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\begin{document} 
\title{Radiation Damage in Semiconductors}
\author{ Dickson C. Goulart\\
	 \\
         Department of Physics\\ 
         University of Cincinnati \\
         Cincinnati, Ohio 45221\\[1em]}
 
\date{March 07, 2001}
\maketitle
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\begin{abstract}
When a high-energy particle transverses the lattice of a crystalline solid, 
it looses energy by several processes introducing lattice imperfections. 
Such impurities may have important influences
on the properties of a solid that has been exposed to high 
energy radiation. A short review on the fundamentals and classification 
of the processes 
envolved is presented. The 
influences on the properties of semiconductors is also briefly discussed 
focusing on the Solid State aspects as opposed to detector maintaning aspects. 
\end{abstract}
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\section{Qualitative Discussion of Damage Events}
\indent

Let's consider a high-energy particle transversing the lattice of a 
crystalline solid. Events of many different natures may take place.
For example, it may itself become lodged in the
lattice. It is very important to consider such a case for proton, deuteron or alpha 
incident particles. Also it may produce a nuclear reaction which is usually an 
important factor when considering reactor irradiations. These efects are 
refered to as {\em chemical impurities}.

The damage events we will be concerned with result from an incident high-energy 
particle hitting the nucleus of an atom of the material being irradiated.
In the case of electron and charged heavy-particles, e.g., protons, deuterons, 
alphas, the coulomb potential governs the dynamics of the particle-nucleus 
collision. In the case of neutrons, the short-range nuclear forces govern. 
In the case of gammas, the dominant displacement interaction is via production 
of Compton electrons which then interact with the nucleus. All of these processes
are well estabilished theoretically and experimentally. A great deal of the 
incident particle's energy can be transfered to the target nucleus. The average 
energy transmitted, however, is considerably lower than this maximum, 
particularly in the case of Coulomb interactions.

As a result of the particle-nucleus collision, energy is transfered to atom. 
The recoiling atom then interacts with its neighboring atoms. The 
corresponding interaction potential can be approximated by, for example, 
the Bohr screened Coulomb potential. With that assumption the interaction energy 
is considered to vary roughly exponentially versus interaction distance. Through 
the atom-atom collisions, energy is transfered from the primary recoil
atom to the rest of the lattice. This excess of energy in the lattice immediately
adjacent to the initial nuclear collision is sometimes characterized as
a temperature and this region is termed a thermal spike.

If the energy of the primary recoil atom is relatively low, all that results 
is a local heating of the lattice. As the energy of the recoil atom gets 
higher, an energy is reached where the recoil atom is displaced to a 
(metastable) interstitial site, leaving a vacancy behind. This type of 
event is called displacement event, the corresponding energy called 
the threshold energy for displacement and the defects are refered to as 
{\em physical impurities}. The detail of the displacement 
process will depend on the energy of the recoil and its direction with 
respect to the other lattice atoms.

\section{Classification of Defects}

\subsection {Point Defect}
\indent

{\em Point defects} include lattice vacancies, interstitial atoms
and chemical impurities. In the damage event described 
we have a single vacancy and a single interstitial.
The specific location of the interstitial with respect to the vacancy is important.
There is a number of sites where the interstitial can be located and be essentially
bound to the vacancy via the distortions each one produces in the lattice. Such
vacancy-interstitial pair is called close-pair or Frenkel pair. In certain
materials, for a certain minimum separation, such complexes may have
appreciable stability and may resist recombination. This defect is produced in
specially appreciable yield by electron bombardmennt. Interstitials
in other than close-pair sites are called free. 

The simple interstitials or vacancies can migrate and agglomerate forming 
di-interstitials or di-vacancies. Di-interstitials and di-vacancies can also 
be directly introduced in the damage
process. The high-energy recoil atom can impart sufficient energy to displace
a secondary atom and still retain energy enough to get displaced. Indeed, as the
primary recoil energy increases such higher-order damage processes become
more likely.

\subsection {Line Defect}
\indent

The passage of a high-energy recoil atom through the lattice can also 
leave a whole trail of
damage which is refered to as ``spike'' region or as ``spike'' damage or 
simply {\em line defect} (as opposed to {\em point defect}).

Vacancies which are produced by a recoil
tend to be in a central core region with interstitials in the surrouding
region. That configuration may collapse and form a disordered region called
``displacement'' spike. There are other aspects of a spike as well. For example,
the core region of vacancies and surrrounding region of interstitials, when they
do not collapse, still have different properties from the equivalent number
of Frenkel pairs randomly distributed through the lattice. A high concentration 
of vacancy and interstitial within a small  volume is specially
important in radiation damage. 

\section{Influence of Lattice Imperfections on the Properties of Solids}

\subsection{Point Defect}
\indent

The point defects just described disturbe the lattice arrengement so that
the periodical electrical potential is disordered by several atomic
distances. The change of the potential around the defect usually introduces
localized eletronic states which are particularly important in non-metallic
crystalls. In the following, some of the most important properties altered 
by the presence of point imperfections are discussed.

\begin{itemize}

\item{Mechanical Properties:}
The presence interstitials or vacancies produces a change in density.
The distortion of the lattice arrangement can be investigated by X-ray 
diffraction techniques such as line-shape analysis and lattice parameter 
measurements for large defect densities ($> 10^{-5}$ fractional concentration).
As a result of the changes in the lattice spacing and interatomic binding,
point defects also change the elastic behavior of solids. This is not to be
confused with changes in the dislocation component of Young's modulus,
which is also associated with point defects, but only through the interaction
of these with line defects. The interactions between point defects and
line defects affect the plastic behavior and are mentioned in a later
section.

\item{Thermal Behavior:}
Point defects scatter phonons, therefore causing a decrease in thermal 
conductivity. Moreover, the presence of imperfections may also have a 
measurable influence on the specific heat of a solid. A special example
of a thermal effect is stored energy which is released as heat when a
specimen containing a high density of Frenkel defects is heated. An amount
of heat equal to about 5 eV (the energy of formation) is stored in the lattice
for each Frenkel pair, and recombination of the components of the defects releases
this thermal energy. 

\item{Electromagnetic Properties:}
Because the electric potential of the crystal is altered in their vicinity, point
defects act as electron scattering centers and therefore increase the electrical
resistivity in metals. Changes in resistivity have been extensively used for
investigations of defects in metals, not because of the ease of fundamental 
interpretation of a change in this property, but rather because of the great ease
of measurement. 

\item{Localized Electronic States:}
The alteration of the crystal potential at the site of the defect usually results
in the introduction of localized electronic states which, though of little 
importance in most metals, have extensive consequences in insulating crystals and
most semiconductors. 

\end{itemize}

\subsection{Line Defect}
\indent

From the standpoint of understanding the mechanical behavior of solids,
the concept of line defect is by far the most important. This concept permits
an understanding not only of the plastic deformation of solids and hence
the magnitude of their tensile strength, but also of the phenomenon of
crystall growth. In essence, a line defect is able to move under stress far below
the yield stress of the perfect crystal. Its motion leads to platic deformation.
A line defect can never end within the crystal. Either it follows a closed
path or it extends to the surface. Every motion, even of parts of the line,
 results in deformation. The motion of a line defect is rectricted as motion
in some planes may require diffusion of vacancies or interstitials. They induce
elastic stress and thus interact with one another. This interaction can lead to
dislocation rection, sometimes to complete anihilation. We see that the presence 
of a small number of line defects leads to a weakining of the crystal, while an 
appreciable increase in the number of dislocations can lead to stregthening.
However the stregthening still does not approach that obtainable in a perfect
crystal.


\section{Semiconductors}
\indent

Semiconductors such as germanium or silicon are widely used in radiation
detectors. Besides their very good charge transport properties, the
extensive experimental and theoretical investigations have led to a clear 
understanding of their nature (intrisic range) and also of their 
behavior after exposure to high-energy radiation (extrinsic range). 

The prime characteristic of semiconductors is the variability over a wide range of
charge-carrier concentration, either by virtue of impurity or defect content, or
as a function of temperature. This is to be contrasted with metals in which
the concentration of charge carriers is fixed and of the same order of magnitude
as the density of atoms in the crystal. 

In the intrinsic range, equal concentrations
of electrons in the conduction band and holes in the valence band are produced
by thermal ionization of atoms (valence bonds) or ions in the crystal. The type
and concentration of charge carriers in the extrinsic range is determined
by structural imperfections, either chemical or physical impurities. They
form localized states in the forbiden energy gap which may occupied with 
electrons (donors) or just be vacant (acceptors).
Manifestations of each are observed in a given material depending on
its initial charge-carrier concentration and type (electron or hole
conductor). However, whether the defects act predominantly as acceptors
or donors depends on the material in question.   

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\section{Conclusions}
\indent


Defects produced by radiation are classified acording to the processes
involved as point defect or line defect.
Each kind of defect is  associated not only to different radiation types, 
but also to the specific degradation of the characteristics of the 
solid. Defects produced by radiation alter important properties of solids
not only at microscopical but also at macroscopical level.

The study of radiation damage in solids is carried out by investigating
their structure-sensitive properties. In that way we learn 
not only about intrinsic characteristics of a solid but also about how to use
radiation damaging as a technique for altering the properties of solids in a 
controled fashion.

The radiation-produced defects, whatever their actual description, have associated
with them localized energy states which alter the concentration of charge
carriers and mobility in a semiconductor. Many semiconductors are well understood
and widely used in radiation detector being exposed to high energy incident 
particles. Their usefullness is therefore connected to a understanding of 
how the degradation of the desired characteristics happens and which further
consequences it may have in the functioning of radiation detectors.


\begin{thebibliography}{99}
\bibitem{ref} Solid State Class Notes, M. Jarrell (2001).
\bibitem{refA} D.S. Billington, J.H. Crawford,\ {\em Radiation Damage in Solids}, Princeton University Press (1961).
\bibitem{refB} J.W. Corbett,\ {\em Electron Radiation Damage in Semiconductors and Metals}, Academic Press (1966).
\bibitem{refC} B.L. Gregory,\ {\em Proceedings of Conference on Radiation Damage and Defects in Semiconductors}, Conference Series Number 16, Intitute of Physics London and Bristol, 302 (1972).
\bibitem{refD} C.F.G. Delaney, E.C. Finch,\ {\em Radiation Detectors}, Claredon Press Oxford (1992).
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