Automated Design for Micromachining

# Suspension, Folded

## Introduction

A suspension is like a spring, designed to be compliant. However, they are also designed to be stiff in the perpendicular direction.

Figure 1: Layout of a folded suspension.

Model 1: Model of a folded suspension.

## Theory

The compliance of the suspension (along its length) can be calculated by using the following formula:

(1)Cx=L3/24EIz
(2)kx=C-1

Where, Cx is the compliance in the 'x' direction (along shuttle), L is the length of the bending beams, E is Young's Modulus, and Iz is the moment of inertia for the beams in the z direction. The value of Cz, the out-of-plane compliance, uses the same formula, except that Ix is used instead. For the standard design, which has square beams, the two compliances will be equal.

For lateral motion, the shuttle displacement is the result of axial stresses on the bending beams. This will be true until the beams buckle. The compliance in the y direction can be calculated by using the following formula:

(3)Cy=L/AE

Where, Cy is the lateral compliance, A is the cross-sectional area of the bending beams, and the other variables are as described above. It should be noted that this compliance will be much smaller than Cx.

The above equations assume that the other sections of the suspension are rigid. In general, the other sections will be considerably wider than the bending beams. However, to be sure, this pcell ensures that the other segments are at least twice as wide as the bending beams.

## 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.

Table 1: Parameters for the 'suspension_folded' parameterized cell.
Name Description Range Units P1 P2
length The length of the compliant beams. [0,∞) um + +
shuttle_length The length of the shuttle, which is the centre piece connecting all of the compliant beams. [0,∞) um + +
shuttle_width The width of the shuttle. If too small, the shuttle width will be increased to include dimples and the necessary enclosure rules. [0,∞) um + +
truss_width The width of the trusses, which are the segments on the outside of the suspension connecting the compliant beams together. [0,∞) um + +
yoke_width The width of the yoke, which are the two regions at the end of the shuttle. The yoke can be specified wider then the shuttle width to ease connection of the shuttle to other structures. [0,∞) um + +
anchor_width The parameter is used to determine the minimum feature size of the anchors. It is automatically increased if smaller then the minimum width specified in the technology file. The main use of this parameter is to create large anchors for structural support or rigidity if required. [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 suspension and the substrate bulk. true/false - + +

## References

[1] R. Liu, B. Paden, and K. Turner. "MEMS restonators that are Robust to Process-Induced Feature Width Variations," Journal of Microelectromechanical Systems. vol. 11, no. 5, pp. 505-11 (2002).

[2] G. Zhou and P. Dowd. "Tilted folded-beam suspension for extending the stable travel range of comb-drive actuators," Journal of Micromechanics and Microengineering. vol. 13, no. 2, pp. 170-7 (2003).