Abstract
Experimentally, dislocations in germanium have a negative core charge due to the filling of some acceptor states. These states do not appear to be related directly to "dangling bonds," since the charge is similar in screw and edge dislocations. A one-dimensional model is investigated in which a small amount of free volume, to represent the core of the dislocation, is inserted into a ring of $N$ atomic potentials. In this model it is found (a) there is a localized state in the gap; (b) it is pulled out of the upper "conduction" band, in agreement with the sign of the core charge; (c) the localized state exists whether there are bonding states below the gap and antibonding above, or vice versa, and thus is not related to the Shockley condition for a surface state; (d) the cause of the extra state is the local decrease in atom density.
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