Page 97 - Principles and Applications of NanoMEMS Physics

3. NANOMEMS PHYSICS: Quantum Wave Phenomena 85

Resonant tunneling devices are implemented in a variety well/barrier
materials systems [116], including, Type-I heterostructures (transport occurs
exclusively in the conduction band) such as GaAs/Al xGa 1-xAs, InAs/AlSb,
In 0.53Ga 0.47As/AlAs, and Type-II heterostructures (transport involves
conduction and valence bands) such as GaSb/AlSb [118]
The ideal RTD current-voltage characteristic is shown in Fig. 3-4(b) and,
with respect to Fig. 3-4(a), an accepted plausible explanation of it is as
follows [116[, [117]. With no voltage applied, the system is in equilibrium as
no forces are experienced by the electrons in the contacts and no current
flows: (1) As the voltage is increased electrons tunnel the left-hand barrier,
propagate through the well and tunnel through the right-hand barrier, and an
increasingly large current flow; (2) When the voltage is such that the energy
of the incoming electron distribution overlaps the first quantized energy of
the well, E , maximum current transmission is achieved, this is the resonant
0
tunneling condition; (3) When the overlap decreases, at higher applied
voltages, the transmission, and thus current, rapidly decreases, thus the
negative resistance region is produced. This explanation assumes the
electron momentum transverse to the well is conserved.
Since the intrinsic time it takes an electron to traverse the structure is
related to Heisenberg’s uncertainty principle, τ = = Γ , where Γ is the
energy width of the quantized level, the process is very fast, i.e., ~1ps, so the
devices are ideal for THz applications [118, 119].
The simulation and modeling of RTDs is a relatively mature subject [116-
123] and includes a variety of approaches ranging from those neglecting
scattering and charge effects to those including them to a variety of degrees.
These models typically reproduce features of the I-V curve related to energy
levels in the device, such as the voltages at which peak and valley currents
occur, but not the magnitudes of these currents. A typical approach is the
two-band tight-binding model, exposed by Schulman [124] for modeling a
GaAs-GaAlAs RTD. In particular, by neglecting scattering and charge
effects it focuses on calculating the transmission coefficient of the structure
by employing an atom-to-atom transfer matrix technique that builds up the
electron wave function as it propagates through the device layers. The model
divides the structure as shown in Figure 3-5, assumes that the wave function
is a combination of s-like orbitals on each cation (Ga, Al) and a p-like orbital
on each anion (As), of the form,
Ψ = C φ + C φ p , (10)
s
p
s
and sets up a tight-binding Hamiltonian of the form,