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SEMI M58-0704 © SEMI 2004 9 RELATED INFORMATION 2 EXAMPLE OF A COMPLETED DA TA AND ANALYSIS SHEET NOTICE: This relate d informat ion is not an offici al part of SEMI M58 and was derive d from information developed d urin…

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

, is obtained by equating the

electric field force of a singly charged particle with the

Stokes friction force,

πµD

DCe

)(

= (R1-2)

where

is the dynamic viscosity of air, and e is the

electron charge. The Cunningham slip correction,

C(D

), 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.

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.

The mobility

of the unknown particle, Z

, is then computed based on

the voltage ratio and the mobility of the 100.7 nm SRM,

SRM

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.

SEMI M58-0704 © SEMI 2004 9

RELATED INFORMATION 2

EXAMPLE OF A COMPLETED DATA AND ANALYSIS SHEET

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.

R2-1 Figure R2-1 shows an example of a completed

data set. This example is the result of using a

spreadsheet that automates the calculations of Section

11. If such a spreadsheet is constructed, once the data

is input as described in Section 10 the results of the test

are found by spreadsheet calculation.

R2-2 In this example the results obtained indicate that

the deposition system is capable of meeting the

requirements of SEMI M52 for all three bottles. Note

that the test was done with an SSIS that was not

calibrated according to SEMI M53.

R2-3 The following sections detail the spreadsheet

example in Figure R2-1 in order to allow it to be easily

duplicated for use with this test method. Information in

the shaded cells is entered in accordance with the

procedures given in Section 10.

R2-3.1 At the top of the spreadsheet, the entries in

rows 1 through 13 are obvious except for those in cells

H10 through H12. Here, the uncertainties on the bottle

are converted to %. In this example, Bottle C does not

have a peak diameter uncertainty given. This is true for

many older bottles where diameters were given in terms

of mean, rather than peak, diameters. To avoid

returning an error result, the formula for the percentage

is =IF(SUM(Ei>0,Ei/Ci," not available" ), where i = 10,

11, or 12 for Bottle A, B, or C, respectively. The cell is

formatted for % with one decimal place.

R2-3.2 In the section on Deposition System Diameters

and the three SSIS Data sections the inputs are taken

directly from the instrumentation as directed in Section

10. As an example, the equation to compute mean in

B23 is: =AVERAGE(B18:B22). The equation to

compute s

Dep

in B24 is: =STDEV(B18:B22)/B23 and is

formatted for % with one decimal place.

R2-3.3 The portion of the data sheet labeled “Dep

System Sizing Corrections” starting at A26 uses all

Bottle A results to correct any offset in the mean

diameter found by deposition system and to evaluate

the pooled relative standard deviation for system

repeatability. Mean

is given by: =(B23+ E23)/2. s

DepA

is given by: =SQRT((B24^ 2+ E24^ 2)/2), and includes

day long contributions from system stability. The bias

correction Cert

−Mean

is given by: =C10-C27.

R2-3.4 Analysis

R2-3.4.1 The value for Dep Peak Uncertainty (row 34)

for Bottle A (or U

relA

) is given by:

=2*SQRT(C28^ 2+ H10^ 2). This combines the

uncertainty in the certified bottle with the uncertainty in

the deposition system at the diameter of Bottle A. The

factor of 2 is needed for expanded uncertainty.

R2-3.4.2 The expanded uncertainty equations for

Bottles B and C are slightly different and are the

combination of the relative uncertainty in the certified

value A (as a percent) and the relative uncertainty of the

deposition system at the broader distribution of

diameter B or C. The equation for the expanded

relative combined standard uncertainty of the

depositions of Bottle B is: =2*SQRT(C24^ 2+ H10^ 2),

and of those of Bottle C is: =2*SQRT(D24^ 2+ H10^ 2).

As noted in the standard (see 11.5 and 11.6), the first

term of this equation accounts for the variation due to

the uncertainty in the finding of the peak diameter of

Bottle B or C by the DMA and the second term

accounts for the uncertainty in the certified peak

diameter of the suspension in Bottle A, which is used to

correct the peak diameter of Bottle B or C as found by

the DMA.

R2-3.4.3 The FWHM (SSIS) values for Bottles A, B,

and C (row 35) are taken directly from D40, D52 and

J29, respectively.

R2-3.4.4 The uncorrected Peak (Dep System)

diameters for Bottles A, B, and C (row 36) are taken

directly from C27, C23, and D23 respectively.

R2-3.4.5 The corrections made in the next row (37)

employ the percentage error found by comparing the

certified peak diameter of Bottle A to the mean peak

diameter found by the deposition system. For Bottle A

this is: =C27+ C29. For Bottle B it is:

=C23*(1+ (C29/C10), and for Bottle C it is:

=D23*(1+ (C29/C10).

R2-3.4.6 The Peak (SSIS) values Bottles A, B, and C

(row 38) are taken directly from B40, B52, and H29,

respectively.

R2-3.4.7 The Measured Counts (row 39) are taken

directly from the SSIS data averages, E40, E52, or K29,

for Bottles A, B, and C, respectively.

R2-3.5 Interpretation of Results

R2-3.5.1 A conditional command is used to

automatically grade results for Uncertainty and FWHM.

R2-3.5.1.1 The equation for Bottle B Uncertainty (row

50) is: =IF(J34>0.03," Fail" ," Pass" ), and the others are

similar.

R2-3.5.1.2 The equation for Bottle B FWHM (row 51)

is =IF(J35>0.05," Fail" ," Pass" ), and the others are

similar.

R2-3.5.2 These are the only two requirements of SEMI

M52 verified by this test method. Two additional

comparisons are made for information only:

R2-3.5.2.1 The SSIS Peak diameter is compared with

the corrected deposition system peak diameter (row 52).

For Bottle B the equation is =B52/J37, and the others

are similar.

R2-3.5.3 Finally, the SSIS mean count is compared

with the count from the deposition system (row 53).

The equation for Bottle B is =E52/$ D$ 13, and the

others are similar.