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Math in the Workplace: Overview

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Math in the Work Place

Math in the Workplace - Algebra

MICRON TECHNOLOGY, INC.,

Semiconductor Manufacturing
Engineer - Yield

 
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.
   


Problem:

Following the fabrication process of memory chips, wafers are tested for functionality. Wafers are tested with voltage that stresses performance causing those devices that do not meet specifications to fail. "Yield" refers to the number or percentage of acceptable units produced on each wafer compared to the maximum possible

Yield vs. Parameter

Use graph paper to create an x-y graph of yields vs. electrical parameters measured in volts.

Parameter Yield
5v 50%
10v 60%
15v 70%

 

a. How does the parameter relate to the yield? (Positive vs. negative correlation)

 

b. Where do we want the parameter to be for the highest yield?

 

c. What’s the equation of the line?

Y = mx+b

yield graph

 

 

Old Data          New Data
Parameter Yield Parameter Yield
5v 50% 20v 80%
10v 60% 30v 30%
15v 70% 40v 20%

 

d. We did more tests, raising the voltage for the parameter. Plot both the old and new data. Now, where does the graph say to set the volts?

yield graph

 

solution 


 

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Solution:

Use graph paper to create an x-y graph of yields vs. electrical parameters measured in volts.

Parameter Yield
5v 50%
10v 60%
15v 70%

a. How does the parameter relate to the yield? (Positive vs. negative correlation)

Positive correlation - As voltage increases, the yield percentage increases

b. Where do we want the parameter to be for the highest yield?

15v would be the parameter that produces the highest yield.

c. What is the equation of the line?

Y = mx + b

50 = mx 5+b

60 = mx 10+b

m=2, b=40

Y=2x+40

 

Solution chart

Old Data New Data
Parameter Yield Parameter Yield
5v 50% 20v 80%
10v 60% 30v 30%
15v 70% 40v 20%

 

d. We did more tests, raising the voltage for the parameter. Plot both the old and new data. Now, where does the graph say to set the volts?

Based on the new data, set the volts at 20

yield graph