1063-7397/04/3301- © 2004 MAIK “Nauka /Interperiodica”
Russian Microelectronics, Vol. 33, No. 1, 2004, pp. 55–61. Translated from Mikroelektronika, Vol. 33, No. 1, 2004, pp. 68–75.
Original Russian Text Copyright © 2004 by Kislelev, Latysheva.
Modern integrated circuits have feature sizes com-
parable with the ranges of ionizing particles and pho-
tons in the material. It is therefore reasonable to expect
that absorbed dose will depend on chip dimensions.
Below we present radiation susceptibilities calcu-
lated for chips of very-large-scale integration when the
ionizing radiation is photons in the energy range 0.06–
10 MeV, following the method proposed by Vickers
. We compare chips that differ in dimensions
but have a ﬁxed surface area. The approach applies to
transients induced by gamma rays in thin chips regard-
less of their purpose.
Radiation susceptibility is deﬁned as the total num-
ber of trapped charge carriers generated per unit length
for a given surface area. Lengths will be stated in cen-
timeters; photon energies in megaelectronvolts; and
incident ﬂuxes in photons or electrons per centimeter
squared per second, as appropriate.
We proceed from the following assumptions:
(i) The chip is a rectangular parallelepiped.
(ii) The incident radiation is isotropic.
(iii) The chip is made of a uniform material.
(iv) The radiation–matter interaction in the chip is
mainly by Compton scattering.
(v) Electrons reﬂected from the front chip side are of
They allow us to avoid making Monte Carlo calcu-
lations. Radiation susceptibility will be evaluated by
the method of chord-length distribution.
In the energy range of interest, radiation–matter
interaction occurs by the photoelectric effect, Compton
scattering, and pair production.
With gamma rays, the photoelectric effect predomi-
nates at relatively low photon energies and large mate-
rial atomic numbers. Its cross section decreases with
increasing photon energy,
. Speciﬁcally, the cross sec-
tion is approximately proportional to 1/
0.2 MeV; for
> 0.5 MeV, it varies as 1/
one observes discontinuity in the behavior of the cross sec-
passes through the binding energy of electrons to
the atom. For
well above the binding energy, the pho-
ton–electron interaction is central elastic collisions.
The cross section of Compton scattering varies
approximately as 1/
. Since scattering probability
depends on the density of electrons in the material, the
macroscopic cross section is proportional to
is the relative molecular mass,
Avogadro constant, and
is the density.
is high enough, the production of electron–
positron pairs occurs in the Coulomb ﬁeld of the
nucleus (or, rarely, in that of the atomic electrons). The
rest energy of an electron or positron being 0.511 MeV,
the threshold value of
is 1.022 MeV. Any excess
energy will be taken up as the kinetic energy of the
Pair-production cross section rises slowly with
varying approximately as ln
> 4.0 MeV. The
newly created electron and positron may annihilate in
the material; the resultant photons are of energy
0.511 MeV and so may make signiﬁcant contribution to
the secondary emission from the back side of the chip.
In silicon the major interaction mechanism is the
photoelectric effect, Compton scattering, or pair pro-
< 0.05 MeV, 0.05 MeV <
< 15 MeV, or
> 15 MeV, respectively. Displacement damage is
mainly caused by energetic Compton electrons and
The initial probability density function of Compton-
electron energy is expressed in terms of the Klein–
1 1 versΦ–()
Reducing Absorbed Dose by Optimizing Chip Dimensions
V. K. Kislelev and N. D. Latysheva
Research Institute of Measuring Systems, Nizhni Novgorod, Russia
Received December 6, 2002
—The radiation susceptibilities of VLSI chips to x- and gamma-ray photons of energy ranging from
0.06 to 10 MeV are calculated. Chips of different dimensions and ﬁxed surface area are considered.