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Damage formation and annealing studies of low energy ion implants ...

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<strong>and</strong> is approximately 25 times faster than (111) Si (40). Regrown (111) substrates have<br />

been observed to contain high levels <strong>of</strong> defects compared to (100) <strong>and</strong> (110) orientated<br />

substrates. In this thesis all experiments were carried out on (100) Si. A model for<br />

recrystallisat<strong>ion</strong> shows that bonds can be broken <strong>and</strong> reformed to produce the crystalline<br />

phase. To be considered a part <strong>of</strong> the crystal each atom should have at least two<br />

undistorted bonds to already aligned atoms <strong>of</strong> the crystal. For the (100) surface, a single<br />

atom can simply attach to any other atom <strong>of</strong> the crystal but for (110) <strong>and</strong> (111) planes<br />

two <strong>and</strong> three adjacent atoms, respectively, must attach simultaneously, to atoms <strong>of</strong> the<br />

crystal, which is less probable, accounting for the differences in rate <strong>and</strong> defects<br />

observed (39).<br />

The regrowth velocity is also temperature dependent <strong>and</strong> is shown to fol<strong>low</strong> an<br />

Arrhenius type express<strong>ion</strong>.<br />

⎛ E A ⎞<br />

v = v 0 exp⎜−<br />

⎟ (nms<br />

⎝ kT ⎠<br />

-1 ) (3.3)<br />

where v is the growth velocity, k is the Boltzmann constant (8.617E-5 eV/K), T the<br />

temperature at which regrowth is occurring <strong>and</strong> EA the activat<strong>ion</strong> <strong>energy</strong>. v0 <strong>and</strong> EA can<br />

both be obtained from a plot <strong>of</strong> regrowth rates against temperature. Values obtained for<br />

intrinsic (100) Si are EA = 2.68 eV, <strong>and</strong> v0 = 3.07 × 10 15 nms -1 (39), although various<br />

<strong>studies</strong> have produced values for the activat<strong>ion</strong> <strong>energy</strong> from 2.3 to 2.9 eV (41). Doping<br />

changes the regrowth rate. For 2 × 10 14 cm -2 As implanted Si, the values for EA <strong>and</strong> v0<br />

are 2.76 eV <strong>and</strong> 3.68 × 10 15 respectively (39). Figure 3.6 shows the trend in regrowth<br />

rate with temperature for <strong>ion</strong> implanted Si. Values for (110) <strong>and</strong> (111) have been<br />

inferred from the (100) values. Values for SPER rates <strong>of</strong> intrinsic <strong>and</strong> doped Si using<br />

equat<strong>ion</strong> 3.3 are given in Table 3.1 be<strong>low</strong>.<br />

44

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