Problem 1 (MUMPs XXXXXXXXXX =24 points (a) Draw a design layout (top view) for the MUMPs process that would produce the following cross section (schematic drawing, not to scale): Note: please use the dimensions given on the axis in your layout (b) Often, you want to make electrical connections to a device built with the MUMPs process. For this purpose, designers add bond pads to the layout. These bond pads are electrically connected to the device, usually with a polysilicon wire. During testing, bond pads provide a convenient way to place a microprobe tip. During packaging, a fine gold wire is permanently bonded to the pad. Describe your optimal design for a bond pad, i.e., what stack of materials would you use for a MUMPs bond pad? (c) In released MUMPs structures that include a gold layer, thermal stress is a severe problem, causing bending and warping of movable structures. This is particularly unpleasant for the fabrication of micromirrors. Show the layout (top view) and cross sectional view of a 30µm × 30µm MUMPs suspended micromirror that minimizes warping induced by thermal stress. Note: this mirror should be as thick and stiff as possible. SP2 Examinations – Introduction to Microelectromechanical Systems 3 Problem 2 (Electrostatic Actuator XXXXXXXXXX + 6 = 36 points Consider the comb drive shown in the figure to the right: ? Number of comb fingers: n = 10 ? Finger height: h = 10µm ? Finger length (overlap region): l = 20µm ? Gap spacing: d = 4µm ? Permittivity of free space: e0 = XXXXXXXXXXF/cm ? Relative permittivity of air: er ˜ 1 a) Assume that the comb is suspended on a spring structure that allows it to move in the ±x direction. Calculate the spring stiffness Kx such that the comb moves by 10µm when a voltage of V=50V is applied. b) Unfortunately, spring suspensions usually also permit motion in undesired directions. Let us consider motion in the ±y direction. If the fingers are exactly centered, then the electrostatic force in the ±y direction is zero. Derive a formula that describes the electrostatic force Fel,y as a function of offset y. Note: for this formula, you do not need to take into account fringing field effects. (c) Plot this function for the range y = -d…d. (d) What does the slope at y=0 indicate? (e) The suspension for the comb also has a spring constant Ky with respect to motion in the ±y direction. To prevent the comb drive from becoming unstable (i.e., snapping sideways and shorting out), how would you choose Ky? Give a brief verbal explanation, a formula, and a specific number for Ky . (f) The calculations above show that the comb suspension has to be much stiffer in the ±y direction than in the ±x direction (i.e., Ky >> Kx). Draw the top view of a layout design for a comb drive suspension that has this property and briefly explain how/why it works. SP2 Examinations – Introduction to Microelectromechanical Systems 4 Problem 3 (LIGA) 12 points A watch manufacturer orders a large quantity of tiny gears from you. You plan to produce the gears with the LIGA process. The X-ray lithography mask will include a large array of gear shapes. Indicate whether you need a clear field mask or a dark field mask. Consider the following two cases and briefly explain your choice: (g) The watch gears will be made of metal. (h) The watch gears will be made of molded plastic. Problem 4 (Various Short Questions) 5 ? 4 + 1 ? 8 = 28 points 1. Explain what is meant by parallel microassembly. Describe the two major subclasses of parallel microassembly, and give an example for each. 2. (a) List the protective gear that you put on before entering the cleanroom. (b) Which of these items protect you from HF burns? 3. Reactive ion enhanced (RIE) etching is increasingly popular because of good selectivity, “dry” processing, and high etch rates. However, sometimes etched trenches develop so-called “grass,” i.e. areas of very high surface roughness at the submicron scale. This can happen even with a flawlessly prepared wafer, and a perfectly clean processing chamber. Explain where this “grass” could come from! 4. Give a sample process for (a) high aspect ratio MEMS, (b) surface micromachining, (c) bulk micromachining, (d) micro molding, (e) a MEMS fabrication process that does not fall into any of these categories. 5. In various microfabrication processes including RIE etching, deposition and etch rates may vary across the wafer, for example with higher etch rates towards the center of the wafer. This is often due to so-called “loading effects” which occur when the process sample influences the conditions inside the chamber. Now suppose you receive a batch of chips from your favorite foundry, and you find that there is some significant variation in film thicknesses or etch depths between them. Is it likely that this variation is due to the loading effects at different locations on the wafer? 6. Suppose you want to detect a specific substance using a MEMS “electronic nose.” The device consists of a cantilever (single crystal silicon, length 200µm, width 5µm, height 2µm). The cantilever surface is chemically treated such that it can adsorb a thin layer (˜10nm) of the substance with very high selectivity. Estimate the change in resonance frequency that the cantilever experiences during adsorption. Young’s Modulus for silicon E = 100GPa, density of silicon ?si = 2.33gr/cm3 , density of the test substance ?T = 1gr/cm3 .