IEOR 130 Methods of Manufacturing Improvement Fall, 2013 Prof ...

After a single exposure is completed, the X-Y stage moves the wafer over for the
exposure of the next field. The fixed time for the mechanical apparatus to move the wafer
and re-align the camera is called the move time (MT). There is no MT before exposing
the first die; all initial motion of the wafer on the X-Y stage is included in AT.
For the die types produced in this factory, there are no "test keys" printed on the wafers.
The entire wafer surface is printed with product dice.
After exposures of all wafers in the cassette are completed, the cassette can be removed
from the machine and the exposed wafers are then sent through a development process.
(Similar to the way the machine can hold two cassettes of inbound wafers, there is room
in the machine for two outbound cassettes. A full outbound cassette can be removed from
the machine while it continues to process wafers into the other cassette.) After
developing, the wafers are inspected under a microscope. If for some reason the exposure
was mis-aligned with earlier mask layers, the current layer can be stripped off in an acid
bath, and the wafers sent back through the stepper for a second try. This repetition is
known as rework. Let RW denote the fraction of total wafer operations performed on the
5X stepper that are rework.
The operational procedures followed in the factory sometimes result in the machine being
completely flushed out of wafers and falling idle. For quality control purposes, the
machine might be deliberately stopped after processing one wafer and held idle while
waiting for the results of the after-develop inspection. When the machine is to be used
again after becoming idle, the machine is inactive while the operator puts in a new reticle,
puts in a new cassette, enters the appropriate recipe, and starts the machine. It then takes
the machine some time to bring the first wafer from the inbound cassette to the X-Y stage
in order to start the basic processing cycle described above. The sum of all these delay
times is called a setup time (ST). Let WPS denote the average number of wafers
processed between setups.
The industrial engineer for the fab has collected the following data about a particular 5X
stepper in the factory:
Parameter Theoretical Average
LI 770 mW/sq cm 720 mW/sq cm
MT 0.46 sec 0.47 sec
AT 27.0 sec 29.0 sec
XT 12.0 sec 12.0 sec
ST
150 sec
(a) Provide a formula for the theoretical processing time (seconds per wafer) as a function
of the number of exposures per wafer (NE), the exposure energy (EE), and the numerical
parameters above.
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