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

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 application-relevant system parameters.

Figure 1

Schematic sketch of the considered coaxially gated nanosystem (see text for more details).

Figure 2

(a) Simulated single-electron tunneling characteristics as a function of the applied gate and drain voltages for $T=77\mathrm{K}$. Here, the absolute value of the drain current is mapped to a nonlinear gray scale. Within the black diamonds of Coulomb blockade the electron number becomes quantized as indicated by white numbers. $\Delta V_G$ and $\Delta V_D$ denote the width and half-height of the first diamond, respectively. (b) Corresponding local density of states and mean-field potential within the channel for selected points $0,1,X$ in map (a). Point $X$ corresponds to a nonequilibrium state with electron number $\approx 0.3$.

Figure 3

(a) Simulated capacitances for the first two electrons as a function of the channel length $L$ with an adaptive gate voltage. The screening length $\lambda \approx 3.7\mathrm{nm}$ and the effective mass $m^{*}=0.05m_e$ are kept constant. (b) Quantum confinement factor $f_{\Sigma }=C_{\Sigma }^{\mathit{hom}}∕C_{\Sigma }^{*}$ and gate efficiency ${\eta }_G=C_G^{*}∕C_{\Sigma }^{*}$ as derived from (a).