1. Narrative Overview Questions

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1 Homework 4 Due Nov. 16, 010 Required Reading: Text and Lecture Slides on Downloadable from Course WEB site: 1. Narrative Overview Questions Question 1 (Major MEMS Projects, Past and Present) In a few sentences, describe the goal of the following MEMS activities: 1. Texas Instruments DMD. IBM Millipede. SiTime (recent Silicon valley start-up) Question (MEMS Community) (a) Name a famous researcher in the field of MEMS (excluding Feynman, Petersen, and anybody from the University of Washington) and state what is his/her specific area of expertise. (b) Find a scientific paper published by this researcher in the past years. Give the full citation (author list, title, journal, date). (c) Describe the content of this paper in a brief paragraph. (Use your own words; please do not copy the abstract of the paper.) (d) Try to judge the paper. State what is new, innovative, unusual, creative, etc. Question (Micromachining Basics) Sometimes, MEMS engineers want to create a narrow hole through a wafer (~ 0.5 mm thick, diameter of hole ~ 50µm). Often, such holes are filled with metal to create an electrical connection between the front and the back of the wafer. Such a connection is called a via. (a) Explain the terms aspect ratio, etch rate and etch selectivity in the context of a microfabrication process that creates a via. (b) Let s assume you use a DRIE etch process to create the via hole. What material would you choose for the mask layer that protects the wafer areas which you don t want to etch? How thick does this mask layer have to be? (c) Describe a microfabrication process to fill the via holes with metal. 1

2 Homework 4 Due Nov. 16, 010 Problems Problem 1 (SCREAM Process) It is possible to make modifications to the SCREAM process, which will lead to cross sections that look different from the original process. But here are some cross sections that are impossible (or at least very difficult) to achieve. For each diagram, explain what is wrong with it. (a) This is a cross section after the first anisotropic silicon etch. (b) This is a cross section after the first anisotropic silicon etch, removal of resist, and conformal deposition of SiO. (c) This is a cross section at the end of the process. (d) Propose a variation of the SCREAM process that produces a significantly different final cross section. Draw a diagram and explain your process modification.

3 Homework 4 Due Nov. 16, 010 Problem (MUMPs Process) The MEMS hinge shown in the figure is fabricated using MUMPs. The mask layout for POLY1 is given below. Draw the mask layout for POLY and any other layers that are needed for this hinge in the boxes provided. POLY1 POLY Layer name: Layer name:

4 Homework 4 Due Nov. 16, 010 Problem (Thermal Actuators) The diagram shows a chevron actuator (top view). It consists of two anchors on the left and right, which are attached to the substrate, plus a movable shuttle supported by slightly angled beams. When a current passes from one anchor to the other, the beams heat up and expand, resulting in a displacement of the shuttle. Such a structure could be fabricated with the MUMPs process, where the beams and shuttle are made of the Poly1 layer. Let s assume the dimensions are as follows: Spacing between the anchor and shuttle of l = 100 µm, angle θ = 15. α Si =.6 ppm/k. (a) The entire structure undergoes a change in temperature of 100 K due to a current passing through it. Give an equation for the length of an individual beam as a function of temperature, l b (T). Then calculate the total displacement D(T) of the shuttle. Ignore any curvature the actuating beams may experience. (b) If the actuator had 1/ as many supporting beams, how would the maximum displacement change (ratio: new/original)? How would the force change (ratio: new/original)? (c) Where would an object need to be placed to feel the maximum amount of force from the actuator applied on it? Why? Answer: (a) l b0 b100 = l / cos( θ ) = 10.5µm l ( T ) = l l b D( T ) = D 100 = l b b0 ( T l = D( T (1 + α ( T T b 0 initial + 100K) = l ( T ) l initial Si initial l b0 )) b K) = 0.104µm (1 + α 100K) = 10.56µm l Si (b) Distance ratio = 1. The same total displacement would occur as the beams still expand by the same amount. Force ratio = 1/. 1/ as many beams would cause 1/ as much force to be applied to the shuttle. (c) An object would need to be placed directly in front of the shuttle before the shuttle moves to experience the greatest amount of force. As the supporting beams expand to be longer, the total stress from the temperature change in the beams will reduce and less total force will be available to apply to the object if placed further away. 4

5 Homework 4 Due Nov. 16, 010 Problem 4 (Anisotropic Etching) Potassium hydroxide (KOH) is a commonly used wet etchant for silicon. The result of a KOH etch is very sensitive to the crystalline planes, which are commonly described with integer normal vectors (the Miller index ). For example, the 100 crystal plane has a normal vector in the x-direction. With KOH etching the etch selectivity between the {100} and the {111} planes is very high, such that the {111} planes practically act as etch stop. Let s assume that this selectivity is 75:1. Now consider a KOH etch into a 100 wafer, which creates sloped side walls consisting of 111 planes. a) What angles do the 111 sidewalls make with the 100 surface? b) What angle will you actually observe for your cavity? c) What etch ratio would be needed to make 45 0 side walls? Problem 5 (Comb-drive Actuator) Below is a scanning electron microscope (SEM) picture of a comb-drive electrostatic actuator. In this picture, there are two stationary combs and two rigidly connected moving combs suspended on silicon beams. When a potential is applied between the stationary and the moving combs then the combs tend to move further into each other. Answer the following questions, making sure to indicate the simplifying assumptions you decided to make: 1. Structure of the actuator: what parts of the device are anchored to the substrate, and what parts are moving freely? Where would the driving voltage be applied?. This device was made with a process similar to SCREAM. Show the layout / design in a few drawings (top and side views).. It can be shown that the electrostatic force F el relates to the comb design (number of comb fingers n, applied voltage V, height of combs h, lateral gap between comb fingers d gap ) according to F h el nε 0ε r V d gap =. Show how this equation is derived. 4. Give the basic performance parameters of this actuator: Given a driving voltage V, give the maximum force F max, maximum displacement d max, and fundamental resonant frequency f res. 5

6 Homework 4 Due Nov. 16, 010 Solutions: Parts 1 and : The figure below is a sketch of the top view of the actuator where different structures have been identified: (1) and () are structures anchored to the substrate, and electrically isolated from each other. The driving voltage is applied on these pads. () is the resonant plate. This structure is freely moving and oscillates laterally between the left and right pads. (5) These 4 suspension beams provide the spring structure necessary for the operation of the device. They attach the moving plate to the top and bottom pads. (4) The interdigitated comb fingers (there are of them, moving, on each side of the resonant plate, and 4, fixed, attached to each of the side pads). Parts and 4: Electrostatic force in comb drive actuator (as a function of driving voltage V): F el dw = dx 1 = V dc 1 ( / gap ) == nε 0ε r V = dx d xh dx d h nε 0ε r d where h is the height of the structure, d gap, the separation gap between interdigitated fingers and n the number of fingers. Fundamental resonant frequency: Tang et al. s paper presents an actuator having a structure similar to the one used in this problem, and they arrive at the following expression for the resonant frequency of their actuator: f res 1 = π k ( M M ) p sys where M p and M are the masses of the plate and supporting beams respectively, and k sys is the spring constant. The masses need to be estimated from the volume of the structure and the density of silicon. Assuming that the comb is a perfectly rigid structure, the suspension system of the comb drive shown in the picture consists of 4 beams in an arrangement illustrated below: I: moment of inertia ( k k sys = = k EI k sys = L, where k is the spring constant of one of the four beams L: length of the beam; E: Young s modulus of the material used here (190GPa for Si) 1 I = hw Eh W, W: width of beam) k sys = 1 4 L gap V 6

7 Homework 4 Due Nov. 16, 010 The maximum displacement (backward and forward) is twice the ratio of the force to the spring constant: x nε 0ε r L max = V E d gap W The height of the structure, h, is found to be equal to 10 μm which is consistent with the SOIMUMPs design rules. It is more difficult to measure accurately the finger widths and gap between fingers. However, since for SOIMUMPs, the minimum separation between features is μm, it is safe to assume that W = d gap = μm (which would maximize the displacement). The number of active fingers is n =, ε r = 1 (for air) and ε 0 = F/m. The length of the suspension beams, L, is approximately equal to 0 μm. The mass of the four suspension beams is M = 4.L.h.W.ρ, where ρ is the density of silicon (=. g/cm ) M = kg. The mass of the resonant plate is M p = ( ) h ρ 5%, where the first term in the sum is the approximate volume of the part of the plate carrying the comb fingers, and the second term is the central part of the plate. The 5% factor is to account for the fact that only about 5% of that estimated volume is made of silicon. M p = kg. If follows that: F max = V (in Newtons) k sys = N/m x max = 1.8 V (in nanometers) f res = 8.74 khz 7

8 Homework 4 Due Nov. 16, 010 Problem 6 (MUMPs Process) The materials used in the MUMPs process include polysilicon, oxide or poly silicate glass (PSG), silicon nitride, and gold. After release of MUMPs structures, normally the only non-conducting material left is the nitride. This results in certain limitations on the device design. 1. Show how to create two structures that are mechanically anchored but electrically isolated (such as, for example, the two combs in an electrostatic comb drive).. Give an example of a MUMPs structure in which some oxide remains even after the HF release etch. Hint: you should employ a timed HF release etch. Can you think of a device where this feature might be useful? Describe the materials and dimensions of your structure and the time of HF etch.. Bonus problem: Give an example of a MUMPs structure in which a single released structure has two areas that are electrically isolated against each other. Can you think of a device where this feature might be useful? Solutions: 1. Refer to the design of the electrostatic motor in the MUMPS design handbook chapter1. Any structures anchored entirely on nitride are electrically isolated with respect to the substrate.. If you design a very large Poly1 or Poly plate (say, 100µm squared) without any anchors, then the timed oxide etch will not be sufficient to release the plate completely, and an oxide anchor will remain underneath the plate. 8

9 Homework 4 Due Nov. 16, 010. Here, I was looking for a freestanding structure with different sections that are electrically isolated against each other. This is difficult to do in MUMPs, but here is an attempt: Finding exactly the right dimensions for this design is crucial. Even so, it is not very reliable in practice. 9