Source-linked AI summary
A virtual instrument to standardise the calibration of atomic force microscope cantilevers
John E. Sader, Riccardo Borgani, Christopher T. Gibson, David B. Haviland, Michael J. Higgins, Jason I. Kilpatrick, Jianing Lu, Paul Mulvaney, Cameron J. Shearer, Ashley D. Slattery, Per-Anders Thorén, Jim Tran, Heyou Zhang, Hongrui Zhang, Tian Zheng
TL;DR
AFM spring-constant calibration is commonly performed without a global standard, hindering robust comparison between laboratories. The paper presents an internet-based Global Calibration Initiative that aggregates existing measurements to standardise calibration and enable non-invasive calibration of any cantilever type. A proof-of-principle demonstration uses independent measurements from five groups across three countries.
Problem
AFM spring-constant calibration is often conducted without reference to a global standard, limiting robust comparison of force measurements between laboratories.
Method
The Global Calibration Initiative uses a single website and existing AFM Thermal measurements to combine calibration data across users and laboratories.
Results
Proof-of-principle validation used independent measurements from five groups across three countries to demonstrate the initiative’s calibration approach.
Takeaways & Limitations
The GCI enables users to compare calibration results, standardise AFM force measurements, and non-invasively calibrate any cantilever type.
Abstract
from arXiv · showhide
Atomic force microscope (AFM) users often calibrate the spring constants of cantilevers using functionality built into individual instruments. This is performed without reference to a global standard, which hinders robust comparison of force measurements reported by different laboratories. In this article, we describe a virtual instrument (an internet-based initiative) whereby users from all laboratories can instantly and quantitatively compare their calibration measurements to those of others - standardising AFM force measurements - and simultaneously enabling non-invasive calibration of AFM cantilevers of any geometry. This global calibration initiative requires no additional instrumentation or data processing on the part of the user. It utilises a single website where users upload currently available data. A proof-of-principle demonstration of this initiative is presented using measured data from five independent laboratories across three countries, which also allows for an assessment of current calibration.
I. INTRODUCTION
AFM spring-constant calibration lacks a global reference, limiting comparison across laboratories because user- and laboratory-dependent uncertainties can vary substantially. The Global Calibration Initiative (GCI) addresses this gap through an internet-based database that combines existing AFM Thermal measurements to standardise calibration and enable non-invasive calibration of cantilevers.
- Global Calibration Initiative: The initiative uploads existing AFM Thermal measurements of spring constant, resonant frequency, and quality factor to a live database for systematic averaging.The approach uses existing equipment and data without additional user effort or data processing.
- Global Calibration Initiative: Global averaging reduces uncertainty in spring-constant calibration while accommodating real variation caused by cantilever material properties and thickness.The dataset can combine independent measurements from laboratories worldwide and assess statistically significant measurements.
- Non-invasive calibration: The averaged data generate the cantilever-specific hydrodynamic A-coefficient, enabling Sader-method calibration from only resonant frequency and quality factor in air.This removes the need to determine each cantilever type’s A-coefficient independently.
- Validation: Proof-of-principle validation used LDV benchmarking and blind AFM Thermal measurements by 11 users from five universities in three countries.The study found spring-constant variation up to a factor greater than four, while averaging reproduced the LDV-derived A-coefficient and recovered the same coefficient for independently procured cantilevers.
- Calibration problem: AFM calibration can vary substantially because cantilever properties and measurement factors differ, with individual spring-constant measurements varying by more than fourfold.Relevant factors include laser spot size and position, z-piezo calibration, optical-lever sensitivity, and deflection-curve nonlinearity.
- Motivation and contribution: The GCI lets AFM users compare calibration results worldwide, standardising force measurements and enabling non-invasive calibration of any cantilever type.It is intended to provide a reference point for calibration across laboratories and users.
II. THEORETICAL FRAMEWORK
The framework combines AFM Thermal measurements with the Sader method to estimate hydrodynamic functions and standardize spring-constant calibration across cantilevers. Averaging multiple measurements yields an A-coefficient for each cantilever geometry while accommodating real variation and reducing uncertainty.
- The GCI combines AFM Thermal calibration data with the Sader method to determine spring constants from resonant frequency and quality factor.
- The combined methods determine the A-coefficient needed to apply the Sader method accurately to any cantilever type.
- The A-coefficient is universal for a particular cantilever geometry and implicitly defines its hydrodynamic function.
- Equation (3) enables AFM Thermal measurements from multiple reference cantilevers to be compared and averaged together.
- Averaging systematically reduces A-coefficient uncertainty, accommodates variation among individual cantilevers, and provides a robust methodology.
III. DESCRIPTION OF THE GLOBAL CALIBRATION INITIATIVE
The GCI is a single-website platform that aggregates calibration data into live A-coefficient estimates. Its two modalities either refine the shared database while comparing measurements or provide non-invasive Sader calibration without uploading data.
- The GCI uses a single website where users upload resonant frequency, quality factor, and spring-constant data for a cantilever type.
- Modality 1: Modality 1 uploads AFM Thermal measurements, updates the A-coefficient, and reports a refined spring constant for comparison with the user's measurement.
- Modality 2: Modality 2 uses only resonant frequency and quality factor to report a Sader spring constant without uploading data or changing the A-coefficient.
- Modality 2: Modality 2 therefore provides non-invasive calibration using the existing database and Sader method.
- The live database displays cumulative A-coefficient information while keeping users' raw uploaded data confidential.
IV. PROOF-OF-PRINCIPLE IMPLEMENTATION
The proof-of-principle implementation evaluated the GCI with five independent groups across three countries using shared and independently procured AC240-R3 cantilevers. The design tested both cross-laboratory comparability and the intended user-procurement workflow.
- Five independent groups across Australia, Ireland, and Sweden participated in the proof-of-principle implementation.
- Participants viewed only cumulative and current A-coefficient histograms, without access to other groups' identities or raw data.
- One set of ten AC240-R3 cantilevers was passed sequentially among all five groups for direct cross-laboratory comparison.
- A second set consisted of unspecified AC240-R3 cantilevers procured independently by four groups.
- The shared set removed variability in cantilever properties, while the independently procured set mimicked the GCI's intended operation.
A. Set of ten AC240-R3 cantilevers
LDV measurements of ten AC240-R3 cantilevers provided independent benchmarks for spring constants and A-coefficients. Despite substantial stiffness variation among nominally identical cantilevers, A-coefficients were more consistent and the two LDV approaches agreed closely.
- a. Plan view dimensions: The ten cantilevers had highly uniform plan-view dimensions, with lengths of 239.3±1.3 µm and widths of 39.3±0.2 µm.
- 1. Laser Doppler vibrometer measurements: Only 5 of 20 LDV spring-constant measurements coincided with the average, showing significantly different stiffness among cantilevers with identical plan-view dimensions.
- 1. Laser Doppler vibrometer measurements: The two LDV approaches produced averaged spring constants differing by only 1%, supporting their expected agreement.
- c. A-coefficient: A-coefficient measurements were more consistent: 16 of 20 error bars encompassed the average value, compared with 5 of 20 spring-constant measurements.
- c. A-coefficient: The results demonstrate that the A-coefficient robustly normalizes data from multiple cantilevers of the same type.
2. AFM Thermal Noise Measurements
Across independent users and AFM systems, resonant frequencies were measured precisely, while quality factors and especially spring constants showed larger user-dependent variation. Comparison with LDV data indicates that averaging AFM measurements and using resonant frequency and quality factor can support the global calibration initiative.
- b. Quality factor: Quality-factor measurements averaged approximately 7% relative SD across users, falling to 3% after excluding Users 11 and 13.Those users reported values approximately 20% lower than others, likely because of insufficient cantilever retraction.
- c. Spring constant: Cantilever 10 spring constants ranged from 0.35 to 1.5 N/m, while the LDV value was 1.1 N/m.The maximum-to-minimum difference exceeded a factor of 4.
- c. Spring constant: AFM Thermal spring constants varied by 19% relative SD across users, increasing to 40% for Cantilever 10.The reported variation reflects substantial differences between users and groups, including users within the same group.
- c. Spring constant: The GCI can standardise spring-constant measurements against a live value derived from independent groups without additional instrumentation.Its calibration relies only on measured resonant frequency and quality factor, and averaging suppresses fluctuations in the A-coefficient.
- c. Spring constant: The averaged A-coefficient was close to the independent LDV result, supporting AFM Thermal measurements across multiple cantilevers.The AFM-derived mean was A = 6.4 nN s^1.3 m^-1, and the results agreed with the independent LDV measurement within uncertainty.
B. Unspecified AC240-R3 cantilevers
Measurements from randomly procured, unspecified AC240-R3 cantilevers show that averaging across many cantilevers can determine the A-coefficient accurately. This supports using unspecified same-type cantilevers in the GCI, while highlighting the importance of sample size and dimensional variation.
- B. Unspecified AC240-R3 cantilevers: The equations apply to same-type cantilevers that do not have identical plan-view dimensions, provided dimensional variations are not large.This assumption is relevant when combining measurements from independently procured cantilevers.
- B. Unspecified AC240-R3 cantilevers: Averaging 103 AFM data points from independently procured AC240-R3 cantilevers produced an A-coefficient that agreed well with the LDV measurement.The measurements were collected by eight users across Groups 2–5.
- B. Unspecified AC240-R3 cantilevers: Unspecified cantilevers of a given plan-view type can be used to accurately determine the A-coefficient.This is important because the GCI must generally use unspecified cantilevers measured by independent users.
- B. Unspecified AC240-R3 cantilevers: The A-coefficients were approximately 10% larger than values from a study based on only four AC240-R3 cantilevers.The earlier study did not measure plan-view dimensions, preventing a rigorous assessment of the difference.
- B. Unspecified AC240-R3 cantilevers: The GCI inherently averages A-coefficients because nominally identical cantilevers can differ slightly in geometry and dimensions.Randomly procured same-type cantilevers are expected to increase scatter, which averaging can reduce.
V. SUMMARY AND CONCLUSION
The Global Calibration Initiative addresses variability and missing shared references in AFM spring-constant calibration by enabling community-wide comparison and non-invasive calibration. Its proof-of-principle used independent measurements from five groups across three countries.
- A round-robin study using 10 cantilevers highlights variability in current AFM force measurements that can hinder robust comparison between independent groups and users.
- The Global Calibration Initiative enables users to compare calibration results, standardise AFM force measurements, and non-invasively calibrate any cantilever type.
- The proof-of-principle demonstration used independent measurements from five groups across three countries.
- The initiative supports standardisation across available and future cantilever models, with users able to propose additional cantilever types for inclusion.
- The initiative is implemented through a website where users upload currently available data, with its URL provided in the cited reference.
Supplementary Information for
The paper presents a virtual instrument for standardising AFM cantilever calibration through an internet-based initiative.
- The paper introduces a virtual instrument to standardise atomic force microscope cantilever calibration.
- The author list includes John E. Sader, Riccardo Borgani, Christopher T. Gibson, and additional collaborators.
3. Spring constants (LDV: red; AFM: blue. Identical vertical scales used in all plots) Cantilever 1
Measurements examine how tip-sample separation affects the quality factor and resonant frequency of an unknown AC240-R3 cantilever in air. Quality-factor changes are substantially larger than resonant-frequency changes at small separations.
- The measurements used an unknown AC240-R3 cantilever in air and included a 3,000 μm reference separation and a 0.75 μm minimum separation.
- Quality factor decreases by approximately 10-20% below 30 μm separation, while separations above 60 μm minimise squeeze film damping.
- Resonant frequency also decreases with tip-sample separation, but the reduction is two orders-of-magnitude smaller than the quality-factor change.