Abstract
It is argued that the topological disorder in a small region of an amorphous solid can be described by the local strain field related to the local reference crystal. A localized state spread only in one distorted region can be viewed as the consequence of superposition among some Bloch waves and its scattering waves caused by the disorder. A semiclassical approximation is used to calculate the phase shift of Bloch waves in the amorphous solid. The inverse participation ratio and the mobility edge positions in the band tails are formulated in terms of the parameters of the disorder potential. The dependence of the band tail decay rates on static and thermal disorders is derived. The model is applied to $a\text{-Si}$, though conceptually it can be implemented to a wide range of disordered systems. The ab initio calculations on $a\text{-Si}$ and the experimental results on $a\text{-Si}$:H are compared to the predictions of our model.
Highlights
It is argued that topological disorder in amorphous solids can be described by local strains related to local reference crystals and local rotations
Key properties like the energy dependence of the Inverse Participation Ratio (IPR), the location of the mobility edges and the decay rate of and tails are expressed in an obscure way, not directly accessible to experiment or simulation[2]
In this Letter we suggest that a local formulation of perturbation theory is effective for the localized states confined to one distorted region and for the first time relate important physical quantities such as the decay rate of band tails and energy dependence of IPR etc. to basic material properties
Summary
+ zIV is the top of the valence band. By Eq (3), under TBA, for a valence state ψkv with energy Ek, the change in phase shift with energy is dδk dE. For a given distorted region, Bloch states close to E0 will suffer larger phase shift. They are more readily localized than the states in the middle of the band. Similar conclusion holds for the Bloch states in the bottom of conduction band. The upper mobility edge of the valence band is the deepest energy level EkVV that the ∗.
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