
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.