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 #8 Reference Materials 8096 and 8097 The MEMS 5-in-1 Test Chips – Residual Stress and Stress Gradient Calculations 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 Stress and Stress Gradient Calculations 1References to consult 2Residual stress and stress gradient a. Overview b. Equations used c. Data sheet uncertainty equations d. ROI uncertainty equation 3Using the data sheet 4Using the MEMS 5-in-1 to verify measurements a. Residual stress b. Stress gradient

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 7, 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. SEMI MS4-1113, “Test Method for Young’s Modulus Measurements of Thin, Reflecting Films Based on the Frequency of Beams in Resonance,” November (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 1. References to Consult

5 2a. Residual Stress/Stress Gradient Overview Residual Stress Definition: The remaining force per unit area within a layer after the original cause(s) during fabrication have been removed yet before the constraint of the sacrificial layer is removed Purpose: To improve the yield in CMOS fabrication processes since high values of residual stress can lead to failure mechanisms in ICs Method: Calculated given Young’s modulus and residual strain Stress Gradient Definition: The through-thickness variation (of the residual stress) in the layer before it is released Purpose: To measure the through-thickness variation of the residual stress in the structural layer of interest before it is released Method: Calculated given Young’s modulus and strain gradient

where  r residual stress EYoung’s modulus  r residual strain 6 2b. Residual Stress Equation Residual Stress Effective value reported? (RM 8096) Effective value reported? (RM 8097) EYes a) debris in corners b) undercutting c) composite oxide Yes a) kinks b) undercutting c) non-rigid support εrεr Yes a) debris in corners b) undercutting c) composite oxide Yes a) kinks b) undercutting c) non-rigid support σ r = E ε r yes

where  g stress gradient EYoung’s modulus s g strain gradient 7 2b. Stress Gradient Equation Stress Gradient Effective value reported? (RM 8096) Effective value reported? (RM 8097) EYes a) debris in corners b) undercutting c) composite oxide Yes a) kinks b) undercutting c) non-rigid support sgsg Yes a) excessive curvature b) composite oxide No σ g = E s g yes

The data sheet (DS) expanded uncertainty equation where k=2 is used to approximate a 95 % level of confidence. where u c  r residual stress combined standard uncertainty u cE Young’s modulus combined standard uncertainty u c  r residual strain combined standard uncertainty 8 2c. Data Sheet Uncertainty Equation for Residual Stress

where u c  g stress gradient combined standard uncertainty u cE Young’s modulus combined standard uncertainty u csg strain gradient combined standard uncertainty 9 2c. Data Sheet Uncertainty Equation for Stress Gradient The data sheet (DS) expanded uncertainty equation is where k=2 is used to approximate a 95 % level of confidence.

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 Find Data Sheet YM.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 YM.3 –Click “Reset this form” –Supply INPUTS to Tables 1, 2, and 4  r and u c  r are found using Data Sheet RS.3 s g and u csg are found using Data Sheet SG.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.” –Residual stress and stress gradient OUTPUTS given in Table 7 –Compare both the inputs and outputs with the NIST-supplied values 3. Using the Data Sheet

12 If your criterion for acceptance is: where D  r positive difference between the residual stress value of the customer,  r(customer), and that appearing on the ROI,  r U  r(customer) residual stress expanded uncertainty of the customer U  r residual stress expanded uncertainty on the ROI, U ROI 4a. Using the MEMS 5-in-1 To Verify Residual Stress Measurements Then can assume measuring residual stress according to SEMI MS4 according to your criterion for acceptance if: –Criteria above satisfied and –No pertinent “wait” statements at the bottom of your Data Sheet YM.3

13 If your criterion for acceptance is: where D  g positive difference between the stress gradient value of the customer,  g(customer), and that appearing on the ROI,  g U  g(customer) stress gradient expanded uncertainty of the customer U  g stress gradient expanded uncertainty on the ROI, U ROI 4b. Using the MEMS 5-in-1 To Verify Stress Gradient Measurements Then can assume measuring stress gradient according to SEMI MS4 according to your criterion for acceptance if: –Criteria above satisfied and –No pertinent “wait” statements at the bottom of your Data Sheet YM.3