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SEMI MF1723-1104 © SEMI 2004 10 13.3.3 Obtain value s for arsenic and alum inum concentrations from photoluminescence (SEMI MF1389) or FT-IR (SEMI MF1630 ) measurement and, if greater than detection limit, correct them b…

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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
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SEMI MF1723-1104 © SEMI 2004 11
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