MEMS Calculator
Standard Reference Database 166 developed
at the National Institute of Standards and Technology for
use with ASTM and SEMI standards and the MEMS 5in1 RMs 
This MEMS
Calculator determines the following thin
film properties from data taken with an optical
interferometer or comparable instrument: a) residual strain from fixedfixed beams, b)
strain gradient from cantilevers, c) step heights or
thicknesses from stepheight test structures, and d)
inplane lengths or deflections. Then, residual stress
and stress gradient calculations can be made after an optical vibrometer
or comparable instrument is used to obtain Young's modulus
from resonating cantilevers or fixedfixed beams. In
addition, wafer bond strength is determined from
microchevron test structures using
a material test machine. 
To help navigate through this web page, the
symbol denotes items applicable to the MEMS 5in1
Test Chips,
reference devices sold as NIST
Reference Materials (RM 8096 and 8097); however, the pertinent data
sheets should be considered generic.

For the MEMS Calculator, the following material is
available:
1)
Preliminary references:
2) Parameters
under consideration and the data sheets used for online
calculations (with the recommended usage of Internet Explorer):


a) 
Young's
modulus with residual stress and stress gradient
calculations (using SEMI standard MS4) 



i) 
Data Sheet YM.1 
To find Young's modulus using single layered resonating
cantilevers (or fixedfixed beams) 



ii) 
Data Sheet YM.2 
To find Young's modulus using single layered resonating
cantilevers (or fixedfixed beams) with the analysis
incorporating a frequency calibration 



iii) 
Data Sheet YM.3
To find Young's modulus using single layered resonating
cantilevers (or fixedfixed beams) with the analysis
incorporating a frequency calibration, a new uncertainty
analysis, and a frequency correction factor 


b) 
Residual
strain (using ASTM standard E 2245) 



i) 
Data Sheet RS.1 
To find residual strain using fixedfixed beam test
structures 



ii) 
Data Sheet RS.2  To find
residual strain using fixedfixed beam test structures with
a more detailed calculation of the combined standard
uncertainty, u_{cεr}




iii) 
Data Sheet RS.3  To find
residual strain using fixedfixed beam test structures with
the analysis incorporating a residual strain correction
factor and with
a more detailed calculation of u_{cεr}, which includes the repeatability component, u_{repeat(samp)} 




a.) 
For RM 8096,
click here for
Sample Data Trace a', a, e, or e' 




b.) 
For RM 8096,
click here for Sample Data
Trace b, c, or d 




c.) 
For RM 8097,
click here for Sample Data
Trace a', a, e, or e' 




d.) 
For RM 8097,
click here for Sample Data
Trace a', a, e, or e' (another possibility) 




e.) 
For RM 8097,
click here for Sample Data
Trace b, c, or d 


c) 
Strain
gradient (using ASTM standard E 2246) 



i) 
Data Sheet SG.1 
To find strain gradient using cantilever test structures 



ii) 
Data Sheet SG.2  To find
strain gradient using cantilever test structures with a more
detailed calculation of u_{csg}




iii) 
Data Sheet SG.3  To find
strain gradient using cantilever test structures with the
analysis incorporating a strain gradient correction factor
and with a more
detailed calculation of u_{csg}, which
includes the repeatability component, u_{repeat(samp)} 




a.) 
For RM 8096,
click here for Sample Data
Trace a or e 




b.) 
For RM 8096,
click here for Sample Data
Trace b, c, or d 




c.) 
For RM 8097,
click here for Sample Data
Trace a or e 




d.) 
For RM 8097,
click here for Sample Data
Trace a or e (another possibility) 




e.) 
For RM 8097,
click here for Sample Data
Trace b, c, or d 


d) 
Step height
(using SEMI standard MS2) 



i) 
Data Sheet SH.1 
To find step heights from one step height test
structure 



i.a)

Data Sheet SH.1.a
To find step heights from one step height test
structure with a more detailed calculation of u_{cSH},
which includes the repeatability component, u_{repeat(samp)} 




a.) 
For RM 8096,
click here for Sample Data
Trace a, b, or c 




b.) 
For RM 8097,
click here for Sample Data
Trace a, b, or c 



ii) 
Data Sheet SH.2  To find
step heights taken during the same data session from
two step height test structures 



ii.a) 
Data Sheet SH.2.a  To find
step heights taken during the same data session from
two step height test structures with a more detailed
calculation of u_{cSH},
which includes the repeatability component, u_{repeat(samp)} 



iii) 
Data Sheet SH.3  To find
step heights taken during different data sessions
from two
step height test structures 



iii.a) 
Data Sheet SH.3.a  To find
step heights taken during different data sessions
from two
step height test structures with a more detailed calculation
of u_{cSH},
which includes the repeatability component, u_{repeat(samp)} 


e) 
Thickness (using SEMI standard MS2) 



i) 
Data Sheet T.1
To find the composite oxide thickness in a commercial CMOS process 



ii) 
Data Sheet T.2  To find the
thicknesses of all the layers in a CMOS process using
an electrophysical technique 



iii) 
Data Sheet T.3

To find the thicknesses in a surfacemicromachining MEMS
process using an optomechanical technique 



iv) 
Data Sheet T.3.a
To find the thicknesses in a surfacemicromachining MEMS process using
an optomechanical
technique and includes an additional calculation of C 


f) 
Inplane
length or deflection (using ASTM standard E 2244) 



i) 
Data Sheet L.0
For all inplane length measurements with the analysis
incorporating an inplane length correction factor and a
more detailed calculation of u_{cL},
which includes the repeatability component, u_{repeat(samp)} 




a.) 
For RM 8096,
click here for Sample Data
Trace a', a, e, or e' 




b.) 
For RM 8097,
click here for Sample Data
Trace a', a, e, or e' 



ii) 
Data Sheet L.1 
To find inplane lengths with two ends anchored (or to find
an inside edgetoinside edge length measurement) 



iii) 
Data Sheet L.2 
To find inplane lengths with transitional edges
oriented in the same direction (or to find an inside
edgetooutside edge length measurement from one data trace) 



iv) 
Data Sheet L.3 
To find inplane lengths with one end anchored (or to
find an inside edgetooutside edge length measurement from
two data traces) 



v) 
Data Sheet L.4 
To find inplane lengths with two ends unanchored (or
to find an outside edgetooutside edge length measurement) 



vi) 
Data Sheet L.5 
To find inplane deflections from released part to
released part 



vii) 
Data Sheet L.6 
To find inplane deflections from released part to
fixed location 


g) 
Wafer bond
strength (using SEMI standard MS5) 



i) 
Data Sheet WBS.1  To find
wafer bond strength using microchevron test structures 
3)
The MEMS 5in1 RMs:
4)
Design files and accompanying tiff
files:

The following design files (in GDSII
format), as shown in the accompanying tiff files, were used to
fabricate the MEMS 5in1 RMs: 

a) 
5n1CMOSthick.gds
5n1CMOSthick.tif



This design file
(in GDSII format) and corresponding tiff file are for chips
fabricated on a multiuser 1.5 mm CMOS
process followed by a bulkmicromachining etch.^{1} 

b) 
5n1MUMPs98.gds
5n1MUMPs98.tif 
 
These design files (in GDSII format) and
corresponding tiff files are for chips fabricated using a
polysilicon multiuser surfacemicromachining MEMS process
with a backside etch. 
5n1MUMPs95.gds
5n1MUMPs95.tif 
5)
List of pertinent SEMI standard test
methods:

Consult the following
three SEMI standards for
details concerning the inputs
to Data Sheets SH, T, YM,
and WBS: 

a)

SEMI MS2, Test Method
for Step Height
Measurements of Thin
Films.
For ordering
information,
click here,
then click on "Published
MEMS Standards," then
click on "SEMI MS2."


b)

SEMI MS4, Test Method
for Young's Modulus
Measurements of Thin,
Reflecting Films Based
on the Frequency of
Beams in Resonance.
For ordering
information,
click here,
then click on "Published
MEMS Standards," then
click on "SEMI MS4."


c)

SEMI MS5, Test Method
for Wafer Bond Strength
Measurements Using
MicroChevron Test
Structures.
For ordering
information,
click here,
then click on "Published
MEMS Standards," then
click on "SEMI MS5."

6)
List of pertinent ASTM standard test methods:

Consult the following three ASTM
standards for details concerning the inputs to Data Sheets
L, RS, and SG, respectively: 

a) 
ASTM E 2244,
Standard Test Method for InPlane Length Measurements of
Thin, Reflecting Films Using an Optical Interferometer.
For ordering information,
click
here
and search using the
designation "E 2244." 

b) 
ASTM E 2245,
Standard Test Method for Residual Strain Measurements of
Thin, Reflecting Films Using an Optical Interferometer.
For ordering information,
click
here
and search using the
designation "E 2245." 

c) 
ASTM E 2246,
Standard Test Method for Strain Gradient Measurements of
Thin, Reflecting Films Using an Optical Interferometer.
For ordering information,
click here and search using the
designation "E 2246." 

These standards are also available
in the
Annual Book of ASTM Standards,
Vol. 03.01.
For ordering information,
click here. 
7)
List of MEMS terminology standards:

a) 
ASTM E 2444,
Terminology Relating to Measurements Taken on Thin,
Reflecting Films. For ordering information, click here
and search using the
designation "E 2444." This
standard is also available in the
Annual Book of ASTM Standards,
Vol. 03.01. For ordering information,
click here. 

b) 
SEMI MS3,
Terminology for MEMS Technology. For ordering information,
click here, then click on
"Published MEMS Standards," then click on "SEMI MS3." 
8)
List of other pertinent references:


Reference Link 

Brief Description 
Pertinent
Parameter(s) 

a) 
EDL.vol.28.11.07.pdf



This Electron Device Letter presents a
method of obtaining the Young's modulus values of all the
layers in a CMOS process. The thicknesses obtained
from the electrophysical technique are among the inputs
for the optimization program. 
Young's modulus & thickness 

b) 
NISTJRes.V115.No5.10.pdf 
 
This NIST Journal of Research article
provides the user with a more indepth understanding of the
SEMI test methods used in Data Sheets YM and SH and it
presents the 20082009 SEMI MEMS Young's Modulus and Step Height
Round Robin Results. 
Young's modulus & step height 

c) 
NISTJRes.V112.No5.07.pdf 
 
This NIST Journal of Research article
presents the electrophysical technique used to obtain all
the thicknesses in a CMOS process using Data Sheet T.2.
It also provides the user with a more indepth understanding
of SEMI standard MS2. 
step height & thickness 

d) 
JMEMS.Thick.2001.pdf 
 
This JMEMS article presents an
optomechanical technique for measuring layer thickness in
a surfacemicromachining MEMS process. Data Sheet T.3.a can be used for the
calculations. 
thickness 

e) 
NISTSP1048.pdf 
 
This 2006 NIST Special Publication (NISTSP
1048) lists (on page 309) the US Measurement System (USMS)
critical measurement targets for accelerating innovation in
Micro Nano Technology. 


f) 
NISTIR7291.pdf 
 
This NIST Internal Report (NISTIR
#7291) presents the 2002 ASTM MEMS Length and Strain Round
Robin Results and uncertainty equations used in Data
Sheets RS, SG, and L. 
residual strain, strain gradient, &
length 

g) 
NISTIR6779.pdf



This NIST
Internal Report (NISTIR #6779) provides the user with a
more indepth understanding of the ASTM standard test
methods used in Data Sheets RS, SG, and L. 
residual strain, strain gradient, &
length 
9) To rate our products and services,
click here.
^{1}Commercial equipment, instruments, or
processes may be identified. This does not imply
recommendation or endorsement by NIST, nor does it imply that the
equipment, instruments, or processes are the best available for the
purpose.
Email questions or comments to memssupport@nist.gov.
Adobe Acrobat Reader (version 4.0x or
greater) will be needed to view many of these documents. If you do
not have this program, you may
download
it free of charge. The software is identified in order to assist
users of this information service. In no case does such
identification imply recommendation or endorsement by the National
Institute of Standards and Technology.
