Repeatable Room Temperature Negative Differential Conductance in GaN/AlN Resonant Tunneling Diodes

Double barrier GaN/AlN resonant tunneling heterostructures have been grown by molecular beam epitaxy on the (0001) plane of commercially available bulk GaN substrates. Resonant tunneling diodes were fabricated; room temperature current-voltage measurements reveal the presence of a negative differential conductance region under forward bias with peak current densities of ~6.4 $kA/cm^2$ and a peak to valley current ratio of ~1.3. Reverse bias operation presents a characteristic turn-on threshold voltage intimately linked to the polarization fields present in the heterostructure. An analytic electrostatic model is developed to capture the unique features of polar-heterostructure-based resonant tunneling diodes; both the resonant and threshold voltages are derived as a function of the design parameters and polarization fields. Subsequent measurements confirm the repeatability of the negative conductance and demonstrate that III-nitride tunneling heterostructures are capable of robust resonant transport at room temperature.


Introduction
Resonant tunneling of electrons in III-V semiconductors has undergone extensive studies since Tsu and Esaki theoretically investigated transport across multi-barrier heterostructures with periods comparable to the electron's wavelength 1 . Quantum confinement introduced by the barriers results in a localized and discrete electronic spectrum, which can be tuned to bring the quasi-bound levels in energy resonance with any adjacent reservoir of electrons. The resonant transport regime has been exploited to design highly efficient injectors of electrons into the upper lasing level of terahertz (THz) quantum cascade lasers (QCLs) 2 . On the other hand, the out-of-resonance regime, identified by the onset of negative differential conductance (NDC), has been harnessed to realize high frequency resonant tunneling diode (RTD) oscillators 3 .
Despite the steady progress in output power and frequency of operation, RTD oscillators are yet to be demonstrated at the miliwatt output power level for >1 THz, which is required for most practical applications 4 . Meanwhile, THz-QCLs fabricated with the well-developed material systems AlGaAs/GasAs and InGaAs/InAlAs have not yet achieved room temperature operation and their lasing frequencies are limited to <5 THz mainly due to Reststrahlen absorption 5 . In this scenario, the GaN/AlGaN material system has emerged as an attractive alternative to realize intersubband emitters within a wide range of frequencies due to the large conduction band energy offset of ~1.75 eV between GaN and AlN 6 . In addition, the high longitudinal optical (LO) phonon energy of the III-nitride materials, ~92 meV in GaN, is expected to prevent the depopulation of the upper lasing level, thus raising hopes for room temperature operation of nitride THz-QCLs 7 .
Double barrier GaN/AlGaN RTDs, being the simplest device to study resonant transport, have been under scrutiny during the last decades with moderate success [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] . Experiments on AlN-barrier RTDs grown on sapphire templates have shown a region of NDC under the forward bias of operation, with the bottom contact layer as the reference of the applied voltage. However, the measurements are also characterized by a lack of repeatability and a clear hysteretic behavior which prevents the measurement of NDC in the downward sweep 10,18,21,22 . It has been suggested that the high density of defects present in GaN films grown on sapphire (~10 9 cm -2 ) can act as electron traps, leading to self-charging and preventing coherent transport of carriers. Low temperature (LT) superlattices 8 and lateral epitaxial overgrown (LEO) films 16 have been also employed in order to reduce the density of defects during growth; however the reported negative conductance still degrades with consecutive measurements 17 . III-nitride RTDs with low Al-composition AlGaN-barriers have been also studied at cryogenic temperatures 19 . These devices were grown on bulk-GaN substrates with low dislocation densities (~5×10 6 cm -2 ) and small mesas of 16 µm 2 were defined to reduce the number of defects per device. Repeatable NDC features were observed only at cryogenic temperatures, below 110 K for a diode with 18%-AlGaN barriers and below 130 K for a diode with 35%-AlGaN barriers 19,20,23 . In this work, GaN/AlN RTDs were grown by molecular beam epitaxy (MBE) and fabricated using conventional lithography techniques. Current-voltage (I-V) measurements show a clear resonant peak and a stable and repeatable NDC region of operation under forward bias, thus demonstrating that III-nitride heterostructures are capable of robust resonant tunneling transport at room temperature. The repeatable operation has helped uncover several unique features in the tunneling spectrum that originate from the spontaneous and piezoelectric polarization in these heterostructures.

Experiment
A symmetric double barrier GaN/AlN heterostructure was grown by MBE on the c-plane of commercially available ntype bulk GaN substrates with a nominal dislocation density ~5×10 4 cm -2 . Metal rich growth conditions were maintained during the whole process at a substrate temperature of ~700 ºC and a nitrogen plasma power of ~200 W. A growth rate of ~5 seconds per monolayer (ML) was estimated by means of post-growth structural characterization methods. The active region comprises a ~3 nm GaN quantum well with ~2 nm AlN barriers and un-intentionally doped (UID) spacers of ~2 nm next to both barriers as indicated in Fig. 1(a). The emitter and collector regions consist of ~100 nm n-type GaN layers with a silicon doping level of ~7×10 18 cm -3 . A highly Si-doped (~8×10 19 cm -3 ) GaN cap layer completes the epitaxial heterostructure allowing for the formation of an ohmic contact at the collector metal-semiconductor junction. MBE growth of GaN films has been studied extensively in recent years, showing that smooth surfaces can be generated under excess metal growth conditions. In this regime, a Ga layer of ~ 2.5 ML is present at the growth interface favoring layer-by-layer incorporation of GaN 24,25 . Thus, Ga-rich conditions have been employed during the growth of the emitter and collector n-GaN layers as well as during the growth of the quantum well. However, using excess Al metal during the growth of AlN barriers leads to thicker AlN layers since the excess Al readily incorporates in the crystal in preference to Ga 26 . An alternative approach to promote layer-by-layer growth of AlN layers exploits the surfactant effects of excess Ga, which decreases the surface energy without getting incorporated into the AlN films 25 . In this work, excess Ga has been employed throughout the epitaxial growth in order to enable layer-by-layer growth and to minimize defect generation. Furthermore, crystal defects stemming from strain relaxation processes should be suppressed since the AlN barriers are thinner than the experimentally identified critical thickness (~5-7 nm) for AlN films pseudomorphically grown on GaN 27,28 Atomic force microscopy (AFM) was employed to image the surface of the as-grown sample, revealing a topology composed by 2 ML atomic steps with a root mean square (rms) roughness of ~0.146 nm over an area of 2×2 µm 2 ( Fig. 1(c)).
The fabrication of the RTDs was carried out using conventional contact photolithography, electron beam evaporation and reactive ion etching techniques. The collector contact was defined by evaporating the Ti/Al/Au/Ni metal stack. Mesas with areas between 6-48 µm 2 were defined using a self-aligned process in which the structure was etched down to the emitter n-GaN layer by reactive ions of the Ar/Cl 2 /BCl 3 gas mixture. Finally, the emitter Ti/Al/Au metal stack was deposited to obtain the structure depicted in Fig. 1(b). Transmission line measurement (TLM) structures were also defined; a specific contact resistance of ~30 Ω-µm 2 was measured in the collector contacts and the emitter contact resistance was estimated in the same order of magnitude. Thus, under injection currents on the order of ~10 kA/cm 2 , a voltage drop of ~3 mV per contact is expected, which is negligible compared to the total voltage used to bias the diodes.

Results
Current-voltage (I-V) characteristics were measured with a semiconductor parameter analyzer at room temperature applying voltage sweeps starting at 0 V up to 16 V, and then back to 0 V (double sweep). Immediately after, a reverse bias double sweep with a minimum voltage of −4.4 V was also performed, completing a closed loop scan (inset of Fig. 2(a)). The polarity of the diode bias is that of the voltage applied to the collector side, having the emitter as reference as shown in the top inset of Fig. 2(a). At forward biases below 5 V, current densities below 10 A/cm 2 were measured. These low injection currents are a result of the combination of a large GaN/AlN conduction band discontinuity (~1.75 eV) and polarization fields that effectively blocks carriers thus preventing transport from the emitter to the collector side. The equilibrium band diagram shown in Fig. 2(b)-which has been calculated using the nominal thicknesses of the layers comprising the heterostructureillustrates this blocking effect.
For voltages larger than 5 V currents larger than 10 A/cm 2 were recorded. During the first forward scan, a resonant peak is measured in the upward sweep at ~10.7 V with a peak current density of ~5.7 kA/cm 2 as shown in Fig. 2 A region of low injection currents (<10 A/cm 2 ) is also measured in reverse bias operation as shown in Fig. 2(a).
However, a transition to a higher current injection regime can be seen after the reverse threshold voltage V TH =−3.6 V, after which, the current increases monotonically, reaching a current level of ~15 kA/cm 2 at −4.4 V. This behavior contrasts with the ~16 V required to achieve similar current levels in the forward direction. This asymmetry in I-V characteristics is a result of the polarization electric fields present in the heterostructure; this interesting connection is discussed in the next section. Subsequent closed-loop bias scans were performed in the same device as shown in Fig 3(a). It was found that the resonant bias increases slightly with additional scans and eventually stabilizes at ~13.2 V (inset of Fig. 3(a)). The peak-tovalley current ratio (PVCR) decreases from its initial value of ~1.5 during the first scan to a stable value of ~1.3 in the eighth and subsequent scans. This trend is caused by the larger increase of the valley current which experiences a ~25.5% increment with respect to its initial value, whereas the peak current increases only ~11.1%. This behavior suggests the presence of defects in the AlN barriers; these imperfections act as current leakage paths and degrade the energy filtering function of the tunneling barriers. However, these leakage paths exhibit limited effects and do not prevent resonant tunneling transport of carriers across the heterostructure. RTDs have also reported the presence of this feature in the rising side of the main resonant peak 29 and this is first time that this behavior is reported in nitride RTDs. As the voltage is further increased to values larger than 10.7 V, the coupling between the accumulation subband (bound state situated below the quasi-continuous scattering states of the emitter, see Fig. 2(c)) and the ground resonant level enhances electron transport across the heterostructure. Eventually, resonant conditions are achieved at ~13.2 V just before the onset of the NDC region, which exhibits a minimum differential conductance of ~ −5.9 kS/cm 2 . The repeatability of the resonant peak and NDC was tested by the additional closed-loop bias scans, which are also presented in Fig 3(b).

GaN/AlN RTD Model and Discussion
An electrostatic model has been developed by calculating the distribution of charge, electric field and conduction band energy along the tunneling direction as depicted in Fig. 4(a) and (b). The spontaneous polarization present in nitride materials, as well as the piezoelectric contribution from the strained atomic layers at the GaN/AlN interfaces have been also considered. Sheets of effective polarization charge with charge densities ±σ π are included at each of the interfaces as can be seen in the charge diagrams of Fig. 4. The magnitude of the polarization fields generated by these interface charges have been extracted by instersubband absorption measurements, yielding a value of F π ~ 10 MV/cm 30 .
Under equilibrium conditions, a depletion region builds up in the collector side while an accumulation well is induced next to the emitter barrier. The depletion width x d and the accumulation charge, modeled by an electron sheet density n s , are both bias dependent. Thus, the electric field F 0 generated by the collector space charge is also bias dependent and will be constant within the spacer region where no mobile charge is available. The polarization fields F π generated by the interface sheet charges flip the sign of the electric field inside the barriers-F 0 −F π is negative -while the electric field inside the GaN quantum well remains F 0 . When a bias is applied to the heterostructure, the space charge regions are modulated and the magnitude of the electric field F 0 is in turn modified. The expression for the bias applied to the heterostructure will be: where ε s is the GaN dielectric constant; N d , the dopant concentration in the collector side and e is the electron charge. All the thicknesses are as shown in Fig. 4 and t c is the centroid of the accumulation layer. Using a Schrödinger-Poisson solver 31 , we have found that t c ≈ 1nm under equilibrium conditions and we will consider this value to be approximately constant.
Thus, given a voltage bias, Eqn.1 can be solved for F 0 as a function of bias, since it is the sole unknown.
Under forward bias operation, F 0 increases due to the larger amount of charge present in the emitter accumulation and collector depletion regions. As a consequence, the electric field inside the well also increases and the quantum confined Stark effect generates a decrease in the energies of the bound-states. Resonant conditions arise when the well eigen-energies align with the bottom of the conduction band in the emitter side (red curve in Fig. 4(a)). The energies of the bound-states can be calculated within the framework of a finite quantum well perturbed by the electric field F 0 present in the well. Thus if we label the unperturbed ground-state energy as E 0 , solving for the electric field that satisfies the resonant condition gives Using this resonant electric field F 0 RES in Eqn. 1 gives the expected theoretical resonant bias. Furthermore, under reverse bias operation conditions, the electric field F 0 will exhibit a decreasing trend as shown in Fig.   4(b). This is a result of the narrowing of the depletion layer in the collector region. As the reverse bias is increased, the electric field within the GaN layers tends to zero and the magnitude of the electric field inside the AlN barriers increases. In addition, as the depletion width narrows, the effective barrier seen by the conduction electrons on the collector side is reduced and the reverse current increases. A critical condition is achieved when F 0 = 0 and the depletion region is completely eliminated. Under these flat-band conditions, all the applied voltage is dropped within the barriers and the electric field within them is exactly the polarization field F π (magenta curve in Fig. 4(b)). Thus for an RTD with symmetric barriers, we will have this critical threshold voltage under reverse bias given by the simple expression:  Fig. 4(b) shows the energy diagram when the reverse threshold bias is applied. Under these conditions, electrons tunneling through the collector AlN barrier will support the overall reverse current. Since the collector barrier is under a high electric field ( F π ), Fowler-Nordheim tunneling is expected to be the main conduction mechanism for voltages above the threshold voltage. This transport regime contrasts with the resonant tunneling transport mechanism supporting the current in forward bias and is a direct consequence of the polarization fields present in the heterostructure. The effects of the internal electric fields on the I-V curves of nitride RTDs have been previously calculated using the transfer matrix formalism 32

CONCLUSIONS
In conclusion, we have experimentally and theoretically investigated the current-voltage characteristics of GaN/AlN double barrier resonant tunneling diodes. The RTD heterostructures were grown by MBE and fabricated into diodes using conventional lithographic techniques. I-V measurements show the negative differential conductance operation at room temperature under forward bias. In contrast, the reverse bias operation is governed by single-barrier tunneling transport and characterized by a well-defined threshold voltage. An electrostatic model is developed, showing that the reverse threshold voltage and forward resonance voltages are intimately linked to the magnitude of the internal polarization fields present in nitride semiconductors. Finally, subsequent measurements show the repeatability of the resonant peak and negative differential conductance, demonstrating that III-nitride RTDs are capable of room temperature resonant tunneling transport.
These findings represent a significant step forward in resonant tunneling, intersubband based physics and devices in IIInitrides.