  Designing tunneling junctions with abrupt on-off characteristics and high
current densities is critical for many different devices including backward
diodes and tunneling field effect transistors (TFETs). It is possible to get a
sharp, high conductance on/off transition by exploiting the sharp step in the
density of states at band edges. The nature of the density of states, is
strongly dependent on quantum dimensionality. To know the current/voltage curve
requires us to specify both the n-side dimensionality and the p-side
dimensionality of pn junctions. We find that a typical bulk 3d-3d tunneling pn
junction has only a quadratic turn-on function, while a pn junction consisting
of two overlapping quantum wells (2d-2d) would have the preferred step function
response. We consider nine physically distinguishable possibilities: 3d-3d,
2d-2dedge, 1d-1dend, 2d-3d, 1d-2d, 0d-1d, 2d-2dface, 1d-1dedge and 0d-0d. Thus
we introduce the obligation to specify the dimensionality on either side of pn
junctions.
  Quantum confinement, or reduced dimensionality on each side of a pn junction
has the added benefit of significantly increasing the tunnel conductance at the
turn-on threshold.
