Edward,
I took the liberty to include your initial question to me in this
general email to the MEMS discussion group. Since it was a question
designed to clarify the mechanical property extraction technique we
used at MIT, I felt that it would be OK.
First let me commend you for making good geometrical measurements, a
point often overlooked in the process of mechanical property
extraction. Second your question about how to define the beam lengths
targets another major issue: understanding the effects of compliant
supports. They can quite significantly affect the overall mechanical
compliance a MEMS device, especially those fabricated by surface-
micromachining, as you find in the MUMPs devices.
The lengths I report in my thesis for the MUMPs devices are labelled
L1 in your drawing below. As you can guess, the added ~5um length
along the lip of the support as well as the vertical anchoring segment
~2um contribute to bending compliance that can be approximated as a
length offset to L1. Since bending compliance goes as 1/L^4, this
effect even on a 300um and 400um beams can be quite significant.
Secondly, you investigate fixed-fixed (double-clamped) beams. The
length offset must be added for each of the two supports.
The lower pull-in voltages (VPI) you report for the beams are not
surprising. Compressive stress in your beams may be much higher than
in the beams I investigated. This can drastically reduce VPI. Errors
in correctly extracting the stress (due perhaps to the exclusion of
the support compliance) will propogate to errors in the extracted
modulus.
Additionally, the concurrent pull-in measurements of cantilever
(singly-clamped) beams, which have no net axial stress unlike the
fixed-fixed beams, will help you separate the compliance due to the
modulus from stress. And to reduce errors even further, I would
suggest fitting our pull-in models to at least five different beam
lengths. If you have high compressive stress, you should design
shorter length beams to avoid out of plane warpage and buckling.
Lastly, W1 below represents the 40um widths of my beams. If my
responses do not completely address your problem, let's talk.
Raj
Raj Gupta
Microcosm Technologies, Inc.
100 S. Ellsworth Ave., Suite 400
San Mateo, CA 94401
(650)696-3198, FAX: (650)6969-3199
------- Forwarded Messages
Date: Tue, 14 Apr 1998 15:32:11 -0700 (PDT)
From: Edward Chan
To: Raj Gupta
cc: chan@gloworm.Stanford.EDU
Subject: Re: Thesis
Hi Raj,
I am trying to use some of the data you presented in your thesis. Could
you clarify the measured beam sizes you used? The MUMPs layout
below describes what I mean:
<------ length 2 --------
<---- length 1 -------
^ -------+
| |
| ^ ----+ +---------------------
width 1 | ////|
| | ////|
| width 2 ////|
| | ////|
| | ////|
| v ----+ +---------------------
| |
v -------+
Did you use/report length 1 or length 2? What is the difference between
length 1 and length 2? What is the width of your stepup (width 1 and 2)?
(These are for the fixed-fixed beams.)
Many thanks in advance!
+=========+=====================+===================================+
| Edward | Tel: (650) 723-1482 | CISX 305, Stanford, CA 94305-4075 |
| Chan | Fax: (650) 725-7731 | chan@gloworm.stanford.edu |
+=========+=====================+===================================+
------- Message 2
Date: Mon, 13 Apr 1998 13:51:37 -0700
From: Edward Chan
Subject: MUMPs 22 properties
To: MEMS@ISI.EDU
Reply-To: Edward Chan , mems-cc@ISI.EDU
Hi,
I'm trying to determine the material properties of the polysilicon
film (POLY1) of the MUMPs 22 run using the pull-in method of
Gupta & Senturia (MIT). I am getting very low values for
Young's Modulus (110 GPa). Biaxial stress is -6MPa.
Compared to Gupta's thesis, I'm getting pull-in voltages of
29V for the 300um beam (compared to 50V by Gupta) and 14V for
a 400um beam (compared to about 25V by Gupta).
I've measured the film thickness (1.96um) and the gap (1.94um).
The dice are placed in the Gel-Pak containers so no vacuum is
applied to the back.
Anyone else measure such values?
Thanks!
+=========+=====================+===================================+
| Edward | Tel: (650) 723-1482 | CISX 305, Stanford, CA 94305-4075 |
| Chan | Fax: (650) 725-7731 | chan@gloworm.stanford.edu |
+=========+=====================+===================================+
------- End of Forwarded Messages