System Prototype
The basic Runto Run Controller
The W2W control scheme:
The is either form AVM or Metrology tool
(or A) is typically chosen to be least square estimates of based on historical data.The control valuable is set to nullify the deviation from target.
CMP Example
is the actual removal amount measured from the metrology tool and is the actual post CMP thickness of run k. The specification of is 2800±150 Angstrom (Å) with 2800 being the target value denoted by Deifned be the one before CMP process, is the polish rate, is the polish time that we can control!
The material removal model for CMP can be divided into two parts, mechanical model and chemical model. The chemical action of slurry is responsible for continuosly softening the silicon oxide. The fresh silicon oxide or metal surface is then rapidly removed by mechanical part.
The is the nominal removal rate, which is empirically simulated by a polynomial curve fitting of parts usage count between PMs (denoted by PU varying from 1 to 600)
Process gain:
Simulation parameters:
Assumption:
is set to 300, and A is set to mean of (also 300)
is set to 700 and is 500
RI is simulated with 0.9 plus some variation, and assume controller can detect any value that is beyond UCL or LCL
yk from AVM is virtual times yz(actual metrodlogy data), where virtual is a normal distribution variable
is simulated as ARIMA(0 1 1)
Control not
yz is atual measurement value, and A is used internal by R2R
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-20-94514a95eb0b> in <module>()
13 from matplotlib.backends.backend_pdf import PdfPages
14 pp = PdfPages('foo1.pdf')
---> 15 pp.savefig(fig)
/usr/local/lib/python2.7/dist-packages/matplotlib/backends/backend_pdf.pyc in savefig(self, figure, **kwargs)
2434 figureManager = Gcf.get_active()
2435 else:
-> 2436 figureManager = Gcf.get_fig_manager(figure)
2437 if figureManager is None:
2438 raise ValueError("No such figure: " + repr(figure))
/usr/local/lib/python2.7/dist-packages/matplotlib/_pylab_helpers.pyc in get_fig_manager(num)
42 figure and return the manager; otherwise return *None*.
43 """
---> 44 manager = Gcf.figs.get(num, None)
45 if manager is not None:
46 Gcf.set_active(manager)
TypeError: unhashable type: 'list'
Round 1
First two rounds, we use actual metrodlogy value
Round2
CASE1 R2R with in-situ metrology
set to 0.35, and all actual metrology data are available
CpK(Process Capability)
Mean-absolute-percentage error (MAPEp)
CASE2 R2R+VM without RI
, apply to following wafers