Damage formation and annealing studies of low energy ion implants ...
Damage formation and annealing studies of low energy ion implants ... Damage formation and annealing studies of low energy ion implants ...
energy deposition. Equation 2.6 shows that significantly σ is proportional to Z1 2 , Z2 2 , E -2 and sin -4 (θ/2). The implications for MEIS analysis are discussed further in section 4.2.2. p dp Figure 2.1 Scattering into a solid angle. From (16). 2.2.2 The Kinematic Factor Using the hard sphere model a collision between an energetic ion and a stationary target atom is illustrated in Figure 2.2. The incident ion (mass M1) moves towards the target atom (mass M2), with some perpendicular distance between the line of the centre of the particles, p, called the impact parameter. The centre of the incident ion will approach the centre of the target atom to a distance of the sum of the radii of the two spheres, 2R0, where a collision takes place. The incident ion will be scattered and energy will be imparted to the target ion causing it to recoil. Because there are no external constraints total energy and momentum are conserved. 19
M1, V0, E0 Figure 2.2 Elastic scattering configuration. The kinematic factor K is defined as the ratio of the energy of an ion after a collision to its energy before a collision, i.e. 1 1 K ⎢ ⎥ E 0 ⎣V0 ⎦ 2 E ⎡ V ⎤ ≡ = (2.8) It can be shown that 2 2 2 ( M − M sin θ ) 1 ⎡ ⎤ ⎡ V ⎤ 2 1 ⎢ 2 1 + M1 cosθ = ⎥ ⎢ ⎥ ⎣V ⎦ ⎢ + ⎥ 0 M 2 M1 ⎢⎣ ⎥⎦ 20 (2.9) where θ is the scattering angle. Therefore the kinematic factor for backscattering, where M1 < M2 is given by (14, 17), K ⎡ = ⎢ ⎢ ⎢⎣ 2 2 2 ( M − M sin θ ) 2 1 p M 2 2R0 1 ⎤ 2 + M1 cosθ ⎥ + M ⎥ 1 ⎥⎦ 2 M1, V1, E1 (2.10) In Chapter 4 it is shown in more detail how this expression allows MEIS analysis to be sensitive to scattering from different masses and hence be sensitive to different elements (9, 10, 17). φ θ M2, V2, E2
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M1, V0, E0<br />
Figure 2.2 Elastic scattering configurat<strong>ion</strong>.<br />
The kinematic factor K is defined as the ratio <strong>of</strong> the <strong>energy</strong> <strong>of</strong> an <strong>ion</strong> after a<br />
collis<strong>ion</strong> to its <strong>energy</strong> before a collis<strong>ion</strong>, i.e.<br />
1 1<br />
K ⎢ ⎥<br />
E 0 ⎣V0<br />
⎦<br />
2<br />
E ⎡ V ⎤<br />
≡ =<br />
(2.8)<br />
It can be shown that<br />
2 2 2<br />
( M − M sin θ )<br />
1<br />
⎡<br />
⎤<br />
⎡ V ⎤<br />
2<br />
1 ⎢ 2 1 + M1<br />
cosθ<br />
=<br />
⎥<br />
⎢ ⎥<br />
⎣V<br />
⎦<br />
⎢<br />
+<br />
⎥<br />
0<br />
M 2 M1<br />
⎢⎣<br />
⎥⎦<br />
20<br />
(2.9)<br />
where θ is the scattering angle. Therefore the kinematic factor for backscattering, where<br />
M1 < M2 is given by (14, 17),<br />
K<br />
⎡<br />
= ⎢<br />
⎢<br />
⎢⎣<br />
2 2 2<br />
( M − M sin θ )<br />
2<br />
1<br />
p<br />
M<br />
2<br />
2R0<br />
1 ⎤<br />
2 + M1<br />
cosθ<br />
⎥<br />
+ M ⎥<br />
1<br />
⎥⎦<br />
2<br />
M1, V1, E1<br />
(2.10)<br />
In Chapter 4 it is shown in more detail how this express<strong>ion</strong> al<strong>low</strong>s MEIS<br />
analysis to be sensitive to scattering from different masses <strong>and</strong> hence be sensitive to<br />
different elements (9, 10, 17).<br />
φ<br />
θ<br />
M2, V2, E2
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