EECS 245 Intro to MEMS

EECS 245 Intro to MEMS Final Exam, Fall 2000 Name : SID :

1) Give a short answer to each of these questions: a. Your friend from Stanford says that xenon difluoride would make a great etchant for releasing polysilicon structures in a MUMPS process. Do you agree?

b. Your friend from UCLA says that for any simple spring-mass system, the deflection due to gravity (a 1-g field) is just given by x = (1 g) / 2 . Prove that she’s right.

c. Your friend from MIT is using the Bosch process in the STS DRIE. He says that the deposition step for the Teflon-like film slows down the process too much, and he plans to run his next wafers without it. What do you tell him?

d. Your friend from Stanford has built a piezoresistive pressure sensor with a thermal compensation circuit. He says that compensating for the thermal coefficient of resistance in his sensor removes all noise, and he can resolve arbitrarily small signals. What do you tell him?

e. Your friend from Davis claims that he can make his ultra-sensitive low- frequency acceleration measurements more accurately if he vacuum packages his accelerometer. Do you believe him? 2)In the Cronos MUMPS process, assume that all oxide etches are perfectly selective to silicon but etch nitride at the same rate as the oxide. Assume that the polysilicon etches are perfectly selective to oxide, but etch nitride and all types of silicon at the same rate. Assume that all etches are perfectly anisotropic. Assume the following simplified process flow:  LPCVD nitride, 0.6 microns  LPCVD poly, 0.5 um /PLY0, no overetch  LPCVD PSG, 2um after anneal / DMP 0.75 micron timed etch  /C1S no overetch  LPCVD poly, 2 um /PLY1, 20% overetch  LPCVD PSG, 0.75 um after anneal /C21 20% overetch  /C2S 20% overetch  LPCVD poly, 1.5um /PLY2 200% overetch

Carefully draw the cross-sections on the following page, and label your layers: C1S DMP C21 DMP C2S

PLY1 PLY2

C2S C21 C21 PLY1 PLY2 C2S

-2um 3. You are testing a Tang-style SOI comb-drive resonator. You predict that the spring support will have a spring constant of 100 N/m. There are 50 moving comb fingers (and 100 gaps). The SOI thickness is 10 microns, and you are using 1 micron line/space lithography for your combs. You drive the resonator with a 15V DC voltage on the structure and ground plane, and a 15V AC voltage on the fixed comb fingers. You calculate the resonant frequency as 10,000 radians/second. You are testing in partial vacuum, so you expect a fairly high Q. a) Calculate the total force f(t). b) Calculate the expected displacement x(t). You may use the magnitude of the force/displacement transfer function ( H(jw) ) in your expression if you wish. c) as you slowly increase the frequency of the AC excitation from low frequency, what is the lowest AC excitation frequency at which you expect to see motion? Assume that with the microscope you can see DC and AC displacements only if they have an amplitude of at least 1 micron. d) When the AC excitation frequency is near 10,000 rad/sec, you measure a peak displacement of 30 microns. What is the approximate Q of your resonator?

a) f(t) = b) x(t) = c)  = d) Q= min 4. You have built a comb drive with gaps of dimension g0 in a film of thickness t. You have designed the comb drive to move in the x direction, and have a suspension with a stiffness Kx in that direction. Motion in the y direction is undesired, but nonetheless there is some compliance in that direction, and you have calculated a spring constant of Ky in that direction. You can ignore rotation because of the way you designed your suspension. You apply a voltage V across your comb drive to generate a force in the x direction, but you also get “gap-closing” forces, equal and opposite, in the y direction. On the graph below, I have sketched the spring force on the moving comb as a function of its y displacement. a. Sketch the gap-closing forces as a function of the comb-finger y displacement, assuming a fairly small voltage on the comb. b. Sketch the total force on the comb finger as a function of y displacement. You should find 3 equilibria – 1 stable, and two unstable. Label them as such. c. Write down an expression for the total y force on the comb finger. Pay close attention to the signs of the three forces! d. As the comb voltage increases, the slope of the total-force curve at the origin becomes less and less negative, ultimately leading to y-direction instability of the comb. Calculate an expression for the y-direction pull-in voltage.

Fy K y

K x L o y V - g0 g0

c) F(y) =

d) Vpullin =