Understanding Coulomb Effects in Nanoscale Schottky-Barrier-FETs

Abstract

Abstract-We employ a novel multiconfigurational selfconsistent Green's function approach (MCSCG) for the simulation of nanoscale Schottky-barrier-field-effect transistors (SB-FETs). This approach allows the calculation of electronic transport with a seamless transition from the single-electron regime to room-temperature FET operation. The particular improvement of the MCSCG stems from a self-consistent division of the channel system into a small subsystem of resonantly trapped states for which a many-body Fock space approach becomes numerically feasible and the rest of the system which can be treated adequately on a conventional mean-field level. The Fock space description allows for the calculation of few-electron Coulomb charging effects beyond the mean-field. We compare a conventional Hartree nonequilibrium Green's function calculation with the results of the MCSCG approach. Using the MCSCG method, Coulomb blockade effects are demonstrated at low temperatures while, under strong nonequilibrium and high-temperature conditions, the Hartree approximation is retained. Finally, the visibility of quantum and single-electron effects in scaled transistor structures is discussed.Index Terms-Coulomb interaction, nanowire, Schottkybarrier-field-effect transistors (SB-FETs).

Modified correlation entropy of a gated nanowire system described by a numerically determined non‐equilibrium many‐body statistical operator

“…The single‐particle density matrix () of the system can be obtained from the non‐equilibrium Green's function , which results from the NEGF formalism. Within the employed NEGF/MCSCG approach , the nanowire channel is described as a 1D single‐band tight‐binding chain in the effective mass approximation, represented by a localized orbital ON basis with spin/site orbitals, where the factor 2 stems from spin degree of freedom and denotes the number of localized spatial sites. Therefore, the dimension of the matrix reads as .…”

“…The underlying physical model assumes the knowledge of the (self-consistent) single-particle density matrix [5] ρ 1 of the whole channel system for given voltages V GS and V DS . In the present case, ρ 1 (V GS , V DS ) is determined self-consistently from a non-equilibrium Green's function (NEGF) [15][16][17][18][19][20] calculation of non-equilibrium electronic transport in the NWFET channel. Following the idea of the multi-configurational selfconsistent Green's function (MCSCG) [16,17] approach, the single-particle Hilbert space of the whole channel system is divided into a small, adaptively chosen relevant subspace and an orthogonal rest.…”

“…In the present case, ρ 1 (V GS , V DS ) is determined self-consistently from a non-equilibrium Green's function (NEGF) [15][16][17][18][19][20] calculation of non-equilibrium electronic transport in the NWFET channel. Following the idea of the multi-configurational selfconsistent Green's function (MCSCG) [16,17] approach, the single-particle Hilbert space of the whole channel system is divided into a small, adaptively chosen relevant subspace and an orthogonal rest. Here, relevant states are defined as those natural orbitals (i.e., eigenstates of ρ 1 ) [5,21], which are quasi-isolated (i.e., resonantly trapped) and exhibit occupation fluctuations (i.e., being neither empty nor fully occupied), thus being responsible for few electron Coulomb blockade [22][23][24] effects.…”

“…The underlying physical model assumes the knowledge of the (self‐consistent) single‐particle density matrix () of the whole channel system for given voltages and . In the present case, is determined self‐consistently from a non‐equilibrium Green's function (NEGF) calculation of non‐equilibrium electronic transport in the NWFET channel.…”

Many-body approach to the terahertz response of Wigner molecules in gated nanowire structures

“…Nevertheless, these relevant degrees of freedom and their associated effective parameters in general are nonlinear functions of the actual experimentally accessible parameters ͑such as gate voltages͒ and not known a priori. In order to address this problem, we have recently introduced a multiconfigurational approach 8,13,14 ͑MCSCG͒ which employs a reduced adaptive basis for the simulation of stationary Coulomb blockade effects in gated nanowire structures.…”