Force Resolution in Force Spectroscopy Experiments: Thermal Noise and Bandwidth (AN104)

By limiting the bandwidth in any of average. This can be implemented in INFLUENCE OF THE MEASUREMENT these ways it is possible to exclude two different ways. First, the ramp rate BANDWIDTH a portion of the thermal noise from and the number of points per curve The thermal noise of the cantilever force measurements. This is perhaps ("Number of Samples" parameter) occurs in a bandwidth near the best illustrated by considering a power determine an overall data capture resonance frequency of the cantilever. spectral density plot of the defl ection rate. For instance, a 1 Hz ramp rate Therefore the measurement bandwidth, signal, as shown in Figure 1. This and 19968 points per curve combine to determined by the sampling rate and shows the thermal noise (blue points) give the maximum data capture rate of any data averaging or other fi ltering, fi t to a simple harmonic oscillator about 40 kHz (1 Hz = 0.5 s per direction, can have a large effect on the observed function (red line). Obviously the noise which at 19968 points per curve is about noise in force data. In aqueous occurs in a peak centered on the 25 µs per point, or about 40 kHz). Using solutions, where many of these resonance frequency of the cantilever. fewer points per curve simply averages piconewton regime measurements are By integrating the area under this peak more points to downconvert the being made, the resonance frequencies we can calculate the RMS force noise. signal to a lower bandwidth. Second, of most cantilevers are quite low, If we set the limits of integration to the a moving average can be applied to typically less than 10 kHz. This is well bandwidth of our measurement we can the data using the "Average Points" within the possible measurement obtain the theoretical RMS force noise parameter found under each "Channel" bandwidth of the AFM. For instance, for a given bandwidth. Experimentally, group in the ramp mode parameter Veeco AFMs running on the NanoScope however, it is impossible to achieve a lists. This results in similar fi ltering of V controller can capture standard force measurement bandwidth that precisely the data but retains more points per curves at data rates of up to 40 kHz. limits the bandwidth to the desired curve, which is important when fi tting Using the High Speed Data Capture range because the fi ltering cutoff functions to the data and in order to feature this can be increased all the frequencies are not infi nitely sharp.maintain good resolution in the distance way up to axis of the data.50 MHz. Experimental RMS force noise measurements were made with the The combined effect of the "Scan However, the measurement bandwidth same cantilever used to measure Rate", "Number of Samples", and is also determined by any data fi ltering the data in Figure 1, which was the "Average Points" parameters results that occurs on the defl ection signal. rectangular cantilever on a Veeco MLCT in a parameter called "Effective