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SEMI E10-0304 E © SEMI 1986, 2004 22 R1-5.6.1 Example 1 — This exam ple, shown in Figure R1-4, is of a multi-path cluster tool with sev en modules. L1 a nd L2 are load l ock modules t h at are used to load units into the…
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R1-5 Modeling Process Flows
R1-5.1 In order to evaluate multi-path cluster tool
availability and reliability, the set of process flows shall
be defined for the multi-path cluster tool. It is
important to differentiate between all the process flows
that are theoretically possible on a given multi-path
cluster tool configuration and those intended process
flows (IPF) that are actually intended for operational
use (i.e., performing its intended function). For
meaningful agreement between any two parties on the
metrics presented in this related information, first there
shall be documented agreement on the set of IPFs used
for evaluation, so that any analyst with the module state
histories can calculate the same values for the metrics.
First, the general case of “up/down” states for an IPF is
presented, and then later the distinction between
unscheduled downtime and total (i.e., scheduled and
unscheduled) downtime for an IPF is presented.
R1-5.2 An IPF “up/down” state is modeled as a
network flow through the modules that make up that
IPF. If there is “connectivity” through the IPF network,
then the IPF is “up;” otherwise it is “down.” The
modules in an IPF network have series and parallel
relationships that determine the connectivity through
the network. Mathematically, each module and each
IPF has a state value equal to 1 when the state is “up”
and 0 when the state is “down.” For example,
M
i
=
1, if module i is up
0, if module i is down
R1-5.3 The general process steps within an IPF have a
mutually serial relationship (i.e., if connectivity is not
possible through any single step, then connectivity is
not possible through the network). This is illustrated in
Figure R1-2. The IPF state value for serial constituents
is calculated as the product of the constituent state
values (e.g., IPF =
Π
i=1 to 4
Si = S1 × S2 × S3
×
S4).
S1 S2 S3 S4
Figure R1-2
Serial Process Steps Within An IPF
R1-5.4 At any general process step, S
x
, the set of
alternative modules, Ai (if any are present), have a
mutually parallel relationship (i.e., if any one of the
alternative modules is up, then connectivity through
that step is still possible). This is illustrated in Figure
R1-3. The state value through this step is calculated as:
IPF = 1 -
Π
i=1 to 3
(1 − Ai)
= 1 − [(1 − A1)
×
(1 − A2) × (1 − A3)]
If any alternative module is “up,” the expression in the
square brackets evaluates to zero, and the IPF state
value evaluates to 1, or “up.” If all of the alternative
modules are “down,” the expression in the square
brackets evaluates to 1, and the IPF state value
evaluates to 0, or “down.”
A2
A3
A1
S
x
Figure R1-3
Parallel Alternative Modules At A Process Step
NOTE 6: In general network modeling, it is possible to have
complicated multi-constituent structures in parallel with other
multi-constituent structures. At the time of this writing, the
need for such structures in evaluating multi-path cluster tool
RAM is not anticipated. Therefore, this exposition is limited
to serial relationships amongst the process steps and single-
constituent parallel relationships for alternatives within any
one step. To model multi-path cluster tool systems that
exceed these limitations, the modeler is encouraged to consult
any text on the modeling of coherent systems for reliability.
R1-5.5 For almost all systems, there will be a subset of
modules that will appear in every IPF regardless of any
process differentiation, called the key group. The key
group includes support modules (e.g., transport, load
locks), common process modules that are used by every
IPF, and the platform itself. A key group may include
alternative modules such as multiple load locks or
multiple cooling stations. The key group’s relationship
to all IPFs is such that if the key group is down, all IPFs
are down. Therefore, the key group has a serial
relationship to each IPF. By modeling a key group and
leveraging it in calculations, substantial redundant
calculations are avoided. Furthermore, understanding
which modules belong to the key group also helps in
understanding and improving overall system reliability.
R1-5.6 Two examples are now presented to illustrate
how to model IPFs, including modeling of the key
group and of IPF state functions.
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R1-5.6.1 Example 1 — This example, shown in Figure
R1-4, is of a multi-path cluster tool with seven
modules. L1 and L2 are load lock modules that are used
to load units into the tool. A single transport arm, T,
performs all point-to-point transportation. The first
process module visited by any unit is either PM1 or
PM2, after which every unit visits PM3. Lastly, L3 is a
load lock that is used to unload units from the multi-
path cluster tool.
R1-5.6.1.1 The key group, K, as shown in Figure R1-5,
is made up of the three load locks and the transport,
which are the common support modules for this multi-
path cluster tool used by any unit. Since all modules
visit PM3 regardless of any IPF distinction, PM3 also is
included in the key group in order to simplify
calculation. Any other system-level failure issues may
be allocated to the abstract platform module, P.
Li
= Load Lock i, i = 1, 2, 3
PMj = Process Module j, j = 1, 2, 3
T = Transport Module
T
L1
L2
PM1
PM2
PM3 L3
Figure R1-4
Multi-Path Cluster Tool Modules, Example 1
L1
L2
T L3
K
=
P
PM3
Figure R1-5
Key Group, Example 1
R1-5.6.1.2 The state value function for the key group is
K = P × [1 − (1 − L1) × (1 − L2)] × T × L3
×
PM3.
For reference, the equivalent truth table for this logic is
shown in Table R1-1:
Table R1-1 Truth Table for Key Group, Example 1
P L1 L2 T L3 PM3 K
1 1 1 1 1 1 1
1 1 0 1 1 1 1
1 0 1 1 1 1 1
else 0
R1-5.6.1.3 IPF1 is a general IPF that uses the key
group and either process module PM1 or PM2, as
shown in Figure R1-6.
PM1
PM2
K
Figure R1-6
IPF1, Example 1
R1-5.6.1.4 The state value function for IPF1 = K
×
[1
− (1 − PM1)
×
(1 − PM2)]. The equivalent truth table
is shown in Table R1-2:
Table R1-2 Truth Table for the State Function,
Example 1
K PM1 PM2 IPF1
1 1 1 1
1 1 0 1
1 0 1 1
else 0
R1-5.6.1.5 IPF2 represents a process engineering issue
where PM2 is not sufficiently matched in performance
to PM1. Therefore for certain processes, all units are
restricted to go through PM1 only as shown in Figure
R1-7.
PM1
K
Figure R1-7
IPF2, Example 1
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R1-5.6.1.6 The state value function for IPF1 = K
×
PM1. The equivalent truth table is trivial and is
therefore not shown.
R1-5.6.2 Example 2 — This example, as shown in
Figure R1-8, is of a more complicated coat/develop
system that has 56 total modules, including four load
locks (L1-L4), four common transport robots (R1-R4),
four coat stations, four develop stations, and four arrays
of heat/chill plates with ten modules in each array.
R1-5.6.2.1 The key group, K, contains the platform,
the four load locks, and the four transport robots, as
shown in Figure R1-9. There are no process modules
that are used in every IPF, therefore no process modules
appear in K.
R1
R2
R3
R4
10X Heat /
Chill
10X Heat /
Chill
10X Heat /
Chill
10X Heat /
Chill
Coat
1,2
Coat
3,4
Develop
1,2
Develop
3,4
L
1, 2, 3, 4
To
E
xposure
Figure R1-8
Modules For A Coat/Develop System
L1
L2
L3
L4
R1 R2 R3 R4
K=
P
Figure R1-9
Key Group Modules, Example 2