Three-Dimensional Electrostatic and Quantum-Confinement Modeling of Silicon Nanowire Double Quantum Dots
We present a three-dimensional simulation study of silicon nanowire double quantum dots (DQDs) with leads at T = 2 K, which extends beyond traditional effective mass or quasi-1D and quasi-2D approaches typically applied to bulk or planar geometries. A 3-D Poisson solver is self-consistently coupled to 2-D Schrodinger along slices normal to transport (width * thickness) to obtain spatially varying subbands and wavefunctions at T = 2 K. The slice approximation is justified by the large aspect ratio (Ltot/W > 20) and by the small (< 1.2 percent) wavefunction variation observed along the transport direction. The resulting effective conduction-band profile is imported into a full-wave, open-boundary Schrodinger solver to compute the transmission spectrum T(E), and the tunnel coupling (tc) is evaluated from the bonding and antibonding splitting of the first two resonances in T(E). The simulations show that narrow dots (W = 5 nm) provide strong confinement and robust single-electron localization but require higher plunger-gate voltage, whereas wider dots (W = 20 nm) load electrons at lower bias but form shallower, more delocalized states. The tunnel coupling decreases as the dot width and length are increased, due to the reduced wavefunction overlap between the dots, and saturates once W > 2LPG, when longitudinal confinement is dominated by the plunger gate length. The simulated tunnel coupling trend agrees with experimental data reported for the Si DQD device.