You can find the relevant information in the manual of the AFM system. It can be determined using the similar indentation process as we follow in general for obtaining force-displacement curves in AFM. However, the sample in this case should have comparatively high hardness in comparison to cantilever. For instance, you can use Silicon Nitride/Alumina sample for cantilever made of Silicon. The inverse of the slope of the curve obtained between the distance traveled by the Piezo and the deflection of the cantilever measured will given you the deflection sensitivity of the system. The units of the deflection sensitivity will be nm/V.

@Harpreet: I am talking about deflection sensitivity correction factor and not deflection sensitivity.

@Werner: No, the correction factor input field do not pop up on nanoscope. This is an advanced setting which usually people don't play with and by default it is 1.06. If you see carefully, there is another factor apart from this: PSD bin width (in Hz). The measured spring constant depends on both these values, but the dependence on PSD bin width can be ignored. However, for the deflection sensitivity correction factor, it is extremely sensitive. Even by changing this value by 0.1, the measured spring constant can be noticeably different (ex: from 0.6 N/m it can become 0.7 N/m).

Even the Bruker scientists (I know) aren't aware of this correction factor.

The way I determine the deflection sensitivity is different than how Bruker does it and so the correction factor may be different. I need to know the details about this correction factor.

I am trying to measure the nanoindentation elastic modulus of duplex and quadruplex DNA. I don't know about anything similar that I can use for reference. Also, my nanoindentation protocol is my own and has no references in any literature. With the ordinary protocol, the error would be too high and that is why people have not reported it yet.

Just an idea - can you measure the spring constant of a cantilever by another method - e.g. on another machine, and then when performing your current method adjust the sensitivity correction factor until the spring constant value matches that obtained by the other method? One problem is that almost all spring constant determination methods have some appreciable degree of error. I have never heard of this correction factor - what is it correcting for?

@Daniel: Good idea, but what other method do you suggest?

When we calibrate the deflection sensitivity, the tip touches the sample, but when we do thermal tuning, the tip is freely oscillating in air. The deflection sensitivity in these two cases are different, and to account for this difference, we need the correction factor. Suppose you calibrate the deflection sensitivity at 0.05 V and 0.3 V, then you will get two different results for deflection sensitivity and thus two different correction factors.

There are quite a few other methods - there are several review papers on the subject if you want to search. You can add known masses to the end and monitor changes in resonant frequency or make force measurements against a reference cantilever for instance. For a beam shaped lever you can calculate it using Saders method from the dimensions and the resonance frequency. All these methods have errors attached, but so does the thermal method.

You mentioned earlier that there is a default setting for the correction factor in the instrument software - would it seem likely that this is the correct correction factor predetermined by the manufacturer, or does the correction factor vary each time you change the cantilever and laser set-up?

The correction factor is supposed to depend on the cantilever shape function which changes with every experiment and so the default value is erroneous.

Not frequency. But the shape, size and position of laser spot matters.

Do you realize why this correction factor is needed? It is because in thermal tuning the oscillations of a free cantilever are recorded. But when we determine the deflection sensitivity, it is not that of a free cantilever. The following paper from HJ Butt solves the 4th order partial differential equation for the free cantilever oscillating due to thermal noise. This equation is valid only for a rectangular cantilever and with laser spot size much less than the cantilever dimensions. There are many other assumptions and simplifications as well. The result of this equation is equation 16 in the Bruker's application note AN094 (page 6).

Reasons for Bruker's default value of 1.08 for rectangular cantilever. Check page 5-6.

Stark suggested a correction factor of 1.12 for V-shaped cantilever. But his derivation is not very tedious and has lots of assumptions and simplifications which are not valid for small cantilevers, where the laser spot spreads out of the cantilever.

I have found that the deflection sensitivity (DS) depends slightly on the amount of cantilever bending. But the correction factor of 1.12 or 1.08 doesn't account for this dependence. So suppose calibrating the DS at a setpoint of 10 mV gives 22 nm/V, and at a setpoint of 100 mV gives 25 nm/V. Now if you use these two different values but the same correction factor, then you shall get two different values of spring constant for the same cantilever, which is obviously not possible.

Make sure that the thermal tuning gains are properly calibrated as well. Usually, it is factory calibrated, but with my experience with 7 Bruker systems, few of them didn't have proper calibration, and the technician who installed the system had no idea about that.

Do you already know the papers "Calculation of thermal noise in an atomic force microscope with a finite optical spot size" (Schaeffer 2005) and "Finite optical spot size and position corrections in thermal spring constant calibration" (Proksch, 2004)?

I found these publications very helpful as they discuss the problem of a pinned vs. free cantilever and the laser spot size and position on the lever very nicely. Also they give a lookup table kind of diagram for estimating values for your own system.

I hope this helps.

Article Finite optical spot size and position corrections in thermal...

Article Calculation of thermal noise in an atomic force microscope w...

Dear Krishnashish,

In a routine force spectroscopy experiment with AFM, you need to convert mV to nN to draw a final plot. You know the spring constant in the form of N/m or nN/nm. Also you can extract correlation between mV & nm (in the form of mV/nm) from slope of an obtained spectroscopy plot. Finally you can divide the first value to second value and acquire nN/mV.

Regards

@Hamid

You shouldn't answer so confidently without understanding the question or reading other comments. 

For people who are still interested in this question:

Simply speaking, you can type 1.106 for a rectangular cantilever and 1.140 for a V-shaped cantilever in deflection sensitivity correction although the default value of your Bruker Nanoscope software might be different from these values. For your reference, you can find the answer of Ben Ohler (the author of the application note that Krishnashish mentioned) at the following website:

http://nanoscaleworld.bruker-axs.com/nanoscaleworld/forums/p/540/1082.aspx