Z Feedback Loop

The key to maintaining constant interaction forces between the probe and the sample surface is Feedback.

What is Feedback?

A feedback loop is any system where an output of the system is monitored and compared with an input to the system, such that a desired state of the output is maintained.

Example: When you drive in your car on the highway, how do you maintain the car's position in the middle of the lane? As as the car begins to drift to one side of the lane, the driver registers a difference between the desired position in the lane and the actual position, and applies a correction to keep the car on the road. The corrections are small and continuously made, such that even if the road has many curves along the way, the car maintains its position in the middle of the lane as it travels along.

There are several key parameters present in this example, as well as in all feedback systems:

Example: In the automobile example, the desired position in the center of the lane would be the setpoint. The difference between actual position and desired position would be the error signal, such that as the car drifts away from the center of the lane, the error signal grows.

After noticing the error, the driver would apply a correction by adjusting the steering wheel. The degree of the correction that the driver applies would be proportional to the magnitude of the error signal as well as the gain. The gain is important to ensure a smooth ride. If the gain is set too low, the car may drift all the way out of the lane before correcting the error. If the gain is too high, the driver may overcorrect such that the car swerves across the lane past the desired location in the middle. With the gain set properly, the car smoothly rides down the highway in the center of the lane with the passengers even never noticing any of the corrections.

Feedback with an AFM

Almost all AFM techniques employ a feedback loop to facilitate keeping a constant interaction between the tip and the sample as the tip scans the surface. The system detects the cantilever motion during the scan, typically either by monitoring the Vertical Deflection (in Contact AFM) or the Amplitude (in TappingMode AFM). The user specifies a desired value to maintain, referred to as either the Deflection Setpoint or the Amplitude Setpoint.

The difference between the setpoint and the actual deflection is measured and referred to as the error. This error is scaled by the gain, and this signal is used to control the Z drive of the scanner. The resulting system keeps the cantilever motion constant as the tips scans along in contact with the surface:

Figure 1: Schematic depicting feedback loops in XY and Z to create an AFM image. This diagram is based on a tube-shaped piezo scanner. Some systems do not use a tube scanner, but the feedback principle remains the same.

If the gains are too low, the system will not respond fast enough to changes in sample topography, the image quality will be poor, and the tip will wear quickly. If the gains are set to high, though, the feedback loop will become unstable and the image will appear excessively noisy.

Integral & Proportional Gains

The error signal in the feedback loop must be scaled properly such that the system responds sufficiently quickly to changes in topography, thus keeping the error signal minimized. There are two gain parameters that control the scaling of the error signal:

The integral gain parameter is typically much more sensitive in affecting the system performance than the proportional gain. In practicality, usually the integral gain is raised until the image begins to become noisy, and then the gain is reduced slightly. The P gain is often surprisingly irrelevant to imaging performance.

For any given set of gain values, the feedback loop’s performance may be improved by simply scanning more slowly. This allows more time for the feedback loop to respond to changes in topography, and reduces the magnitude of the error signal.

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