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SEMI MF1527-1104 © SEMI 2003, 2004 13 A 3 = constant given in Table R1-1 for values of m from 6 to 10. R1-2.6 Determ ine the upper and lower cont rol limit s for the s control chart from the following equations: 11 s B L…

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SEMI MF1527-1104 © SEMI 2003, 2004 12
RELATED INFORMATION 1
PROCEDURES FOR DETERMINING THE PRESENCE OF OUT-OF-
CONTROL CONDITIONS AND THE NEED FOR CORRECTIVE ACTION
NOTICE: This related information is not an official part of SEMI MF1527. It was derived from
information developed during the original preparation of the standard in ASTM Committee F-1 in 1994.
This related information was approved for publication by full letter ballot procedures.
R1-1 Types of Control Charts
R1-1.1 Three types of control charts are employed for
various purposes in connection with the use of
resistivity reference wafers.
R1-1.2 Two
X
and s charts are used for the control of
primary resistivity measuring instruments. One of these
is the usual type of chart for which the control limits are
established from measurements made with the
instrument (see Section 7.1.1). The second, intended to
ensure traceability, differs from the usual control chart
in that it has limits that are based not on the
measurements themselves but instead on the
characteristics of the CRMs used for the measurements
(see Section 7.1.2). These two types of control charts
are of the types intended to provide control with no
standard given and control with respect to a given
standard, respectively.
10
R1-1.3 The third type of chart is one based on
individual measurements and the moving range, which
is the difference between one measurement and the
next. The control limits for this chart are based on the
measurements. This type of chart is used for control of
instruments for routine resistivity measurements (see
Section 10.2).
R1-2 Control Charts for Primary Resistivity
Measuring Instruments
R1-2.1 Since there is no standard given for these
charts, the limits are based on the initial series of
resistivity determinations. First, select an appropriate
number of measurements (six to ten) for the resistivity
determination, and make the same number of
measurements for each determination. Begin
construction of the instrument
X
and s charts by
making 25 to 30 center-point resistivity determinations
in accordance with the procedure of Section 7.1.1 on
one or more resistivity reference wafers covering the
resistivity range of the specimens to be measured. If no
other acceptable material is available, CRMs or other
commercially obtained calibrated wafers can be
employed until suitable reference wafers have been
10 Manual on Presentation of Data and Control Chart Analysis:
MNL 7, 6th Edition, (ASTM, West Conshohocken, PA, (1991) §3-3.
prepared. Measurements should be taken regularly,
every day or every shift, as appropriate. If variations
between operators are suspected, separate control charts
should be maintained by different operators.
R1-2.2 Record the date, time, sample identification,
operator, number of separate resistivity measurements
(six to ten), m; each resistivity value obtained, X
ij
; the
average of each group of m measurements,
;
i
X and the
sample standard deviation of each group, s
i
.
NOTE 1: The average and standard deviation of each group
of measurements are obtained as follows:


m
j
m
j
iijiiji
XX
m
sX
m
X
11
2
)(
1
1
and
1
R1-2.3 Construct
X
and s run charts of these data for
each wafer measured by plotting on separate graphs the
values of
X
and s in the order in which they were
obtained as shown in Figure R1-1.
R1-2.4
Calculate the grand averages,
X
and s of the
i
X and s
i
values, respectively, as follows:
n
i
i
n
i
i
s
n
sX
n
X
11
1
and
1
(R1-1)
where:
n = number of measurements (25 to 30, see Section
R1-2.1).
Take these grand averages as the central lines of the
X
and s control charts, respectively.
R1-2.5 Determine the upper and lower control limits
for the
X
control chart from the following equations:
11
sAXLCLsAXUCL
33
and (R1-2)
where:
UCL = upper control limit,
LCL = lower control limit, and
11 Manual on Presentation of Data and Control Chart Analysis:
MNL 7, 6th Edition, (ASTM, West Conshohocken, PA, (1991) §3-9,
Tables 5 and Tables 6.
SEMI MF1527-1104 © SEMI 2003, 2004 13
A
3
= constant given in Table R1-1 for values of m
from 6 to 10.
R1-2.6 Determine the upper and lower control limits
for the s control chart from the following equations:
11
sBLCLandsBUCL
34
(R1-3)
where:
UCL = upper control limit,
LCL = lower control limit, and
B
3
and B
4
= constants given in Table R1-1 for values
of m from 6 to 10.
R1-2.7 Divide the region between the central line and
the upper control limit (UCL) into thirds. Divide the
region between the central line and the lower control
limit (LCL) in thirds. Label the zones from the UCL as
A, B, C, C, B, A (see Figure R1-2).
R1-2.8
Using these control limits, continue to collect
data on the reference wafers periodically in accordance
with the procedures of Section R1-2.1, recording the
information specified in Section R1-2.2.
Table R1-1 Patterns that Indicate Possible Out-of-
control Conditions in Control Charts Constructed
with No Prior Information
Pattern Indication
1 Single point outside of control limits
2 Two out of three successive points in Zone A
3 Four out of five successive points in Zones A or B
4 Eight successive points on one side of centerline
R1-2.9 Observe the
X
and s control charts for out-of-
control conditions as listed in Table R1-2. If out-of-
control conditions are noted, annotate the chart to
highlight the out-of-control condition and take
corrective action as follows:
R1-2.9.1
Verify that the out-of-control indication is
due to the instrument and not the reference wafer by
checking other similar reference wafers (see Section
7.1.1).
Table R1-2 Factors for Computing Control Limits of Instrument Control Charts
Factors for Charts Constructed with No Prior Information
Factor for CRM
X
Chart
m (Number of
Measurements)
A
3
B
3
B
4
A
6 1.287 0.030 1.970 1.225
7 1.182 0.118 1.882 1.134
8 1.099 0.185 1.815 1.061
9 1.032 0.239 1.761 1.000
10 0.975 0.284 1.716 0.9492
Figure R1-1
Example of Instrument
X
and s Run Charts for a Resistivity Reference Wafer with Nominal Resistivity of
1.2
·cm; 6 Measurements per Determination
SEMI MF1527-1104 © SEMI 2003, 2004 14
NOTE: Central line, control limits, and zones are based on the data in the run charts of Figure R1-1.
Figure R1-2
Example of Instrument
X
and s Control Charts for a Resistivity Reference Wafer with Nominal Resistivity
of 1.2
·cm; 6 Measurements per Determination
R1-2.9.2 If the reference wafer appears to be at fault,
resurface it and begin the process using it as a fresh
control wafer.
R1-2.9.3 If instrument is at fault, check the probe
assembly and electrical equipment in accordance with
7.1.3, and repair or replace as needed.
R1-2.10
Record the cause of the out-of-control
condition on the control chart.
R1-2.11 After completing any necessary
modifications, note the action taken on the chart and
repeat Sections R1-2.1 through R1-2.7 to determine if
the modification has changed the instrument control
limits.
R1-2.12
Using new control limits, if appropriate,
continue data collection and observation in accordance
with Sections R1-2.8 through R1-2.10.
R1-3 CRM Control Charts
R1-3.1 Data for these control charts are collected
similarly to the data for the instrument control charts
(see Section R1-2). However, because they are based
on known information, the central lines and control
limits for both
X
and s are constructed differently.
R1-3.2 Begin by constructing
X
and s run charts in
accordance with Sections R1-2.1 through R1-2.3.
R1-3.3
Take the central line for the
X
control chart
as
0
, the certified resistivity value for the CRM at
23°C.
R1-3.4 Determine the upper and lower control limits
for the
X
control chart from the following equations:
12
0000
and
ALCLAUCL
(R1-4)
where:
UCL = upper control limit,
LCL = lower control limit,
0
=
the resistivity of the CRM, in ·cm, as show
n
on the certificate,
0
= the standard deviation of resistivity of the
CRM, in ·cm, as listed in Table R1-3, and
A = a constant given in Table R1-1 for values of m
from 6 to 10.
NOTE 2: If the stated uncertainty of the resistivity CRM is
based on the variabilities associated with the certifying
laboratory only,
0
should be determined as follows:
22
0 c
us
where:
s = grand average sample standard deviation found i
n
construction of the CRM s control chart, in ·cm,
and
u
c
= stated uncertainty of the resistivity of the CRM, i
n
·cm. (Note that u
c
is 1/k of the uncertainty, U,
stated on the certificate for NIST resistivity SRMs,
where k = 2, unless otherwise stated.)
12 Manual on Presentation of Data and Control Chart Analysis:
MNL 7, 6th Edition, (ASTM, West Conshohocken, PA, (1991) §3-19,
Tables 13 and Tables 16.