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Background Statement for SEMI Draft Document 5118REVISION TO SEMI MS4-1109, STANDARD TEST METHOD FOR YOUNG’S MODULUS MEASUREMENTS OF THIN, REFLECTING FILMS BASED ON THE FREQUENCY OF BEAMS IN RESONANCENote: This background statement is not part of the balloted item. It is provided solely to assist the recipient in reaching an informed decision based on the rationale of the activity that preceded the creation of this document.

Note: Recipients of this document are invited to submit, with their comments, notification of any relevant patented technology or copyrighted items of which they are aware and to provide supporting documentation. In this context, “patented technology” is defined as technology for which a patent has issued or has been applied for. In the latter case, only publicly available information on the contents of the patent application is to be provided.

BackgroundSEMI MS4-1109 provides a test method to determine the Young’s modulus for a thin, reflecting film, based on the average resonance frequency of a single-layered cantilever (or fixed-fixed beam). Young’s modulus measurements are an aid in the design and fabrication of MEMS devices and ICs.

SEMI MS4 became publicly available in November of 2007 without precision and bias data. It was written for use with a single beam laser vibrometer (or comparable instrument). The MEMS Young’s Modulus and Step Height Round Robin Experiment was held from December 2008 through April 2009. The SEMI MS4 standard was rewritten to include a) the round robin precision and bias data, b) a procedure for a dual beam laser vibrometer, and c) a procedure for a stroboscopic interferometer and was published in November 2009 after a successful reballot.

Standard reference materials (SRM 2494 and SRM 2495) are being developed to aid customer’s in their use of five documentary standard test methods (including SEMI MS4). During the review process of the standard reference materials, most sections of this test method were modified as reflected by the changes in this SEMI Document 5118, resulting in what can be considered a complete rewrite of this test method. Of particular note is the following:

1. Those definitions obtained from ASTM are modified (except for the main parameters measured in the ASTM standards),

2. A calibration procedure for frequency measurements is included,

3. Double-stuffed anchor designs for a surface-micromachining process are included to provide a rigid support,

4. A frequency correction term is added to the Young’s modulus equation, and

5. The combined standard uncertainty equations are modified to obtain relative uncertainties using the propagation of uncertainty technique.

This SEMI Document 5118 is now being balloted and the complete set of changes can be seen in the redlined version of this document. SEMI Document 5118 was approved for letter balloting in July 2011.

Review and Adjudication InformationTask Force Review Committee Adjudication

Group: MEMS Materials Characterization TF NA MEMS / NEMS CommitteeDate: Monday, October 24, 2011 Monday, October 24, 2011Time & Timezone: 1:30 PM to 2:30 PM, Pacific Time 3:00 PM to 5:00 PM, Pacific TimeLocation: SEMI Headquarters

3081 Zanker RoadSEMI Headquarters3081 Zanker Road

City, State/Country: San Jose, CA San Jose, CALeader(s): Janet Cassard (NIST, [email protected]) Mark Crocket (MEMSMART,

[email protected])Win Baylies (BayTech Group, [email protected])

Standards Staff: Paul Trio (SEMI NA)408.943.7041 /[email protected]

Paul Trio (SEMI NA)408.943.7041 / [email protected]

This meeting’s details are subject to change, and additional review sessions may be scheduled if necessary. Contact the task force leaders or Standards staff for confirmation.

Telephone and web information will be distributed to interested parties as the meeting date approaches. If you will not be able to attend these meetings in person but would like to participate by telephone/web, please contact Standards staff.

mailto:[email protected]



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Informational (Blue) Ballot1000AInformational (Blue) Ballotjn l

SEMI Draft Document 5118REVISION TO SEMI MS4-1109, STANDARD TEST METHOD FOR YOUNG’S MODULUS MEASUREMENTS OF THIN, REFLECTING FILMS BASED ON THE FREQUENCY OF BEAMS IN RESONANCENOTICE: This document was completely rewritten in 2009.

1 Purpose1.1 The absence of a generally accepted method to determine Young’s modulus has provided a challenge to the MEMS community for many years. Without a standard measurement technique, measurements between different laboratories cannot be meaningfully compared. This standard provides a test method to determine Young’s modulus for thin, reflecting films, based on the average resonance frequency of a single-layered cantilever. It also provides a test method to determine Young’s modulus based on the average resonance frequency of a single-layered fixed-fixed beam, but this method is only to be used if a cantilever is not available for measurement.

1.2 Young’s modulus measurements are an aid in the design and fabrication of MEMS devices and ICs. For example, high values of residual stress can lead to failure mechanisms in ICs such as electromigration, stress migration, and delamination. So, methods for its characterization are of interest for IC process development and monitoring in order to improve the yield in CMOS fabrication processes.1 The residual stress of a thin film layer is calculated in this test method based on the Young’s modulus value also obtained in this test method.

2 Scope2.1 This test method covers a procedure for measuring Young’s modulus in thin films. It applies only to films, such as found in microelectromechanical system (MEMS) materials that can be imaged using a non-contact optical vibrometer, stroboscopic interferometer or comparable instrument that is capable of obtaining the resonance frequency of a beam oscillating out-of-plane. (Measurements from beams that are touching or touch the underlying layer are not acceptable.) The average resonance frequency of a single-layered cantilever is used in Young’s modulus calculations. (If a cantilever is not available for measurement, the average resonance frequency of a single-layered fixed-fixed beam can be used, but this approach is not recommended due to a higher combined standard uncertainty value.) The Young’s modulus value can then be used in calculations of residual stress and stress gradient.

2.2 The fabrication, including the etching steps required to release the beams, is considered outside the scope of this test method. The determination of the beam’s length, width, thickness, and density, as well as whether the beam is exhibiting stiction is also considered outside the scope of this test method.

2.3 If the test instrument incorporates a laser, this test method only applies if the laser is Class 1 or Class 2.

NOTICE: This standard does not purport to address safety issues, if any, associated with its use. It is the responsibility of the users of this standard to establish appropriate safety and health practices and determine the applicability of regulatory or other limitations prior to use.

3 Limitations3.1 To ensure that the resonance frequency of the cantilevers or fixed-fixed beams is not altered by squeeze film or other damping phenomena, the beams should be suspended high enough above the underlying layer such that its motion is not altered by the underlying layer. In other words, for cantilevers, the gap, d, between the suspended beam and the underlying layer should adhere to the following equation:2

, (1)

1 Marshall, J. C., Herman, D. L., Vernier, P. T., DeVoe, D. L., and Gaitan, M., “Young’s Modulus Measurements in Standard IC CMOS Processes using MEMS Test Structures,” IEEE Electron Devices Letters, Vol. 28, No. 11 (November 2007): p. 960–963.2 Gregory T. A. Kovacs, “Micromachined Transducers Sourcebook,” McGraw-Hill, New York, NY (1998): p. 312.

This is a Draft Document of the SEMI International Standards program. No material on this page is to be construed as an official or adopted Standard or Safety Guideline. Permission is granted to reproduce and/or distribute this document, in whole or in part, only within the scope of SEMI International Standards committee (document development) activity. All other reproduction and/or distribution without the prior written consent of SEMI is prohibited.

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Semiconductor Equipment and Materials International3081 Zanker RoadSan Jose, CA 95134-2127Phone: 408.943.6900, Fax: 408.943.7943

DRAFTDocument Number:

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Informational (Blue) Ballot1000AInformational (Blue) Ballotjn lwhere Wcan is the width of the cantilever. These damping phenomena are expected to be present in surface micromachining processes without the use of a backside etch, unless the measurement is performed in a vacuum. The damping may not be present in bulk-micromachining processes. It is dependent upon the depth of the cavity and the vicinity of the sides of the cavity to the beam. (Squeeze film and other damping phenomena routinely lead to amplitude dependent resonance frequencies and shifts in the natural frequency of the system, which may limit the accuracy of the technique.)

3.2 For cantilevers, this test method assumes clamped-free boundary conditions, which implies that there is no undercutting of the beam. Therefore, this test method is limited by the accuracy of this assumption.

4 Referenced Standards and Documents4.1 SEMI Standard

SEMI MS2 — Test Method for Step Height Measurements of Thin Films

4.2 ANSI Standard3

ANSI Z136.1 — Standard for the Safe Use of Lasers

4.3 ASTM Standards4

ASTM E2244 — Standard Test Method for In-Plane Length Measurements of Thin, Reflecting Films Using an Optical Interferometer

ASTM E2245 — Standard Test Method for Residual Strain Measurements of Thin, Reflecting Films Using an Optical Interferometer

ASTM E2246 — Standard Test Method for Strain Gradient Measurements of Thin, Reflecting Films Using an Optical Interferometer

ASTM E2444 — Standard Terminology Relating to Measurements Taken on Thin, Reflecting Films5

NOTICE: Unless otherwise indicated, all documents cited shall be the latest published versions.

5 Terminology5.1 Abbreviations and Acronyms

5.1.1 CMOS — complementary metal oxide semiconductor

5.1.2 CMP — chemical mechanical planarization

5.1.3 FFT — fast Fourier transform

5.1.4 FOV — field of view

5.1.5 IC — integrated circuit

5.1.6 LED — light emitting diode

5.1.7 MEMS — microelectromechanical systems

5.1.8 PZT — piezoelectric transducer

5.2 Definitions

5.2.1 anchor — in a surface-micromachining process, the portion of the test structure, in a surface-micromachining process, where a structural layer is intentionally attached to its underlying layer. [ASTM E2444]

3 American National Standards Institute, Headquarters: 1819 L Street, NW, Washington, DC 20036, USA. Telephone: 202.293.8020; Fax: 202.293.9287. New York Office: 11 West 42nd Street, New York, NY 10036, USA. Telephone: 212.642.4900; Fax: 212.398.0023; http://www.ansi.org4 American Society for Testing and Materials, 100 Barr Harbor Drive, West Conshohocken, Pennsylvania 19428-2959, USA. Telephone: 610.832.9585; Fax: 610.832.9555; http://www.astm.org5 Referenced definitions reprinted, with permission, from the Annual Book of ASTM Standards, copyright ASTM International, 100 Barr Harbor Drive, West Conshohocken, PA 19428.


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http://www.astm.org/

http://www.ansi.org/

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Informational (Blue) Ballot1000AInformational (Blue) Ballotjn l5.2.2 bulk micromachining — a MEMS fabrication process that removeswhere the substrate is removed at specified locations. [ASTM E2444]

5.2.3 cantilever — a MEMS test structure that consists of a freestanding beam that is fixed at one end. [ASTM E2444]

5.2.4 fixed-fixed beam — a MEMS test structure that consists of a freestanding beam that is fixed at both ends. [ASTM E2444]

5.2.5 interferometer — a non-contact optical instrument used to obtain topographical 3-D ddata (such as 3-D data sets and 2-D data traces). [ASTM E 2444]

5.2.5.1 Discussion — The height of the sample is measured along Tthe z-axis of the interferometer is used to measure the height of the sample. The interferometer’s x-axis is typically aligned parallel or perpendicular to the measured transitional edges to be measured.

5.2.6 microelectromechanical systems — in general, thisa term is used to describe micron-scale structures, sensors, and actuators, or the and technologies used for their manufacturemanufacture (such as, silicon process technologies), or combinations thereofboth.

5.2.7 [ASTM E2444]

5.2.8 open area — in a bulk-micromachining process, a region on the chip where the silicon surface is exposed to the ambient after fabrication but before the post-processing etch that releases the beams.

5.2.9 quality factor — a measure of the sharpness of a resonance peak.

5.2.10 residual strain — in a MEMS process, the amount of deformation (or displacement) per unit length constrained within the structural layer of interest after fabrication yet before the constraint of the sacrificial layer (or substrate) is removed (in whole or in part). [ASTM E2444]

5.2.11 residual stress — the remaining forces per unit area within the structural layer of interest after the original cause(s) during fabrication have been removed yet before the constraint of the sacrificial layer (or substrate) is removed (in whole or in part).

5.2.12 sacrificial layer — to allow freestanding microstructures, a single thickness of material that is intentionally deposited (or added) then removed (in whole or in part) during the micromachining micromachining process, to allow freestanding microstructures. [ASTM E2444]

5.2.13 stiction — adhesion between the portion of a structural layer that is intended to be freestanding and its underlying layer. [ASTM E2444]

5.2.14 (residual) strain gradient — a through-thickness variation (of the residual strain) in the structural layer of interest before it is released. [ASTM E2444]

5.2.15 (residual) stress gradient — a through-thickness variation (of the residual stress) in the structural layer of interest before it is released.

5.2.16 structural layer — a single thickness of material that is present in the final MEMS device. [ASTM E2444]

5.2.17 substrate — in a fabrication process, the thick, starting material (often single crystal silicon or glass) in a fabrication process that can be used to build MEMS devices. [ASTM E2444]

5.2.18 support region — in a bulk-micromachining process, the area that marks the end of the suspended structure in a bulk-micromachining process. [ASTM E2444]

5.2.19 surface micromachining — a MEMS fabrication process where micron-scale components are formed on a substrate by the deposition (or addition) and removal (in whole or in part) of structural and sacrificial layers. [ASTM E2444]

5.2.20 test structure — a fabricated component (such as, a fixed-fixed beam or cantilever) that is used to extract information (such as, the residual strain or the strain gradient of a layer) about thea fabrication process. [ASTM E2444]


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Informational (Blue) Ballot1000AInformational (Blue) Ballotjn l5.2.21 thickness — the height in the z-direction of one or more designated thin -film layers.

5.2.22 transitional edge — the side of a MEMS structure that is characterized by a distinctive out-of-plane vertical displacement as seen in a 2-D data trace.

5.2.23 underlying layer — the single thickness of material (which can be the substrate) located directly beneath the material of interest. [ASTM E2444]

5.2.24 Discussion — This layer could be the substrate.

5.2.25 vibrometer — an instrument for non-contact measurements of surface motion.

5.2.26 Young’s modulus — a parameter indicative of material stiffness that is equal to the stress divided by the strain when the material is loaded in uniaxial tension, assuming the strain is small enough such that it does not irreversibly deform the material.

5.2.26.1 Discussion — It is also called the elastic modulus, the modulus of elasticity, and the tensile modulus.

5.3 Symbols

5.3.1 For Calibration

5.3.1.1 meter — for calibrating the time base of the instrument: the standard deviation of the measurements used to obtain fmeter.

5.3.1.2 calf — the calibration factor for a frequency measurement.

5.3.1.3 f instrument — for calibrating the time base of the instrument: the frequency setting for the calibration measurements (or the manufacturer’s specification for the clock frequency).

5.3.1.4 f meter — for calibrating the time base of the instrument: the calibrated average frequency of the calibration measurements (or the calibrated average clock frequency) taken with a frequency meter.

5.3.1.5 u certf — for calibrating the time base of the instrument: the certified uncertainty of the frequency measurements as specified on the frequency meter’s certificate.

5.3.1.6 u cmeter — for calibrating the time base of the instrument: the uncertainty of the frequency measurements taken with the frequency meter.

5.3.2 For Young’s Modulus Measurements and Calculations

5.3.2.1 — viscosity of the ambient surrounding the cantilever.

5.3.2.2 — density of the thin film layer.

5.3.2.3 E — calculated Young’s modulus value of the thin film layer.

5.3.2.4 Eclamped — calculated Young’s modulus value obtained from the average resonance frequency of a fixed-fixed beam assuming clamped-clamped boundary conditions.

5.3.2.5 Einit — initial estimate for the Young’s modulus value of the thin film layer.

5.3.2.6 Esimple — calculated Young’s modulus value obtained from the average resonance frequency of a fixed-fixed beam assuming simply-supported boundary conditions at both supports.

5.3.2.7 fcan — average calibrated undamped resonance frequency of the cantilever, which includes the frequency correction term.

5.3.2.8

5.3.2.9 f correction — correction term for the cantilever’s resonance frequency.

5.3.2.10 fffb — average uncalibrated resonance frequency of the fixed-fixed beam.

5.3.2.11 Lcan — suspended cantilever length.


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Informational (Blue) Ballot1000AInformational (Blue) Ballotjn l5.3.2.12 Lffb — suspended fixed-fixed beam length.

5.3.2.13 Q — oscillatory quality factor of the cantilever.

5.3.2.14 t — thickness of the thin film layer.

5.3.2.15 Wcan — suspended cantilever width.

5.3.3 For Combined Standard Uncertainty Calculations

5.3.3.1 — one sigma uncertainty of the value of .

5.3.3.2 — one sigma uncertainty of the value of .

5.3.3.3 σ cantilever — uncertainty in the cantilever’s resonance frequency due to geometry and/or composition deviations from the ideal.

5.3.3.4 Einit — estimated standard deviation of Einit.

5.3.3.5

fQ — the calibrated standard deviation of the frequency measurements (used to obtain fcan) that is due to damping.

freq — the calibrated standard deviation of the frequency measurements used to obtain fcanone sigma uncertainty of the value of fcan..

freqcal — the calibrated standard deviation of the frequency measurements (used to obtain fcan) that is due to the calibration of the time base for which the uncertainty is assumed to scale linearly.

5.3.3.6 fresol — the calibrated standard deviation of the frequency measurements (used to obtain fcan) that is due to the frequency resolution.

5.3.3.7 fundamped — one sigma uncertainty of the calibrated undamped resonance frequency measurements.

5.3.3.8 L — one sigma uncertainty of the value of Lcan.

5.3.3.9 support — the estimated uncertainty in the cantilever’s resonance frequency due to a non-ideal support (or attachment conditions).

5.3.3.10 thick — one sigma uncertainty of the value of t.

5.3.3.11 W — one sigma uncertainty of the value of Wcan..

5.3.3.12 Emax — maximum Young’s modulus value as determined in an uncertainty calculation.

5.3.3.13 Emin — minimum Young’s modulus value as determined in an uncertainty calculation.

5.3.3.14 fresol — uncalibrated frequency resolution for the given set of measurement conditions.

5.3.3.15 pdiff — estimated percent difference between the damped and undamped resonance frequency of the cantilever.

5.3.3.16

5.3.3.17 U E — the expanded uncertainty of a Young’s modulus measurement.u — component in the combined standard uncertainty calculation for Young’s modulus that is due to the uncertainty of .

5.3.3.18 ucE — combined standard uncertainty value of a Young’s modulus measurement(that is, the estimated standard deviation of the result) as obtained from the resonance frequency of a cantilever.

5.3.3.19 udamp — component in the combined standard uncertainty calculation for Young’s modulus that is due to damping.


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Informational (Blue) Ballot1000AInformational (Blue) Ballotjn l5.3.3.20 u E — uncertainty of a Young’s modulus measurement as obtained from the resonance frequency of a fixed-fixed beam.ufreq — component in the combined standard uncertainty calculation for Young’s modulus that is due to the measurement uncertainty of fcan.

5.3.3.21 ufresol — component in the combined standard uncertainty calculation for Young’s modulus that is due to fresol.

5.3.3.22 uL — component in the combined standard uncertainty calculation for Young’s modulus that is due to the measurement uncertainty of Lcan.

5.3.3.23 uthick — component in the combined standard uncertainty calculation for Young’s modulus that is due to the measurement uncertainty of t.

5.3.4 For Residual Stress and Stress Gradient Calculations

5.3.4.1 r — residual strain of the thin film layer.

5.3.4.2 g — stress gradient of the thin film layer.

5.3.4.3 gmax — maximum stress gradient value as determined in an uncertainty calculation.

5.3.4.4 gmin — minimum stress gradient value as determined in an uncertainty calculation.

5.3.4.5 r — residual stress of the thin film layer.

5.3.4.6 rmax — maximum residual stress value as determined in an uncertainty calculation.

5.3.4.7 rmin — minimum residual stress value as determined in an uncertainty calculation.

5.3.4.8 sg — strain gradient of the thin film layer.

5.3.4.9

5.3.4.10 U g — the expanded uncertainty of a stress gradient measurement.

5.3.4.11 U r — the expanded uncertainty of a residual stress measurement.

5.3.4.12 u cr — combined standard uncertainty value for residual strain.

5.3.4.13 u cg — combined standard uncertainty value for stress gradient.

ur(r) — component in the combined standard uncertainty calculation for residual stress that is due to the measurement uncertainty of r.

ucr — combined standard uncertainty value for residual strain.

ucg — combined standard uncertainty value for stress gradient.

ucr — combined standard uncertainty value for residual stress.

5.3.4.14 u csg — combined standard uncertainty value for strain gradient.uE(g) — component in the combined standard uncertainty calculation for stress gradient that is due to the measurement uncertainty of E.

5.3.4.15 uE(r) — component in the combined standard uncertainty calculation for residual stress that is due to the measurement uncertainty of E.

5.3.4.16 usg(g) — component in the combined standard uncertainty calculation for stress gradient that is due to the measurement uncertainty of sg.

6 Summary of Method6.1 This test method can be used to obtain Young’s modulus measurements of thin films and their combined standard uncertainty values. A PZT is used in this test method to create out-of-plane excitations in beams comprised of one layer (such as shown in Figures 11 andthrough Figure 23). For each beam, an optical vibrometer, stroboscopic interferometer, or comparable instrument records an excitation-magnitude versus frequency plot from which the resonance frequency is found.


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Informational (Blue) Ballot1000AInformational (Blue) Ballotjn l1: Although this test method uses a PZT to excite the beams; it does not imply that a PZT is the only means available for excitation (for example, thermal excitation6 is possible). For alternate means of excitation, modifications will need to be made, as appropriate, to obtain the required data.

6.2 A single-layered cantilever is used to obtain the Young’s modulus value of that layer. Three measurements of resonance frequency are taken and the average undamped resonance frequency of the cantilever is calculated. Given this value, the Young’s modulus value is determined assuming clamped-free boundary conditions and assuming a density value. The combined standard uncertainty value, ucE, is determined in Appendix 1 from the uncertainty components for the cantilever thickness, density, length, resonance frequency, frequency resolution, and damping.

6.3 If a cantilever is not available for measurement, a fixed-fixed beam can be used. (However, this approach is not recommended due to a higher resulting uncertainty value for the combined standard uncertainty.) Given the average resonance frequency of the fixed-fixed beam, two values of Young’s modulus are calculated; one assuming simply-supported boundary conditions at both supports (Esimple) and one assuming clamped-clamped boundary conditions (Eclamped). Given these two Young’s modulus values, the average Young’s modulus is calculated and recorded as the Young’s modulus value for the thin film layer. The combined standard uncertainty is calculated assuming Esimple and Eclamped are three sigma values.

6.4 Residual stress and stress gradient calculations for the thin film layer can be found in Appendix 2.

6.5 The procedure specified in the body of this test method is for use with an optical vibrometer or comparable instrument. The procedure specified in Appendix 3 is for use with a stroboscopic interferometer or comparable instrument.

6 Gabrielson, T.B., “Mechanical-Thermal Noise in Micromachined Acoustic and Vibration Sensors,” IEEE Transactions on Electron Devices, Vol. 40, No. 5 (May 1993): pp. 903–909.Oden, P.I., “Gravimetric sensing of metallic deposits using an end-loaded microfabricated beam structure,” Sensors and Actuators B, 53 (1998): pp. 191–196.Lawrence, E. M., Rembe, C., “MEMS Characterization using New Hybrid Laser Doppler Vibrometer/Strobe Video System,” SPIE Proceedings Vol. 5343, Reliability, Testing, and Characterization of MEMS/MOEMS III (January 2003): pp. 45–54.


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Three-Dimensional View of Surface-Micromachined Cantilever

a)


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b)

c)

NOTE 1: The underlying layer is beneath the entire test structure. NOTE: NOTE 2: The structural layer is included in both the light and dark gray areas.

NOTE: NOTE 3: The dark gray area (the anchor) is the designed cut in the sacrificial layer. This is where the structural layer contacts the underlying layer.

NOTE: NOTE 4: The light gray area is suspended in air after fabrication.Figure 1

For Surface Micromachined Cantilever a) the Design Dimensions, b) Cross Section along Trace a in a), and c) Cross Section along Trace b in a)Design Dimensions for

Cantilever in Figure 1


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NOTE: NOTE 1: The central beam is suspended above a micromachined cavity. NOTE: NOTE 2: The dark gray areas are the visible parts of the micromachined cavity.

NOTE: NOTE 3: The remaining light gray area around the outside of the visible portion of the cavity and including the black dimensional markers is either suspended in air or attached underneath to the substrate.NOTE: NOTE 4: The black dimensional markers are typically made of polysilicon or metal encapsulated

in oxide to obtain a more accurate measurement of Lffb after the post-processing etch.

Figure 2Top View of Bulk-Micromachined Fixed-Fixed Beam

7 Interferences7.1 Stiction — Measurements from beams that are touching the underlying layer are not accepted.

2: To determine if a cantilever is adhered to the top of the underlying layer, consult ASTM E2246. To determine if a fixed-fixed beam is adhered to the top of the underlying layer, consult ASTM E2245. This is considered outside the scope of this test method.

7.2 Damping — Measurements from certain beams in certain ambient environments experience more damping than others. Measurements from these beams are not recommended. See ¶ 10.2.4 for some geometrical considerations.

8 Apparatus8.1 Non-Contact Optical Vibrometer, Non-Contact Optical Stroboscopic Interferometer, or an Instrument Comparable to one of these — Capable of non-contact measurements of surface motion in the z-direction. Additional specifications for this instrument are given in ¶¶ 8.1.18.1.6.

3: A schematic of a typical setup for a single beam laser vibrometer is shown in Figure 34. A signal generator provides an excitation signal, which excites the sample via a PZT. The measurement beam is positioned to a scan point on the sample (by means of mirrors) and is reflected back. The reflected laser light interferes with the reference beam at the beam splitter. A photodetector records the interference signal, converting it into an electrical signal. The frequency difference between the beams is proportional to the instantaneous velocity of the vibration parallel to the measurement beam. (The Bragg cell is instrumental in determining the sign of the velocity.) The velocity decoder provides a voltage proportional to the instantaneous velocity.

4: A dual beam laser vibrometer incorporates two beams. The measurement beam is positioned to a scan point on the sample (for example, positioned near the tip of a cantilever). The reference beam emanates from the beam splitter (BS) shown in Figure 34 and is positioned to a point on the sample (for example, positioned on the support region at the base of the cantilever). The two scattered beams optically combine at the beam splitter where the reference beam is used to directly eliminate any movement of the sample also experienced by the measurement beam.

A simplified schematic of a typical setup for a stroboscopic interferometer is shown in Figure 45a. When operated in the static mode, the interferometer is used to determine surface profiles. The incident light travels through the microscope objective to the beam splitter. Half of the light travels to the sample surface and then back to the beam splitter. The other half is reflected to a reference surface and then back to the beam splitter. These two paths of light recombine at the beam splitter to form interference light fringes. As the interferometer scans downward, an intensity envelope incorporating these fringes is determined by the software (see Figure 45b). The peak contrast of the fringes, phase, or both are used in determining the sample height at that pixel


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Informational (Blue) Ballot1000AInformational (Blue) Ballotjn llocation. The surface profile is found by collecting sample height data for each pixel within the FOV. When operated in the dynamic mode, the incident light is strobed at the same frequency as that used to actuate the device. The sample is actuated, in this test method, after securing it to the top of a PZT. The phase, frequency, and drive signal to the strobe and PZT are varied, performing a downward scan as is done for static devices at each combination to obtain successive 3D images as the sample cycles through its range of motion.

5:

6:

7:

NOTE: NOTE: PBS indicates a polarizing beam splitter; BS indicates a beam splitter; P indicates a prism; and PD indicates a photodetector.

Figure 3Schematic of a Typical Setup for a Single Beam Laser Vibrometer

a) b)


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Informational (Blue) Ballot1000AInformational (Blue) Ballotjn lFigure 4

For a Typical Stroboscopic Interferometer (a) a Schematic and (b) an Intensity Envelope Used to Obtain a Pixel’s Sample Height

8.1.1 The microscope objective or objectives should be chosen to allow for sufficient resolution of the cantilever or fixed-fixed beam and a portion of the surrounding sample. The objective(s) should have a FOV that can encompass at least half of the length of the cantilever or fixed-fixed beam being measured. For the dimensions of the example beams described in this document, objectives of 4× and 20× will suffice.

8.1.2 The signal generator should be able to produce a waveform function (such as a periodic chirp function or a sine wave function) if applicable, such that from its use, a reproducible resonance frequency can be obtained and good 3-D oscillating images can be obtained such that it is obvious by inspection that the beam is in resonance.

8: The periodic chirp function mentioned above enables quick results without averaging. For the periodic chirp function, sinusoidal signals (within the selected frequency range and of the same amplitude) are emitted simultaneously for all FFT lines. The periodic chirp function is periodic within the time window and the phases are adapted to maximize the energy of the resulting signal.

9: The periodic chirp function produces a reproducible resonance frequency. A sine wave sweep function produces a resonance frequency that can be affected by the direction of the sweep if there is not a sufficient amount of time between measurements.

8.1.3 The instrument shall be capable of producing a magnitude versus frequency plot from which the resonance frequency can be obtained.

8.1.4 The instrument should be capable of obtaining 3-D images of oscillations in order to ascertain if the correct frequency peak has been chosen as the beam’s resonance frequency.

8.1.5 An estimate for the maximum frequency of the instrument needed for a resonating cantilever, fcaninit, is at least the value calculated using the following equation:7

, (2)

where details concerning the parameters in this equation can be found in § 5.3 and § 13.7. An estimate for the maximum frequency of the instrument needed for a resonating fixed-fixed beam, fffbinithi, is at least the value calculated using the following equation:Error: Reference source not found7

, (3)

where details concerning the parameters in this equation can be found in § 5.3 and § 13.7.

8.1.6 An instrument that can make differential measurements (e.g., with the use of two laser beams) is recommended for use with fixed-fixed beams. It is also recommended for use with cantilevers, especially for estimated resonance frequencies less than 10 kHz and also if the value for pdiff as calculated in the following equation is greater than or equal to 2%:Error: Reference source not foundError: Reference source not found

. (4)

7 By inserting the inputs into the correct locations on the appropriate NIST MEMS Calculator NIST Wweb Ppage (http://www.eeel.nist.gov/812/test-structures/MEMSCalculator.htm), the calculations in this test method can be performed on-line in a matter of seconds. The MEMS Calculator Web Site (Standard Reference Database 166) is accessible via the NIST Data Gateway (http://srdata.ni s t. gov /gateway/ ) with the keyword “MEMS Calculator.”Also consult Cassard, J. M., Geist, J., Vorburger, T. V., Read, D. T., and Seiler, D. G., “Standard Reference Materials: User’s Guide for SRM 2494 and 2495: The MEMS 5-in-1, 2011 Edition,” NIST Special Publication 260-174, National Institute of Standards and Technology, September 2011.


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Informational (Blue) Ballot1000AInformational (Blue) Ballotjn lIn the above equation, fdampedn is the nth calibrated damped resonance frequency measurement and fundampedn is the nth calibrated undamped resonance frequency to be discussed later in § 14.1this test method. For a cantilever, the Q-factor, Q, in Equation (4) can be estimated using the following equation:Error: Reference source not foundError:Reference source not found, 8

, (5)

wWhere is the viscosity of the ambient (in air, =1.84e5 Ns/m2 at 20°C).9 and Wcan is the suspended width of the cantilever obtained in the most accurately available fashion. This is considered outside the scope of this test method. Details concerning the other parameters in this equation can be found in § 5.3 and § 13.7.

8.2 Amplifier (optional) — With a gain of 10 and bandwidth of 8 kHz for the vibrometer and with a gain of 50 and bandwidth of 200 kHz for the stroboscopic interferometer, to amplify the excitation signal going to the PZT.

8.3 Low Voltage PZT (with two wire leads) — To cause out-of-plane vibrations in the chip and excite the cantilevers and fixed-fixed beams on the chip. The dimensions of a representative PZT are approximately 5 mm by 5 mm and 2 mm in height. It can achieve a 2.2 m (±20%) displacement at 100 V from DC to 100 kHz and has an electrical capacitance of 250 nF (±20%). It has a resonance frequency greater than 300 kHz, at which or above which it shall not be operated because it could damage the PZT.

8.4 The PZT can be mounted within a package using a low stress non-conducting epoxy, which allows movement and which does not electrically short the PZT. The two wire leads can provide contact to their respective package pins with the red wire is driven with a voltage that is positive relative to the black wire.

8.5 Low Stress Non-conducting Epoxy Double-Stick Tape (for example, removable) — For mounting the chip to the top of the PZT, unless a more permanent gluing technique is preferred to allow movement and to not electrically short the PZT. It can also be used to permanently attach the PZT to the microscope slide or to a package.

8.6 Microscope Slide — Serves as a non-conductive substrate upon which the PZT is permanently securely mounted. An alternate mounting, e.g., within a a package, can be used as long as the PZT is not electrically shorted.

8.7 Solderless Breadboarding Socket (optional) — To aid stability to the package sample assembly during setup and measurement, if applicable.

8.8 Small Mirror — To check the spot size of the measurement beam, if applicable.

8.9 Frequency Meter — With a resolution capability of at least 10 digit/sec, to calibrate the time base of the instrument.

8.10 Oscilloscope (optional) — To monitor waveforms, such as the drive signals to the PZT.

8.11 Thermometer (optional) — To record the temperature during measurement.

8.12 Humidity Meter (optional) — To record the relative humidity during measurement.

9 Safety Precaution9.1 If the light source of the optical vibrometer, stroboscopic interferometer, or comparable instrument is a laser, do not look directly into the laser beam or into the reflected laser beam (see ANSI Z136.1). If a laser light source is used, this test method only applies to Class 1 and Class 2 lasers.

10: Class 1 lasers are exempt from control measures because they do not emit harmful levels of radiation. However, as a general practice, unnecessary exposure to Class 1 laser light should be avoided.

11: Class 2 lasers can cause eye damage through chronic exposure. When exposed to Class 2 laser light, the human eye will generally blink within 0.25 seconds, which protects the eye. However, eye damage can be caused by overcoming this blink reflex and staring into the laser.

8 Kiesewetter, L., Zhang, J. – M., Houdeau, D., and Steckenborn, A., “Determination of Young’s moduli of micromechanical thin films using the resonance method,” Sensors and Actuators A, vol. 35 (1992) pp. 153–159.9 CRC Handbook of Chemistry and Physics, 91st Edition, 2010-2011 (on-line edition), Accessed August 15, 2011 at http://208.254.79.26/ (subscription required).


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Informational (Blue) Ballot1000AInformational (Blue) Ballotjn l10 Test Specimen10.1 The design of a representative cantilever or fixed-fixed beam comprised of one layer in a surface-micromachining process is specified below in § 10.2. For a bulk-micromachining process, the design is specified in § 10.3. The specific process steps, necessary to realize the beams specified in this section, are considered outside the scope of this test method.

10.2 Cantilever and Fixed-Fixed Beam Test Structure Design Comprised of One Layer in a Surface-Micromachining Process

10.2.1 Structural Layer — The beam consists of the thin-film layer under investigation for Young’s modulus calculations.

10.2.2 Width — The final beam width shall be greater than the beam thickness. The width should be at least 5 m and it shall be no less than one third the spot size of the measurement beam. The cantilever or fixed-fixed beam width should be small enough (e.g., less than 50 m) such that there are no curling issues due to compressive stresses along the beam’s projected width on the anchor lip. The width of the beam shall be small enough such that holes or openings in the layer along the beam are not required (e.g., to successfully release the beams). Also dimples that are protruding from the bottom of the beam are not allowed. (Such dimples are often used to minimize stiction.)

12: The width of the beam should be at least 5 m to ascertain whether or not the cantilever or fixed-fixed beam is exhibiting stiction, if applicable, using ASTM E2246 or ASTM E2245, respectively. The stiction criteria may need to be modified for double stuffed anchor designs such as the one shown in Figure 1.

13: The cantilever or fixed-fixed beam width shall be no less than one third the optical spot size of the measurement beam. The limiting factor is the amount of light reflected off the cantilever or fixed-fixed beam in comparison to the “background” of the cantilever or fixed-fixed beam. For example, given a 1.5 m spot size, if you try to measure a 1 m wide cantilever and if the background of the cantilever did not reflect any light, a good measurement should result. However, if more signal came from the background than the cantilever, then the measurement would be in question. It is estimated that with a 1.5 m spot size, the smallest cantilever or fixed-fixed beam that can be measured is around 0.5 m, assuming the conditions are right. To simplify the measurement, cantilevers or fixed-fixed beams at least ten times this minimum width are preferable.

10.2.3 Length — The beam length shall be significantly greater than the beam thickness (e.g., the length should be at least 100 m if the beam thickness is 2 m). The maximum length of both cantilever and fixed-fixed beam is dictated by process limitations (such as, stiction).

10.2.4 Combined Dimensions — For each cantilever geometry under consideration, calculate an estimate for the Q-factor using Equation (5). Values for Wcan, Lcan, and t [used in Equation (5)] should be such that pdiff as calculated in Equation (4) is kept as small as possible (e.g., less than 2%) in order to get a reasonable size resonance frequency peak for measurement.

10.2.5 Anchor — For a representative anchor, such as a double stuffed anchor for p1 cantilevers shown in Figure 1, theEach anchor to p1 (called anchor1) shall extend beyond the width of the beam in the ±y-directions at least 5 m, as shown in Figure 2 for a cantilever. The cut in the sacrificial layer that defines the p1 anchor should be at least 50 m × 50 m (as shown in Figure 12a) to resemble an infinite support, to provide an area to place the reference beam for use with a dual beam vibrometer, and to provide a possible area for the reference region for use with a stroboscopic interferometer. The dimensions for the other layers in the double stuffed pad design are given in Figure 1a. determine if the beam has adhered to the top of the underlying layer as ascertained in ASTM E2246 for a cantilever (and ASTM E2245 for a fixed-fixed beam). [For a fixed-fixed beam, the additional anchor added to the free end of the cantilever (thereby making it a fixed-fixed beam) should be a mirror image of the one shown in Figure 12a, however the cut in the sacrificial layer for this extra anchor can be reduced in size to 50 m in the y-direction and 8 m in the x-direction.]

10.2.6 Anchor Lip — The width of the anchor lip from which the suspended layer extends should be between 5 m and 10.0 m, inclusive, as shown in Figure 2. The anchor lip is anchored on either side of the cantilever (such as shown in Figure 1a with the specified design dimensions) to make a more rigid support for the cantilever. [For a fixed-fixed beam, the additional anchor added to the free end of the cantilever (thereby making it a fixed-fixed beam) should be a mirror image of the one shown in Figure 1a such that these additional anchors are also included.]

10.2.7 Additional Underlying Layers — The underlying layer shall be unpatterned beneath the structural layer of interest and should extend at least 5 m beyond the outermost edges of this patterned, structural layer (as shown in Figure 2). However, the underlying layer should extend at least 50 m beyond the anchor lip in the minus x-


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Informational (Blue) Ballot1000AInformational (Blue) Ballotjn ldirection (as shown in this figure) to permit a determination of whether or not the beam has adhered to the top of the underlying layer, if necessary (see ASTM E2245 or ASTM E2246). No other layers should be patterned within 4 µm of the pad design shown in Figure 1a and no other layers should be patterned within 10 µm of the suspended cantilever. However, if the beam width is greater than 30 µm, no other layers should be patterned within Wcan/3 of the suspended cantilever. These rules do not apply to any layers associated with aNo other structures should be designed on the underlying layer within the outermost dimensions given in Figure 2. However, Iif a backside etch that isis used to eliminate stiction concernsand squeeze film damping phenomena. Contact the fabrication service or facility for ,will be used, follow the design guidelines for use with a backside etch.the underlying layer as specified by the fabrication facility.

10.2.8 Each anchor shall support only one beam.

14: If the anchor lip vibrates, the measured resonance frequency of the beam of interest can be affected. If this anchor hosts two beams, the additional beam can create additional vibrations in the anchor lip, thus potentially adversely affecting the measured resonance frequency of the beam of interest. This shall be avoided.

10.2.9 Number — A sufficient number of cantilevers should be fabricated in order to obtain at least one cantilever after fabrication that is viable and has not adhered to the top of the underlying layer, if applicable. It is recommended that at least six different length (yet same width) cantilevers be designed of the same layer in order to safeguard against stiction at the longer lengths and also to potentially verify the consistency of the Young’s modulus results as a function of length, if desired. Although not recommended as the test structure from which to obtain Young’s modulus, a sufficient number of fixed-fixed beams can be fabricated in order to obtain at least one fixed-fixed beam after fabrication that is viable and has not adhered to the top of the underlying layer, if applicable. It is recommended that at least six different length (yet same width) fixed-fixed beams be designed of the same layer in order to safeguard against stiction at the longer lengths.

10.2.10 Backside Etch — A backside etch may be required for surface micromachining processes to eliminate stiction and squeeze film damping issues, in which case, follow the design guidelines specified by the fabrication service or facility to locate the areas to be etched and to make any necessary modifications to the other design layers. This backside etch is considered outside the scope of this test method. As a general guideline, avoid or minimize the placement of any design or subsequently fabricated edges a) within the structural layer under investigation for Young’s modulus measurement or b) coincident with the edges of this structural layer. Also, it is recommended that the edge of the nitride layer be as close to the pad design as can be successfully fabricated without being within the pad design in order to minimize or eliminate any residual damping effect due to the presence of the nitride layer.

10.2.11 Post-Processing Etch — The post-processing etch that removes the sacrificial layer (in whole or in part) after fabrication is considered outside the scope of this test method.Backside Etch — A backside etch may be required for surface micromachining processes to eliminate stiction and squeeze film damping issues, in which case, follow the design guidelines specified by the fabrication facility to locate the areas to be etched and to make any necessary modifications to the other design layers. This backside etch is considered outside the scope of this test method.

10.2.12 Post-Processing Etch — The post-processing etch that removes the sacrificial layer (in whole or in part) after fabrication is considered outside the scope of this test method.

10.3 Cantilever and Fixed-Fixed Beam Test Structure Design Comprised of One Layer in a Bulk-Micromachining Process — Apply the specifications given in ¶¶ 10.2.1–10.2.4, ¶¶ 10.2.8–10.2.9, and ¶ 10.2.111 to a bulk-micromachined test structure. Also, adhere to the specifications given below in ¶¶ 10.3.1–10.3.5. Modifications to these specifications are expected for CMP processes.)

15: The bulk micromachined fixed-fixed beam design in Figure 2, as specified below (along with a similar cantilever design) consists of four layers of oxide (the field oxide, two deposited oxides, and a glass layer).10 These four SiO2 layers may have different material properties thus causing deviations from a single-layered cantilever model as used in this test method. Therefore, the resulting Young’s modulus would be considered an effective Young’s modulus.

10.4

10 Cassard, J. M., Geist, J., Vorburger, T. V., Read, D. T., and Seiler, D. G., “Standard Reference Materials: User’s Guide for SRM 2494 and 2495: The MEMS 5-in-1, 2011 Edition,” NIST Special Publication 260-174, National Institute of Standards and Technology, September 2011.


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Informational (Blue) Ballot1000AInformational (Blue) Ballotjn l10.4.1 Support Region — The layer comprising the beam should extend well within the support region (e.g., 20 m), if applicable.

10.4.2

10.4.3 Open Area Construct — The designed “open area” is adjacent to the three unsupported sides of the designed cantilever (or the two unsupported sides of the fixed-fixed beam) where the raw silicon will be exposed to air for a subsequent post-processing etch. The design layers and rules for such a construct must be acquired from the fabrication service or facility. For a CMOS process that does not utilize any CMP steps, the open area typically consists of the following design layers: active area, contact, via (one or more), and glass. For a CMOS process incorporating one or more CMP process steps, the design should be determined in consultation with the fabrication service or facility.

10.4.4 Open Area Dimensions — The open area shall be large enough such that the post-processing etchant of choice can remove enough silicon directly beneath the designed open area as well as underneath the designed beam [(see Equation (1)]) such that the resonance frequency of the beam will not be affected by the presence of the remaining silicon both beneath and beside it. In addition, the 90° corners of the open area where the beam protrudes from the support region should be well defined, enabling an accurate length measurement and not adversely affecting the resonance frequency of the beam. (The larger open areas tend to have more well defined corners.) For each cantilever designed with, for example, a zero degree orientation, consider including a cantilever designed with a 180 degree orientation to ensure a high quality fabrication for at least one of these cantilevers since the fabrication of well defined corners can be directionally dependent.

16: The choice of etchant can affect the design of the open area.

10.4.5 Distance Between Open Areas — The distance between the open areas of neighboring test structures is typically designed close to 90 m initially so that the open areas do not merge together. For the given etch, this dimension may need to be increased if the etchant is highly isotropic such that the rate of undercutting is approximately equal to the rate of the vertical etch. Likewise, this dimension may be decreased if the amount of undercutting is insignificant for the given etch.

10.4.6

10.4.7 Dimensional Markers — It is recommended that markers be designed near the open area of the support region of the beam (positioned as shown in Figure 23). They are typically made of polysilicon or metal encapsulated in oxide and are designed approximately 16 m in width and 16 m away from the designed open area. These markers can be used to ascertain a) the completeness of the post-processing etch and b) the post-processing length of the beam. For example, during the post-processing etch, if the oxide on the support region becomes reduced in size, this reduction can be measured (using ASTM E2244) and the new length of the beam calculated.

10.4.8 Etch Stop — An etch stop can be designed around the outer parts of the open areas to inhibit the etch away from the test structure, thereby shielding neighboring featurescircuitry and devices from the etch. An etch stop consisting of n-implant designed to surround the active area is typically used; however, it depends upon the choice of etchant. Although not pictured in Figure 23, the active area can be designed about 12 m in width and about 8 m from the outer edge of the open area. The design layer for the implant can overlap the active area by 4 m on each side. However, consult the design rules for the latest dimensions.

The distance between the open areas of neighboring test structures is typically designed close to 90 m initially so that the open areas do not merge together. For the given etch, this dimension may need to be increased if the etchant is highly isotropic such that the rate of undercutting is approximately equal to the rate of the vertical etch. Likewise, this dimension may be decreased if the amount of undercutting is insignificant for the given etch.

11 Preparation of Apparatus11.1 If a laser light source is to be used, it should be allowed to warm up for sufficient time to become thermally stable, as specified in the manufacturer’s instructions.

11.2 Set up the apparatus.


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Informational (Blue) Ballot1000AInformational (Blue) Ballotjn l11.2.1 Permanently mount the PZT at or near the center of the microscope slide, if appropriate and if not already mounted (see ¶Note 8.5). Alternatively, the PZT can be mounted within a package using two coats of a low stress non-conducting epoxy. Applying two coats can ensure that the PZT is not electrically shorted.

11.2.2 Connect the amplifier, if it will be used, between the signal generator and the PZT. Ensure that the PZT is connected with the correct polarity. Typically, this means that the red PZT wire is driven with a voltage that is positive relative to the black PZT wire; however some amplifiers may have reversed polarity (see the manufacturer’s instructions).

11.3 Check the diameter of the light source’s spot, if applicable. If a laser light source is used, base all observations on the spot’s image seen on the computer screen. Do not try to do this while looking through the microscope as specified in the safety precaution in § 9. Most laser accidents in research settings occur during alignment procedures.

11.3.1 Place a small mirror under the microscope. While observing the spot size of the measurement beam on the computer screen, adjust the focus. For a dual beam system, also focus the reference beam.

11.3.2 If the spot size of the measurement beam (or the reference beam, if applicable) is larger than what the manufacturer specifies, make sure the microscope is mechanically aligned and that everything is “tight.”

12 Calibration12.1 If the measurement beam is compared to a reference beam, an internal calibration is automatically performed with each measurement. However, the beams may become out of alignment and require an adjustment by the instrument manufacturer. Consult with the instrument manufacturer for alignment guidelines and recommended maintenancerecalibration intervals. Perform any additional calibration that the manufacturer may recommend.

12.2 To calibrate the time base of the instrument, the following steps are taken:

12.2.1 Contact the instrument manufacturer to ensure that the appropriate signal(s) are measured. Typically, only the maximumone frequency (from which all other signals are derived) needs to be measured and this case will be considered. Therefore, given the maximum frequency, finstrument, of the instrument as specified by the manufacturer, take at least three measurements with a calibrated frequency meter and record the average of these measurements, fmeter, and the standard deviation of these measurements, meter.

12.2.2 Record ucertfmeter (the certified uncertainty of thea frequency meter)measurement) from the frequency meter’s certificate for the frequency being measured (that is, fmeter). If the calibration certificate for the frequency meter says that the uncertainty is negligible for this frequency, set ucertf equal to 0 Hz.equate meter with ucmeter for use in Appendix 1. Calculate the uncertainty of a frequency measurement for use in Appendix 1 as follows:

. (6)

12.2.3 Calculate the calibration factor, calf, using the following equation:

. (76)

17: The frequency measurements are multiplied by calf to obtain calibrated values.

13 Procedure18: The following steps are for measurements taken with an optical vibrometer or comparable instrument and may not pertain to all instruments, therefore modifications will need to be made, as appropriate, to obtain the required data. For measurements taken with a stroboscopic interferometer or comparable instrument consult Appendix 3.

13.1 Adhere to the safety precaution in § 9 by making sure the laser beam can not be viewed through the microscope objective.


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Informational (Blue) Ballot1000AInformational (Blue) Ballotjn l13.2 Obtain the resonance frequency values for a cantilever using the following five steps (given in §§ 13.3–13.7, inclusive): (a) mount the chip, (b) prepare the instrument, (c) record a data scan to a data file, (d) record the resonance frequency values, and (e) obtain the other calculation inputs.

19: It is recommended that Young’s modulus is found from the average resonance frequency of a cantilever. However, if a cantilever is not available for measurement, a fixed-fixed beam can be used with the understanding that a larger uncertainty value for uc will result.

13.3 Mount the Chip

13.3.1 If the chip is not already mounted to the top of the PZT, mount the chip using two coats of a low stress non-conducting epoxy. The two coats of epoxy will help ensure that the PZT is not electrically shorted. It is recommended that , place a small square of double-stick tape flush with the top of the PZT. Mount the chip be centered on the PZT and mounted flush with the top of the PZTdouble-stick tape, centered on the PZT, and making the chip as perpendicular as possible to the z-axis of the instrument, where the z-axis is parallel to the measurement beam. Ensure that the PZT is not electrically shorted. Note that a more permanent gluing technique, for example using a low stress non-conducting epoxy, may be preferred.

20: Tape should not be used for mounting because the heat from the optics can unglue the tape which can alter the resonance frequency peak and create additional peaks.

13.3.2 Place the sample assembly under the microscope and clamp the microscope slide, if applicable, to the microscope stage. If the chip and PZT are mounted within a package, the package can be inserted into a solderless breadboarding socket to increase the stability of the sample assembly during setup and measurement.

13.4 Prepare the Instrument

13.4.1 If the previous settings were saved in ¶ 13.4.9, load these settings, otherwise:

13.4.1.1 Select an appropriate waveform function (such as the periodic chirp function with an amplitude of 2 V and offset of 2 V) for the signal generator. (This implies that if an amplifier with a gain of 10 is used, the PZT will be activated between 0 V and 40 V for the specified periodic chirp function.) To obtain optimum voltage settings for a particular setup, an oscilloscope can monitor the amplifier output when connected to the PZT. Select to take an average of at least 3 measurements per scan point.

21: The periodic chirp function is discussed in Notes 6 and Note 7.

22: For peaks that can be difficult to locate (for example, higher frequency peaks), taking an average of 100 or more measurements per scan point may be appropriate.

13.4.1.2 Select the smallest possible range for the velocity decoder in which the output signal is not clipped.

23: For some instruments, the clipping of the signal can be monitored by observing LED lights both before (in ¶ 13.4.8) and during (in ¶ 13.5.2) the taking of the measurements. If clipping occurs, choose the next higher measurement range.

13.4.1.3 Choose a relatively large frequency range. For example, for cantilevers, choose a range ±10 kHz to ±20 kHz around the estimate for fcaninit calculated in Equation (2) and for fixed-fixed beams, a range ±20 kHz around the average of fffbinithi as calculated in Equation (3) and fffbinitlo as calculated below:Error: Reference source not found7

, (678)

where details concerning the parameters in this equation can be found in § 5.3 and § 13.7, and where E is substituted for Einit in Equation (3) and Equation (876), if available. Modify the instrumental settings (for example, by choosing the maximum number of FFT lines and by choosing a slightly smaller frequency range) if a smaller value for the frequency resolution, fresol, is possible. Record this uncalibratede frequency resolution, fresol.

13.4.2 Focus the sample using a low magnification objective (e.g., a 4× objective).

13.4.3 Locate the cantilever or fixed-fixed beam for measurement under the microscope and center it within the FOV.


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Informational (Blue) Ballot1000AInformational (Blue) Ballotjn l13.4.4 Switch to the highest magnification objective that is available and feasible (e.g., a 20× objective) and focus the measurement beam (while viewing the computer screen or, if applicable to the instrument chosen, while monitoring the LED lights) at a location midway between an anchor or support region and the farthest point along the beam at which measurements are expected to be taken. The measurement beam will have its smallest diameter when it is in focus and, if applicable to the instrument chosen, more LED lights will be activated. For a dual beam system, also, position the reference beam on the anchor or support region as described in more detail below.

24: It is not necessary that the entire length of the cantilever or fixed-fixed beam be within the FOV, but a portion of an anchor or support region should be.

25: Using a high magnification objective (for example, 20×) will help ensure that the scanned data points are actually on the beam being measured. In other words, it will be easier to be sure that the alignment is satisfactory. Also, it is easier to focus at higher magnification thus enabling larger resonance frequency peaks. In addition, higher magnification objectives are recommended for beams with excessive curl.

13.4.5 Align the coordinates of the instrument (with respect to the points given in Figure 56) to further ensure the location of the measurement beam.

26: Multiple beams may appear on the computerized image due to multiple reflections. Therefore, align the coordinates with respect to the beam whose reflections disappear when it traverses over a trench. Only one beam should qualify. Consult with the instrument manufacturer for ways to minimize or eliminate the reflections on the computer screen.

27: For a fixed-fixed beam, the alignment points shown in Figure 6 5 can be used if the fixed-fixed beam does not fit within the FOV. If it does fit within the FOV, two additional alignment points can be added on the other anchor or support region.

13.4.6 Test the alignment by ensuring that the measurement beam reaches several key locations (such as those shown in Figure 56) on the sample. If the alignment is off, repeat from ¶ 13.4.4.

Figure 5Aligning the Coordinates on a Bulk-Micromachined Cantilever

13.4.7 Define the scan points for the measurement. For cantilevers, a recommended scan point arrangement is given in Figure 67a if the entire beam does not fit within the FOV or if there is excessive curvature to the cantilever. For shorter cantilevers, the arrangement of points shown in Figure 67b is recommended.

28: For a fixed-fixed beam, a recommended scan point arrangement would be similar to the arrangement given in Figure 67c. Additional scan points are not necessary on the other anchor or support region.

29: If a narrow cantilever or fixed-fixed beam is being measured, include only one or two rows of scan points.


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Figure 6Recommended Scan Point Arrangement for a Typical Bulk-Micromachined

(a) Cantilever, (b) Shorter Length Cantilever, and (c) Fixed-Fixed Beam

13.4.8 Position and focus the measurement beam on a scan point midway between the lowest and highest z-locations of the scan points along the beam (see Figure 67). Since the beam may be bowed, focusing the measurement beam at this location will help ensure data collection for all the selected scan points. The measurement beam will have its smallest diameter when it is in focus and, if applicable to the instrument chosen, more LED lights will be activated. If the measurement beam is not in focus, the resonance frequency peak decreases in amplitude and may be difficult to locate.

30: If the instrument indicates that the output signal is clipped, choose the next higher measurement range as specified in ¶ 13.4.1.2. If the highest measurement range is already in use, then slightly defocus the measurement beam or alter the z-positioning of the sample assembly(while keeping the sample in close contact with the PZT) until the output signal is not clipped and, if applicable to the instrument, a significant number of LED lights are activated.

13.4.9 Save the instrument settings for future use in ¶ 13.4.1.


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Figure 7Recommended Scan Point Arrangement for a Typical Bulk-Micromachined

(a) Cantilever, (b) Shorter Length Cantilever, and (c) Fixed-Fixed Beam

13.5 Record a Data Scan to a Data File

13.5.1 Start the data scan, if not already done, afterand recording the room temperature and relative humidity for informational purposes..

31: After the save operation in ¶ 13.4.9, the signal generator may automatically turn on and the PZT may have a high-pitched sound.

32: The measurement beam follows the scan points while measuring and storing data until all points are measured at least once.

13.5.2 If possible, monitor the instrument during the data scan to determine if clipping has occurred. If clipping has occurred, stop the scan, switch to the next higher measurement range as specified in ¶ 13.4.1.2, check the frequency range in ¶ 13.4.1.3, record the uncalibrated frequency resolution, fresol, and continue with ¶ 13.5.1.

33: If the highest measurement range is already in use, see Note 2876.

13.5.3 Turn the waveform generator off, if still active, after the scan is complete.

13.6 Record the Resonance Frequency Values

13.6.1 Locate any potential resonance frequency peaks, with the aid of the instrument’s software, in a plot of magnitude versus frequency. Record the frequency of each peak.

34: For optical vibrometry, the resonance frequency peaks are most easily found in the velocity versus frequency plots.

13.6.2 Animate the vibration at each frequency peak to ascertain if the beam is oscillating as expected, for a beam in resonance, for the given instrument. [For example, for a dual beam laser vibrometer, the base of a cantilever would appear stationary (at z=0 m). The tip of the cantilever would go from its resting position (at z=0 m) to a maximum positive z-value, back through its resting position to a minimum negative z-value, then back to its resting position to repeat the cycle again. The positive and negative amplitudes of vibration would appear comparable. A similar motion takes place for all points along the cantilever with the amplitude of vibration getting smaller as the base of the cantilever is approached. The cantilever would appear to be rigid throughout the entire oscillation.] To obtain good oscillations, it may be necessary to invalidate one or morea data points. If the beam is oscillating as


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Informational (Blue) Ballot1000AInformational (Blue) Ballotjn lexpected, record the frequency of the peak(s). (Consider using a band cursor to smooth out the data and extract theis frequency.)

13.6.3 Determine the resonance frequency of the beam. For cantilevers, ascertain whether or not the frequency of a peak recorded in ¶ 13.6.2 is near the estimate of the fundamental resonance frequency calculated in Equation (2). This would be the chosen resonance frequency of the beam. Record this value.

35: For fixed-fixed beams, if there is only one peak recorded in ¶ 13.6.1, that would be the chosen resonance frequency peak for the beam. If there are two peaks, the larger peak is typically the resonance frequency peak, assuming that peak cannot be considered a data spike.

36: For cantilevers and fixed-fixed beams, if uncertain whether or not you have chosen the correct resonance frequency peak (e.g., if there is a data spike or a higher mode of vibration) or if no peaks can be found, one or more of the following bulleted items may be helpful to locate the resonance frequency peak:

Additional measurements taken on the beam support can help to narrow in on the resonance frequency by eliminating any similar peaks.

If an amplifier is being used, make sure that it is turned on, that the sample is centered and flush with the top of the PZT (if applicable), that the PZT is operational with the red wire driven with a voltage that is positive relative to the black wire, and that the laser is sufficiently warmed up.

Starting at ¶ 13.3.1, make sure that tape is not used for mounting, that the PZT is not shorted, and reposition the sample assembly so it is better aligned perpendicular to the measurement beam.

Starting at ¶ 13.4.1.1, make sure an appropriate waveform function (such as the periodic chirp function) is being used, if applicable. Also, increasing (to 100 or more) the number of measurements averaged together per scan point is recommended.

For cantilevers, recheck the calculation of the Q-factor in Equation (5). (Cantilevers with low Q-factors have low peaks.) Is pdiff as calculated in Equation (4) less than 2%? If not, using an instrument capable of differential measurements (e.g., one with two laser beams that can be positioned at strategic locations) is recommended.

For beams with low Q-factors, a small value for fresol is required. Therefore, emphasis should be placed upon finding the smallest possible range for the velocity decoder in ¶ 13.4.1.2. This can be accomplished at the expense of a sharp focus and at the expense of an accurate z-alignment of the sample assembly; however, if double-stick tape was used to mount the chip to the top of the PZT, the sample still should remain flush with the top of the PZT.

Recheck the sample calculations for the expected resonance frequency of the cantilever [using Equation (2)] or the expected resonance frequency range for the fixed-fixed beam [found from Equation (3) and Equation (876)]. Starting at ¶ 13.4.1.3, choose a relatively large frequency range.

Starting at ¶ 13.4.4, make sure the highest magnification lens is being used that is appropriate for these measurements. Starting at ¶ 13.4.5, realign the coordinates to make sure the correct measurement beam is being used and not one of its

reflections. Starting at ¶ 13.4.7, redefine the scan points to an arrangement similar to an arrangement shown in Figure 67, if not already

being used. If the cantilever or fixed-fixed beam is narrow, perhaps the measurement beam recorded more background data than

cantilever or fixed-fixed beam data so reposition the cantilever or fixed-fixed beam in the y-direction and continue from ¶ 13.4.7 (using only one row of scan points, if not already done), or choose a wider cantilever or fixed-fixed beam and continue from ¶ 13.4.1.3.

Starting at ¶ 13.4.8, recheck the focus so that the measurement beam is approximately midway between the lowest and highest z-locations for the scan points along the beam.

Starting at § 13.5, make sure the smallest possible measurement range for the velocity decoder is being used in which the output signal is not being clipped during the measurement.

The 3-D oscillations of a fixed-fixed beam in resonance can look strange. Using an instrument capable of differential measurements (e.g., one with two laser beams that can be positioned at strategic locations) is recommended for fixed-fixed beam measurements.

Check for stiction using ASTM E2246 for cantilevers and ASTM E2245 for fixed-fixed beams, if appropriate.

13.6.4 Decrease the frequency range of the instrument (e.g., to ±0.5 kHz or ±1.0 kHz around the resonance frequency found above) in order to obtain more FFT lines within a smaller range, resulting in a smaller value for fresol (for example, ≤2 Hz). Record this new value for the uncalibrated frequency resolution, fresol.

13.6.5 Take and record three uncalibrated resonance frequency measurements (fmeas1, fmeas2, and fmeas3) for this smaller frequency range, each time focusing the beam as specified in ¶ 13.4.8 before continuing to § 13.5. If the


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Informational (Blue) Ballot1000AInformational (Blue) Ballotjn lmeasurements were performed in a vacuum, calibrate the measurements (by multiplying by calf) andshould be recorded them as fundamped1, fundamped2, and fundamped3., respectively.

13.7 Obtain the Other Calculation Inputs

13.7.1 Obtain the thickness, t, of the suspended layer and the standard deviation, thick (for use in Appendix 1) in the most accurately available fashion.11 This is considered outside the scope of this test method.

37: SEMI MS2 can be used to obtain step-height measurements, which can be used in thickness calculations Error: Referencesource not found for both surface-micromachining and bulk-micromachining processes.

13.7.2 Obtain the suspended length of the cantilever, Lcan, or fixed-fixed beam, Lffb, and the standard deviation, L, of the cantilever length (for use in Appendix 1), in the most accurately available fashion. This is considered outside the scope of this test method.

13.7.3 Obtain the suspended width of the cantilever, Wcan, and the standard deviation, W, for use in Appendix 1. This is considered outside the scope of this test method.

13.7.4 Obtain the density, , of the suspended layer and the standard deviation, (for use in Appendix 1) in the most accurately available fashion.12Error: Reference source not found This is considered outside the scope of this test method.

13.7.5 Obtain the viscosity, , of the ambient and the standard deviation, (for use in Appendix 1).10,11 At 20°C in air, =1.84e5 Ns/m2.

14 Calculations14.1 If a cantilever is used in § 13 or § A3-1 to obtain resonance frequency measurements:

14.1.1 If damped resonance frequencies were recorded as fmeas1, fmeas2, and fmeas3 in ¶ 13.6.5 or § A3-1.5, calibrate them (by multiplying by calf) and record them asrename these measurements fdamped1, fdamped2, and fdamped3, respectively. For each calibrated damped resonance frequency value (fdamped1, fdamped2, and fdamped3) calculate a corresponding calibrated undamped resonance frequency, fundamped1, fundamped2, and fundamped3 using the equation below:Error: Reference source not found7

, (987)

where the trailing n in the subscript of fdampedn and fundampedn is 1, 2, or 3 and where Q is calculated using Equation (5), this time with the calculation inputs obtained in § 13.7. On the other hand, if undamped resonance frequencies (for example, if the measurements were performed in a vacuum) were recorded in ¶ 13.6.5 or § A3-1.5 as fmeas1, fmeas2, and fmeas3, then calibrate these measurements (by multiplying by calf) and record them as rename these measurements fundamped1, fundamped2, and fundamped3., respectively.

14.1.2 With the three values obtained in ¶ 14.1.1 for fundampedn, calculate the average calibrated undamped resonance frequency of the single-layered cantilever, fcundampedavean, using the following equation:

11 Marshall, J. C., and Vernier, P. T., “Electro-physical technique for post-fabrication measurements of CMOS process layer thicknesses,” NIST J. of Research, Vol. 112, No. 5 (2007): p. 223–256.

Gupta, R. K., Osterberg, P. M., and Senturia, S. D., “Material Property Measurements of Micromechanical Polysilicon Beams,” Microlithography and Metrology in Micromachining II, SPIE, Vol. 2880 (October 14–15, 1996): pp. 39–45.

Jensen, B. D., de Boer, M. P., Masters, N. D., Bitsie, F., and LaVan, D. A., “Interferometry of Actuated Microcantilevers to Determine Material Properties and Test Structure Nonidealities in MEMS,” Journal of Microelectromechanical Systems, Vol. 10 (September 2001): pp. 336–346.

Marshall, J. C., “New Optomechanical Technique for Measuring Layer Thickness in MEMS Processes,” Journal of Microelectromechanical Systems, Vol. 10 (March 2001): pp. 153–157.12 CRC Handbook of Chemistry and Physics, 87th Edition, 2006-2007 (on-line edition), Accessed February 28, 2007 at http://208.254.79.26/ (subscription required).


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, (10)

and the calibrated standard deviation fundampedreq (for use in Appendix 1). Given fundampedave, calculate fcan using the following equation:

, (11)

where fcan is the average calibrated undamped resonance frequency of the cantilever, which includes the resonance frequency correction term, fcorrection, intending to correct for deviations from the ideal cantilever geometry and composition.

14.1.3 Given fcan from ¶ 14.1.2, calculate the Young’s modulus value, E, of the suspended layer assuming clamped-free boundary conditions (and assuming the cantilever is in its first natural mode of vibration) using the following equation:Error: Reference source not found7

, (1298)

where t is the thickness of the suspended layer (as obtained in ¶ 13.7.1), Lcan is the suspended length (as obtained in ¶ 13.7.2), and is the density of the thin film layer (as obtained in ¶ 13.7.43). If a bulk-micromachined cantilever consisting of multiple layers (see Note 13) was measured, E would be considered an effective Young’s modulus.

14.1.4 Calculate ucE using the method presented in Appendix 1. Residual stress and stress gradient calculations for this thin film layer can be found in Appendix 2.

14.2 If a fixed-fixed beam is used in § 13 or § A3-1 to obtain resonance frequency measurements (not recommended):

14.2.1 From the three resonance frequency values obtained in ¶ 13.6.5 or § A3-1.5, calculate the average uncalibrated resonance frequency of the single-layered fixed-fixed beam, fffb.

38: The assumption is being made that damping is negligible for the fixed-fixed beam.

14.2.2 Calculate the Young’s modulus value, Esimple, using fffb from ¶ 14.2.1 andfor simply-supported boundary conditions at both supports using fffb from ¶ 14.2.1 (and assuming the fixed-fixed beam is in its first natural mode of vibration) using the following equation:Error: Reference source not found7

, (13109)

where is the density of the thin film (as obtained in ¶ 13.7.43), Lffb is the suspended length of the fixed-fixed beam (as obtained in ¶ 13.7.2), and t is the thickness of the suspended layer (as obtained in ¶ 13.7.1).

14.2.3 Calculate the Young’s modulus value, Eclamped, using fffb from ¶ 14.2.1 forand clamped-clamped boundary conditions using fffb from ¶ 14.2.1 (and assuming the fixed-fixed beam is in its first natural mode of vibration) using the following equation:Error: Reference source not found7

.

(14110)


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Informational (Blue) Ballot1000AInformational (Blue) Ballotjn l14.2.4 Calculate E and ucE (assuming a Gaussian distribution) using the following equations:Error: Referencesource not found7

, (15121)

and

. (16132)

This is a Type B analysis. If a bulk-micromachined cantilever consisting of multiple layers (see Note 13) was measured, E would be considered an effective Young’s modulus.

14.2.5 Residual stress and stress gradient calculations for this thin film layer can be found in Appendix 2 after replacing ucE with uE..

15 Reporting Results15.1 Report the results as follows:13

15.1.1 If a cantilever test structure is used for the measurement:

15.1.1.1 Since it can be assumed that the possible estimated values of the uncertainty components are either either approximately uniformly or Gaussianly distributed or Gaussian (as specified in Appendix 1) with approximate combined standard uncertaintydeviation ucE, the Young’s modulus value is believed to lie in the interval E ± ucE (expansion factor k=1) representing with a level of confidence of approximately 68% assuming a Gaussian distribution.

15.1.2 If a fixed-fixed beam test structure is used for the measurement:

15.1.2.1 Since it can be assumed that the estimated value of the uncertainty component is approximately Gaussianly distributed (as specified in ¶ 14.2.4) with approximate uncertainty uE, the Young’s modulus value is believed to lie in the interval E ± uE (expansion factor k=1) representing a level of confidence of approximately 68%.

16 Precision and Accuracy16.1 The Round Robin — SEMI conducted a MEMS Young’s Modulus and Step Height Round Robin Experiment14

from December 2008 to April 2009 (using the original versions of revised documents for SEMI MS4 and SEMI MS2, respectively). There were eight participants for the Young’s modulus portion of the round robin.

39: This test method uses the term participant to refer to a single data set from a unique combination of measurement setup and researcher. That is, a single researcher equipped with multiple, unique instruments (e.g., a dual beam vibrometer and a single beam vibrometer) or different forms of excitation (e.g., PZT and thermal excitation) could serve as multiple “participants” in this round robin.

16.2 The Round Robin Test Chips — The round robin test chips were fabricated in a commercial CMOS process, followed by a post-processing CF4+O2 etch, followed by a XeF2 etch. These bulk-micromachined round robin test chips include cantilevers consisting only of oxide (as specified in Note 13) with a design width of 28 m and design lengths of 200 m, 300 m, and 400 m. There are five cantilevers designed at each length.

16.3 Relative Uncertainties — Relative uncertainties are used in this test method because it allows one to more easily determine the most sensitive parameters as well as allowing one to determine how accurate the parameters must be to assume a pre-determined accuracy. The combined standard uncertainty equation in this test method

13 Taylor, B. N., and Kuyatt, C. E., “Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results,” NIST Technical Note 1297, National Institute of Standards and Technology (September 1994).

EUROCHEM / CITAC Guide CG 4, “Quantifying Uncertainty in Analytical Measurement,” Second Edition, QUAM: 2000.1.14 Marshall, J., Allen, R. A., McGray, C. D., and Geist, J., “MEMS Young’s Modulus and Step Height Measurements with Round Robin Results,” NIST J. Res., Vol. 115, No. 5, pp. 303-342, 2010.


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Informational (Blue) Ballot1000AInformational (Blue) Ballotjn l[Equation (A1-1)] uses relative uncertainties whereas the combined standard uncertainty equation (from SEMI MS4-1107) used in the round robin (which produces comparable resulting combined standard uncertainty values) uses absolute uncertainties.

16.3.1 Table 1 provides example relative uncertainty values from a round robin bulk-micromachined CMOS chip. This table also includes the resulting combined standard uncertainty value (ucE = 3.1 GPa) as calculated using Equation (A1-1), for which it is assumed that calf=1 and freqcal=0.0 Hz since frequency calibrations were not done in the round robin. Also, it is assumed that fcorrection=0 kHz, σsupport=0 Hz, and σcantilever=0 Hz. Using the same data set, a comparable value for the combined standard uncertainty (ucE = 3.2 GPa) was obtained using the combined standard uncertainty equation in SEMI MS4-1107 with σW=0.1 µm, σEnit=5 GPa, and σµ=0.01×10 5 Ns/m2 .

16.4 The Repeatability Data — At one laboratory using a dual beam vibrometer, Young’s modulus values were found from twelve different cantilevers four times, with each Young’s modulus value determined from the average of three resonance frequency measurements as calculated in § 14. Therefore, 48 Young’s modulus values were obtained. Sixteen of these values were from four different cantilevers with L=400 m, 16 from four different cantilevers with L=300 m, and 16 from four different cantilevers with L=200 m.

16.5 The Reproducibility Data — Each participant was supplied with a test chip and asked to obtain the Young’s modulus value from three cantilevers with design lengths of 200 m, 300 m, and 400 m. The participant could choose to measure any one of five cantilevers of the given length that were available on the test chip as long as it passed a visual inspection. Each Young’s modulus value was determined from the average of three resonance frequency measurements as calculated in § 14. The eight participants used a variety of instruments to obtain the measurements including a dual beam vibrometer, a single beam vibrometer, and a stroboscopic interferometer. In addition, thermal excitation measurements are included for comparison with PZT excitation measurements on the same chip.

16.6 Precision — The repeatability and reproducibility data for Young’s modulus and for the combined standard uncertainty areis presented in Table 21 and Table 32, respectively. In these tables, , where n indicates the number of cameasurementslculated Young’s modulus values and Eave is the average of the Young’s modulus measurements results. Following this, Tthe 95 % limits for E awere calculated as follows: (a) the standard deviation of the Young’s modulus measurementss iswere found, (b) thisese value iss were multiplied by 2.08 (assuming a Gaussian distribution), and (c) the resulting values iswere turned into a percent by dividing by Eave and multiplying by 100. For these approximate 95 % limits, it is assumed that the other uncertainty components equal zero. Next, the standard deviation (σE) of these measurements is given. Then, the ±2σE limits are listed followed by the average of the combined standard uncertainty values (ucEave)is provided. reported as percents.

16.6.1 The Young’s modulus round robin results are plotted in Figure 78, where both repeatability and reproducibility data are plotted. The average Young’s modulus value for the repeatability data (Eave) is specified at the top of Figure 78 along with the average 3ucEave uncertainty error bars for this value. These repeatability values of Eave±3ucEave se quantities are also plotted in this figure with both the repeatability and reproducibility data. As an observation, all of the reproducibility results fall comfortably between these bounds of Eave ±plus or minus 3ucEave.

16.6.2 In Figure 78, the repeatability data areis grouped according to the cantilever length with the L=200 m data plotted first, followed by the L=300 m data, then the L=400 m data. In like manner with the reproducibility data, for each participant, the L=200 m data areis plotted first, followed by the L=300 m data, then the L=400 m data. The repeatability data and the reproducibility data both indicate a length dependency. This could be due to a number of things including debris in the attachment corners of the cantilevers to the beam support, which would cause larger errors for shorter length cantilevers.

16.6.3 The repeatability data in Figure 78 shows a clustering of the data at each length. In other words, the absolute value of the ±2σE95 % limits for E at each length (which are plotted in this figure along with Eave for each length) are all less than ±1.5 2%, which is much less than the ±104.3 40% value (as given in Table 2) when all the lengths are considered. This suggests that when Young’s modulus values extracted by different measurement instruments or excitation methods are compared, the cantilevers should have the same length. This length dependency can be due to a number of things including debris in the attachment corners of the cantilevers to the beam support, which would cause larger errors for shorter length cantilevers.


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Informational (Blue) Ballot1000AInformational (Blue) Ballotjn l16.6.4 Round robin participant #1, participant #2, and participant #3 took measurements on the same chip (chip #1) using a dual beam vibrometer, a single beam vibrometer, and a stroboscopic interferometer, respectively. The results given in Figure 78 indicate that comparable results were obtained from these instruments.

16.6.5 Round robin participant #4, participant #5, and participant #6 took data from the same chip (chip #2); however, round robin participant #5 used thermal excitation to obtain the required data while participant #4 and participant #6 used PZT excitation. No significant difference in the results for these measurements is seen in Figure 78.

16.7 Accuracy — No information can be presented on the bias of the procedure in this test method for measuring Young’s modulus because there is not a certified MEMS material for this purpose. In addition, the SiO2 beam consists of four layers (field oxide, two deposited oxides, and a glass layer) where the material properties of each layer are expected to be different.no material having an accepted reference value is available.


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Informational (Blue) Ballot1000AInformational (Blue) Ballotjn lTable 1 Example Relative Uncertainty Values From a Round Robin Bulk-Micromachined CMOS Chip

uncertainty Type A or B example value

1.

(using =2.2 g/cm3 and =0.05 g/cm3 )B 0.023

2.

(using fmeas1=26.82625 kHz,

fmeas2=26.8351 kHz,

fmeas3=26.8251 kHz,

calf =1, and Q=65.8,

such that fundampedavecan=26.8296 kHz,

and using fcorrection =0 kHz)

0.00029

2a.

(using Wcan=28 m,

Einit=70 GPa,

and =1.8410 5 Ns/m2 )

AA 0.0002

2b.

(using fresol=1.25 Hz)

B 0.000013

2c.

(using Wcan=28 m and W=0.1 m,

using Einit=70 GPa and Einit=5 GPa,

and using =1.8410 5 Ns/m2 and =0.0110 5 Ns/m2 )

B 0.0002

2cd.

(using freqcal=0.0 Hz)

B 0.0

2d.

(support and attachment assumed to be ideal, support=0.0 Hz)

B 0.0

2e.

(using cantilever=0.0 Hz)

B 0.0

3.

(using Lcan=300 m and L=0.2 m)

B 0.00067

4.

(using t=2.743 m and thick=0.058 m)

B 0.0211

0.048

(using E = 65.35 GPa)

3.1 GPa


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Table 2 Repeatability Data (one participant, one laboratory, one instrument, one chip,a twelve different cantilevers)

Lcan=200 m Lcan=300 m Lcan=400 m Lcan=200 m to 400 m

n 16 16 16 48

Eave (in GPa) 59.8 GPa 65.4 GPa 67.5 GPa 64.2 GPa

σE 0.40 GPa 0.17 GPa 0.38 GPa 3.3 GPa

±2σE95 % limits for E ±01.81 GPa(±1.44 %)

±0.33 GPa(±0.51 %)

±0.76 GPa(±1.1 %)

±6.6 GPa(±10.3 %)

ucEave (in GPa) 2.9 GPa(4.9 %)

3.2 GPa(4.8 %)

3.3 GPa(4.8 %)

3.1 GPa(4.8 %)

a Fabricated in a bulk-micromachining CMOS process.

Table 3 Reproducibility Data (eight participants, five laboratories, seven instruments, four chipsa )

L=200 m L=300 m L=400 m L=200 m to 400 m

n 8 8 8 24

Eave (in GPa) 58.7 GPa 63.7 GPa 66.0 GPa 62.8 GPa


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L=200 m L=300 m L=400 m L=200 m to 400 m

σE 1.3 GPa 1.8 GPa 1.4 GPa 3.4 GPa

±2σE limits ±2.6 GPa(±4.4 %)

±3.5 GPa(±5.5 %)

±2.9 GPa(±4.4 %)

±6.9 GPa(±11 %)

95 % limits for E ±4.4 % ±5.5 % ±4.4 % ±11.0 %

ucEave (in GPa) 2.8 GPa(4.9 %)

3.1 GPa(4.8 %)

3.2 GPa(4.9 %)

3.0 GPa(4.9 %)

a Fabricated in a bulk-micromachining CMOS process.

Repeatability Precision Data (one participant, one laboratory, one instrument, one chip, twelve different cantilevers)

L=200 m L=300 m L=400 m L=200 m to 400 m

n 16 16 16 48

Eave (in GPa) 59.79 65.35 67.51 64.22

95% limits for E ±1.89% ±0.71% ±1.59% ±14.40%

ucave (in GPa) 2.899 3.162 3.266 3.109

(4.848%) (4.839%) (4.838%) (4.841%)

95% limits for uc ±1.897% ±0.712% ±1.602% ±14.159%


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Informational (Blue) Ballot1000AInformational (Blue) Ballotjn lTable 4 Reproducibility Precision Data (eight participants, five laboratories, seven instruments, four chips)

L=200 m L=300 m L=400 m L=200 m to 400 m

n 8 8 8 24

Eave (in GPa) 58.67 63.69 65.99 62.79

95% limits for E ±6.18% ±7.70% ±6.09% ±15.33%

ucave (in GPa) 2.844 3.082 3.200 3.042

(4.848%) (4.839%) (4.849%) (4.845%)

95% limits for uc ±6.182% ±7.721% ±6.233% ±15.341%


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Young's Modulus vs. Plot #(For repeatability: E ave = 64.2 GPa

with 3u cEave = 9.3 GPa)

30

40

50

60

70

80

0 20 40 60 80 100Plot #

E (G

Pa)

L =200 m L =300 m L =400 m

single beam

dual beam

same beamE ave =65.2 GPa95 % limits for E =.%

E L=200ave = 59.8 GPa95 % limits for E L=200 =1. %

E L=300ave = 65.4 GPa95 % limits for E L=300 =.5 %

E L=400ave = 67.5 GPa95 % limits for E L=400 =1.1 %

strobe thermal

chip #1 chip #2

#1 #2 #3 #4 #5 #7 #8#6

chip#3

repeatability reproducibility

chip#4

participant

Young's Modulus vs. Plot #(For repeatability: E ave = 64.2 GPa

with 3u cave = 9.33 GPa)

30

40

50

60

70

80

0 20 40 60 80 100Plot #

E (G

Pa)

L =200 m L =300 m L =400 m

single beam

dual beam

same beamE ave =65.20 GPa95 % limits for E =.%


E L=300ave = 65.35 GPa95 % limits for E L=300 =. %


strobe thermal

chip #1 chip #2

#1 #2 #3 #4 #5 #7 #8#6

chip#3

repeatability reproducability

chip#4

participant

Figure 8Young’s Modulus Round Robin Results


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APPENDIX 1CALCULATION OF THE COMBINED STANDARD UNCERTAINTY FOR A YOUNG’S MODULUS MEASUREMENT OBTAINED FROM A RESONATING CANTILEVERNOTICE: The material in this appendix is an official part of SEMI MS4 and was approved by full letter ballot procedures on September 4, 2009.

A1-1 For the calculated Young’s modulus value (E) obtained from the average calibrated undamped resonance frequency of a cantilever (fcan) that includes a frequency correction term and assuming clamped-free boundary conditions as obtained in ¶ 14.1.3, determine the combined standard uncertainty value, ucE, using the following equation:7Error: Reference source not found,Error: Reference source not found 112

, (A1-1)

where , , Lcan, L, t, and thick are obtained in § 13.7, where fcan is calculatedobtained in ¶ 14.1.2, and where fcan is given by the following equation:

, (A1-2)

where

. (A1-3)

Wherewhere fundampedreq is obtained in ¶ 14.1.2 and where fresol, fQ, and freqcal , and correction and are obtained below in A1-1.1 through A1-1.3, respectively. Table 1 provides example relative uncertainty values and specifies the type of analysis used for each component. uthick, u, uL, ufreq, ufresol, and udamp are found below in § A1-1.1 through § A1-1.6, respectively.

1: Equation (A1-1) was obtained by applying the propagation of uncertainty technique (see Note 3938) for parameters that multiply to Equation (129) and assuming that ucE is equal to E. The parameters in Equation (129) are assumed to be uncorrelated.

2: For a function, f, consisting of uncorrelated input parameters, the combined standard uncertainty (which is equated here with the standard deviation) can be calculated using the law of propagation of uncertainty techniqueError: Reference source notfound1 1 as given by the following equation:

, (A1-43)

where y is a function of x1, x2,…, xN. Therefore, given the uncorrelated input parameters x and y in a multiplicative relationship, as given in the following equation:

, (A1-54)

where a, n, and m are constants, Equation (A1-43) can be rewritten as follows:

. (A1-65)

And, given the uncorrelated input parameters x and y in an additive relationship, as given in the following equation:


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Informational (Blue) Ballot1000AInformational (Blue) Ballotjn l , (A1-76)

where a and b are constants, Equation (A1-43) can be rewritten as follows:

. (A1-87)

A1-1.1 Calculate fresol, the calibrated standard deviation of the frequency measurements (used to obtain fcan) that is due to the frequency resolution, using the following equation:

, (A1-98)

where fresol was obtained in ¶ 13.6.4 (or ¶ A3-1.5.1) and calf was obtained in § 12. The above equation assumes a uniform distribution.

Determine fQ, the calibrated standard deviation of the frequency measurements (used to obtain fcan) that is due to damping. However, if undamped resonance frequencies (for example, if the measurements were performed in a vacuum) were recorded in ¶ 13.6.5 or § A3-1.5, set fQ equal to 0.0 Hz and skip ¶¶ A1-1.2.1–A1-1.2.2.

Equation (8) can be written as follows:

(A1-9)

where the letters “ave” at the end of a subscript implies that an average of the measurements is being considered. (The damped and undamped measurements were recorded in ¶ 14.1.1.)

Calculate fQ using the following equation as obtained by applying the propagation of uncertainty technique (see Note 38) more than once to Equation (A1-9):

(A1-10)

A1-1.2 where fdamped is the calibrated standard deviation of the damped resonance frequency measurements, where Q is given in Equation (5), and where Q is found by applying the propagation of uncertainty technique (see Note 38) to Equation (5), such that:

A1-1.3 (A1-11)

A1-1.4 where Wcan, W, , and are found in § 13.7, where Einit is the initial estimate for the Young’s modulus value of the thin film layer, and where Einit is the estimated standard deviation of this initial estimate.

A1-1.5 Calculate freqcal, the calibrated standard deviation of the frequency measurements (used to obtain fcan) that is due to the calibration of the time base, using the following equation:

, (A1-10)

where ucmeter and fmeter are found in § 12 and fundampedave is calculated in Equation (A1-3). The above equation assumes that the uncertainty scales linearly.


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Informational (Blue) Ballot1000AInformational (Blue) Ballotjn lA1-1.6 Calculate fcorrection, the estimated standard deviation of the correction factor, fcorrection. For this estimate, the following equation can be used:

A1-1.7

, (A1-11)

assuming uncorrelated input parameters. If the parameters are correlated, set σsupport =0 Hz, and include the uncertainty associated with the support into σcantilever.

A1-2 The expanded uncertainty for Young’s modulus, UE, is calculated using the following equation:

, (A1-12)

where the k value of 2 approximates a 95 % level of confidence.

(A1-12)

where ucmeter and fmeter are found in § 12. The above equation assumes that the uncertainty scales linearly.Calculate uthick, given thick from ¶ 13.7.1, assuming a Gaussian distribution, using the following equations:

(A1-2)

(A1-3)

(A1-4)

(A1-5)

where fcan was found in ¶ 14.1.2 and Lcan, t, and were found in § 13.7.

Calculate u, given from ¶ 13.7.4, assuming a Gaussian distribution, using the following equations:

(A1-6)

(A1-7)

. (A1-8)

Calculate uL, given L from ¶ 13.7.2, assuming a Gaussian distribution, using the following equations:

(A1-9)


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(A1-10)

. (A1-11)

Calculate ufreq, given freq from ¶ 14.1.2, assuming a Gaussian distribution, using the following equations:

(A1-12)

(A1-13)

. (A1-14)

Calculate ufresol, given fresol from ¶ 13.6.4 or § A3-1.5, assuming a uniform (that is, rectangular) probability distribution, using the following equations:

(A1-15)

(A1-16)

. (A1-17)

Calculate udamp, given W, L, , thick, and from § 13.7, assuming a Gaussian distribution, using the following equations:

(A1-18)

(A1-19)

(A1-20)

where:

(A1-21)

and uW(f), uL(f), u(f), ut(f), uE(f), and u(f) are found below in ¶¶ A1-1.6.1–A1-1.6.6, respectively. On the other hand, if undamped resonance frequencies (for example, if the measurements were performed in a vacuum) were recorded in ¶ 13.6.5 or § A3-1.5, then set udamp equal to 0.0 Pa and skip ¶¶ A1-1.6.1–A1-1.6.6.

Determine uW(f) using the following equations:Error: Reference source not found


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(A1-22)

(A1-23)

(A1-24)

(A1-25)

where E was calculated in ¶ 14.1.3 and Wcan, Lcan, t, , and were obtained in § 13.7. Also, fdampedave is the average of the three damped resonance frequency values (fdamped1, fdamped2, and fdamped3) found in ¶ 14.1.1 and fundampedave is fcan as found in ¶ 14.1.2.

Determine uL(f) using the following equations:

(A1-26)

(A1-27)

. (A1-28)

Determine u(f) using the following equations:


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(A1-29)

(A1-30)

. (A1-31)

Determine ut(f) using the following equations:

(A1-32)

(A1-33)

. (A1-34)

Determine uE(f) using the following equations:

(A1-35)

(A1-36)

(A1-37)


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. (A1-38)

Determine u(f) using the following equations:

(A1-39)

(A1-40)

2a. A 0.0002

2b. B 0.000013

2c. B 0.0002

2d. B 0.0


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APPENDIX 2RESIDUAL STRESS AND STRESS GRADIENT CALCULATIONSNOTICE: The material in this appendix is an official part of SEMI MS4 and was approved by full letter ballot procedures on September 4, 2009.

A2-1 The residual stress calculation of a thin film layer is found below in § A2-1.1 and the stress gradient calculation is found below in § A2-1.2.

A2-1.1 Residual Stress Calculation

A2-1.1.1 Find the residual strain of a thin film layer, r, and its combined standard uncertainty value, ucr, from a fixed-fixed beam test structure comprised of that layer using ASTM E2245.

1: It is possible that the fixed-fixed beam used to find fffb in ¶ 14.2.1 may also be used for this residual strain measurement. Consult ASTM E2245. However, it is recommended that the Young’s modulus value be obtained from the average resonance frequency of a cantilever due to a lower resulting uncertainty value for uc.

A2-1.1.2 Calculate the residual stress of the thin film layer, r, using the following equation:Error: Referencesource not found7

, (A2-1)

where E is the Young’s modulus value of that thin film layer as calculated in ¶ 14.1.3 or ¶ 14.2.4.

A2-1.1.3 Calculate the combined standard uncertainty for residual stress, ucr, using the following equation:

, (A2-2)

which becomes (after equating ucE with E and ucr with r):

, (A2-3)

where ucE is found in Appendix 1, where r and ucr are found in ASTM E2245 for residual strain, and where |x| is the absolute value of x.

2: In Equation (A2-3), replace ucE with uE [from Equation (16)] if the Young’s modulus value was obtained from the average resonance frequency of a fixed-fixed beam.

3: Equation (A2-2) was found by applying the propagation of uncertainty technique (see Note 39) for parameters that multiply to Equation (A2-1) where the parameters in Equation (A2-1) are assumed to be uncorrelated.

A2-1.1.4 Calculate the expanded uncertainty for residual stress, Ur, using the following equation:

, (A2-4)

where the k value of 2 approximates a 95 % level of confidence.

Calculate the combined standard uncertainty for residual stress, ucr, using the following equation:

, (A2-2)

which becomes (after equating ucE with E and ucr with r):


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(A2-3)

where ucE is found in Appendix 1 (A2-2)

where uE(r) is found below in ¶ A2-1.1.4 and ur(r) is found below in ¶ A2-1.1.5,. where r and ucr are found in ASTM E2245 for residual strain, and where |x| is the absolute value of x.

Replace ucE with uE in Equation (A2-3) if the Young’s modulus value was obtained from the average resonance frequency of a fixed-fixed beam.

Equation (A2-2) was found by applying the propagation of uncertainty technique (see Note 38) for parameters that multiply to Equation (A2-1) where the parameters in Equation (A2-1) are assumed to be uncorrelated.

Calculate uE(r), assuming a Gaussian distribution, using the following equations:

(A2-3)

(A2-4)

(A2-5)

where uc is found in Appendix 1 or in ¶ 14.2.4 and |x| is the absolute value of x.

Calculate ur(r), assuming a Gaussian distribution, using the following equations:

(A2-6)

(A2-7)

(A2-8)

where uc was found in ASTM E2245 for residual strain.

A2-2 A2-2.1 Stress Gradient Calculation

A2-2.1.1 Find the strain gradient of a thin film layer, sg, and its combined standard uncertainty value, ucsg, from a cantilever test structure comprised of that layer using ASTM E2246.

4: It is possible that the cantilever used to find fcan in § 14 may also be used for this strain gradient measurement. Consult ASTM E2246.

A2-2.1.2 Calculate the stress gradient of the thin film layer, g, using the following equation:Error: Referencesource not found7

, (A2-954)

where E is the Young’s modulus value of that thin film layer as calculated in ¶ 14.1.3 or ¶ 14.2.4.

A2-2.1.3 Calculate the combined standard uncertainty for the stress gradient, ucg, using the following equation:


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, (A2-6)

which becomes (after equating ucE with E and ucsg with sg):

, (A2-7)

where ucE is found in Appendix 1 and where sg and ucsg are found in ASTM E2246 for strain gradient.

5: In Equation (A2-7), replace ucE with uE [from Equation (16)] if the Young’s modulus value was obtained from the average resonance frequency of a fixed-fixed beam.

6: Equation (A2-6) was found by applying the propagation of uncertainty technique (see Note 39) for parameters that multiply to Equation (A2-5) where the parameters in Equation (A2-5) are assumed to be uncorrelated.

A2-2.1.4 Calculate the expanded uncertainty for stress gradient, Ug, using the following equation:

, (A2-8)

where the k value of 2 approximates a 95 % level of confidence.culate the combined standard uncertainty for the stress gradient, ucg, using the following equation:

(A2-10)

where uE(g) is found below in ¶ A2-1.2.4 and usg(g) is found below in ¶ A2-1.2.5.

, (A2-5)

which becomes (after equating ucE with E and ucsg with sg):

(A2-6)

where ucE is found in Appendix 1 and where sg and ucsg are found in ASTM E2246 for strain gradient.

Replace ucE with uE in Equation (A2-6) if the Young’s modulus value was obtained from the average resonance frequency of a fixed-fixed beam.

Equation (A2-5) was found by applying the propagation of uncertainty technique (see Note 38) for parameters that multiply to Equation (A2-4) where the parameters in Equation (A2-4) are assumed to be uncorrelated.

Calculate uE(g), assuming a Gaussian distribution, using the following equations:

(A2-11)

(A2-12)

(A2-13)

where uc is found in Appendix 1 or in ¶ 14.2.4.

Calculate usg(g), assuming a Gaussian distribution, using the following equations:

(A2-14)


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(A2-15)

(A2-16)

where uc was found in ASTM E2246 for strain gradient.


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APPENDIX 3YOUNG’S MODULUS MEASUREMENTS USING A STROBOSCOPIC INTERFEROMETER OR COMPARABLE INSTRUMENTNOTICE: The material in this appendix is an official part of SEMI MS4 and was approved by full letter ballot procedures on September 4, 2009.

1: An attempt is made in this appendix to specify how to obtain Young’s modulus measurements with a stroboscopic interferometer, such as shown in Figure 45, or a comparable instrument. Therefore, this appendix may not specifically pertain to all instruments such that modifications may need to be made, as appropriate, to obtain the required data. For measurements taken with an optical vibrometer or comparable instrument, consult § 13.

A3-1 Obtain the resonance frequency values for a cantilever using the following seven steps (given below in ¶¶ A3-1.1–A3-1.7, inclusive): (a) mount the chip, (b) take preliminary static measurements, (c) set up for the comprehensive dynamic measurements, (d) determine a phase angle and an approximate resonance frequency, (e) obtain the resonance frequency measurements, (f) view a movie of the 3-D oscillation, and (g) obtain the other calculation inputs.

2: It is recommended that Young’s modulus is found from the average resonance frequency of a cantilever. However, if a cantilever is not available for measurement, a fixed-fixed beam can be used with the understanding that a larger value for the uncertainty uc will result. So, fixed-fixed beams will also be mentioned in this section.

A3-1.1 Mount the Chip

A3-1.1.1 Follow the steps in § 13.3 to mount the chip.

A3-1.2 Take Preliminary Static Measurements

A3-1.2.1 Orient the length of the beam sample in the instrument’s x-direction or y-direction. If the instrument’s pixel-to-pixel spacing is smaller in the x-direction, an orientation of the length of the beam sample in the x-direction is recommended, assuming more of the sample can fit within the FOV of the instrument.

A3-1.2.2 Choose the objective and FOV lens that just barely includes the sample area to be measured within the FOV.

A3-1.2.3 Select the detector array size that achieves the best lateral resolution.

A3-1.2.4 Adjust the intensity.

A3-1.2.4.1 Focus the sample in the FOV so the fringes are visible on a flat portion of the sample (for example, on the beam support for a bulk micromachined sample or on the underlying layer for a surface micromachined sample) and are parallel to the cantilever or fixed-fixed beam. Ensure that the fringes are not drifting.(The presence of fringes helps to account for systematic errors.) Ensure that the fringes are not drifting.

A3-1.2.4.2 Set the intensity to a point just below saturation.

A3-1.2.5 Recheck the sample alignment.

A3-1.2.6 Move the fringes to just past the uppermost part of the sample. (This could be, for example, to just past the very tip of the cantilever or to just past the midpoint of the fixed-fixed beam).

A3-1.2.7 Take one or more static measurement to determine the appropriate objective, FOV lens, scan length, etc. To obtain high quality data on top of the cantilever or fixed-fixed beam, it may be best to halt the scan before it reaches the bottom of the etch pit (as shown in Figure. A3-1 for a bulk-micromachined cantilever). During the measurement, monitor the fringes in the intensity window to ensure that data is obtained on the critical parts of the sample.

A3-1.2.7.1 If data is missing on the tip of a cantilever, for example, due to excessive curvature, make sure that before the measurement the fringes are just past the uppermost part of the sample. If they were and if there is still missing data, a higher magnification can be used even though less of the beam may be included in the FOV.

A3-1.2.7.2 If data is missing on top of the beam support, for example, the scan length can be increased.


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Figure A3-1Defining the Regions of Interest for a Bulk-Micromachined Cantilever

A3-1.3 Set up for the Comprehensive Dynamic Measurements

A3-1.3.1 Connect the PZT to the generator (via the amplifier), if not already done keeping in mind that the red PZT wire should be driven with a voltage that is positive relative to the black PZT wire and that some amplifiers may have reversed polarity.

A3-1.3.2 Check to see if the PZT vibration is barely audible when it is activated at 10V, 0V offset (that is, so that no negative voltages are obtained), and 7000 Hz.

3: If uncertain that 10V (with 0V offset) is the optimum voltage configuration, an oscilloscope can be used to monitor the amplifier output when connected to the PZT.

A3-1.3.3 Engage the illuminator and adjust its intensity with the fringes visible on a flat portion of the sample.

A3-1.3.3.1 Pull out the shaft of the strobe selector so that the illuminator (the LED) can be activated with the software.

4: The white light will no longer be visible on the sample.

A3-1.3.3.2 Keep the intensity knob where it was for the static measurement.

A3-1.3.3.3 Start the illuminator using the software. A red dot from the LED will become visible on the sample.

A3-1.3.3.4 Adjust the intensity of the illuminator by setting the duty cycle (to be between 2% and 4%) and by setting the current to the LED (to approximately 200 mA to 300 mA) so that it is just below saturation.

5: The smaller the duty cycle (for example 2% as opposed to 4%) the better to minimize any blurring effects.

A3-1.3.4 Set up a template file.

A3-1.3.5 Take one static measurement with the strobe.

A3-1.3.5.1 Position the fringes to just past the uppermost part of the sample. (This could be, for example, to just past the very tip of the cantilever or to just past the midpoint of the fixed-fixed beam).

A3-1.3.5.2 Start the illuminator using the software.

A3-1.3.5.3 Take a static measurement with the illuminator.

A3-1.3.5.4 Save the acquired file.

A3-1.3.6 Create a template.


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Informational (Blue) Ballot1000AInformational (Blue) Ballotjn lA3-1.3.6.1 Define two or more regions of interest (such as shown in Figure A3-1) within which to have data analyzed.

A3-1.3.6.1.1 Create region #1 (R01) and the reference region to be the same, defining it as a rectangular area on top of the beam support (in the case of bulk-micromachined samples) or on top of a relatively flat layer such as the underlying layer or within the double stuffed anchor (in the case of surface-micromachined samples).

A3-1.3.6.1.2 Create region #2 (R02). For a cantilever, R02 can be defined with a rectangle within the FOV near the furthermost part of the cantilever. For a fixed-fixed beam, R02 can be defined with a rectangle at or near the mid-point of the fixed-fixed beam. Create other regions, such as R03 shown in Figure A3-1, if uncertain whether or not data can be obtained in R02 for all the frequencies.

A3-1.3.7 Choose (or create) an appropriate display screen.

A3-1.3.8 Take a single dynamic measurement, watching to make sure the fringes pass through all the pertinent areas of the sample.

A3-1.3.8.1 Check to see that the data on the selected display screen gets updated during the single dynamic measurement.

A3-1.3.9 Define the database options.

A3-1.3.9.1 Choose from the possible dynamic measurements to record, for example, the sample amplitude, sample frequency, and sample phase.

A3-1.3.9.2 Choose from the possible analysis options to record, for example, the average height of R01 (the reference area), the average height of R02, and the average height of R03.

A3-1.3.10 Select key plots to view during the comprehensive dynamic measurement.

6: For the comprehensive dynamic measurements, the key plots could be the average height of R01 (the reference area) versus frequency, the average height of R02 versus frequency, the average height of R01 (the reference area) versus phase, and the average height of R02 versus phase.

A3-1.4 Determine a Phase Angle and an Approximate Resonance Frequency

A3-1.4.1 For the first comprehensive dynamic measurement to be taken, set up the software to vary the phase (for example, from 0 degrees to 350 degrees in 10 degree steps) while for each phase varying the frequency (for example, from fresest minus 5 kHz to fresest plus 5 kHz in 50 Hz steps). Select an appropriate setting for the voltage (for example, 10 V).

7: For cantilevers, fcaninit calculated in Equation (2)Error: Reference source not found7 can be used for fresest.

8: For fixed-fixed beams, the average of fffbinithi calculated in Equation (3)Error: Reference source not found 7 and fffbinitlo

calculated in Equation (876)Error: Reference source not found7 can be used for fresest.

9: The frequency range and step sizes may need to be adjusted depending upon the value for fresest.

A3-1.4.2 Make sure the intensity window is displayed so that the fringes can be monitored periodically during the data session to ensure that they do not drift significantly during the comprehensive dynamic measurement.

A3-1.4.3 Take the comprehensive dynamic measurement while maintaining a constant room temperature. Record the room temperature and the relative humidity for informational purposes.

A3-1.4.4 With all the data, make plots of the average height of region #2 (R02) minus the average height of region #1 (R01) versus frequency, such as shown in Figure A3-2, and versus phase, such as shown in Figure A3-3. Figure A3-2 confirms the existence of a resonance frequency. From Figure A3-3, interpolate, if necessary, to record the phase for the maximum value of R02 minus R01.

A3-1.4.5 At or near the recorded phase value plot R02 minus R01 versus frequency, such as shown in Figure A3-4. If there is a trend in the data indicating a resonance peak, interpolate to record the approximate resonance frequency, fresapp.


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Informational (Blue) Ballot1000AInformational (Blue) Ballotjn l10: If it is not obvious that the approximate resonance frequency was located, return to ¶ A3 -1.4.1 with a modified beginning frequency, ending frequency, frequency step size, beginning phase, ending phase, and phase step size until it is obvious that the approximate resonance frequency has been located.

For L =300 m, R02 R01 vs. Frequency

7

8

9

10

11

12

13

26.0 26.5 27.0 27.5 28.0Frequency (kHz)

R02-

R01

(m

)

Figure A3-1Plot of R02-R01 Versus Frequency for 36 Different Phase Angles

For L =300 m, R02 R01 vs. Phase(choose phase = 255 degrees)

789

10111213

0 50 100 150 200 250 300 350Phase (degrees)

R02

-R01

(m

)

z

Figure A3-2Plot of RO2-R01 Versus Phase for 101 Different Frequencies


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For L =300 m, Phase = 250 degreesR02 R01 vs. Frequency

(f resapp = 26.820 kHz)

8

9

10

11

12

13

26.0 26.5 27.0 27.5 28.0Frequency (kHz)

R02

-R01

(m

)

Figure A3-3Plot of R02-R01 Versus Frequency for a Phase of 250 Degrees

A3-1.5 Obtain the Resonance Frequency Measurements

A3-1.5.1 Set up the software (a) to use the phase angle obtained in ¶ A3-1.4.4, (b) to use a frequency range encompassing fresapp, (c) to use a predetermined frequency step size (for example, 2 Hz) also called the uncalibrated frequency resolution, fresol, and (d) to take 3 cycles of measurements. Record fresol.

A3-1.5.2 Make sure the intensity window is displayed so that the fringes can be monitored periodically during the data session to ensure that they do not drift significantly during the comprehensive dynamic measurement.

A3-1.5.3 Take the comprehensive dynamic measurement while maintaining a constant room temperature. Record the room temperature and the relative humidity for informational purposes.

A3-1.5.4 Plot R02 minus R01 versus frequency with the three cycles included in the same plot. If the data reveals significant drifting, repeat from ¶ A3-1.5.1.

A3-1.5.5 For each cycle, plot R02 minus R01 versus frequency. Keeping in mind that an extraneous data point may appear, interpolate to find the frequency at which the maximum value of R02 minus R01 is obtained. For the first cycle, record this uncalibrated frequency as fmeas1. For the second cycle, record this uncalibrated frequency as fmeas2. For the third cycle, record this uncalibrated frequency as fmeas3.

A3-1.6 View a Movie of the 3D Oscillation

A3-1.6.1 Take a dynamic measurement that (a) uses the average of fmeas1, fmeas2, and fmeas3 as the frequency at which to take measurements and (b) varies the phase angle from 0 degrees to 350 degrees in 10 degree steps. Use the acquired data to compose the movie. If the movie does not produce a resonating beam, plot R02 minus R01 versus phase. If the resulting plot does not look sinusoidal, repeat from ¶ A3-1.4.1Note 5147.

A3-1.7 Obtain the Other Calculation Inputs

A3-1.7.1 Follow the steps in § 13.7 to obtain the other calculation inputs.

A3-2 Go to § 14 to continue with the calculations for Young’s modulus, combined standard uncertainty, residual stress, and stress gradient, if appropriate.


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