Analysis of the extended defects in 3C-SiC.pdf - Nelson Mandela ...
Analysis of the extended defects in 3C-SiC.pdf - Nelson Mandela ...
Analysis of the extended defects in 3C-SiC.pdf - Nelson Mandela ...
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4M 1M<br />
2 2 <br />
2 <br />
T E<br />
s<strong>in</strong> T s<strong>in</strong><br />
2<br />
m<br />
(3.6)<br />
( M M ) 2 2<br />
1<br />
2<br />
26<br />
From this <strong>the</strong> differential cross-section d 2pdp<br />
may be obta<strong>in</strong>ed us<strong>in</strong>g <strong>the</strong><br />
impact parameter p which <strong>in</strong> turn is determ<strong>in</strong>ed by us<strong>in</strong>g equation 3.6. Follow<strong>in</strong>g this<br />
<strong>the</strong> nuclear stopp<strong>in</strong>g power Sn(E) may be determ<strong>in</strong>ed by solv<strong>in</strong>g equation 3.2 between<br />
<strong>the</strong> limits 0 to <strong>the</strong> maximum energy transferred<br />
4M<br />
M<br />
E<br />
1 2<br />
Tm (3.7)<br />
2<br />
( M 1 M 2 )<br />
In f<strong>in</strong>d<strong>in</strong>g Sn(E) <strong>the</strong> differential cross-section dσ is found which <strong>in</strong> turn depends<br />
heavily on <strong>the</strong> choice <strong>of</strong> <strong>the</strong> <strong>in</strong>teratomic potential V(r) used. Also <strong>in</strong> most cases <strong>the</strong><br />
scatter<strong>in</strong>g <strong>in</strong>tegral cannot be solved analytically and numerical methods should be<br />
employed which br<strong>in</strong>gs with it an added complexity. The most widely used <strong>the</strong>ory <strong>in</strong><br />
<strong>the</strong> prediction <strong>of</strong> ion ranges <strong>in</strong> a solid is <strong>the</strong> LSS <strong>the</strong>ory developed by L<strong>in</strong>hard, Scharf<br />
and Schiott. In <strong>the</strong> follow<strong>in</strong>g section <strong>the</strong> ma<strong>in</strong> results <strong>of</strong> this <strong>the</strong>ory will be discussed<br />
but it is left to <strong>the</strong> reader to consult fur<strong>the</strong>r references for a more detailed<br />
understand<strong>in</strong>g.<br />
3.2.3. The L<strong>in</strong>hard, Scharff and Schiott (LSS) Theory<br />
The LSS <strong>the</strong>ory uses a Thomas-Fermi model <strong>of</strong> <strong>the</strong> <strong>in</strong>teraction between heavy ions to<br />
derive a nuclear stropp<strong>in</strong>g power Sn and electronic stopp<strong>in</strong>g power Se. The electronic<br />
stopp<strong>in</strong>g power is proportional to <strong>the</strong> velocity <strong>of</strong> <strong>the</strong> mov<strong>in</strong>g atom s<strong>in</strong>ce <strong>the</strong> process <strong>of</strong><br />
energy loss is dependent on <strong>the</strong> k<strong>in</strong>etic energy <strong>of</strong> <strong>the</strong> mov<strong>in</strong>g atom and <strong>the</strong> nuclear<br />
stopp<strong>in</strong>g power is obta<strong>in</strong>ed through <strong>the</strong> procedure shown <strong>in</strong> <strong>the</strong> previous section.<br />
The <strong>in</strong>teratomic potential used has <strong>the</strong> form,<br />
2<br />
Z1Z<br />
2e<br />
r <br />
V ( r)<br />
<br />
<br />
(3.8)<br />
4 r a <br />
0