1 N.CHEUNG EE143, F2010 Homework Assignment # 12 (Due Dec 3 ,Fri 9am) THIS IS THE LAST HW ASSIGNMENT FOR THE SEMESTER Reading Assignment 1) Jaeger Textbook, Chapter 11 on MEMS 2) Reprint in Bspace: “Stress in Thin Films” Reprint. 3) Reprint Bspace , Sections of Kovac “Mechanical Transducers” -qualitative understanding of MEMS principles 4) EE143 Lecture Notes Problem 1 Thermal Stress in thin films A 1 m thick Al film is deposited without thermal stress on a 50 m thick Si wafer at a temperature 100°C above ambient temperature. The wafer and film are allowed to cool to the ambient. Using the values provided in the table and assuming a Poisson ratio = 0.272 for Si Thermal Expansion coefficient ( 10 -6/ o C) Youngs Modulus ( 10 11 N/m2) Al 24.6 0.7 Sl 2.6 1.9 (a) Calculate thermal strain and stress for T = 100°C. (b) Calculate the radius of curvature of the substrate Problem 2 Stress of dual films A 500 m -thick bare Si wafer is originally has a radius of curvature of +300 m. After a 300nm-thick oxide deposition, the wafer radius of curvature is measured to be +200 m. (a) Calculate the stress of the oxide film . Indicate compressive or tensile. (b) A 600nm nitride film is then deposited on top of the oxide and the wafer radius of curvature becomes +240m.. Calculate the stress of the nitride film alone. Is the nitride stress compressive or tensile? (Given: Si= 0.272, ESi = 1.9 x 10 11Newton/m2 ) RADIUS OF CURVATURE RELATIONSHIP : f = Es ts2 ( 1- )s 6 rtf ) Problem 3 Cantilever Deflection and Resonate Frequency A polysilicon beam is 50 µm wide by 500 µm long and 0.5 µm thick. a) Determine the deflection of the end caused by gravity (g = 9.81 m/s2 and 1N = 1 Kg m/s2). b) Determine the fundamental resonant frequency of the beam. c) Now assume that one monolayer of chemicals is uniformly adsorpted on both sides of the beam which can be modeled by a mass increase of 1% (but no change in thickness). Find the change in the end deflection in µm and the change in the resonate frequency in cycles/sec. d) With the results obtained in part c, discuss which method is easier to detect the changes. Problem 4 MEMS Processing (Previous Exam question) The following brief description is taken from a MEMS textbook :2 “Doering, et al. demonstrated a thermal bimorph cantilever that combined the use of the Coanda effect with forced convection, to allow a laminar flow to be steered into one of two outlet ports under electrical control (see figure at left). They used an electro-chemical etch-stop and plasma etch edge release to form 11 m thick n-epitaxial cantilevers that included a p++ boron diffusion for heating resistors and an 11 m aluminum layer to form the bimorph with silicon (see cross section at right figure).” Principle of a thermal bimorph cantilever directing fluid flow into one of two outlets [Background information- The n+ contact for etch stop is an n+ island fabricated on the n-type epitaxial Si. By applying a voltage at the n+ contact during KOH etch of the p-type substrate, etching rate will stop at the pn boundary.] (a) To aid your understanding of how this device operates, draw a top-view of the device. Label all important boundaries. (b) When the p++ resistor pattern is heated up by resistive heating, will the cantilever structure curve upward or downward? Briefly explain. (c ) Starting with a p-type Si wafer with an n-type epitaxially grown Si, design a process flow to fabricate the bimorph device. Describe the process steps in the left column and sketch the cross-sections in the right column PROCESS DESCRIPTION CROSS-SECTIONS Problem 5 MEMS-before-IC Process The following cross-section shows a poly-Si MEMS integrated with CMOS devices. The CMOS uses a p-well inside the n-type epitaxial layer. For simplicity, only the NMOS transistor is shown [the PMOS transistor fabricated on the n-type epi layer is not shown explicitly]. Al is used as Metal-1. Start with the epitaxial layer on Si substrate, design a process flow to fabricate this microsystem. Show cross-sections at major process
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