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3.3.3 Electronic Stopping Process
Modeling the electronic stopping process is very complicated, because
several physical effects contribute to the inelastic energy loss.
 Excitation of conduction and band electrons (nonlocalized weakly bound
electrons).
 Excitation or ionization of target atoms (promotion of localized
electrons).
 Ionization or electron capture of the projectile.
All these effects occur due to coreelectron and electronelectron interaction.
The most widely used technique for modeling the electronic stopping process is
based on the local density approximation. It assumes that in each (infinitesimal)
volume element of the target the interaction between the projectile and the
target electrons depends only on one property of the target, namely the local
electron density within this volume element. The local electron density
at a position is

(3.99) 
are the single electron wavefunctions of all electrons in the
target. Furthermore the local density approximation assumes that the interaction
of the moving ion with the electrons in a certain volume element equals the
interaction of the moving point charge with electrons in an infinite free
electron gas with the same homogeneous electron density. An infinite free electron
gas is a theoretical model which assumes that electrons with a definite electron
density are homogeneously distributed in the whole space and that no forces act
on the electrons.
The local density approximation neglects:
 Effects arising from a gradient in the target electron density in the
sphere of influence of the projectile
 The influence of the solid state energy spectrum of the target electrons,
because free electrons are characterized by a continuous energy spectrum,
because no force act on the electrons.
Applying this approximation the remaining problems are to derive the
energy loss of a point charge in a free electron gas and to determine an
effective charge of the point charge in a free electron gas which optimally
represents the behavior of the projectile in the solid.
Subsections
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A. Hoessiger: Simulation of Ion Implantation for ULSI Technology