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SEMI MF1723-1104 © SEMI 2004 9 13 Calculation 13.1 After m easurement of th e acceptor, donor, and carbon impurities in the cut wafers, relate these values to the levels in the p olysilicon by making the fo llowing calcu…

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SEMI MF1723-1104 © SEMI 2004 8
of zone lengths required to reach the flat portion of the
axial concentration profile determines the length of
ingot that must be grown to achieve an accurate carbon
value. Figure 4 shows an axial doping profile for
carbon where a 20-mm diameter sample core was zoned
to a 10-mm diameter ingot with a zone length of 15
mm. The effective segregation coefficient was 0.175.
In this case, growing the ingot to a zone length of 12
ensures that the maximum amount of carbon has been
incorporated into the ingot. Sampling the ingot for
carbon at a zone length of 12 gives reproducible carbon
values that accurately reflect the amount of carbon in
the polysilicon sample.
12.6.2.5 Slice Locations — Once the concentration
gradient for each element for the individual zoner
conditions is established, establish sampling rules for
each element. Boron, with a high segregation
coefficient, has a relatively flat profile. A wafer taken
from the ingot at 6 zone lengths has a value nearly
equal to that taken at 12 zone lengths. If one value is
significantly higher than the other, a contamination has
probably occurred, and the analysis should be repeated.
Phosphorus, with a smaller segregation coefficient, has
different values at the 6- and 12-zone length points.
The midpoint should have a value about 10 to 15%
lower than the end point. If not, contamination is
indicated and the analysis should be repeated. Carbon,
with a very small segregation coefficient, varies greatly
between the 6- and 12-zone length points. If not,
contamination is indicated and the analysis should be
repeated. Carbon value at the maximum ingot length
should be reported.
12.6.3 Perpendicular Cores — For perpendicular cores
(see Section 10.2.2), single crystal ingot size is about
14-mm diameter with a length determined by the poly
rod diameter, about 100 mm. For these ingots,
sampling for acceptor-donor content is different than
the carbon sampling, due to the small segregation
coefficient for carbon. Sampling points are selected
according to the following:
12.6.3.1 Resistivity Profile — Determine the
distribution of acceptor/donor impurities along the
length of the ingot by plotting a resistivity profile of the
ingot at 10-mm intervals, in accordance with SEMI
MF397. Also profile conductivity type, in accordance
with SEMI MF42, at 10-mm intervals. Due to the
segregation effects discussed in Section 12.6.2.1,
characteristic purity of the filament, and other
interferences discussed in Section 3, the resistivity
profile will differ between laboratories. A typical
resistivity/type profile is established after repeated runs
on control rods and production samples. Significant in
the resistivity profile indicates point contamination or
nonuniformity of the deposition layer.
12.6.3.2 Slice Locations — Establish sampling rules
for each element based on the resistivity/type profile.
The single crystal ingot length is correlated to the
polysilicon rod diameter; take a slice at the
representative midpoint between the filament and the
outer skin of the polysilicon rod. Analyze this wafer
for acceptor/donor values in accordance with SEMI
MF1389 or SEMI MF1630. For the cross section of a
polysilicon rod, these values represent the R/2 location.
If the resistivity/type profile has significant variation
from the standard profile, other locations may be
sampled to determine the distribution of each impurity.
Repeat the analysis for ingots with significant variation
suggesting point contamination.
Figure 4
Axial Doping Profile for Carbon
12.6.3.3 Carbon Analysis — Since accurate carbon
values can not be obtained on short ingot lengths,
perform the analysis on polysilicon sections that have
been annealed.
6
Take a second perpendicular
polysilicon core sample and anneal it at approximately
1360°C for 2 h. Take two 2-mm thick slices for the
carbon measurement in accordance with SEMI
MF1391. Take one sample from the point
representative of the midpoint of the growth layer and
the other sample at the point representative of the
filament location. If desired, sample other locations for
measurement of radial distribution.
6 Hwang, L. L., Bucci, J., McCormick, J. R., “Measurement of Car-
bon Concentration in Polysilicon Using FTIR,” J. Electrochem. Soc.
138, 576-581 (1991).
SEMI MF1723-1104 © SEMI 2004 9
13 Calculation
13.1 After measurement of the acceptor, donor, and
carbon impurities in the cut wafers, relate these values
to the levels in the polysilicon by making the following
calculations.
13.2 Parallel Cores — For sampling parallel cores (see
Section 10.2.1) in cases where the filament may be
doped or have a different composition than the
deposition layer, make the following calculation in
order to determine values for the total rod product:
t
LDftff
TRP
A
CAACA
C
..
)()(
(3)
where:
C
TRP
= total rod product concentration of impurity, in
p
pba for donor and acceptor, and in ppma fo
r
carbon,
A
f
= area of filament, in cm
2
,
C
f
= concentration of impurity in the filament, in
p
pba for donor and acceptor, and in ppma fo
r
carbon,
A
t
= area of polysilicon rod, in cm
2
, and
C
D.L.
= concentration of impurity in deposition layer,
in ppba for donor and acceptor, and in ppma
for carbon.
13.2.1 This calculation assumes that the deposition
layer is uniform across the diameter of the polysilicon
rod. Verify this assumption by taking sufficient core
samples to cover the entire deposition layer.
13.3
Perpendicular Cores — For sampling
perpendicular cores (see Section 10.2.2) where ingots
have been grown as in Section 12.6.3, make the
following calculation in order to determine values for
the total rod product.
13.3.1
Correlate the single crystal ingot length to the
polysilicon rod cross section as shown in Figure 5. A
zone length is related to a cross section area. Boron,
with a large segregation coefficient, is assumed to have
an even distribution throughout the entire cross section.
Phosphorus, with a smaller segregation coefficient,
needs to be corrected for segregation factor for each
zone length across the cross section. Determine the
effective segregation coefficient for phosphorus, based
on repeated measurements of control rods for a specific
sample diameter, coil design, and pull rate.
NOTE 3: At one laboratory, segregation factors, based on an
effective segregation factor of 0.5, were calculated for the
zone lengths of Figure 5 as shown in Table 1.
Figure 5
Polisilicon Rod Cross Section
Table 1 Example of Phosphorus Segregation
Factors
Zone Length Segregation Factor
1 0.697
2 0.816
3 0.888
4 0.932
5 0.959
6 0.975
7 0.985
8 0.991
13.3.2 Use spectrophotometric values for boron
concentration (see SEMI MF1389 or SEMI MF1630)
directly in the following formula to calculate the total
boron concentration in the total rod product with no
correction for segregation:
A
f
2A1A
AfCf2C2A1C1A
C
VAC
K
K
(4)
where:
C
VAC
= volume averaged concentration,
A1,
A2,
Af
= corresponding area of poly rod cross section (see
Figure 5), and
C1,
C2,
Cf
= concentration of impurity at corresponding area,
corrected for segregation factor, where
necessary.
SEMI MF1723-1104 © SEMI 2004 10
13.3.3 Obtain values for arsenic and aluminum
concentrations from photoluminescence (SEMI
MF1389) or FT-IR (SEMI MF1630) measurement and,
if greater than detection limit, correct them by a
measured segregation coefficient. Then calculate the
concentrations in the total rod product from Equation 4
using the corrected concentrations at each location in
the rod.
13.3.4
Obtain the bulk phosphorus value by photolumi-
nescence measurement at the midpoint between the
filament and the outer skin.
13.3.5
Calculate the phosphorus concentrations from
each point of the resistivity profile measurement of
12.6.3.1 using the following equation:
As-AlB
85
P
ρ
(5)
where:
P
= calculated phosphorus concentration at the desired
point, in ppba,
=
measured resistivity at the desired point, in ·cm,
B = measured boron concentration at the desired point,
in ppba,
Al = measured aluminum concentration at the desired
point, in ppba, and
As = measured arsenic concentration at the desired point,
in ppba.
13.3.5.1 This equation assumes that the conversion
factor for phosphorus is approximately 85 in the 100 to
5000 ·cm resistivity range, as indicated in SEMI
MF723. Take the boron, arsenic, and aluminum from
the photoluminescence or FT-IR data (see Sections
13.3.2 and 13.3.3). Use these values and resistivity data
to calculate the P value for use in Equation 4 to obtain
the volume averaged calculation of phosphorus.
13.3.6
Carbon Calculation — Calculate carbon
values, analyzed as described in 12.6.3.3, according to
the procedure described in 13.2.
14 Precision and Bias
14.1 In Section 11, the use of control rod samples to
monitor was discussed. Data was collected for 156
control rods, as discussed in Section 11 for monitoring
interfering contamination levels in the sample prepara-
tion, etch procedure, and zoner furnace. The rods were
zoned in three different growth furnaces, over a 1-year
period. All samples were etched by the same
procedure, using freshly prepared acid for each etch
bath. Boron and phosphorus values were measured by
photoluminescence spectroscopy. Carbon values were
measured by cryogenic FTIR spectroscopy. Boron was
measured at 6 zone lengths of the ingot, phosphorus at
12 zone lengths, and carbon at 12 zone lengths. Results
are shown in Table 2. Precision for the boron and
phosphorus measurement, as two sigma, is stated in
SEMI MF1389 as 0.002 ppba. Precision for the carbon
measurement for SEMI MF1391 is stated as 0.02 ppma.
Table 2 Control Rod Analysis Using Three Zoners
Zoner 1 Zoner 2 Zoner 3
Avg.
Std.
Dev.
Avg.
Std.
Dev.
Avg.
Std.
Dev.
Phos-
phorus
(ppba)
0.011 0.007 0.010 0.010 0.010 0.004
Boron
(ppba)
0.008 0.006 0.006 0.006 0.009 0.006
Carbon
(ppma)
0.06 0.03 0.05 0.05 0.06 0.03
14.2 To compare sample preparation, etching
techniques, and zoning techniques between different
laboratories, polysilicon rod sections were cut from one
large polysilicon rod and the sections sent to three
different laboratories. Following the procedures
outlined in this practice, each laboratory prepared,
etched, and zoned its own samples, using different
diameters. Each laboratory zoned the ingots in one pass
in argon, and then prepared the samples for
photoluminescence analysis. Data is shown in Table 3.
Table 3 Comparison of Zoned Ingots
Boron (ppba) Phosphorus (ppba)
Laboratory A 0.008 0.008
Laboratory B 0.007 0.010
Laboratory C 0.012 0.013
15 Keywords
15.1 contaminants; float-zone crystal growth; impuri-
ties; polycrystalline silicon; polysilicon evaluation;
segregation coefficient; single crystal silicon
NOTICE: SEMI makes no warranties or
representations as to the suitability of the standards set
forth herein for any particular application. The
determination of the suitability of the standard is solely
the responsibility of the user. Users are cautioned to
refer to manufacturer's instructions, product labels,
product data sheets, and other relevant literature,
respecting any materials or equipment mentioned
herein. These standards are subject to change without
notice.