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SEMI MF1392-1103 © SEMI 2003 7 surface region may be obtained from spreading resistance measurements through the use of a calibration curve only, without the need for using correction factors. Since the procedures for ch…
SEMI MF1392-1103 © SEMI 2003 6
7.10.5 Spin Dryer, for drying the wafers in an air
atmosphere.
7.10.6 Hot Plate, for p-type wafers or other means for
baking the wafer at 120 ± 10° C in air may also be
required.
7.10.7 Interval Time, for controlling treatment times.
7.10.8 Nonmetallic Tweezers or Vacuum Wand, for
holding and manipulating wafers.
8 Reagents and Materials
8.1 Purity of Reagents — All chemicals for which such
specifications exist shall adhere to Grade 1 SEMI
specifications for those specific chemicals. Other
grades may be used, provided it is first determined that
the chemical is of sufficiently high purity to permit its
use without lessening the accuracy of the test.
8.2 Mercury shall be triple distilled and conform to
reagent grade, as specified in Reagent Chemicals.
8
It
shall be changed regularly or otherwise maintained in a
clean state to avoid interference from surface scum (see
Section 3.5) (Warning—see Section 7.1).
8.3 Purity of Water — Reference to water shall be
understood to mean Type E-3 or better water as
described in ASTM Guide D 5127.
8.4 Reference Wafers — One or more polished bulk
silicon wafers of the same conductivity type as the layer
or wafer to be tested. If one reference wafer is used, its
net carrier density shall lie between one-half and two
times the net carrier density of the layer or wafer to be
tested. If several reference wafers are used, their net
carrier densities shall cover the range of net carrier
densities of the layers or wafers to be tested. Bulk
reference wafers shall have the following
characteristics:
8.4.1 Flat spreading resistance profile over a depth
equal to or greater than that to be profiled in this test
method. The flat profile is required to ensure correct
determination of C
comp
(see Section 3.7, Section 10.2).
Determine that the spreading resistance profile is flat in
the following manner:
8.4.1.1 Measure the spreading resistance profile in
accordance with SEMI MF672 on a small chip from a
portion of the wafer. Use a minimum of 10 spreading
resistance values in constructing the spreading
resistance profile.
8.4.1.2 Fit the spreading resistance data to a straight
line by a least-squares method.
8 “Reagent Chemicals, American Chemical Society Specifications,”
Am. Chemical Soc., Washington, DC.
8.4.1.3 For the profile to be considered flat, the fitted
values at the beginning and end of the profile shall be
equal to within ± 2% and the maximum deviation of
any measured value from the fitted line shall not exceed
5%.
8.4.2 Resistivity variation over the central region of the
wafer ≤ 5%. Resistivity variation over this region
should be as small as possible to obtain maximum
accuracy of the determination of the net carrier density
of the reference wafer; accurate determination of the net
carrier density is required for accurate determination of
the probe contact area (see Section 10.3).
8.4.2.1 Determine radial unformity from resistivity
measurements taken at 2.0 mm intervals along two
perpendicular diameters for a distance of 6 mm from
the center of the wafer in each direction. Analyze the
data in accordance with the maximum/minimum
convention of Sample Plan D of SEMI MF81.
8.4.2.2 Establish axial uniformity (see Section 3.7) by
spreading resistance measurements across a cleaved
portion of the wafer or by some other method agreed
upon by the parties to the test.
8.4.3 Known Net Carrier Density — Determine the net
carrier density as follows:
8.4.3.1 Measure the resistivity at the center of the
wafer and correct it to 23° C in accordance with SEMI
MF84.
8.4.3.2 Convert the resistivity value to net carrier
density using the computational methods given in
Section 7.2 of SEMI MF723.
NOTE 7: In applying this conversion procedure in either
direction it is assumed that the net carrier density is equal to
the dopant density. The appropriate equation given in this
section for resistivity must be solved iteratively for the net
carrier density. It is necessary to use the same equation for
conversion from net carrier density to resistivity and vice
versa in order to eliminate the self-consistency errors in SEMI
MF723. The choice of conversion direction in this test
method was made so that the more laborious, iterative
procedure is applied to the less frequently measured reference
wafers and the direct conversion procedure is applied to
material being evaluated by this test method.
8.4.3.3 Record the net carrier density just obtained, as
N
ref
, in cm
−3
.
NOTE 8: The advantage of using bulk reference wafers is
that the net carrier density can be related to that of resistivity
standard reference materials issued by the National Institute
of Standards and Technology. However, material
inhomogeneity may make it difficult to obtain accurate values
of net carrier density from bulk reference wafers (see Section
3.7). As an alternative, epitaxial wafers may be used as
reference wafers. In this case, the epitaxial layer thickness
should be large enough that the resistivity profile in the near-
SEMI MF1392-1103 © SEMI 2003 7
surface region may be obtained from spreading resistance
measurements through the use of a calibration curve only,
without the need for using correction factors. Since the
procedures for characterizing such reference wafers have not
been standardized, epitaxial wafers should be used as
reference wafers only if agreed upon between the parties to
the test. If used, the epitaxial reference wafer should meet the
requirements of Section 8.41 for a flat spreading resistance
profile. Net carrier density should be determined using an
metal oxide silicon (MOS) capacitor structure in accordance
with SEMI MF1153 or by another mutually acceptable
method.
8.5 Reagents for Surface Treatment — If surface
treatment is required, the following chemicals may be
needed. Grade 1 chemicals are preferred (see Related
Information 1).
8.5.1 Hydrofluoric Acid, HF, concentrated, 49.00 ±
0.25%, in accordance with grade 1 of SEMI C28 or
dilute, 4.9 ± 0.1%, in accordance with grade 1 of SEMI
C29.
8.5.1.1 Once a week, fill the hydrofluoric acid tank
with fresh HF, either concentrated or dilute.
8.5.2 Hydrogen Peroxide, H
2
O
2
, unstabilized, 30%, in
accordance with grade 1 of SEMI C30.
8.5.2.1 Every 8 h, fill the hydrogen peroxide tank with
a fresh 15% H
2
O
2
solution by mixing equal volumes of
H
2
O
2
(30%) and water. Wait until the freshly poured
bath reaches 70 ± 5° C before using to treat wafer
surfaces.
8.5.2.2 During use, approximately every 2 h (or when
the H
2
O
2
level falls below the wafers being treated),
replenish the tank by adding 30% H
2
O
2
.
9 Sampling
9.1 It is generally impractical to measure every wafer
in a particular lot owing to the potential for
contamination from the handling and chemical
treatments involved. A wafer sampling plan shall
therefore be agreed upon between the parties to the test.
9.2 Locations on the wafer where measurements are to
be made shall also be agreed upon between the parties
to the test.
10 System Calibration and Control
10.1 Frequency of Calibration and Control Procedures
10.1.1 Calibrate the capacitance meter and voltmeter in
accordance with manufacturer’s instructions on initial
installation and following hardware or software
modifications. Calibration of the capacitance meter and
voltmeter may be carried out in-house or by a qualified
testing laboratory.
10.1.2 Determine the compensation capacitance and
effective area of the mercury probe in accordance with
the procedures of this section on initial installation and
after any corrective action has been carried out to bring
the system back into control.
10.1.3 Conduct periodic tests and maintain control
charts in accordance with the procedures in this section
to demonstrate that the instruments are in control and
that the variability is within the requirements of this test
method.
10.2 Determination of Compensation Capacitance,
C
comp
10.2.1 Measure a series of capacitance-voltage pairs on
the reference wafer carrier density of 1 × 10
−14
cm
−3
or
less or, if such a reference wafer is not available, on the
reference wafer with the lowest value of net carrier
density (see Section 8.4) in accordance with Procedure
(Section 11), using either the front- or back-surface-
return-contact configuration depending on the type of
wafer to be tested (see Section 7.2). Be certain that the
series resistance of the diode circuit formed with the
reference wafer meets the requirements of Section
11.4.1.7 or Section 11.4.2.7 before proceeding with the
measurement of the capacitance-voltage pairs. Record
each measured capacitance, C
i
, and its associated
voltage, V
i
. Determine the value of C
comp
either from
the net carrier density profile (Section 10.2.2) or from
V
i
as a function of C
i
−2
(Section 10.2.3).
10.2.2 Net Carrier Density Profile
10.2.2.1 Measure a total of n pairs, sufficient to
calculate at least five values of net carrier density, N
i
,
and depth, W
i
.
NOTE 9: If the incremental method of calculation (see
Section 12.3) is used, n ≥ k + 5, where k is an integer chosen
such that C
i + k
is between 80 and 85% of C
i
; if the curve-
fitting method of calculation (see Section 12.4) is used, n ≥ 5.
10.2.2.2 Calculate the net carrier density profile in
accordance with the incremental method (see Section
12.3) or the curve-fitting method (see Section 12.4)
taking C
comp
= 0 (see Section 12.1).
NOTE 10: If an approximate value of C
comp
is known, this
procedure may be shortened by starting with this approximate
value. In this case, if the slope of the net carrier density
profile is positive, increase C
comp
as directed in Section
10.2.2.3 and Section 10.2.2.4 and decrease it after the first
slope change as directed in Section 10.2.2.5; if the slope is
negative, decrease C
comp
initially and increase it after the first
slope change.
10.2.2.3 Increase C
comp
by 0.1 pF and recalculate the
net carrier density profile (see Note 10). For the
recalculation, correct each of the C
i
to C
′
i
as follows:
SEMI MF1392-1103 © SEMI 2003 8
compii
CCC +=
′
(1)
NOTE 11: On some instruments, it may be necessary to enter
a new value for C
comp
and remeasure the reference wafer each
time the value of C
comp
is changed.
10.2.2.4 Repeat Section 10.2.2.3, increasing the value
of C
comp
by 0.1 pF each time until the slope of the
calculated net carrier density profile changes sign.
10.2.2.5 After the slope of the calculated net carrier
density profile changes sign, repeat Section 10.2.2.3,
decreasing the value of C
comp
by 0.02 pF each time until
the slope of the calculated net carrier density profile
changes sign again.
10.2.2.6 Record as C
comp
the average of the values
obtained just before and just after the sign change of the
slope.
10.2.3 V
i
as a Function of C
i
−
2
10.2.3.1 Measure at least 50 capacitance-voltage pairs
over the entire range to be measured.
10.2.3.2 Taking C
comp
= 0, fit a straight line to the
V
i
− C
i
−2
data by the least-squares method, and compute
the sum of the squares of the normalized residuals as
follows:
2
1
1
ˆ
∑
=
−=
n
i
i
i
N
V
V
R (2)
where:
R
N
= sum of the squares of the normalized residuals,
V
i
= measured voltage corresponding to the
capacitance C
i
,
V
i
^
= voltage corresponding to the capacitance C
i
,
calculated from the least-squares fit, and
n = number of measured capacitance-voltage pairs.
10.2.3.3 Set C
comp
= 0.1 pF.
10.2.3.4 Correct each of the C
i
to C
′
i
using Eq. 1, fit a
straight line to the new data, and recompute the sum of
the squares of the normalized residuals using Eq. 2.
10.2.3.5 If the sum of the squares of the normalized
residuals is less than the sum obtained from the
previous case, increase C
comp
by 0.1 pF, and repeat
Section 10.2.3.4.
10.2.3.6 Repeat Section 10.2.3.5, increasing the value
of C
comp
by 0.1 pF each time until the sum of the
squares of the normalized residuals increases.
10.2.3.7 At this point, decrease the value of C
comp
by
0.02 pF.
10.2.3.8 Correct each of the C
i
to C
′
i
using Eq. 1, fit a
straight line to the new data, and recompute the sum of
the squares of the normalized residuals using Eq. 2.
10.2.3.9 If the sum of the squares of the normalized
residuals is less than the sum obtained from the
previous case, decrease C
comp
by 0.02 pF, and repeat
Section 10.2.3.8.
10.2.3.10 Repeat Section 10.2.3.9, decreasing C
comp
by
0.02 pF each time until the sum of the squares of the
normalized residuals again increases.
10.2.3.11 Record as C
comp
the average of the values
obtained just before and just after the second increase in
the sum of the squares of the normalized residuals.
10.3 Determination of Effective Mercury Probe
Contact Area
10.3.1 Using the value of C
comp
recorded in Sections
10.2.2.6 or 10.2.3.11, determine the net carrier density
profile in the central region (see Section 8.4.2) of each
reference wafer five times in accordance with
Procedure (Section 11) and Calculations (Section 12).
Be certain that the series resistance of the diode circuit
formed with the reference wafer meets the
requirements of Section 11.4.1.7 or Section 11.4.2.7
before proceeding with the measurement of the
capacitance-voltage pairs. For these measurements,
take the area of the mercury probe contact as the
nominal area of the capillary tube holding the mercury,
determined as follows:
400
2
d
A
π
= (3)
where:
A = nominal capillary tube area, cm
2
, and
d = nominal diameter of the capillary tube, mm.
NOTE 12: If the nominal diameter of the capillary tube is not
known, it can be measured with a toolmaker' s microscope or
other appropriate instrument. The area need not be known
precisely, an estimate within about 20% is adequate for the
purpose.
10.3.2 In each of the five measurement sets ( j from 1
to 5), record each measured capacitance, C
ij
, and its
associated voltage, V
ij
, for a total of n pairs (i from 1 to
n, where n is sufficient to calculate at least five values
of net carrier density, N
ij
, and depth, W
ij
, see Note 7).
Measure the same number of pairs in each of the five
net carrier density profiles.
10.3.3 Calculate the average net carrier density, N
avg
, in
cm
−3
, as the grand average of the individual net carrier
densities: