Measurement of the Casimir force between a spherical gold tip and Si(111)-(7 × 7) surfaces

Abstract

We have performed the measurement of Casimir force between a spherical Au tip and an atomically flat Si(111)-(7×7) surface at tip-sample distances ranging from 15 to 50 nm in an ultrahigh vacuum of

Analytical method for the measurement of the electrostatic force and the contact potential difference excluding the effect of the Casimir force with a conventional atomic force microscope

“…A B ts It was calculated to be 8% and the electrostatic force caused by local charges could be negligible in comparison with the measured Casimir force in this experimental condition. In our previous measurement, 13) s r is calculated to 16% which is larger than this work. In Ref.…”

“…As a reference, the theoretically calculated dependence depicted as a black dashed line in the figure. 6,13,18) To evaluate the deviation of the measured values from the theoretical ones, the rms deviation…”

“…In Ref. 13, the net force was measured with an applying voltage which is the estimated CPD. When the applying voltage Minus value of the displacement indicates the direction toward the tip.…”

“…The Si substrate was outgassed and flashed to obtain a flat surface by the same treatment discussed in Ref. 13. The rms roughness of the surface was given to be 1.8 nm from the AFM image as shown in Fig.…”

“…To discuss the electrostatic force in the latter experimental condition, the force between a spherical tip with micrometer-scale radius and an infinite plate sample separated by a nanometer-scale distance has been often explored involving the Casimir force. [5][6][7][8][9][10][11][12][13][14][15] The Casimir force is an attractive force induced by the exclusion of modes of electromagnetic fields in the region bounded by metallic plates, [16][17][18] which becomes non-negligible in such experimental geometry. The Casimir force has also been attracted attention for MEMS applications.…”