Casimir force measurements from silicon carbide surfaces

Using an atomic force microscope we performed measurements of the Casimir force between a gold- coated (Au) microsphere and doped silicon carbide (SiC) samples. The last of these is a promising material for devices operating under severe environments. The roughness of the interacting surfaces was measured to obtain information for the minimum separation distance upon contact. Ellipsometry data for both systems were used to extract optical properties needed for the calculation of the Casimir force via the Lifshitz theory and for comparison to the experiment. Special attention is devoted to the separation of the electrostatic contribution to the measured total force. Our measurements demonstrate large contact potential ${\mathrm{V}}_0(\approx 0.67\mathrm{V})$, and a relatively small density of charges trapped in SiC. Knowledge of both Casimir and electrostatic forces between interacting materials is not only important from the fundamental point of view, but also for device applications involving actuating components at separations of less than 200 nm where surface forces play dominant role.

Figure 1

Dielectric function of SiC and Au at imaginary frequencies, which it is used as input for Casimir force calculations via the Lifshitz theory. The inset shows the imaginary part ${\varepsilon }^{\prime \prime }\left(\omega \right)$ of the dielectric response functions as obtained by ellipsometry [22].

Figure 2

(a) Top view scanning electron microscopy (SEM) image of a sphere attached on a cantilever. (b) AFM topography of the sphere after Au deposition obtained by scanning on top of the sphere. (c) Height distribution of the sphere roughness, which provides the dominant contribution $d_{\mathrm{o},\mathrm{sp}}$ to distance upon conduct (for the SiC-Au system) due to the sphere roughness. Comparison shows that $d_{\mathrm{o},\mathrm{sp}}\gg d_{\mathrm{o},\mathrm{SiC}}$.

Figure 3

(a) Cantilever deflection versus applied voltage $-4<V<3$ with the voltage at the minimum providing the contact potential $V_{\mathrm{o}}$. The different deflection for the same potential corresponds to different sphere-plate separation. (b) Variation of $V_{\mathrm{o}}$ vs. separation. (c) Remnant cantilever deflection (with potential compensation $V=V_{\mathrm{o}}$) due to uncompensated charges on the SiC plate. Fitting with the logarithmic form ${\mathrm{F}}_{\mathrm{e}2}\left(\mathrm{z}\right)=\mathrm{k}[{\mathrm{c}}_1\log \left(\mathrm{z}\right)+{\mathrm{c}}_2]$ yields the parameter values $c_1=0.52$ nm and $c_2=0.27$ nm.

Figure 4

Experimental force measurements at compensating potential $V=V_{\mathrm{o}}$, and comparison to the Lifshitz theory calculations of the Casimir force in the range between 10-200 nm (using as input for SiC the optical data from Fig. 1, and for Au measured data from [11]). The inset shows a log-log fit to obtain the scaling exponent for Casimir force $F_{\mathrm{Cas}}\sim z^{-\mathrm{m}}$.