Laser heating of cantilevered tips: Implications for photoinduced force microscopy

Photoinduced force microscopy (PiFM) measures changes in the force between an atomically sharp tip and the sample under the influence of applied radiation. Several mechanisms contribute to the overall force, including forces introduced due to thermal heating of the sample and the tip. In this paper, we study the effect of laser heating of the retracted tip under illumination conditions relevant to PiFM and how it affects the mechanical resonance properties of the cantilever. Using a gold-coated silicon cantilever with its tip irradiated by a tightly focused 532-nm laser beam, we find that the tip temperature increases linearly at 7.5 K/mW of average laser power, irrespective of whether the laser is pulsed or continuous wave. The temperature rise gives rise to a decrease of the cantilever's spring constant and an increase of the damping coefficient. We demonstrate that for retracted tips, these thermally induced changes to the mechanical resonance only moderately impact the measured photoinduced force, as the measured scattering force is at least an order of magnitude stronger than the effective force introduced by laser heating under experimentally relevant conditions.

Figure 1

FEM simulation of the tip/cantilever system in the presence of a thermal load. (a) Dimensions of the ACL type cantilever with tetrahedral blocks chosen as the finite elements. (b) Temperature distribution of cantilever in the stationary state. The surface temperatures of A and B are fixed and form the boundary conditions in the simulation. The inset graph shows the temperature gradient in the cantilever beam. (c) Simulated first and (d) second eigenmodes of the cantilever.

Figure 2

Simulation of the relative resonance frequencies of the first and second eigenmodes of the tip/cantilever system as a function the tip temperature. Cantilever dimensions are based on the cantilever used in the experiments. Results are shown for different diameters $D$ of the base of the apex cone.

Figure 3

Spot size measurement in PiFM when the tip is illuminated by (a) cw laser and (b) pulsed laser. White arrows in each panel show the position where cross sections are taken, displayed in (c) and (d).

Figure 4

Resonance curves as a function of average laser power. (a) First and (b) second eigenmodes of the cantilever while illuminated by the cw laser. Laser powers in focus are 0.00 mW (red squares), 0.32 mW (orange circles), 0.63 mW (yellow triangles), 0.95 mW (green triangles), 1.26 mW (blue triangles), and 1.58 mW (purple triangles). (c) First and (d) second eigenmodes of the cantilever while illuminated by the pulsed laser. Laser powers in focus are 0.00 mW (red squares), 0.18 mW (orange circles), 0.35 mW (green triangles), 0.70 mW (blue triangles), and 1.12 mW (purple triangles).

Figure 5

(a) Relative resonance frequency and (b) relative quality factor as a function of average laser power at the tip apex. $f_0$ and $Q_0$ are the values obtained in the absence of laser light. (c) Extracted change in the cantilever's spring constant and (d) extracted change in the damping coefficient. First eigenmode is indicated by black squares and second eigenmode by red circles. Solid symbols denote CW irradiation and open symbols indicate illumination with pulsed laser light. Solid lines represent linear fits to the combined data (cw and pulsed) for each eigenmode.

Figure 6

Estimated temperature rise $\mathrm{\Delta }T$ as a function of the incident average laser power. The temperature rise is obtained by relating the measured changes in $f/f_0$ to the corresponding simulation results.

Figure 7

(a) Oscillation amplitude $A_1$ as a function of average laser power as measured in PiFM. Each data point is the average value of various measurements in the range from 30 to 150 nm for the tip/sample. (b) Change in the spring constant $\mathrm{\Delta }{k}_2$ obtained by measuring $A_2$ and ${\theta }_2$ during the PiFM measurement. (c) Change in the damping coefficient $\mathrm{\Delta }{b}_2$. (d) Retrieved photoinduced force.

Figure 8

Decomposition of the measured force $F_{\mathrm{opt}}$ (open circles) into the scattering force $F_{\mathrm{scat}}$ (blue triangles) and an effective force $F_{\mathrm{heat}}$ due to laser heating (red squares). $F_{\mathrm{scat}}$ increases linearly with laser power while $F_{\mathrm{heat}}$ shows a quadratic dependence.