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On the influence of short and medium range order on the material band gap in hydrogenated amorphous silicon Amorphous silicon carbide ͑a-SiC͒ networks generated from melted SiC at various quench rates ͑from 10 14 to 5 ϫ 10 11 K / s͒ are studied with Tersoff potential based molecular-dynamics simulations. With the decreasing quench rates, dramatic changes are observed in chemical order, as well as in its topological orders over both short and medium ranges. The corresponding modification of topological short-range order is manifested not only by improvement of the characteristic tetrahedral configuration, but also by variation in the spatial distributions of the homonuclear bonds. On the other hand, the corresponding development over medium range gives rise to a more compact and more homogeneous structure. The essential mechanisms determining the atomic arrangements on both length scales are further explored. It is reasonable to argue that chemical order, as a function of the quench rate, should be mainly responsible for the topological features of a-SiC.