semi合集-English.pdf - 第243页
SEMI E35-0305 © SEMI 1995, 2005 12 APPENDIX 1 METHODOLOGY FOR DE TERMINING ALPHA A ND BETA ERRORS NOTICE : The material in this appendix is an official part of SEMI E35 and was approved by full letter ballot procedures o…
SEMI E35-0305 © SEMI 1995, 2005 11
Category (k) Cost Element (m) Description Method
Labor
Engineering Costs of the engineering labor
required to support the equipment
set needed to meet the wafer start
requirements of the equipment
user.
Calculate the number of engineering labor hours
required based on equipment and manufacturing
specifications. Multiply the actual burdened costs
for labor-hours of effort by the total number of
hours for equipment purchaser’s engineers.
Labor
Support Services Costs of the support service labor
required to support operations and
engineering.
Calculate the number of support service labor hours
required. Multiply the actual burdened costs for
labor-hours of effort by the total number of hours
for equipment purchaser’s support service
personnel.
#1
The cost of monitor units includes both their initial acquisition cost and any initial preparation or reprocessing costs, if applicable. Preparation
and reprocessing costs may be calculated by summing the COOs from separate COO analyses of each of the preparation and reprocessing steps
performed.
Table 3 Elements of Recurring Scrap Cost
Category Cost Element Description Method
Scrap Equipment Yield
(EY) Loss
Costs of units lost, broken, or
irreversibly misprocessed by the
piece of equipment.
Calculate the EY Loss as the fraction of units lost,
broken, or irreversibly misprocessed by the piece of
equipment to the total number of units through the
piece of equipment (i.e., 1-EY). Multiply EY Loss
by the total number of units started through the
piece of equipment and by the actual total costs
invested in a unit at that step in the process (e.g.,
sum of initial unit starting material cost and COOs
for all prior process steps).
Scrap Defect Limited
Yield (DLY) Loss
Costs of units lost due to
electrical or inspection rejects
due to defects caused by the
piece of equipment.
Calculate the DLY Loss as the fraction of units lost
due to electrical or inspection rejects due to defects
caused by the piece of equipment (i.e., 1-DY). For
wafers, DY may be calculated using a modified
Seed’s formula:
1
DY = (10)
1 + (AA
D
P)
where AA is the active area of the device, D is the
defect density, and P is the probability that a defect
caused by the piece of equipment will be fatal.
Multiply DLY Loss by the total number of units
started through the piece of equipment and by the
actual total costs invested in a unit at that step in the
process where it is lost (e.g., sum of initial unit
starting material cost and COOs for all prior process
steps to the end of the process where it is tested).
Scrap Parametric Limited
Yield (PLY) Loss
Costs of units lost due to
electrical or inspection rejects
due to unit operating parameters
being outside the required range
caused by the piece of
equipment.
Calculate the PLY Loss as the fraction of units lost
(i.e., 1-PY). Multiply PLY Loss by total number of
units started through the piece of equipment and by
actual total costs invested in a unit at that step in the
process where it is lost (e.g., sum of initial unit
starting material cost and COOs for all prior process
steps to the end of the process where it is tested).
#1
The cost of cleanroom space per unit area of effective usable production space includes both the fixed and recurring operations costs as
determined by a separate COO analysis outside the scope of this document.
SEMI E35-0305 © SEMI 1995, 2005 12
APPENDIX 1
METHODOLOGY FOR DETERMINING ALPHA AND BETA ERRORS
NOTICE: The material in this appendix is an official part of SEMI E35 and was approved by full letter ballot
procedures on December 10, 2004.
A1-1 Purpose
A1-1.1 In silicon manufacturing product disposition is typically contingent on metrology equipment output. For
example, a unit may be shipped, scrapped, or reworked based on information from one or more measured output
characteristics.
A1-1.2 This appendix provides a standard methodology to include the cost due to misclassification of product
because of measurement variability and bias during testing of the product for conformance to a specification.
A1-1.3 This appendix is also intended to be useful for pre-purchase evaluation of pieces of measurement equipment
with different P/T ratios. It is also intended to be useful when comparing the operation of a single measurement
instrument in different throughput modes where P/T ratio changes with the throughput mode utilized or other
equipment setup factors. This appendix can help users select the optimum cost solution based on their specific
process capability and requirements.
A1-2 Scope
A1-2.1 This appendix covers a methodology to determine the alpha and beta probabilities associated with
misclassification of product due to variability and bias of measurement equipment. Alpha probability (α) is
associated with failing units that conform to specifications. Beta probability (β) is associated with passing units that
do not conform to specifications.
A1-2.2 This appendix can be applied to make relative misclassification cost comparisons as part of a COO analysis
between two or more measurement gauges operating under conditions specified by the user. These conditions may
include any aspects of the measurement system affecting the measurement results directly or indirectly (e.g.,
ambient conditions, throughput, recipe). This appendix can also be used to compare the relative costs of a single
instrument under different operating conditions.
A1-2.2.1 A measurement gauge is defined by a specific realization of systems and subsystems required to make
measurements. Gauges that differ in at least one system or subsystem may be considered different for the purpose
of comparison.
A1-2.3 This appendix can be applied to any piece of metrology equipment or to the metrology portion of any piece
of equipment that includes metrology.
A1-2.4 This appendix covers the case in which the piece of metrology equipment is used to make binary decisions
about the item being measured, that is, only two outcomes are possible (e.g., pass/fail, go/no-go, ship/scrap).
Models for decisions with more than two outcomes, such as the binning of data, are beyond the scope of this
Appendix.
A1-2.5 To apply the formulae in this appendix, the user must estimate either the probability density function (PDF)
or cumulative distribution function (CDF) of the process characteristic or characteristics of interest. The
distributions can be based on a theoretical model or on empirical information obtained from manufacturing data.
A1-2.6 To apply the formulae in this appendix, the user must be able to estimate all biases and variances associated
with the piece of equipment being compared under the specified operating conditions and with respect to the process
characteristic(s) of interest. These values can be obtained from a measurement system capability analysis (see SEMI
E89).
A1-2.7 This appendix does not consider costs associated with other components of uncertainty outside of
measurement variability and bias.
SEMI E35-0305 © SEMI 1995, 2005 13
A1-3 Limitations
A1-3.1 Application of this appendix requires that all measurement variances, biases, and process characteristic
distributions be accurately characterized. If this is not done, the resulting calculation may be in error.
A1-3.2 Application of this appendix also requires that measurement variances and biases be constant over the
measurement range interval of interest. If this is not the case, the resulting calculation may be in error.
A1-3.3 This appendix considers only the case of two convolved distributions, process characteristic variability and
measurement variability; consideration of additional distributions (such as would be required if the measurement
bias or variance were assumed to be a function of the measured value) is beyond the scope of this appendix.
A1-3.4 Extension of the model to the cases of decisions based on (1) measurements on multiple gauges, (2)
multiple inspections with the same gauge, or (3) on multiple characteristics is provided in §A1-5.
A1-4 Procedure
A1-4.1 Estimate the PDF for the process characteristic to be studied. This can be done using empirical data that
represents the process. Although actual data may be used to create a discrete PDF, it is sometimes convenient to use
the data to parametrically fit a PDF model (e.g., log normal).
A1-4.2 Unless already known, establish the bias and standard deviation for each measurement gauge to be
compared in accordance with SEMI E89.
A1-4.3 In all cases take the measurement influence into account so that it does not broaden the PDF. This may be
done by taking repeated measurements at each point in the measurement range and calculating the mean, or by
deconvolving the process characteristic PDF, f(x), and the measurement variability CDF, G(u), generally assumed to
be a Gaussian (or normal) distribution with arithmetic mean equal to the bias, so that:
x
x
uuG
M
u
M
d
2
exp
2
1
2
2
(1)
where:
= bias,
M
= standard deviation of the measurement distribution.
NOTE 1: The quantity σ
M
includes the effects of the change in bias over the time interval in which σ
M
has been established.
A1-4.4 Calculate
and
as follows. Note that the symbols in the equations for
and
have the following
meanings:
f(x) = PDF of process characteristic x,
USL = upper specification limit,
LSL = lower specification limit, and
(u) = Gaussian CDF (see Equation (1) in ¶A1-4.3).
A1-4.4.1 For a characteristic with only a USL, use the following equations to calculate
and
:
xxf
xUSL
USL
M
d1
(2)
xxf
xUSL
USL
M
d
(3)
A1-4.4.2 For a characteristic with only an LSL, use the following equations to calculate
and
:
xxf
xLSL
LSL
M
d
(4)