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SEMI MF1392-1103 © SEMI 2003 9 ∑∑ == = 5 11 5 1 j n i ij avg 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 (…
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.
SEMI MF1392-1103 © SEMI 2003 10
10.5.2 Connect the cables to one of the precision
capacitors. Measure and record the capacitance in pF to
three significant figures. Disconnect the capacitor.
Repeat for the other precision capacitors.
10.5.3 If the measured capacitance values are not
within 1% of the known values, make necessary
adjustments consistent with the appropriate instrument
instruction manuals to bring the instrument to within
specifications before proceeding with measurements of
test specimens.
10.6 Voltmeter Verification
10.6.1 Measure the precision voltage source at five or
more voltages within the range from 0 to ± 200 V,
inclusive to verify that the digital voltmeter is within
specification over this range.
10.6.2 If any measured voltage value is not within
0.5% of the known value, make necessary adjustments
consistent with the appropriate instrument instruction
manuals to bring the instrument to within specifications
before proceeding with measurements of test
specimens.
11 Procedure
11.1 Refer to Related Information 2 for suggested data
sheet formats for recording the data if the data
collection and calculations are carried out manually or
off-line.
NOTE 14: The following procedures are given in sufficient
detail for manual data collection and calculations to be carried
out. However, it is strongly recommended that both data
collection and analysis be carried out using computer con-
trolled equipment, with data storage and display capabilities.
In such cases, the procedures and algorithms employed must
be equivalent to those given in this test method.
11.2 If not known, determine the conductivity type and
surface orientation of the test wafers in accordance with
SEMI MF42 and SEMI MF26, respectively.
11.3 Estimate the reverse bias voltage range over
which the measurements are to be made based on the
curve in Figure 1, an estimate of the value for the
dopant density of the test specimen, and the range of
depth over which the profile is desired. Do not exceed
200 V or 80% of the breakdown voltage, whichever is
lower.
11.4 Determination of the Series Resistance of the
Diode Circuit — Determine the series resistance of the
diode circuit in one of the following ways:
11.4.1 Measurement of Forward Resistance — If the
capacitance bridge or meter measures capacitance only,
measure the diode forward resistance, R, in ohms, at 1
V forward bias as follows:
11.4.1.1 Connect the curve tracer to the mercury probe
column and to the return contact of the probe fixture.
11.4.1.2 Place the wafer to be tested onto the mercury
probe fixture set up in the configuration used to
determine C
comp
(see Section 10.3) in such a way that
the mercury column(s) will contact the polished or
epitaxial surface of the wafer. If the back-surface-
return-contact configuration is used, make a suitable
return contact to the substrate or back surface of the
wafer.
11.4.1.3 Bring the mercury column(s) into contact with
the surface of the wafer.
11.4.1.4 Measure and record as I
1
the current through
the diode at 0.9 V forward bias, in mA, to two
significant figures.
11.4.1.5 Measure and record as I
2
the current through
the diode at 1.1 V forward bias, in mA, to two
significant figures.
11.4.1.6 Calculate the forward resistance, R, in kΩ, as
follows:
12
2.0
II
R
−
=
(6)
where:
I
1
= current at 0.9 V forward bias, mA, and
I
2
= current at 1.1 V forward bias, mA.
11.4.1.7 If the forward resistance is 1 kΩ or less,
proceed to Section 11.5. If the forward resistance
exceeds 1 kΩ, improve the return contact, and repeat
Section 11.4.1.
NOTE 15: The diode forward resistance at 1 V, R,
determined in this way is a measure of the total series
resistance of the test circuit that includes the bulk, cable, and
return contact resistances.
11.4.2 Direct Determination of Equivalent Series
Resistance — For capacitance meters or bridges
capable of measurement of phase angle, conductance,
or total impedance, determine the equivalent series
resistance directly as follows:
11.4.2.1 Place the wafer to be tested onto the mercury
probe fixture set up in the configuration used to
determine C
comp
(see Section 10.3) in such a way that
the mercury column(s) are just above but do not contact
the polished or epitaxial surface of the wafer. If the
back-surface-return-contact configuration is used, make
a suitable return contact to the substrate or back surface
of the wafer.
11.4.2.2 Zero the meter in accordance with the manu-
facturer' s instructions.