Casimir and electrostatic forces from ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ thin films of varying thickness

We explore here the decisive role of film thickness on Casimir and electrostatic forces from topological insulating ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ films. The forces were measured for the Au-${\mathrm{Bi}}_2{\mathrm{Se}}_3$ system under ambient conditions to simulate realistic applications. It is shown that the electrostatic forces associated with a nonzero contact potential of $V_{\mathrm{o}}\sim 200\mathrm{mV}$ played a dominant role, and could not be compensated for thinner films ($\le 20\mathrm{nm}$ thick). However, for thicker films the measured force, after voltage compensation, started to approach the genuine Casimir force in very good agreement with Lifshitz theory. Our results point out that any gradual deviation from theory for thinner films underlies the presence of strong electrostatic effects.

Figure 1

Cantilever deflection versus applied voltage in the range −1.5 to 1.5 V. Different colors correspond to different sets of measurement, and within the same color different data points at a specific voltage correspond to different separations (more than 100 nm) between the interacting surfaces, where the electrostatic force is the dominant force and the Casimir effect can be neglected. The minimum of all the data points meet at −200 mV which is considered as the contact potential between ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ and Au. The inset shows the height topography of the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ surface having a nominal thickness of 100 nm. The triangular features indicate the high-quality growth, and the rms roughness of this sample is 2.85 nm.

Figure 2

(1) Oxygen $1s$ core level spectra for the (a) Bi sample, (b) Se sample, and (c) ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ sample (film thickness 10 nm). Bi and Se samples are used as a reference. The O $1s$ envelopes look different for all the samples. The peak positions for the Se sample are shifted towards higher binding energies compared to the other two samples. (2) (d) UPS spectra (He I, photon energy 21.2 eV) for the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ sample (film thickness 10 nm) to determine the work function (sample was biased with −5 V). The black arrow shows the secondary electron cutoff (SECO). (e) UPS spectra for the Au (111) single crystal which was used as a reference. The measurement conditions were the same as for the ${\mathrm{Bi}}_2{\mathrm{Si}}_3$ sample.

Figure 3

Imaginary part of the frequency dependent dielectric function for ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ and the substrate ${\mathrm{Al}}_2{\mathrm{O}}_3$. The peak at (1.96 eV) for ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ is associated with transitions from the valence band (v) to the conduction band (c) and the strong peaks in ${\mathrm{Al}}_2{\mathrm{O}}_3$ are the phonon polariton absorption peaks. The inset shows the calculated dielectric function of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ and ${\mathrm{Al}}_2{\mathrm{O}}_3$ at imaginary frequencies, which is the necessary input for the calculation of the Casimir force with Lifshitz theory.

Figure 4

Experimental Casimir force data together with the Lifshitz theory calculation for separations below 100 nm for different thicknesses of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$. The experimental data for the shortest separation are restricted by surface roughness leading to a deviation from the power law behavior. The lower inset shows the variation of the power law exponent versus film thickness.