1063-7397/05/3403- © 2005 MAIK “Nauka /Interperiodica”
Russian Microelectronics, Vol. 34, No. 3, 2005, pp. 181–186. Translated from Mikroelektronika, Vol. 34, No. 3, 2005, pp. 218–224.
Original Russian Text Copyright © 2005 by Grafutin, Ilyukhina, Myasishcheva, Kalugin, Prokopiev, Timoshenkov, Khmelevskii, Funtikov.
Positron-annihilation spectroscopy (PAS) offers a
new way to investigate why and how defects arise,
change, and disappear in a material being produced,
ﬁnding use in electronics and nucleonics [1–33].
PAS measurements employ
, etc., sources
of positrons with energies of 0–700 keV. Such positrons
are usually annihilated near the surface, their range
lying within 150
m for most materials [1–10]. In micro-
electronics, slow positrons (energy under 7 keV) are used
to examine materials at submicrometer depths .
Positron annihilation is mainly evaluated by the
angular and time distribution of annihilation photons
and the Doppler broadening of the annihilation peak.
From the time distribution, the annihilation-photon
and positron lifetime
are deduced for each
th positron state. The Doppler broadening is com-
monly measured by the lineshape parameter
, i.e., the
ratio of the area of a central region in the annihilation
peak to the total area of the peak.
POSITRON STATES IN REAL METAL AND
We assume for simplicity that positron states in
metal and semiconductor crystals are mainly thermal-
ized positrons; positronium states and Wheeler com-
plexes in the bulk; and trapped states at point or
extended defects, which may have a charge of any sign
or may be neutral [1–4]. Such defects will be referred
to as positron-sensitive defects.
Let us derive formulae that will yield the mean den-
sities and sizes of positron-sensitive defects from the
above PAS characteristics. Due to a reduced electron den-
sity near defects, trapped positrons have a longer lifetime,
and the resulting annihilation photons are characterized by
narrower angular and energy distributions.
This study is concerned with positron annihilation
in silicon. Let
be the total number of types of positron-
sensitive defect in a crystal and and be the
defect mean size and density, respectively, in the near-
surface region examined. The defect size and density
should be treated as random variables. In a discrete
case, we write
is the probability mass function [29–33].
In a continuous case with the probability density functions
, the mean values are written
of Proton-Induced Defects in Silicon
V. I. Grafutin*, O. V. Ilyukhina*, G. G. Myasishcheva*, V. V. Kalugin**,
E. P. Prokopiev*, S. P. Timoshenkov**, N. O. Khmelevskii*, and Yu. V. Funtikov*
*Institute of Theoretical and Experimental Physics, Moscow, Russia
**Moscow Institute of Electronic Engineering (Technical University), Moscow, Russia
Received July 8, 2004
—General approaches are considered to the structural characterization of defects in solids by positron-
annihilation spectroscopy. Positron annihilation is studied experimentally on proton-irradiated silicon wafers
made to different speciﬁcations, using the angular distribution of annihilation photons. A parabolic and a Gaus-
sian component are identiﬁed in the distribution curves. They are associated with the annihilation of Wheeler
states in the bulk and near Si-ion cores, respectively. The densities of radiation-induced defects are deduced
from the experimental data.