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Physical Measurement Laboratory Semiconductor and Dimensional Metrology Division

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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Physical Measurement Laboratory Semiconductor and Dimensional Metrology Division

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  1. 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 Photo taken by Curt Suplee, NIST

  2. List of MEMS 5-in-1 RM Slide Sets

  3. Outline for Residual Strain Measurements

  4. 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. • User’s 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: 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). • 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.orgfor 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.

  5. 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.

  6. 2b. Residual Strain Equation (for one trace) 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 where

  7. 2c. Data Sheet Uncertainty Equations • Residual strain combined standard uncertainty, ucr, equation where uWdue to variations across the width of the fixed-fixed beam uLdue to measurement uncertainty of L uzresdue to the resolution in the z-direction of the interferometer uxcaldue to the calibration uncertainty in the x-direction uxresdue to the resolution in the x-direction of the interferometer as pertains to the five data points chosen along the beam uRavedue to the sample’s surface roughness unoisedue to interferometric noise ucertdue 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

  8. 2c. Data Sheet Uncertainty Equations • Continued…. where udriftdue to the amount of drift during the data session ulineardue to the deviation from linearity of the data scan ucorrectiondue 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 k=2 is used to approximate a 95 % level of confidence.

  9. 2c. Data Sheet Uncertainty Equations where • Effective value for RM 8097 due to: • Kinks in cantilevers • Undercutting of the beam • Non-rigid support Effective value for RM 8096 due to: 1. Debris in the attachment corners 2. Undercutting of the beam 3. Multiple SiO2 layers

  10. 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

  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 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

  12. 3a. Location of Fixed-Fixed Beam on RM 8096 Top view of a fixed-fixed beam Locate the fixed-fixed beam in this group given the information on the NIST-supplied data sheet 12

  13. 3b. Location of Fixed-Fixed Beam on RM 8097 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

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

  15. 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 Young’s 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′

  16. 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

  17. 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 > 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

  18. Lmeas α Lalign (x2uppera΄, ya΄) (x1uppera΄, ya΄) Lmeasa΄ Trace a΄ Δx1 α2 Δy Edge 1 Edge 2 α1 Lmease΄ Δx2 Trace e΄ (x2uppere΄, ye΄) (x1uppere΄, ye΄) 6. Measurement Procedure (continued) • Determine the misalignment angle,  • Use the two outermost data traces (a and e) if , then and and if , then and

  19. Data Derived from Trace b, c, or d (x3F, z3F) = (x1S, z1S) z (x2F, z2F) (x2S, z2S) (x1F, z1F) (x3S, z3S) x x3F= x1S x2F x3S x2S x1F x2ave x1ave 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 • x3S is slightly smaller than x2ave

  20. Edge 1 Edge 2 x3F calx = x1S calx x2F calx x2S calx f=x1ave calx x1F calx x3S calx Loffset/2 x2ave calx Trace a΄ α g h i Lalign j Loffset/2 k Trace e΄ l L v 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 f=x1avecalx g=(x1Fcalxf)cos+f h=(x2Fcalxf)cos+f i=(x3Fcalxf)cos+f j=(x2Scalxf)cos+f k=(x3Scalxf)cos+f l=(x2avecalxf)cos+f • L=Lalign + Loffset = l – f + Loffset • Endpoints: v1end = f – Loffset/2 • v2end = l + Loffset/2

  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, Lc • 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 where v1end<v<i To find w1F, consult ASTM E 2245 s = 1 (for downward bending beams) s = 1 (for upward bending beams) where i<v<v2end To find w3S, consult ASTM E 2245

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

  23. 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

  24. 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

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