Atomic Force Microscopy control system for electrostatic measurements based on mechanical and electrical modulation

Atomic Force Microscopy (AFM) has excellent potential ability for quantitative electrostatic measurements of surface potential and dielectric permittivity of materials with nanoscale resolution. Implementation of this ability, however, requires overcoming several challenges. The first task is developing an accurate computational model for electrostatic tip-sample interaction; the second - efficient instrumentation and a control system that supports the measurements. An analytical model of nanoscale tip-sample capacitance on thin dielectric films was introduced (Gomila, Toset, and Fumagalli, 2008). This model allows describing the electrostatic tip-sample interaction force in a form suitable for the AFM dynamic control model (Belikov, Magonov, 2009). This dynamic model contains integrals over the tip-sample forces that can be presented in a closed form for the Gomila-Toset-Fumagalli analytical model. These results allow for developing very efficient electrostatic AFM computational model. As for the second task (instrumentation and control), the above mentioned AFM dynamic model with (amplitude-phase) state variables can be used for the control system design that combines mechanical Amplitude Modulation mode and consequent electrical modulation of the mechanical phase cosine. The cosine is monitored by lock-in amplifiers at the electrical modulation frequency, and twice that frequency; surface potential and dielectric permittivity of the sample can then be mapped. This paper presents the model derivation, description of instrumentation and control schematics, and their implementation on NT-MDT microscopes. Results are illustrated with practical measurements on different materials.