Dissipation modulated Kelvin probe force microscopy method

We review a new implementation of Kelvin probe force microscopy (KPFM) in which the dissipation signal of frequency modulation atomic force microscopy (FM-AFM) is used for dc bias voltage feedback (D-KPFM). The dissipation arises from an oscillating electrostatic force that is coherent with the tip oscillation, which is caused by applying the ac voltage between the tip and sample. The magnitude of the externally induced dissipation is found to be proportional to the effective dc bias voltage, which is the difference between the applied dc voltage and the contact potential difference. Two different implementations of D-KPFM are presented. In the first implementation, the frequency of the applied ac voltage, $f_\mathrm{el}$, is chosen to be the same as the tip oscillation ($f_\mathrm{el} = f_\mathrm{m}$: $1\omega$D-KPFM). In the second one, the ac voltage frequency, $f_\mathrm{el}$, is chosen to be twice the tip oscillation frequency ($f_\mathrm{el}= 2 f_\mathrm{m}$: $2\omega$D-KPFM). In $1\omega$D-KPFM, the dissipation is proportional to the electrostatic force, which enables the use of a small ac voltage amplitude even down to $\approx 10$\,mV. In $2\omega$D-KPFM, the dissipation is proportional to the electrostatic force gradient, which results in the same potential contrast as that obtained by FM-KPFM. D-KPFM features a simple implementation with no lock-in amplifier and faster scanning as it requires no low frequency modulation. The use of a small ac voltage amplitude in $1\omega$D-KPFM is of great importance in characterizing of technically relevant materials in which their electrical properties can be disturbed by the applied electric field. $2\omega$D-KPFM is useful when more accurate potential measurement is required. The operations in $1\omega$ and $2\omega$D-KPFM can be switched easily to take advantage of both features at the same location on a sample.