University of California, Berkeley
Electrical Engineering and Computer Sciences Department
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EE245, Fall 2008
Introduction to MEMS Design

Tuesday and Thursday:  3:30 - 5:00 pm
3106 Etcheverry Hall

Discussion Section:
Section 101 - Monday, 5:30 to 6:30 pm, 3109 Etcheverry.

Prerequisite:  Graduate standing in engineering or science; undergraduates with consent of instructor.

Note that the prerequisite requirement (or apparent lack of one) for this course reflects the fact that the course itself is meant to serve all engineering departments.  this is not to say that no prior knowledge is required for this course; rather, it is more a statement that if you lack the necessary background knowledge, you will need to study and learn the material somewhat independently.   In particular, although some of the background material will be covered in lecture, there is simply not enough time to do a thorough job of it.   Thus, those less familiar with the material will need to turn to supplementary materials, such as the reference texts.

Note that this course will rely on concepts from numerous disciplines, from electrical engineering, to mechanical engineering, to materials science, to bioengineering.   Thus, it is likely that nearly everyone will need to struggle with unfamiliar material at some point in the course.



  • S. Senturia,  Microsystem Design, 2nd Printing
  • Various material to be distributed throughout the course.


  • G. Kovacs,  Micromachined Transducers Sourcebook
  • Jaeger,  Introduction to Microelectronic Fabrication (Vol. V of the Molecular Series on Solid State Devices), 2nd Edition

References:  (on reserve)

  • C. Liu,  Foundations of MEMS
  • N. Maluf,  An Introduction to Microelectromechanical Systems Engineering
  • J. Pelesko & D. Bernstein,  Modeling MEMS and NEMS


Professor Clark T. Nguyen
574 Cory Hall
Phone: (510) 642-6251

Office Hours:
Monday, 14:30-16:00
Wednesday, 10:00-11:30
(to be modified in case of conflicts)
574 Cory Hall

Teaching Assistants:

Mehmet Akgul
373 Cory Hall
Phone: (510) 642-1143

Office Hours:
Monday, 11:00-12:00
Tuesday, 11:00-12:00
Moore Room, Cory Hall Courtyard

Ilya Gurin
373 Cory Hall
Phone: (510) 643-9825

Office Hours:
Wednesday, 15:00-16:00
Thursday, 11:00-12:00
Moore Room, Cory Hall Courtyard

Course Administrative Assistant:
Rosita Alvarez-Croft
(510) 643-4976

Course Details:
Course Information
Grading Procedure
Academic Dishonesty Policy

Office Hours are the primary mechanism for individual contact with Professor Nguyen and the TA's. All Students are strongly encouraged to make use of office hours.

Course Description:
Physics, fabrication, and design of micro-electromechanical systems (MEMS). Micro- and nano-fabrication processes, including silicon surface and bulk micromachining and non-silicon micromachining. Integration strategies and assembly processes. Microsensor and microactuator devices: electrostatic, piezoresistive, piezoelectric, thermal, magnetic transduction. Electronic position-sensing circuits and electrical and mechanical noise. CAD for MEMS. Design project is required. Also listed as Mechanical Engineering C218.

Course Format:   Two one and a half hour lectures and one hour of discussion per week.

[4 Units]


  • Dec. 11, 2008
    The LF1356 Data Sheet and the SPICE netlist have been posted in the Handouts section below with the Design Project information.

    The Final Exam on Sat., Dec. 20, 2008 in 247 Cory Hall from 12:30 - 3:30 pm (sharp).

  • Dec. 10, 2008
    Solutions to homework 6 have been posted below.

    An error has been found in the strain formula on page 9. The solutions have been reposted with a revised page 9.

  • Dec. 9, 2008
    Information about the final and Final Solutions, Fall 2007

    Pre-lecture 27 notes have been posted in the lecture section below.

  • Old announcements:

  • Dec. 1, 2008
    HSpice templates have been posted in the homework section. The two files work together in a modular way (via the .include statement). Run HSpice using the analysis file as input; the data in the equivalent-circuits file will be included automatically. You may want to make one copy of the analysis file for each of the four analyses that you will do for parts (e) and (f), and modify it accordingly.

    Circuit elements and element values relevant to the homework have been blanked out and replaced with the symbol '*****' as a placeholder. If you try to run the files as they are, HSpice will abort. You need to replace each placeholder with a syntactically correct expression in order for HSpice to run successfully.

    You may use other versions of SPICE if you wish. (For instance, AIM-Spice is distributed for free and runs on Windows.) However, you may need to modify the files. (For instance, for AIM-Spice, you will need to remove the .ac command, and the asterisk may no longer work as a comment indicator.)

    Full documentation for HSpice is available here (login is required). You will probably need hspice_quickref.pdf to learn HSpice. For more depth, you can download hspice_command_ref.pdf and hspice_sim_analysis.pdf. AWaves is simpler, but you may also want to download avanwaves.pdf.

  • Nov. 26, 2008
    Ilya's office hours today are canceled. Make-up office hours will be held next Tuesday, 17:00-18:00.

    The read-ahead notes on gyro design have been posted in the Handouts section below. These specifically address determination of the minimum detectable signal (MDS) of a gyroscope, but are also useful to help you with concepts like scale factor, which you should be reading about in the literature. This file also shows the equivalent circuit of the sense mode of a gyroscope. Note how the Coriolis force is applied to the lcr mechanical equivalent circuit representing the mass-spring-damper in the sense mode. Also, note how the Coriolis force factors into the expression for scale factor.

    You know enough to understand the first few slides of this; the rest of this gives a complete account of the noise analysis needed to determine the MDS. As I mentioned in class, I would like to define some parameters that do not require that you understand noise, but that still allow you to design to meet the ARW spec. Pursuant to this, slide 4 of the attached defines the ARW, and you can see that it depends on the ratio between an equivalent rms noise current ieqTOT and the scale factor A. You should be able to determine the scale factor from what you’ve already learned. For the noise current, just use the following expression:

    ieqTOT = √[is2/Δf] + ieq
    Removed by ivg, 11/28 - see updated formula in PDF sent today

    where is2/Δf is given on slide 6, and ieq = 1.3 x 10-13 A/√Hz (which I am now just giving to you, but the notes actually derive this for sense circuit used in the notes).

    For ARW, the design specification says 0.1 deg/√Hz. This is actually not the right units; they should be deg/√hr. Please use ARW = 0.1 deg/√hr for the project.

    This should be enough information now for you to be able to design the mechanical structure for your gyroscope. Please go ahead an email me if you have questions, or see me in office hours.

  • Nov. 25, 2008
    Homework 6 has been posted. Sorry about the delay; we had some last-minute difficulites.

  • Nov. 21, 2008
    Lecture 23 has been posted in the Lecture section below.

  • Nov. 20, 2008
    Because Prof. Nguyen anticipates missing a lecture later in the semester, next week's discussion (Nov. 24) will be turned into a lecture.

    Pre-lecture 23 has been posted in the Lecture section below.

  • Nov. 19, 2008
    Lecture 22 has been posted in the Lecture section below.

  • Nov. 18, 2008
    Solutions to homework 5 have been posted.

    Pre-lecture 22 has been posted in the lecture section below.

    Important clarification regarding resonance frequency. √(k/m) gives the frequency in radians/s. You then need to divide by 2π to get the frequency in cycles/s (Hz).

  • Nov. 14, 2008
    The EE245 Design Project has been posted in the Handout section below.

  • Nov. 10, 2008
    Review of Op Amps notes from Fall 2007 have been posted in the Handout section below.

  • Nov. 6, 2008
    Lecture 20 has been posted in the Lecture section below.

  • Nov. 4, 2008
    A short summary of HSPICE and example netlists are posted in the Discussion Section Materials section.

  • Nov. 4, 2008
    Pre-lecture 19 has been posted in the Lecture section below.

  • Nov. 2, 2008
    Homework 5 has been posted.

    Ilya's Thursday office hour this week has been moved.

    The notes for Monday's dicussion have been posted.

  • Oct. 28, 2008
    Two more corrections to the homework 4 solutions have been posted.

  • Oct. 23, 2008
    The solutions for homework 4 problem 1(c) should read: "w = 165 nm" for the tip elevation, according to both solution methods.

  • Oct. 21, 2008
    Updated Information about the midterm (Errors fixed)

  • 10/20/2008
    Special office hours for the day before the midterm have been posted. Ilya's regular office hour that day will move by one hour.

    An outline for today's discussion has been posted.

    An error has been uncovered in the discussion outline. The displacement v0 is correct as shown, but the stiffness kc equals 3EIL-3, and the stiffness kt is half of that.

  • Oct. 16, 2008
    Information about the midterm and Midterm 1 Solutions from Fall 2007

  • 10/15/08
    In case any of your Cadence keyboard shortcuts have not been working, a keyboard shortcuts file and readme has been uploaded. The link is in the homework section.

  • 10/13/08
    Solutions to homeworks 2 and 3 have been posted.
    Based on preliminary examination of the submitted homework 3, all students are highly encouraged to look at the solutions for parts (a) and (b).

    Some clarifications and corrections to Homework 4 have been posted. A second problem has been added, and the deadline has been extended until next Tuesday.

  • 10/9/08
    The techfile is posted for HW#4 in the homework section.
    The included hw4_README.txt file can help you to get started with Cadence.

  • 10/9/08:
    Homework 4 is posted in the homework section.

  • 10/7/08:
    Some clarifications on homework 3 have been posted.

    The notes from last night's discussion have been posted.

    The solutions to homework 1 have been fixed; all the images are visible now.

  • 9/28/08:
    Homework 3 is posted in the homework section.

    Sorry about the delay posting homework 3; we're still working out the details.

  • 9/25/08:
    Three new Micromachining handouts have been posted in the handouts section.

  • 9/24/08:
    The solid solubility curves from Jaeger have been posted in the handouts section, and the clarifications have been updated.

  • 9/23/08:
    Some clarifications regarding homework 2 have been posted in the homework section.

  • 9/21/08:
    Professor Nguyen's office hour has been moved for Monday, 9/21 only.

  • 9/16/08:
    Mehmet's office hours have changed, effective immediately.
    Ilya's office hours will change, effective next week, to avoid conflicting with the BSAC seminar.
    See above for details.

  • 9/15/08:
    Two references for Cadence have been posted in the Handouts section.

  • 9/11/08:
    The discussion handouts from Wednesday have been posted (see bottom of page). Apologies for the poor quality; see the TAs for better-quality hardcopies.

    The discussion time and location have been changed. The discussion will be in 3109 Etcheverry, Mondays, 5:30-6:30.

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Lecture Notes:
Lecture 1,   Aug. 28, 2008
Course Overview / Definition and Incentives for MEMS
Lecture 2,   Sept. 2, 2008
Benefits of Scaling
Lecture 3,   Sept. 4, 2008
Benefits of Scaling II
Lecture 4,   Sept. 9, 2008
Benefits of MEMS II / Process Modules I
Lecture 5,   Sept. 11, 2008
Process Modules II:   Lithography
Lecture 6,   Sept. 16, 2008
Process Modules III:   Lithography, Etching
Lecture 7,   Sept. 18, 2008
Process Modules IV:   Etching, Implantation, Diffusion
Lecture 8,   Sept. 23, 2008
Surface Micromachining I
Lecture 9,   Sept. 25, 2008
Surface Micromachining II

Additional Reference Material:
Surface Micromachining for Microelectromechanical Systems;   James M. Bustillo, Roger T. Howe, Fellow IEEE and Richard S. Muller, Life Fellow, IEEE
Etch Rates for Micromachining Processing;   Kirt R. Williams, Student Member, IEEE and Richard S. Muller, Life Fellow, IEEE
Etch Rates for Micromachining Processing - Part II;   Kirt R. Williams, Senior Member, IEEE, Kishan Gupta, Student Member, IEEE and Matthew Wasilik
Lecture 10,   Sept. 30, 2008
Surface Micromachining III / Mechanics of Materials

Additional Reference Material:
SUMMIT VTM Five Level Surface Micromachining Technology Design Manual, Version 1.3 - 09/22/2005
PolyMUMPs Design Handbook
Lecture 11,   Oct. 2, 2008
Mechanical Properties
Lecture 12,   Oct. 7, 2008
Mechanical Properties / Microstructural Elements
Lecture 13,   Oct. 9, 2008
Microstructural Elements
Lecture 14,   Oct. 14, 2008
Beam Bending
Lecture 15,   Oct. 16, 2008
Beam Combos
Lecture 15 (pre-lecture),   Oct. 16, 2008
Beam Combos
Lecture 16,   Oct. 21, 2008
Energy Methods I
Lecture 16 (pre-lecture),   Oct. 21, 2008
Energy Methods I
Lecture 17,   Oct. 28, 2008
Energy Methods II
Lecture 17 (pre-lecture),   Oct. 28, 2008
Energy Methods II
Lecture 18,   Oct. 30, 2008
Resonance Frequency
Same as lecture 17.
Lecture 19,   Nov. 04, 2008
Resonance Frequency II
Lecture 19 (pre-lecture),   Nov. 4, 2008
Resonance Frequency II
Lecture 20,   Nov. 06, 2008
Equivalent Circuits I & Gyroscopes
Lecture 20 (pre-lecture),   Nov. 6, 2008
Equivalent Circuits I & Project
Lecture 21,   Nov. 13, 2008
Gyros & Capacitive Transducers
Lecture 21 (pre-lecture),   Nov. 13, 2008
Gyros & Capacitive Transducers
Lecture 22,   Nov. 18, 2008
Capacitive Transducers
Lecture 22 (pre-lecture),   Nov. 18, 2008
Capacitive Transducers
Lecture 23,   Nov. 20, 2008
Electrical Stiffness
Lecture 23 (pre-lecture),   Nov. 20, 2008
Electrical Stiffness
Lecture 24,   Nov. 24, 2008
Input / Output Modeling
Lecture 24 (pre-lecture),   Nov. 24, 2008
Input / Output Modeling
Lecture 25,   Nov. 25, 2008
Output Sensing
Lecture 25 (pre-lecture),   Nov. 25, 2008
Output Sensing
Lecture 26,   Dec. 2, 2008
Output Sensing & MDS
Lecture 26 (pre-lecture),   Dec. 2, 2008
Output Sensing & MDS
Lecture 27,   Dec. 9, 2008
Noise & Integration
Lecture 27 (pre-lecture),   Dec. 9, 2008
Noise & Integration

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Discussion Section Materials:
Homework # 1:  Issued Sept. 9, 2008
Due 5:00 pm Thurs., Sept. 18th in class.
Homework #1 Solutions: PDF (exported)
The PDF is fixed with the images visible now.

Correction: On page 4, the expression for AAl should read "40 μm x 4 μm." The rest of the calculation is correct as it is written.
Homework # 2:  Issued Sept. 18, 2008
Due 5:00 pm Thurs., Sept. 25th in class.
    Problem 1
  • In the notation used in Jaeger and in the lecture, the acceptor (gallium) concentration NA is a "background concentration."
  • POCl3 doping was mentioned only briefly in lecture. It is described more thoroughly in Jaeger, section 4.10.2. What you need to know is that a film of P2O5 is deposited on the wafer, and acts as an unlimited, high-concentration reservoir of phosphorus for the duration of the diffusion step. Before any other processing (such as the CVD steps), this film is removed.
  • Don't forget to account for the electrical activity limit when calculating the electrical properties. This is explained in the handout.
  • Problem 2
  • The unlabeled rectangular block is polysilicon.
  • The unlabeled incline on the right side is 45°.
Homework #2 Solutions: PDF
Homework # 3:  Issued Sept. 28, 2008
Due 5:00 pm Tue., Oct. 7 Thurs., Oct. 9th in class.
    Clarifications and corrections:
  • Positive photoresist is used throughout the process.
  • The silicon etch in step 14.4 should be the same as that in step 6.2.
  • Add step 4.5: "Remove PR, piranha clean wafers."
  • The 30% overetch applies to every etch step, including the release. For the release, the important dimension is, of course, not the thickness.
  • The fingers on the shuttle (movable plate) are 2 μm wide, and the fingers on the drive and sense electrodes are 2.5 μm wide.
  • The poly2 comb fingers have identically shaped poly1 fingers underneath. The reason why this is done will be explained later in the course.
  • When a layer has been partially etched due to an overetch of an overlying layer, neglect the slope of this profile. Also, if the overetch removes less than 100 nm or 20% of the layer (as specified in part (a), you can neglect the overetch entirely.
  • Some of the etch profiles will start at one slope and then switch to a different slope, but you can neglect this effect. Both slopes will be considered correct.
Homework #3 Solutions: PDF (exported)

Cross-sections (scanned JPEG):

Homework # 4:   Issued Oct. 9, 2008
Due 5:00 pm Thurs., Oct. 16th Tues., Oct. 21st in class.
HW #4 Techfile: RAR, ZIP.
Key Bindings for Cadence: ZIP.
The archives include the necessary files and instructions.
    Clarifications and corrections:
  • One more problem has been added to the homework, and the due date has been extended from Thursday to the following Tuesday.
  • You must use Cadence for the layout (other software is not allowed).
  • Please email your finished layout to both of the GSIs as an exported GDS file. You can find instructions at the very end of the Cadence tutorial PDF on the course website. Please use your name for the GDS file, in the following format: HW4.<first>.<last>.GDS
  • For part (c), give the height of the wing tips above the center of the poly2 structure, not above the substrate. (For example, with no stress gradient, the answer would be zero, regardless of buckling.)
Homework #4 Solutions: PDF
Exported GDS File

    Clarifications and corrections:
  • Lc in part (b) should be 250 μm; consequently the critical stress is -31.6 MPa. The final answer is the same.
  • "Less" at the end of part (b) should read "more negative."
  • The tip elevation in part (c) should be w = 165 nm for both solution methods.
Homework # 5:   Issued Nov. 2, 2008
Due 5:00 pm Thurs., Nov. 13th in class.
Homework #5 Solutions: PDF
Homework # 6:   Issued Nov. 25, 2008
Due 5:00 pm Tues., Dec. 9th in class.
HW #6 SPICE templates:
Equivalent circuits template
Analysis file template
    Clarifications and corrections:
  • Part (b) should refer to "the suspension beams for the outer drive-mode mass."
  • In Fig. 1-3b, the wide capacitive gap is 15 μm. Please include it in your calculations if you consider it to be important.
Homework #6 Solutions: PDF
    Clarifications and corrections:
  • The formula for kd0/kd on page 8 should have a coefficient of 1/2. The numerical answers on page 9 are correct.
  • The formula for ε on page 9 should have a coefficient of 1/2. If your copy of the solutions does not have this coefficient, please download the new version.

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Last updated 12/11/08 by RSAC