Outline
- Introduction
- Double Barrier Quantum Wells (DBQW)
- Theoretical Advances
- The NDR Mechanism
- Capacitance of the DBQW
- Equivalent Circuit Models
- Time-Dependent Behaviour and Switching
- Emitter Dynamics
- Advances in Materials Systems
- GaAs/AlGaAs
- InGaAs/InAlAs
- Pseudomorphic InGaAs/AlAs
- InAs/AlSb
- Theoretical Advances
- Resonant Interband Tunneling (RIT) Devices
- Double Well RIT
- Double Barrier RIT
- Applications
- Detectors
- Oscillators
- Mixers
- Multipliers
- Sample and Hold
- Trigger Circuits
- Pulse Generators
- A/D Circuits
- Conclusions
- References
1. Introduction
The concept of using resonant tunneling in a double barrier device was first proposed in 1963 [Dav63], in the
context of a "double barrier triode". The more familiar double-barrier diode was first proposed several months
later [Iog64]. A decade passed before the first practical resonant tunneling devices emerged [Cha74], and a further
decade passed before the tremendous bandwidth of the RTD was first demonstrated by Sollner et al [Sol83]. However,
Sollner's demonstration of detection and mixing at 2.5 THz (albeit at 25 K) sparked a tremendous surge in interest
in the resonant tunneling diode, leading to impressive advances since 1983. Figure 1.1 shows the almost exponential
improvement in the operating speeds of the fastest RTDs with time. Brown [Bro91] demonstrated a fundamental-mode
RTD oscillator at 712 GHz, which makes the RTD the fastest solid state source currently available [Bor95].
Indeed, the achievement of 712 GHz oscillation is all the more impressive since it was measured at room
temperature. This is one of the more exciting aspects of the RTD - by coupling a quantum effect (the quantum wells)
with a macroscopic effect (the semiconductor energy gap), the overall effect is preserved despite the relatively
high temperature. This allows the RTD to be seriously considered as a general purpose switching element for
integration into mass-produced circuitry, if the fabrication technology itself (currently dominated by MBE) can be
adapted for high volume.
This paper discusses the state of the art in basic RTD structures and material systems. The basic structures can
be broadly classified as the traditional double-barrier quantum wells (DBQWs), and the more recent resonant
interband tunneling devices (RITs). Theoretical advances are discussed where the contribute significantly to the
qualitative understanding of RTDs (as opposed advances in quantitative simulations and calculations). At the end,
several demonstrated applications of RTDs are discussed.
2. Double Barrier Quantum Wells (DBQW)
The DBQW was the original, and is still the most common, resonant tunneling diode structure. The energy band
diagrams for the DBQW under several biases are shown in Figure 2.1. The basic operation of the device is plain to
see: when the bias is such that the energy level in the quantum well is aligned with a population of electrons
above EC in the emitter, the electrons may tunnel from the emitter, to the quantum well, and through to
the collector. When the quantum well energy level is below EC, no current may flow by this tunneling
mechanism (although thermionic currents can flow by thermally surmounting the emitter-barrier, and other tunneling
currents may flow if higher energy levels exist in the well.)
2.1 Theoretical Advances
2.1.1 The NDR Mechanism
In the past, some confusion has arisen regarding the origins of the negative differential resistance (NDR) exhibited by the DBQW. One school of thought considered the NDR to be a direct result of the reduction in dimensionality as the electrons tunnel from the emitter to the well. Specifically, in the emitter, the electron energy is given by
(2.1.1.1)
and in the well,
(2.1.1.2)
Conservation of momentum dictates that kXY is equal in both (2.1.1) and (2.1.2), hence one can write:
(2.1.1.3)
Evidently, if the electron energy in the emitter is below that of the quantum well energy level, kZ
will not be real and the current will stop flowing, resulting in the NDR. This view of the NDR phenomena does not
require that the electron wave function in the well be coherent, and is called incoherent, or sequential
tunneling.
A second school of thought considered the case where the electron wave function in the well was assumed to be
coherent. In this case, the barrier structure is analogous to a Fabry-Perot etalon, and constructive interference
of the electron wave functions occurs when the electrons have an energy equal to the bound state energy. For other
energies, destructive interference occurs, resulting in the NDR. As is true with the optical Fabry-Perot resonator,
the transmissivity of the double barrier will display a peak when the transmissivity of the individual barriers are
equal [Cap89].
It was previously believed that these two effects were entirely separate. In [Cap86] Capasso wrote, "Negative
differential resistance arises simply from momentum and energy conservation and does not require the presence of a
Fabry-Perot effect". However, Hu [Hu93] has shown this to be incorrect. The development of equation (2.1.1.3)
assumes the presence of an energy level at Ewell, without considering if such a level can exist in the
presence of an incoherent wave function. Hu has shown that the presence of a stable energy level in the quantum
well implies the existence of a Fabry-Perot resonance. Wave-function scattering in the well will reduce the
coherence and the Fabry-Perot resonance, but it will also broaden the quasi-2D states around Ewell,
until in the limit of complete incoherence, the quasi-2D states become essentially 3D, and the NDR predicted by
equation (2.1.1.3) disappears.
Hu has proposed a "damped Fabry-Perot" approach [Hu93] that covers the entire range of coherency. This approach
is expanded in [Hu93b], which allows the prediction of the dependence of the intrinsic bistability in RTDs upon the
structural parameters.
2.1.2 Capacitance of the DBQW
One of the reasons that the tunnel diode (i.e., the non-resonant Esaki diode [Esa58]) never obtained the
widespread use that was initially expected of it is that the high doping required to obtain a narrow depletion
region commensurate with tunneling also creates a large junction capacitance. The barriers and quantum wells in an
RTD, in contrast, are usually undoped. This limits the switching speed of the best tunnel diodes to about 12 ps
[Yan94], compared to the best reported switching times of RTDs of 1.2 ps [Özb93]. Similarly, the highest
fundamental mode oscillations observed in tunnel diodes were at 103 GHz (at a very low power level) [ Bro87]
compared to 712 GHz for RTDs [Bro91].
However, despite the fact that the barrier and quantum wells are undoped, it is not obvious at a glance that RTDs have a lower capacitance than Esaki tunnel diodes. Figure 2.1.2.1 shows the energy band diagram of a DBQW RTD. When the device is conducting heavily, one might expect that the carriers in the emitter would form a parallel-plate capacitance with the electrons in the well, resulting in a specific capacitance of:
(2.1.2.1)
where and L refer to the permittivity and width, respectively, of the emitter-well barrier. However, it was found that when this expression was used to estimated fmax the experimentally determined fmax was underestimated by three orders of magnitude [Lur85].
For the purposes of calculating fmax, a better value of capacitance is found by the formula
(2.1.2.2)
where LD is the width of the collector depletion region width, LW is the width of the
barrier-well-barrier structure, and LA is the width of the emitter accumulation region [Bro89]. This
equation shows a slight dependence on bias through the LD term, however it does not explain the large
capacitance peak observed experimentally near resonance [Jo94].
More recent approaches to estimating the capacitance have been equally problematic. Genoe et al presented a more
elaborate derivation of the capacitance in a DBQW [Gen91]. The essence of their model is illustrated in Figure
2.1.2.2, where
(2.1.2.3a,b)
The quantum well capacitance is determined by considering the change in the quasi-Fermi necessary to allowed
extra charged to be stored. (The electron seas in the emitter and collector can charge or discharge with virtually
no change in the Fermi level; this is not true in the restricted quantum well.) However, it is assumed in their
derivation that the electrons in the well are totally scattered, such that the electrons are completely
"thermalized", or in equilibrium. In their words, "we limit our calculations to the case of complete sequential
tunneling" [Gen91]. However, as discussed in the previous section, this corresponds to the case of no NDR! As a
result, these derivations cannot be realistically used.
Hu and Stapleton [Hu91] presented a quasi-static derivation of the quantum well capacitance by calculating the
charge stored QQW(VD) in the well, and calculating the capacitance as
(2.1.2.4)
While this method did have the desirable result of lowering the capacitance by several orders of magnitude
compared to (2.1.2.1), it also predicted a minimum in capacitance at resonance. Experimental results [Jo94]
unequivocally showed a capacitance maximum at resonance (which indeed one might expect intuitively). This
quasistatic approached is shown to be incorrect in [Lio94] by virtue of the fact that the quantum well is charged
through the emitter and discharged through the collector. Thus a different mechanism is at work for a positive
dVD than for a negative dVD, rendering useless a quasistatic analysis based on a succession
of DC points.
Liou and Roblin [Lio94] have presented the results of simulations run on a quantum simulator, which solves the
Poisson and Schrödinger equations self-consistently using a harmonic balance method. This method appears to
provide both the lower capacitance expected from the high fmax measurements, and the prediction of a
capacitance peak at resonance. Unfortunately, the simulated results have not yet been compared quantitatively to
experimental structures. Also, the nature of the simulation approach prevents any simple analytical solutions from
being obtained from the theory. These simulations were performed on a Cray Y-MP supercomputer. These facts suggest
that there is still ample room for improvement in the modeling of the DBQW capacitance.
It is remarkable that the nature of the DBQW's low capacitance has been so poorly understood until very
recently, in light of the fact that this low capacitance is one of the key features of the RTD.
2.1.3 Equivalent Circuit Models
Despite the poor understanding of the DBQW capacitance, the generally accepted equivalent circuit of the DBQW
has remained in use for several years, and is shown in Figure 2.1.3.1.It consists of a fixed parasitic series
resistance RS, the differential conductance G(VD) representing the RTD's nonlinearity, the
capacitance C(VD) as discussed above, and LQW(VD), a quantum-well related
inductance given by
(2.1.3.1)
where is the ground-state lifetime. This inductance accounts for the fact that the wavefunction in the well can
not change instantaneously in reaction to a voltage step. These leads to a current lag, and hence an inductive
behaviour.
This model has the advantage over other possible models [Lio94] that all of its elements are frequency
independent.
2.1.4 Time-Dependent Behaviour and Switching
In light of the confusion surrounding the calculation of the DBQW capacitance, it is not surprising that there
has been some controversy in predicting the DBQW switching times. The first method proposed [Liu87] for estimating
the switching time of RTDs was based on that of the Esaki diode [Gia77], giving
(2.1.4.1)
where IP and IV are the peak and valley currents, V1 and V2 are the
initial and final voltage states, and C is the diode capacitance. Whitaker's [Whi88] experimental results for
GaAs/AlAs diodes apparently showed reasonable agreement with equation (2.1.4.1). Switching times of 1.9 ps were
measured, versus a predicted 2.9 ps. However, these experimental results have been criticized as unreasonably fast,
due to the nature of the electrooptic measurements made [Özb93 and references therein]. A higher switching
time of about 12 ps has been suggested as a more reasonable expectation for such a device [Cho92].
Diamond et al have studied equation (2.1.4.1) and have predicted that it will grossly underestimate the
switching time [Dia89]. They have shown that rather than considering an average negative resistance, as in
(2.1.4.1), it is more realistic to approximate the I-V in the switching region as two linear segments, one with
negative resistance, and one with positive resistance. This analysis typically yields values of tR 4 to
10 times larger than that of equation (2.1.4.1). As a general rule of thumb, a value 4 to 5 times the value of
(2.1.4.1) is used for tR estimates [Cho92b,Yu94].
However, this approach has also been shown to have inadequacies. In one experiment [Mat93] the measurement
switching time was 12 times larger than predicted. However, the fallacy of this theoretical approach should be
obvious given the discussion of the previous section, where it was noted that the RTD capacitance becomes
significantly larger near resonance. In the two calculations discussed above, the capacitance has been treated as a
constant, usually estimated using equation (2.1.2.2). Mattia attributed the discrepancy in the results to the fact
that the quantum-well charging time is not accounted for in the simple estimates of capacitance, and indeed, this
is consistent with the Poisson-Schrödinger simulations discussed above.
Some analytical formulas have been proposed to account for both the RC delay and the quantum well charging time
[Joo93]. The well charging time can be approximated as the steady-state charge in the well divided by the peak
current (this quantity is called the "dwell time"), which leads to the expression:
(2.1.4.2)
where L, m*, h, k3, and B2 are the width of the well, the electron effective mass,
Plancks's constant, the resonance wave number in the well, and the transmission probability for tunneling through
the second barrier at resonance. The RC time is calculated as
(2.1.4.3)
where QE represents the charge stored in the emitter region. This will be approximately equal to the
off-resonant capacitance. In practice, td and are of the same order of magnitude, and either may
dominate. This explains why sometimes the 4-5RC rule for tr sometimes appears to work well, and other
times it does not. It is most useful as an estimate of the minimum achievable switching time, rather than the
actual switching time.
Thus far this discussion has primarily dealt with the effect of capacitance on switching time. Obviously, the
NDR is the other important factor. Equation (2.1.4.1), and the subsequent modifications presented above, show that
a low NDR is desirable for high speed operation. Thus, devices with high peak-to-valley current ratios (i.e.
devices with a large I for a given peak-to-valley voltage difference) are desirable for the highest-speed
applications. It has been shown that the NDR can be estimated as [Coo86]
(2.1.4.4)
where is the energy linewidth of the quantum well energy level. A smaller linewidth will increase Rn and decrease speed. (Interestingly, as 0, equation 2.1.4.4 also predicts that there is a non-zero minimum achievable Rn.) Furthermore, it is well known from quantum mechanical scattering theory that the tunneling time through a resonant structure is given by [Pee92,Ric84]
(2.1.4.5)
This provides the counter-intuitive result that scattering in the well, which leads to an increase in , is
absolutely essential for high-speed operation of an RTD. It also provides the interesting insight that neither the
purely incoherent tunneling nor purely coherent tunneling will lead to a useful device.
2.1.5 Emitter Dynamics
This fact that the tunneling speeds decreases as 0 leads to some interesting results regarding the effect of the
doping of the emitter on the overall speed of the RTD. Zohta has shown that the current through a DBQW can be
considered as consisting of two components, with different properties: one with electron energies E <
ER + op, and one with E ER + op, where ER is the quantum
well energy level and op is the energy of a longitudinal-optical phonon [Zoh94,Zoh95]. The component
with E ER + op will experience phonon scattering, and hence have a much lower tunneling time
than the lower energy electrons. Figure 2.1.5.1 shows how this relates to the doping of the emitter. A more highly
doped emitter will have a higher EF, which will lead to a higher population of electrons above
ER at resonance. This increases the probability of phonon-scattered tunneling occurring, and results in
a faster device.
It has also been shown that the doping of the emitter layer has a very large influence of the formation of the
plateau seen in the NDR region of some I-V measurements on RTDs [Nak94]. Nakano found that in order to simulate an
I-V curve that displayed the plateau effect, is was necessary to perform time-steps of 2.4 fs in their simulator.
With a time-step size of 24 fs, the plateau was not observed at all. This was explained by the fact that the
electrons in the emitter rearrange in response to an electric field on a time scale given by the plasma-oscillation
time, which is
(2.1.5.1)
For ND = 2 1018 cm-3, tP = 74 fs, explaining the tiny time-step
required for simulations. With the dynamics of the n+ emitter region accounted for, it was found that the
calculated I-V curves demonstrated excellent qualitative and quantitative agreement with experimental results.
However, these calculations were performed on a massively-parallel, 8192 processor computer. The simulation scheme
used for these calculations is more complicated than the Poisson-Schrödinger approach described earlier, used
by Liou and Roblin [Lio94] to calculate the C(V) characteristics. To quote from [Nak94], "starting with the
equilibrium wave functions, we switch on a uniform electric field suddenly at time t=0, and follow the real-time
evolution of the system by solving the time-dependent Kohn-Sham equations self-consistently with the Poisson
equation and the exchange-correlation potential. Also the Langevin equation is solved concurrently for the
center-of-mass motion of the electrons".
In general, the emitter is not uniformly doped. It has been found that by using a two-step emitter spacer layer
an improved PCVR can be obtained. (The spacer layer in the region between the barrier layer and the very heavily
doped contact region, which is a part of the emitter.) The doping is increased in steps, or continuously, away from
the barriers. Originally, it was believed that this improved the material quality and reduced impurity densities,
leading to higher PCVR. However, experiments [Che89] proved this to be untrue, by deliberately introducing
doping-induced defects into the AlAs barriers. Instead, the two-step spacers in the emitter induce band-bending, as
shown in Figure 2.1.5.2. This leads to a wide, low barrier in the emitter, meaning that the device now functions as
a pseudo-triple barrier, rather than a double barrier. Since a triple barrier displays a sharper transmission peak,
it is not surprising that the PCVR should improve.
It should be noted that discrete energy levels may form in the emitter, at the emitter-barrier junction, because
of the band bending. Electrons may then occupy the lower energy levels in the band-bend well, or in the higher
energy "Fermi sea" that extends throughout the entire emitter. This distinction has some significance when
calculating the shot noise of the DBQW [She94].
2.2 Advances in Material Systems
Numerous materials systems have been proposed and demonstrated for RTDs. Figure 2.2.1 shows the trends in RTDs
over the past few years. In general, higher PVCR values indicate higher device quality within groups of devices
with similar composition. Historically, GaAs/AlGaAs devices were the first to be developed, and have remained
popular ever since. InGaAs/InAlAs devices were introduced to improve the barrier heights relative to GaAs/AlGaAs,
and as a result, they are seen to have larger PVCRs. Eventually it was discovered that the critical lengths for
pseudomorphic crystal growth were somewhat larger than typical structure widths, leading to a further element of
flexibility in bandgap engineering and to devices with improved PVCRs. Also included in Figure 2.2.1 are the RIT
devices, which are discussed later. InAs/AlSb devices have also generated considerable interest, since these
material systems offer much higher electron mobilities and lower contact resistances. For this reason, they are
currently the fastest RTDs available.
Each of these materials systems is discussed in more detail below.
2.2.1 GaAs/AlGaAs
The very first resonant tunneling diode consisted of a GaAs well between two Al0.7Ga0.3As
barriers, with GaAs emitter and collector regions [Cha74]. This device showed a very small NDR region at 77 K.
Sollner's famous 2.5 THz device consisted of GaAs wells between Al0.25Ga0.75As barriers, with
GaAs emitter and collector regions, and showed pronounced NDR (PVCR of 6) below 50 K [Sol83]. The first RTD with
room-temperature NDR was built of a similar structure [She85]. Diodes with AlAs barriers also became common
[Tsu85]. It was discovered that the minimum usable thickness of AlGaAs barriers was considerably higher than the
minimum thickness of AlAs barriers, due to the random alloy nature of the tertiary compound [Liu92]. The thinner
AlAs barriers permit higher current densities and hence higher speeds.
The major advantage of the GaAs/AlGaAs systems for RTDs is that it is based upon a mature fabrication
technology, both for high speed digital integrated circuits and microwave circuits. It is relatively
straightforward to integrate these RTDs, especially because of the proton-implantation isolation technique, which
allows good device isolation and a planar surface [Yan94]. Air bridge interconnects are not required. Also,
GaAs/AlAs diodes have the significant advantage that it is easier to grow binary compounds than the tertiary
compounds necessary in the indium-based RTDs.
However, the GaAs/AlGaAs system has several major disadvantages. The primary disadvantage is the low effective
barrier height of the lattice-matched GaAs/AlGaAs system, which for the X bandgap is only 0.23 eV [Meh90]. This
results in a relatively large thermionic current, and hence a rather low PVCR. In fact, this effect limits the PVCR
to about 4.
A second important drawback of the GaAs/AlGaAs system is the fact that GaAs makes relatively poor contacts to
metal, since it forms Schottky barriers rather than ohmic contacts [Mön90]. This increases the contact
resistance, and lowers fmax. Furthermore, the mobility of electrons in GaAs is not as high as that of
other materials systems due to a higher effective electron mass, which also increases the series parasitic
resistance and decreases fmax.
For these reasons, GaAs/AlGaAs systems offer the lowest PVCR and the lowest speed of the competing materials
systems. However, in many applications these considerations are outweighed by the easier of integration. For this
reasons, GaAs/AlGaAs RTDs are still quite popular.
The fastest GaAs/AlAs device reported was used in a 412 GHz fundamental-mode oscillator [Bro89]. Switching times
as fast as 6 ps have been observed [Özb93]. Current densities as high as 1 to 2 105
A/cm2 have been reported, although at relatively low levels of PVCRs [Söd90]. This is lower than
the other popular material systems, and is a reflection of the relatively high resistance of GaAs/AlAs.
A modification of the standard GaAs/AlAs diode, shown in Figure 2.2.1.1, has been proposed in several papers
[All93,Kon93,Smi94] that would partially alleviate the high resistance drawbacks of this materials system.
Essentially, the highly-doped collector region is replaced with a Schottky metal, significantly reducing the series
parasitic resistance. The relatively simple modification compared to the standard fabrication approach is shown in
Figure 2.2.1.2 [Kon93]. An fmax of 900 MHz has been computed for a diode fabricated by this method
[Smi94]. Of course, this method could also be extended to other materials systems.
2.2.2 InGaAs/InAlAs
The InGaAs/InAlAs material systems evolved to address the drawbacks of the GaAs/AlGaAs RTDs. For instance, the
barrier in In0.53Ga0.47As/In0.52Al0.48As is about 0.53 eV, more than
twice that of the GaAs/AlGaAs system discussed above. In addition, the effective electron mass in
In0.52As0.48As is 0.075 m0, compared to 0.092 m0 for
Al0.30Ga0.70As [Meh90]. The minimum thickness of the AlAs barriers in GaAs/AlAs barriers was
limited by the fact that as the width was reduced, the point in the GaAs became comparable to the X point in the
AlAs, limiting the usefulness of the barrier [Sug88]. InGaAs/InAlAs barriers do not have this limitation. For these
reasons these diodes offered some of the highest PVCRs available at their introduction [Sen87, Sug88]. However,
they rapidly became obsolete after the introduction of the material system discussed in the next section.
2.2.3 Pseudomorphic InGaAs/AlAs
Although the InGaAs/InAlAs system was superior to the GaAs/AlGaAs systems, it was found that dramatically
improved results could be obtained with a InGaAs/AlAs system. Removing the In from the barrier results in a much
higher effective bandgap (possibly about 1.2 eV [Meh90]), and a reduction in alloy scattering, since the barrier is
binary rather than tertiary. However, the InGaAs/AlAs system is not lattice-matched. Indeed, a 3.7% lattice
mismatch exists. It was discovered that the critical maximum thickness for pseudomorphic growth was longer than
typical barrier widths, resulting in a feasible device [Meh90]. PVCRs as high as 25 and very high current densities
of 3.1 105 A/cm2 were obtained simultaneously with simple InGaAs/AlAs systems
[Cho92b].
Broekaert et al introduced [Bro88] a slightly more complicated variation on the InGaAs/AlAs system, by adding an
InAs layer in the quantum well. The resulting band diagram is shown in Figure 2.2.3. The addition of the InAs
induces a dip in the conduction band. From simple quantum mechanics, it is obvious that this offset reduces the
well width required to create a quantized state at a given energy level, which can be expected to lead to a high
current density (and hence speed). (The offset means that the resonant energy level is higher relative to the
ground state than in the case of a well without an offset. The higher energy difference implies a smaller deBroglie
wavelength, and thus a narrower well for resonance.) The use of a binary compound in the well also reduces alloy
scattering. PVCRs as high as 50 have been obtained at room temperature with this technique [Sme92]. Extremely high
current densities of up to 4.5 105 A/cm2 have also been obtained with this system.
Although faster than GaAs/AlGaAs systems, InGaAs/InAlAs systems do have drawbacks, primarily related to
fabrication. In particular, the tertiary nature of the InGaAs compounds complicates growth, and proton isolation
techniques are not effective for InAs and InGaAs-based diodes [Özb93].
2.2.4 InAs/AlSb
InAs/AlSb RTDs have emerged as the best choice high ultra-high speed operation. The InAs/AlSb - barrier is about
1.8 eV high for electrons, and the -X barrier is about 1.2 eV (comparable to InGaAs/AlAs). More importantly, the
Fermi level in InAs is pinned in the conduction band, so excellent ohmic contacts can be made with metal/InAs
contacts. Also, the both electron mobility and the saturation velocity are about five times higher in InAs than in
GaAs [Luo88]. This results in current densities as high as 5 105 A/cm2.
This material system was used to construct the 712 GHz oscillation reported in [Bro91], which is currently the
fastest solid state microwave source known. Switching times of 1.2 ps have also been reported [Özb93].
The relatively exotic nature of the materials (compared to the relatively mature GaAs technology) is a
disadvantage. However, in has been shown that InAs can be successfully grown on GaAs substrate, despite the large
7.2% lattice mismatch. Surprisingly, it has been reported that the large number of dislocations caused by this
mismatch do not appear to significantly affect the tunneling process [Söd91]. Figure 2.2.4.1 shows one
example of a microwave-IC compatible structure [Özb93].
A graph comparing the relative merits of the three major materials systems is shown in Figure 2.2.4.2
[Liu92].
3. Resonant Interband Tunneling (RIT) Devices
The discussion thus far has focused exclusively on double-barrier quantum well structures with resonant
intraband tunneling. However, these are not the only promising resonant tunneling diode structures. Obviously
interband tunneling has prospects as well - indeed, the Esaki diode is an interband tunneling device (although not
a resonant one). This section discusses some of the developments in this more recent field. Unfortunately, the
experimental results available at this time are limited almost exclusively to DC measurements (i.e. PVCRs). No
high-frequency data, either theoretical or experimental, is available for the first interband device considered
(the DQWRIT), and very sparse data is available for the second (the DBRIT).
3.1 Double Well RIT
The double quantum-well resonant interband tunnel diode (DQWRIT) was originally proposed by Sweeny and Xu
[Swe89]. The band diagram of this device is shown in Figure 3.1.1. The electrons in the well on the left (region
II) tunnel into the well on the right (region IV). At first glance this may not seem like resonant tunneling,
however, band bending induces two smaller barriers at the boundaries of regions I and II, and at III and IV. A key
aspect of the DQWRIT is immediately apparent: the tunneling barrier and the thermionic emission barrier are
decoupled, since the tunneling is an interband process, and the thermionic emission is an intraband process. This
allows considerably more flexibility in design than is possible with DBQWs. Since the off-resonant current is
blocked by the action of the p-n junction, a very high PVCR can be expected. The valley current is also very low
due to the fact that RIT structures are less prone than DBQWs to phonon-assisted transmission, due to the symmetry
difference between electron and hole states [Lya95]. PVCRs as high as 144 have been demonstrated at room
temperature [Tsa94]. However, the reported current densities of approximately 200 A/cm2 have been orders
of magnitude smaller than those reported for state-of-the-art DBQWs. This result raises the question of whether or
not they will be useful as high frequency devices. As noted above, no high frequency measurements have been
reported.
The fact that the diode contains a pn junction implies that a DQWRIT has an asymmetrical I-V charactisteric
about the zero bias point, in contrast to the odd symmetry of the ideal DBQW. (In practice, the nature of the
crystal growth in the manufacture of DBQWs can affect the symmetry of the IV curve.)
The choice of barrier and well thickness is much more restricted than for the case of the DBQW. For the
InAlAs/InGaAs systems used in [Day93, Tsa94], one finds that for x < 40 Å (approximately) no bound states
exist within the wells, and that for x > 40 Å, the states exist below the conduction band (or above the
valence band edge, as appropriate) such that a resonant line-up of populated energy levels can not occur. Hence,
the ideal well width is about 40 Å [Yan92]. As for the central barrier width (between regions II and III),
one finds that the optimum transmission occurs for [Day93]
(3.1.1)
TLEFT and TRIGHT depend on the band bending. For devices with a wide central barrier, this
match condition is not met - TLEFT and TRIGHT are generally too high. The match is improved
by either lowering TLEFT and TRIGHT or by increasing TCENTRAL-BARRIER. It is more
desirable to increase the middle transmissivity, by narrowing the central barrier. (Decreasing TLEFT or
TRIGHT would decrease the peak current density.) No theoretical predictions have been made as to the
actual optimum central barrier width, but experiments have shown it to be around 20 Å. However, one would
expect this to depend on the doping in the emitter and the collector, since these dopings control the degree of
band bending, and hence TLEFT and TRIGHT. It would appear that this doping dependence has not
been explored.
Unfortunately, at this time no high frequency results, either experimental or theoretical are available for the
DWRIT. However, the co-inventor of the DBRIT, Jingming Xu [Swe89], has high hopes for the device, as expressed in
private communication with the author of this report [Xu95]: "We never measured fmax ourselves as the
samples are not suitable for straight forward microwave measurements. There are good reasons from physics point of
view to expect a much higher speed in RITs than in Tunnel Diodes or even in RTDs. These include: (1) in RITs the
doping levels can be 2 orders of magnitude lower than in Esaki Tunnel Diodes, and the transition region can be even
undoped; and (2) the peak current density in RITs should be much larger than in RTD, as RIT is a bipolar device.
Experimentally, the potential of RIT has not been fully realized, far from it. We had just one experimental trial,
got the record P/V, we then stopped and went on to our main bussiness - optoelectronics."
3.2 Double Barrier RIT
One other general class of structures has attracted considerable interest - the double barrier RIT (DBRIT)
diode. Two possible band diagrams are shown in Figure 3.2.1. Essentially, the DBRIT takes advantage of
heterostructures (specifically, InAs/AlSb/GaSb) where the valence band edge of one region (GaSb) lies above the
conduction band edge of another region (InAs), permitting tunneling. Söderström reported one such device
using the symmetrical structure of Figure 3.2.1a that demonstrated a PVCR of 20 at room temperature with a peak
current density of 600 A/cm2 [Söd89b]. A device based on Figure 3.2.1b has been reported with a
lower PVCR of 5 but a significantly higher peak current density of 7600 A/cm2 [Yan90]. Researchers at
Motorola have examined methods for integrating InAs/AlSb/GaSb heterostructures onto patterned substrates, with some
success (although at relatively low peak current densities) [Wal95]. This suggests that these devices will be
useful for the fabrication of complex high-speed circuits. However, GaSb suffers from a low melting point
temperature of 712 °C, compared to 1240 °C for GaAs [Mil93]. This poses fabrication difficulties, and may
prevent the incorporation of GaSb-based RTDs into integrated circuits. More experimental evidence is required
before it can be seen whether these devices will achieve a status higher than that of "laboratory
curiosity".
Some theoretical work has been presented regarding the time-dependent operation of DBRITs. Wang et al [Wan94]
have estimated the dwell time of these diodes to be on the order of 100 fs. Thus we can expect the actual speed of
practical devices to be limited by RC time constants. Actual measured capacitances for a DBRIT have been presented
[Fob94], however, the C(V) characteristic was studied primarily in the positive differential resistance region
rather than in the more interesting NDR region. (As in the case of DBQWs, the capacitance is strongly peaked at
resonance, in the NDR region). Theoretical estimates of the C(V) characteristic, also presented in [Fob94], are not
yet sufficiently well developed to accurately predict the capacitance peak.
4. Applications
The use of the RTD has been proposed in many applications, as will be discussed below. Naturally, as a nonlinear
device, it is of interest as a detector, oscillator, mixer, and multiplier. As few scattered results have been
presented in each of these applications. However, the RTD has shone in several applications where it is used as a
switching elements, such as in sample and hold amplifiers, and particularly trigger circuits. Indeed, it will
probably first appear as a successful commercial device in high-speed oscilloscopes as an indirect replacement for
conventional tunnel diodes. The RTD also has potential for use in very high speed, and very simple, A/D
converters.
Each of these areas will be discussed (briefly) below. The coverage is not comprehensive, but is intended to
convey an idea of the current state of the art.
4.1 Detectors
The RTD has demonstrated an enormous bandwidth when used as a detector. As noted in the introduction, Sollner
demonstrated detection at 2.5 THz (at 25 K) in 1983 [Sol83]. More recently, Scott observed detection at 3.9 THz at
room temperature [Sco94]. However, these papers were intended to demonstrated the high intrinsic speed of the RTD,
rather than as serious examples of microwave detectors. Nonetheless the RTD does hold promise as a practical
detector, by virtue of the fact that it can act as a purely reactive detector when biased at or near the NDR
region. In this case, the power dissipated in the PDR region can be balanced by the power generation in the NDR
region, leading to zero DC power consumption. A second advantage over passive detectors such as the Schottky diode
is that an RTD biased near the current peak will exhibit full-wave rectification, rather than half-wave, as
demonstrated in Figure 4.1.1 [Ger88]. This is desirable for detection, and other applications like frequency
doubling. Gering [Ger88] has demonstrated detection, and compared it to theoretical predictions, at frequencies up
to 10 GHz. The bandwidth was limited by the packaging parasitics.
- Oscillators
Figure 1.1 shows the impressive progress in the development of very high frequency fundamental oscillators with
RTDs. Again, however, these particular results were intended as proof of the RTD's high speed rather than serious
demonstration of practical, useful oscillators. In real applications, noise and linewidth are of concern.
Brown has reported a 100 GHz oscillator using a semiconfocal, "quasioptical" open cavity resonator, as
illustrated in Figure 4.2.1 [Bro92]. This provided a very high Q, and a very small linewidth of 10 kHz, at 10 dB
down from the peak. Closed cavity and radial transmission line resonators exhibit a more rapid falloff of Q at high
frequencies, due to the increasing ohmic losses in the metallic surfaces.
Blundell used a very similar construction technique to demonstrate the use of an RTD as the local oscillator for
a SIS receiver intended for space-borne applications [Blu93]. The RTD oscillated in a fundamental mode at 200 GHz,
and its noise performance was compared to that of a frequency-multiplied Gunn diode source. It was found that the
noise temperature of the two sources was almost identical. However, the RTD was found to be more attractive for
space applications due to its extremely low DC power consumption.
4.3 Mixers
RTDs are attractive for use in mixers, and particular in self-oscillating mixers. Millington has demonstrated a
self-oscillating mixer at 11 GHz, with a conversion gain of 10 dB, and a noise figure of 11.5 dB [Mil91]. Due to
the self-oscillating configuration, the circuit is considerably simpler that conventional mixers, such as
Schottky-diode based circuits. Hayes has presented a similar circuit, operating at 18 GHz [Hay93]. Both of these
mixers were relatively unoptimized, and used the slower GaAs/AlAs RTDs. Significant improvements in operating
frequencies can certainly be expected in the future.
4.4 Multipliers
An early example of frequency multiplication using GaAs/AlAs RTDs demonstrated 1.2% efficiency and 0.8mW output
power, operating as a tripler with a 250 GHz output frequency [Ryd89]. Oddly, this experiment used the RTD biased
about zero volts. It would seem that better performance could be expected from the RTD if it were biased about the
peak current, where the I-V current is far more nonlinear. "Proof of principle" frequency multipliers using
series-connected tunnel (Esaki) diodes biased at the peak current have been demonstrated at 2 GHz, with the
intention of leading the way to the use of RTDs at much higher frequencies [Bor95]. In a circuit using two
series-connected tunnel diodes, a harmonic generator was demonstrated that generated roughly equal power (-27 dBm)
fundamental and third harmonic components. Boric-Lubecke et al [Bor95] have speculated that it will be possible,
using series-connected RTDs, to generated 10 W at 1.2 THz using a tripler circuit.
4.5 Sample and Hold Amplifers
As mentioned above, the most interesting applications of RTDs have arisen in applications where they are used as
fast switches. As an example, Miura et al demonstrated a sample-and-hold amplifier with a bandwidth of 26 GHz
(limited by the packaging) [Miu90]. Conventional sample-and-hold circuits use step-recovery diodes to gate a
Schottky diode bridge. However, SRDs are limited by switching rise times of about 30 ps and greater. In the circuit
of Figure 4.5.1, RTDs were integrated on a common substrate with the Schottky-diode bridge, and gate switching
times of less than 10 ps were achieved, significantly improving the speed over conventional circuits. Pseudomorphic
InGaAs/AlAs RTDs were used, as shown in the fabrication scheme of Figure 4.5.2.
4.6 Trigger Circuits
Perhaps the RTD application closest to commercialization is in trigger circuits. Researchers at Hewlett-Packard have presented a GaAs/AlAs RTD trigger circuit, with a view to improving the bandwidth of the 18 GHz HP54118A trigger instrument [Yan94]. The circuit configuration and relevant waveforms are shown in Figure 4.6.1.With appropriate biasing (through the adjustable "level" control), the arming diode will switch from a high-current state into the current valley near the peak of the input signal. This increases the current through the trigger diode, which biases it closer to the peak current. The falling input signal induces a further increase in the trigger diode current, until it too switches to the low current state. The bias is adjusted such that trigger diode switches at the zero-crossing of the input signal - in other words, where the voltage rate of change is the highest. This is important for obtaining low jitter. Figure 4.6.1 shows that the arming diode transition is quite jittery, since it triggers where dV/dt 0. The use of a staggered switching scheme greatly reduces the jitter. This circuit does not require an expensive phase-splitter, as their current instrument does.
The actual circuit was constructed with integrated GaAs/AlAs RTDs in a 50 coplanar waveguide. The waveguide
consisted of Ti/Au on a semi-insulating GaAs substrate. The RTDs were isolated using the proton implantation
technique, allowing a planar surface and eliminating the need for air-bridge interconnects. With a constant power
dissipation of 30 mW in the RTDs, no degradation in performance was observed over two years. Overall, the circuit
was shown to operate from 5 GHz to 50 GHz. The bandwidth was limited by the measuring equipment; the researchers
estimate that the actual circuit bandwidth is 60 GHz. A jitter of less than 1 ps was observed; however, the jitter
of the oscilloscope was specified as 0.9 ps. The researchers estimate that the jitter due to the sampling circuit
is about 0.5 ps rms.
Özbay and Bloom demonstrated a trigger circuit for operating at 110 GHz [Özb91]. However, as discussed
in [Yan94], it is essentially a narrowband circuit. This circuit used a construction approach very similar to that
presented in [Yan94], with GaAs/AlAs RTDs integrated with coplanar waveguides, using proton isolation.
4.7 Pulse Generators
The incorporation of RTDs into nonlinear transmission lines can be used to generate pulses with extremely fast
transition times. A pulse sharpener using 27 GaAs/AlAs RTDs, placed at 47 m intervals along a 75 transmission line,
has been used to generated 400 mV pulses with 3.5 ps rise times, into a 50 load [Yu94]. The switching time of one
of these RTDs used in isolation was measured to be 6 ps. Even more impressive results can be expected in the
future, if more advanced RTDs are used. For instance, as noted earlier, switching times of 1.2 ps have been
measured for lumped-element InAs/AlSb RTDs.
4.8 A/D Circuits
Several clever RTD circuits have been presented for use as ultra-high-speed analog-to-digital converters,
although no such circuits have yet been experimentally proven at the gigasample/second conversion rates claimed for
them. One such circuit is shown in Figure 4.7.1 [Wei93]. The key subcircuit, shown in Figure 4.7.2, consists of a
multipeaked RTD switch with an RTD load. The switching RTD I-V curve, superimposed with the load line of the load
RTD is also shown. For an RTD with N current peaks, there are 2N+1 stable I-V operating points, and two stable
output currents (IL and IP). These are converted to binary voltages by the sensing resistor.
As the voltage VIN across the diode is increased, the output switches state every V/2, where V is the
voltage difference separating the current peaks. If the full input voltage is placed on one RTD, the diode switches
every V/2. If VIN/2 is placed on an RTD, the diode will switch for every V change in VIN.
Similary, for VIN/4, the the diode will switch for every 2V change in VIN. Clearly, a binary
A/D converter can be built this way. Figure 4.7.2 shows a 4-bit converter. The major advantage of this circuit is
that to achieve an N-bit converter, the number of buffers, switches, and RTDs required is proportional to N. In
comparision, an N-bit flash A/D converter requires 2N-1 comparators. Thus, the RTD A/D converter will be
considerably smaller and less complex.
A simple 2-bit converter using this scheme at very low conversion rates has been built. Wei et al [Wei93] have
performed simulations suggesting that a 4-bit converter could operate at 5 GHz. It remains to be seen whether or
not this will emerge as a truly practical circuit approach, particularly since it requires RTDs with multiple
peaks.
This circuit example also shows the great potential of RTDs for use in digital logic, particularly in
multi-valued logic systems (i.e. systems with more than two basic logic states).
5. Conclusion
This paper has reported some of the theoretical and practical advances in RTDs. DBQWs show great promise as ultra-high speed nonlinear microwave devices, and to some extent, this promise has been demonstrated in experiments. As an analog switching device, the RTDs also show great promise, and indeed, may well be commercialized in the very near future in oscilloscope trigger circuits, and in sample and hold circuits. Several applications for RTDs as essentially digital devices, such as the A/D converter discussed above and various multi-valued logic circuits, has also been proposed, but this area has not yet been explored meaningfully in experiments.
The resonant interband devices have demonstrated exceeding high peak-to-valley current ratios, but almost no high frequency data is available to judge their usefulness. Significant advances in this field can be expected in the next few years.
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