1 Physical Measurement Laboratory Semiconductor and Dimensional Metrology Division Nanoscale Metrology Group MEMS Measurement Science and Standards Project MEMS 5-in-1 RM Slide Set #4 Reference Materials 8096 and 8097 The MEMS 5-in-1 Test Chips – Residual Strain Measurements Photo taken by Curt Suplee, NIST

2 List of MEMS 5-in-1 RM Slide Sets Slide Set #Title of Slide Set 1OVERVIEW OF THE MEMS 5-IN-1 RMs 2PRELIMINARY 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) 11REMAINING DETAILS

3 Outline for Residual Strain Measurements 1References to consult 2Residual strain a. Overview b. Equation used c. Data sheet uncertainty equations d. ROI uncertainty equation 3Location of fixed-fixed beam on RM a. For RM 8096 b. For RM Fixed-fixed beam a. For RM 8096 b. For RM Calibration procedure 6Measurement procedure 7Using the data sheet 8Using the MEMS 5-in-1 to verify measurements

4 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 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 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 , March 21, User’s guide (Section 3, pp ) 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 , February 2013 ( Standard 5. ASTM E e1, “Standard Test Method for Residual Strain Measurements of Thin, Reflecting Films Using an Optical Interferometer,” September (Visit for ordering information.) Fabrication 6. The RM 8096 chips were fabricated through MOSIS on the 1.5 µ m On Semiconductor (formerly AMIS) CMOS process. The URL for the MOSIS website is 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 Miscellaneous 8. J. C. Marshall, “MEMS Length and Strain Measurements Using an Optical Interferometer,” NISTIR 6779, National Institute of Standards and Technology, August References to Consult

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. 2a. Residual Strain Overview

6 where  r residual strain  rt residual strain obtained from trace “t”   rcorrection relative residual strain correction term Lin-plane length of fixed-fixed beam L 0 length of the fixed-fixed beam when no applied axial- compressive forces L c length of the curved fixed-fixed beam L e ′ effective length of the fixed-fixed beam tthickness 2b. Residual Strain Equation (for one trace) where

7 2c. Data Sheet Uncertainty Equations Residual strain combined standard uncertainty, u c  r, equation where u W due to variations across the width of the fixed-fixed beam u L due to measurement uncertainty of L u zres due to the resolution in the z-direction of the interferometer u xcal due to the calibration uncertainty in the x-direction u xres due to the resolution in the x-direction of the interferometer as pertains to the five data points chosen along the beam u Rave due to the sample’s surface roughness u noise due to interferometric noise u cert due to the uncertainty of the value of the step height standard used for calibration u repeat(shs) due to the repeatability of measurements taken on the step height standard

Continued…. where u drift due to the amount of drift during the data session u linear due to the deviation from linearity of the data scan u correction due to the uncertainty of the correction term u repeat(samp) due to the repeatability of similar residual strain 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

9 Effective value for RM 8096 due to: 1. Debris in the attachment corners 2. Undercutting of the beam 3. Multiple SiO 2 layers Effective value for RM 8097 due to: 1.Kinks in cantilevers 2.Undercutting of the beam 3.Non-rigid support 2c. Data Sheet Uncertainty Equations where

10 U ROI expanded uncertainty recorded on the Report of Investigation (ROI) U DS expanded uncertainty as obtained from the data sheet (DS) U stability stability expanded uncertainty 2d. ROI Uncertainty Equation

11 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 µ m CMOS process followed by a bulk-micromachining etch –Material properties of the composite oxide layer are reported –Chip dimensions: 4600 µ m x 4700 µ m Lot 95Lot 98

12 3a. Location of Fixed-Fixed Beam on RM Locate the fixed-fixed beam in this group given the information on the NIST-supplied data sheet For RM 8096 Structural layercomposite oxide W ffb ( µm) 40 L ffb ( µm) 200, 248, 300, 348, and 400 t ( µm) ≈2.743 Orientation0º0º Quantity of beams 3 of each length (or 15 beams) Top view of a fixed-fixed beam

13 3b. Location of Fixed-Fixed Beam on RM 8097 Locate the fixed-fixed beam in this group given the information on the NIST-supplied data sheet Top view of two fixed-fixed beams For RM 8097 Structural layerpoly1 or poly2 W ffb ( µm) 16 L ffb ( µm) 400, 450, 500, 550, 600, 650, 700, 750, and 800 t ( µm)≈ 2.0 (for poly1) and ≈ 1.5 (for poly2) Orientation0 º (for poly1 and poly2) and 90 º (for poly1) Quantity of beams 3 of each length and each orientation (or 54 poly1 and 27 poly2 beams) Lot 95 Lot 98

14 4a. Fixed-Fixed Beam (For RM 8096) L Edge 1Edge 2 y x a b c d e exposed silicon to be etched (design layers include active area, contact, via, and glass) metal2 (m2) dimensional marker etch stop (n-implant encompassing active area) e΄ a΄ Top view of a fixed-fixed beam

15 4b. Fixed-Fixed Beam (For RM 8097) Top view of a p2 fixed-fixed beam (Lot 95) Data along Trace a ′, a, e, or e ′ 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 Young’s modulus group, but these tabs make it more difficult to locate traces a ′, a, e, and e ′.)

16 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

17 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 (x1 uppert and x2 uppert ) for Edge 1 and Edge 2 –To find x upper »The x value that most appropriately locates the upper corner of the transitional edge is called x upper or x1 uppera for Edge 1 with Trace a The values for n1 t and n2 t –The maximum uncertainty associated with the identification of x upper is n t x res cal x »If it is easy to identify one point, n t = 1 »For a less obvious point that locates the upper corner, n t > 1 The uncalibrated values for y a and y e –Determine the uncalibrated endpoints 6. Measurement Procedure t indicates the data trace (e.g., a, a, e, or e) x res = uncalibrated resolution in x-direction

18 6. Measurement Procedure (continued) Trace a΄ Trace e΄ (x1 uppera΄, y a΄ ) (x2 uppera΄, y a΄ ) (x1 uppere΄, y e΄ ) (x2 uppere΄, y e΄ ) Edge 2Edge 1ΔyΔy Δx2 Δx1 α1α1 α2α2 L measa΄ L mease΄ α L meas L align Determine the misalignment angle,  Use the two outermost data traces (a and e) if, then and and if, then and

19 6. Measurement Procedure (continued) For Traces b, c, and d Eliminate the data values at both ends of the trace (i.e., less than x1 ave and greater than x2 ave ) 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: (x 1F, z 1F ), (x 2F, z 2F ), (x 3F, z 3F ) = (x 1S, z 1S ), (x 2S, z 2S ), (x 3S, z 3S ) x 1F is slightly larger than x1 ave (x 2F, z 2F ) is located near an inflection point (x 3F, z 3F ) = (x 1S, z 1S ) x 3F is at or near the x-value with the max or min y-value (x 2S, z 2S ) is located near an inflection point x 3S is slightly smaller than x2 ave

20 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 x1 ave, x 1F, x 2F, x 3F = x 1S, x 2S, x 3S, and x2 ave become f, g, h, i, j, k, and l, respectively, along the v-axis Trace a΄ Trace e΄ Edge 2 Edge 1 g h i j k l L offset /2 x 3F cal x = x 1S cal x x 2S cal x x 3S cal x x 2F cal x x 1F cal x x2 ave cal x α L L align f=x1 ave cal x v L=L align + L offset = l – f + L offset Endpoints: v1 end = f – L offset /2 v2 end = l + L offset /2 f=x1 ave cal x g=(x 1F cal x  f)cos  +f h=(x 2F cal x  f)cos  +f i=(x 3F cal x  f)cos  +f j=(x 2S cal x  f)cos  +f k=(x 3S cal x  f)cos  +f l=(x2 ave cal x  f)cos  +f

21 6. Measurement Procedure (continued) Two cosine functions are used to model the out-of-plane shape of the beam to obtain the curved length, L c Plot the data with the model using the following equations: If the data doesn’t match the plot, try one or more different data points To find w 1F, consult ASTM E 2245 s = 1 (for downward bending beams) s =  1 (for upward bending beams) To find w 3S, consult ASTM E 2245 where i < v < v2 end where v1 end < v < i

22 Consult the reference (NISTIR 6779) for a derivation. (for one trace) where 6. Measurement Procedure (continued)

23 Find Data Sheet RS.3 –On the MEMS Calculator website (Standard Reference Database 166) accessible via the NIST Data 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 7. Using the Data Sheet

24 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, U ROI 8. Using the MEMS 5-in-1 To Verify Residual Strain Measurements 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