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Background Statement for SEMI Draft Document 5434NEW STANDARD: TEST METHOD FOR IN-LINE MEASUREMENT OF LATERAL DIMENSIONAL CHARACTERISTICS OF SQUARE AND PSEUDO-SQUARE PV SILICON WAFERS

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.

The lateral dimensions of PV Si wafers are widely specified, assuming that a standardized test method for measuring them exists. So far this is not the case. Therefore a standardized test method has to be developed in order to avoid potential quality conflicts and claims when tighter tolerances will be required.

The corresponding SNARF was approved by the PV Materials Committee in its meeting in Munich on June 13, 2012. The draft document was developed since July 2012 and was approved for yellow letter ballot in cycle 1 2013 by the PV Materials Committee in its meeting in Dresden on October 9, 2012, to be adjudicated in Berlin in March 2013 in the meetings in conjunction with the PV Fab Manager Forum.

The ballot results will be reviewed and adjudicated at the meetings indicated in the table below. Check www.semi.org/standards under Calendar of Events for the latest update.

Review and Adjudication InformationTask Force Review Committee Adjudication

Group: PV Si Materials Task Force PV Materials CommitteeDate: March 13, 2013 March 13, 2013Time & Timezone: 9:00, CET 13:00, CETLocation: Leonardo Royal Hotel Berlin Alexanderplatz Leonardo Royal Hotel Berlin AlexanderplatzCity, State/Country:

Berlin, Germany Berlin, Germany

Leader(s): P. Wagner H. Aulich, P. WagnerStandards Staff: Y. Guillou Y. Guillou

Meeting date and time are subject to change, and additional TF review sessions may be scheduled if necessary. Contact the task force leaders or Standards staff for confirmation. If you have any questions, please contact the SEMI staff [email protected]

mailto:[email protected]

http://www.semi.org/standards

DRAFTDocument Number:

Date: 5/8/23

SEMI Draft Document 5434NEW STANDARD: TEST METHOD FOR IN-LINE MEASUREMENT OF LATERAL DIMENSIONAL CHARACTERISTICS OF SQUARE AND PSEUDO-SQUARE PV SILICON WAFERS1 Purpose1.1 The geometrical dimensions of PV silicon (Si) wafers are key specification parameters (SEMI PV22).

1.2 Parameters such as edge length and diagonal of a wafer appear to be obvious, if the wafers are perfectly square or pseudo-square.

1.3 However, SEMI PV22 allows deviations of the side lengths and corner angles of the nominally square wafers within a specified range, potentially resulting in non-square wafers.

1.4 In addition, the edges of real wafers usually cannot be represented by straight lines. They are curved to some extent.

1.5 This creates an ambiguity in measuring the edge lengths and other geometrical dimensions of wafers.

1.6 This test method defines selected terms and a test method for measuring corresponding parameters.

2 Scope2.1 The test method covers square and pseudo-square Si wafers for photovoltaic (PV) applications, with a nominal edge length ≥ 125 mm and a nominal thickness ≥ 100 µm.

2.2 This test method measures lateral geometrical dimensions of crystalline PV Si wafers.

2.3 This method employs an in-line, non-contacting and non-destructive method for characterizing clean, dry PV Si wafers supported by a mechanism that move the test specimen through the measurement equipment.

2.4 The surface condition of the wafers may be as cut, etched or passivated.

2.5 The test method is intended for in-line high throughput measurements. Therefore it is mandatory to operate the measurement system under statistical process control (SPC, e.g. ISO 11462) in order to obtain reliable, repeatable and reproducible measurement data.

2.6 The test method is based on recording and evaluating images of the wafer surface obtained by a digital camera under diffuse white light illumination.

2.7 The test method does not include the measurement of wafer thickness or thickness variation. For this measurement see SEMI PV41.

2.8 Other measurement techniques may also provide similar information, but they are not the subject of this test method.

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 Limitations3.1 Excessive tilt and warp of the wafer on the transport belts may result in distorted wafer image and may impact the measurement result.

3.2 Large edge chips or v-grooves on the wafer edges also may result in erroneous measurement results.

4 Referenced Standards and Documents4.1 SEMI Standards and Safety Guidelines

SEMI E89 –– Guide for Measurement System Analysis (MSA)

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.

Page 1 Doc. jn l SEMI

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


Date: 5/8/23

SEMI MF1569 –– Guide for Generation of Consensus Reference Materials for Semiconductor Technology

SEMI PV22 — Specification for Silicon Wafers for Use in Photovoltaic Solar Cells

SEMI PV32 –– Specification for Marking of PV Silicon Brick Face and PV Wafer Edge

SEMI PV41 –– Test Method for In-Line, Noncontact Measurement of Thickness and Thickness Variation of Silicon Wafers for PV Applications Using Capacitive Probes

4.2 ISO Standards1

ISO 11462-1 — Guidelines for implementation of statistical process control (SPC) – Part 1: Elements of SPC

ISO 11462-2 –– Guidelines for implementation of statistical process control (SPC) – Part 2: Catalogue of tools and techniques

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

5 Terminology(Refer to the SEMI Standards Compilation of Terms (COTs) for a list of the current Abbreviations, Acronyms, Definitions, and Symbols.)

5.1 Abbreviations and Acronyms

5.1.1 MSA – Measurement System Analysis

5.1.2 SPC – Statistical Process Control

5.2 Definitions

5.2.1 cathetus, of a nominally square or pseudo-square Si wafer –– a line segment between a wafer corner and an adjacent chamfer corner.

5.2.2 cathetus length –– the shortest distance between a wafer corner and an adjacent chamfer corner point.

1: The cathetus length of a nominally square or pseudo-square wafer is denoted by ”F” in SEMI PV22.

5.2.3 chamfer line, of a nominally square or pseudo-square Si wafer –– second order polynomial line fit to the corner chamfer of a wafer.

5.2.4 chamfer length, of a nominally square or pseudo-square Si wafer –– the shortest distance between adjacent intersections of the chamfer line and the adjacent edge lines.

5.2.5 corner, of nominally square or pseudo square Si wafer –– the intersection of adjacent edge lines.

5.2.6 corner angle, of a nominally square or pseudo-square Si wafer –– the included angle between adjacent edge lines.

5.2.7 diagonal length, of a nominally square Si wafer –– the shortest distance between opposite corners of a wafer.

5.2.8 diagonal line, of a nominally square Si wafer –– a straight line through opposite wafer corners.

2: The diagonal length of a nominally square wafer is denoted by “G” in SEMI PV22.

5.2.9 edge length, of a nominally square or pseudo-square Si wafer — the shortest distance between adjacent corners.

3: The edge length of a nominally square or pseudo-square wafer is denoted by “A” in SEMI PV22.

5.2.10 edge line, of a nominally square or pseudo-square Si wafer — first or second order polynomial line fit to the wafer edges, excluding chamfers at wafer corners.

5.2.11 fit line –– a line fit to a set of x-y-coordinates.

1 International Organization for Standardization, ISO Central Secretariat, 1 rue de Varembé, Case postale 56, CH-1211 Geneva 20, Switzerland; Telephone: 41.22.749.01.11, Fax: 41.22.733.34.30, http://www.iso.ch




http://www.iso.ch/


Date: 5/8/23

5.2.12 reference points, of a nominally square or pseudo-square Si wafer –– points on the wafer perimeter/edges used for assigning metrics to the wafer

5.2.13 short diagonal length, of a nominally square Si wafer –– the shortest distance along a diagonal line between an intersections of a chamfer line and a diagonal line.

4: The short diagonal length of a nominally square wafer is denoted by “E” in SEMI PV22.

5.2.14 short edge length, of a nominally square or pseudo-square Si wafer –– the shortest distance between adjacent chamfer corner points along one wafer edge.

5: The short edge length of a nominally square wafer is denoted by “C” in SEMI PV22.

6 Summary of Test Method6.1 The wafer resting on the transport mechanism is moved in the x-direction, the direction of travel, past a diffuse white light source and a digital camera (see Figure 1).

6.2 A gray scale picture of the wafer is recorded by the digital camera and processed according to § 12 .

6.3 Edge lengths, corner angles, diagonals and chamfer lengths are reported according to § 13 .

7 Apparatus (see Figure 1)7.1 Light source — illuminates the wafer homogeneously with diffuse white light. Light shields prevent light from entering the camera directly.

7.2 Camera –– a digital camera with a resolution of at least 2048 pixels, positioned above the wafer surface. The line of sight of the camera is nominally perpendicular to the wafer surface and the camera-wafer surface distance is ≥ 3 times wafer diagonal. The exposure time of the camera has to be set so that the image does move less than 3 pixels during exposure. The noise level (3 ) of the camera shall be ≤ 1 % of the peak signal and the dynamic range shall be ≥ 255 gray levels.

7.3 Computer –– for controlling the measurement system and with software for recording and processing the camera images according to § 13 .

7.3.1 Wafer Transport — consisting of a mechanism that transports the wafer continuously through the measurement apparatus without obstructing the line of sight of the camera and the illumination. The mechanism shall not leave traces or residue on the wafer surface.

8 Safety Precautions8.1 The entire equipment must be placed in a closed housing and secured with a safety lock that switches the tool off, and stops the transport mechanism when the housing is opened.

9 Test Specimens9.1 Clean, dry Si surface.

10 Preparation of Apparatus10.1 The suitability of the equipment is determined by performing a statistically based MSA (Measurement System Analysis) to ascertain that the equipment is operating within the manufacture’s stated specification, e.g. according to SEMI E89.

10.2 Verify that the camera, illumination and wafer are aligned and adjusted according to the manufacturer’s specifications.

10.3 Determine the SPC control limits for the measurement equipment using a set of selected wafers.

6: As this test method is intended for a high throughput, high volume measurement the equipment cannot be calibrated for measuring each individual wafer. Therefore careful SPC has to be performed.





Date: 5/8/23

11 Calibration and Standardization11.1 Verify that the camera, illumination and wafer are aligned and adjusted according to the manufacturer’s specifications.

11.2 Calibrate the equipment using reference material with known dimensions.

11.3 Measure the reference material according to § 12 .

11.4 Compare the measured side lengths with the known dimensions of the reference material and determine correction factors cfx and cfy for the x- and y-axes, respectively.

12 Procedure 12.1 Adjust the equipment and calibrate it according to the supplier's instructions.

12.2 Verify the equipment is within SPC limits.

12.3 Measure the wafer.

12.3.1 Place a wafer on the transport mechanism so that its surface normal is tilted ≤ 3° with respect to the line of sight of the camera.

12.3.2 Align the wafer so that its leading edge is perpendicular to the transport direction.

12.3.3 Move the wafer through the measurement station.

12.3.4 Capture a raw image RI and process it according to § 13 .

12.3.5 Report the side lengths, diagonals, corner angles, chamfer lengths and chamfer radius, if applicable, according to § 15 .

12.4 Repeat with the next wafer.

13 Image Processing13.1 Assign a coordinate system to the image so that the x-axis is parallel to the wafer transport direction and the y-direction perpendicular to it. The origin of the coordinate system is at the lower left corner of the wafer (corner K1).

13.2 Process the raw wafer image RI according to the two main steps (see Figure 2):

13.3 Step 1: wafer edge detection

13.3.1 Exclude, for fitting, any segments of the wafer edge where intentional marks such as notches (see SEMI PV32) are applied.

13.3.2 Apply an appropriate filter to the raw image RI for detecting the wafer edges and define the x-y-coordinates representing the wafer edges by a sub-pixeling procedure. Report the type of filter used.

13.4 Step 2, line fitting (see Figures 3 and 5):

13.4.1 Fit a straight line to the x-y-coordinates representing the wafer edges excluding the chamfers resulting in four edge lines ai with i = 1 to 4.

1: If a higher order polynomial fit line is used report it.

13.4.2 The intersections of the edge lines of adjacent edges define four imaginary reference points, the corner points Ki(x,y) with i = 1 to 4.

13.4.3 For nominally square wafers, fit a first order polynomial to the x-y-coordinates in the chamfer regions, resulting in four chamfer fit lines hi with i = 1 to 4.

13.4.4 For nominally pseudo-square wafers, fit a second order polynomial to the x-y-coordinates in the chamfer regions, resulting in four chamfer fit lines hi with i = 1 to 4.

13.4.5 Identify four pairs of reference points, where the chamfer corner points Bi,j(x,y) – with i = 1 to 4 denoting the wafer corner and j = 1 to 4 denoting the wafer sides that are intersected by the chamfer line – by the intersections of the chamfer fit lines hi with the adjacent edge fit lines ai.





Date: 5/8/23

13.4.6 Draw straight diagonal lines g1,3 and g2,4 through opposite corners K1, K3 and K2, K4, respectively. The intersection of g1,3 and g2,4 defines the wafer center M.

13.4.7 Identify additional auxiliary reference points on each edge line Xj,k(x,y) with j denoting the edge line and k = 1, 2 or 3 as follows:

13.4.7.1 Xi,2 at the center between the adjacent corners

13.4.7.2 Xi,1 and Xi,3 at a distance V from the adjacent corners.

13.4.8 For square wafers only: Identify the intersections of g1,2 and g2,4 with hi by Bi,g with m = 1 to 4.

14 Calculations (see Figure 2)14.1 Multiply any x-coordinate with cfx and any y-coordinate with cfy.

7: The labeling of the lines, lengths and points follows SEMI PV22 where possible. Lines are labeled by lower case letters, lengths and points by capital letters.

14.2 For square and pseudo-square wafers (see Figures 4 and 6):

14.2.1 Calculate and report the four side lengths Ai of the wafer as the shortest distances between adjacent corners points Ki.

14.2.2 Calculate and report the four short side lengths Ci of the wafer as the shortest distance between adjacent chamfer corners points Bm,n.

14.2.3 Calculate and report the wafer widths Wp,q,r with p,q = 1,3 or 2,4 and r = 1, 2 or 3 as follows:

14.2.3.1 The widths W1,3,2 and W2,4,2 as the distances between X1,2 and X3,2 and between X2,2 and X4,2, respectively.

14.2.3.2 The widths W1,3,1 and W1,3,3 as the distances between X1,1 and X3,1 and between X1,3 and X3,3

14.2.3.3 The widths W2,4,1 and W2,4,3 as the distances between X2,1 and X4,1 and between X2,3 and X4,3.

14.2.4 Calculate the four corner angles i, i = 1 to 4, as the inner angles between adjacent fit lines at the four corners. Report the corner angles i.

14.2.5 Calculate for each pair of chamfer corner points the four chamfer lengths Hi as the shortest distances between adjacent chamfer corner points Bi,j. Report the chamfer lengths Hi.

8: The chamfer lengths are not the lengths of 2nd order polynomials between the corresponding intersections.

14.3 Calculate and report the cathetus lengths Fi,j as the distances between the wafer corners points Ki and the adjacent chamfer corner points Bi,j.

14.4 For square wafers only:

14.4.1 Calculate and report the diagonal lengths G1,3 and G2,4 as the shortest distances between

14.4.1.1 The corner points K1 and K3, and

14.4.1.2 The corner points K2 and K4.

14.4.2 Calculate and report the diagonal lengths E1,3 and E2,4 as the shortest distances between

14.4.2.1 The intersections of the chamfer lines h1 and h3 and the diagonal lines g1, and

14.4.2.2 The intersections of the chamfer lines h2 and h4 and the diagonal line g2.

14.4.3 Calculate and report the chamfer angles i,j (see Figure 7). They are determined either by the chamfer lengths Hi and the adjacent cathetus lengths Fi,j or by the corner angles i and the adjacent cathetus lengths Fi,j

according to the laws of planar trigonometry using

(1)

or any equivalent relation.




cos αi , j=(H

i2F

i , j2−F

i , j2)

2 H i F i , j


Date: 5/8/23

14.5 For pseudo-square wafers only:

14.5.1 Calculate and report the diameters D1,3 and D2,4 as the shortest distance between opposing rounded chamfers through the center of the wafer.

15 Report15.1 Report the following elements.15.1.1 General information

15.1.1.1 Date and time of test.

15.1.1.2 Identification of operator.

15.1.1.3 Identification number of measurement equipment.

15.1.1.4 Software revision.

15.1.1.5 Calibration and SPC status of measurement equipment.

15.1.1.6 Ambient temperature.

15.1.1.7 Lot identification

15.1.1.8 Each wafer’s ID.

15.1.2 Image processing parameters

15.1.2.1 The order of the polynomial used for fitting the wafer edges, if applicable

15.1.2.2 The type of filter for used for finding the wafer edges.

15.1.3 Dimensional parameters.

9: The order in which the results for the 4 wafer edges, corners and angles are reported may depend on the orientation of the wafer during measurement.

15.1.3.1 Four side lengths Ai.

15.1.3.2 Four short side lengths Ci.

15.1.3.3 Four chamfer lengths Hi

15.1.3.4 Eight cathetus lengths Fi,j.

15.1.3.5 Distance V.

15.1.3.6 Six wafer widths Xp,q,r.

15.1.3.7 Four corner angles 1, 2,3, 4.

15.1.3.8 Four chamfer angles ai.

15.1.3.9 For square wafers only

15.1.3.9.1 Two diagonal lengths G1,3 and G2,4.

15.1.3.10 Two short diagonal lengths E1,3 and E2,4 .For pseudo-square wafers only

15.1.3.10.1 Two diameters D1,3 and D2,4.

16 Precision and Bias16.1 The precision of the method has been determined experimentally by performing an MSA. Summary results regarding repeatability and reproducibility are reported in Tables 1 through 3. Details of the MSA are reported in Related Information 1.

16.2 Establishing bias requires certified reference materials which are currently unavailable.

16.3 Provisional reference materials may be qualified by using equipment capable measuring certified reference materials and as silicon wafers (SEMI MF1569).





Date: 5/8/23

16.4 In the absence of inter-laboratory test data to establish its reproducibility this test method should be used only after the parties to the test have established reproducibility and correlation satisfactory to each party involved.

16.5 For calculating the precision over tolerance ratios (P/T) the tolerances T as follows were used:

16.5.1 Side length, diagonal or diameter: T = 2000 µm, according to SEMI PV22.

10: In PV22 this tolerance is reported in millimeter units as 2 mm, not in micrometer units.

16.5.2 Chamfer length of square wafers: T = 1500 µm, according to SEMI PV22.

11: In PV22 this tolerance is reported in millimeter units as 1.5 mm, not in micrometer units.

16.5.3 Chamfer length of pseudo-square wafers: T = 4800 µm. This tolerance is not specified in PV22, it is derived from the tolerances in 16.5.1 by planimetry, see Related Information 3.

16.5.4 Cathetus length: T = 3400 µm or T = 1000 µm for pseudo-square or square wafers, respectively. These tolerances are not specified in PV22, they are derived from the tolerances in 16.5.1 by planimetry, see Related Information 3.

16.5.5 Angles: 1°. Again, this tolerance is not specified in PV22, it is assumed to be a reasonable choice.

16.6 Precision was defined as 6r with r as the total standard deviation, combined for repeatability and reproducibility.

16.7 r was pooled for single crystalline and multicrystalline wafers for side lengths and corner angles, but was determined separately for the remaining metrics.

Table 1 MSA Results for Side Lengths and Corner Angles

Crystal mono and multi

Metric r/µm P/T Metric r/deg P/TW241 7.8 3.1% 1 0.24 3.1%W133 7.3 2.7% 2 0.24 4.6%W243 9.0 4.0% 3 0.25 3.4%W131 9.5 4.5% 4 0.25 3.1%W132 7.3 2.6%W242 8.6 3.7%

Table 2 MSA results for Chamfer Lengths, Cathetus Lengths and Diameters/Diagonals

Crystal mono multi

Metric r/µm P/T r/µm P/T

H1 6.9 2.3% 6.9 3.1%H2 8.3 2.5% 8.3 4.6%H3 7.1 2.1% 7.1 3.4%H4 6.8 3.3% 6.8 3.1%F11 5.8 1.1% 5.8 3.3%F14 5.8 1.1% 5.8 3.3%F21 6.6 1.3% 6.6 4.3%F22 7.0 1.1% 7.0 4.9%F43 5.8 1.5% 5.8 3.3%F44 5.8 1.6% 5.8 3.3%





Date: 5/8/23

F33 6.0 0.9% 6.0 3.6%F32 6.0 1.0% 6.0 3.6%

D13/E13 9.7 4.7% 12.2 7.4%D24/E24 11.0 6.0% 10.3 5.3%

Table 3 MSA Results for Cathetus Angles

Crystal mono multi

Metric r/deg P/T r/deg P/T 0.20 4.2% 0.21 4.3% 0.20 3.8% 0.21 4.5% 0.23 5.3% 0.22 4.9% 0.22 4.7% 0.21 4.5% 0.22 4.7% 0.21 4.3% 0.22 5.1% 0.19 3.6% 0.24 5.8% 0.19 3.7% 0.23 5.1% 0.20 3.9%





Date: 5/8/23

NOTE: The light gray dashed lines depict the field of view of the camera. The set-up of light sources is only an example, other set-ups may be used.

Figure 1Schematic drawing of set-up for measuring geometry of PV Si wafers.

Figure 2Flow Diagram Illustrating the Sequence of Image Processing and Calculating Steps



surface normal and line of sight of camera

digital camera

wafer transport direction, x-direction

wafer

transport belts

diffuse white light source with shield

diffuse white light source with shield

leading edge of wafer

trailing edge of wafer

detect wafer edges

fit lines to the wafer

edges

identify the reference

points

calculate the side lengths

Ai

calculate the short side lengths Ci

calculate the wafer

widths Wp,q,r

calculate the corner

angles i

calculate the chamfer

lengths Hi

calculate the cathetus

lengths Fi,j

calculate the diagonal

lengths Gi,j

calculate the short

diagonal lengths Ei,j

calculate the chamfer angles i

calculate the diameters

Di,j

wafer shape

pseudo-squaresquare

Image processing Calculations



Date: 5/8/23

NOTE: The full circles depict the corner points, the full squares indicate the chamfer and other edge points. The full hexagon depicts the wafer center. The black lines depict the fit lines. The undulations of the wafer edges are greatly exaggerated.

Figure 3 Schematic Drawing Depicting the Fit Lines and the Reference Points of a Square Wafer.



K1 K2

K3K4

B1,4

B1,1 B2,1

B2,3

B3,2

B3,3B4,3

B4,4

a4

a3

a2

a1

h4

h3

h2h1

g1,3g2,4

M

X1,1 X1,2 X1,3

X4,1

X4,2

X4,3

X2,1

X2,2

X2,3

X3,1 X3,2X3,3

V

V

V

V

VV

VV

B1,gB2,g

B3,gB4,g



Date: 5/8/23

NOTE: The reference points are the full circles, squares and the hexagon.Figure 4

Schematic Drawing of the Metrics and the Reference Points of a Square Wafer.



K1 K2

K3K4

B1,4

B1,1 B2,1

B2,3

B3,2

B3,3B4,3

B4,1

1

2

3

4

A4

A3

A2

A1

H4

H3

H2

H1

G1,3G2,4

W2,4,2

W1,3,2

F1,2

F1,4

F2,1

F2,3

F3,2

F3,3F4,3

F4,1

C2

W1,3,1

W1,3,3

W2,4,1

W2,4,3

V

V

V

V

C1

C3

C4

E2,4

E1,3

X2,2

X2,1

X2,3

X1,1 X1,2 X1,3

X4,1

X4,2

X4,3

X3,1 X3,2 X3,3



Date: 5/8/23

NOTE: The black lines depict the fit lines.Figure 5

Schematic Drawing Depicting the Fit Lines and the Reference Points of a Pseudo-Square Wafer



K1 K2

K3K4

B1,4

B1,1 B2,1

B2,3

B3,2

B3,3B4,3

B4,4

M

g1,3 g2,4

a1

a2

a3

a4

h2

h1

h3

h4

V

VV

V

V V

V V

X4,3

X4,2

X4,1

X1,1 X1,2 X1,3

X2,1

X2,2

X2,3

X3,1 X3,2 X3,3



Date: 5/8/23

NOTE: The reference points are the full circles, squares and the hexagon.Figure 6

Schematic Drawing of the Metrics and the Reference Points of a Pseudo-Square Wafer.

Figure 7 Schematic Drawing Outlining the Relations between Fi,j, Hi, i and i,j.



K1 K2

K3K4

B1,4

B1,1 B2,1

B2,3

B3,2

B3,3B4,3

B4,4

D1,3 D2,4

C1

C2C4

C3

A1

A2

A3

A4

F3,2

F3,3F4,3

F4,1

F2,2

F2,1F1,1

F1,4

V

V

VV

1 2

34

H1 H2

H3

H4

W2,4,1

W1,3,2

W2,4,3

W1,3,1

W2,4,2

W1,3,3

X4,1

X4,2

X4,3

X1,1 X1,2 X1,3

X2,1

X2,3

X2,3

X3,1 X3,2 X3,3

i i,j

Ki

Hi

Fi,j

Fi,k

aj

ak

wafer



Date: 5/8/23

RELATED INFORMATION 1MEASUREMENT SYSTEM ANALYSIS (MSA)NOTICE: This related information is not an official part of SEMI draft doc. 5434 and was derived from the global PV Materials Committee. This related information was approved for publication by full letter ballot on (date of approval).

R1-1 PurposeR1-1.1 The MSA was performed for establishing the capability of the test method for usage in large volume Si wafer manufacturing.R1-1.2 The measurements were performed on standard production equipment.

R1-2 Parameter SettingsR1-2.1 Parameter V was set to 1/4 of nominal side length.R1-2.2 The measured values are reported in micrometer units and degrees as provided by the measurement equipment used.

R1-3 Results of MSAR1-3.1.1 Test specimen –– 5 single crystalline and 5 multicrystalline Si wafers with nominal size of 156 mm × 156 mm.R1-3.1.2 Test conditions –– 2 times 5 repeats per day on 3 subsequent days on the same measurement equipment.R1-3.1.3 Results –– the result for all dimensional wafer parameters defined in this test method are reported in the following Tables R1-1 and R1-2. Selected individual measurement results for side length, diagonals, diameters and angles are displayed in the Figures R1-1 through R1-8.

Table R1-1 Summary of the MSA for Pseudo-square Single Crystalline Si wafers

Crystal mono

MetricWafer

Statistic1 2 3 4 5

Side Lengths W/µm

W242mean 156070.6 156059.6 156063.2 156088.6 156091.3

std.dev. 13.1 9.2 11.0 12.0 12.6

W241mean 156053.2 156077.5 156051.6 156092.8 156081.5

std.dev. 11.6 9.2 12.1 10.5 8.9

W243mean 156077.7 156065.4 156082.2 156084.7 156106.6

std.dev. 13.5 11.6 11.0 12.1 14.0

W132mean 156074.6 156040.1 156076.7 156067.3 156077.1

std.dev. 10.8 9.3 9.3 8.0 7.3

W131mean 156082.3 156087.3 156088.6 156076.9 156091.4

std.dev. 17.8 18.5 15.5 13.9 13.1

W133mean 156037.2 155995.1 156039.0 156033.2 156043.0

std.dev. 10.6 8.8 8.0 7.3 8.0

Corner Angles /deg

mean 89.98 89.95 89.98 90.00 89.99

std.dev. 0.01 0.01 0.01 0.01 0.01

mean 90.03 90.04 90.04 89.99 90.03

std.dev. 0.01 0.01 0.01 0.01 0.01 mean 89.99 89.99 89.98 89.97 89.98





Date: 5/8/23

std.dev. 0.01 0.01 0.01 0.01 0.01

mean 90.00 90.02 90.00 90.03 90.00

std.dev. 0.01 0.01 0.01 0.01 0.01

Chamfer Lengths H/µm

H1mean 15618.1 15729.8 15638.3 15656.0 15629.0

std.dev. 7.4 7.5 7.4 7.0 8.9

H2mean 15631.3 15613.8 15644.3 15706.3 15597.0

std.dev. 8.3 8.8 7.4 8.4 8.3

H4mean 15620.5 15632.8 15640.5 15620.5 15678.3

std.dev. 9.7 11.0 8.4 13.1 10.7

H3mean 15724.5 15622.7 15730.9 15614.1 15737.9

std.dev. 6.6 8.3 6.6 6.8 6.6

Cathetus Lengths

F/µm

F11mean 11044.7 11127.6 11062.0 11068.5 11050.6

std.dev. 5.3 6.1 5.4 5.7 6.9

F14mean 11040.1 11132.4 11055.5 11063.7 11052.1

std.dev. 6.0 6.5 5.6 5.6 6.7

F21mean 11049.6 11049.6 11061.3 11111.5 11031.4

std.dev. 6.6 6.5 5.1 6.2 6.0

F22mean 11041.8 11035.7 11051.5 11097.1 11022.6

std.dev. 6.8 7.2 5.4 6.2 5.6

F43mean 11047.3 11054.3 11065.3 11045.7 11087.7

std.dev. 6.9 8.3 6.6 10.7 8.9

F44mean 11037.8 11053.8 11053.8 11045.3 11080.6

std.dev. 7.6 8.3 6.7 10.4 8.8

F33mean 11120.6 11057.6 11128.4 11042.0 11135.1

std.dev. 4.7 6.5 5.0 5.0 5.1

F32mean 11107.8 11038.5 11113.6 11032.0 11117.6

std.dev. 5.2 6.6 5.0 5.8 5.1

Chamfer Angles 180-

/deg

mean 135.00 134.98 134.99 135.02 135.01

std.dev. 0.01 0.01 0.01 0.01 0.01

mean 135.02 134.97 135.01 134.98 135.00

std.dev. 0.01 0.00 0.01 0.01 0.00

mean 135.00 135.01 134.98 135.00 135.00

std.dev. 0.01 0.00 0.01 0.01 0.01

mean 135.00 134.96 134.98 135.00 134.98

std.dev. 0.01 0.01 0.01 0.00 0.01

mean 135.01 134.95 135.00 135.02 134.99

std.dev. 0.01 0.01 0.01 0.01 0.01

mean 135.05 135.02 135.04 135.03 135.02

std.dev. 0.01 0.01 0.01 0.01 0.01

mean 135.03 134.99 135.02 134.99 135.02

std.dev. 0.01 0.01 0.01 0.01 0.01

mean 135.05 135.03 135.04 135.04 135.04

std.dev. 0.01 0.01 0.01 0.01 0.01





Date: 5/8/23

Diameters D/µm

D13mean 205034.9 205059.6 205034.7 205044.9 205049.2

std.dev. 19.6 14.2 14.6 11.8 15.0

D24mean 205044.4 205057.3 205041.4 205073.2 205079.5

std.dev. 16.7 13.2 21.4 19.8 19.1

Table R1-2 Summary of the MSA of Square Multicrystalline Si Wafers

Crystal multi

MetricWafer

Statistic1 2 3 4 5

Side Lengths W/µm

W242mean 155714.6 156111.0 156046.4 156112.1 155919.7

std.dev. 13.3 10.8 12.1 9.9 10.3

W241mean 155723.3 156105.4 156060.3 156104.9 155997.9

std.dev. 9.9 8.3 8.7 7.7 8.7

W243mean 155732.6 156101.7 156052.8 156097.7 156010.4

std.dev. 15.4 10.5 13.7 11.4 10.6

W132mean 155498.5 156084.0 156015.5 156073.9 155888.8

std.dev. 7.7 6.7 9.5 7.1 6.2

W131mean 155535.2 156097.2 156055.0 156090.3 156002.1

std.dev. 14.4 7.5 9.3 8.6 7.2

W133mean 155473.7 156015.5 155991.8 156009.9 155912.2

std.dev. 7.3 8.2 11.0 8.2 6.3

Corner Angles deg

1mean 89.93 90.00 89.99 90.00 89.99

std.dev. 0.01 0.01 0.01 0.01 0.01

2mean 90.08 89.99 90.01 89.99 90.02

std.dev. 0.01 0.01 0.01 0.01 0.01

4mean 90.04 89.95 89.97 89.95 89.96

std.dev. 0.01 0.00 0.01 0.01 0.01

3mean 89.96 90.05 90.03 90.05 90.03

std.dev. 0.01 0.01 0.01 0.01 0.01

Chamfer Lengths H/µm

H1mean 1651.0 1055.1 1272.8 1080.7 1636.6

std.dev. 7.2 8.3 8.0 6.8 8.2

H2mean 1551.2 1212.5 1344.9 1193.4 1636.9

std.dev. 10.8 12.1 11.4 10.9 11.7

H4mean 1646.4 1152.0 1349.3 1163.8 1699.4

std.dev. 8.1 7.1 8.3 7.3 7.1

H3mean 1636.3 1026.6 1362.5 1022.1 1621.0

std.dev. 8.4 6.5 10.6 8.2 7.5Cathetus Lengths

F/µmF11

mean 1168.1 745.8 900.0 763.9 1160.1

std.dev. 5.1 5.9 5.7 4.8 5.8F14 mean 1169.4 745.6 900.1 763.8 1160.1





Date: 5/8/23

std.dev. 5.1 5.9 5.7 4.8 5.8

F21mean 1096.1 857.4 951.9 843.8 1160.5

std.dev. 7.6 8.5 8.1 7.7 8.4

F22mean 1097.0 856.6 950.7 843.2 1159.5

std.dev. 7.6 8.5 8.0 7.7 8.3

F43mean 1163.7 814.6 954.2 823.0 1204.8

std.dev. 5.8 5.0 5.9 5.2 5.1

F44mean 1164.3 814.2 954.7 822.7 1204.4

std.dev. 5.8 5.0 6.0 5.2 5.0

F33mean 1157.5 725.6 964.2 722.3 1149.2

std.dev. 6.0 4.7 7.6 5.8 5.3

F32mean 1157.7 724.7 963.2 721.6 1147.7

std.dev. 6.0 4.6 7.5 5.8 5.3

Chamfer Angles 180-

deg

mean 134.98 135.03 135.01 135.03 134.88

std.dev. 0.01 0.01 0.01 0.00 0.00

mean 135.05 135.00 134.95 135.01 134.87

std.dev. 0.01 0.00 0.01 0.01 0.01

mean 135.03 135.00 135.00 135.00 134.87

std.dev. 0.01 0.01 0.01 0.01 0.01

mean 134.99 135.03 134.97 135.04 134.87

std.dev. 0.01 0.01 0.01 0.01 0.01

mean 134.90 135.02 134.99 135.02 134.86

std.dev. 0.01 0.01 0.01 0.01 0.01

mean 134.99 135.04 135.01 135.03 134.90

std.dev. 0.01 0.01 0.01 0.01 0.00

mean 134.98 135.01 134.96 135.01 134.87

std.dev. 0.01 0.00 0.01 0.00 0.01

mean 134.96 135.08 135.00 135.08 134.93

std.dev. 0.01 0.00 0.01 0.01 0.01

Diagonal E/µm

E13mean 218559.8 219606.8 219352.9 219590.6 219080.6

std.dev. 23.2 16.6 23.4 22.3 25.4

E24mean 218380.8 219568.6 219361.9 219566.9 219072.3

std.dev. 24.6 15.6 15.5 13.9 8.8





Date: 5/8/23



NOTE: The upper row of the x-axis labels denote the repeat, the lower row denotes the day.

Figure R1-1 Individual Measurements of Width W241

155600

155700

155800

155900

156000

156100

156200

11

11

11

11

11

21

21

21

21

21

12

12

12

12

12

22

22

22

22

22

13

13

13

13

13

23

23

23

23

23

W241/

µm

Repeat/Day

mono1

mono2

mono3

mono4

mono5

multi1

multi2

multi3

multi4

multi5

200000

205000

210000

215000

220000

225000

11

11

11

11

11

21

21

21

21

21

12

12

12

12

12

22

22

22

22

22

13

13

13

13

13

23

23

23

23

23

D 13

or E

13/µ

m

Repeat/Day

mono1

mono2

mono3

mono4

mono5

multi1

multi2

multi3

multi4

multi5

NOTE: The upper row of the x-axis labels denote the repeat, the lower row denotes the day.Figure R1-2

Individual Measurements of Diameter D13 or Diagonal E13, respectively



Date: 5/8/23




Individual Measurements of Corner Angle 1

89.9

89.92

89.94

89.96

89.98

90

90.02

90.04

90.06

90.08

90.1

11

11

11

11

11

21

21

21

21

21

12

12

12

12

12

22

22

22

22

22

13

13

13

13

13

23

23

23

23

23

1/

deg

Repeat/Day

mono1

mono2

mono3

mono4

mono5

multi1

multi2

multi3

multi4

multi5

15500

15550

15600

15650

15700

15750

15800

11

11

11

11

11

21

21

21

21

21

12

12

12

12

12

22

22

22

22

22

13

13

13

13

13

23

23

23

23

23

H 1/µ

m

Repeat/Day

mono1

mono2

mono3

mono4

mono5


Individual Measurements of Chamfer Length H1 of Pseudo-Square Wafers



Date: 5/8/23



10960

10980

11000

11020

11040

11060

11080

11100

11120

11140

11160

11

11

11

11

11

21

21

21

21

21

12

12

12

12

12

22

22

22

22

22

13

13

13

13

13

23

23

23

23

23

F 11/

µm

Repeat/Day

mono1

mono2

mono3

mono4

mono5


Individual Measurements of Cathetus Length F11 of Pseudo-Square Wafers

0

200

400

600

800

1000

1200

1400

1600

1800

11

11

11

11

11

21

21

21

21

21

12

12

12

12

12

22

22

22

22

22

13

13

13

13

13

23

23

23

23

23

H 1/µ

m

Repeat/Day

multi1

multi2

multi3

multi4

multi5

NOTE: The upper row of the x-axis labels denote the repeat, the lower row denotes the day. Figure R1-6

Individual Measurements of Chamfer Length H1 of Square Wafers



Date: 5/8/23



0

200

400

600

800

1000

1200

1400

11

11

11

11

11

21

21

21

21

21

12

12

12

12

12

22

22

22

22

22

13

13

13

13

13

23

23

23

23

23

F 11/

µm

Repeat/Day

multi1

multi2

multi3

multi4

multi5

NOTE: The upper row of the x-axis labels denote the repeat, the lower row denotes the day. Figure R1-7

Individual Measurements of Cathetus Length F11 of Pseudo-Square Wafers

134.75

134.8

134.85

134.9

134.95

135

135.05

135.1

11

11

11

11

11

21

21

21

21

21

12

12

12

12

12

22

22

22

22

22

13

13

13

13

13

23

23

23

23

23

14/

deg

Repeat/Day

mono1

mono2

mono3

mono4

mono5

multi1

multi2

multi3

multi4

multi5


Individual Measurements of Chamfer Angle 14



Date: 5/8/23

RELATED INFORMATION 2DETERMINATION OF WAFER AREASNOTICE: This related information is not an official part of SEMI draft document 5434 and was derived from the global PV Materials Committee. This related information was approved for publication by full letter ballot on (date of approval).

R2-1 IntroductionR2-1.1 The main text of this test method defines metrics for measuring characteristic lengths and angles of PV silicon wafers.R2-1.2 For some specifications, e.g. the solar cell efficiency, it is necessary to know the wafer area.R2-1.3 Two ways for determining the wafer area are proposed in the following paragraphs.

R2-2 Pixel Based MethodR2-2.1 Count the pixels fully within the perimeter of the wafer as determined in § 13.3 .R2-2.2 Determine the fraction of the partial pixels that is within the perimeter.R2-2.3 Add the full pixels and fractions of the partial pixels and multiply the result by the scaling factors cfx and cfy

according to § 11.4 to obtain the wafer area.

R2-3 Trigonometric MethodR2-3.1 This method uses basic trigonometric relations for approximating the wafer area based on the measured lengths and angles.R2-3.2 Square wafers:R2-3.2.1 Consider the wafer split in two triangles (see Figure 3) and, e.g. one with the sides a1, a4 and g2,4 and the angle 1, and one with the sides a2, a3 and g2,4 and the angle 3.R2-3.2.2 Calculate the areas 1 and 2 of the two triangles as:

(R2-1)

(R2-2)

R2-3.2.3 Similarly calculate the areas of the missing triangles (see Figure 7) at the wafer corners as:

(R2-3)

with i = {1, 2, 3, 4} (the braces define a cyclic group of natural numbers).R2-3.2.4 Add 1 and 2 and subtract the four to obtain the wafer areaR2-3.3 Pseudo-square wafers (see Figure R2-1):R2-3.3.1 Calculate the area of an ellipse with short and long axes D1,3 and D2,4 as:

(R2-4)

R2-3.3.2 Approximate the areas of the four missing ellipse segments by circle segments I (i = 1, 2, 3, 4)

(R2-5)

with

(R2-6)




δ1=12

A1⋅A4⋅sin ω1

δ2=12

A2⋅A3⋅sin ω3

θi=12

Fi ,i−1⋅F i , i⋅sin ωi

ε=π⋅D1,3⋅D2,4

σ i=R2

2( 2π180

arcsin Y i−Y i )

R=12( D1,3+D2,4 )


Date: 5/8/23

and

(R2-7)

R2-3.3.3 Subtract the four i from to obtain the approximate wafer area.

NOTE: The light gray areas depict the circle segments that are cut off the round wafer. Figure R2-1

Schematic Drawing of a Pseudo-Square Wafer Outlining the Calculation of the Wafer Area.



C1

C2

C3

C4

D1,3

D2,4

wafer

1

2

3

4


Y i=C i√R2−

Ci2

4R2


Date: 5/8/23

RELATED INFORMATION 3 ESTIMATION OF TOLERANCES

NOTICE: This related information is not an official part of SEMI draft doc. 5434 and was derived from the global PV Materials Committee. This related information was approved for publication by full letter ballot on (date of approval).

R3-1 PurposeR3-1.1 SEMI PV22 specifies only a few tolerances in millimeter units for the wafer parameters used in this test method.R3-1.2 Therefore additional tolerances are estimated based on the specified tolerances in PV22 for being able to assess the capability of the test method for use in high volume wafer manufacturing.

R3-2 EstimationsR3-2.1 Cathetus length of pseudo-square wafers:R3-2.1.1 The cathetus length F is obtained by (see Fig. 6)

(R3-1)

assuming that the square and the circle in Fig. 5 are centered with respect to each other.

R3-2.1.2 The tolerance for F is then obtained as 3400 µm by putting the specified maximum and minimum values for A and D according to PV22 in R3-1.R3-2.2 Chamfer length of pseudo-square wafers (see Fig. 6):R3-2.2.1 The chamfer length H is obtained by

(R3-2)

R3-2.2.2 The tolerance for H is then obtained as 4800 µm by putting the specified maximum and minimum values for A and D according to PV22 in R3-2.R3-2.3 Cathetus length of square wafers:R3-2.3.1 The cathetus length F is obtained by (see Fig. 4) by

(R3-3)

R3-2.3.2 The tolerance for F is then obtained as 1000 µm by putting the specified maximum and minimum values for H according to PV22 in R3-3.

NOTICE: Semiconductor Equipment and Materials International (SEMI) makes no warranties or representations as to the suitability of the Standards and Safety Guidelines set forth herein for any particular application. The determination of the suitability of the Standard or Safety Guideline 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. Standards and Safety Guidelines are subject to change without notice.

By publication of this Standard or Safety Guideline, SEMI takes no position respecting the validity of any patent rights or copyrights asserted in connection with any items mentioned in this Standard or Safety Guideline. Users of this Standard or Safety Guideline 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.




F=A− D√2

H=A √2−D

F= H√2


Date: 5/8/23


