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Physical Measurement Laboratory

Semiconductor and Dimensional Metrology Division

Nanoscale Metrology Group

MEMS Measurement Science and Standards Project

MEMS 5-in-1 RM Slide Set #5

Reference Materials 8096 and 8097The MEMS 5-in-1 Test Chips– Strain Gradient Measurements

Photo taken by Curt Suplee, NIST

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List of MEMS 5-in-1 RM Slide SetsSlide Set # Title of Slide Set

1 OVERVIEW OF THE MEMS 5-IN-1 RMs

2 PRELIMINARY DETAILS

THE MEASUREMENTS:

3 Young’s modulus measurements

4 Residual strain measurements

5 Strain gradient measurements

6 Step height measurements

7 In-plane length measurements

8 Residual stress and stress gradient calculations

9 Thickness measurements (for RM 8096)

10 Thickness measurements (for RM 8097)

11 REMAINING DETAILS

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Outline forStrain Gradient Measurements

1 References to consult

2 Strain gradient a. Overview b. Equation used c. Data sheet uncertainty equations d. ROI uncertainty equation

3 Location of cantilever on RM chip a. For RM 8096 b. For RM 8097

4 Cantilever description a. For RM 8096 b. For RM 8097

5 Calibration procedure

6 Measurement procedure

7 Using the data sheet

8 Using the MEMS 5-in-1 to verify measurements

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• Overview1. J. Cassard, J. Geist, and J. Kramar, “Reference Materials 8096 and 8097 – The Microelectromechanical Systems 5-in-1

Reference Materials: Homogeneous and Stable,” More-Than-Moore Issue of ECS Transactions, Vol. 61, May 2014.

2. J. Cassard, J. Geist, C. McGray, R. A. Allen, M. Afridi, B. Nablo, M. Gaitan, and D. G. Seiler, “The MEMS 5-in-1 Test Chips (Reference Materials 8096 and 8097),” Frontiers of Characterization and Metrology for Nanoelectronics: 2013, NIST, Gaithersburg, MD, March 25-28, 2013, pp. 179-182.

3. J. Cassard, J. Geist, M. Gaitan, and D. G. Seiler, “The MEMS 5-in-1 Reference Materials (RM 8096 and 8097),” Proceedings of the 2012 International Conference on Microelectronic Test Structures, ICMTS 2012, San Diego, CA, pp. 211-216, March 21, 2012.

• User’s guide (Section 4, pp. 76-95)4. J.M. Cassard, J. Geist, T.V. Vorburger, D.T. Read, M. Gaitan, and D.G. Seiler, “Standard Reference Materials: User’s Guide for

RM 8096 and 8097: The MEMS 5-in-1, 2013 Edition,” NIST SP 260-177, February 2013 (http://dx.doi.org/10.6028/NIST.SP.260-177).

• Standard5. ASTM E 2246-11e1, “Standard Test Method for Strain Gradient Measurements of Thin, Reflecting Films Using an Optical

Interferometer,” September 2013. (Visit http://www.astm.org for ordering information.)

• Fabrication6. The RM 8096 chips were fabricated through MOSIS on the 1.5 µm On Semiconductor (formerly AMIS) CMOS process. The

URL for the MOSIS website is http://www.mosis.com. The bulk-micromachining was performed at NIST.

7. The RM 8097 chips were fabricated at MEMSCAP using MUMPs-Plus! (PolyMUMPs with a backside etch). The URL for the MEMSCAP website is http://www.memscap.com.

• Miscellaneous8. J. C. Marshall, “MEMS Length and Strain Measurements Using an Optical Interferometer,” NISTIR 6779, National Institute of

Standards and Technology, August 2001.

1. References to Consult

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2a. Strain Gradient Overview

• Definition: The through-thickness variation of the residual strain in the structural layer before it is released

• Purpose: To determine the maximum distance that a MEMS component can be suspended, say, in air, before it begins to bend or curl

• Test structure: Cantilever• Instrument: Interferometric microscope or comparable instrument• Method: Three data points (from one data trace) are obtained along

the length of the cantilever that bends out-of-plane. The strain gradient for this data trace is calculated using these data points and taking into account misalignment. The strain gradient is the average of the strain gradient values obtained from multiple data traces.

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wheresg strain gradientsgt strain gradient from trace “t”Rint radius of the circle used to characterize the shape of

the topmost surface of the cantileversgcorrection length-dependent strain gradient correction term

2b. Strain Gradient Equation

ngcorrectiointgt sRs /1

3/gdgcgbg ssss

(for one trace)

• Strain gradient combined standard uncertainty, ucsg, equation

where uW due to variations across the width of the cantilever uzres due to the resolution in the z-direction of the interferometer uxcal due to the calibration uncertainty in the x-direction uxres due to the resolution in the x-direction of the interferometer uRave due to the sample’s surface roughness unoise due to interferometric noise ucert due to the uncertainty of the value of the step height

standardused for calibration

urepeat(shs) due to the repeatability of measurements taken on the stepheight standard

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2c. Data Sheet Uncertainty Equations

2)(

2222)(

2222222

samprepeatcorrectionlineardriftshsrepeat

certnoiseRavexresxcalzresW

csguuuuu

uuuuuuuu

• Continued….

where udrift due to the amount of drift during the data session ulinear due to the deviation from linearity of the data scan ucorrection due to the uncertainty of the correction term urepeat(samp) due to the repeatability of similar strain gradient measurements

• The data sheet (DS) expanded uncertainty equation is

where k=2 is used to approximate a 95 % level of confidence.8

2c. Data Sheet Uncertainty Equations

csgsgDS uUU 2

2)(

2222)(

2222222

samprepeatcorrectionlineardriftshsrepeat

certnoiseRavexresxcalzresW

csguuuuu

uuuuuuuu

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Effective value for RM 8096 due to:1.Multiple SiO2 layers2.Excessive curvature

For RM 8097, the value for sg is reported (not an “effective” value) and sgcorrection is used for a given length.

2c. Data Sheet Uncertainty Equations

ngcorrectios

3

|| ngcorrectiotcorrectioncorrection

suu

ngcorrectioint

gt sR

s 1

where3

gdgcgbg

ssss

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UROI expanded uncertainty recorded on the Report of Investigation (ROI)

UDS expanded uncertainty as obtained from the data sheet (DS)

Ustability stability expanded uncertainty

2d. ROI Uncertainty Equation

22stabilityDSROI UUU

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3. Location of Cantilever on RM Chip (The 2 Types of Chips)

• RM 8097– Fabricated using a polysilicon

multi-user surface-micromachining MEMS process with a backside etch

– Material properties of the first or second polysilicon layer are reported

– Chip dimensions:

1 cm x 1 cm

• RM 8096– Fabricated on a multi-user

1.5 µm CMOS process followed by a bulk-micromachining etch

– Material properties of the composite oxide layer are reported

– Chip dimensions:

4600 µm x 4700 µm

Lot 95 Lot 98

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3a. Location of Cantilever on RM 8096

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For RM 8096

Structural layer composite oxide

Wcan (µm) 40

Lcan (µm) 200, 248, 300, 348, and 400

t (µm) ≈2.743

Orientation 0º and 180º

Quantity of beams

3 of each length and each orientation (or 30 beams)

Locate the cantilever in this group given the information on the NIST-supplied data sheet

Top view of a cantilever

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3b. Location of Cantilever on RM 8097

Locate the cantilever in this group given the information on the NIST-supplied data sheet

Top view of two cantilevers

For RM 8097

Structural layer poly1 or poly2

Wcan (µm) 16

Lcan (µm) 400, 450, 500, 550, 600, 650,700, 750, and 800

t (µm) ≈2.0 (for poly1) and ≈1.5 (for poly2)

Orientation 180º (for poly1 and poly2) and 90º (for poly1)

Quantity of beams

3 of each length and each orientation (or 54 poly1 and 27 poly2 beams)

Lot 95

Lot 98

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4a. Cantilever Description (For RM 8096)

y

x

a

bc

d

e

Edge 2 Edge 3Edge 1

Lmetal2 (m2) dimensional marker

exposed silicon to be etched (design layers include active area, contact, via, and glass)

Top view of a cantilever

etch stop (n-implant encompassing active area)

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4b. Cantilever Description (For RM 8097)

Top view of a cantilever (Lot 95)

These “tabs” are not present in the strain gradient group on Lot 98.(The original intent was to keep the same anchor design as used in the Young’s modulus group, but these tabs make it more difficult to locate traces a and e.)

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• Calibrate instrument in the z-direction– As specified for step-height calibrations

• Calibrate instrument in the x- and y-directions– As specified for in-plane length calibrations

5. Calibration Procedure

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• Five 2D data traces are extracted from a 3D data set

• For Traces a and e– Enter into the data sheet

• The uncalibrated value (x1uppert) for Edge 1– To find xupper

» The x value that most appropriately locates the upper corner of the transitional edge is called xupper or x1uppera for Edge 1 with Trace a

• The value for n1t

– The maximum uncertainty associated with the identification of xupper is ntxrescalx» If it is easy to identify one point, nt = 1» For a less obvious point that locates the upper corner, nt > 1

• The uncalibrated values for ya and ye

– Determine the uncalibrated endpoint

Note: With 0 orientation, all x-values should be > x1ave

6. Measurement Procedure

t indicates the data trace (e.g., a or e)

xres = uncalibrated resolution in x-direction

2uppereuppera

ave

1x1x1x

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• Determine the misalignment angle,

• For Traces b, c, and d– Eliminate the data values at both ends of the trace (all data

outside and including Edges 1 and 2)– Choose 3 representative data points (sufficiently separated)

• Enter the 3 points into the data sheet(x1, z1), (x2, z2), (x3, z3)

•For a 0 orientation, x1ave < x1 < x2 < x3 •For a 180 orientation, negate the x values of all the points such that x1ave > x1 > x2 > x3 > x2ave

6. Measurement Procedure (continued)

Trace a

Edge 1

α

Δx

Trace e

Δy

(x1uppera, ya)

(x1uppere, ye)

uppereuppera 1x1xx

y

x

cal

cal

y

x1tan

ea yyy

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• Account for the misalignment angle, , and the x-calibration factor

– The v-axis is assumed to be aligned with respect to the in-plane length of the cantilever

– x1ave, x1, x2, and x3 become f, g, h, and i, respectively, along the v-axis

6. Measurement Procedure (continued)

Trace a

Edge 1

g

h

i

x2 calx

x1 calx

α

f=x1ave calx

x3 calx

v

f=x1avecalxg=(x1calxf)cos+fh=(x2calxf)cos+fi=(x3calxf)cos+f

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• A circular arc is used to model the out-of-plane shape of the cantilever• Plot the data with the model using the following equation:

where f < v < j = (x2uppert calx f)cos + f

s = 1 (for downward bending beams) s = 1 (for upward bending beams)

• If the data doesn’t match the plot, try one or more different data points

6. Measurement Procedure (continued)

Use calibrated values for z1, z2, and z3 in these equations

22 )( avRsbz int

den

2num1num

a

aaa

223

22

22

232

22 izzzizzzzzgza 1111num

22

223

23

23

23 zzhzzzzzhzgza 11122num

11den izizgzhzgzhza 22332

Qzb 1

22 QagRint

)(2 2

22

22

1

1

zz

zzahagQQ

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6. Measurement Procedure (continued)

ngcorrectiointgt sRs /1

3/gdgcgbg ssss

(for one trace)

Consult the reference (NISTIR 6779) for a derivation.

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• Find Data Sheet SG.3– On the MEMS Calculator website (Standard Reference Database 166)

accessible via the NIST Data Gateway (http://srdata.nist.gov/gateway/) with the keyword “MEMS Calculator”

– Note the symbol next to this data sheet. This symbol denotes items used with the MEMS 5-in-1 RMs.

• Using Data Sheet SG.3– Click “Reset this form”– Supply INPUTS to Tables 1 through 3– Click “Calculate and Verify”– At the bottom of the data sheet, make sure all the pertinent boxes say

“ok.” If a pertinent box says “wait,” address the issue and “recalculate.”

– Compare both the inputs and outputs with the NIST-supplied values

7. Using the Data Sheet

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• If your criterion for acceptance is:

whereDsg positive difference between the strain gradient value

of the customer, sg(customer), and that appearing on theROI, sg

Usg(customer) strain gradient expanded uncertainty of the customerUsg strain gradient expanded uncertainty on the ROI, UROI

8. Using the MEMS 5-in-1To Verify Strain Gradient Measurements

22)()( sgcustomersggcustomergsg UUssD

• Then can assume measuring strain gradient according to ASTM E2246 according to your criterion for acceptance if:– Criteria above satisfied and– No pertinent “wait” statements at the bottom of your Data Sheet SG.3