1063-7397/04/3304- © 2004 MAIK “Nauka /Interperiodica”
Russian Microelectronics, Vol. 33, No. 4, 2004, pp. 209–219. Translated from Mikroelektronika, Vol. 33, No. 4, 2004, pp. 259–272.
Original Russian Text Copyright © 2004 by Ivin, Makhviladze, Valiev.
The ﬁrst part of this study was concerned with ulti-
mate-resolution imaging by off-axis illumination in
optical lithography . It has been shown how major
types of source aperture can be optimized in the context
of two-beam interference. Below we address the trans-
fer of features whose size approaches the resolution
limit. For the reader’s convenience, we also give the
most relevant facts from the ﬁrst part without making
Figure 1 presents the major types of light-source
aperture: the simple circular aperture (Fig. 1a), the cir-
cular dipole (Fig. 1b), the circular quadrupole (Fig. 1c),
the simple annular aperture (Fig. 1d), the annular dipole
(Fig. 1e), and the annular quadrupole (Fig. 1f). The
simple circular aperture is not considered in this study,
because it is associated with on-axis illumination.
When it is used with a one-dimensional (1D) periodic
mask, the depth of focus is limited by three-beam inter-
ference. The other apertures of Fig. 1 provide off-axis
illumination, in which case the depth of focus can be
increased by setting up two-beam interference.
2. CIRCULAR DIPOLE AND QUADRUPOLE
An optimal circular dipole (Fig. 1b) has
made as small as possible. Here,
sponds to two-beam constructive interference and is
is the wavelength employed,
is the mask
is the numerical aperture of the objective.
Theoretically, an optimal circular dipole ensures an
inﬁnitely large depth of focus, so that the contrast of the
image is unaffected by variations in defocusing param-
The circular dipole is best suited for imaging mask
features perpendicular to the line through the centers of
the constituent apertures (Fig. 2). However, it works
much worse for longitudinal features, effectively acting
as an on-axis source.
The circular quadrupole (Fig. 1c) is appropriate for
both orientations. An optimal aperture of this type has
made as small as possible. In principle, this
aperture also provides an inﬁnitely large depth of focus.
(Eq. (1)), it is convenient to
introduce the dimensionless parameter
is twice the Rayleigh resolution:
Equation (1) then becomes
= 1/2 for
= 1 . Let us now determine the
fundamental limits to resolution for the circular dipole
and the circular quadrupole.
2.2 Reducing Mask Pitch
With a binary mask, one way to enhance resolution
is to reduce the mask pitch
while maintaining the
Practical Aspects of Off-Axis Illumination in Optical
V. V. Ivin, T. M. Makhviladze, and K. A. Valiev
Institute of Physics and Technology, Russian Academy of Sciences, Moscow, Russia
Received January 21, 2004
—The practical aspects are analyzed of off-axis illumination in optical lithography below the Ray-
leigh resolution. For major light-source aperture conﬁgurations, fundamental lower limits are identiﬁed on the
lithographic factor , where
is the mask linewidth,
is the numerical aperture of the objective,
is the wavelength. A practical approach is discussed to the calculation of the attainable values of
different aperture conﬁgurations, allowing for the forbidden-pitch phenomenon.