Crowdsourcing AFM calibration
Calibrations are an important parameter for all metrological instrumentation and measurements. You need to have confidence in what you are measuring whether it’s the x and y dimensions (critical for most microscopy applications), or in the case of AFM, the x, y and z dimensions, as well as the force the cantilever exerts on the sample.
There are several calibrations needed to successfully operate an AFM: x, y, and z motion of the piezo scanner and then parameters associated with the individual cantilever. Fortunately, in the days of closed loop scanning with independent sensors, scanner calibrations are not the ordeal they used to be in the open-loop days when frequent calibration was required to deal with the piezo nonlinearities such as creep and hysteresis (see example below of an AFM image of a grating where the feature sizes are growing in size due to piezo nonlinearities). Some instruments no longer even require calibration of the scanners.
Image of grating nonlinearity with uncalibrated piezo operating in open-loop
Cantilever spring constant calibrations remain a different story. Cantilever spring constants basically tell us how stiff the lever is. Higher spring constants mean stiffer levers. Today’s commercial levers come in a wide range from 0.01 N/m to 100N/m and higher. If you want to know the actual force you are exerting on your sample you would need to perform this calibration.
Spring constant calibrations remain more error-prone. A recent round robin study by John Sader, an Australian applied mathematician who has been working with the AFM community for almost 20 years, showed errors of upto 50% in spring constant measurements of the identical cantilever by different users from different labs. Ouch!
Fig 7b from Sader. Reproduced from Rev. Sci. instrum, 87 093711 (2016)
One of the most common calibration methods implemented into many commercial systems is the “thermal method” that monitors the Brownian motion of a cantilever coupled with the equipartition theorem. However this method is known to have uncertainties. Another popular method was developed by the same John Sader to develop equations to model AFM levers based on their resonant frequency, quality factor, and a universal A coefficient (related to the hydrodynamic function from his original papers). It is universal in the sense that the A-coefficient is the same for a cantilever of a particular geometry. His method was appropriately called “The Sader Method” and there was an even an iphone app developed for it!
Professor Sader has now enhanced his method through an internet-based initiative entitled “global calibration initiative” that crowd-sources the calibration of the A-coefficient. This initiative only requires an input of the resonance frequency and quality factor of your lever. Once you have these measurements, you can either calculate the spring constant using the currently available database for the A-factor, or you can contribute to the A-factor crowd-sourcing with your own spring constant value (from a thermal calibration). All the details of Professor Sader’s methodology have been published here. See an example of the interface below for a popular cantilever to which I have also contributed my measurement. You can see the histogram of the A-coefficients calculated so far – the more data inputted into these initiative the more accurate our spring constant measurements can be!
An example of the Sader software
I encourage users to try it. The interface is easy to use and understand. At the very least, it could be informative to see how much deviation you are seeing between your value and the crowd-sourced value (a potential warning sign on your measurement if there is significant deviation), and at the very best, you would be contributing to a much needed effort to standardize the A-coefficient and help all AFM users get better spring constant values for their experiments! As a reminder, this is a calibration for the cantilever spring constant only. Again, the global calibration initiative can be found here.
Dalia Yablon, Ph.D.