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ME 119: Introduction to MEMS

MIDTERM

October 26, 2004

90 minutes

Name:_______________________________

Student ID:___________________________

Instructions: Write your answers on these pages, showing all steps of your work. Partialcredit will be awarded only to the extent that we can understand what you are doing. Someparts of the exam may be harder than others; if you get stuck, go on to the other parts andcome back later if you have time. This is a closed-book exam; however, you may use onlyone 3 x 5 crib sheet of your choosing.

GOOD LUCK!

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1. Quickies

a. What distinguishes surface micromachining from bulk micromachining?

b. Name 3 methods of creating a SiO2layer on a silicon wafer.

c. Fill in the blanks: To achieve an isotropic etch during reactive ion etching, one can

use ________________ gas pressures. This is in contrast to anisotropic etching during

reactive ion etching, where the gas pressures are ___________________.

d. Name 3 ways to move fluid through a microfluidic channel. How are they different fromone another?

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e. Determine the resolution of a mask aligner if the wavelength of light = 436 nm, thenumerical aperture N.A. = 0.35, and the constant for the lithography process is k1= 1.61.

f. Scaling laws: Determine how the following scale with length:

i. Magnetic force between two wires

F= 2rn o

IaIb dl

where o is the permittivity constant, Ia and Ib are the currents flowing throughwires aand b, l is the length of the wires (assuming they have the same length),and dis the distance between the two wires.

ii. Resonant frequency of a cantilever

fo =2r

1mk

where

k=l 33EI

Here, E is the Youngs Modulus, m is the mass cantilever, I is the moment ofinertia, lis the length of the cantilever.

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iii. Diffusion

D=6r hrkB T

where kB is the Boltzman constant, T is temperature, is viscosity, and r is theradius of a particle (assuming a spherical particle).

g. Outline (i.e. sketch) the steps for Deep Reactive Ion Etching.

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h. Thermal oxidation may either take place in a wet (H2O vapor) or dry (H2) environment. Inwhich environment does the oxide grow faster? Which environment leads to a better qualityoxide?

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2. The (100) silicon wafer has 0.3 m of silicon dioxide at specific locations (see figurebelow).

a) Calculate the oxide thickness after a wet thermal oxidation at 1000oC for 1 hour in bothregions. The following constants may be helpful to you.

Deal-Grove rate constants:Temp (oC) A( m) B( m2/hr) B/A ( m/hr)1000 0.226 0.287 1.27

b) What would the oxide profile be after oxidation?

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b. In cantilever design, we require high flexibility beams to minimize the forces exerted onthe sample and as such minimize distortion and damage to the substrate while scanning.

AFM cantilevers are typically designed with a spring constant of about 0.5 N/m. We alsodesire a quick response during the AFM scanning process which requires the cantilever tobe designed for high resonant frequency. Suppose we can deposit a 2 m thick, defect

free, silicon carbide film, and that 100 m is a typical cantilever length. What would be thewidth of the cantilever, if would like to operate at 200 KHz (the density of silicon carbide is3.2 g/cm3)?

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4. Suppose you have an Electrostatic Actuator shown below.

TOP VIEW SIDE VIEW

The actuator works by applying a voltage across the lower electrode while the upperelectrode is held at ground. In so doing, the two electrodes are capacitively coupled and theupper electrode can flex depending on the applied voltage. The distance between the twoelectrodes is g

o= 1 m and the voltage applied is V = 2 V.

a. Sketch a process diagram which would allow you to make such an actuator. You mayassume a silicon substrate.

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b. What is the areaAof the lower electrode in m2such that the electrostatic force on the

plate is 100 N. The permittivity of free space o= 8.85 x 10-12C2N-1m-2. Hint: The energy

stored in a capacitor is

U=2

1CV2

c. What is the electrical spring constant ke in N/m for the applied voltage and lower

electrode area you found in (b). If you were unable to solve part (b), please useA= 2500m2.

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