HW_3-Solutions2007

# HW_3-Solutions2007 - EECS 414 Introduction to MEMS Homework...

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1 EECS 414 Introduction to MEMS Fall 2007 Homework #3 Total: 180 Points Handed Out: Friday Sept. 21, 2007 Due: Friday Sept. 28, 2007 1. This problem deals with etching of the silicon device shown below. The figure shows the cross section and the top view of the device before it is etched in EDP. The device is now etched in an orientation-dependent etchant like EDP. Assume that EDP does not etch silicon oxide, and assume that it etches (111) silicon at a much slower rate than (100) silicon. The device is made in (100) silicon and the layout is aligned with the <110> flat as shown. Now etch the device in EDP for a long time and then pull the device out of the etchant. Show a cross-sectional view of the device along the A-A' line as shown and also show a view of the device from the bottom of the wafer. Note that you should label all of the relevant areas, and show all of the important dimensions on your drawings. Please make sure everything is clear to be able to obtain partial credit for your solutions. 20 points

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2 Solution: The final cross section is shown below. The etch will proceeed from the back and will stop as usual on the (111) planes. When the etch reaches the bottom of the square defined by the trench, it will continue to etch towards the top oxide layer, but now a new set of (111) planes will appear inside the square as shown. These planes will go down at an anngle of 54.7 until they reach the top oxide and the etch will stop there. Note that there is a region where you have (111) planes on the inside of the square.
3 2. It was said in lecture that usually anisotropic wet etching of silicon is more desirable than isotropic wet etching. Name 3 uses of isotropic etching. 5 points Solution: Isotropic etching is used for : Removal of damage or polishing Si Creating structures with round surfaces Thinning silicon wafers Delineation of electrical junctions or defects 3. In the top-view diagram below, the shaded part of a p-type (100) Si wafer has a thin p++ (meaning heavily boron doped) layer with concentration of 10 20 cm -3 . The chevrons are at the same level as the shaded region, but are of plain undoped Si. The dimensions are as follows: L1=50μm, L2=25μm, L3=100μm, t 50μm. (a) Draw the cross sections A-A’ and B-B’ after etching for a long time in EDP. Find the etch depth d. Label the angle between {111} and (100) planes. Also label d and L1. (b) Now t=25μm. Repeat (a) with this new value of t (note: you can assume that the diastance t is just a bit smaller than 25μm, this will influence your final answer). 30 points Solution: (a) Etching is stopped by the {111} planes shown in the A-A’ cross section.

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4 7 . 54 tan 2 / 1 = L d m L d μ 3 . 35 7 . 54 tan 2 1 = = m d L L 50 7 . 54 tan 2 3 4 = ! = (b) Now t= 25 µ m. Since the top edge of the{111} planes in the A-A’ cross section just meet
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## This note was uploaded on 09/23/2008 for the course EECS 414 taught by Professor Maharbiz during the Fall '06 term at University of Michigan.

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HW_3-Solutions2007 - EECS 414 Introduction to MEMS Homework...

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