Notice: Additions are indicated by underline and deletions are strikethrough. Review and Adjudication Information

Transcription

1 Background Statement for SEMI Draft Document 5804 Revision of SEMI M PRACTICE FOR CALIBRATING SCANNING SURFACE INSPECTION SYSTEMS USING CERTIFIED DEPOSITIONS OF MONODISPERSE REFERENCE SPHERES ON UNPATTERNED SEMICONDUCTOR WAFER SURFACES Notice: 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. Notice: 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. This standard is due for 5-year review as required by SEMI Standards Regulations. The International Advanced Automated Surface Inspection Task Force s review resulted in changes summarized below. ( 2.5), Appendix 1: Deleted. Single-point calibration was not recommended and is not generally practiced. New NOTE 1: (follows renumbered 2.5): Acknowledges use of DUV-stable deposition materials while maintaining continuity with LSE sizing. NOTE 1: Now NOTE 2: Updated current minimum practical deposition sizes to nm. ( 3.6): Clarified the utility of monotonic response curves. (NOTE 3): Eliminated. (NOTE 8): Mentions automated size peak extraction that many SSISs now have; simplified wording. ( 9.15): M52 Table III, row 5.3, states FWHM < 5%, which would imply σ 1<FWHM / 2.355=2.1%. ( 10.1, R1-6): M52 Table III, row 5.3, states expanded uncertainly at 95% conf < 3%. Editorial: ( 1.3): Missing. ; 4.1 updated title of SEMI M52; Ref to NOTE 2 to NOTE 3; Ref to NOTE 3 eliminated; ( 2.6): Renumbered 2.5, reference to Appendix 2 changed to Appendix 1; corrected reference to the table in M52. Notice: Additions are indicated by underline and deletions are strikethrough. Review and Adjudication Information Task Force Review Committee Adjudication Group: Int l Automated Advanced Surface Inspection TF Silicon Wafer Europe TC Chapter Date: October 6, 2015 October 7, 2015 Time & Timezone: 3:00-4:00 PM CET 2:00-3:30 PM CET Location: Messe Dresden Messe Dresden City, State/Country: Dresden, Germany Dresden, Germany Leader(s): Kurt Haller (KLA-Tencor) Peter Wagner (Self) Fritz Passek (Siltronic) Standards Staff: Kevin Nguyen, knguyen@semi.org Kevin Nguyen, knguyen@semi.org 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. Check on calendar of event for the latest meeting schedule.

2 SEMI Draft Document 5804 Revision of SEMI M PRACTICE FOR CALIBRATING SCANNING SURFACE INSPECTION SYSTEMS USING CERTIFIED DEPOSITIONS OF MONODISPERSE REFERENCE SPHERES ON UNPATTERNED SEMICONDUCTOR WAFER SURFACES Notice: Additions are indicated by underline and deletions are strikethrough. 1 Purpose 1.1 This practice describes calibration of scanning surface inspection system (SSIS) dark field detector channels so that the SSIS will accurately size PSL (polystyrene latex) spheres deposited on unpatterned polished, epitaxial, or filmed semiconductor wafer surfaces. 1.2 The purpose of this calibration is to ensure that different SSISs of a given manufacturer and model will assign the same light scattering equivalent (LSE) diameter to a specific localized light scatterer (LLS). 1.3 This practice defines the use of LSE diameters, as defined in SEMI M59, as a means of reporting real surface defects whose identity, true size, and morphology are unknown. 1.4 This practice provides a basis for quantifying SSIS performance as used in related standards concerned with parameters such as sensitivity, repeatability, and capture rate. 2 Scope 2.1 This practice covers: Requirements for the surface and other characteristics of the semiconductor substrates on which the reference spheres are deposited to form reference wafers (see 8.1), Selection of appropriate certified depositions of reference spheres for SSIS calibration, including size distribution requirements to be met by the reference sphere depositions, but not the deposition method (see 8.3), Generation of calibration curves using model-predicted scatter data that have response curve oscillations and are thus not monotonic, and Generation of monotonic calibration curves using model-predicted scatter data. 2.2 Although it was developed primarily for use in calibration of SSISs to be used for detection of localized light scatterers (LLSs) on polished silicon wafers with geometrical characteristics as specified in SEMI M1, this practice can be applied to SSISs to be used for detection of LLSs on other unpatterned semiconductor surfaces, provided that suitable reference wafers are employed. 2.3 This practice does not in any way attempt to define the manner in which LSE values are used to define the true size of LLSs other than PSL spheres (see 3.1). 2.4 This practice supports requirements listed in SEMI M Appendix 1 covers a single-point calibration procedure that may be used in limited production applications but which does not support requirements listed in SEMI M Appendix 2 Appendix 1 describes a method that may be used to determine the index of refraction of reference spheres that are not PSL. NOTE 1: Repeated exposure to deep UV (DUV) illumination is known to alter the light scattering response of PSL sphere depositions. Therefore, manufacturers and end-users of DUV SSISs generally use monodisperse depositions of DUV-stable materials, silica (SiO2) for example, for long-term periodic calibration of SSISs. To maintain continuity with LSE sizing, the light scattering intensity of such materials are usually assigned to the diameter of hypothetical PSL sphere depositions that would produce the same intensity, rather than their actual physical diameters. As such, wafers with deposited spheres of any material in this practice serve as light scattering intensity reference wafers rather than size standards. Page 1 Doc SEMI

3 NOTICE: SEMI Standards and Safety Guidelines do not purport to address all safety issues associated with their use. It is the responsibility of the users of the Documents to establish appropriate safety and health practices, and determine the applicability of regulatory or other limitations prior to use. 3 Limitations 3.1 LLSs are normally assigned only LSE sizes, not physical diameters, because the response of an SSIS to an LLS depends on the SSIS optical system characteristics as well as the size, shape, orientation and composition of the LLS. The LSE size assigned to a particular LLS by an SSIS calibrated against PSL spheres may be different from that assigned to the same LLS by another similarly calibrated SSIS of a different model, because different SSISs have different optical system characteristics. 3.2 Reference spheres as sold in bulk may have specified characteristics (mean diameter uncertainty, diameter distribution, spread between mean and modal diameter) that differ significantly from the characteristics of the resulting deposition due to the transfer function of the deposition system. For this reason the practice is limited to the use of reference sphere depositions that are appropriately characterized in accordance with SEMI M58 and properly certified (see 8). 3.3 The largest reference sphere diameter that can be used in this practice depends on individual SSIS characteristics, but is often limited to a diameter of about ten times the light source wavelength. 3.4 The smallest reference sphere diameter that can be used in this practice is determined by the sensitivity of the SSIS under calibration. NOTE 1:NOTE 2: At the time of development of this edition of the practice, the smallest practical deposited reference spheres have physical diameters approaching nm, but as IC technology evolves to smaller and smaller critical dimensions, it is expected that depositions of smaller diameter reference spheres will become available. 3.5 The SSIS signal is not necessarily monotonic with the diameter of a PSL sphere, especially for those having diameters approaching the wavelength of the light. As a result, the response curve (RC) determined by this practice may not provide a unique determination of LSE diameter for all LLS. 3.6 If athe monotonic response curve is used and if the usable signal range of the detector channel under calibration extends into a region where there are response curve oscillations in the physicalnon-monotonic response curve, then the LSE size assigned to a PSL sphere sizing accuracy will be reduced in thethat region is not necessarily accurate. Nevertheless, this practice ensures an SSIS assigns reproducible LSE size to an LLS of any size, shape, and material composition. 3.7 Background Contamination Both the deposition process and calibration procedures must be carried out in a Class 4 or better environment as defined in ISO The presence of contamination with LSE sizes near that of the nominal reference sphere diameter on the reference wafer may skew the results. This condition may result in a large error or poor sizing accuracy High levels of contamination on the reference wafer or wafers may overload the SSIS or obscure the peak of the deposited reference sphere diameter distribution. This condition may also result in a large error or poor equivalent sizing accuracy For these reasons, both the deposition process and calibration procedures must be carried out in a clean environment, and the reference wafers must be handled in such a way as to avoid contamination between deposition process and calibration. 3.8 If the surface roughness of the reference wafer or wafers is excessive, the peak of the reference sphere diameter distribution may be obscured or distorted. 3.9 If the SSIS being calibrated is not operating in a stable condition, the calibration may not be appropriate for subsequent use of the system. System stability can be evaluated by making repeated calibrations, in accordance with this practice, over suitable time periods. Page 2 Doc SEMI

4 4 Referenced Standards and Documents 4.1 SEMI Standards SEMI M1 Specifications for Polished Single Crystal Silicon Wafers SEMI M12 Specification for Serial Alphanumeric Marking of the Front Surface of Wafers SEMI M20 Practice for Establishing a Wafer Coordinate System SEMI M50 Test Method for Determining Capture Rate and False Count Rate for Surface Scanning Inspection Systems by the Overlay Method SEMI M52 Guide for Specifying Scanning Surface Inspection Systems for Silicon Wafers for the 130 nm to 11nm, 90 nm, 65 nm, and 45 nm Technology Generations SEMI M58 Test Method for Evaluating DMA Based Particle Deposition Systems and Processes SEMI M59 Terminology for Silicon Technology 4.2 ISO Standard 1 ISO Cleanrooms and Associated Controlled Environments Part 1: Classification of Air Cleanliness NOTICE: Unless otherwise indicated, all documents cited shall be the latest published versions. 5 Terminology 5.1 Acronyms, definitions, and symbols used in silicon technology may be found in SEMI M Other acronyms used only in this standard are as follows: GNF Gain-nonlinearity function MPRC Monotonic predicted response curve MRC Monotonic response curve PRC Predicted response curve RC Response curve 5.3 Other terms used only in this standard are as follows: gain-nonlinearity function (GNF) the relationship between the actual SSIS response and the modelpredicted SSIS response, given as a function with two or more independent and adjustable parameters. The GNF should be independent of the reference sphere material, because it is a relationship between the SSIS detector response and the amount of light predicted to be incident upon the detector LSE sphere sizing uncertainty an estimate of the relative uncertainty in the diameter reported by an SSIS for a PSL sphere having any diameter in the calibration range, determined by combining contributions from the calibration diameter errors and the certified deposition uncertainty monotonic predicted response curve (MPRC) a predicted response curve derived from a PRC and modified to be monotonic. A subscript appended to the MPRC (e.g., MPRC silica or MPRC PSL), indicates the sphere material for which the MPRC applies monotonic response curve (MRC) the monotonic relation between the actual SSIS signal and sphere diameter, which differs from the RC PSL by being derived from the MPRC rather than the PRC PSL. A subscript appended to the MRC (e.g., MRC silica or MRC PSL), indicates the sphere material for which the MRC applies predicted response curve (PRC) the model-predicted relation between scattered light intensity (or SSIS signal response) and sphere diameter that is used to analyze scanner response near various sphere diameters. The 1 International Organization for Standardization, ISO Central Secretariat, 1 rue de Varembé, Case postale 56, CH-1211 Geneva 20, Switzerland. Telephone: ; Fax: ; Page 3 Doc SEMI

5 PRC depends upon sphere material and scanner design and is in general non-linear. It may contain regions with response curve oscillations that make the response-diameter relationship multi-valued. A subscript appended to the PRC (e.g., PRC silica or PRC PSL), indicates the sphere material for which the PRC is calculated response curve (RC) the relation between actual SSIS signal and sphere diameter. A subscript appended to the RC (e.g., RC silica or RC PSL), indicates the sphere material for which the RC applies. The RC depends on scanner design and is in general non-linear. It may contain regions with response curve oscillations that make the responsediameter relationship multi-valued response curve oscillations peaks and valleys in the response curve, which prevent the response curve from being monotonic. 6 Summary of Practice 6.1 The SSIS being calibrated is set up with machine conditions identical with those to be used in examining wafers. 6.2 Reference wafers with appropriate certified depositions are scanned by the SSIS. 6.3 The peak of the reference sphere diameter distribution deposited on each reference wafer is assigned to the peak value of the SSIS signal units. 6.4 A predicted response curve is determined for each reference sphere material and for PSL using its index of refraction and the appropriate parameters for the measurement conditions. 6.5 The actual SSIS signals and the predicted responses are used to determine the gain-nonlinearity function (GNF). 6.6 The PRC PSL and the GNF are used to determine the response curve for PSL (RC PSL), which may have response curve oscillations Discussion If PSL spheres were used as reference spheres, a graph of the RC PSL will lie very close to, but may not exactly match, a graph of the recorded signal versus reference sphere diameter. If another sphere material were used, a graph of the RC PSL will not match a graph of recorded signal versus reference sphere diameter. That is, an SSIS calibrated to assign LSE diameters to LLSs will not correctly size non-psl reference spheres. 6.7 The expanded PSL sphere sizing uncertainty is determined and compared to the requirements of SEMI M A monotonic predicted response curve (MPRC PSL) may be generated from the PRC PSL to remove response curve oscillations. 6.9 The MPRC PSL and the GNF may be used to determine the monotonic response curve (MRC PSL), which does not have response curve oscillations A separate RC PSL and MRC PSL are developed for each detector channel Either the RC PSL or the MRC PSL is used to determine and report the LSE diameter. 7 Apparatus 7.1 Scanning Surface Inspection System Designed to detect, size, and map localized light scatterers (LLSs) on unpatterned semiconductor wafers, that has the following capabilities: Scans the entire fixed quality area of the surface of a wafer with a laser beam, Detects localized light scatterers as laser-light scattering events (see Note 32), Has a user definable sensitivity threshold used to distinguish between background noise and real LLSs, (see Note 3), Can create a histogram of SSIS signals (i.e., number of laser light scattering events as a function of raw SSIS signal) for any given region on the wafer, Can either evaluate the histogram peak or output a data set file that can be imported to a spreadsheet or other application program that can be used to generate the histogram peak, Can either accept a user-provided calibration curve for each detector channel or can automatically perform the steps given in 9 below, Page 4 Doc SEMI

6 7.1.7 Is sufficiently repeatable for the intended application, and Handles wafers in a Class 4 or better clean environment as defined in ISO NOTE 2:NOTE 3: The amplitude of the LSE signal into a single detector, as measured for any combination of incident beam direction and collection optics, does not by itself convey topographic information, for example, whether the LLS is a pit or a particle. It does not allow the observer to deduce the size or origin of the scatterer without other detailed knowledge, such as its index of refraction and shape. NOTE 3: Thresholds may be set to discriminate between true counts and surface or electrical noise (nuisance or false counts, respectively) or between different sizes of light scatterers. Because of spatial non-uniformity of the intensity of the scanning beam and the general use of overlapping scans in an SSIS, a localized light scatterer with equivalent size near the threshold may generate a signal greater than or less than the threshold depending on its location with respect to the path of the scanning beam. The former is identified as a true count and the latter is identified as a missing count. 8 Reference Wafers 8.1 Substrates Use bare semiconductor wafers with a native oxide (or other filmed) surface of the type intended to be tested with the SSIS to be calibrated as substrates for the certified depositions of the reference spheres. This is particularly important because SSIS response is affected by the optical properties of the substrate. Bare silicon wafer surfaces have different optical properties than wafers with film layers or wafers of different material. The wafers must meet the dimensional requirements of SEMI M1 for the appropriate nominal wafer diameter. Wafers nominally 200 mm in diameter and smaller shall be laser marked in accordance with SEMI M12, and wafers nominally 300 mm in diameter shall be laser marked in accordance with of SEMI M1, including the optional alphanumeric mark described in of SEMI M Certified Depositions The deposition property value that must be certified is the peak sphere diameter. The diameter distribution on the wafer and the reference sphere material must be specified. The diameter distribution is determined by the deposition process, and the reference sphere material affects its index of refraction. 8.3 Range and Number of Calibration Diameters Choose the diameters of the reference spheres for the certified depositions so that the measurement range for the intended application is significantly covered. Use spheres of size ranging from less than the largest measurable size down to a size greater than that with an estimated capture rate of 95% and spaced approximately evenly on a logarithmic scale. The minimum and maximum sphere sizes do not need to be at the extremes of the required calibration range, since this practice allows for extrapolation. Do not exceed the signal range of the SSIS detector channel being calibrated. The number of certified depositions should be at least 4 more than the number of adjustable parameters used for the GNF. A reference wafer may contain one or more certified depositions. NOTE 4: The useful signal range is limited on the small signal side by the background noise or the inherent resolution of the instrument and on the large signal side by saturation of the detector and/or the related electronics. The small signal limit is usually defined as the smallest LSE sphere diameter than can be measured with a capture rate of at least 95% The index of refraction of the reference spheres may not be the same as that of the bulk material. In the case of PSL spheres, industry practice is to use the index of refraction of bulk polystyrene, given by: B C n = A + + (1) λ 2 λ 4 where A = , B = µm 2, C = µm 4, and λ is the wavelength of light. A method suitable for determining the index of refraction of non-psl spheres is described in Appendix 2. NOTE 5: The above coefficients have been shown to be valid over the wavelength range 0.42 < λ (um) < Some state-ofthe-art SSIS may use excitation at shorter wavelengths. However, good sizing correlation has been observed using this equation at shorter wavelengths. NOTE 6: Best results are typically achieved when using the number, the sizes of reference spheres, and the extent of allowable extrapolation recommended by the SSIS manufacturer. 8.4 Background Contamination Handle and store reference wafers with great care to avoid contamination and damage. Page 5 Doc SEMI

7 8.4.2 Establish that the unimodal peaks in the SSIS LLS histogram generated from the reference sphere depositions are well defined and well above the background level over all the response curve except near the low signal threshold. Also verify that each unimodal curve extends to less than 50% of its peak value on both sides of the peak within a diameter range of ±2.5% of the reference sphere diameter at the peak of the distribution. Do not use depositions that fail either of these criteria. NOTE 7: The RC depends on scanner design and is in general non-linear. It may contain regions with response curve oscillations that make the response-diameter relationship multi-valued. 8.5 Data to Accompany Reference Wafers The following information must accompany each reference wafer For each certified deposition on a reference wafer provide: The deposition peak diameter and the uncertainty in accordance with the requirements of Row 54.3 of Table 3 of SEMI M The maximum possible value of the deposition diameter distribution full width at half maximum (FWHM) expressed as a percentage of peak diameter The approximate particle count of each certified deposition The approximate location of each certified deposition on the reference wafer by the x- and y-coordinates (as specified in SEMI M20) of the center of the deposition area or by a map or drawing of the wafer Identification of the deposition system used for the deposition by model and serial number The date of production Wafer identification Name and address of the reference wafer manufacturer Identification of the deposited reference spheres by material, supplier, lot number and model. 9 Procedure 9.1 Obtain the required number of suitable reference wafers with certified depositions (see 8.3) to cover each established signal range. 9.2 Set up the SSIS in accordance with the manufacturer s instructions for the wafer diameter, sizes of reference spheres, and other machine conditions to be used during the calibration procedure. Ensure that machine conditions are identical with those to be used in examining wafers with the calibrated SSIS. 9.3 Ensure that the SSIS is operating properly for the selected machine conditions. 9.4 Load the first reference wafer into the SSIS. 9.5 Scan the wafer. 9.6 Generate a data set file of the distribution of localized light scatterers as a function of reported SSIS signal. 9.7 Repeat for each of the remaining certified depositions. 9.8 Determine the peak of the reference sphere diameter distribution for each of the certified depositions used for the calibration. NOTE 8: Many SSISs now feature automated determination of the peak of sphere diameter distributions. For SSISs where the determination is manual, users should carefully note histogram aspects such as scaling and non-uniform bin widths which may bias peak position. NOTE 8: The data set is usually partitioned into bins of equal size on either a linear or logarithmic scale, as appropriate. The bins at the low and high ends of the data set variable range are customarily plotted with the same width as the remainder of the histogram even though they may represent a larger or smaller range of the independent variable than the rest of the bins. 9.9 For each reference sphere material and for PSL, create a PRC using the SSIS detector channel geometry, source wavelength, source polarization and appropriate material constants over the range from less than the minimum certified deposition diameter to greater than the maximum certified deposition diameter with a recommended Page 6 Doc SEMI

8 diameter spacing of approximately the illumination wavelength divided by 50 in order to accurately predict RC oscillations. Calculate the PRC using the Bobbert-Vlieger model provided in the Modeled Integrated Scatter Tool (MIST) program. 2 Alternatively, use another program suggested by the instrument manufacturer, provided that it can be shown to have as good or better results. Record the PRC values for each certified deposition by interpolating the PRC for the reference sphere material at its certified diameter Obtain the GNF by adjusting the independent parameters for a best fit to the SSIS signals found in 9.8 versus the corresponding PRC values obtained in 9.9. Typically the curve is a smooth straight line on a log-log graph, so use the following form: GNF = α (predicted response) γ (2) This function has two adjustable parameters (α and γ). Alternatively, use another function form, provided that the number of adjustable parameters is small, it is monotonic, and it describes a typical non-linearity for the type of detector used Create an RC for each reference sphere material by applying the GNF determined in 9.10 to the PRC for that material. Graph the RCs (as curves) and the peak SSIS signals determined in 9.8 (as points) against diameter on a log-log scale Determine the calibration diameter error between the points and the curve for the corresponding reference sphere material shown in the graph created in If a monotonic response is to be used for large particles, create the MPRC PSL from the PRC PSL using the method specified by the SSIS manufacturer. If a non-monotonic response is to be used for large particles, go to Create an MRC PSL by applying the GNF determined in 9.14 to the MPRC PSL Determine the expanded PSL sphere sizing uncertainty by: σ 2 U = 2 σ + / N M, (3) PSL where σ 1 is the relative standard uncertainty in the peak reference sphere diameters for the certified depositions, σ 2 is the standard deviation of the relative calibration diameter error (determined in 9.12), N is the number of certified depositions, and M is the number of independent parameters in the GNF. SEMI M52 requires that σ 1 be less than 2.1.5%; in the absence of specific values for σ 1, the maximum value accepted by SEMI M52 can be used Repeat the procedure of for all of the SSIS detector channels being calibrated Related Information 1 presents an example of this procedure based on one detector channel of a commercially available SSIS. 10 Interpretation of Results 10.1 The expanded reference sphere sizing uncertainty found for each detector channel in 9.15 should be less than 32% in order to meet the requirements of SEMI M If the decision has been made to allow the response to be non-monotonic for large particles, then use the RC PSL to establish the LSE size of LLSs If the decision has been made to use the monotonic response for large particles, then use the MRC PSL to establish the LSE size of LLSs. 11 Report 11.1 Report the following information: Operator identification; 2 This program can be downloaded without charge from the website of the National Institute of Standards and Technology: Page 7 Doc SEMI

9 Date and location of measurement; Manufacturer, model, serial number, and software version of the SSIS; Reference wafer characteristics as outlined in the certificates accompanying the reference wafers (see 8); Histogram for each data set and the assigned peak value of the distribution of reported diameters together with the certified peak diameter of the PSL sphere distributions used to generate the histogram; and The GNF, the RC PSL, and the associated certified reference sphere diameters. If a monotonic response is to be used for large particles, also report the MRC PSL. Page 8 Doc SEMI

10 APPENDIX 1 SINGLE-POINT CALIBRATION NOTICE: The material in this appendix is an official part of SEMI M53 and was approved by full letter ballot procedures on November 29, A1-1 Choose a single reference wafer with PSL sphere deposition CRM size near the LSE size of the smallest LLS to be tested for in meeting a wafer specification. NOTE 9: Because of possible non-linearities in the SSIS, single-point calibration is not recommended except in the immediate vicinity of a single sphere size of interest, for example, the smallest size to be tested for in meeting a wafer specification. A1-2 Set up the SSIS to be calibrated in accordance with 9.2 and 9.3. A1-3 Load the appropriate reference wafer into the SSIS. A1-4 Scan the wafer. A1-5 Generate a data set file of the distribution of localized light scatterers as a function of reported size (LSE). A1-6 Construct a histogram for the distribution in the data set file. A1-7 Determine the standard deviation and peak diameter value from curve fits of the histogram. A1-8 Associate the peak value of reported size (LSE) found to the certified value of PSL sphere diameter deposited on the reference wafer. A1-9 The procedure outlined in this appendix does not support the requirements of SEMI M52. Page 9 Doc SEMI

11 APPENDIX 2APPENDIX 1 REFERENCE SPHERE INDEX DETERMINATION NOTICE: The material in this appendix is an official part of SEMI M53 and was approved by full letter ballot procedures on January 2, A2-1 A1-1 This appendix describes a method for determining the index of refraction of non-psl reference spheres. It requires an SSIS, but it does not require that the SSIS be of the same design as that for which the reference spheres will be used to calibrate. A2-2 A1-2 Obtain two sets of reference wafers with certified depositions (see 8.2), one with PSL spheres and the other with reference spheres of unknown index (the unknown reference spheres ). A2-3 A1-3 Follow using the PSL spheres. For the index of refraction of the PSL spheres, use where A = , B = µm 2, and C = µm 4. Report the GNF. B C n = A + + (A2-1) λ 2 λ 4 A2-4 A1-4 Repeat the measurement steps ( ) for the unknown reference spheres, to obtain the signal S i for each unknown reference sphere i. A2-5 A1-5 Estimate the anticipated minimum and maximum possible indices for the unknown reference spheres. A2-6 A1-6 For each index n ranging from the minimum to the maximum with a small step n, create a PRC n as per 9.9. Record the PRC n values for each unknown reference sphere i and for each index n, PRC ni. A2-7 A1-7 For each index n and each unknown reference sphere i, calculate the GNF error from E = GNF(PRC ) S (A2-2) ni ni i A2-7.1 A1-7.1 For each index n, calculate the sum of squares GNF error from F n = E (A2-3) i A2-8 A1-8 Plot F n versus n. If there is no minimum, go back to 1.4, starting over with a new range of possible indices. A2-9 A1-9 Find the best value of n by fitting the data close to the minimum to a parabola and finding the minimum. Use the best value of n for the index of the reference spheres at the operating wavelength of the SSIS. A2-10 A1-10 Follow steps of the standard using the data from the reference spheres instead of the PSL spheres and report the calibration diameter errors and the GNF. A2-11 A1-11 If the index of refraction, n bulk, for the bulk form of the material is known at the operating wavelength of the SSIS, then an effective medium void fraction may be estimated from 2 ni 2 bulk bulk bulk ( nbulk 1)(2 nbulk + n ) ( n n)( n + n)(2n + 1) x = (A2-4) A2-12 A1-12 If both the effective medium void fraction and the wavelength dependence n bulk( ) of the index of refraction of the bulk material are known, then the index of refraction of the reference spheres at other wavelengths can be estimated from: n( λ) = n ( ) 2 1 2[ bulk ( λ)] ( 1) + 2 bulk λ 2 1 x + [ nbulk ( λ)] ( x + 2) n x x (A2-5) Page 10 Doc SEMI

12 RELATED INFORMATION 1 EXAMPLE OF MULTI-POINT CALIBRATION WITH FIT TO MODEL- PREDICTED DATA NOTICE: This related information is not an official part of SEMI M53 and was derived from the Automated Wafer Surface Inspection Task Force. This related information was approved for publication by full letter ballot on January 2, R1-1 This related information provides an example of the procedure described in 9. In all of this related information, the reference spheres were PSL; subscripts on PRC, RC, MPRC, and MRC have been omitted and are assumed to be PSL. R1-2 Data were obtained on one detector channel of a commercially available SSIS. Column 1 of Table R1-1 lists the certified diameters that were used in the calibration procedure. Column 2 of the table lists the measured peak signals for each of the certified diameters. These signals have been multiplied by an unknown and arbitrary constant. The peak signals range from S min = to S max = R1-3 The predicted response curve (PRC) was calculated using the Modeled Integrated Scatter Tool (MIST) program. 3 The parameters used for the model are given in Table R1-2. The PRC is shown in Figure R1-1. The model-predicted response for each certified diameter is given in the third column of Table R1-1. R1-4 Figure R1-2 shows a graph of the measured response values (second column of Table R1-1) versus the modelpredicted response values (third column of Table R1-1). On a log-log scale, it appears to be a straight line, so that the GNF is chosen to be: GNF = α (predicted response) γ (R1-1) A best fit to the data yields the two adjustable parameters α = and γ = The best fit curve is also shown in Figure R1-2. R1-5 The RC was developed by applying the function of Equation R1-1 to the signal values of the PRC. The RC is shown in Figure R1-3. The signals for the certified depositions are shown as points. R1-6 The calibration diameter error is shown in the fourth column in Table R1-1. These deviations represent the estimated errors in the measured diameters. The maximum value of this deviation is 1.5% and the standard deviation is 0.6%. Since there are 14 calibration points and 2 degrees of freedom to the GNF, the expanded PSL sphere sizing uncertainty is: 2 2 U PSL = 2 (1.5%) + (0.6%) / 14 2 = 0.9%. (R1-2) Since this value is below 32%, the calibration meets the requirements of SEMI M52. R1-7 An MPRC was generated from the PRC by the following procedure: (A) The PRC was re-evaluated with diameters spaced by 2% over the range 30 nm to 1 µm. (B) For each diameter on the re-evaluated PRC, a straight line was fit (on a log-log graph) to points having diameters within 25% of the given diameter. (C) The MPRC at each diameter was then given by evaluating the straight line at that diameter. The MPRC is shown with the PRC in Figure R1-1. In order to demonstrate the procedure, the method for creating an MPRC was adopted in lieu of one provided by the manufacturer, and the range of particle sizes were extended. R1-8 The MRC generated by applying the GNF to the MPRC is shown in Figure R1-3 with the RC. This MRC can be used to size particles throughout the diameter range shown, since it is monotonic. Page 11 Doc SEMI

13 Table R1-1 Example of Data for Calibration Procedure Certified Diameter (nm) Measured Response (arb. units) Predicted Response (arb. units) Calibration Diameter Error % % % % % % % % % % % % % % Table R1-2 Parameters Used in MIST Parameter Value Model Bobbert_Vlieger_BRDF_Model Wavelength 488 nm Refractive index of substrate i Refractive index of substrate oxide Refractive index of PSL sphere Thickness of substrate oxide: 1.6 nm Incident angle 70 Incident polarization p (electric field in plane of incidence) Collection geometry All polar angles between 25 and 70. Page 12 Doc SEMI

14 Predicted Response (arb. units) Predicted Response Curve Monotonic Predicted Response Curve PSL Sphere Diameter (nm) Figure R1-1 Predicted Response Curve (PRC) Calculated from MIST and the Monotonic Predicted Response Curve (MPRC) 1000 Measured Response (arb. units) Measurement Gain-Nonlinearity Function Predicted Response (arb. units) Figure R1-2 Measured Response Values as a Function of Model-Predicted Response Values (points) and the Gain-Nonlinearity Function (line) Page 13 Doc SEMI

15 Response Curve (arb. units) Measurement Response Curve Monotonic Response Curve Certified PSL Sphere Diameter (nm) Figure R1-3 Response Curve (RC) and the Monotonic Response Curve (MRC) NOTICE: SEMI makes no warranties or representations as to the suitability of the standard(s) set forth herein for any particular application. The determination of the suitability of the standard(s) is solely the responsibility of the user. Users are cautioned to refer to manufacturer s instructions, product labels, product data sheets, and other relevant literature respecting any materials or equipment mentioned herein. These standards are subject to change without notice. By publication of this standard, Semiconductor Equipment and Materials International (SEMI) takes no position respecting the validity of any patent rights or copyrights asserted in connection with any item mentioned in this standard. Users of this standard are expressly advised that determination of any such patent rights or copyrights, and the risk of infringement of such rights are entirely their own responsibility. Page 14 Doc SEMI