Demonstration of the Difference in the Casimir Force for Samples with Different Charge-Carrier Densities

Abstract

A measurement of the Casimir force between a gold coated sphere and two Si plates of different carrier densities is performed using a high vacuum based atomic force microscope. The results are compared with the Lifshitz theory and good agreement is found. Our experiment demonstrates that by changing the carrier density of the semiconductor plate by several orders of magnitude it is possible to modify the Casimir interaction. This result may find applications in nanotechnology. PACS numbers: 12.20.Fv, 12.20.Ds, 68.37.Ps, 73.25.+i The Casimir effect [1] implies that there is a force acting between closely spaced neutral bodies determined by the zero-point oscillations of the electromagnetic field. In the last few years the Casimir force was extensively investigated experimentally (see, e.g., Refs,[2,3,4,5,6,7,8] and review [9]). It has found many diverse applications ranging from Bose-Einstein condensation [10], carbon nanotubes [11], and to the testing of predictions of new physics beyond the standard model [7,8,9]. One of the most important applications of the Casimir effect is in the design, fabrication and function of MEMS and NEMS such as micromirrors, nanotweezers and nanoscale actuators [12,13,14]. The combined action of the Casimir and electrostatic forces can result in nonlinear dynamics, bistable phenomena and even cause device failure by the abrupt "pull-in" and attachment of one surface to the other [12,13,14]. The Casimir force also changes the operation bandwidth and tunability of MEMS. The actuation of MEMS using the Casimir force has been demonstrated [14].The modification of the Casimir force by changing parameters of the system other than the separation is a complicated problem since it requires modification of the optical properties of materials within a relatively wide frequency region. The attempt to modify the Casimir force due to a coating with a hydrogen-switchable mirror did not lead to any observed effect [15]. We pioneer the demonstration of the difference Casimir force between a gold coated sphere and two Si samples which possess different resistivities and charge carrier densities. We use a high vacuum (2 × 10 −7 Torr) based AFM to measure the Casimir force between a gold coated polystyrene sphere with a diameter 2R = 201.8 ± 0.6 µm and two 4 × 7 mm 2 size Si plates placed next to each other. The thickness of gold coating on the sphere was measured to be 96 ± 2 nm. The details of the setup were described [16] in the previous experiment with one Si plate. For this experiment two identical polished, single crystal, 100 orientation Si plates were chosen, 500 µm thick and with a resistivity 0.1−1 Ω cm. They were n-type and doped with P. The resistivity of the plates was measured using the 4-probe technique to beρ ≈ 0.43 Ω cm leading to the concentration of charge carriersñ ≈ 1.2 × 10 16 cm −3 . One of these samples was used as the first Si plate in the experiment. The other one was subjected to thermal diffusion doping to prepare the second, lower resistivity, plate. A phosphorous based...

Modifying the Casimir force between indium tin oxide film and Au sphere

“…[45][46][47][48]52 It was claimed that anomalous dependences of the residual potential difference and separation on contact on the separation distance observed in several experiments cast doubts on the measurements of the Casimir force performed to date. It was also suggested that inasmuch electrostatic calibrations are based on a fitting procedure there is no principal difference detween independent measurements of the Casimir force [20][21][22][23][24][25][26][27][28][29][30][35][36][37][39][40][41][42][43][44]71 and deriving the Casimir force by means of a fit from some much larger measured force of hypothetical origin. 31 In this respect we would like to note that the calibration consists in determination of the parameters of a setup using well established physical laws (in our case of electrostatics) and involves only well understood and precisely measured forces.…”

“…First, we briefly consider the preparation of the sphere which was done similar to previous experiments. [20][21][22]27,28,39,40,43,44 We used a polystyrene sphere which was glued with silver epoxy (20 × 20 µm 2 spot) to the tip of a triangular silicon nitride cantilever with a nominal spring constant of order 0.01 N/m. The cantilever-sphere system was then coated with a 10 nm Cr layer followed by 20 nm Al layer and finally with a 105 ± 1 nm Au layer.…”

“…[20][21][22][23][24][25][26][27][28][40][41][42][43][44] The AFM system consists of a head, piezoelectric actuator, an AFM controller and computer. The head includes a diode laser which emits a collimated beam with a waist of tens of micrometers at the focus, an Au-coated cantilever with attached sphere that bends in response to the sphere-plate force, and photodetectors which measure the cantilever deflection through a differential measurement of the laser beam intensity.…”

“…The Casimir force takes the largest magnitude when both test bodies are made of good metal, e.g., of Au, which is characterized by high reflectivity over a wide frequency region. It was demonstrated [20][21][22] that the Casimir force between an Au sphere and a Si plate is smaller by 25%-40% than in the case of two Au bodies. This was explained by the fact that the dielectric permittivity of Si along the imaginary frequency axis is much smaller than that of Au.…”

What Is Credible and What Is Incredible in the Measurements of the Casimir Force

“…2,5 Independent on separation contact potential was also reported in experiments by U. Mohideen. 2,4,5,[23][24][25] It is notable that all these experiments were performed in high vacuum with small spheres of order 100 µm curvature radii.…”