Interplay of Highfrequency Replicas with Transport Properties
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Interplay of highfrequency replicas with transport properties in the terahertz resonanttunneling double barrier nanostructures on the base of GaAs/AlAs
Abstract. The periodicalinvoltage features of the negative differential conductance (NDC) region in the currentvoltage characteristics of a highquality GaAs/AlAs terahertz resonanttunneling diode have been detected. The found oscillations are considered taking account of the LOphonon 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 IV characteristics of the resonanttunneling diode as a consequence of the topological transformation of a measurement circuit from the circuit with the series resistance R_{s }to the circuit with the shunt R_{p }have been experimentally studied and analyzed. The revealed substantial changes in the currentvoltage characteristics of the resonanttunneling diode are discussed schematically using Kirchhoff’s voltage law.
1. Introduction
Quantum effects, harmonics generation and highfrequency 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 quantumeffect 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 currentvoltage characteristics with the measured IV curves, as usual distorted externally. There are several reasons of the distortions, causing the measured currentvoltage 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 buildup and longitudinalopticalphonon (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 IV curve, to place a resistor (Rp) in parallel with the resonant tunneling diode, which could stabilize most of test circuits, etc. [5].
These means are used here to extract the reasons of experimentally found periodicalinvoltage features [6] of the negative differential conduction exhibited by the currentvoltage
Figure 1. IV curves for a doublebarrier RTD with and without incident subTHz power. T=300 K, active layers of AlAs/GaAs barriers/well 23/45/20 ˚A. Inserts show more details
characteristics of a highquality THz resonant tunneling diode [7]. Rearrangements in the IV
characteristics of the resonanttunneling diode as a consequence of the topological transformation of a measurement circuit from the circuit with the series resistance R_{s }to the circuit with the shunt R_{p }have been experimentally studied and analyzed. The found substantial changes in the currentvoltage characteristics of the resonanttunneling diode are discussed schematically using Kirchhoff’s voltage law. It is argued that, due to the conductionband profiles disposition in a manner of the inversionlike nonequilibrium cascade, the tunneling current supplies the revealed electromotive force in the currentvoltage characteristics of a resonanttunneling diode. The found periodicalinvoltage oscillations of the negative differential conductance in a highquality GaAs/AlAs terahertz resonanttunneling diode are considered taking account of the LOphonon excitation stimulated by the resonanttunnelingelectron current through the quantum active region in the resonance nanostructure where an undoped quantum well layer is sandwiched between two undoped barrier layers.
2. Periodicalinvoltage oscillations of the negative differential conductance
The periodicalinvoltage regular oscillations of the negative differential conductance in the currentvoltage characteristics of a highquality GaAs/AlAs terahertz resonanttunneling diode have been detected at room temperature and below [6]. To extract the reasons of these regular features of NDC we used here the means discussed in [5]: to monitor the oscillation status of the resonant tunneling diode by measuring the second derivative of IV curve and to place a resistor R_{p }in parallel with the RTD, which could stabilize most of test circuits. A detailed information on the sample design is provided by [6]. The studied resonanttunneling diodes have been grown by a molecularbeamepitaxy 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 mesastructures were defined by the lithography and chemical
Figure 2. Second derivatives of IV curves shown in the Figure 1 for a doublebarrier RTD with and without incident subTHz 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 conductionband profiles under an applied bias voltage V, may be found in [6] and [4,7], respectively.
The regular oscillations of NDC in the IV curve are shown in the Figure 1 for a doublebarrier RTD with and without an incident subTHz (0.1292 THz) power at room temperature. Second derivatives of the IV curves, obtained from the data points of Figure 1 by machineroutine computations, are presented in the Figure 2. Inserts in the figures show more details of the IV curves and derivatives. From comparisons of the date shown in the figures and those presented in [5] 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 lowervoltage point where circuit oscillations would begin. The typical measured derivative curves with diodecurcuit oscillations are shown in Fig. 2(c) in [5]. This feature corresponds to the ”smoothedinfinity discontinuity” and looks like a derivative of a valley, i. e. of a negative peak originating in a negative hat of the ”diffuse former deltafunction” in the first derivative of IV curve, which in turn is a derivative of a step − a negative step of the ”diffuse former thetafunction” in the IV curve. This triplet of features may be considered as a classical continuousmediaelectrodynamics illustration of a creationannihilation 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 doublebarrier RTD with an incident subTHz power and, contrary, are practically indistinguishable for an RTD without an incident power.
So the observed NDC regularinvoltage oscillations in the IV 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 R_{p }= 37.5Ω, and with slightly different geometrical parameters. The worse regularity of NDC oscillations in the shown in the Figure 3 IV curve points to the presence of parasitic external oscillations in the test circuit for this RTD.
, V
RTD
S
S
Figure 3. IV curves for total and RTD currents for the measurement circuit with a shunt R_{p }of different values and with and without the series resistance R_{s}
3. Distinctions of RTD’s currentvoltage characteristics with the series resistance and with the shunt
To verify the concluded above intrinsic nature of the observed NDC periodicalinvoltage oscillations in the IV 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 [5]. If there would be sharp oscillatory characteristics present in the second derivative curve, like in the RTD’s curve with an incident subTHz 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 IV curve. In order to narrow the oscillation range and obtain the freeofoscillation range in the IV 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 IV curve was measured after the known shunt resistance R_{p }was placed to the terminals
of the resonanttunneling diode. The diode current can easily be obtained by Kirchhoff’s laws
Itotal = IRTD + IR_{p}, 
(1) 

which result in 
V = VRTD = VRp = RpIRp, 
(2) 
, (3)
where I_{RTD }is the resonanttunneling diode current, I_{total }is the total measured system current, and I_{R}_{p }is the current through shunt resistor, V = V_{RTD }= V_{R}_{p }is the measured dc bias applied to the connectedinparallel RTD and shunt.
The better regularity of NDC oscillations in the IV curve shown in the Figure 3 for the circuit with the resistance R_{p }= 14.4Ω shunted to the two terminals of the series of resistance R_{s }= 0.3Ω and RTD, in comparisons with the worse regularity for the circuit with zero series resistance and shunt R_{p }= 37.5Ω in the Figure 3, points to the stabilization of test circuit and suppression of parasitic external oscillations in this lower R_{p }RTD’s circuit.
The data presented in Figures 3 and 4 show that cardinal rearrangements in the IV characteristics of a resonanttunneling diode as a consequence of the topological transformation of a measurement circuit from the circuit with the series resistance R_{s }to the circuit with the shunt R_{p }(cf. the curve I_{RTD }in Figure 4 with curves I_{total }and I_{R}_{s }in Figures 1, 3 and 4) are extracted from experimental data using Kirchhoff’s voltage law in the form of Equation (3).
p
Figure 4. IV curves for total and RTD currents for the measurement circuit with a shunt R_{p }of different values
4. Discussion
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 IV characteristics of an RTD as a consequence of the topological transformation of a measurement circuit from the circuit with the series resistance R_{s }to the circuit with the shunt R_{p }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 conductionband profiles of which are disposed in the inversionlike nonequilibrium cascade manner. Schematic conductionband 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 currentvoltage characteristics of a resonanttunneling 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 spatiallydispersive zerofrequency 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 [8]. 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 continuousmedia 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 continuousmediaelectrodynamical considerations as the spatial dispersion. The effects of the boundarydependent local fields in conducting media were considered in [9] 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 currentvoltage characteristics of a resonanttunneling 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 tunneleffect mechanism of conductivity, corresponding to the alternation of conductorsandwichedbetweeninsulator spatial regions at the microscopic scale of distances, similar to a superlattice, is of the principle importance in these phenomena. A resonanttunneling 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 LOphonons under conditions of the slight asymmetry of barriers, number of these periods (7 periods in Figures 1 and 2 or 4 periods in [7]) 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 [7]), and excessive energy of the discussed above cascade inversion provide evidences in support of the resonant tunneling process assisted by a stimulated excitation of LOphononbranch 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 waveretardation operating principle: backwardwave and travellingwave tubes, LINACs etc., and may be considered as the artificial nanoaccelerator. 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 centralcellcorrection type for Al atoms at the cites of Ga atoms in the barrier monolayers, but in a planewave, onedimensional, not centralsymmetrical configuration, the barrier monolayers play the role of corrugations in the retardation system of backwardwave 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 LOphonon 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 [10], if one substitutes the spatial factor in Eq. (3) of Ref. [10] with the proper constitutive parameters.
This equation corresponds to the discussed above illustration of a creationannihilation operator.
5. Conclusions
The periodicalinvoltage features of the negative differential conductance (NDC) region in the currentvoltage characteristics of a highquality GaAs/AlAs terahertz resonanttunneling 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 IV characteristics of the resonanttunneling diode under the topological variation of the measurement circuit from the circuit with the series resistance R_{s }to the circuit with the shunt R_{p }have been experimentally studied and analyzed. The revealed substantial changes in the currentvoltage characteristics of the resonanttunneling diode are discussed schematically using Kirchhoff’s voltage law and point to the importance of the electromotive force in RTDs.
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