10.3. RESONANT TUNNELING 493
E
0
kπ/azone edgeE
0
k2πReduced
zone edgenaanaCrystalSuperlatticeFigure 10.3: An increase in periodic spacing through the use of a superlattice can reduce the
k-space an electron has to traverse before it reaches the zone edge. The reduced zone edge may
allow the possibility of Bloch-Zener oscillations.
region. A particularly interesting outcome of resonant tunneling is “negative differential resis-
tance.” In Fig. figure 10.4a we show a typical potential profile for a resonant tunneling structure.
As shown the double barrier structure of figure 10.4 has a quasi-bound ground state at energyE 0
as shown. The levelE 0 is close to the level in the quantum well formed within the double barrier
region but it is broadened due to the escape lifetime. The broadening comes from the Heisenberg
energy-time uncertainty. If the electrons coming from the left have energies close toE 0 they are
able to transmit through the structure. The operation of a resonant tunneling structure is under-
stood conceptually by examining figure 10.4. At zero bias, point A, no current flows through the
structure since the allowed level in the well is not aligned with the energy of electrons coming
from the left.. At point B, when the Fermi energy lines up with the quasibound state, a maximum
amount of current flows through the structure. Further increasing the bias results in the structure
of point C, where the current through the structure has decreased with increasing bias (negative
resistance). Applying a larger bias results in a strong thermionic emission current and thus the
current increases substantially as shown at point D.
To understand the tunneling behavior, the potential profile (say, the conduction band lineup)
is divided into regions of constant potential. The Schrodingerequation is solved in each region ̈
and the corresponding wavefunction in each region is matched at the boundaries with the wave-
functions in the adjacent regions as shown in figure 10.5.