Ion Implantation and Synthesis of Materials - Studium

8.4 Dechanneling by Defects101Dechanneling is greatly enhanced by the presence of defects. First, displacedatoms in the center of the channel provide much stronger scattering than theelectrons. The probability of dechanneling per unit depth dP D /dz is then given bythe product of the defect dechanneling factor, σ D , and defect density, n D ,dPDdz= σ nDD( z)(8.4)The probability of dechanneling per unit depth σ D n D has units of cm −1 . Forpoint-scattering centers, as for interstitial atoms, σ D can be though of as a crosssection for dechanneling, and n D is given by the density of interstitial atoms perunit volume at a given depth.The calculation is for a uniform beam incident on isolated atoms in a channel(Fig. 8.7). Since we are only interested in scattering angles greater than the criticalangle (ψ c ~ 1°), the impact parameter is relatively small (r 1 ~ 10 −2 Å ); thus we usethe unscreened Coulomb potential. In this calculation the dechanneling is a resultof binary scattering by isolated displaced atoms in an otherwise perfect crystal.The defect dechanneling factor under these conditions for isolated atoms in achannel is the cross section for the close-impact collision probability of scatteringa particle through an angle θ greater than the critical angle ψ c . The unscreenedscattering cross section (Rutherford scattering cross section with M1 = M )2 isgiven by2dσ⎡ ZZe ⎤1 2= ⎢ 2 ⎥dΩ⎢⎣4Esin ( θc/2) ⎥⎦2(8.5)in center-of-mass coordinates. This expression does not include the small M 1 /M 2corrections found in exact calculation for laboratory coordinates (Chu et al. 1978).Equation 8.5 is integrated over angles greater than ψ c for the cylindricallysymmetrical case of axial channeling to yieldATOM ROWSINTERSTITIALATOMSDECHANNELED PARTICLEFig. 8.7. Scattering of a beam of channeled particles by interstitial atoms