Defect scaling in non-crystalline floppy/under-constrained and rigid/over-constrained thin films: Applications to a-Se, a-Si, and a-Si(H)

Bond constraint theory provides insights into glass and intermediate phase formation in covalently-bonded non-crystalline networks. Metrics are the average number of bonds/atom, N av , and average number of bending and stretching constraints per atom, C av . C av is a linear function of N av :C av = 2.5N av - 3, with ideal, low defect density glasses and thin films having values of N av and C av equal to 2.4, and 3.0, respectively. In over-constrained films, it has been argued and demonstrated experimentally, that the density of intrinsic defects is proportional to N av - 2.4. In this paper we demonstrate that this scaling relationship, with the same empirical constants applies to floppy or under-constrained films with the example being a-Se where N av has been determined from EXAFS studies and is ∼2.2. In addition we demonstrate that the density of defects in as deposited a-Si with a 6% density deficit, and broken bonding constraints, can be treated in the same way as spacing-filling over-constrained networks.