Neuro-fuzzy Approach - Computational Intelligence in Time Series Forecasting - page 261

because of several distinct advantages of rapid thermal processing (RTP) over
other batch processing, such as significant reduction in thermal budget and better
control over the processing environment, rapid thermal processing has been
extensively used in high-density integrated circuit manufacturing on single wafers.
Wafer temperature measurement and control are two critical issues here.
Currently, a single-wavelength pyrometer is used as a non-contact temperature
sensor. However, for applications where the characteristics of the surface change
with the time, the wafer emissivity also varies simultaneously. This can lead to
temperature errors in excess of 50 degree Celsius in a few seconds. Various
methods were suggested to overcome this problem, such as use of a dual-
wavelength pyrometer, model-based emissivity correction, etc . A global
mathematical model for the rapid thermal process, which includes the temperature
sensor along with a control loop and lamp system, was developed and simulated by
Lai and Lin (1999). In the same model, emissivity changes during oxidation are
calculated according to reflections, refraction within thin dielectric films on a
silicon substrate. The oxide thickness as a function of oxidation time at various
temperatures, is simulated by a linear parabolic model. Using the basic heat
transfer law, a pyrometer model to simulate the temperature sensor in the rapid
thermal process is derived and, thereafter, a neural-fuzzy network is used to learn
and predict the variations of oxidation growth rate of the film under different
process temperatures. Based on this neural-fuzzy prediction and an already
available optical model the emissivity of the wafer can be correctly computed.

T s ( k +1)

T w ( k +1)

P ( k +1)

NF
controller

RTP plant

EmissCh w ( k +1)

T p ( k +1)

Z -1

Converter Pyrometer

T c ( k +1)

EmissCh ´ w ( k +1)

T p = pyrometer measurement temperature
T c = corrected temperature, T s = desired temp.
T w = wafer actual temperature, EmissCh ´ w ( k ) =
predicted wafer emissivity change

T c ( k )

NF
predictor

Figure 6.10. Block diagram of the neural-fuzzy method to predict wafer emissivity variation
and to correct the pyrometer readings

Another neural-fuzzy network was used by Lai and Lin (1999) to control the
temperature of an RTP system by using the inverse model of the RTP system to
achieve two control objectives: trajectory following and temperature uniformity on
the wafer. Figure 6.10 shows the block diagram of the neural-fuzzy method to
predict wafer emissivity variation and to correct the pyrometer readings. The
previous corrected temperature value T c ( k ) and the current processing time k are
used as the inputs of the neural-fuzzy network to predict the current film thickness,
which is further used to compute the emissivity of the wafer ew´ ( k +1) according to