L3 - MEMS Statics

Question 1

What is the formula for Axial Stress?

Answer 1

σ = F/A

Where σ is the stress in N/m² or Pa, F is the force applied, and A is the area.

Question 2

What does Axial Strain represent?

Answer 2

ε = ΔL/L0
Axial strain is defined as the deformation of a material along its length when subjected to an axial load.

Where ε is the axial strain, ΔL is the change in length, and L0 is the original length.

Question 3

What is Young’s Modulus?

Answer 3

E = σ/ε

stress over strain

Young’s modulus measures a material’s resistance to elastic deformation.

Question 4

What does Hooke’s Law state?

Answer 4

Stress and strain are linear in the elastic region

It relates force per unit area to displacement in the elastic region.

Question 5

What is the yield strength (σy)?

Answer 5

Stress required to produce a slight but specified amount of plastic strain

Typically noted with an offset of 0.002.

Question 6

What is Poisson’s ratio (ν)?

Answer 6

ν = -εl/εa
Applying axial strain (εl) causes lateral strain (εa).

It is the negative ratio of lateral to axial strains for elastic deformation.

Question 7

What is the formula for Shear Stress?

Answer 7

τ = F/A

Where τ is shear stress in N/m² or Pa.

Question 8

What is Shear modulus?

Answer 8

G = τ / γ

Shear stress over strain

Question 9

What is the formula for Shear Strain?

Answer 9

γ = ΔX/L

Where γ is shear strain measured in radians.

Question 10

What is the relationship between Young’s Modulus (E) and Shear Modulus (G) for isotropic bodies?

Answer 10

2G = E/(1+ν)

This relationship holds for isotropic materials.

Question 11

What is the most common Silicon Miller Index ?

Answer 11

[100]

perfect alignment with the YZ plane

Question 12

What is a Miller Index?

Answer 12

Silicon waffers properties change depending on the crystal alignment.
The Miller Index indicates the wafers crystal alignment.

Question 13

How is the Miller Index Calculated?

Answer 13

An M.I. of [1 0 1] could be drawn as a plane that intersects:
The X axis at 1
The Y axis at 0
The Z axis at 1

Question 14

What are the types of support in plane statics?

Answer 14

• Built-in (Encastré)
• Fixed / Pinned
• Constrained Roller

Rollers are very uncommon

Question 15

What are the joint types used in MEMS designs?

Answer 15

• Fixed
• Pinned (able to rotate)

Question 16

In MEMS statics what are the Load types?

Answer 16

• Point Load (N)
• Distributed load (N/m)

Question 17

What is the significance of bending of beams in MEMS devices?

Answer 17

Many MEMS devices are based on moving elements supported by flexural suspensions

Bending effects must be considered for accurate design.

Question 18

A silicon bean has dimensions x, y, z and is subject to an axial load of 1uN
calculate the increase in length

x between 75 and 200um, y between 2 and 10um, z between 1 and 5 um.

Question 19

True or False: Gravitational loads are always significant in micromechanical devices.

Answer 19

False

Gravitational loads are almost always negligible in MEMS design.

Question 20

What is the mechanical behavior of materials described by Young’s modulus?

Answer 20

Material’s resistance to elastic deformation

The greater the modulus, the stiffer the material.

Question 21

What is one major advantage to square diaphragms over circular ones?

Answer 21

The ease with which they can be manufactured with intergrated sensors. The sides can be made with piezoresistive elements.

Question 22

A Cantilever beam with dimensions x,y,z has a point load applied at the free end. Calculate the deflection

x (75 to 200um) y (2 to 10um) z (1 to 5 um) F (1 to 5um)

Question 23

A circular diaphragm is subject to a pressure of 1 atm
Calculate the deformation at the centre.

t = 1.5um r = 50um y=0.22 E=160GPa