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SEMI MF1392-1103 © SEMI 2003 8 comp i i C C C + = ′ (1) NOTE 11: On some instruments, it may be necessary to ente r a new value for C comp and remeasure the refer ence wafer each time the value of C comp is changed. 10.2…
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:
SEMI MF1392-1103 © SEMI 2003 9
∑∑
==
=
5
11
5
1
j
n
i
ijavg
N
n
N (4)
where:
N
ij
=
net carrier density, cm
−3
, for the i
th
depletion
depth in the j
th
measurement set, as calculated in
accordance with Calculations (Section 12), and
n = number of capacitance-voltage pairs measured
in each of the five measurement sets.
10.3.4 Calculate the effective mercury probe contact
area, A
eff
, in cm
2
, for each reference wafer as follows:
kref
kavg
keff
N
N
AA
)(
)(
)( = (5)
where:
A = nominal capillary area, cm
2
,
(N
ref
)
k
= known net carrier density of reference wafe
r
k, cm
−3
, and
(N
avg
)
k
= the calculated average net carrier density o
f
reference wafer k, cm
−3
.
10.3.4.1 If one reference wafer was measured, record
this value as the effective mercury probe contact area,
A
eff
.
10.3.4.2 If more than one reference wafer was
measured, determine and record the effective mercury
probe contact area, A
eff
, as the average of the effective
contact areas for each of the reference wafers.
10.3.5 For control charting purposes, repeat Sections
10.3.2 and 10.3.3 using A
eff
as the area of the mercury
probe contact. If the value of average net carrier
density for any reference wafer differs from the known
value by more than 2%, condition the surfaces of the
appropriate reference wafer or wafers (see Related
Information 1) and repeat the calibration procedure
(Sections 10.2 and 10.3). If it is impossible to achieve
deviations of 2% or less for all wafers, it may be
necessary to subdivide the net carrier density range and
assign effective probe contact areas to each subgroup.
NOTE 13: Recommended chemical surface treatment
procedures are described in Related Information 1.
10.4 Control Procedures — Periodically carry out tests
and maintain control charts to ensure proper operation
of the electronics (Section 10.4.1), the electronics plus
the mechanical functionality of the probe station
(Section 10.4.2), and the entire system (Section 10.4.3).
10.4.1 Monitor the performance of the electronic
components with a moving range control chart of the
net carrier density of a packaged Schottky diode.
10.4.1.1 Determine the net carrier density as follows:
Attach the diode to the capacitance meter terminals and
carry out the procedure, beginning with Section 11.6.4,
and Calculations, Section 12.
10.4.1.2 If out-of-control conditions are noted, or if the
control limits are wider than is desirable for the
application, verify the performance of the capacitance
meter and voltmeter independently in accordance with
Sections 10.5 and 10.6, respectively, to establish which
requires adjustment or recalibration.
10.4.2 Monitor the performance of the electronic
components together with the mechanical functionality
of the probe station with a moving range control chart
of the oxide capacitance, C
ox
, of an oxidized reference
wafer.
10.4.2.1 Determine C
ox
of an oxidized reference wafer
in accordance with SEMI MF1153, with the mercury
probe serving as the metal capacitor electrode.
10.4.2.2 If out-of-control conditions are noted, or if the
control limits are wider than is desirable for the
application, and the electronics are known to be
performing as expected, inspect the mercury capillary
carefully for dirt or damage. If it is dirty, clean it
thoroughly and refill with clean mercury. If it appears
to be damaged, repair or replace the capillary and refill
with clean mercury.
10.4.3 Monitor the overall system performance with
moving range control charts of net carrier density of the
reference wafers (see Sections 8.4 and 10.3) or test
specimens used as controls.
10.4.3.1 Determine the net carrier density of these
specimens in accordance with this test method. Two or
more controls are required to ensure that the control
wafers are stable; if one control becomes unstable,
retreat the surface (see Related Information 1) and
redetermine its net carrier density. If this does not
bring the specimen into control, discard it and replace
with a fresh control.
10.4.3.2 If system out-of-control conditions are noted,
or if the control limits are wider than is desirable for the
application, and they cannot be attributed to control
wafer instability, mechanical malfunctions (Section
10.4.2) or electronic malfunction (Section 10.4.1),
redetermine C
comp
(see Section 10.2) and the effective
area of the mercury probe contact (see Section 10.3).
10.5 Capacitance Meter Adjustment and Verification
10.5.1 Connect to the capacitance bridge or meter
shielded cables of a length suitable for measuring the
precision capacitors. Zero the capacitance bridge or
meter with the cables attached only to the bridge or
meter, not to a precision capacitor.