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SEMI MF1527-1104 © SEMI 2003, 2004 6 respectively). Further, the procedur es for determining micro-scale depth profiles are destructive and cannot be carried out on the reference wafe r itself. Consequently, for this app…
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
SEMI MF1527-1104 © SEMI 2003, 2004 7
correction factor for such geometries varies rapidly
with thickness (see Section 8.6).
8.3.1 Because of the relative insensitivity of the
calculated center-point resistivity to the exact value of
diameter for large diameter wafers, it is usually
adequate to assume the nominal diameter of standard
commercially available wafers specified in accordance
with SEMI M1. However, diameter correction factors
are usually required for off-center resistivity
measurements made in accordance with SEMI MF81.
When required, diameter measurements should be made
at the positions outlined in SEMI MF2074.
8.4 Axial Resistivity Uniformity — The uniformity of
the resistivity along the crystal axis is important for all
applications in which the sampling volume of the
measuring instrument in the direction perpendicular to
the wafer surface is different from that of the certifying
or calibrating instrument. In addition, gross axial
uniformity along a crystal section may be ascertained in
order to qualify the section as a source of resistivity
reference wafers of a particular resistivity prior to
slicing the section.
8.4.1 Very crude indications of the range of center-
point resistivity within a crystal section may be
obtained from measurements made on the ends of the
section in accordance with the Four-probe Method of
SEMI MF43. While these measurements provide a
useful preliminary screen for the crystal section, they
cannot be relied upon to give accurate values of
resistivity.
8.4.2 Somewhat more accurate but still gross
indications of axial resistivity uniformity may be
obtained from measurements of the resistivity at the
center of wafers in accordance with SEMI MF84 as a
function of position along the crystal section. However,
because of local fluctuations in dopant incorporation as
the crystal was grown, this procedure does not yield
reliable information about the center-point resistivity of
any wafer that is not measured. In addition, it does not
yield information about the local variation in resistivity
as a function of depth from the wafer surface, even if
center-point resistivity measurements are made on each
wafer in the section.
8.4.3 For use in connection with measurements in
which the sampling volume differs from the sampling
volume of an in-line four-point probe with 1.59
[10/(2)] mm spacing as specified in SEMI MF84,
transfer accuracy is affected by local resistivity
uniformity. In particular, the resistivity in the near-
surface region sampled by spreading resistance or
mercury probes may differ significantly from the
average resistivity of the resistivity reference wafer.
Depth profiles of resistivity near the wafer surface may
be obtained from spreading resistance measurements on
beveled sections in accordance with SEMI MF672. To
obtain depth profiles across the entire wafer, spreading
resistance measurements can be made on a cleaved or
polished perpendicular section; special fixtures are
required for these measurements, which do not provide
the depth resolution of an angle beveled section. Since
relative measurements only are required, accurate
calibration of the spreading resistance probe is not
necessary; however, linearity is important. Two
difficulties with this approach must be recognized.
First, if beveled specimens are employed, the
possibility of mixing the vertical and horizontal
resistivity variations must be considered. Second,
because the method is destructive, the resistivity
variation of the actual material being used for the
resistivity reference wafer cannot be determined
directly at the center of a resistivity reference wafer; it
can only be inferred from measurements on nearby
sections or adjacent wafers.
8.5
Radial Resistivity Uniformity — The uniformity of
the resistivity along the surface of the resistivity
reference wafer is important for all applications in
which the measuring instrument samples a different
area than the certifying or calibrating instrument. Since
all resistivity measurements other than those conducted
in accordance with SEMI MF84, including four-point
probe measurements made with probes with different
probe-tip spacing, sample different areas, this factor is
one of the most significant limitations in transfer of
resistivity values from one instrument to another.
8.5.1 Large scale (macro) variations in resistivity
across the surface of a wafer can be measured with a
four-point probe.
8.5.1.1 Coarse indications can be obtained using an in-
line four-point probe in accordance with SEMI MF81
modified to yield a nine-site map of resistivity variation
over the central 38-mm diameter region of the wafer.
In addition to four-point probes, eddy current
instruments are frequently used for these
measurements. Although the procedures for using eddy
current instruments for measuring resistivity variation
are not standardized, they provide an adequate measure
of radial resistivity variation, especially in the central
region of the wafer where edge effects are not
significant. Although more dense patterns may be
measured, they are very inconvenient to obtain
manually using either a four-point probe or an eddy
current instrument.
8.5.1.2 Several commercial automated mapping
instruments that utilize dual-configuration, in-line, four-