Information acquistion & processing in scanning probe microscopy: data processing advances have prompted a shift away from phase-sensitive detectors and growing interest in spectroscopic measurement techniques.
Signal processing in SPM
The operation principle of all force-based SPMs involves the interaction of the movable local probe with the surface. Spatially resolved data is obtained by rastering the probe across a sample and linking parameters determined from probe response to a particular pixel. The probe, a silicon microcantilever with a specialized tip, is excited mechanically, electrically, or magnetically through microscope electronics coupled to an appropriate transducer. The time-averaged mechanical behavior of the cantilever (e.g. deflection, oscillation amplitude, and phase) changes as the probe interacts with the sample. The signal from the probe is interpreted to obtain information about the scanned surface.
The contact AFM is based on static, or DC, detection of the force signals, typically operating in the bandwidth from DC to ~1-10 kHz. The primary limitations of the static measurements are that (a) all force interactions are measured simultaneously and cannot be separated, (b) 1/f noise limit can be a significant limitation at low frequencies, and (c) the higher frequency dynamic properties of material are inaccessible. An alternative is offered by dynamic methods, in which a specific functionality of the probe is modulated, and the oscillatory response is detected. Generally, the probe is excited and response is detected at a single frequency. Data processing then links the high frequency scale of the cantilever to the ~1 kHz frequency range of the feedback loops and image acquisition. This "downconversion" makes the signal manageable (1 datapoint/pixel, rather than many thousands) but at the same time limits the information obtained from the experiment. Traditionally, the SPM methods to date are based on either (a) homodyne or lock-in detection (LIA) or (b) phase-locked loop detection (PLL).
A LIA (or phase sensitive) detector returns a signal related to the detection amplitude and phase of the input at the frequency or harmonics of the modulation signal. This effectively provides information on response at one selected point in Fourier space, or its multiples.
A PLL utilizes the phase sensitive signal of a LIA to maintain the system at a specific phase value, typically resonance. The PLL is generally limited to techniques where the phase and amplitude of the driving force is constant.
Limits of conventional processing
The LIA or PLL data processing method in conventional SPM plays a crucial role of making the data stream manageable. In this process, the information about single-time or aperiodic events is essentially lost or averaged over many cycles and thus becomes a very small signal on a relatively large background. Moreover, the details of linear and non-linear tip-surfaces interactions are either lost or extremely difficult to reconstruct. Similarly, the capability to respond and control events in the tip-surface junction is limited. This is because the response occurs on the time scale of a single oscillation, and feedback becomes active only after several hundred or thousand cycles. Most strikingly, LIA and PLL processing limits the potential to (a) probe dissipative processes on the nanoscale, i.e. energy losses due to tip-surface interaction and (b) utilize resonance enhancement for techniques based on e.g. electrical excitation.
These limitations can be understood as follows. In the absence of nonlinearities, the tip-surface interactions can be represented by a simple mass-spring model (simple harmonic oscillator), characterized by three independent parameters: resonant frequency, amplitude at resonance, and Q-factor (or peak width). The conservative tip-surface interactions results in a change of the oscillation amplitude and resonance frequency, readily measurable by conventional electronics. However, the dissipation is related to the amplitude and the width of the resonant peak. For both PLL and LIA, only two out of three independent parameters defining the tip dynamics are measured. As a result, single frequency measurements give only two time-averaged parameters, while three are needed to uniquely determine conservative and dissipative interactions even assuming prior knowledge of SHO-type response.
This limitation can be circumvented if the force driving the system is constant, and the system follows the SHO dynamics, thus providing an additional constraint on the measured variables.
However, in methods based on the electrical excitation of the tip such as Kelvin probe force microscopy (KPFM) and piezoresponse force microscopy (PFM), the relationship between the phase of the excitation force and driving voltage strongly depends on material properties. In these cases, the amplitude and phase of the local response are a convolution of material response to external field, and cantilever response to the material-dependent local force, which cannot be separated unambiguously.
Even for techniques with mechanical excitation, the transfer function of the cantilever or oscillator can couple to the signal, resulting in systematic errors in PLL detection. In other words, the voltage sent to the oscillator is constant as imposed by microscope electronics. The driving force is determined both by voltage and oscillator and cantilever transfer functions, which have non-zero frequency dispersion and depend on tip-surface interactions, and hence the effective force is frequency dependent. The situation becomes even more complex when tip-surface interactions are non-linear and SHO model is inapplicable.
The obvious approach to overcome these limitations is the measurement of the full response-frequency curve, either within the full bandwidth of the detections system or in the vicinity of the resonance. The resulting 3-D data can then be analyzed using available models for linear or non-linear dynamics. In particular, dissipation can be ascertained as the local changes in the Q-factor of the cantilever (i.e. peak width). In principle, this can be accomplished using frequency sweeps in a standard lock-in method measuring response at all frequencies sequentially. However, this approach implemented on commercially available lock-ins results in large data acquisition times (~tens of hours), incompatible with imaging. The following alternatives have been developed:
* Thermal (white noise) excitation. The cantilever is exited by thermal fluctuations that can be modeled as excitation force with a uniform-amplitude and random-phase in frequency domain. The changes of the cantilever response as a function of tip-surface separation allows using the response as a feedback signal. The obvious limitation of this method is that the excitation force amplitude is not controlled, and the phase information on the response is lost.
* Ring down. This approach for measuring the cantilever transfer function was suggested by Proksch and Dahlberg and the Stark group. This technique is based on measuring the response to a step-function excitation and subsequent detection of the cantilever response. The Fourier transform of the response signal yields the transfer function of the system, from which response amplitude and dissipation can be extracted.
* Dual-frequency resonance tracking (DFRT). An alternative for single-frequency detection is developed based on dual-AC measurements. This approach overcomes the fundamental limitation of LIA and PLL detection--insufficient number of detected parameters--by performing exaltation and detection simultaneously at two frequencies. DFRT allows one to implement the amplitude-based feedback for maintaining resonance and directly determine the dissipation from peak width or response phases.
* Fast lock-in sweep. Very recently, an approach for fast sequential frequency scanning has been developed by Kos and Hurley. This approach allows determination of the full amplitude- and phase-frequency response curves at each point of the image, from which resonance frequency can be determined obviating the need for PLL-type feedback.
* Band excitation (BE). The BE approach provides an alternative to standard LLA and PLL methods and frequency sweeps by exciting and detecting response at all frequencies simultaneously. BE introduces a synthesized digital signal that spans a continuous band of frequencies and monitors the response within the same (or larger) frequency band. The cantilever response is detected using high speed data acquisition methods and then Fourier transformed. The resulting amplitude-frequency and phase-frequency curves are collected at each point and stored in 3-D data arrays. This data is analyzed to extract relevant parameters of the cantilever behavior.
Real-space control methods
An alternative to the detection in Fourier domain is the analysis of the real-space trajectory of the probe. Similarly to Fourier methods, this approach relies on the rapid acquisition of spectroscopic data in each spatial point of the image, and subsequent deconvolution of resulting 3-D dataset to yield 2-D maps of relevant parameters. The prototype of this approach is the force-volume imaging in contact AFM, in which force-distance curves are acquired at each pixel and are analyzed to derive local elasticity, adhesion, etc. The primary limitation of this method is large time requirements.
Control techniques mark future of SPM
The development of commercially available fast data acquisition and flexible control electronics, which has recently crossed the 10-100 MHz barrier required for real-time control of the SPM probe, has enabled new generations of data processing methods in SPM. The future will undoubtedly see the commercial implementation of the non-sinusoidal excitation and detection methods emerging in academic and industrial environments. In the next decade, SPM developments based on active control of the tip trajectory in ~MHz range, active feedbacks to lower thermomechanical noise, and advanced Fourier modes will emerge. Eventually, all the machinery of modern signal processing can lead to future serendipitous discoveries in this field.
* Asylum Research, Santa Barbara, Calif., 805-696-6466, www.asylumresearch.com
* Oak Ridge National Laboratory, Tenn., 865-574-4160, www.ornl.gov
--Sergei Kalinin, Oak Ridge National Laboratory
--Stephen Jesse, Oak Ridge National Laboratory
--Roger Proksch, Asylum Research
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|Title Annotation:||MICROSCOPY/IMAGE ANALYSIS|
|Author:||Kalinin, Sergei; Jesse, Stephen; Proksch, Roger|
|Publication:||R & D|
|Date:||Aug 1, 2008|
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