1063-7397/03/3205- $25.00 © 2003 MAIK “Nauka /Interperiodica”
Russian Microelectronics, Vol. 32, No. 5, 2003, pp. 307–314. Translated from Mikroelektronika, Vol. 32, No. 5, 2003, pp. 381–390.
Original Russian Text Copyright © 2003 by Goryachev, Zakharov.
In advanced microprocessors, on-chip interconnec-
tion delay and electromagnetic interference (EMI) have
become comparable in importance with clock rate, data
transfer rate, and power consumption [1, 2]. Smaller
feature sizes and greater circuit complexity imply
larger wiring densities and, regrettably, higher degrees
of cross coupling between wiring lines .
In some cases, designers compromise on noise mar-
gin in order to increase clock rate; an example is the
4 processor, which has a 0.18-
imum feature size and offers more than 2.0 GHz of
clock rate [2, 3]. The problem thus arises of reducing
delays and crosstalk in on-chip interconnections. With
closely spaced lines, it is difﬁcult to introduce shields
between them. In fact, shielded lines may also show
cross coupling . This acts through a certain distance
and results from incomplete shielding when the shield
is not grounded. A similar side effect may well occur in
multilevel metallization systems.
Recent years have seen an increasing interest in ana-
lytical models of on-chip interconnections. Davis and
Meindl [5, 6] solved the problem on response voltage in
interconnections subject to the internal resistance
of the signal source, with the solutions represented as
series in the small parameter . On this basis,
the following investigations were carried out: (i) An in-
depth transient analysis was conducted of semi-inﬁnite
and ﬁnite lines [5, 7]. (ii) Parameter values were found
at which the inductive properties of the lines outweigh
their capacitive ones [7, 8]. (iii) Cross coupling was
explored between identical
lines [6, 8].
The results may be useful for both identifying the
physical phenomena involved and improving the meth-
ods of numerical modeling [9, 10]. At the same time,
we point out that the above research into transients and
cross coupling did not cover lines differing in
, nor did it explore shielded lines.
The aim of the present study is to analytically solve
the problem on the effect of shielding on transients and
cross coupling in on-chip interconnections. This ave-
nue of research should help one to accurately predict
the magnitudes of crosstalk, common-mode noise, and
clock skew [9, 11].
2. BASIC EQUATIONS
The transient analysis of a shielded line should
include the coupling between the line and the shield;
the latter both experiences electromagnetic induction
and propagates disturbances in different directions.
This study is based on telegrapher’s equations,
which might be seen as a one-dimensional analog of
Maxwell’s equations. Telegrapher’s equations are suit-
able for modeling the transient behavior of current and
voltage and the propagation of electromagnetic waves
if the transverse dimensions are much smaller than rel-
evant wavelengths. Basically, the model examined here
is distinct from the one addressed earlier [6, 8] in that
the lines and the shields differ in transverse dimensions
and electrical constants.
Consider a section of a signal line and a section of a
shield. The sections are assumed to be uniform and par-
allel. Below the subscripts
refer to the line and
the shield, respectively. The symbols
denote the resistance, inductance, and capacitance per
unit length, respectively.
Let there be inductance–capacitance coupling
between the sections:
Telegrapher’s equations describing the two sections
constitute a system of four simultaneous partial differen-
tial equations of ﬁrst order; they are identical to Eqs. (1) of
Transient Analysis of Shielded On-Chip Interconnections
V. A. Goryachev and S. M. Zakharov
Institute of Microprocessor Systems, Russian Academy of Sciences, Moscow, Russia
e-mail: VAG@imvs.ru, Zakharov@imvs.ru
Received December 23, 2002
—Transients in shielded on-chip interconnections are studied theoretically for grounded and
ungrounded shields. The model is based on analytical solutions to telegrapher’s equations. The properties of
interconnections and shields are identiﬁed that affect transients and propagation delays in signal lines. It is
shown that cross coupling may exist between lines using a common shield. The magnitude of electromagnetic
interference in shielded lines is estimated.