In document Ion-induced damage in alkali halide crystals (Page 31-34)

Characteristic X- radiation may be emitted when an inner shell


2.2.5 Dechanneling

In the foregoing treatments the target was assumed to be perfectly crystalline, and the beam was divided into two components, associated with channeled and random contributions. It was further assumed that the transverse energy of the channeled component was

conserved. However as the particles progress through the crystal, their transverse energy will be modified by multiple scattering from electrons, nuclei, defects and impurities in the crystal,, In this way, some

particles will achieve sufficient energy to overcome the channel potential barrier and transfer from the channeled component to the

random component; this phenomena is called dechanneling and it causes an increase in .

In sections 2.2.1 and 2.2.2, where energy-losses from multiple scattering were ignored, it was indicated that ^ could be estimated from geometrical considerations. If no scattering of the beam took place then Xm j_n w°uld be independent of depth, with the value x * (0) estimated from the projection of the areal cross section onto the surface,,

However, multiple scattering processes do change the

transverse energy, so the random fraction of the beam increases as the particles traverse the crystal. Hence, we may write

, , . dech, .

W x> = W 0 ) + Xmin (X) (2.34)


become dechanneled up to depth x. The study of the yield of back-

scattered particles from a thick crystal has been the major technique

for investigating the dechanneled fraction as a function of depth. By

analogy with the treatment of stopping power, where contributions from

electrons and nuclei are additive, the dechanneling contributions may be

written as dech ^min (x) [ dech [^min (x) + electronic




(x) Jnuclear +


dech (X) defects (2.35)

Previous investigations have mainly concentrated on dechanneling in

"perfect" crystals, in which the contribution from defects has been


One theoretical approach to describe the dechanneling process

was proposed by Lindhard [Li 65]; he suggested that the changes in

transverse energy could be considered by the solution to a diffusion

equation. The diffusion coefficient is related to changes to the

transverse energy of the channeled particles. Bjorkqvist et at.

[Bj 72] assumed that the transverse*energy increased steadily as the

particles penetrated the crystal, and when it became greater than a

critical cutoff value, the particles became dechanneled.

Some experimental studies of dechanneling caused by defects

have been reported [e.g. B0 68, De 7 0 ] 0 Channeled ions are sensitive to

the position of atoms in a crystal, so it would be expected that lattice

defects will affect the dechanneling rate by either slightly perturbing

or drastically altering the ion trajectories. A complication in using

back-scattering observations to probe radiation damage is the inability

to distinguish in a simple manner between reactions involving displaced

or undisplaced atoms with the channeled or dechanneled components of the


The main emphasis of radiation damage investigations has been

in connection with ion-implantation of semiconductors. In these studies

a semiconducting material is bombarded with low-energy heavy ions

(< 200 keV) and then the damaged region is probed with high energy light

ions (> 500 keV H + or H e + i o n s ) , using the back-scattering technique.

in mass between the implanted and the host atoms, enables one to observe the whole of the damaged region and often determine the location of the

introduced ions relative to the lattice. In these investigations one

should ensure that the probing beam does not greatly change the amount of damage.

B0gh [B0 68] considered two mechanisms by which displaced

atoms increase the measured yield of b a ck-scattering0 The aligned beam

can be back-scattered directly from displaced atoms, and, defects can dechannel particles which then interact with all atoms in the same way

as a random beam does. He expressed this in the form,

y' (x) y (x)


(l - X ' (x))

+ X' (x)


where y'(x) is the back-scattered yield from depth x, y^(x) is the

normal random yield, X* (x) is the random fraction of the beam, N' (x) the

density of scattering centres and N is the atomic density, Equation (2.36) can be rearranged as follows:

W x)

y' y (x)(x) n 1 N'


N X' (X) + N '(x) N (2.37)

To evaluate (x) an understanding of both the dechanneling process and

the variation of stopping power is necessary; usually it is assumed

that the stopping power is the same for both the channeling and the random components.

A great deal of effort has been directed towards trying to associate single scattering and multiple or plural scattering with the

dechanneling process [Gr 74, Ei 74], For dechanneling due to single

deflections through an angle greater than \p1 then, according to B0gh,

X' (x) = 1 - {1 - Xl (x) } e Y (X) (2.38)

where Xi(x) is the normalized aligned yield from an undamaged crystal, and

Y (x) P (\/>1 , x' ) N' (x' ) dx' , (2.39)

being dechanneled by the displaced atoms N ' (x) dx. B0gh estimated

P (ip1 , x) to be

7TZ2Z 2e 4

P(lK , x) = -- . (2.40)




Feldman and Rogers [Fe 70], using a similar approach to B0gh,

estimated the part of x '(x) due to multiple scattering as

X' (x) = Xi (x) + (l - Xi (x)) F (x) , (2.41)

where F(x) is the fraction of the aligned beam which has been scattered

beyond i>1 at depth x. F(x) can be expressed as

F(x) e 1 (x) , (2„42) where (x) fz iz : Z-n (l„ 29 e) • x n '(x ') dx' . o (2.43)

From a comparison of their experimental back-scattering yields

with the prediction for single and multiple scattering processes, they

found that, over most of the range of defect densities, multiple

scattering is the dominant dechanneling mechanism. However, for

slightly damaged crystals they found that the single scattering process

becomes more important.

The usual method of calculating damage distributions from the

above equations is to perform an iterative calculation, using eqs.

(2.36), (2.39) and (2038), starting at x = 0 for which

X' (0) = X x (0) , (2.44)

according to eq. (2.38)„ One may then calculate N ' (0) and use it to

calculate X* f°r the next depth increment in the distribution, and so on.

In document Ion-induced damage in alkali halide crystals (Page 31-34)