semi合集-English.pdf - 第7410页
SEMI MF1527-1104 © SEMI 2003, 2004 16 R1-4.6 Determ ine the upper and lower cont rol limit s for the m oving range c h art from the followi ng equations: 13 0 and 27 . 3 LCL R UCL ( R1-7) where: UCL = upper control l…
SEMI MF1527-1104 © SEMI 2003, 2004 15
R1-3.5 Calculate the grand average, s, of the s values
in accordance with Section R1-2.4. Take s as the
central line for the s control chart.
R1-3.6 Determine the upper and lower control limits
for the s control chart in accordance with Section R1-
2.6.
R1-3.7 Using these control limits, continue to collect
X
and s 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.
R1-3.8 Observe the
X
and s control charts for out-of-
control conditions as listed in Table R1-4. If out-of-
control conditions are noted, annotate the chart to
highlight the out-of-control condition and take
corrective action as follows:
R1-3.8.1
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),
R1-3.8.2 If the reference wafer appears to be at fault,
resurface it and begin the process using it as a fresh
control wafer,
R1-3.8.3 If instrument is at fault, check the probe
assembly and electrical equipment in accordance with
Section 7.1.3, and repair or replace as needed, and
R1-3.9 After completing any necessary modifications,
annotate the chart to record both the cause of the out-of-
control condition and the action taken, and continue to
collect and record data using the same control limits as
before.
R1-4 Control Charts for Instruments for
Routine Resistivity Measurements
R1-4.1 For control of resistivity measuring equipment
used in routine applications, a control chart for
individuals with moving range is appropriate. Select
reference wafers in accordance with the instructions in
the applicable test method (see Table 2) covering the
resistivity range of the specimens to be measured.
Begin construction of the control chart by making 25 to
30 center-point resistivity determinations on the
selected reference wafer in accordance with the
procedures in the method governing the type of
instrument being controlled.
R1-4.2
Record the date, time, sample identification,
operator, and value obtained. For all measurements
after the first, calculate and record the magnitude of the
difference between the current value and the previous
value.
R1-4.3 Construct an X (individuals) chart by plotting
the measured resistivity values in the order in which the
data were obtained. Construct a moving R (range) chart
by plotting the differences in the order in which they
were obtained.
R1-4.4
Calculate the averages of the initial 25 to 30
readings,
X
and ,R of the values and the differences,
respectively as follows:
1
11
1
1
and
1
n
i
i
n
i
i
R
n
RX
n
X
(R1-5)
where:
X
i
= the i
th
individual resistivity value,
R
i
=
the difference, X
i+1
X
i
, and
n = number of measurements (25 to 30).
Take these averages as the central lines of the
individuals and moving range charts, respectively.
R1-4.5 Determine the upper and lower control limits
for the individuals chart as follows:
13
RXLCLandRXUCL 66.266.2 (R1-6)
where:
UCL
=
upper control limit,
LCL
=
lower control limit, and
X
=
average resistivity, ·cm, (see Section R1-4.4)
and
R
=
average of the ranges, ·cm (see Section R1-4.4)
13 Manual on Presentation of Data and Control Chart Analysis:
MNL 7, 6th Edition, (ASTM, West Conshohocken, PA, (1991) §3-30,
Table 24.
Table R1-3 Estimates of Standard Deviation for
Four-point Probe Measurements of Resistivity
Resistivity,
0
,
·cm
Estimate of Standard Deviation,
0
,
·cm
0.0008 to 120
0.0067 ×
0
120 to 500
0.0167 ×
0
500 to 2000
<0.05 ×
0
Table R1-4 Patterns that Indicate Possible Out-of-
control Conditions for CRM
X
Control Chart
Pattern Indication
1 Single point outside of control limits
5 Five successive points without change of
direction
6 Six consecutive up and down pairs
SEMI MF1527-1104 © SEMI 2003, 2004 16
R1-4.6 Determine the upper and lower control limits
for the moving range chart from the following
equations:
13
0and27.3 LCLRUCL (R1-7)
where:
UCL = upper control limit,
LCL = lower control limit, and
R
=
average of the ranges, ·cm (R1-4.4).
R1-4.7 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 A, B, and C
similarly to the
X
and s charts shown in Figure R1-1.
R1-4.8 Using these control limits, continue to collect
data on the reference wafers periodically in accordance
with the procedures of Section R1-4.1, recording the
information specified in Section R1-4.2.
R1-4.9 Observe the 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:
R1-4.9.1
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).
R1-4.9.2 If the reference wafer appears to be at fault,
resurface it and begin the process using it as a fresh
control wafer.
R1-4.9.3 If instrument is at fault, check the probe
assembly and electrical equipment in accordance with
Section 7.1.3, and repair or replace as needed.
R1-4.10 After completing any necessary
modifications, note the action taken on the chart and
repeat Sections R1-4.1 through R1-4.7 to determine if
the modification has changed the instrument control
limits.
R1-4.11 Using new control limits, if appropriate,
continue data collection and observation in accordance
with Sections R1-4.8 through R1-4.10.
SEMI MF1527-1104 © SEMI 2003, 2004 17
RELATED INFORMATION 2
ERRORS IN RESISTIVITY DETERMINATION BY THE FOUR-POINT
PROBE METHOD (SINGLE CONFIGURATION) RESULTING FROM
UNCERTAINTIES IN WAFER DIAMETER, WAFER THICKNESS, AND
PROBE-TIP SPACING
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 the Silicon Wafer Committee on July 15, 2004.
R2-1 The resistance of an infinitely thin uniform sheet
of infinite extent as measured with an equal spaced, in-
line four-point probe is given as follows:
2ln
m
s
I
V
(R2-1)
where:
s
=
resistance of the infinite sheet, , and
(V/I)
m
= average of the forward and reverse voltage-
current ratios, .
The resistivity of the sheet can be obtained by
multiplying the sheet resistance by the sheet thickness
as follows:
w
s
4
10
(R2-2)
where:
=
resistivity, ·cm,
s
=
resistance of the infinite sheet, , and
w =
thickness, m.
R2-2 Corrections to this equation can be made to
obtain the resistivity of a wafer that has finite thickness
and diameter, as measured with a four-point probe with
slightly unequal probe-tip spacings with an average
value of
S at a temperature slightly different from the
reference temperature. The general solution to this
problem must take account of its three-dimensional
aspect. Solutions are available for the case of a semi-
infinite medium or for an infinitely thin sheet. If the
deviation from the thin sheet approximation is
sufficiently small, the correction factors can be
determined from independent solutions of two-
dimensional electrostatic problems and multiplied
together as follows:
Tsp
m
C
FF
D
S
F
S
w
wF
I
V
2ln
10
4
23
(R2-3)
where:
23°C
= wafer resistivity at a reference temperature
of 23°C, ·cm,
w =
wafer thickness, m,
(V/I)
m
= average of the forward and reverse voltage-
current ratios, ,
F(
S /D)
= correction factor to account for finite wafe
r
diameter (see Section R2-3.1),
S
= average probe-tip spacing, mm,
D = wafer diameter, mm,
F(w/
S
)
= correction factor to account for finite wafe
r
thickness (see Section R2-3.2),
F
sp
= correction factor to account for slightly
unequal probe-tip spacings (see Section R2-
3.3), and
F
T
= correction factor to account for differences
b
etween measurement and reference
temperature.
NOTE 1: The correction factor F
2
in SEMI MF84 is equal to
F( S /D)/ln 2.
R2-3 The relative variation in resistivity for small
variations in these factors is given by the following
relationship:
14
T
T
sp
sp
C
C
F
F
F
F
DSF
DSF
SwF
SwF
w
w
I
I
V
V
d
d
)/(
)/(d
)/(
)/(d
ddd
d
23
23
(R2-4)
The relative variations of the correction factors
F(w/
S ), F( S /D), and F
sp
may be related to variations
in wafer diameter, wafer thickness, and probe-tip
spacing as follows:
14 Bullis, W. M., “Standard Measurements of the Resistivity of
Silicon by the Four-probe Method,” NBSIR 74-496 (August 1974),
73 pp. Available from the National Technical Information Service,
Springfield, VA 22161, as COM 74-11576.