Graph Theoretical Representation, Analysis and Synthesis of Amorphous Metal Oxide Networks

Abstract

With the advent of amorphous oxide semiconductors (AOS) like amorphous indium gallium zinc oxide (a-IGZO), the analysis and prediction of amorphous structures has regained importance, more so, since first principles based studies are being increasingly employed to explain device behavior. Negative bias illumination stress in a-IGZO thin film transistors is one such example. However, the amorphous atomic structure is complex and defect or dopant studies require each site to be modeled independently and this leads to significant computational costs. Therefore, a simplification in the representation of the amorphous oxide network is effected so that it may lead to identifying similar atomic sites. The amorphous network is visualized as a network of polyhedra. The polyhedra has at its center a cation with the bonded oxygen atoms at the vertices and it comprises the short range interactions characterized by bond lengths and bond angles. Based on a first principles study of 10 a-IGZO models containing 36 cations each, it was found that the 360 polyhedra of the a-IGZO models can actually be described with only ten polyhedral motifs. These polyhedra are then connected to each other via a shared vertex or an edge; face-sharing was not observed in these models. Graph theory is used to map this network using either a graph of cationic polyhedra as the nodes or a bipartite graph (composed of cations and anions as individual nodes), each of which is described using the respective adjacency matrix. The second nearest interactions are characterized by the degree of each vertex and each atomic site is now characterized by a polyhedron and network metrics; and hence, can be compared with same-element sites. The changes in network itself, are quantified as the composition changes, when varying the ratio of In:Ga:Zn in a-IGZO. For example, the average vertex connectivity of a pair of indium sites reflects on the continuity of overlap between the In-5s orbitals which compose the conduction band minimum in a-IGZO, which, in turn, affects the transport properties of the semiconductor. Thus, the long range interactions of the physical amorphous network are described by the graph metrics. Moreover, evolutionary algorithm in conjunction with this graph theoretic representation can be used to generate new amorphous models. Two parent graph are chosen and then spliced and then bred. The new graph is then reverse-engineered to form an amorphous model which then undergoes ionic and volume relaxation in the framework of density functional theory. The resulting graph is the child and the new amorphous model, with the energy as the fitness criteria.