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Interplay of high-frequency replicas with transport properties in the terahertz resonant-tunneling double barrier nanostructures on the base of GaAs/AlAs
Abstract. The periodical-in-voltage features of the negative differential conductance (NDC) region in the current-voltage characteristics of a high-quality GaAs/AlAs terahertz resonanttunneling diode have been detected. The found oscillations are considered taking account of the LO-phonon excitation stimulated by tunneling of electrons through the quantum active region in the resonance nanostructure where an undoped quantum well layer is sandwiched between two undoped barrier layers. Rearrangements in the I-V characteristics of the resonant-tunneling diode as a consequence of the topological transformation of a measurement circuit from the circuit with the series resistance Rs to the circuit with the shunt Rp have been experimentally studied and analyzed. The revealed substantial changes in the current-voltage characteristics of the resonant-tunneling diode are discussed schematically using Kirchhoff’s voltage law.
Quantum effects, harmonics generation and high-frequency rectification mechanisms in highspeed resonant tunneling diodes (RTDs) are rather promising to increase the operation frequency of semiconductor nanoelectronic devices toward the terahertz and subterahertz range. The resonant tunneling diode is a quantum-effect semiconductor device using quantum mechanical tunneling which operating principle is based on the resonant tunneling effect A rigorous tunneling theory is crucial to optimize the fabricated resonant tunneling diode and to analyse its interaction with an ac field [1,2]. To elaborate a resonant tunneling diode with advanced frequency properties it is necessary to compare the computed current-voltage characteristics with the measured I-V curves, as usual distorted externally. There are several reasons of the distortions, causing the measured current-voltage characteristic to have the hysteresis, bistability, discontinuities, humps, plane and stepped sections in the negative differential conduction (NDC) region. The most basic are the excessive series resistance (Rs), parasitic oscillation, charge build-up and longitudinal-optical-phonon (LO) replicas of a tunneling peak [3–5]. There have been several means to extract the parameters of a test resonant tunneling diode accurately: to monitor the oscillation status by measuring the second derivative of I-V curve, to place a resistor (Rp) in parallel with the resonant tunneling diode, which could stabilize most of test circuits, etc. .
These means are used here to extract the reasons of experimentally found periodical-involtage features  of the negative differential conduction exhibited by the current-voltage
Figure 1. I-V curves for a double-barrier RTD with and without incident sub-THz power. T=300 K, active layers of AlAs/GaAs barriers/well 23/45/20 ˚A. Inserts show more details
characteristics of a high-quality THz resonant tunneling diode . Rearrangements in the I-V
characteristics of the resonant-tunneling diode as a consequence of the topological transformation of a measurement circuit from the circuit with the series resistance Rs to the circuit with the shunt Rp have been experimentally studied and analyzed. The found substantial changes in the current-voltage characteristics of the resonant-tunneling diode are discussed schematically using Kirchhoff’s voltage law. It is argued that, due to the conduction-band profiles disposition in a manner of the inversion-like nonequilibrium cascade, the tunneling current supplies the revealed electromotive force in the current-voltage characteristics of a resonant-tunneling diode. The found periodical-in-voltage oscillations of the negative differential conductance in a high-quality GaAs/AlAs terahertz resonant-tunneling diode are considered taking account of the LO-phonon excitation stimulated by the resonant-tunneling-electron current through the quantum active region in the resonance nanostructure where an undoped quantum well layer is sandwiched between two undoped barrier layers.
2. Periodical-in-voltage oscillations of the negative differential conductance
The periodical-in-voltage regular oscillations of the negative differential conductance in the current-voltage characteristics of a high-quality GaAs/AlAs terahertz resonant-tunneling diode have been detected at room temperature and below . To extract the reasons of these regular features of NDC we used here the means discussed in : to monitor the oscillation status of the resonant tunneling diode by measuring the second derivative of I-V curve and to place a resistor Rp in parallel with the RTD, which could stabilize most of test circuits. A detailed information on the sample design is provided by . The studied resonant-tunneling diodes have been grown by a molecular-beam-epitaxy technique and are based on an AlAs/GaAs double barrier resonant tunneling structure. Active layers of the AlAs/GaAs barriers/well structure have the widths of 23/45/20 ˚A. Rectangular RTD mesa-structures were defined by the lithography and chemical
Figure 2. Second derivatives of I-V curves shown in the Figure 1 for a double-barrier RTD with and without incident sub-THz power. T=300 K, active layers of AlAs/GaAs barriers/well 23/45/20 ˚A. Inserts show more details
etching. The test samples have a mesa diagonal order of 15 µm. An Au pad on the top of an RTD mesa provides an ohmic electrical contact. The second ohmic contact was disposed laterally on the topside of the substrate also. Further information on experimental techniques and RTD working principles, including schematic conduction-band profiles under an applied bias voltage V, may be found in  and [4,7], respectively.
The regular oscillations of NDC in the I-V curve are shown in the Figure 1 for a double-barrier RTD with and without an incident sub-THz (0.1292 THz) power at room temperature. Second derivatives of the I-V curves, obtained from the data points of Figure 1 by machine-routine computations, are presented in the Figure 2. Inserts in the figures show more details of the I-V curves and derivatives. From comparisons of the date shown in the figures and those presented in  one can conclude the absence of parasitic external oscillations in a circuit with our test RTD. The second derivative curve should show a sharp valley immediately followed by a sharp peak at the lower-voltage point where circuit oscillations would begin. The typical measured derivative curves with diode-curcuit oscillations are shown in Fig. 2(c) in . This feature corresponds to the ”smoothed-infinity discontinuity” and looks like a derivative of a valley, i. e. of a negative peak originating in a negative hat of the ”diffuse former delta-function” in the first derivative of I-V curve, which in turn is a derivative of a step − a negative step of the ”diffuse former theta-function” in the I-V curve. This triplet of features may be considered as a classical continuous-media-electrodynamics illustration of a creation-annihilation operator.
At the second point corresponding to a higher voltage, as the NDR is smaller negative, oscillations are quenched. The same characteristic of a sharp valley immediately followed by a sharp peak should appear in the second derivative curve at this point also. This pair of the oscillatory features in the second derivative curve can be used to monitor the circuitoscillation status in the measurement circuit and determine the bias voltage range in which circuit oscillations occur. Such pairs of the oscillatory features in the second derivative curve, monitoring the oscillation status in the measurement circuit, can be found, being periodically repeated, in the insert of Figure 2 for a double-barrier RTD with an incident sub-THz power and, contrary, are practically indistinguishable for an RTD without an incident power.
So the observed NDC regular-in-voltage oscillations in the I-V curves are of the intrinsic nature not dependent on the RTD’s test circuit. This conclusion is supported by comparisons with the demonstrated in Figure 3 data for another similar RTD sample measured in the circuit with zero series resistance, shunt Rp = 37.5Ω, and with slightly different geometrical parameters. The worse regularity of NDC oscillations in the shown in the Figure 3 I-V curve points to the presence of parasitic external oscillations in the test circuit for this RTD.
Figure 3. I-V curves for total and RTD currents for the measurement circuit with a shunt Rp of different values and with and without the series resistance Rs
3. Distinctions of RTD’s current-voltage characteristics with the series resistance and with the shunt
To verify the concluded above intrinsic nature of the observed NDC periodical-in-voltage oscillations in the I-V curves of the resonant tunneling diode we have measured it in a circuit where a shunt resistor is placed in parallel with the RTD and which could stabilize most of test circuits . If there would be sharp oscillatory characteristics present in the second derivative curve, like in the RTD’s curve with an incident sub-THz power in Figure 2, it could mean the measurement circuit had been unstable and oscillations had been present between two bias voltages in the measured I-V curve. In order to narrow the oscillation range and obtain the free-of-oscillation range in the I-V curve as wide as possible, a resistor with a suitable resistance should be shunted to the two terminals of the RTD, since either too large or too small shunt resistance could not suppress oscillations effectively.
The I-V curve was measured after the known shunt resistance Rp was placed to the terminals
of the resonant-tunneling diode. The diode current can easily be obtained by Kirchhoff’s laws
Itotal = IRTD + IRp,
which result in
V = VRTD = VRp = RpIRp,
where IRTD is the resonant-tunneling diode current, Itotal is the total measured system current, and IRp is the current through shunt resistor, V = VRTD = VRp is the measured dc bias applied to the connected-in-parallel RTD and shunt.
The better regularity of NDC oscillations in the I-V curve shown in the Figure 3 for the circuit with the resistance Rp = 14.4Ω shunted to the two terminals of the series of resistance Rs = 0.3Ω and RTD, in comparisons with the worse regularity for the circuit with zero series resistance and shunt Rp = 37.5Ω in the Figure 3, points to the stabilization of test circuit and suppression of parasitic external oscillations in this lower Rp RTD’s circuit.
The data presented in Figures 3 and 4 show that cardinal rearrangements in the I-V characteristics of a resonant-tunneling diode as a consequence of the topological transformation of a measurement circuit from the circuit with the series resistance Rs to the circuit with the shunt Rp (cf. the curve IRTD in Figure 4 with curves Itotal and IRs in Figures 1, 3 and 4) are extracted from experimental data using Kirchhoff’s voltage law in the form of Equation (3).
Figure 4. I-V curves for total and RTD currents for the measurement circuit with a shunt Rp of different values
More detailed analyses of the experimental findings will be expanded elsewhere and just primary ideas will be briefly outlined here. The revealed striking rearrangements of I-V characteristics of an RTD as a consequence of the topological transformation of a measurement circuit from the circuit with the series resistance Rs to the circuit with the shunt Rp have been found (Figures 1, 3 and 4) and analysed schematically using Kirchhoff’s voltage law in the form of Equation (3), where the electromotive force, possibly originating in an RTD, is not incorporated. However, the tunneling current flows from an emitter to a collector via a quantum well, the conduction-band profiles of which are disposed in the inversion-like nonequilibrium cascade manner. Schematic conduction-band profiles under an applied bias voltage V may be found in [4,7]. This cascade inversion supplies a possibility of an effect of an electromotive force in the current-voltage characteristics of a resonant-tunneling diode revealed in the Figure 4, which should be incorporated in Equations (2) and (3.) The electromotive force originates in the charge dipole field between the emitter accumulation and collector depletion regions connected by the tunneling current. It may be considered as a force resulting from a spatially-dispersive zero-frequency limit of the Abraham force produced by an external field in the matter.
Noteworthy dependencies of sample properties on topology of the circuit connected to the sample are typical of such materials as ferro- or antiferroelectrics . It corresponds to the dependence of constitutive properties, such as permittivity or conductivity, on the boundary conditions or on the electric induction in the macroscopic continuous-media electrodynamics via the local fields. The electrodynamics problem becomes nonlocal, the permittivity or conductivity becomes an operator. The interior states begin to depend on the boundary states. That should be taken into account in the macroscopic continuous-media-electrodynamical considerations as the spatial dispersion. The effects of the boundary-dependent local fields in conducting media were considered in  as the partial incorporation of the induction in the form of phenomenological operator into the force expression in the equation of motion, and the consequent derivation of conductivity. They suggested the existence of conducting state associated with the ferroelectricity at finite frequencies. The effect of an electromotive force in rearrangements of current-voltage characteristics of a resonant-tunneling diode, illustrated in the Figure 4, is absent at the zero bias voltage and may be associated with the antiferroelectricity at finite distances or, to be more correct, with the tunneling antiferroelectricity as a novel conducting state – the state of tunneling conductor. In this terminology the usual electric cell should be considered as the tunneling ferroelectric. The dominant role of the tunnel-effect mechanism of conductivity, corresponding to the alternation of conductor-sandwiched-betweeninsulator spatial regions at the microscopic scale of distances, similar to a superlattice, is of the principle importance in these phenomena. A resonant-tunneling diode may be considered as a unit cell of such superlattice.
The observed in the Figure 1 low averaged value of the oscillatory NDC order of 1/300 Ω−1, period of NDC oscillations order of 72 mV corresponding to the energy 72 meV of two LO-phonons under conditions of the slight asymmetry of barriers, number of these periods (7 periods in Figures 1 and 2 or 4 periods in ) depending on the barrier width (asymmetric of 20 and 23 ˚A in our RTD or symmetric of 12 and 14 ˚A in two RTDs in ), and excessive energy of the discussed above cascade inversion provide evidences in support of the resonant tunneling process assisted by a stimulated excitation of LO-phonon-branch polariton replicas. And again the stimulated excitation of polaritons in the RTD is provided by the effects of the boundarydependent local fields in conducting media. In this process an RTD operates in a manner of certain active devices, e.g. vacuum tubes with the wave-retardation operating principle: backward-wave and travelling-wave tubes, LINACs etc., and may be considered as the artificial nano-accelerator. The retardation of electromagnetic waves results in the enhancement of their interaction with electrons and is provided by the barrier monolayers. Due to the effect of the central-cell-correction type for Al atoms at the cites of Ga atoms in the barrier monolayers, but in a plane-wave, one-dimensional, not central-symmetrical configuration, the barrier monolayers play the role of corrugations in the retardation system of backward-wave tube. The RTD generates pairs of the coherent in space and time polaritonic waves with the same wavenumber: one decreasing in time and another increasing in time. These pairs of coherent polaritonic waves may be interpreted as the electronic states in the dynamic superlattice formed by the standing phonon wave.
Both phenomena of the electromotive force and of the excitation of LO-phonon replicas in the RTD can be described by the expression of the current density, which flows after the end of an external perturbation, obtained with the incorporation of the spatial dispersion , if one substitutes the spatial factor in Eq. (3) of Ref.  with the proper constitutive parameters.
This equation corresponds to the discussed above illustration of a creation-annihilation operator.
The periodical-in-voltage features of the negative differential conductance (NDC) region in the current-voltage characteristics of a high-quality GaAs/AlAs terahertz resonant-tunneling diode have been detected. The found oscillations are considered taking account of the LOphonon emission stimulated by tunneling of electrons through the quantum active region in the resonance nanostructure where an undoped quantum well layer is sandwiched between two undoped barrier layers. Rearrangements of the I-V characteristics of the resonant-tunneling diode under the topological variation of the measurement circuit from the circuit with the series resistance Rs to the circuit with the shunt Rp have been experimentally studied and analyzed. The revealed substantial changes in the current-voltage characteristics of the resonant-tunneling diode are discussed schematically using Kirchhoff’s voltage law and point to the importance of the electromotive force in RTDs.
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