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 #7 Reference Materials 8096 and 8097 The MEMS 5-in-1 Test Chips – In-Plane Length 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 In-Plane Length Measurements 1References to consult 2In-plane length a. Overview b. Equation used c. Data sheet uncertainty equations d. ROI uncertainty equation 3Location of test structure on RM chip a. For RM 8096 b. For RM Test structure 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 6, 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 In-Plane Length 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 1. References to Consult

5 2a. In-Plane Length Overview 5 Definition: The straight-line distance between two transitional edges Purpose: For use when interferometric measurements are preferred over using the design dimensions (e.g., when measuring in-plane deflections and when measuring lengths in an unproven fabrication process) Test structure: In-plane length test structure Instrument: Interferometric microscope or comparable instrument Method: Multiple key corner points are identified and recorded along with their uncertainties for an in-plane length calculation, taking into account offset and misalignment L

6 where Lmeasured in-plane length L meas measured in-plane length used to calculate L align L meast measured in-plane length from trace “t” L align measured in-plane length after correcting for misalignment L offset measurement-specific in-plane length correction term x1 uppert x-value that locates the upper corner associated with Edge 1 in Trace “t” x2 uppert x-value that locates the upper corner associated with Edge 2 in Trace “t” cal x x-calibration factor 2b. In-Plane Length Equation (for one trace) (to account for misalignment) (including a correction term)

7 In-plane length combined standard uncertainty, u cL, equation where u L due to uncertainty in the calculated length u repeat(L) due to uncertainty in the in-plane length measurement from four data traces u xcal due to uncertainty in the x-calibration u align due to alignment uncertainty u offset due to uncertainty of the value for L offset u repeat(samp) due to repeatability The data sheet (DS) expanded uncertainty equation is where k=2 is used to approximate a 95 % level of confidence 2c. Data Sheet Uncertainty Equations

For RMs 8096 and 8097, L offset due to: 1.Edges facing each other For 8096, it also corrects for measuring the edges of the covering oxide (as opposed to the m2 edges) 2.Averaging of pixels 2c. Data Sheet Uncertainty Equations and

9 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

10 3. Location of Structure 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

11 3a. Location of Structure on RM 8096 For RM 8096 Structural layerm2 W ( µm) 28 L ( µm) 24, 80, 200, 500, and 1000 Orientation0º0º Quantity of beams 3 structures/grouping outside edge-to-outside edge length (L oo ) meas inside edge-to-inside edge length (L ii ) meas inside edge-to-outside edge length (L io ) meas 3 groupings/length Locate the structure in this group given the information on the NIST-supplied data sheet Top view of in-plane length test structures L oo L io L ii

12 3b. Location of Structure on RM 8097 Locate the structure in one of these arrays given the information on the NIST-supplied data sheet Top view of in-plane length test structure For RM 8097 Structural layerpoly1 or poly2 W ( µm) 20 L ( µm) 24, 80, 200, 500, and 1000 OrientationFor fixed-fixed beams: 0 º (poly1 and poly2) and 90 º (poly1) Quantity of beams 3 of each length for each orientation (or 30 poly1 and 15 poly2 fixed-fixed beams) p1 p2

13 4a. Test Structure Description (For RM 8096) Edge 4Edge 3 y x L a΄ Edge 3 Edge 4 m2 a e e΄ Top view of in-plane length test structures

14 4b. Test Structure Description (For RM 8097) a΄ e L Edge 1Edge 2Edge 5 p q poly0 poly1 poly1 anchor to poly0 y x e΄ a Top view of in-plane length test structure

15 Calibrate instrument in the z-direction to obtain cal z –As specified for step-height calibrations Calibrate instrument in the x- and y-directions –On a yearly basis, or after the instrument as been serviced –A 10 µm grid (or finer grid) ruler is used –Orient the ruler in the x-direction Record ruler x as the maximum FOV in the x-direction (as measured on the screen of the interferometric microscope) Estimate  xcal (standard deviation in a ruler measurement) Calculate cal x (the x-calibration factor) Record x res –Repeat the above in the y-direction to obtain cal y Supply the following inputs to the data sheet: –cal x, ruler x,  xcal, x res, cal y, and cal z 5. Calibration Procedure scope x = the maximum x-value obtained from an extracted 2D data trace

16 6. Measurement Procedure Four 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 : »Examine the x values between Point “p” and Point “q” (as shown in figure for Trace a Edge 1) »The x value that most appropriately locates the upper corner of the transitional edge is called x upper or x1 uppera in this case 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 L meas a΄ e L Edge 1Edge 2Edge 5 p q poly0 poly1 poly1 anchor to poly0 y x e΄ a t indicates the data trace (a, a, e, or e) x res = uncalibrated resolution in x-direction

if, then and 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 L align and if, then and

18 6. Measurement Procedure (continued) Determine L offset Obtain 12 3D data sets L align is calculated for each data set Calculate L alignave L offset = L des – L alignave Or, obtain 4 3D data sets Determine L align for both L ii and L oo Calculate L iialignave Calculate L ooalignave L offset = (L ooalignave – L iialignave )/2 Determine L L = L align + L offset L oo L ii y x Edge 1 Edge 2 Edge 3 Edge 4 m2

19 Find Data Sheet L.0 –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 L.0 –Click “Reset this form” –Supply INPUTS to Tables 1 and 2 –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

20 If your criterion for acceptance is: where D L positive difference between the in-plane length value of the customer, L (customer), and that appearing on the ROI, L U L(customer) in-plane length expanded uncertainty of the customer U L in-plane length expanded uncertainty on the ROI, U ROI 8. Using the MEMS 5-in-1 To Verify In-Plane Length Measurements Then can assume measuring in-plane length according to ASTM E2244 according to your criterion for acceptance if: –Criteria above satisfied and –No pertinent “wait” statements at the bottom of your Data Sheet L.0