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Novel Quantum Hydrodynamic Equations for Semiconductor Devices

The Liouville equation for the distribution function is solved and a series solution for the Wigner distribution function is derived. In this solution, potential is nonlocal so that the distribution function in each point is influenced by the potential of the entire space. By computing the carrier density, an effective classical potential is defined. In a quantum system this effective potential replaces the classical potential. Based on the solution of the Liouville equation a novel set of three-dimensional quantum hydrodynamic equations (QHD) is derived. The form of the resulting QHD equations is similar to the classical hydrodynamic (HD) equations but there are explicit quantum corrections which appear in the pressure tensor of electron gas and energy density.