Quantum confinement corrections to the capacitance of gated one-dimensional nanostructures

Abstract

With the help of a multiconfigurational Green's function approach we simulate single-electron Coulomb charging effects in gated ultimately scaled nanostructures which are beyond the scope of a self-consistent mean-field description. From the simulated Coulomb-blockade characteristics we derive effective system capacitances and demonstrate how quantum confinement effects give rise to corrections. Such deviations are crucial for the interpretation of experimentally determined capacitances and the extraction of applicationrelevant system parameters. DOI: 10.1103/PhysRevB.74.113310 PACS number͑s͒: 73.63.Ϫb, 72.10.Ϫd, 73.22.Ϫf, 73.23.Ϫb One of the major challenges for the simulation of electronic transport in low-dimensional nanostructures consists in an adequate description of the Coulomb interaction. In ultimately scaled semiconductor nanosystems, only a few electrons constitute the current. Thus, the details of the electron-electron interaction may become crucial for the electronic properties, as can be seen in experimentally observed single-electron charging effects in carbon nanotubes and III-V nanowhiskers.1,2 The channel region of a typical application-relevant nanostructure involves on the order of 100 single-particle states ͑or sites͒ and can be highly inhomogeneous and anisotropic. Here, external contacts and gate electrodes in general introduce nonlinear perturbations to the system. Hence, highly idealized interacting few-level models with a small number of effective parameters ͑constants͒ become inadequate. For a realistic simulation of quantum transport in application-relevant nanodevices, various approaches have been used, differing in the formulation of Coulomb interaction and contact coupling. While the orthodox theory 3,4 correctly describes few-electron effects such as single-electron tunneling in quasi-isolated quantum dot systems, the nonequilibrium Green's function ͑NEGF͒ formalism 5-8 also accounts for contact renormalization and dissipation terms. However, the NEGF formalism becomes unable to describe the details of charging effects of a few fluctuating electrons as soon as a mean-field approximation is introduced.Recently, we have presented a multiconfigurational selfconsistent Green's function ͑MCSCGF͒ approach, 9 which represents a consistent extension of the mean-field NEGF method for the inclusion of single-electron effects under application-relevant conditions. This approach combines the simplicity and scalability of the mean-field NEGF approach with a many-body Fock space description of the Coulomb interaction of those electrons that are resonantly trapped within the nanostructure. As a key element, the algorithm identifies "relevant" trapped single-particle states that are subject to occupation fluctuations. Within the resulting relevant Fock subspace, many-body "configurations" and associated weights w are defined as eigenstates and eigenvalues of the projected many-body statistical operator MB , respectively. Consequently, the system Green's functions are written as weighted avera...

Understanding Coulomb Effects in Nanoscale Schottky-Barrier-FETs

“…Furthermore, coupling to the contacts with nonequilibrium carrier injection and coupling (tunneling) to the rest of the system is described by means of self-energy kernels, depending on the chosen Fock space method. For the latter, various choices with different levels of sophistication are possible, for example: 1) Exact diagonalization with entropy maximization and Dyson's equation [3], [4] as subsidiary condition [15], [21]; 2) RTRG [5], [6]; or 3) Fock space Green's functions [7]. In the following, we will discuss the first option based on diagonalization.…”

“…The effective total capacitance C * is proportional to the classical total capacitance of the channel [21], however, with a proportionality factor which, in general, also depends on L, d ox , the electron number, and other parameters due to quantum effects. In principle, this factor has to be determined from the many-body quantum calculations, as was discussed in the study in [21].…”

“…In principle, this factor has to be determined from the many-body quantum calculations, as was discussed in the study in [21].…”

“…A possible solution is the combination of the numerically well scaling mean-field NEGF with a Fock space description for those states where many-body Coulomb effects may become important for the device characteristics. In this context, we have recently proposed a multiconfigurational self-consistent Green's function approach (MCSCG) [15], [21] for the realistic simulation of nanodevice systems under application-relevant conditions with reasonable numerical efforts. Fig.…”

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.…”