High-Order Element Effects of the Green´s Function in Quantum Transport Simulation of Nanoscale Devices

High-order element (HOE) effects of the Green´s function are studied by virtue of a comparative study between the recursive Green´s function (RGF) method and the contact block reduction approach in double-gate metal-oxide-semiconductor field-effect transistor simulations. In general, quantum-mechanical simulations of 2-D and 3-D nanoscale devices are very computationally challenging. An efficient and widely used approach for the multidimensional problems is the RGF method. As the tridiagonal or block tridiagonal property of a self-energy matrix is exploited in the RGF method, the HOEs of the gate contact self-energy matrix are often omitted. This study on the HOE effects offers a good physical insight as well as provides a necessary measure on the applicability of the RGF method. Specifically, effects on gate current, electron density, and current density are investigated.