semi合集-English.pdf - 第7368页

SEMI MF1392-1103 © SEMI 2003 12 chemical process (see Related Inform ation 1), and repeat the procedure be ginning with Section 11.4. 11.5.7 When the Scho ttky contact is satisfactory, disconnect the curve tracer or othe…

100%1 / 7923
SEMI MF1392-1103 © SEMI 2003 11
11.4.2.3 Bring the mercury column(s) into contact with
the surface of the wafer.
11.4.2.4 Set the bias to a nominal value of 0 V, and
read the capacitance, C, and the phase angle,
θ
, or the
conductance, G
m
.
11.4.2.5 If the phase angle and capacitance were
measured, calculate the series resistance, R
s
, in kΩ, as
follows:
θπ
tan2
10
3
Cf
R
s
=
(7)
where:
θ
= measured phase angle, degrees,
C = measured capacitance, pF, and
f = measurement frequency, MHz.
11.4.2.6 If the capacitance and conductance were
measured, calculate the series resistance, R
s
, in kΩ, and
the phase angle,
θ
, in degrees, as follows:
232
)102(
−
×+
=
CfG
G
R
m
m
s
π
(8)
and
−=
−
CRf
s
π
θ
2
10
tan
3
1
(9)
where:
G
m
= measured conductance, S,
f = measurement frequency, MHz, and
C = measured capacitance, pF.
11.4.2.7 If the series resistance is 1 kΩ or less and the
phase angle is between −87° and −90° , proceed to
Section 11.5. If either of these conditions is not met,
improve the return contact, and repeat Section 11.4.2.
If improvement of the return contact decreases the
series resistance but does not bring the phase angle
within the desired range, qualify the Schottky contact in
accordance with Section 11.5; when the Schottky
contact is satisfactory, repeat Section 11.4.2 to verify
that the phase angle is within the desired range.
11.5 Qualification of Schottky Contact — To qualify
the Schottky contact, determine the reverse current
characteristics of the mercury probe contact as follows:
11.5.1 If a curve tracer was used to determine the diode
forward resistance, do not disconnect it. If the series
resistance was measured directly, connect a curve tracer
or other apparatus for monitoring the current-voltage
characteristics of the mercury probe contact (see
Section 7.7). Apply a reverse bias voltage of about 1 V
to the mercury column. Warning: Avoid physical
contact with the probe fixture when bias is applied.
11.5.2 Measure and record this voltage as V
1
, and
measure the current that exists at this voltage.
Calculate the current density at this value of reverse
bias voltage, J
r1
, in mA·cm
−2
, as follows:
eff
r
r
A
I
J
1
1
= (10)
where:
I
r1
= current, mA, at the reverse bias voltage V
1
, and
A
eff
= mercury probe contact area, cm
2
, see Section
10.3.4.
11.5.3 Increase the magnitude of the reverse voltage at
intervals until the maximum reverse bias voltage that is
to be applied during the test (see Section 11.3) is
reached. Measure each current and calculate the
current density, J
r
, at each value of voltage. In
addition, calculate the rate of increase of the reverse
current density with voltage, in mA·V
−1
·cm
−2
, as
follows:
ii
riir
r
VV
JJ
V
J
−
−
=
∆
∆
+
+
1
)1(
(11)
where:
∆
J
r
/
∆
V
= rate of increase of the reverse current
density with voltage,
J
ri
= current density at voltage, V
i
, and
J
r(i+1)
= current density at voltage, V
i+ 1
.
11.5.4 Also observe whether or not the reverse current
density is stable with time.
11.5.5 If the reverse current density, J
r
, equals or
exceeds 3 mA/cm
2
at any voltage up to the maximum
value applied, first determine if this is due to carrier
density variations in the structure. In this case, reduce
the maximum applied reverse bias voltage to be used in
the test to the highest value for which the reverse
current density is less than 3 mA·cm
−2
.
NOTE 16: If the depletion depth extends to a region with a
rapidly increasing doping density, the breakdown voltage may
be significantly lower than estimated from the expected net
carrier density. For example, if the test specimen consists of a
lightly doped epitaxial layer on a heavily doped substrate and
if the profile extends deeper into the structure than the flat
region of the layer, the breakdown voltage would be lower
than that estimated from the expected net carrier density in the
flat region.
11.5.6 Otherwise, if J
r
> 3 mA·cm
−2
, or if ∆J
r
/∆V > 0.3
mA·V
−1
·cm
−2
, or if the reverse current is unstable in
time, treat the wafer surface with an acceptable
SEMI MF1392-1103 © SEMI 2003 12
chemical process (see Related Information 1), and
repeat the procedure beginning with Section 11.4.
11.5.7 When the Schottky contact is satisfactory,
disconnect the curve tracer or other apparatus for
monitoring the current-voltage characteristics of the
mercury probe contact.
NOTE 17: To ensure the greatest possible accuracy of the
measurement, monitor the attributes of the Schottky contact
during the collection of data (Section 11.6) and discontinue
data collection if any of the conditions in Section 11.5.6 are
violated.
11.6 Collection of Data — Measure a series of
capacitance-voltage pairs from which the net carrier
density profile can be calculated.
11.6.1 Disconnect the curve tracer from the mercury
probe fixture if one was used to determine the diode
current density.
11.6.2 Connect the capacitance bridge or meter to the
mercury probe fixture in accordance with the manu
-
facturer' s instructions and zero the capacitance bridge
or meter, if required.
11.6.3 Bring the mercury column(s) into contact with
the test wafer surface, and apply a nominal 1 V reverse
bias between the mercury probe contact and the return
contact (Warning—see Section 11.5.1).
11.6.4 Read and record the capacitance and applied
voltage, each to three or more significant figures, as C
1
and V
1
, respectively. Use a data table format
appropriate to the calculation method to be selected. In
all cases, record the voltages as positive numbers even
though reverse biases are involved.
11.6.5 Adjust the bias voltage to obtain a new value of
capacitance that is up to 5% lower than the previous
value. Read and record the capacitance and applied
voltage, each to three or more significant figures, as C
2
and V
2
, respectively (Warning—see Section 11.5.1).
11.6.6 Repeat Section 11.6.5, adjusting the voltage for
a decrease in capacitance such that the ratio of C
i+1
to
C
i
is approximately equal to C
2
/C
1
at each step, until the
maximum applied reverse bias voltage (see Section
11.3) is reached. Discontinue the measurement before
the maximum applied reverse bias voltage is reached if
the capacitance values start to increase with increased
reverse bias. Obtain a minimum of n capacitance-
voltage pairs, where n is sufficient to calculate at least
five values of net carrier density, N
i
, and depth, W
i
(see
Note 9).
11.7 Shut-Down Cycle — When the measurement
sequence is complete, reduce the reverse bias voltage to
0 V, disengage the mercury column(s) from the wafer
surface, and remove the test wafer from the probe
fixture.
12 Calculations
12.1 Subtract the compensation capacitance, C
comp
,
from each measured capacitance, C
′
i
, to obtain the
corrected capacitance, C
′
i
:
compii
CCC −=
′
(12)
Record these values of C
′
i
.
12.2 Calculate the net carrier density profile by the
Incremental Method (see Section 12.3) or by the Curve-
Fitting Method (see Section 12.4).
12.3 Incremental Method:
9
12.3.1 Calculate the average depletion depth
corresponding to each interval as follows:
12.3.1.1 Calculate and record the dimensionless
quantity S
i
for each value of i from 1 to n
−
k as follows:
′
′
+
+
=
+
+
ki
i
i
ki
i
C
C
V
V
S
ln
6.0
6.0
ln
(13)
where:
V
i
= i
th
recorded voltage, V,
V
i+k
= (i + k)
th
recorded voltage, V,
C
′
i
= i
th
corrected capacitance, pF,
C
′
i+k
= (i + k)
th
corrected capacitance, pF,
k = whole number such that C
i+k
is between 80 and
85% of C
i
, and
n = number of measured capacitance-voltage pairs.
12.3.1.2 Calculate and record the depth, W
i
′
, in µm,
corresponding to each corrected capacitance, C
i
′
, as
follows:
i
eff
i
C
A
W
′
=
′
10359 (14)
where:
A
eff
= mercury probe contact area, cm
2
, as determined
in 10.4.4, and
C
′
i
= the i
th
corrected capacitance, pF.
9 Niehaus, W. C., van Gelder, W., Jones, T. O., and Langer, P.,
“Variations of a Basic Capacitance-Voltage Technique for
Determination of Impurity Profiles in Semiconductors,”
Semiconductor Device Processing , NBS Spec. Publ. 337, (U.S.
National Institute of Standards and Technology, Washington, DC,
1970) pp. 266–268.
SEMI MF1392-1103 © SEMI 2003 13
12.3.1.3 Calculate and record the average depth, W
i
, in
µm, for each value of i from 1 to n − k as follows:
()()
()
1
1
−
⋅
′
−
′
′
−
′
=
+
+
iikii
S
i
S
ki
i
SWWS
WW
W
ii
(15)
where:
W
′
i
=
i
th
calculated depth, µm,
W
′
i+k
=
(i + k)
th
calculated depth, µm,
S
I
= i
th
dimensionless value calculated in Section
12.3.1.1,
k = whole number such that C
i+k
is between 80 and
85% of C
i
, and
n = number of measured capacitance-voltage pairs.
12.3.2 Calculate and record the net carrier density, N
i
,
in cm
−3
, corresponding to each average depth, W
i
, as
follows:
()
ikii
iki
i
WWW
VV
N
′
−
′
−
×=
+
+
14
10466.6
(16)
where:
V
i
= i
th
recorded voltage, V,
V
′
i+k
= (i + k)
th
recorded voltage, V,
W
i
′
=
i
th
calculated depth, µm,
W
′
i+k
=
(i + k)
th
calculated depth, µm, and
k = whole number such that C
i+k
is between 80 and
85% of C
i
.
12.3.3 Proceed to Section 12.5.
12.4 Curve-Fitting Method
12.4.1 Fit a polynomial of the following form
10
to the
capacitance-voltage pairs, C
i
− V
i
:
k
iki
i
fi
VaVa
Vaa
C
′
′
+++++
++=
)6.0()6.0(
)6.0(
1
2
2
10
2
K
(17)
where:
k
′
= order of the polynomial, chosen so that it
represents the lowest-order fit for which
| (C
i
′ − C
fi
)/C
i
′| ≤ 0.01 for all values of i and
for which k
′
≤ 10 or n − 1, whichever is
smaller (see Note 18).
n = number of capacitance-voltage pairs
determined in the test,
C
fi
= i
th
value of capacitance, pF, calculated fro
m
the fit,
a
0
... a
k
= coefficients determined such that the quan-
tity (C
i
′ − C
fi
)
2
summed over all values of i
is minimized,
10 Daniel, C., and Wood, F. S., Fitting Equations to Data (Wiley-
Interscience, New York, NY) 1971, p. 19.
C
′
i
= i
th
corrected capacitance, pF, and
V
i
= i
th
recorded (positive) voltage, V.
NOTE 18: Failure to meet this condition for a low-order
polynomial (k
′
≤ 3) may be caused by a single outlier; in such
cases, the polynomial should be redetermined without this
datum. Failure to meet this condition may also suggest that
the method is inappropriate for analysis of the data set; in
such cases, use of the incremental method is preferred.
12.4.2 Record the values of C
fi
and a
0
, a
1
, ... a
k
′
.
12.4.3 Calculate and record D
i
, the derivative of the
polynomial for 1/C
fi
2
with respect to diode voltage at
the depth appropriate to the i
th
voltage-capacitance pair,
as follows:
1
21
)6.0()6.0(2
−
′
+
′
++++=
k
iii
VkVaaD K (18)
where the other symbols are defined following Eq. 15.
12.4.3.1 Calculate and record the depletion depth, W
i
,
in µm, and the net carrier density, N
i
, in cm
−3
,
corresponding to each capacitance-voltage pair as
follows:
fi
eff
i
C
A
W
10359= (19a)
and
ieff
i
DA
N
2
7
102050.1 ×
−= (19b)
where:
A
eff
= mercury probe contact area, cm
2
, as determined
in Section 10.3.4,
C
fi
= the i
th
calculated capacitance, pF, and
D
i
= the derivative of the polynomial for 1/C
fi
2
with
respect to diode voltage at the depth W
i
.
12.5 Determine the average net carrier density as
follows:
12.5.1 Take the number of individual values of net
carrier density to be averaged as the number of values
that fall within the flat zone of the epitaxial layer or
within the depth range of the specimen over which the
average net carrier density is desired. Record this
number as m; m may not exceed n − k if the incremental
method was used for the calculations or n if the curve-
fitting method was used for the calculations.
12.5.2 Calculate the average net carrier density, N
avg
, in
cm
−3
, as follows:
∑
=
=
m
i
iavg
N
m
N
1
1
(20)
where: