1063-7397/02/3101- $27.00 © 2002 MAIK “Nauka /Interperiodica”
Russian Microelectronics, Vol. 31, No. 1, 2002, pp. 21–26. Translated from Mikroelektronika, Vol. 31, No. 1, 2002, pp. 24–30.
Original Russian Text Copyright © 2002by Strizhkov.
Statistical methods play a key role in quality assur-
ance throughout the product cycle.
As the microelectronic industry progresses toward
larger scales of integration and more complex manufac-
turing processes, the problem of in-process product
control is becoming ever more pressing.
A system of quality control for microelectronic
applications cannot be regarded as comprehensive and
efﬁcient if it neglects the speciﬁcs of IC manufacture.
The most important factor to be allowed for is the wide-
spread use of batch processes. Accordingly, the statisti-
cal characteristics of a product should be viewed as a
This paper presents a categorization of existing
approaches to statistical process control (SPC) in IC
manufacture, together with a discussion of their spe-
2. CONCEPTS OF MATHEMATICAL STATISTICS
IN PROCESS QUALITY CONTROL
If we seek to evaluate the degree to which a manu-
facturing process conforms to speciﬁcations (e.g., for
the purpose of process certiﬁcation), we examine quan-
titative rather than qualitative characteristics of quality,
since the latter are normally applied to the ﬁnished
With respect to electronic-device manufacture, pro-
cess quantitative characteristics to be evaluated are
thoroughly deﬁned by a national standard .
We start by outlining the basic concepts of mathe-
matical statistics that are useful for SPC.
For a random variable
, a set of values
experiments is called a sample of size
. This definition assumes that the experiments are car-
ried out under identical and independent conditions.
As the size of a sample increases, it approaches that
of the population from which the sample is obtained.
The main statistical characteristics of a population and
a sample are listed in Table 1. These characteristics are
called population parameters and sample statistics,
2.1. Normal Distribution
The normal distribution, also known as the Gaussian
distribution, lies at the heart of mathematical statistics.
It has many important properties and often serves as a
good approximation to another distribution.
Let a manufacturing process be considered in terms
of a quantitative characteristic, or variable. If the pro-
cess runs properly, the empirical values of the variable
conform to the normal distribution, as follows from the
Central Limit Theorem.
If a process is affected by many causes, each item is
fabricated under a random combination of these causes,
and each cause acts throughout the processing period,
then the process is said to be in (statistical) control .
It follows that if the causes are independent, equal in
efﬁciency, and large in number, then the resultant distri-
bution is the normal distribution. Thus, the distribution
of any item variable approaches the normal distribution
as the number of items increases.
For all practical purposes, variables can be regarded
as normally distributed if none of the causes dominates.
The normal distribution of a random variable
Statistical Process Control in IC Manufacture
S. A. Strizhkov
Received April 18, 2001
—The principles and microelectronic applications of statistical process control are considered. The
feasibility of various statistical methods for process quality control is evaluated in terms of IC manufacture.
Application speciﬁcs are discussed.
Main statistical characteristics of a population and
Moments Statistics Parameters
First moment (about zero)
Also known as the variance.