1. Absolute Displacement Calibration for Atomic Force Microscopy
Joe T. Evans, Jr.
Spencer T. Smith
Naomi B. Montross
Scott P. Chapman
Radiant Technologies, Inc.
May 8, 2017

2. To paraphrase the title of a famous novel:
To paraphrase the title of a famous novel: How I learned to stop worrying and love the butterfly loop!

3. Summary How an AFM works on the inside.
Measuring complete butterfly loops using internal AFM signals.
The procedure for calibrating the AFM internal displacement signals using a known-accurate displacement reference.

4. Images vs Displacement
Atomic Force Microscopes (AFMs) are optimized to produce images where spatial contrasts generate 2-D or 3-D relative geometries in the human mind -> i.e. photographs.
AFM photographs do not need to reproduce precise vertical scaling in order to illuminate the targeted features.
AFMs may seem to be perfect for studying piezoelectric properties of thin films but piezoelectric characterization requires precise vertical displacement information.

5. Surface Scan Calibration
Atomic scale piezoelectric butterfly loops are captured by directly measuring the internal control signals of an AFM during piezoelectric actuation of the sample.
The standard AFM Force-Distance curve cannot provide absolute displacement calibration.
Calibration solution:
Measure the AFM displacement signals during a surface scan across a known step reference!

6. Any AFM
The calibration procedure described here will work with any AFM as long as the internal displacement signals of the AFM can be accessed by the ferroelectric tester.
The Radiant Precision NanoDisplacement System has been optimized for measuring butterfly loops. It does not execute PFM.
The PNDS will be used to highlight the proposed calibration technique on known good samples.

7. Signal Access
To measure butterfly loops, the output of the AFM photosensor and the voltage command to the piezoelectric chuck must be accessed. Radiant’s PNDS provides these signals. Asylum has a built-in signal mux to provide such signals. Other AFMs use breakout boxes.

8. Control System Architecture
Quad Cell
Laser
PID
Filter
HVA
Sample Chuck
PZT Actuator
Gain  - +
Cantilever
Set Point in Volts
Vertical position of laser reflection creates unique output voltage 1
Subtract laser position voltage from set point voltage 2
Position Error 3
Actuator’s commanded position in voltage 4
PID command amplified to piezo-level voltages. 5
In AFM mode, negative feedback forces Position Error to remain zero.
During X:Y scan of normal AFM operation, the chuck moves the sample up or down so the cantilever remains stationary in space despite sample roughness.
The image is a plot of the inverse chuck signal versus X:Y position.

9. Butterfly Loop Measurement
No X:Y scan
Voltage on sample forces its surface to move vertically.
One of two signals is captured during piezoelectric actuation:
Micron displacements
The voltage commanded to the chuck in AFM mode.
Ångstrom displacements
The voltage from the laser photosensor with negative feedback loop turned OFF.

10. Use this 10V signal to follow the chuck motion.
Measuring Sub-Micron
Quad Cell
Laser
PID
HVA
PZT Actuator
Gain  - +
Set Point in Volts
Use this 10V signal to follow the chuck motion.
DO NOT USE THIS 150V SIGNAL!
Tester
SENSOR Input
Tester DRIVE
Tester RETURN
The chuck motion will move in the opposite direction as the surface of the piezoelectric film so use a negative scale factor to flip the butterfly loop up!
Set the PID coefficients so the chuck is fast . Set the test for a slow hysteresis loop more than 1 second long so the chuck moves faster than the test.

11. Measuring Ångstroms
Quad Cell
Laser
HVA
PZT Actuator
Gain  - +
Set Point in Volts
This signal follows the cantilever motion.
Tester
SENSOR Input
Tester DRIVE
Tester RETURN
PID = 0
With the PID coefficients set to zero, the feedback loop is interrupted and the chuck should be stationary. [Some AFMs may only allow slow settings. ]
Set the test for a fast hysteresis loop about 1 millisecond second long so ambient noise is slower than the test.

12. Calibration Procedure
Scan the cantilever across a calibrated step reference to measure the change in the output for a known vertical position change of the cantilever.
This works for either configuration: large or small displacements.
Measure the other signal simultaneously as an indicator of cantilever error using the SENSOR input(s) of your tester.
Calculate the signal scale factor:
Chuck motion requires a “-” sign.
Photosensor motion requires a “+” sign.

13. Example: App Nano SHS-0.1-3 1000Å Reference Grid
Step Reference
A classic AFM X:Y surface scan will identify the position of a single pit in the step reference.
Scan artifact. Silicon wafer surface is flat.
Example: App Nano SHS Å Reference Grid
104 nm calibrated depth

14. Eliminating Tilt
No sample can be mounted on the AFM chuck perfectly flat so calibration scans will be tilted as taken. Samples should be mounted as flat as possible and the remaining tilt removed mathematically.
Vision provides tools for removing tilt from measurements made in the Sensor Oscilloscope Task. Gwyddion can be used as well as spread sheet tools.

15. Example Calibration Scan
An AFM mode scan conducted using a slow scan speed with fast PID while capturing the voltage commanded to the AFM piezoelectric chuck and the voltage from the photosensor. The chuck motion should follow the step reference. The cantilever should not move at all.
Scale Factor = 1.13m/V ± 0.12m
-4.987V
-5.082V
-4.984V V
-87mV
+128mV
Photosensor voltage
The spikes in the photosensor output mean that the feedback system could not perfectly follow the step that the X:Y scan speed. The PID speed should be increased and/or the scan velocity reduced.
Step Reference = 104nm

16. Membrane Displacement
1m-thick 4/20/80 PNZT with platinum electrodes. One of the two largest capacitors has the silicon substrate underneath etched out by DRIE.
Distorted Butterfly
Large Error!
Always monitor the “other” channel during a test as it indicates the deviation of the position tracking that occurred during the test.

17. Membrane Capacitor Displacement
30-second loop
Undistorted
Butterfly
Tiny Error

18. Thin PZT Film Displacement
A fast scan conducted with PID set to zero feedback. Scale factor is:
- 460 Ångstroms/volt averaging 10 loops.
Note: for clean Ångstrom-level butterfly loops, a scale factor of 500Å/V or less is necessary.

19. Conclusions
It is possible to measure the absolute displacement of a thin piezoelectric film or a piezoelectric MEMS structure using an AFM.
Measurement of either type of device requires the capture of the internal photosensor signal and the commanded voltage to the AFM’s piezoelectric chuck.
The feedback loop from the laser photosensor to the AFM piezoelectric chuck in the AFM must be adjusted to fast or to zero depending on the type of signal being measured during calibration and measurement.
Capturing the butterfly loop consists of driving the piezoelectric sample while capturing the designated displacement signal inside the AFM.
The displacement signals can be precisely calibrated by executing X:Y surface scans across calibrated step references.