4. Two Applications in the Semiconductor Industry
4.1 Ramp Up Yield Using the TCP Method
As introduced in Chapter 1, semiconductor manufacturing has a very long process cycle including 150-400 process steps to complete the entire manufacturing process. After completing all process steps, each lot is inspected via WAT, WST and FT (final test) with approximately 100 test items for each inspection test. We analyze the “Srow” measurement for each lot which is one of the key test items in wafer sort testing. A larger value of the Srow measurement indicates a worse yield
performance. The considered the Srow data consist of 439 lots with the sample mean 5.98 and the sample standard deviation 1.85. For this Srow measurement, the engineers have found 52 suspected steps from 221 process steps by performing ANOVA for tool comparison for each process step. In particular, the 10th process step is one of the suspected steps. The box plots and the related statistics of the Srow measurements for various tools in the 10th step are shown in Figure 4.1 and Table 4.1, respectively. It clearly shows that two tools, SPU03 and SPU05, have relatively worse performance at this problematic step.
Table 4.1. The sample mean, sample standard deviation, and the counts for the Srow measurements for various tools in the 10th process step.
Tool Mean Std Count SPU03 9.05 1.85 14 SPU04 5.79 1.51 48 SPU05 7.17 1.27 96 SPU07 5.54 1.4 36 SPU14 5.83 1.7 93 SPU16 5.16 1.78 152
S P U 0 3 S P U 0 4 S P U 0 5 S P U 0 7 S P U 1 4 S P U 1 6 T o o l
1 5 9 1 3
data
Figure 4.1. Box plots of the Srow measurements for various tools in the 10th process step.
(a)
For this problem, according to the engineering knowledge, the acceptance tolerance of difference is set to be 1. We carry out the TCP method by running 5
independent chains with 50,000 iterations, including 5,000 burn-in iterations, and
monitor the convergence of RJMCMC samplers by examining v.s. , v.s.
, and v.s. , as described in Chapter 2.5. The convergences of the above three sets of comparisons can be visualized in Figures 4.2 (a)-(c).
^
Figure 4.3. Estimated posterior distribution of the partition (the partitions with probability less than 0.005 are not displayed).
Finally, we summarize the results based on the last 10,000 MCMC iterations and the posterior distribution for the tool partition is displayed in Figure 4.3 where the partitions with probability less than 0.005 are not shown. The best partition for the set of tools, {SPU16, SPU14, SPU07, SPU05, SPU04, SPU03}, with the highest posterior probability 0.2244 is {SPU16, SPU14, SPU07, SPU04}, {SPU05}, and {SPU03} (denoted as (111213) in Figure 4.3). This partition result is consistent with that obtained by the CART method [46] with cost-complexity=30 shown in Table 4.2
and Figure 4.4. Although two different approaches reach the same partition result, it is somehow difficult for engineers to understand and interpret the meaning of cost-complexity=30 in CART method. In contrast, the engineering tolerance control is much easy to set and interpret in the TCP method.
Table 4.2. The partitioning results using the CART method with different values of the cost complexity.
Partitioning result Cost-complexity (1,2,3,4,5,6) 0 (1,2,2,3,2,4) 5 (1,1,1,2,1,3) 30 (1,1,1,2,1,2) 45
|
SPU16
SPU07
SPU04 SPU14
SPU05 SPU03
Figure 4.4. Tree obtained by the CART method with cost complexity=30.
After further checking on this problematic step, the engineers find that there
are two different tool types: one type includes SPU03 and SPU05 and another type
includes SPU16, SPU14, SPU07, and SPU04. Because different tool types use
different process chemicals, the contaminated chemical is the main source of bad performance of SPU03 and SPU05. After eliminating the contaminated chemical, the performance of SPU03 and SPU05 becomes regular and the Srow measurements are as same as those for other tools. Accordingly, the overall sample mean for Srow among tools reduces from 5.98 to 5.4 and the sample variance reduces from 1.85 to 1.52 after the adjustment. It really enhances the product yield.
System automatically
verifies the difference among tools by T-test or Kruskal - Wallis test
No
System automatically
detects each process step every
day Engineers take related
actions to eliminate the phenomenon
System automatically passes the information to engineers
Is there more than 1 group?
System automatically partitions tool according to their performances and
engineers’ tolerance by TCP
Yes
Figure 4.5. Engineer daily trouble shooting flow by combining statistical tests and TCP method.
From this application, we suggest to integrate the TCP method with statistical tests into a statistical dashboard [4] to form an analysis flow, as shown in Figure 4.5.
After building automatic systems according to the analysis flow, systems could execute the analysis automatically at night for each item of each product to compare the tool performances according to the pre-defined tolerances. Then, at the beginning
of the daily work, the engineers could quickly detect the possible problematic tools for yield enhancement as demonstrated in Table 4.3. This will dramatically shorten the time for engineers to find out the root causes of yield variance and eliminate the problematic tools. This working flow for yield enhancement not only avoids the subjective engineering judgments in tool comparisons, but also links with a well management plan through an engineering discussion about the reasonable tolerances.
Based on the example, we have shown the TCP method can really help engineers enhance yield by automatically partitioning the tools according their performances.
Table 4.3. An illustration example for automatically detecting the performance difference among tools for each process step.
Step
P value of T or Kruskal Wallis Test
TCP Result (Group, Tool List; Mean) Step 10 0.000005 (1.SPU03; 9.05);(2.SPU05; 7.17);
(3.SPU04,SPU07,SPU14,SPU16; 5.58)
Step 15 0.0003 (1.TEC02; 8.32);(2.TEC01; 8.08);
Step 2 0.06 (1.ACE01,ACE02; 8.1);
Step 4 0.08 (1.PHO01,PHO0202, PHO03; 8.21);
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