  Theoretical treatments of tunneling in electronic devices are often based on
one-dimensional (1D) approximations. Here we show that for many nanoscale
devices, such as widely studied semiconductor gate-defined quantum dots, 1D
approximations yield an incorrect functional dependence on the tunneling
parameters (e.g., lead width and barrier length) and an incorrect magnitude for
the transport conductance. Remarkably, the physics of tunneling in 2D or 3D
also yields transport behavior that appears classical (like Ohm's law), even
deep in the quantum regime.
