Stochastic mechanism of energy dissipation in noncontact atomic force microscopy studied using molecular dynamics with Langevin boundary conditions

Based on the stochastic friction force theory of energy dissipation in non-contact atomic force microscopy (NC-AFM), we performed realistic molecular dynamics (MD) simulations on the $\mathrm{MgO}\left(001\right)$ surface to complement previous studies which only considered low frequency phonons in detail. We employed and calibrated Langevin boundary conditions to reduce effects due to the finite system size and thus to mimic an infinite lattice. The calculated dissipation energies are many orders of magnitude smaller than those observed experimentally and are similar to those calculated previously using simple analytical models. These findings suggest that this mechanism is not responsible for the observed energy dissipation.

Figure 1

Comparison of the phonon DOS calculated via MD ($\gamma =10$ and $100{\mathrm{ps}}^{-1}$) and LD.

Figure 2

Comparison of the phonon DOS calculated via MD with $\gamma =0$ and LD.

Figure 3

Outline of system configuration with Langevin boundary conditions.

Figure 4

(a) Tip force autocorrelation function $4\mathrm{\AA }$ directly above a $\mathrm{Mg}$ atom in the surface for $\gamma =0$ and $\gamma =10{\mathrm{ps}}^{-1}$; (b) the corresponding time smoothed integrals of Eq. (1) as a function of the upper limit $\tau$ and that of the smaller 864 atom surface cluster system with $\gamma =10{\mathrm{ps}}^{-1}$.

Figure 5

System size dependence of the tip friction coefficient 3 and $4\mathrm{\AA }$ directly above a $\mathrm{Mg}$ atom in the surface.

Figure 6

Tip friction coefficient as a function of tip height for the tip above $\mathrm{Mg}$ and $\mathrm{O}$ surface atoms.

Figure 7

Dissipated energy as a function of tip closest approach above $\mathrm{Mg}$ and $\mathrm{O}$ surface atoms.

Figure 8

Dissipated energy as a function of system temperature above a $\mathrm{Mg}$ atom at a distance of closest approach of $3.75\mathrm{\AA }$.