Adding an Independent, Quantitative Measurement of Cantilever Displacement to Atomic Force Microscopes

The Asylum Research Interferometric Displacement Sensor (IDS) Option incorporates an autonomous, quantitative measurement of cantilever displacement to the Cypher AFM, complementing the regular optical beam deflection (OBD) technique. OBD is usually used in commercial AFMs; it is comparatively easy to execute and remarkably quiet across a broad dynamic range. However, it is essentially proportional to angular changes rather than displacement, and interpreting the tip displacement necessitates an accurate model of the cantilever mode shape. While adequate for certain AFM measurements, it can result in errors in others. The IDS solves this shortcoming by offering a complementary, quantitative measurement of cantilever displacement across all dynamic measurement modes.

Standard optical beam deflection:

  • Calibration assumes cantilever mode shape
  • Quantitative deflection needs calibration
  • These assumptions can fail, particularly in contact modes

The OBD measures angle, Θ

The OBD measures angle, Θ

Interferometric Displacement Sensor:

  • Displacement sensitivity is intrinsically calibrated by the wavelength of light (λ = 632.8 nm).
  • Compatible with all dynamic AFM modes (1 kHz and above)

The IDS measures displacement, d

The IDS measures displacement, d

The IDS option does not affect the regular OBD measurement or other standard functions of the AFM. The IDS detection laser can be positioned anywhere in the field of view: on the cantilever or the sample, or programmed to step through a range of locations. The technology can thus be used in a wide range of measurements, from quantitatively characterizing material properties, to enhancing one’s understanding of cantilever dynamics and the confines of traditional AFM measurement modes.

The IDS Option quantifies the “last axis” in atomic force microscopy.

Types of Applications Modes and Measurements
Quantitative Material Characterization Modes
The OBD signal can be misinterpreted when the cantilever diverges from its estimated or modeled shape. In contrast, the IDS offers an absolute measure of cantilever amplitude and deflection.
  • On- and off-resonance contact methods
  • Multi-frequency methods
  • Experiments in viscous media
  • Fast force mapping
  • Characterization of the tip-sample contact stiffness
Accurate Cantilever Calibration
OBD-based calibrations depend on assumptions about cantilever mode shape. In contrast, the IDS can directly calibrate the sensitivity and stiffness of the first and higher flexural modes.
  • Stiffness and sensitivity of higher eigenmodes
  • Quantitative torsional/lateral modes
Mapping Thermal and Driven Mode Shapes
The IDS spot can be programmed to step along the breadth and length of the cantilever, enabling an accurate measurement of the true cantilever mode shape during dynamic measurements
  • Quantify the effects of cantilever modes on standard AFM experiments
  • Test theoretical cantilever physics models

 

Applications in Electromechanics

Piezoresponse Force Microscopy (PFM) is a robust tool for nanoscale imaging, spectroscopy, and manipulation of piezoelectric and ferroelectric materials. Nevertheless, and despite major efforts, it can still be difficult to quantitatively resolve the true coupling between a material’s mechanical and electrical phenomena at these very short length scales. A Periodically Poled Lithium Niobate (PPN) test sample is a beneficial model system for examining the origins of measurement artifacts in electromechanical measurements.

Characteristics of the PPLN Test Sample

  1. Frequency-independent response: The small size of the intermittently poled domains means their ferroelectric response is considerably faster (~GHz) than the bandwidth of the AFM measurement.
  2. Phase shift of 180° across oppositely polarized domains: Domains are slanted perpendicular to the sample surface.
  3. Amplitude autonomous of polarization direction: Due to sample symmetry, the “up” and “down” domains should deliver the same amplitude of response

Frequency Independent Response

Characteristic 1: Frequency Independent Response (above): Simultaneous OBD and IDS measurements of the effective piezoelectric sensitivity, deff. The frequency response of the OBD measurement is dominated by cantilever dynamics: it varies by a factor of 1000 X, while the IDS measurement is nearly frequency independent

Phase Shift Is 180° and Amplitude Does Not Depend on Polarization Direction

Characteristics 2 and 3: Phase Shift Is 180° and Amplitude Does Not Depend on Polarization Direction (above): Effective piezoelectric sensitivity deff and phase domains measured simultaneously by OBD and the IDS. The IDS channel correctly shows the amplitude is the same and the phase is 180° out of phase in the oppositely poled domains. Drive frequency: 25 kHz. Scan size: 5 μm x 10 μm.

Quantitative Measurements Are Repeatable

Characteristic 4: Quantitative Measurements Are Repeatable (above): The graph shows the results from five different cantilevers. The histograms of the effective piezoelectric sensitivity, deff, derived from the OBD channel (in blue) show variations of an order of magnitude, and the results from each measurement have two maxima, originating from the “up” and “down” domains. In contrast, the results derived from the IDS measurements show consistent results for piezoelectric sensitivity (in red), with no dependency on domain direction.

What’s Going On?

The IDS just measures the electromechanical response of the sample. That is, it measures the displacement because of the expansion or contraction of the sample only, whereas, OBD measures the cantilever’s angular variations. With regards to these electromechanical measurements, electrostatic interactions between a charged sample and the body of the cantilever cause cantilever vibrations that are unconnected to sample movement. These vibrations are amplified by the cantilever resonance causing a definite frequency dependence that overwhelms the signal of interest. [Appl. Phys. Lett. 106, 253103 (2015)]

Spring Constant Calibration

Multimodal methods use two or more cantilever flexural modes to quantitatively map material viscoelastic properties,expanding the need for accurate cantilever calibration to higher eigenmodes. IDS can basically and accurately characterize the stiffness of any eigenmode (up to 2.5 MHz) for any type of cantilever.

 IDS calibration of cantilever spring constant

Above: IDS calibration of cantilever spring constant for the first three eigenmodes of an Olympus AC240 cantilever using the thermal method. These stiffness measurements are based on the wavelength of light, and don’t require any assumptions or measurements of the cantilever geometry or its mode shape. [Appl. Phys. Lett. 87, 073705 (2016)]

Tip-Sample Contact Mechanics

Quantitative mechanical or electromechanical property measurements need an accurate model of the tip-sample contact stiffness. The IDS permits comparisons between the sample movement and the cantilever displacement, with the difference between the two defining the stiffness of the contact.

Tip-sample stiffness effects in piezoelectric sensitivity measurements.

Above: Tip-sample stiffness effects in piezoelectric sensitivity measurements. The IDS was used to measure the true displacement of the gold pad (blue) and the cantilever (red). The gold pad is the top surface of a lead zirconate titanate device. In this experiment, it is actuated by applying a bias through the cantilever. The cantilever is moving only 50% relative to the sample expansion indicating that at this load, the contact stiffness is roughly equivalent to the cantilever stiffness.

Mode Shape Mapping

Quantitative, dynamic material property mapping methods are only as accurate as the characterization of the vibration mode. For any particular experiment, there are a number of factors that can result in a deviation from an anticipated cantilever mode shape: non-uniformities in the dimensions or stiffness of the cantilever, weakly characterized cantilever drag (from working in liquid), or weakly characterized loading (because of interactions with the sample surface). IDS can be employed to quantitatively measure the mode shape of any type of AFM cantilever in any type of medium.

IDS measurements

Above: IDS measurements of the first three eigenmodes compared with finite element analysis simulations for an Olympus AC240 cantilever. This is a typical cantilever used for tapping mode imaging in air: the cantilever geometry is not uniform along its length, and the tip is set back from the end of the cantilever – see image below. These characteristics, among others, contribute to deviations from Euler-Bernoulli behavior. [Appl. Phys. Lett.87, 073705 (2016)]

Integration and Specifications

  • The OBD and the IDS signal are measured at the same time
  • Spots are controlled independently
  • IDS spot < 3 μm enabling highly localized measurements, or cantilever mode shape mapping

The IDS interfaces the existing optical system of the Cypher AFM with an external laser Doppler vibrometer. It does not change or interfere with the instrument’s standard functions.

Specifications

  • Operational bandwidth: 1 kHz to 2.5 MHz
  • Detection noise floor: < 200 fm/rtHz (> 10 kHz)
    < 100 fm/rtHz (> 100 kHz)
  • Largest measurable amplitude: > 1 μm
  • Required cantilever reflectivity (@633 nm): > 80% (in order to meet specifications)
  • Laser spot size: < 4 μm (1/e2 diameter of circular spot)
  • Spot positioning range: > 500 μm × 500 μm (software controlled)
  • NOT compatible with blueDrive

Measurement Modes

  • Electromechanics
    • Piezoresponse Force Microscopy
    • Electrochemical Strain Microscopy
  • Nanomechanics
    • AMFM Viscoelastic Property Mapping
    • Contact Resonance AFM
    • Fast Force Mapping
    • Nanorheology
  • Dynamic (AC) Force Measurements
  • Sub-resonance dynamic Measurements
  • And more

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