Introduction
This cell creates an array of cantilevers that have varying lengths. Cantilever, or singly supported beams, can be used for two tests. First, cantilevers can be used to test the maximum release length. Second, cantilevers can be used to measure the non-uniform residual stress.
Theory
Peeling Number
The peeling number is a ratio of the elastic energy to the adhesion energy, and can be used to predict whether or not a cantilever will stick to the substrate once in contact [1,2]
Above, E is Young's modulus, t is the cantilever's thickness, h is the height of the cantilever from the substrate, γ is the energy of adhesion per unit area, and l is the length of the cantilever.
When the peeling number is greater than 1, the cantilever will peel from the substrate, and so not stick to the sruface. However, if the peeling number is greater than 1, this indicates that the minimum energy configuration includes some portion of the cantilever stuck to the surface.
Elastocapillary Number
Similar to the peeling number described above, there is the elastocapillary number [3], which is a compares the elastic energy of the cantilever to the adhesion force due to a liquid droplet between the cantilever and the substrate.
Two parameters were introduced: I is the bending moment of inertia, and θ is the contact angle of the liquid.
Parameters
Any parameter may be modified, if necessary, to meet design rules. Typically, this involves increasing parameters that specify distances, so that minimum line width and minimum line spacing rules will not be violated. This has been extended to the convention of specifying a zero for some parameters to obtain an instance of the minimum size.
In addition to the parameters listed below, several technology parameters also influence the implementation of parameterized cells. This data must be present in the technology library.
| Name | Description | Range | Units | P1 | P2 |
|---|---|---|---|---|---|
| length_min | The length of the shortest cantilever. | [0,∞) | um | + | + |
| length_max | The length of the longest cantilever. | [0,∞) | um | + | + |
| length_step | When creating the array, this parameter determines the difference in cantilever lengths. | [0,∞) | um | + | + |
| width | This parameter determines the width of the cantilevers. If this value is less then the nominal width it will be increased. | [0,∞) | um | + | + |
| anchor | The size of the anchors used to connect the cantilevers to the substrate. If this value is less then the nominal width it will be increased. | [0,∞) | um | + | + |
| include_poly0 | If true, a POLY0 ground plane will be included in the cell. The POLY0 ground plane can eliminate most electrostatic attraction between the cantilevers and the substrate bulk. | true/false | - | + | + |
