NC State University

Guide for Designing Microelectromechanical Systems in MUMPS

John C. TuckerIntroduction

The design of microelectromechanical systems can be very challenging to the designer at times. What makes this field particularly challenging is that the designer must have the knowledge of several different engineers to design a working system. He/she must not only be knowledgeable with integrated circuit layout, but also with the following,
  • structural engineering, such as mechanical spring design;
  • materials engineering, such as thin film residual stresses,
  • solid state engineering, such as contact resistances and parasitic, and
  • semiconductor process engineering, such as photolithography tolerances or how surface topography effects etch rates.
This is a heavy load for a designer to bear. The purpose of this guide is to provide some guidelines for a designer with mainly IC layout experience to design MEMS. This guide geared to the designer using the Multi­User MEMS Processes at the MCNC. MCNC has a guide handbook[1] of their own that explains the process in more detail than this guide. This guide is meant to be a starting point for the designer.

MEMS design is changing rapidly. CAD tools have risen such as the Microcosm's MEMCAD that assist in the whole MEMS design process. Still, the design process can be extremely iterative with each of the design aspects listed above being improved on each process run. 

Spring Design

Figure 1: MEMS Actuator

Polysilicon springs are widely used in MEMS. There are several choices to make when designing a polysilicon spring such as length, thickness, shape, and number of beams. A good starting place for spring design is with simple beam theory. A beam will deflect under force according to:

Equation: Beam Deflection

where F is the applied force, L is the beam length, E is Young's modulus of elasticity of the material, and I is the centroid moment of inertia. For a rectangular beam,

Equation: Centroid Moment of Inertia

where x is the width and z is the thickness of the beam. If a 'T' or 'I' shaped beam is used, then the moment of inertia about the centroid would be different. These moments of inertia can be found in a statics book. For the derivation of these equations see Appendix A.

Combining equations 1 and 2 gives the spring constant for the beam,

Equation: Beam Spring Constant

where,

Equation: Spring force

For structures with more than one beam the approximate spring constant is the sum of each individual spring constant,

Equation: Approximate Spring Constant

This is only an approximation because when beams are attached to platforms as in Figure 4, the spring constant of each individual beam increases. This is due to the fact that the maximum beams now have attached points on each end and the location of maximum slope is no longer at the end of the beam. For more details refer to Appendix AFigure 2: Beam Designs

Typically springs with lower spring constant are desired. To make a spring with a lower spring constant the following can be done:

  • Increase the length
  • Decrease the thickness (This parameter is hard to change using the MUMPS process if the bending motion is perpendicular to the substrate. The only choices you have are between the Poly1's 2 µm or Poly2's 1.5 µm thickness.
  • Add bends for torsion components and extra length
  • Add dimples

Actuator Design

Figure 5: Voltage vs. Displacement Figure 4: Symetrical Actuator

Capacitors and springs can be used together in MEMS to make bi-stable actuators. The force between two parallel plates of a capacitor is,

Equation: Force between two parallel plates of a capacitor

Where, A is the plate area, h is the distance between the plates, and the V is the applied voltage. Thus, the equation for applied voltage versus deflection can be found by combining equations [4] and [6] and rearranging,

Equation: Applied Voltage

where N is the number of support beams and K is determined by

Equation: Actuator Spring Constant

In practice, a designer must pay attention to how field fringing will occur when the device capacitor plates are far apart. Also, actuators are made symmetrically (Figure 4) with at least two support beams so that the top capacitor plate comes down parallel to the bottom. Figure 5 shows a theoretical voltage actuation curve for an actuator made out of Poly2 with capacitor area of 6 µm by 70 µm and beams 3 µm by 70 µm.

Etching Poly Stacks

Figure 7: Poly Stack Process Figure 6: Poly Stack Layout

Thick structures of Poly1 and Poly2 can be fabricated with perfect alignment between the layers by using the POLY2 mask to transfer the image on to both layers. This is done by leaving a large sheet of Poly1 under the Poly2 and using a large POLY1_POLY2_VIA (enclosing POLY1 by 5 µm) to connect the two. The over etch during the POLY2 image transfer etches the underlying Poly1 layer too. Figure 6 shows this layout design. Figure 7 shows what happens during processing. Remember, if Poly1 leads are to extend from the structure then the POLY2 mask must extend over the POLY1_POLY2_VIA by 5 µm so that the Poly1 leads are protected during the Poly2 etch. 

Incomplete Polysilicon Etching

Figure 8: Polysilicon Redeposition

One common problem when patterning thick polysilicon films (especially stacked films) is the deposition of polysilicon stringers or incomplete etching in holes during the reactive ion etching (RIE) of the polysilicon. As shown in Figure 8, when the separation x is to small the polysilicon is not completely removed from the hole. Although the minimum spacing has not been thoroughly investigated, a good rule of thumb is a minimum separation of 10 µm. 

Conductive Paths

Getting electrical signals to the MEMS can be very frustrating. Any polysilicon line can carry electrical signals to the devices. However, there paths are very resistive. For instance, a Poly0 line 30 µm wide and 600 µm long will have a total resistance of 600 ohms (20 sqrs at 30 ohms/sqr). Lines of Poly1 and Poly2 would of the same shape would have resistances of 100 ohms and 200 ohms respectively. However, if the Poly2 line had only 6 µm wide metal on it the resistance would be only 6 ohms . Thus, it is important to use metal when possible lower the path resistances. Sometimes it is necessary to use only polysilicon lines. This occurs when paths need to cross under or between other layers. If this is necessary pay attention to how wide you make your paths. Obviously, the wider the less resistive the path will be. Also, corners and contact methods can effect the resistance of the path. For more information refer to an introductory semiconductor fabrication text[4].
Film Sheet Resistance (ohms/sqr.) Resistivity (milli-ohms-cm) Substrate Capacitance (aF/um2) Released / Anchored
Poly 0
30
1.5
-/111
Poly 1
10
2.0
4.3/136
Poly 2
20
3.0
3.1/140
Metal
0.06
0.00312
-/-
Table 1. Path resistances and path to substrate capacitances (Data taken from the MCNC MUMPS Design Handbook[1])

Another consideration in the electrical design is the contact resistances between different layers. This contact resistances is mainly due to the band alignment and mobility change at the junction of two different materials. Table 2. shows the contact resistivities between poly layer. Metal to poly contact resistances are currently being tested.

Contact Contact Resistivity, (ohms-um2)
Poly0 - Poly1
3060
Poly0 - Poly2
3150
Poly1 - Poly2
1530
Table 2. Contact Resistivities (Table derived from data in the MCNC MUMPS Design Handbook[1])

From the equation,

Equation: Contact Resistivities

the Poly0 to Poly1 contact of contact area 5 µm by 5 µm (2.5e-7cm 2) the resistance would be 122 ohms . Thus, contact resistances can play an important role. To minimize contact resistances make large contact areas. Of course, sometimes this sacrifices area.

Substrate Charges

Figure 9: Substrate Charging

Some measurement of actuator deflection versus voltage have showed that reverse biasing the actuation voltage changes the deflection behavior. One cause for this could be the collection of charges in the substrate just under the nitride in figure 9. Thus, testing is being done to measure the voltage that is being induced in the substrate due to the voltages being applied to the actuators. Substrate contacts have also been made to set the substrate to a desired voltage (possibly ground).

MCNC Design Rules

The following are the tables of design rules described in the "MUMPS Design Guidelines and Rules". The purpose of these rules are to ensure that the designer gets what he wants even with photolithography alignment and resolution limitations. Remember that MUMPs films are very thick, wafer surfaces are non-planar, and very thick photoresists must be used. Thus, photolithography tolerances are very large. In other words, be conservative and don't break the rules unless willing to take chances.

For further explanation of these rules including diagrams, refer to the "MUMPS Design Guidelines and Rules" at http://mems.mcnc.org/smumps/Mrules.html.

Mnemonic Level Name CIF Level Name Nominal Line/Space (µm) Minimum Line (µm) Minimum Space (µm)
POLY0 CPZ 3.0 2.0 2.0
ANCHOR1 COF 3.0 3.0 2.0 
DIMPLE COS 3.0 2.0 3.0
POLY1 CPS 3.0 2.0 2.0
POLY1_POLY2_VIA COT 3.0 2.0 2.0
ANCHOR2 COL 3.0 3.0 2.0
POLY2 CPT 3.0 2.0 2.0
METAL CCM 3.0 3.0 3.0
HOLE0 CHZ 3.0 2.0 2.0
HOLE1 CHO 3.0 2.0 2.0
HOLE2 CHT 3.0 2.0 2.0
HOLEM CHM 3.0 3.0 3.0
Table 3. Critical Dimensions (Data from the MCNC MUMPS Design Handbook[1])
Design Rule Rule Letter Minimum Value (µm) Explanation
POLY0 space to ANCHOR1 A 4.0 Placement ANCHOR1 to PLOY0
POLY0 enclose ANCHOR1 B 4.0 Placement ANCHOR1 to PLOY0
POLY0 enclose POLY1 C 4.0 Enclosure of POLY1
POLY0 enclose POLY2 D 5.0 Enclosure of POLY2
POLY0 enclose ANCHOR2 E 5.0 Placement ANCHOR2 to POLY0
POLY0 space to ANCHOR2 F 5.0 Placement ANCHOR2 to POLY0
POLY1 enclose ANCHOR1 G 4.0 POLY1 coverage of lower levels
POLY1 enclose DIMPLE N 4.0 POLY1 coverage of lower levels
POLY1 enclose POLY1_POLY2_VIA H 4.0 Poly2 does not overlap Poly1
POLY1 space to ANCHOR2 K 3.0 Avoid Poly1 - Poly2 contact
Spacing between lateral etch holes (HOLE1) in POLY1 R <30 (max. value) Release of Poly1 structures
POLY2 enclose ANCHOR2 J 5.0 Poly2 coverage of anchor hole
POLY2 enclose POLY1_POLY2_VIA  L 4.0 Poly2 coverage of via hole
POLY2 cut­in POLY1 P 5.0 Ensure overlap of Poly1 and Poly2
POLY2 cut­out POLY1 Q 4.0 Ensure overlap of Poly1 and Poly2
POLY2 enclose METAL M 3.0 Ensure entire Metal area is on Poly2
POLY2 space to POLY1 I 3.0 Ensure separation of Poly1 and Poly2
HOLE2 enclose HOLE1 T 2.0 Good release results of stacked poly
HOLEM enclose HOLE2 U 2.0 Good release results of poly
Spacing between lateral etch holes (HOLE2) in POLY2 S <30 (max. value) Release of Poly2 structures
Table 4. Design Considerations (Data from the MCNC MUMPS Design Handbook[1])

Don't over look rule R and S make lateral etch hole in large sheets of Poly1 or Poly2 so they will have all the oxide removed from under them during the release step. NCSU has found that 3 µm holes are sufficient to ensure release. For double stacked poly be sure to have both HOLE1 and HOLE2 and follow rule T. Also, if there is metal on the poly follow rule U. 

Process Variations

Process variations can play on important role in the design of a system. For example, if an array of actuators is to be fabricated the across wafer variation can be vary important. The cross chip variations in polysilicon films thickness can cause extreme variations in the actuation voltages. These effects can be extreme because the spring constants have a z3 dependence.

Polysilicon thickness standard deviations are listed at http://mems.mcnc.org/mumpst.html. Some can be quite high while other runs have low standard deviations. For example, one run the standard deviation for the Poly2 layer was 548 Å. Figure 5 shows the difference between actuators with the mean Poly2 thickness of 1.5 µm and actuators with ±548 Å thickness. Also note that the distance between the plates can vary too when the Oxide1 and Oxide2 films vary. 

Bowing of Large Polysilicon Sheets Due to Residual Stress

Figure 10: Residual Stress

Large polysilicon sheets have a noticeable bowing after release due to residual stresses. These stresses can be caused by both thermal stresses and intrinsic stresses[2]. Thermal stress developed when two or more films have a different coefficient of expansion. Intrinsic stresses develop when a file is deposited at a temperature lower than its flow temperature. Thus, a sheet of polysilicon has non-uniform residual stresses through its thickness that causes it to curl up after release[3]. This film is said to be deposited in compression All the polysilicon films are deposited in in tension. As a note some other processes have films deposited in tension and these films bend down. The residual stress is reduced after the annealing step, but large sheets still show bending due to residual stress. As a designer, one must simply pay attention to the fact that there are residual stresses in films that cause them to bend after release. The residual stresses in the MUMPS run can cause about a 4% curl up at the edges of polysilicon beams. Thus, a beam of 100 µm length will be higher on each end by 4 µm than it is in the center. Some measures to reduce bowing are to

  • reduce the ratio of length to width of the sheet,
  • increase the thickness such as with a poly stack, and
  • add reliefs to the sheet as shown in figure 10.

References

  1. Koester, David A., Mahadevan Ramaswamy, Shishkoff Alex , Markus Karen W., "SmartMUMPs Design Handbook including MUMPs Introduction and Design Rules (rev. 4)," MEMS Technology Applications Center, 1996.
  2. Saif, M.T.A., MacDonald, N.C., "Planarity of Large MEMS," Journal Of Microelectromechanical Systems, vol. 5, no. 2, June 1996, p. 9.
  3. Senturia, Steohen D., "Microfabricated Structures fot the Measurement of Mechanical Properties and Adhesion of Thin Films," Transducers '87 Rec. of the 4th Int. Conf. on Solid-State Sensors and Actuators, 1987, pp 11-16.
  4. Jaeger, Richard C., Introduction to Microelectronic Fabrication, vol. V, Addison and Wesley, 1993, pp.66-69. 
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