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 #5 Reference Materials 8096 and 8097 The MEMS 5-in-1 Test Chips – Strain Gradient 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 Strain Gradient Measurements 1References to consult 2Strain gradient a. Overview b. Equation used c. Data sheet uncertainty equations d. ROI uncertainty equation 3Location of cantilever on RM chip a. For RM 8096 b. For RM Cantilever description 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 4, 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 ( 177) Standard 5. ASTM E e1, “Standard Test Method for Strain Gradient 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

5 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.

6 where s g strain gradient s gt strain gradient from trace “t” R int radius of the circle used to characterize the shape of the topmost surface of the cantilever s gcorrection length-dependent strain gradient correction term 2b. Strain Gradient Equation (for one trace)

Strain gradient combined standard uncertainty, u csg, equation where u W due to variations across the width of the cantilever 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 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 7 2c. Data Sheet Uncertainty Equations

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 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

9 Effective value for RM 8096 due to: 1.Multiple SiO 2 layers 2.Excessive curvature For RM 8097, the value for s g is reported (not an “effective” value) and s gcorrection is used for a given length. 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 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 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 Cantilever on RM For RM 8096 Structural layercomposite oxide W can ( µm) 40 L can ( µm) 200, 248, 300, 348, and 400 t ( µm) ≈2.743 Orientation0 º and 180 º 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

13 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 layerpoly1 or poly2 W can ( µm) 16 L can ( µm) 400, 450, 500, 550, 600, 650, 700, 750, and 800 t ( µm)≈ 2.0 (for poly1) and ≈ 1.5 (for poly2) Orientation180 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. Cantilever Description (For RM 8096) y x a b c d e Edge 2Edge 3 Edge 1 L metal2 (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)

15 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.)

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 Five 2D data traces are extracted from a 3D data set For Traces a and e –Enter into the data sheet The uncalibrated value (x1 uppert ) for Edge 1 –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 value for n1 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 endpoint Note: With 0  orientation, all x-values should be > x1 ave 6. Measurement Procedure t indicates the data trace (e.g., a or e) x res = uncalibrated resolution in x-direction

18 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 (x 1, z 1 ), (x 2, z 2 ), (x 3, z 3 ) For a 0  orientation, x1 ave < x 1 < x 2 < x 3 For a 180  orientation, negate the x values of all the points such that x1 ave > x 1 > x 2 > x 3 > x2 ave 6. Measurement Procedure (continued) Trace a Edge 1 α ΔxΔx Trace e ΔyΔy (x1 uppera, y a ) (x1 uppere, y e )

19 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 –x1 ave, x 1, x 2, and x 3 become f, g, h, and i, respectively, along the v-axis 6. Measurement Procedure (continued) Trace a Edge 1 g h i x 2 cal x x 1 cal x α f=x1 ave cal x x 3 cal x v f=x1 ave cal x g=(x 1 cal x  f)cos  +f h=(x 2 cal x  f)cos  +f i=(x 3 cal x  f)cos  +f

20 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 = (x2 uppert cal x  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 z 1, z 2, and z 3 in these equations

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

22 Find Data Sheet SG.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 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

23 If your criterion for acceptance is: where D sg positive difference between the strain gradient value of the customer, s g(customer), and that appearing on the ROI, s g U sg(customer) strain gradient expanded uncertainty of the customer U sg strain gradient expanded uncertainty on the ROI, U ROI 8. Using the MEMS 5-in-1 To Verify Strain Gradient Measurements 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