probe at a fixed distance above a surface. He outlined the following steps for scanning a probe at a fixed distance above a surface:
From the paper
"...Before the photo-etching experiment it is necessary to gauge the roughness and any tilt of the substrate material to avoid crashing the tip into surface features of the substrate when it is scanned at close spacing from the substrate.."
First:
"...The substrate was first scanned via the tunneling mode with the tip moved along a predefined path and the positional data, including roughness and tilt, were stored on a floppy disk.."
Then:
"...The spacing between tip and substrate was about 1 micron and this adjustment was maintained by the computer based on the data found in the preliminary scan.."
This method of scanning a probe over a surface and storing the topography data and then using the data to lift a probe above a surface can be applied to many other types of scanned probe techniques such as the magnetic force microscope(MFM) and the electric force microscope(EFM).
References
- R. Young, J. Ward, F. Scire, The Topografiner: An Instrument for Measuring Surface Microtopography, Rev. Sci. Inst., Vol 43, No 7, p 999
- U.S. Patent #4,359,892
- G. Binnig, H. Rohrer, Ch. Gerber, E. Weibel, Surface Studies by Scanning Tunneling Microscopy, Vol. 49, No 1, 1982, p 57
- G. Binnig, C.F. Quate, Ch. Geber, Atomic Force Microscope, Phys. Rev. Letters, Vol. 56, No 9, 1986 p 930
- Omicron, Gmbh. The SPM CU Technical Reference Manual
- A. Hartoonian, E. Betzig, M. Isaacson, A. Lewis, Super-resolution fluorescence near-field scanning optical microscopy, Appl. Phys. Lett. 49(11), 15 Sept. 1986, p 674
- C. Lin, F.F. Fan, A.J. Bard, High Resolution Photoelectrochemical Etching of n-GaAs with the Scanning Electrochemical and Tunneling Microscope, J. Electro. Soc. Vol. 134, No. 4, 1987, p 1038
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