Dislocation Kink Motion - AB-Initio Calculations and Atomic Resolution Movies
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261 Mat. Res. Soc. Symp. Proc. Vol. 408 @1996 Materials Research Society
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Fig. 1. Projection down (111) of atomic structure of reconstructed 300 partial dislocation with kinks at A. Dotted lines trace dislocation cores. Unit cell used for calculations and stacking sequences indicated. N-membered rings in middle layer (bold lines) numbered. In recent years we have used both atomic resolution TEM imaging and ab-initio computations to estimate these critical energy barriers for kink nucleation and motion on the two dominant partial dislocations in silicon, and to try to determine the obstacles to kink motion at the atomic scale. The following is a review of our most recent work, which includes the first direct experimental observations of kink motion, and our calculations of the migration energy for reconstructed kinks on the 300 Shockley partial dislocation lying on (111) in silicon. AB-INITIO CALCULATIONS FOR KINK ENERGIES Dislocations in silicon are dissociated into partial dislocations, separated by ribbons of stacking fault SF, as shown in Fig. 1 and in the experimental images discussed later. Dislocation motion results if thermal fluctuations throw a segment of line forward, generating kink pairs (one of which is shown at A in Fig. 1), which are driven apart along the line by the application of an external stress. Measurements of dislocation velocity by TEM, intermittent loading and internal friction [5] give 1.8 < Q < 2.5 eV for the sum of the mobility and nucleation energies. For our calculation of the mobility energy, we have used a centrosymmetric supercell containing 186 Si atoms and two 300 partial dislocations forming a dipole, as shown in Fig. I. The driving force for kink motion is the tendency for the dipole to annihilate, which provides a stress on each dislocation of about 198 MPa (We take the stacking fault energy y = 76 ergs/cm 2
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[ 16]) . Each partial contains a kink (of opposite signs), and the monoclinic supercell used is periodically continued without severe bond distortion. The lateral alignment of kinks minimizes kink-kink forces. The structure corresponds to a line of geometric kinks running 10.820 away from [1-10] . The atomic model used for our dislocation core calculations was partly derived from high resolution electron micrographs [17] . Since a reconstructed structure is favored for the dislocation core [18,19,20] we have adopted Hirsch's reconstructed model [6] for the kink, and do not consider anti-phase defects, which may be rare [5]. We denote the initial state of the kink by A and the final state, in which it has moved one period along the dislocation line, by B (Fig. 1). The first step is to compute the total internal energy of the supercell as a function of some configuration coordinate representing the motion of the kink from A to B. An approximate first-principles electronic structure method [21 ] was used which closely matches more rigorous calculations, but greatly reduces computational effort. Previous applications include surface reconstructions, cla
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