Numerical solution of the Schrödinger equation in nanoscale side-contacted FED applying the finite-difference method

• Quantum characteristics of side-contacted field-effect diode is studied using the finite-difference method. • Schrödinger equation is solved regarding assessed potentials in the ON and OFF states. • Potential profiles, energy levels, and time-independent/dependent wave functions are studied. • Remarkable potential barriers in the OFF state result in an inability of electron movement from source to drain in low energies. • The transport is feasible in higher states, so that minority carriers contribute to transport mechanism in the highest energies. Numerical approaches play an outstanding role in solution of quantum mechanical problems with due attention to the complexity of analytic solutions for open systems. This paper studies quantum characteristics of the previously proposed side-contacted field-effect diode (S-FED) as an emerging device in the modern system-on-chips (SoCs) using the finite-difference method (FDM). The characteristics obtained by solving the Schrödinger equation and regarding the distinguished potentials in ON and OFF states include energy levels and time-independent/dependent wave functions. The cosine dependency of eigenvalues on longitudinal position conveys level broadening in high states stringing a sequence of probability oscillations in the ON state. Remarkable potential barriers in the OFF state result in an inability of electron movement from source to drain in low energies; nevertheless, by overcoming the total energy to potential barrier, the transport is feasible in higher states, so that minority carriers contribute to transport mechanism in the highest energies.