A contribution to optimal lamp design in rapid thermal processing
Cho, Y.M.
Paulraj, A.
Kailath, T.
Guanghan Xu
Inf. Syst. Lab., Stanford Univ., CA;
This paper appears in: Semiconductor Manufacturing, IEEE Transactions on
Publication Date: Feb 1994
Volume: 7,
Issue: 1
On page(s): 34-41
ISSN: 0894-6507
References Cited: 25
CODEN: ITSMED
INSPEC Accession Number: 4704281
Digital Object Identifier: 10.1109/66.286831
Current Version Published: 2002-08-06
Abstract
Recent studies of wafer temperature control in rapid thermal
processing systems have indicated that a multiring circularly symmetric
lamp configuration with independent (multivariable) control of the power
applied to each ring is likely to be more successful than the earlier
lamp design approaches. An important issue in such multiring lamp
systems is the optimal shaping of the output heat flux profile (HFP) of
each ring to provide maximum controllability of the wafer temperature.
In this paper we seek to optimize the ring HFP's via the lamp design
parameters: ring positions and widths. We start by determining the heat
loss profiles over the wafer surface for a variety of temperature
setpoints and processing conditions. In order to maintain temperature
uniformity across the wafer at a given setpoint, the lamp system should
provide a compensating HFP. The total lamp HFP is the sum of the
individual ring HFPs weighted by their respective applied powers. The
HFP's are, in turn, functionally dependent on the lamp design parameters
and this dependence can be measured through a calibration process.
Therefore, the resulting optimization problem reduces to determining the
lamp design parameters that result in lamp HFP's which best approximates
the collection of the wafer heat loss profiles. Our method provides a
practical technique for determining the optimal lamp design parameters
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