Electronic properties of an amorphous solid. III. The cohesive energy and the density of states

The effect of topological disorder on the cohesive energy and the electronic density of states of amorphous Si and Ge is investigated. The methods used include moment expansions and various exactly soluble models that include the Bethe lattice and Husimi cactus lattices, for which an extremely compact derivation of the density of states is presented. An isolated topological defect in a diamond cubic lattice is also studied. The question of the existence of square-root band edges in topologically disordered systems is examined. A review of recent experimental evidence, relating to the shape of the density of states, is given.