Casimir’s Force or Van der Waal’s Force Interaction : Ambiguity in NEMS Logic design

While doing the design of NEMS Logic gate, the most important points we should think wisely whether to go for Casimir’s force interaction or Van der Waal’s force interaction that occur between cantilever beam and electrode surface, otherwise we could do great blunder in the designing our NEMS logic system . Presently, I have successfully design considering both forces  separately and simulated it in COMSOL Multiphysics software. However, we don’t have still the NEMS processing tools for designing NEMS logic that is in nanometre range, where we can verify the reliability issues of our designed logic gates in device form. First of all we should distinguish between Casimir force and Van der Waal’s force properly.

Casimir Force

●Quantum fluctuations in zero point electromagnetic fields.

●In the presence of plates at nm distance, the boundary conditions on the electromagnetic field are altered from free space/vacuum.

●As a result, energy density between the plates is less than that outside which gives rise to a attractive force.

where L is length of cantilever beam used in my Cantilever switch (Inverter) or electrode length. It shows that Casimir’s force will increase rapidly when we are reducing the spacing towards nanometer range and become the dominant force. However, this Casimir’s force equation, also called retarded Van der Waal’s force equation,  doesn’t hold after certain reduction is spacing and need to break it so that it become Van der Waal’s Force equation.

Van der Waals forces

● Includes attractions between atoms, molecules, and surfaces

● Caused by correlations in the fluctuating polarizations of nearby particles

● Force between a permanent dipole and a corresponding induced dipole

● Force between two instantaneously induced dipoles

We have one parameter called plasma wavelength, which will actually determine whether we shall opt Vanderwaal’s force or Casimir’s force. Considering plasma frequency properties of materials, it  has been said that, for separations much less than the plasma wavelength (for a metal) or much less than the absorption wavelength (for a dielectric) of the material constituting the surfaces (typically below 20 nm), the retardation, which is a result of the finite propagation speed of the electromagnetic field, is not significant. In this case, the inter-molecular force between two surfaces is simplified as the Van der Waals attraction. When the separation is large enough (typically above 20 nm) so that the retardation is pronounced, the intermolecular force between two surfaces can be described by the Casimir’s (retarded van der Waals) interaction i.e.

Casimir force acts if initial gap length > Plasma wavelength

Van der Waal’s Force acts if initial gap length  < Plasma wavelength

If this above findings are correct, then we have no issues of being in ambiguity, however, we can actually be sure only when we can have our NEMS Logic gate in devices form and we can check its reliability and functionality issues.

References:

1. Lamoreaux SK (2005) Rep Prog Phys 68:201–236

2. Ramezani et al. Microsyst Technol (2008) 14:145–157

3. Ramezani et al.  Microsyst Technol (2006) 12:1153–1161

4. http://en.wikipedia.org/wiki/Plasma_oscillation

5. http://en.wikipedia.org/wiki/Casimir_force