Two dimensional (2D) materials with a finite band gap and high carrier mobility are sought after materials from both fundamental and technological perspectives. In this paper, we present the results based on the particle swarm optimization method and density functional theory which predict three geometrically different phases of carbon phosphide (CP) monolayer consisted of sp2 hybridized C atoms and sp3 hybridized P atoms in hexagonal networks. Two of the phases, referred to as {alpha}-CP and b{eta}-CP with puckered and buckled surfaces, respectively are semiconducting with highly anisotropic electronic and mechanical properties. More remarkably, they have lightest electrons and holes among the known 2D semiconductors, yielding superior carrier mobility. The {gamma}-CP has a distorted hexagonal network and exhibits a semi-metallic behavior with Dirac cones. These theoretical findings suggest the binary CP monolayer to be yet unexplored 2D materials holding great promises for applications in high-performance electronics and optoelectronics.
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