$1.(25$ points$)$ A process development team has almost completed development of a new

fabrication process flow, but it is having trouble achieving a stable process meeting specification

limits for the critical dimension $($CD$)$ at an etching step. The team has set up statistical process

control based on sampling five positions on a wafer; the current control limits are LCL $=320$

angstroms and UCL $=396$ angstroms.

The product to be produced in the process needs to meet specification limits for the etch CD

whereby LSL $=320$ angstroms and USL $=375$ angstroms. Company management faces two

choices: The development team could continue to work on the problem until the etch CD yield

limiter is better mitigated, or the process could be transferred into manufacturing as is$,$ with the

manufacturing team taking over responsibility for mitigating the etch CD problem.

At present, the overall yield, accounting for both line yield and die yield, is $6\%.$ If transferred as

is$,$ it is estimated that ramp time to a mature yield of $90\%$ will be $180$ days. If the development

team continues to work on the problem, it is estimated that it will take them $30$ days to raise Cp

for the etch step to $0\mathrm{.}5$ and raise Cpk for the etch step to $0\mathrm{.}35,$ at which time the process would be

transferred to manufacturing. It is estimated that, in that case, the ramp time after transfer to a

mature yield of $90\%$ will be only $135$ days.

It is estimated that the revenue per $100\%-$yielding wafer is declining $75\%$ per year and product

lifetime is two years if transfer from development to manufacturing is immediate; if transfer is

delayed by $30$ days, lifetime is reduced by $30$ days. Assume production volume will be constant

over the remaining lifetime of the product after transfer. It is estimated that the yield learning

rate in manufacturing after transfer is such that two$-$thirds of the yield improvement towards

mature yield will be achieved halfway through the ramp time. This learning rate applies

regardless of the initial yield at time of transfer.

$($a$)$ Let$$s define CD$-$limited yield of the etch step as the fraction of wafers meeting the

upper and lower specification limits for the CD$.$ Estimate the current CD$-$limited yield of the etch

step.

$($b$)$ What are the current values of Cp and Cpk for the etch step?

$($c$)$ If the development team continues to work on the etch CD problem to raise Cp for

the etch step to $0\mathrm{.}5$ and raise Cpk for the etch step to $0\mathrm{.}35$ but makes no other changes to the

process, estimate the overall yield when that work is done. You may assume the etch CD

mechanism is independent of other yield loss mechanisms.

$($d$)$ Which choice should management make? Explain.