Measurement of electrostatic tip–sample interactions by time-domain Kelvin probe force microscopy

• Christian Ritz,
• Tino Wagner and
• Andreas Stemmer

Beilstein J. Nanotechnol. 2020, 11, 911–921, doi:10.3762/bjnano.11.76

• to the applied bias voltage. A state observer based on an extended Kalman filter is used to continuously fit the resulting parabola. The output of the time-based controller is an estimation of the topography-induced frequency shift Δftopo (which is not affected by Δfrem), the surface potential Ulcpd

• . Due to the nonlinearity of the system, nonlinear state estimation is required. The extended Kalman filter (EKF) is a straightforward and computationally efficient method for dealing with such systems. The implementation shown uses the notation of Simon [30]. The algorithm starts with an arbitrary

• topography and electrostatic properties can be directly estimated and separated from the frequency-shift signal. The state-space representation of FM-KFM was derived and an extended Kalman filter was introduced as a state observer. The estimation uses a linearization around the output matrix of the Kelvin