Influence of van der Waals forces on the waveguide deformation and power limit of nanoscale waveguide devices

The ultrashort-range force, the van der Waals force (VWF), rises rapidly when one nanoscale waveguide (NW) is close to another one, and is stronger than the external transverse gradient force. We theoretically investigate the great influence of the VWF on the device performance in a typical NW optomechanical system consisting of a suspended silicon waveguide and a silica substrate including waveguide deformation stiction and failure mechanism. The device shows unique optically activated plastic and elastic behaviors and stiction due to the VWF. When the input optical power is above the critical power, the waveguide is sticking to the substrate and the deformation is plastic and unrecoverable, even though the total force is less than the yield strength of the waveguide material. This is important and helpful for the design and applications of optomechanical devices.

Figure 1

(a) 3D illustration of the structure. (b) The cross-section view of the structure. The width of the waveguide is $a=500$ nm; the height of the waveguide is $d=110$ nm; $g$ is the designed gap between the waveguide and the substrate, in the absence of deformation. The drawing is not to scale.

Figure 2

(a) The relationship between the VWF per unit length and the gap. (b) The relationship between the TGF per unit length per unit power and the gap. (c) The difference between the VWF and the TGF. The unit is μNm${}^{-1}$. The dashed line is the power-gap curve when TGF = VWF.

Figure 3

The force-deformation response at the simplest case of an assumed uniform load (the solid black lines) and the averaged force for different optical input power at a given shape $u$($x$) = −$D_{\max }$(2$/L$)⁴$x^2$($x$–$L$)² (the dashed colored lines) when considering (a) TGF + VWF and (b) TGF only. In (a), the left intersection is the approximate stable solution at specific optical power. The intersection A represents the original shape caused by the VWF when the optical power is zero. B is the critical point above which the solid black line cannot cross the dashed colored line and there is no stable solution.

Figure 4

The evolution of the deformation shape versus the optical power by (a) the total force (TGF + VWF) and (b) TGF only. The white and red shaded areas are the elastic and plastic deformation range, respectively.

Figure 5

(a) The relationship between the final $D_{\max }$ and the optical power for TGF, VWF, and TGF + VWF, respectively. (b) The critical power at different waveguide lengths for TGF + VWF. The horizontal part of the blue triangle line means that when the gap is smaller than a critical value (which is 49.65 nm for $L=35$ μm), the VWF will pull the waveguide straight to the substrate without the existence of the TGF. It can be estimated that there will be the same phenomenon for $L=25$ μm and $L=30$ μm.