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SEMI MF1527-1104 © SEMI 2003, 2004 5 recently issued CRM s are calibrated and certi fied by this technique. 6 8 Selection and Qualification of Materials for Resistivity Reference Wafers 8.1 Factors that m ust be consider…
SEMI MF1527-1104 © SEMI 2003, 2004 4
control charts (see Section 7.1.1), (3) return measured
resistivity values of appropriate CRMs to within desired
limits through measurement of resistivity CRMs at
regular intervals (see Section 7.1.2), and (4) be operated
within the temperature range specified in SEMI MF84
(see Section R2-4 of this guide).
7.1.1 Instrument Control Charts —
X
and s control
charts should be maintained to establish the stability of
the instrument over the range of resistivity that the
instrument is expected to measure. A separate control
chart should be maintained for each reference wafer
used. Initially, resistivity CRMs or other wafers with
adequate radial resistivity uniformity (see Section 8.5.1)
should be used for this purpose. As resistivity reference
wafers are prepared, these should be used for
maintaining the control charts. After in-house
resistivity reference wafers become available, it is
recommended that three wafers at each resistivity level
be set aside for control charting. Two of these should
be used for maintaining the
X
and s charts on a regular
basis. The third is retained as a reference to ensure that
any apparently out-of-control conditions are due to the
instrument and not to changes in sample surface
conditions, as might occur after prolonged use of a
particular sample. Each resistivity determination
should consist of six to ten measurements made in
accordance with SEMI MF84. Established procedures
for generating and maintaining the control charts and
for determining the existence of out-of-control
conditions and the need for corrective action should be
used. A suggested procedure for these determinations
is given in Section R1-2 for use in organizations
without previously established procedures.
7.1.2
Comparison with CRMs — To provide
traceability, measurements of the resistivity of available
CRMs that encompass the range of resistivity expected
to be encountered should be made on a periodic, but
less frequent, basis. In addition to being in control, the
instruments should return measured values of the
resistivity of the CRMs that do not deviate from their
certified value by more than the root mean square of the
two-sigma (95 % confidence level estimate) uncertainty
of the CRM (Note 1) and the two-sigma instrument
variability determined by control charting procedures
(Note 2). A suggested procedure for control charting of
CRMs is given in Section R1-3 for use in organizations
without previously established procedures.
NOTE 1: A laboratory issuing a CRM should provide a
comprehensive statement of its uncertainty associated with
the measurement and reporting of the CRM value. This
should include evaluations, or estimates, of both random and
systematic “errors” following ISO procedures for Type A and
Type B evaluations of components of uncertainty. The result
would be expressed as a Combined Standard Uncertainty
(standard deviation, or square-root of a sum of variances of
uncertainty components), or as an “Expanded Uncertainty” (2
times the Combined Standard Uncertainty). If based on
sufficient statistical degrees of freedom, the Combined
Standard Uncertainty is a one-sigma estimate, and the
Expanded Uncertainty is a two-sigma, or 95% confidence-
level, estimate. If there are insufficient statistical degrees of
freedom, the effective number of degrees of freedom should
be reported by the CRM-issuing laboratory. It is then
necessary to multiply the uncertainty value provided by the
student-t factor appropriate to that number of degrees of
freedom in order to obtain values for the one-sigma or two-
sigma (95% confidence-level) measurement uncertainty.
NOTE 2: A laboratory following this procedure to establish
traceability to resistivity CRMs incorporates a value of its
measurement uncertainty based on its control chart
measurements, which evaluate random components of
uncertainty only. If the laboratory then measures a value for
the CRM within the total uncertainty interval, calculated
following the root-mean-square procedure, above, about the
certified value, its instrument is validated for use. If it
measures a value outside the prescribed interval, this is an
indication that its measurement bias with respect to true value
is statistically significant at the 95% level, and instrument
repair, or “calibration” is necessary before proceeding.
7.1.3 Probe Assembly and Electrical Equipment Tests
— Should an out-of-control or out-of-specification
condition be encountered, the probe assembly and
electrical equipment can be tested in accordance with
the section on Suitability of Test Equipment in SEMI
MF84. These tests may serve to isolate the cause of the
problem encountered. Either or both of these
components should be repaired or replaced if they fail
to meet the requirements specified in this section of
SEMI MF84.
NOTE 3: The stringent requirements on control of probe-tip
spacing as well as the need for off-center diameter correction
factors required for determination of radial resistivity
uniformity (see Section 8.5) are a consequence of the single-
configuration method of using the four-point probe in
accordance with SEMI MF84. Errors resulting from
uncertainty in probe-tip spacing when using the single-
configuration method are considered in Related Information
2. The probe-tip spacing requirements can be relaxed
significantly if the dual-configuration method
5
of measuring
resistivity with a four-point probe is used. Use of this method
is recommended for determination of the radial resistivity
uniformity (see Section 8.5). However, the dual-
configuration method has not yet been standardized for bulk
resistivity measurements because appropriate thickness
correction factors have not yet been published. Such
corrections are required for thickness to probe spacing ratios
greater than 0.36. Nevertheless, it is noted that the most
5 Perloff, D. S., “Four-point Probe Correction Factors for Use in
Measuring Large Diameter Doped Semiconductor Wafers,” J.
Electrochem. Soc. 123, 1745–1750 (1976).
SEMI MF1527-1104 © SEMI 2003, 2004 5
recently issued CRMs are calibrated and certified by this
technique.
6
8 Selection and Qualification of Materials for
Resistivity Reference Wafers
8.1 Factors that must be considered in selecting
materials for resistivity reference wafers are nominal
resistivity (see Section 8.2), wafer diameter (see
Section 8.3), axial and radial uniformity of the
resistivity (see Sections 8.4 and 8.5, respectively),
wafer thickness (see 8.6), wafer conductivity type and
surface orientation (see Section 8.7), and surface finish
(see Section 9.1.2). It is generally desirable to qualify a
crystal section for the desired parameters and then
verify that individual wafers meet the requirements
during the calibration procedure. The uniformity
requirements, in particular, depend on the specific
application of the reference wafers because different
resistivity measuring instruments are sensitive to
different volumes of material.
8.1.1
Four-point Probes — The most straightforward
application of resistivity reference wafers is for control
of four-point probes used for measurement of resistivity
and resistivity variation. If the wafer under test has the
same geometry and surface characteristics as the
reference wafer and if the same probe geometry is used
for the measurement of both the reference wafer and the
wafer under test, the transfer is direct and no special
precautions need be observed. If the wafer under test
has different thickness or diameter from the resistivity
reference wafer or if four-point probes with different
probe-tip spacings are used to measure the test and
reference wafers, attention must be paid to the use of
the appropriate correction factors. In particular, if the
ratio of thickness to probe-tip spacing becomes too
large, (Note 3) while the ratio of diameter to probe-tip
spacing becomes too small, second order errors due to
the use of two two-dimensional corrections for a three-
dimensional geometry may become significant. Also, if
different probe-tip spacings are used, differences in
sampling volume must be recognized; in this case,
resistivity uniformity of both the reference wafer and
the wafer under test limits the transfer accuracy. If the
wafer under test has a different surface condition from
that of the reference wafer, it is necessary to
demonstrate the equivalence of the resulting
measurement value with that which would have been
obtained had the same surface condition been employed
for both. These considerations apply to single-
6 See, for example, Ehrstein, J. R., and Croarkin, M. C., “Standard
Reference Materials: The Certification of 100 mm Diameter Silicon
Resistivity SRMs 2541 through 2547 Using Dual-Configuration
Four-point Probe Measurements, NIST Special Publication 260–131,
1999 edition, 106 pp. Available from the National Technical
Information Service, Springfield, VA 22161, as PB 98-113731.
configuration four-point probes. Because the standard
test method for use of dual-configuration four-point
probes is intended for sheet resistance, rather than bulk-
resistivity measurement, these concerns with thickness
and diameter issues can be ignored. However, if the
thickness is too great, an unknown thickness correction
factor must be used if bulk resistivity values are to be
compared.
8.1.2 Eddy-current Gages — The eddy-current
detector is sensitive to the integrated sheet resistance
across the thickness of the wafer; in this respect it is
similar to the four-point probe. However, the eddy-
current probe may weight various elements of the
volume sampled differently than that of a four-point
probe. Therefore, the weighted average resistivity seen
in nonuniform wafers by the eddy current gage may not
be the same as the center-point average resistivity value
determined by the four-point probe. As a result, the
accuracy of transfer between these types of instruments
depends strongly on the macro-scale uniformity of the
resistivity over the central area of the reference wafer.
Because the eddy-current gage is a bulk measurement
device, the thickness uniformity over the area sampled
by the eddy-current probe is also important. The upper
limit of the expected reduction of transfer accuracy is
given as follows:
1001
TTV
11
reductionpercent maximum
w
(1)
where:
= average center-
p
oint resistivity of resistivity
reference wafer, corrected to 23°C, in ·cm,
= radial resistivity variation of resistivity reference
wafer, corrected to 23°C, in ·cm, over the area
sampled by the eddy-current probe,
TTV = total thickness variation of resistivity reference
wafer, in m, over the area sampled by the
eddy-current probe, and
w = average thickness of resistivity reference wafer,
in m.
8.1.3
Spreading Resistance Probes — Because the
spreading resistance probe samples a volume that is
exceedingly small compared with the volume sampled
by the four-point probe, the most critical reference
wafer parameter for accurate transfer of resistivity
value is the micro-variation of the resistivity both
axially and radially. Very complex and time-
consuming procedures are required to determine the
micro-scale depth and lateral variations of resistivity in
a reference wafer (see Sections 8.4.3 and 8.5.2,
SEMI MF1527-1104 © SEMI 2003, 2004 6
respectively). Further, the procedures for determining
micro-scale depth profiles are destructive and cannot be
carried out on the reference wafer itself. Consequently,
for this application crystals should be grown by
procedures that result in the best possible uniformity.
These include neutron transmutation doping of very
high purity FZ crystals to obtain high resistivity
(neutron transmutation doped (NTD)) n-type wafers
and magnetic Czochralski (MCz) growth of crystals for
both n- and p-type wafers.
8.1.4 Mercury Probes — Similar conditions exist for
reference wafers intended for calibration and control of
mercury probe systems that are primarily used for
determining the net carrier density of epitaxial layers
from capacitance measurements. Such probes sample a
lateral area much smaller than the four-point probe and
a depth that is only a very tiny fraction of the wafer
thickness. To ensure that the resistivity in the region
sampled by the mercury probe can be taken as the
resistivity measured by the four-point probe, it is
necessary to establish that both the macro- and micro-
scale variations in resistivity of the reference wafer are
within tolerable limits. Thus, it is desirable to use
highly uniform crystal such as NTD FZ or MCz crystal
for resistivity reference wafers for this application (see
Section 8.1.3). It is further required in this case to
establish the net carrier density of the reference wafer
from the resistivity measurement (see Section 9.2.4).
8.2
Resistivity — The center-point resistivity of the
reference wafer should be chosen to meet the
requirements of the measuring instrument to be
calibrated or controlled. Most of the test methods cited
in Section 1.2 specify the resistivity range of the
required resistivity reference wafers.
8.2.1 Four-point Probes — For control of
instrumentation for making four-point probe resistivity
measurements in accordance with SEMI MF84, it is
recommended that a minimum of three resistivity
reference wafers, with resistivity values in the upper,
middle, and lower portions of the resistivity range of
interest be used (Note 4). It is preferable to use more
closely spaced resistivity reference wafers to ensure
instrument linearity over the entire measurement range.
If only a narrow resistivity range (less than ±25% of the
nominal value) needs to be measured, it is sufficient to
use two resistivity reference wafers at the extremes of
this range. Similar considerations apply for control of
instrumentation for making sheet resistance
measurements in accordance with SEMI MF1529,
except that, in this case, of course, the parameter of
interest is the sheet resistance rather than the resistivity.
NOTE 4: For control of instrumentation for making four-
point probe measurements over a narrow resistivity range, it
may be appropriate to use only one or two resistivity
reference wafers.
8.2.2 Eddy–Current Gages — For calibration of eddy
current resistivity measuring instruments, SEMI MF673
specifies that for calibration by Method I, five reference
wafers that span the full resistivity range of the
instrument are required. However, many organizations
prefer to use many more reference wafers for the
Method I calibration. Two resistivity reference wafers
at the extremes of a narrow resistivity range (typically
less than about ±25 % of the nominal value) are
required for Method II calibration.
8.2.3 Spreading Resistance Probes — For calibration
of spreading resistance equipment, SEMI MF672
recommends use of at least three resistivity reference
wafers per decade over the range of resistivity to be
measured. Regular spacing is desirable, but it may not
be possible to secure samples with adequate uniformity
with arbitrary nominal resistivity values. Selection of
samples for micro-scale uniformity should take
precedence over regular spacing.
8.2.4 Mercury Probes — The resistivity of a resistivity
reference wafer intended for use in calibrating mercury
probe systems for making net carrier density
measurements in accordance with SEMI MF1392 or
SEMI MF1393 is specified to be between one-half and
two times the resistivity of the specimens to be
measured. However, there is some benefit to employ
several resistivity reference wafers with a range of
resistivity from very high (net carrier density less than
about 1 × 10
14
cm
3
) to the lowest value to be
measured.
8.3 Wafer Diameter — Resistivity reference wafers do
not need to be the same diameter as the wafers to be
measured by the system; any diameter that fits the
instrumentation and its associated wafer handling is, in
principle, acceptable. However, advances in crystal
growing design and control together with certain aspect
ratio considerations make it likely that superior radial
resistivity uniformity in the central region of the wafer
can be obtained with larger diameter (100 mm) wafers
as compared to that of smaller diameter wafers. In
addition, the diameter correction factor for wafers 100
mm in diameter and larger measured with a four-point
probe with probe-tip spacing of 1.59 mm is within 0.2%
of its limiting value of /ln2 ( = 4.5324).
Consequently, errors due to small variations in diameter
or probe placement at the wafer center are negligibly
small (see Section R2-3.1), and the second order errors
associated with the combination of the thickness and
diameter correction factors can also be neglected. The
latter point is particularly significant when four-point
probes with small probe-tip spacings are employed on
standard thickness wafers because the thickness