
20-26
REFERENCE
DATA
FOR ENGINEERS
is
A,
then the probability that a chip has
n
flaws is, in
the simplest case, given by the
Poisson
distribution
P,(DA).
The probability of a good chip is:
Po
(DA)
=
e-DA
(Eq.
5)
While this equation is not rigorously applicable to fab-
rication processes, it is a good approximate model for
estimating the yield of various design alternatives.
IC
DESIGN*
The design of integrated circuits requires the syn-
thesis and analysis of a large number of active ele-
ments. The classical form of analysis can be extended
to integrated circuits, whereas the focus of synthesis
goes beyond the classical notions inasmuch as the geo-
metric layout
of
the circuit topography for integrated
circuits
is
a major fraction of the circuit synthesis. The
electrical aspects of circuit design derive
from
the con-
siderations that are laid out in Chapter
18,
with certain
constraints based on the scale of integration. The
design of
the
circuit topography is unique to integrated
circuits and has evolved as a major discipline.
Modeling and Simulation
The design of integrated circuits requires the electri-
cal analysis of circuits that contain a large number of
elements. For
LSI
or VLSI circuits,
this
involves the
simulation of up to tens of millions
of
circuit elements
if the total circuit response is to be examined. The eval-
uation of
this
class of circuits is extremely computer-
intensive.
In
most cases, it is not practical to simulate
the circuit with classical time- or frequency-domain
analysis at the transistor level. The current practice for
simulation and analysis of such classes of circuits is to
adopt a hierarchical procedure with different levels of
abstraction at each level. The design
of
an
LSI
logic cir-
cuit would involve a typical modeling hierarchy such as
that in Chart
1.
The top of the hierarchy is an abstract definition of
the architecture of the circuit, which is used to provide
a guideline for the various ways of accomplishing the
objective of the circuit. It trades off, for example, the
use of pipeline processing versus serial processing.
The
behavioral level
of
simulation actually involves
CHART 1.
DESIGN
HIERARCHY
FOR
LSI CIRCUITS
Architecture
simulation
Behavioral simulation
Functional simulation
Logic simulation
Transistor simulation
the definition of the major blocks of the circuit and
their interaction, with the details of the overall data or
control flow to accomplish the objective of the chip
being examined. The functional level actually
describes the overall logical response of the major
blocks, relating
the
logical inputs and outputs with
no
details of internal realization of logic in the block. The
logic-simulation level details the realization of each
block at the gate level, provides logic minimization,
and in some cases introduces the notion of relative tim-
ing. The transistor-level simulation considers the tran-
sient response of the circuit, including the detailed
simulation of all elements of the circuit. The key to the
usefulness of this hierarchical simulation
is
the ability
to mix the different levels of abstraction to examine
the performance of the entire circuit with focus on one
block at a time. Such mixed-mode simulators are being
evolved, and common hardware-description languages
that operate on a unified data base that is accessed by
any level
of
the hierarchy are now available.
Topological Realization of
Circuits
The design of integrated circuits differs from the
design of board-level circuits in the importance of the
actual physical realization of the active elements and
interconnections. Typical LSI circuits have many thou-
sands of active elements and interconnections that
must be topologically related to each other. This
requires the interaction of the device physics, process
technology constraints, and topological constraints. To
obtain a practical solution to this complex interactive
design environment, it is generally accepted practice to
describe the process constraints
in
the form of a design
rule package. This design rule package is a simple
description of the lateral spatial relationship of the var-
ious active-element forming geometries as well as the
wiring.
A
simple example of design rules is shown in
Fig.
13.
The original concept
of
the design rules was
governed by the constraints of the technology only.
However, the design data base for the geometrical
description
of
the circuit for VLSI circuits is very
large, and some constraints that limit the size of this
data base have been introduced into the design rules.+
This is simply
a
quantization
of
the minimum spatial
distance describing any technology constraint. This
kind of quantization is equivalent to the definition of
the finest grid
on
which a geometry must fall.
There
are
two major approaches to the realization
of
the geometrical data base for an IC. The first is the
classical approach in which the complete drawing
of
each individual section is introduced into the data
base in detail. This is a tedious and inefficient way
of
generating data. The preferred approach
to
data entry
is through a symbolic description of the layout
in
which the definitions of the often-used elements are
*
Reference
9.
C
Reference
9.