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19.5.2.1 First-Pass Yield. The first-pass yield equation derives from the Wiebel probability failure equations.11 Equation 19.12 is of a more general form of the equation typically used to predict ASIC yields by defect density. FPY% = 100 Exp[(log CI/A)^B] (19.12)
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FPY= first-pass yield CI = complexity index A,B = constants
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To determine the constants A and B in Eq. 19.12, a fabricator will need to characterize their manufacturing process. Selecting a number of printed circuits currently being produced that have various complexity indexes does this, ideally some low, medium, and high. The first-pass yield (at electrical test without repair) of these printed circuits for several production runs is recorded. Any statistical software program12 that has a model-based regression analysis can now determine A and B from the model (Eq. 19.13). FPY = f[ ] = 100 EXP{LOG(complexity PARM[1])^PARM[2]} where PARM[1] = A PARM[2] = B (19.13)
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The first-pass yield will follow the examples in Fig. 19.14. Constant A determines the slope of the inflection of the yield curve, whereas constant B determines the x-axis point of the inflection.
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20 DEFECT MODEL: Yield=100/EXP[LOG(COMPLEXITY/A)^B] 0 1E4
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1E10
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1E14
1E16
COMPLEXITY
A=12.5, B=7 A=11.5, B=7
INDEX
A=11.5, B=9 A=11.5, B=5
A=10.5, B=7
FIGURE 19.14 Estimated first-pass yield as a function of PWB design complexity.
Alternatively, any spreadsheet can be used to determine constants A and B. The [REGR] function in a spreadsheet like ExcelTM or Lotus 1-2-3TM is used. The [REGR] function is defined as: (=LINEST(known_y s,known_x s,TRUE,TRUE). To use this function, you must first put the FPY function into the form y = Ax + B. This is done by creating two columns: complexity index (which we will call X1) and yield. A third column is created for {log[log(X1)]}, whereas a fourth column is created for {log[ln(-yield/100)]}. Provide the regression function with column 4 as known_ys and column 3 as known_xs. The regression function will return 10 values; FIT (slope & int.), sig-M (slope & int.), r2, sig-B(slope & int.), F,df (slope & int.), and reg sum sq (slope & int.). The constant B is equal to the FIT (slope) and the constant A is 10^[ FIT(int.)/FIT(slope)]. (Remember, to calculate an array, follow these steps: highlight the array on the spreadsheet; type the array formula, making sure that the cursor is in the edit bar; then press CTRL + SHIFT + ENTER.) 19.5.2.2 Yield Calculation Steps. six steps: To calculate the first-pass yield coefficients, there are
1. Collect design attributes of 10 to 15 currently running boards with various size and layers (see Table 19.4). 2. Collect the first-pass yield information for these selected boards, at least 10 runs (see Table 19.5).
PRINTED CIRCUITS HANDBOOK
TABLE 19.4 Example of PCB Part Information and Calculated Complexity Index PCS SIZE Length Width (in.) (in.) 11.500 11.500 6.050 5.210 6.050 7.240 11.460 9.600 11.790 12.780 6.050 5.380 1.250 9.210 8.900 1.090 4.330 1.410 11.460 6.510 10.370 9.490 4.200 1.455 5.670 2.660 Min. Trace width (mil.) 6 5 6 6 6 5 6 5 5 6 6 7 7 Min. Annular ring (mil.) 4 5 5 5 5 5 5 5 5 5 5 5 8 Min. Hole size (mil.) 12 8 12 10 14 14 8 13 12 10 14 18 14
P/N #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13
Hole quantity 4842 3217 379 1538 868 5274 6015 4970 6034 4038 554 1118 220
Hole density 45.7 31.4 57.5 68.2 101.8 63.6 80.6 49.9 53.9 75.2 62.9 36.7 66.2
Layers 6 8 4 6 6 8 8 12 10 12 6 4 4
Thickness (mil.) 82.7 62.0 46.2 72.4 50.0 61.9 61.9 47.0 62.0 62.0 50.0 55.1 32.0
Aspect ratio 6.89 7.75 3.85 7.24 3.57 4.42 7.74 3.62 5.17 6.20 3.57 3.06 2.29
Complexity x1 1.14E+06 2.01E+06 1.49E+04 5.46E+05 1.62E+05 2.17E+06 8.00E+06 4.77E+06 5.60E+06 1.08E+07 6.40E+04 1.27E+04 2.72E+03
3. 4. 5. 6.
Calculate the board complexity index and average yield. Prepare a spreadsheet of transformed CI (x1) and Yield (Y) (see Table19.6) Calculate regression coefficients (see Table 19.7). Calculate A and B from regression fits.
19.5.2.3 PCB Part Information. Collect design attributes of 10 to 15 currently running boards with various size and layers (see Table 19.3). 19.5.2.4 PCB Production Yield Data. Collect the first-pass yield information for these selected boards, for at least 10 runs (see Table 19.5)
TABLE 19.5 Example of PCB Production Yields from 10 Runs P/N Run #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 First pass yield (at Electrical test) 1 92.6 85.6 95.6 92.3 94.8 86.8 90.3 89.3 87.2 86.6 92.7 93.8 99.2 2 84.9 85.7 93.9 93.3 97.6 85.3 80.9 87.0 87.9 88.1 92.7 95.3 98.6 3 86.9 94.2 93.6 95.0 96.4 88.1 86.3 86.6 86.6 82.6 97.2 98.2 99.1 4 82.9 86.2 97.8 92.6 96.6 90.8 87.9 83.5 85.7 84.4 95.1 96.3 98.7 5 90.0 86.6 97.3 94.5 94.1 86.5 87.1 91.6 89.4 88.0 96.9 94.1 97.9 6 95.2 86.7 95.1 95.5 93.2 87.0 92.7 90.1 87.3 87.0 94.3 95.9 99.6 7 90.1 86.6 94.2 93.5 94.3 88.0 87.3 87.5 90.6 79.0 93.4 94.2 99.6 8 92.4 89.7 96.2 89.7 93.2 87.2 87.6 86.2 86.5 87.0 95.3 92.3 99.1 9 93.0 95.6 96.9 88.8 91.8 86.5 82.4 88.1 85.9 88.0 91.6 94.8 99.0 10 92.0 85.6 91.6 89.8 91.2 88.9 88.9 87.3 82.9 80.0 96.6 95.6 99.3
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