Math in the Workplace - Numbers & Operations / Analysis & Probability
MICRON TECHNOLOGY, INC.
Semiconductor Manufacturing Engineer
- Yield
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Job Description: Develop
wafer level test strategies and test programs. Provide failure
analysis reporting. Monitor device yields, failure rates,
and repair rates. Interact with various engineering and product
groups to optimize device yields and minimize costs. |
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Problem:
Following the fabrication process of memory chips, wafers are tested
for functionality. "Yield" refers to the number or percentage of
acceptable units produced on each wafer compared to the maximum
possible.
Backend yields examples:
| Test1 => 95% |
Test2 => 90% |
Test3 => 98% |
Test4 => 99% |
| In |
Out |
In |
Out |
In |
Out |
In |
Out |
| 1000 |
950 |
950 |
855 |
855 |
838 |
838 |
830 |
| 1500 |
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| 1750 |
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| 2150 |
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| 500 |
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1. Given the number of parts sent into
the first test and the yield of this test, calculate the number
of parts out of test one. (Round to the nearest whole part.)
2. Calculate the number of parts out after the
2nd, 3rd and last tests.
3. What is the % yield of all 4 tests together?
4. How many parts do I need to send into the 1st
test to get 1000 after the last test?
| |
Test 1 |
Test 2 |
Test 3 |
Test 4 |
| Process |
In |
Out |
Yield |
In |
Out |
Yield |
In |
Out |
Yield |
In |
Out |
Yield |
| A |
500 |
415 |
|
415 |
403 |
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403 |
395 |
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395 |
392 |
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| B |
450 |
385 |
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385 |
312 |
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312 |
309 |
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309 |
306 |
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5. Calculate the yield for each test. Compare
the yields of process A with those of process B.
Which is better? Which test saw the biggest difference?
MICRON TECHNOLOGY, INC.
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Solution:
Backend yields examples:
1. Given the number of parts sent into the first
test and the yield of this test, calculate the number of parts out
of test one. (Round to the nearest whole part.)
| Test1 => 95% |
| In |
Out |
| 1000 • .95 |
950 |
| 1500 • .95 |
1425 |
| 1750 • .95 |
1663 |
| 2150 • .95 |
2043 |
| 500 • .95 |
475 |
2. Calculate the number of parts out after the
2nd, 3rd and last tests.
| Test1 => 95% |
Test2 => 90% |
Test3 => 98% |
Test4 => 99% |
| In |
Out |
In |
Out |
In |
Out |
In |
Out |
| 1000 |
950 -> |
950 • .9 |
855 -> |
855 • .98 |
838 -> |
838 • .99 |
830 |
| 1500 |
1425 -> |
1425 • .9 |
1283 -> |
1283 • .98 |
1227-> |
1257 • .99 |
1244 |
| 1750 |
1663 -> |
1663 • .9 |
1497 -> |
1497 • .98 |
1467-> |
1467 • .99 |
1452 |
| 2150 |
2043 -> |
2043 • .9 |
1839 -> |
1839 • .98 |
1802-> |
1802 • .99 |
1784 |
| 500 |
475 -> |
475 • .9 |
428 -> |
428 • .98 |
419-> |
419 • .99 |
415 |
3. What is the % yield of all 4 tests together?
.95 x .90 x .98 x .99 = .8295 = 82.95%
4. How many parts do I need to send into the 1st
test to get 1000 after the last test?
1000 parts 
82.95%
= 1206 parts
5. Calculate the yield for each test.
Out In
= %Yield
| |
Test 1 |
Test 2 |
Test 3 |
Test 4 |
| Process |
In |
Out |
Yield |
In |
Out |
Yield |
In |
Out |
Yield |
In |
Out |
Yield |
| A |
500 |
415 |
83% |
415 |
403 |
97% |
403 |
395 |
98% |
395 |
392 |
99% |
| B |
450 |
385 |
86% |
385 |
312 |
81% |
312 |
309 |
99% |
309 |
306 |
99% |
Compare the yields of process A with those of process B.
Which is better? Process A:
| Process A: = |
Out (Test4)
In (Test1)
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= |
392
500 |
= 78.4% |
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| Process B: = |
Out (Test4)
In (Test1) |
= |
306
450 |
= 68% |
Which test saw the biggest difference?
Test 2: from 97% to 81%