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NIST MEMS Calculator
NIST Standard Reference Database 166
Last Update to Data Content: 2014
DOI: http://dx.doi.org/10.18434/T4CS3T
Developed
at the National Institute of Standards and Technology for
use with ASTM and SEMI standards and the MEMS 5-in-1 RMs. |
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This MEMS
Calculator determines the following thin
film properties from data taken with an optical
interferometer or comparable instrument: a) residual strain from fixed-fixed beams, b)
strain gradient from cantilevers, c) step heights or
thicknesses from step-height test structures, and d)
in-plane 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 fixed-fixed beams. In
addition, wafer bond strength is determined from
micro-chevron test structures using
a material test machine. |
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To help navigate through this web page, the
symbol  denotes items applicable to the MEMS 5-in-1
Test Chips,
reference devices sold as NIST
Reference Materials (RM 8096 and 8097); however, the pertinent data
sheets should be considered generic.
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For the MEMS Calculator, the following material is
available:
1)
Preliminary references:
2) Parameters
under consideration and the data sheets used for on-line
calculations (with the recommended usage of Internet Explorer):
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a) |
Young's
modulus with residual stress and stress gradient
calculations
(using SEMI standard MS4) |
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i) |
Data Sheet YM.1 -
To find Young's modulus using single layered resonating
cantilevers (or fixed-fixed beams) |
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ii) |
Data Sheet YM.2 -
To find Young's modulus using single layered resonating
cantilevers (or fixed-fixed beams) with the analysis
incorporating a frequency calibration |
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iii) |
Data Sheet YM.3-
To find Young's modulus using single layered resonating
cantilevers (or fixed-fixed beams) with the analysis
incorporating a frequency calibration, a new uncertainty
analysis, and a frequency correction factor |
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b) |
Residual
strain (using ASTM standard E 2245) |
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i) |
Data Sheet RS.1 -
To find residual strain using fixed-fixed beam test
structures |
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ii) |
Data Sheet RS.2 - To find
residual strain using fixed-fixed beam test structures with
a more detailed calculation of the combined standard
uncertainty, ucεr
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iii) |
Data Sheet RS.3 - To find
residual strain using fixed-fixed beam test structures with
the analysis incorporating a residual strain correction
factor and with
a more detailed calculation of ucεr, which includes the repeatability component, urepeat(samp) |
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a.) |
For RM 8096,
click here for
Sample Data Trace a', a, e, or e' |
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b.) |
For RM 8096,
click here for Sample Data
Trace b, c, or d |
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c.) |
For RM 8097,
click here for Sample Data
Trace a', a, e, or e' |
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d.) |
For RM 8097,
click here for Sample Data
Trace a', a, e, or e' (another possibility) |
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e.) |
For RM 8097,
click here for Sample Data
Trace b, c, or d |
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c) |
Strain
gradient (using ASTM standard E 2246) |
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i) |
Data Sheet SG.1 -
To find strain gradient using cantilever test structures |
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ii) |
Data Sheet SG.2 - To find
strain gradient using cantilever test structures with a more
detailed calculation of ucsg
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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 ucsg, which
includes the repeatability component, urepeat(samp) |
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a.) |
For RM 8096,
click here for Sample Data
Trace a or e |
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b.) |
For RM 8096,
click here for Sample Data
Trace b, c, or d |
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c.) |
For RM 8097,
click here for Sample Data
Trace a or e |
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d.) |
For RM 8097,
click here for Sample Data
Trace a or e (another possibility) |
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e.) |
For RM 8097,
click here for Sample Data
Trace b, c, or d |
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d) |
Step height
(using SEMI standard MS2) |
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i) |
Data Sheet SH.1 -
To find step heights from one step height test
structure |
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i.a)
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Data Sheet SH.1.a-
To find step heights from one step height test
structure with a more detailed calculation of ucSH,
which includes the repeatability component, urepeat(samp) |
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a.) |
For RM 8096,
click here for Sample Data
Trace a, b, or c |
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b.) |
For RM 8097,
click here for Sample Data
Trace a, b, or c |
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ii) |
Data Sheet SH.2 - To find
step heights taken during the same data session from
two step height test structures |
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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 ucSH,
which includes the repeatability component, urepeat(samp) |
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iii) |
Data Sheet SH.3 - To find
step heights taken during different data sessions
from two
step height test structures |
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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 ucSH,
which includes the repeatability component, urepeat(samp) |
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e) |
Thickness (using SEMI standard MS2) |
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i) |
Data Sheet T.1-
To find the composite oxide thickness in a commercial CMOS process |
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ii) |
Data Sheet T.2 - To find the
thicknesses of all the layers in a CMOS process using
an electro-physical technique |
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iii) |
Data Sheet T.3
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To find the thicknesses in a surface-micromachining MEMS
process using an optomechanical technique |
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iv) |
Data Sheet T.3.a-
To find the thicknesses in a surface-micromachining MEMS process using
an optomechanical
technique and includes an additional calculation of C |
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f) |
In-plane
length or deflection (using ASTM standard E 2244) |
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i) |
Data Sheet L.0-
For all in-plane length measurements with the analysis
incorporating an in-plane length correction factor and a
more detailed calculation of ucL,
which includes the repeatability component, urepeat(samp) |
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a.) |
For RM 8096,
click here for Sample Data
Trace a', a, e, or e' |
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b.) |
For RM 8097,
click here for Sample Data
Trace a', a, e, or e' |
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ii) |
Data Sheet L.1 -
To find in-plane lengths with two ends anchored (or to find
an inside edge-to-inside edge length measurement) |
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iii) |
Data Sheet L.2 -
To find in-plane lengths with transitional edges
oriented in the same direction (or to find an inside
edge-to-outside edge length measurement from one data trace) |
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iv) |
Data Sheet L.3 -
To find in-plane lengths with one end anchored (or to
find an inside edge-to-outside edge length measurement from
two data traces) |
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v) |
Data Sheet L.4 -
To find in-plane lengths with two ends unanchored (or
to find an outside edge-to-outside edge length measurement) |
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vi) |
Data Sheet L.5 -
To find in-plane deflections from released part to
released part |
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vii) |
Data Sheet L.6 -
To find in-plane deflections from released part to
fixed location |
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g) |
Wafer bond
strength (using SEMI standard MS5) |
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i) |
Data Sheet WBS.1 - To find
wafer bond strength using micro-chevron test structures |
3)
The MEMS 5-in-1 RMs:
4)
Design files and accompanying tiff
files:
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The following design files (in GDS-II
format), as shown in the accompanying tiff files, were used to
fabricate the MEMS 5-in-1 RMs: |
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a) |
5n1CMOSthick.gds
5n1CMOSthick.tif
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This design file
(in GDS-II format) and corresponding tiff file are for chips
fabricated on a multi-user 1.5 mm CMOS
process followed by a bulk-micromachining etch.1 |
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b) |
5n1MUMPs98.gds
5n1MUMPs98.tif |
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These design files (in GDS-II format) and
corresponding tiff files are for chips fabricated using a
polysilicon multi-user surface-micromachining MEMS process
with a backside etch. |
5n1MUMPs95.gds
5n1MUMPs95.tif |
5)
List of pertinent SEMI standard test
methods:
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Consult the following
three SEMI standards for
details concerning the inputs
to Data Sheets SH, T, YM,
and WBS: |
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a)
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SEMI MS2, Test Method
for Step Height
Measurements of Thin
Films.
For ordering
information,
click here,
then click on "SEMI MS2."
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b)
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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 "SEMI MS4."
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c)
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SEMI MS5, Test Method
for Wafer Bond Strength
Measurements Using
Micro-Chevron Test
Structures.
For ordering
information,
click here,
then click on "SEMI MS5."
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6)
List of pertinent ASTM standard test methods:
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Consult the following three ASTM
standards for details concerning the inputs to Data Sheets
L, RS, and SG, respectively: |
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a) |
ASTM E 2244,
Standard Test Method for In-Plane Length Measurements of
Thin, Reflecting Films Using an Optical Interferometer.
For ordering information,
click
here
and search using the
designation "E 2244." |
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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." |
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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." |
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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:
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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. |
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b) |
SEMI MS3,
Terminology for MEMS Technology. For ordering information,
click here, then click on "SEMI MS3." |
8)
List of other pertinent references:
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Reference Link |
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Brief Description |
Pertinent
Parameter(s) |
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a) |
EDL.vol.28.11.07.pdf
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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 electro-physical technique are among the inputs
for the optimization program. |
Young's modulus & thickness |
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b) |
NISTJRes.V115.No5.10.pdf |
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This NIST Journal of Research article
provides the user with a more in-depth understanding of the
SEMI test methods used in Data Sheets YM and SH and it
presents the 2008-2009 SEMI MEMS Young's Modulus and Step Height
Round Robin Results. |
Young's modulus & step height |
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c) |
NISTJRes.V112.No5.07.pdf |
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This NIST Journal of Research article
presents the electro-physical technique used to obtain all
the thicknesses in a CMOS process using Data Sheet T.2.
It also provides the user with a more in-depth understanding
of SEMI standard MS2. |
step height & thickness |
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d) |
JMEMS.Thick.2001.pdf |
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This JMEMS article presents an
optomechanical technique for measuring layer thickness in
a surface-micromachining MEMS process. Data Sheet T.3.a can be used for the
calculations. |
thickness |
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e) |
NISTSP1048.pdf |
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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. |
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f) |
NISTIR7291.pdf |
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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 |
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g) |
NISTIR6779.pdf
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This NIST
Internal Report (NISTIR #6779) provides the user with a
more in-depth understanding of the ASTM standard test
methods used in Data Sheets RS, SG, and L. |
residual strain, strain gradient, &
length |
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