NANODYNAMICS SYSTEMS LAB
 

Atomic Force Microscopy:

 

 

  • Real-time detection of probe-loss in atomic force microscopy
  • Transient force-atomic force microscopy (TF-AFM): a new interrogation method
  • Thermally driven non-contact atomic force microscopy
  • Systems viewpoint to AFM based nano-interrogation
  • Study of complex dynamics in atomic force microscopy

 

  • Real time detection of probe-loss

    • In AFM imaging the cantilever is the main and only probe of the sample. Thus when the cantilever loses interaction with the sample no information about the sample can be derived. Detection of probe-loss seems like a difficult problem; how does one conclude the loss of the measuring device itself. Conventional imaging signals like the amplitude signal and the control signal that regulates the tip-sample separation can not identify the areas of probe-loss.
    • NDSL group has devised a real-time methodology to determine regions of dynamic atomic force microscopy based image where the cantilever fails to be an effective probe of the sample.  A quantitative measure called reliability index is proposed as diagnostic measure for determining probe-loss.  This signal, apart from indicating the probe-loss affected regions, can be used to minimize such regions of the image, thus aiding high speed AFM applications.
    • This method is the first reported result that identifies spurious data due to probe-loss in real-time. Probe-loss is also referred to as "parachuting" in some literature.
       

  • Thermally driven non-contact atomic force microscopy (ThNcAfm): using noise for useful purposes.

    • ThNcAfm is a method to maintain the cantilever in the attractive part of the tip-sample interaction potential. This region of the tip-sample interaction potential is a good observation "outpost" for the cantilever as it does not intrude the sample process being observed excessively neither is it so far that observation of the sample process evolution becomes difficult.
    • ThNcAfm uses the cantilever's thermal noise response to actively position the sample using the piezo positioner, in such a manner that the the cantilever tip can be maintained in the attractive part for greater than 30 minutes. It uses the thermal noise response to cancel the drift effects.
    • As the observation period is long, one can dig out small but persistent deformations of the sample evolution. ThNcAfm is capable of detecting sample deformation in the sub-Angstrom regime.

  • Transient force-atomic force microscopy (TF-AFM): a new interrogation method

    • TF-AFM imaging was invented in the NanoDynamics Systems Lab. Prior to this method of imaging most imaging methods used steady-state signals like amplitude and phase for imaging purposes. These signals and the related imaging techniques are fundamentally limited by the quality factor (Q) of the cantilever. TF-AFM interrogation bandwidth is independent of the Q of the cantilever and thus the bandwidth can be improved by a factor in the order of Q.
    • The TF-AFM method employs a model of the cantilever. The model of the cantilever is determined by standard frequency response methods. This model of the cantilever is built into a Field Programmable Gate Array (FPGA) card. The main concept is to compare the output as produced by the FPGA card that implements the model and the actual cantilever output. The notion utilized is that any mismatch between the FPGA output and the actual cantilever output is derived due to fact that the sample affects the actual cantilever but not the FPGA implemented model. This observer based method can detect the sharp transitions in the sample features.
    • The images on the side show that the TF-AFM based interrogation of DNA produces a highly resolved image of DNA when other imaging signals like height, phase and amplitude provide a poor image of the DNA. The DNA sample is a Lammda DNA that is approximately 2 nanometer in height. The lateral scan size is 2 micrometers. The scan rate was 12 Hz. The images were obatined in real-time in the sense that the image can be viewed as the scan proceeds. The experiment was done on a Veeco Multimode AFM, with one of the auxiliary imaging signals being the output of the FPGA board. The scanner used was the J-scanner.
    • Similar high fidelity images were obtained at higher scan rates near 25 Hz. The limiting factor at such high rate imaging was found to be the nanopositioning system that introduced imaging artifacts. 
    • This method is now patented under patent number 7,066,014:  Method to Transiently Detect Samples in Atomic Force Microscopes. For a demonstration of experimental data driven animation of how TF-AFM does bit detection click here. This application of TF-AFM is particularly well-suited for high density data storage applications.

  • Fundamental limitations in AFM based nano-interrogation

    • The dynamic mode AM-AFM operation is the preferred mode of AFM interrogation due to its gentleness, high resolution and its ability to function under fluids that makes it possible to use AFM for bio investigation under native conditions.
    • In most earlier literature, the first harmonic of the cantilever oscillation data is utilized to obtain sample characteristics. Our work has demonstrated that the first harmonic behavior can  be explained by using a piecewise linear model of the tip-sample interaction potential. Though this aspect of dynamic AFM is operationally desirable, it also points to fundamental limitations on how well the first harmonic data can discern different tip-sample interaction potentials. Motivated by the possibility of using higher harmonic, we have found upper bounds on the magnitude of higher harmonics assuming coarse information on the tip-sample interaction characteristics. Thus the analysis does not require the precise knowledge of the tip-sample interaction characteristics; only an approximate knowledge of the tip-sample interaction potential is needed.  The framework also allows to flag when the assumed model is not valid. These bounds are the first step in study the fundamental limitations of dynamic AFM imaging.

  • Systems viewpoint to AFM based nano-interrogation

    • Prior to the work of our group, the AFM system was not interpreted from a systems point of view i.e. in terms of blocks that process input and produce outputs. Our work for the first time, visualized the AFM dynamics as a interconnection of two systems where one system is the cantilever system and the other system is the tip-sample interaction system. The cantilever system takes in as inputs the force from the sample and any other external drive input and produces the tip-deflection as the output. The tip-sample interaction system takes in as inputs the tip position and possibly the tip velocity and produces as the output the sample force on the cantilever.
    • The viewpoint of AFM as an interconnection of two systems streamlines the management of known information and the associated uncertainty in AFM. The cantilever system is often precisely known and can be well modeled as a Linear Time Invariant system with well determined parameters and the tip-sample nonlinearity is the unknown that may admit a coarse characterization but does not admit a precise characterization.
    • The systems viewpoint has facilitated new ways of nano-interrogation (see TF-AFM) and has led to basic understanding of the dynamic mode AFM operation.

  • Study of complex dynamics in atomic force microscopy

    • Behavior of periodic orbits under perturbation is of considerable interest for dynamical systems. If the sample is absent in the tapping-mode setup, it can be shown that the cantilever dynamics approximated by its first mode has a single homoclinic orbit, which is formed by the stable and the unstable manifolds of the saddle type, fixed points. Under the perturbation formed by the sinusoidal forcing and the sample presence the single homoclinic orbit would break into separate stable and unstable manifolds. Conley-Moser and Smale-Birkhoff results show that if the stable and the unstable manifolds intersect transversely then there is an invariant set where the dynamics is topologically equivalent to the shift map on N symbols. The shift map on N symbols exhibits complex behavior. It has a countable infinity of periodic orbits and a dense orbit. Because of the topological equivalence under transverse intersections, the micro-cantilever dynamics under the perturbation will exhibit such a rich behavior.
    • The Melnikov function provides a measure of the distance between the stable and the unstable manifolds of the perturbed system, which intersect if the Melnikov function evaluates to zero.
    • Under this topic, we have studied the possibility of such rich behavior for the dynamics of the micro-cantilever under a Lennard-Jones potential, which consists of long-range attractive and short-range repulsive forces. The Melnikov function is evaluated and the parameter space for which the Melnikov function is zero is identified. Further, control strategies are devised that eliminate the possibility of the complex-dynamics.