MEMS Test Working Group

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MEMS 5-in-1 RM Slide Set 4
Reference Materials 8096 and 8097 The MEMS 5-in-1
Test Chips Residual Strain Measurements
Physical Measurement Laboratory Semiconductor
and Dimensional Metrology Division Nanoscale
Metrology Group MEMS Measurement Science and
Standards Project
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List of MEMS 5-in-1 RM Slide Sets
Slide Set Title of Slide Set
1 OVERVIEW OF THE MEMS 5-IN-1 RMs
2 PRELIMINARY DETAILS
THE MEASUREMENTS
3 Youngs 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 for Residual Strain Measurements
1 References to consult
2 Residual strain a. Overview b. Equation used c. Data sheet uncertainty equations d. ROI uncertainty equation
3 Location of fixed-fixed beam on RM a. For RM 8096 b. For RM 8097
4 Fixed-fixed beam 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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1. References to Consult

• Overview
• 1. 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.
• Users guide (Section 3, pp. 51-75)
• 4. J.M. Cassard, J. Geist, T.V. Vorburger, D.T.
  Read, M. Gaitan, and D.G. Seiler, Standard
  Reference Materials Users 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).
• Standard
• 5. ASTM E 2245-11e1, Standard Test Method for
  Residual Strain Measurements of Thin, Reflecting
  Films Using an Optical Interferometer, September
  2013. (Visit http//www.astm.org for ordering
  information.)
• Fabrication
• 6. 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.
• Miscellaneous
• 8. J. C. Marshall, MEMS Length and Strain
  Measurements Using an Optical Interferometer,
  NISTIR 6779, National Institute of Standards and
  Technology, August 2001.

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2a. Residual Strain Overview

• Definition The amount of deformation (or
  displacement) per unit length constrained within
  the structural layer after fabrication and before
  the constraint of the sacrificial layer (or
  substrate) is removed
• Purpose To measure the strain present in parts
  of a microsystem before they relax after the
  removal of the stiff oxides that surround them
  during manufacturing
• Test structure Fixed-fixed beam
• Instrument Interferometric microscope (or
  comparable instrument)
• Method The curved length of the fixed-fixed
  beam is determined from five data points
  extracted from one data trace along the length of
  the fixed-fixed beam. The in-plane length of the
  fixed-fixed beam is also measured. The residual
  strain for the data trace is calculated given
  these measurements and taking into account offset
  and misalignment. The residual strain is the
  average of the residual strain values obtained
  from multiple data traces.

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2b. Residual Strain Equation
(for one trace)
where

• where
• ?r residual strain
• ?rt residual strain obtained from trace t
• ??rcorrection relative residual strain
  correction term
• L in-plane length of fixed-fixed beam
• L0 length of the fixed-fixed beam when no
  applied axial-
• compressive forces
• Lc length of the curved fixed-fixed beam
• Le' effective length of the fixed-fixed beam
• t thickness

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2c. Data Sheet Uncertainty Equations

• Residual strain combined standard uncertainty,
  uc?r, equation
• where
• uW due to variations across the width of
  the fixed-fixed beam
• uL due to measurement uncertainty of L
• 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 as
• pertains to the five data points chosen along
  the beam
• uRave due to the samples surface roughness
• unoise due to interferometric noise
• ucert due to the uncertainty of the value
  of the step height standard
• used for calibration
• urepeat(shs) due to the repeatability of
  measurements taken on the step
• height standard

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2c. Data Sheet Uncertainty Equations

• 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 residual strain measurements
• The data sheet (DS) expanded uncertainty equation
  is
• where k2 is used to approximate a 95
  level of confidence.

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2c. Data Sheet Uncertainty Equations
where
Effective value for RM 8096 due to 1. Debris in
the attachment corners 2. Undercutting of the
beam 3. Multiple SiO2 layers

• Effective value for RM 8097 due to
• Kinks in cantilevers
• Undercutting of the beam
• Non-rigid support

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2d. ROI Uncertainty Equation

• UROI expanded uncertainty recorded on the
  Report
• of Investigation (ROI)
• UDS expanded uncertainty as obtained
  from the
• data sheet (DS)
• Ustability stability expanded
  uncertainty

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3. Location of Fixed-Fixed Beam 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 Fixed-Fixed Beam on RM 8096
For RM 8096
Structural layer composite oxide
Wffb (µm) 40
Lffb (µm) 200, 248, 300, 348, and 400
t (µm) 2.743
Orientation 0º
Quantity of beams 3 of each length (or 15 beams)
Top view of a fixed-fixed beam
Locate the fixed-fixed beam in this group given
the information on the NIST-supplied data sheet
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3b. Location of Fixed-Fixed Beam on RM 8097
For RM 8097
Structural layer poly1 or poly2
Wffb (µm) 16
Lffb (µm) 400, 450, 500, 550, 600, 650, 700, 750, and 800
t (µm) 2.0 (for poly1) and 1.5 (for poly2)
Orientation 0º (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
Top view of two fixed-fixed beams
Locate the fixed-fixed beam in this group given
the information on the NIST-supplied data sheet
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4a. Fixed-Fixed Beam (For RM 8096)
Top view of a fixed-fixed beam
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4b. Fixed-Fixed Beam (For RM 8097)
These tabs are not present in the residual
strain group on Lot 98. (The original intent was
to keep the same anchor designs as used in the
Youngs modulus group, but these tabs make it
more difficult to locate traces a', a, e, and e'.)

Top view of a p2 fixed-fixed beam (Lot 95)
Data along Trace a', a, e, or e'
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5. Calibration Procedure

• 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

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6. Measurement Procedure

• Seven 2D data traces are extracted from a 3D data
  set
• For Traces a?, a, e, and e?
• Enter into the data sheet
• The uncalibrated values (x1uppert and x2uppert)
  for Edge 1 and Edge 2
• 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 values for n1t and n2t
• 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 gt 1
• The uncalibrated values for ya? and ye?
• Determine the uncalibrated endpoints

t indicates the data trace (e.g., a?, a, e, or e?)
xres uncalibrated resolution in x-direction
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6. Measurement Procedure (continued)

• Determine the misalignment angle, ?
• Use the two outermost data traces (a? and e?)

if , then
and
and if ,
then and
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6. Measurement Procedure (continued)

• For Traces b, c, and d
• Eliminate the data values at both ends of the
• trace (i.e., less than x1ave and greater than
• x2ave)
• Divide the remaining data into two data sets
• Choose 3 representative data points
• (sufficiently separated) within each data set.
• Enter into the data sheet five points
• (x1F, z1F), (x2F, z2F),
• (x3F, z3F) (x1S, z1S),
• (x2S, z2S), (x3S, z3S)
• x1F is slightly larger than x1ave
• (x2F, z2F) is located near an inflection point
• (x3F, z3F) (x1S, z1S)
• x3F is at or near the x-value with the max or min
  y-value
• (x2S, z2S) is located near an inflection point

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6. Measurement Procedure (continued)

• Account for the misalignment angle, ?, and the
  x-calibration factor
• The v-axis is used to measure the length of the
  beam
• x1ave, x1F, x2F, x3F x1S, x2S, x3S, and x2ave
• become f, g, h, i, j, k, and l, respectively,
  along the v-axis

fx1avecalx g(x1Fcalx?f)cos?f h(x2Fcalx?f)cos?
f i(x3Fcalx?f)cos?f j(x2Scalx?f)cos?f k(x3Sca
lx?f)cos?f l(x2avecalx?f)cos?f

• LLalign Loffset l f Loffset
• Endpoints v1end f Loffset/2
• v2end l Loffset/2

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6. Measurement Procedure (continued)

• Two cosine functions are used to model the
  out-of-plane shape of the beam to obtain the
  curved length, Lc
• Plot the data with the model using the following
  equations
• If the data doesnt match the plot, try one or
  more different data points

where v1end lt v lt i
To find w1F, consult ASTM E 2245 s 1 (for
downward bending beams) s ?1 (for upward
bending beams)
where i lt v lt v2end
To find w3S, consult ASTM E 2245
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6. Measurement Procedure (continued)
(for one trace)
where

• Consult the reference (NISTIR 6779) for a
  derivation.

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7. Using the Data Sheet

• Find Data Sheet RS.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 RS.3
• Click Reset this form
• Supply INPUTS to Tables 1 through 5
• 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

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

• If your criterion for acceptance is
• where
• D?r positive difference between the residual
  strain value
• of the customer, ?r(customer), and that
  appearing on the
• ROI, ?r
• U?r(customer) residual strain expanded
  uncertainty of the customer
• U?r residual strain expanded uncertainty on the
  ROI, UROI

• Then can assume measuring residual strain
  according to ASTM E2245 according to your
  criterion for acceptance if
• Criteria above satisfied and
• No pertinent wait statements at the bottom of
  your Data Sheet RS.3