Lyapunov estimation for high-speed demodulation in multifrequency atomic force microscopy.

David M Harcombe,Michael R P Ragazzon,Michael G Ruppert,Andrew J Fleming

doi:10.3762/bjnano.9.47

Abstract

An important issue in the emerging field of multifrequency atomic force microscopy (MF-AFM) is the accurate and fast demodulation of the cantilever-tip deflection signal. As this signal consists of multiple frequency components and noise processes, a lock-in amplifier is typically employed for its narrowband response. However, this demodulator suffers inherent bandwidth limitations as high-frequency mixing products must be filtered out and several must be operated in parallel. Many MF-AFM methods require amplitude and phase demodulation at multiple frequencies of interest, enabling both z-axis feedback and phase contrast imaging to be achieved. This article proposes a model-based multifrequency Lyapunov filter implemented on a field-programmable gate array (FPGA) for high-speed MF-AFM demodulation. System descriptions and simulations are verified by experimental results demonstrating high tracking bandwidths, strong off-mode rejection and minor sensitivity to cross-coupling effects. Additionally, a five-frequency system operating at 3.5 MHz is implemented for higher harmonic amplitude and phase imaging up to 1 MHz.

Highlights

Atomic force microscopy (AFM) [1] has been integral in the field of nanoscale engineering since its invention in 1986 by Binnig et al By sensing microcantilever tip–sample interactions [2], atomic scale resolution imaging is achieved, which far exceeds the optical diffraction limit
The Lyapunov filter was implemented on a high-speed field-programmable gate array (FPGA) to achieve the necessary sample rate for accessing higher harmonics during imaging
The FPGA clock is synchronized with the high-speed I/O card at 250 MHz

Summary

Introduction

Atomic force microscopy (AFM) [1] has been integral in the field of nanoscale engineering since its invention in 1986 by Binnig et al By sensing microcantilever tip–sample interactions [2], atomic scale resolution imaging is achieved, which far exceeds the optical diffraction limit. Where as in dynamic modes, for example intermittent-contact constant-amplitude AFM [4], the control loop acts to maintain a constant cantilever oscillation amplitude. This is achieved by feeding back the demodulated fundamental frequency present in the deflection signal. In intermittent-contact mode AFM [5], the tapping amplitude is chosen such that only gentle tip–sample interactions occur. This is suitable for studying biological samples, allowing for biophysical processes to be studied [6,7,8]

Methods

Results

Conclusion