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SEMI M58-0704 © SEMI 2004 7 RELATED INFORMATION 1 BACKGROUND INFORMATION ON THE OPERATION OF A DIFFERENTIAL MOBILITY ANALYZER NOTICE: This relate d informat ion is not an offici al part of SEMI M58 and was derive d from …

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SEMI M58-0704 © SEMI 2004 6
Lab: Identification of deposition system used:
1
Contact Supplier/Model #
2
Address
System S/N
3
System S/W Revision
4
Phone
Date of Test
5
email Date of Last Previous Test
6
7
Characteristics of Suspensions Used for Test
8
u
B
ottle i
%FWHM
i
9
B
ottle A, Certified
nm ±
nm (1
σ
) or
10
nm ±
nm (1
σ
) or
11
nm ±
nm (1
σ
) or
12
Particles Deposited (
N
)
13
S
upplier
P
art No.
L
ot No.
14
Deposition System Diameters (nm)
B
ottle A
15
B
ottle A
B
ottle B
B
ottle
C
B
ottle A
B
ottle B
16
D
ay
nm nm nm nm
B
ottle
C
17
1
18
2
19
3
SSIS Data: Bottle C
20
4
21
5
22
M
ean
D
ay
nm nm %
23
s
D
ep
1
24
2
25
Dep System Sizing Corrections
3
26
M
ean
A
=
nm
4
27
s
D
epA
= 5
28
Cert
A
−
Mean
A
=
nm
M
ean
29
Std Dev
30
SSIS Data: Bottle A
31
Analysis
32
B
ottle A
B
ottle B
B
ottle
C
33
D
ay
nm nm %
D
ep Peak Uncertainty
34
1
F
WHM (SSIS)
35
2
P
eak (Dep System)
36
3
P
eak (Dep Sys Corrected)
37
4
P
eak (SSIS)
38
5
M
easured Count
39
M
ean
40
Std Dev
Compare Quantity with Limit
41
42
SSIS Data: Bottle B
Uncertainty Limit
43
F
WHM Limi
t
44
SSIS Peak
45
D
ay
nm nm %
SSIS Count
46
1
47
2
Interpretation of Results
48
3
B
ottle A
B
ottle B
B
ottle
C
49
4 Uncertainty
50
5
51
M
ean SSIS/Dep Peak Comp
52
Std Dev SSIS/Dep Count Comp
53
A B C D E F G H I J K
M
easured Pea
k
S
uspension
P
eak Diamete
r
B
ottle B
B
ottle
C
R
elative
F
WHM
Count
F
WHM
F
WHM on
Wafer
Quantity
L
imi
t
Count
R
elative
F
WHM
M
easured
Peak
F
WHM
on Wafer
3.0% (SEMI M52)
Count
5.0% (SEMI M52)
Dep Sys Corrected Peak (Info only)
Dep System Count (Info only)
M
easured
Peak
F
WHM
on Wafer
R
elative
F
WHM
Figure 1
Example of Data, Calculation, and Analysis Sheet for Test Procedure
SEMI M58-0704 © SEMI 2004 7
RELATED INFORMATION 1
BACKGROUND INFORMATION ON THE OPERATION OF A
DIFFERENTIAL MOBILITY ANALYZER
NOTICE: This related information is not an official part of SEMI M58 and was derived from information
developed during drafting of the standard. This related information was approved for publication by full letter ballot
procedures on April 22, 2004.
R1-1 Deposition systems include a nebulizer for
producing a PSL sphere aerosol by spraying and
evaporating a suspension of PSL spheres in high purity
water, a differential mobility analyzer (DMA) for
selecting a monodisperse fraction of the aerosol, and
then a chamber to electrostatically deposit the spheres
onto wafers. Here we focus on the DMA, which is used
for both isolating a monodisperse size fraction and for
sizing the particles. A brief description of the
instrumentation and methodology is given below; a
detailed description is given by Kinney et al.
3
R1-2 The particles leaving the nebulizer pass through a
bipolar charger that produces a charge distribution that
depends only on the size of the particles and not on
their initial charge. For 100 nm particles, about 45% of
the particles are uncharged, about 20% have + 1 electron
charge, another 20% have –1 electron charge, and much
smaller fractions have multiple charges. As illustrated
in Figure R1-1, the DMA consists of an inner
cylindrical rod connected to a variable high voltage dc
power supply and an outer annular tube connected to
ground. Clean sheath air flows through the axial
region, while the charged aerosol enters through an
axisymmetric opening along the outer cylinder. The
positively charged PSL spheres move radially towards
the center rod under the influence of the electric field.
Near the bottom of the classifying region, a fraction of
the air flow consisting of near-monodisperse aerosol
exits through a slit in the center rod. The quantity
measured by the DMA is the electrical mobility, Z
p,
defined as the velocity a particle attains under a unit
electric field. Knutson and Whitby
4
derived an expres-
sion for the average value of Z
p
for particles entering
the slit involving the peak electrode voltage, V, the
sheath air flow rate, Q
c
, the inner and outer radii of the
cylinders, r
1
and r
2
, and the length of the central
electrode down to the slit, L:
3 Kinney, P.D., Pui, D. Y. H., Mulholland, G. W., and Bryner, N.,
“Use of the Electrostatic Classification Method to Size 0.1 µm
SRM Particles − A Feasibility Study,” J. Res. Natl. Inst. Technol.,
96, 147−176 (1991).
4 Knutson, E. O., and Whitby, K. T. “Aerosol Classification by
Electric Mobility: Apparatus, Theory, and Applications,” J. Aer. Sci.
6: 443–451 (1975).
Monodisperse
Aerosol
Excess Ai
r
Charged
Aerosol
Clean
Air
High Voltage
Figure R1-1
Monodisperse Aerosol Selected in a Differential
Mobility Analyzer from a Polydisperse Aerosol
Based on the Size Dependence of the Electrical
Mobility
π
=
1
2
ln
2 r
r
VL
Q
Z
c
p
(R1-1)
R1-3 This equation is valid provided the sheath air
flow, Q
c
, is equal to the excess flow, Q
m
, leaving the
classifier. They derived an expression for the transfer
function, defined as the probability that a particle will
leave the sampling slit. The transfer function is of great
importance, because the size distribution of the aerosol
exiting the DMA is proportional to the convolution of
the transfer function with the particle size distribution
function. The transfer function has a triangular shape
with a peak value of 1. The ratio of the base of the
transfer function triangle in terms of voltage divided by
the peak voltage is predicted to be 2(Q
s
/Qc), where Q
s
is the flow of monodisperse aerosol.
R1-4 This ratio is also equal to the ratio of the full
width of the mobility distribution to the peak value.
For a flow ratio of 1 to 20, one finds that the full width
at half maximum of the peak mobility (FWHM) is
equal to 5% of the peak mobility. For 100 nm particle
SEMI M58-0704 © SEMI 2004 8
size, the corresponding FWHM in terms of particle
diameter is about 3%.
R1-5 The relationship between electrical mobility and
particle diameter, D
p
, is obtained by equating the
electric field force of a singly charged particle with the
Stokes friction force,
p
p
p
πµD
DCe
Z
3
)(
= (R1-2)
where
µ
is the dynamic viscosity of air, and e is the
electron charge. The Cunningham slip correction,
C(D
p
), corrects for the non-continuum gas behavior on
the motion of small particles.
R1-6 For increased accuracy, the DMA can be
calibrated using the NIST SRM
1963 (100 nm) PSL
spheres.
5
The voltage corresponding to the peak
particle concentration for the 100.7 nm SRM is
determined and then the peak voltage is determined for
the unknown. The electrical mobility of the 100.7 nm
SRM
, Z
SRM
,
is computed from Equation (R1-2) using
the
best available values for
the viscosity, Cunningham
slip correction, and the electron charge.
6
The mobility
of the unknown particle, Z
x
, is then computed based on
the voltage ratio and the mobility of the 100.7 nm SRM,
Z
SRM
:
SRM
x
SRM
x
Z
V
V
Z =
(R1-3)
The peak particle diameter is computed using Equation
(R1-2). Because the slip correction is a function of the
diameter, an iterative process is used. In cases where
samples have a broad size distribution, a correction
factor is used that is based on the instrument
convolution integral and involves the product of the
transfer function times, the charging probability, and
the size distribution (see Related Information 1 of
SEMI M53 for a further discussion of the effect of the
transfer function).
5 Donnelly, M. K., Mulholland, G. W., and Winchester, M. R.,
“NIST Calibration Facility for Sizing Spheres Suspended in Liquids,”
Characterization and Metrology for ULSI Technology (AIP, Mellville,
N. Y., 2003), pp. xxx−yyy..
6 Donnelly, M. K., and Mulholland, G. W., “Particle Size
Measurements for Spheres with Diameters of 50 nm to 400 nm,” U.S.
Department of Commerce, NISTIR 6935, National Institute of
Standards and Technology, Gaithersburg, November 2002.