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

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!

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.

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.

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!

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.

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.

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.

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.

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.

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.

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.

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-0.1-3 1000Å Reference Grid 104 nm calibrated depth

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.

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 -5.0725V -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

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.

Membrane Capacitor Displacement 30-second loop Undistorted Butterfly Tiny Error

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.

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.