MEMS Calculator

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.

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.

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.

For the MEMS Calculator, the following material is available:

1) Preliminary references:

a)	TechBeat.2013	-	This article from the NIST Tech Beat attracted the news media.
b)	FCMN.2013.pdf	-	This four-page article provides an overview of the MEMS 5-in-1 RMs and is accompanied by a handout (MEMS.5n1.handout.pdf).
c)	ICMTS.2012.pdf	-	This six-page article provides an overview of the MEMS 5-in-1 RMs with a tabular summary.
d)	ECST.2014.pdf	-	This nine-page article provides homogeneity and stability test results.
e)	NIST SP 260-177	-	This NIST Special Publication (2013 Edition, 253 pages) provides comprehensive details associated with the MEMS 5-in-1 Test Chips (RM 8096 and 8097).
f)	NIST SP 260-174	-	This NIST Special Publication (2011 Edition, 244 pages) provides comprehensive details associated with the MEMS 5-in-1 Test Chips (now called RM 8096 and 8097).
g)	Slide Sets: 1-Overview 2-Preliminary Details 3-Young's Modulus 4-Residual Strain 5-Strain Gradient 6-Step Height 7-In-Plane Length 8-Residual Stress/Stress Gradient 9-Thickness (for RM 8096) 10-Thickness (for RM 8097) 11-Remaining Details	-	These slide sets are provided for teaching/training purposes and can be used as a quick reference.

2) Parameters under consideration and the data sheets used for on-line 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 fixed-fixed beams)
	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
	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
b)	Residual strain (using ASTM standard E 2245)
	i)	Data Sheet RS.1 - To find residual strain using fixed-fixed beam test structures
	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, u_cεr
	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 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 electro-physical technique
	iii)	Data Sheet T.3 - To find the thicknesses in a surface-micromachining MEMS process using an optomechanical technique
	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
f)	In-plane length or deflection (using ASTM standard E 2244)
	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 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 in-plane lengths with two ends anchored (or to find an inside edge-to-inside edge length measurement)
	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)
	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)
	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)
	vi)	Data Sheet L.5 - To find in-plane deflections from released part to released part
	vii)	Data Sheet L.6 - To find in-plane 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 micro-chevron test structures

3) The MEMS 5-in-1 RMs:

a)	RM number, name, and description:		Status
	RM 8096: CMOS MEMS 5-in-1 Test Chip -		Now Selling
		Using a multi-user 1.5 μm CMOS/MEMS process followed by a bulk-micromachining etch
	RM 8097: MEMS 5-in-1 Test Chip -		Now Selling
		Using a polysilicon multi-user surface-micromachining MEMS process with a backside etch
b)	To help determine which RM to order: RM.Selection.Table.r2.pdf
c)	Contact information to order a MEMS 5-in-1 RM (that comes with the five applicable standard test methods):
	mailing address: Measurement Services Division NIST, 100 Bureau Drive, Stop 2300 Gaithersburg, MD 20899-2300
	phone: 301-975-6776 or 301-975-2200
	fax: 301-948-3730
	email: srminfo@nist.gov
	URL: http://www.nist.gov/srm/
d)	Technical contact: mems-support@nist.gov

4) Design files and accompanying tiff files:

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:
a)	5n1CMOSthick.gds 5n1CMOSthick.tif	-	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
b)	5n1MUMPs98.gds 5n1MUMPs98.tif	-	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:

	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 "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 "SEMI MS4."
	c)	SEMI MS5, Test Method for Wafer Bond Strength Measurements Using Micro-Chevron Test Structures. For ordering information, click here, 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 In-Plane 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 "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 electro-physical 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 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
c)	NISTJRes.V112.No5.07.pdf	-	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
d)	JMEMS.Thick.2001.pdf	-	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
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 in-depth 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.

¹Commercial 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 mems-support@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.

NIST is an agency of the U.S. Commerce Department.
The Semiconductor and Dimensional Metrology Division is within the Physical Measurement Laboratory.
The MEMS Measurement Science and Standards Project is within the Nanoscale Metrology Group.

Date created: 3/12/2002
Last updated: 5/22/2014