Fully analytic compact model of ballistic gate-all-around MOSFET with rectangular cross section

We develop a fully analytic compact model of gate-all-around metal-oxide-semiconductor field-effect transistors in the ballistic transport. The potential shape in the wire cross section is approximated by a parabolic function. With the model potential, electron energy levels are derived analytically and have an unknown parameter. The electron energy levels are determined by solving approximately the coupled equation of charge densities derived from quantum mechanics and electrostatics. We solve the coupled equation with the Aymerich approximation technique. The unknown parameter and also electron energy levels can be derived analytically. Device characteristics calculated from the analytic model are compared with the model with the unknown parameter obtained numerically, demonstrating an excellent accuracy. We carry out a circuit simulation with the analytic model of ballistic gate-all-around metal-oxide-semiconductor field-effect transistors.