Energy dissipation in dynamic force microscopy on KBr(001) correlated with atomic-scale adhesion phenomena

Atomic-scale adhesion phenomena between KBr tip and sample were studied by dynamic force spectroscopy with a small amplitude of down to $285\mathrm{p}\mathrm{m}$ at room temperature. The high-resonance frequency of the second flexural mode of a silicon cantilever ($\approx 1\mathrm{M}\mathrm{Hz}$) suppresses an apparent dissipation energy caused by undesirable mechanical couplings in between the cantilever and the dither piezo actuator. Further, the Joule heating dissipation contribution and the noise-equivalent dissipation energy were reduced by setting a smaller amplitude. Usage of a high resonance frequency and a smaller amplitude enables us to perform highly sensitive measurements of the atomic-scale adhesion and the tip-instability-related energy dissipation. Tip changes, caused by tip-sample interactions and thermal energy, resulted in three different dissipation energy levels ($\Delta E_{\mathrm{ts}}\approx 25\mathrm{m}\mathrm{e}\mathrm{V}/\mathrm{cycle}$). This infrequent change of the tip apex condition often prevents a stable imaging with small amplitude. Our systematic measurement shows that the atomic adhesion is caused mainly in the tip itself, and a sharper and softer tip induced a larger energy dissipation.

Figure 1

(a) Increase of excitation amplitude $A_{\text{exc}}/A_{\text{exc},0}$ as a function of phase shift. (b) Frequency shift cased by phase shift. The inset shows in the wider phase range. Calculation of cantilever parameters gives $f_{\text{1st}}=172389\mathrm{Hz}$, $Q_{\text{1st}}=27468$, $f_{\text{2nd}}=1064632\mathrm{Hz}$, and $Q_{\text{2nd}}=13136$.

Figure 2

Frequency response spectra of amplitude around (a) first flexural mode and (b) second flexural mode. Transfer-function-induced $A_{\text{exc}}/A_{\text{exc},0}$ vs frequency around (c) first flexural mode and (d) second flexural mode. Measured cantilever parameters are $f_{\text{1st}}=172389\mathrm{Hz}$, $Q_{\text{1st}}=27468$, $f_{\text{2nd}}=1064632\mathrm{Hz}$, and $Q_{\text{2nd}}=13136$.

Figure 3

Frequency response spectra of phase around (a) first flexural mode and (b) second flexural mode. The phase shifts by the cantilever resonance are calculated with Eq. (2). Phase shifts caused by the mechanical coupling around (c) first flexural mode and (d) second flexural mode.

Figure 4

Phase-shift-induced $A_{\text{exc}}/A_{\text{exc},0}$ vs frequency for (a) first and (b) second flexural modes. Phase-shift-induced apparent frequency shift for (c) first and (d) second flexural modes. Total effects of mechanical coupling in $A_{\text{exc}}/A_{\text{exc},0}$ for (e) first and (f) second flexural modes.

Figure 5

[(a) and (b)] Computed distance dependencies of the first and second flexural resonance frequency shifts with a tip-sample interaction, modeled with a Morse potential and a Hamaker-type potential. [(c) and (d)] Distance dependencies of the apparent dissipation energy for the first and second resonance modes. Calculation parameters: resonance frequency $f_{\text{1st}}=172389\mathrm{Hz}$, $k_{\text{1st}}=36\mathrm{N}/\mathrm{m}$, $Q_{\text{1st}}=27468$, $f_{\text{2nd}}=1064632\mathrm{Hz}$, $k_{\text{2nd}}=1500\mathrm{N}/\mathrm{m}$, and $Q_{\text{2nd}}=13136$.

Figure 6

(a) Series of distance dependence of the dissipative interaction energy per oscillation cycle $E_{\text{ts}}$ recorded with different $A_{\text{2nd}}$ on KBr(001). The inset image was obtained with $A_{\text{2nd}}=12.8\mathrm{n}\mathrm{m}$ at $\Delta f_{\text{2nd}}=-3.6\mathrm{Hz}$. (b) Interaction force $F$ curves extracted via measured $\Delta f_{\text{2nd}}$. Measurement parameters are $f_{\text{2nd}}=1039369\mathrm{Hz}$, $k_0=33\mathrm{N}/\mathrm{m}$, $k_{\text{2nd}}=1442\mathrm{N}/\mathrm{m}$, and $Q_{\text{2nd}}=11727$.

Figure 7

Noise-equivalent dissipative energy as a function of amplitude.

Figure 8

(a) Schematic of tip and sample. [(b)–(d)] $XYZ$ shifts between DFS measurements detected with an atom-tracking function. $A_{\text{2nd}}=285\mathrm{p}\mathrm{m}$ and $\Delta f_{\text{2nd}}=-150\mathrm{Hz}$.

Figure 9

[(a)–(c)] Three different states of measured $E_{\text{ts}}$ and extracted interaction force via measured $\Delta f_{\text{2nd}}$. Arrows indicate the hysteresis loop between forward and backward in one spectroscopic measurement. The cantilever was the same as that in Fig. 6, but was annealed again before measurements. $A_{\text{2nd}}=285\mathrm{p}\mathrm{m}$.

Figure 10

[(a)–(c)] Unstable distance-dependent curves of $E_{\text{ts}}$ and $\Delta f_{\text{2nd}}$.

Figure 11

Tip instabilities on KBr(001) revealed with a small amplitude of $400\mathrm{p}\mathrm{m}$. (a) $\Delta f_{\text{2nd}}$, (b) $E_{\text{ts}}$, and (c) $A_{\text{2nd}}$ were recorded with a small tip-sample separation during $5\mathrm{s}$. The anticorrelated jumps of the top two signals are due to tip changes. Parameters are $f_{\text{2nd}}=1039372\mathrm{Hz}$, $A_{\text{2nd}}=400\mathrm{p}\mathrm{m}$, $Q_{\text{2nd}}=6964$.