The intensive terahertz electroluminescence induced by Bloch oscillations in SiC natural superlattices
© Sankin et al.; licensee Springer. 2012
Received: 9 July 2012
Accepted: 19 September 2012
Published: 9 October 2012
We report on efficient terahertz (THz) emission from high-electric-field-biased SiC structures with a natural superlattice at liquid helium temperatures. The emission spectrum demonstrates a single line, the maximum of which shifts linearly with increases in bias field. We attribute this emission to steady-state Bloch oscillations of electrons in the SiC natural superlattice. The properties of the THz emission agree fairly with the parameters of the Bloch oscillator regime, which have been proven by high-field electron transport studies of SiC structures with natural superlattices.
KeywordsTerahertz emission Natural superlattice Bloch oscillations Wannier-Stark localization Transport in high electrical fields 78.66 Fd; 73.20.Dx
where l is the electron mean free path, E1 is the width of the allowed electron band (the subscript 1 corresponds to the bottom electron band), and F t is the threshold electric field of the BO regime. A thorough analysis of the electron localization effect in high electric fields has revealed that the energy continuum splits into the discrete, so-called Wannier-Stark ladder states in the electric field, which are the frequency-domain equivalent of Bloch oscillations. Esaki and Tsu, in their pioneering work on semiconductor superlattices, pointed out that BO of electrons in superlattices with narrow minibands can be observable even for modest fields. Photocurrent, photoluminescence, and electroreflectance experiments on biased structures with artificial superlattices of GaAs/AlGaAs[5, 6] have proven the existence of the Wannier-Stark localization (WSL) effect in semiconductor superlattices. The most substantial evidence for BO in artificial superlattices was found in experiments with ultrashort light pulses[7–12]. The results of[7–12] demonstrated a few cycles of BO, which, however, were damped after 1 to 2 ps. It was suggested that the fast damping of BO in artificial superlattices originates from electron scattering at the interfaces of heterojunctions and also from breaking the equidistance of the Wannier-Stark levels. The fast decay of BO leaves room for doubts about the possibility of the practical application of this phenomenon. Apparently, the present level of semiconductor technology cannot provide artificial superlattices with sufficient quality suitable for the creation of terahertz (THz) emitters based on BO.
One interesting system demonstrating superperiodicity and potentially having none of the aforementioned drawbacks is a natural superlattice (NSL) in SiC crystals. It is known[14, 15] that all SiC polytypes, excluding the cubic 3C-SiC and hexagonal 2H-SiC, exhibit superperiodicity in the direction along the crystal c-axis in a similar way to crystals with artificial superlattices. The superperiodicity is absolutely stable and has precise crystalline parameters. This superperiodicity is self-organized in the main SiC crystal lattice, and the NSL periods, d, for such polytypes as 4H-, 6H-, and 8H-SiC are equal to 5, 7.5, and 10 Å, respectively. The elementary cell of the hexagonal polytype 4H-, 6H-, and 8H-SiC contains 8, 12, and 16 atoms, which is many times higher than the number of atoms in the 2H-SiC polytype elementary cell. Therefore, in accordance with the theory of Brillouin Zones (BZ), the electron spectrum, for example, of the 6H-SiC crystal in the direction of the c-crystal axis should be considered in the extended BZ composed of six classical Brillouin zones of the crystal. In this case, the electron energy is not a continuous function of wave vector but undergoes breakups at certain planes in k-space. It was shown that the major energy breakups occur at 2Π/c and 4Π/c points for 6H-SiC, and at 2Π/c, 4Π/c, and 6Π/c points for 8H-SiC, where c is the size of the elementary cell along the c-axis. It explains the appearance of the NSL with the period d = c/2 and the miniband electron spectrum in hexagonal SiC polytypes.
Electron transport studies on SiC structures with the natural superlattices[17, 18] have demonstrated pronounced effects of the negative differential conductivity (NDC) caused by the Wannier-Stark localization phenomenon. The threshold fields of the NDC onset at 300 K were found to be F t ≈ 110 ± 25 kV/cm, F t ≈ 150 ± 30 kV/cm and F t ≈ 290 ± 60 kV/cm for the 8H, 6H, and 4H polytypes, respectively, which is in good agreement with Equation 2. It is important to note that the observed values of the NDC were two orders of magnitude higher compared with that reported for artificial superlattices (see, for example,[19–21]). These results mean that there is a well-grounded hope of achieving THz emission due to the Bloch oscillations in SiC NSL. This paper reports on the experimental observation and studies of THz electroluminescence (1.5- to 2-THz spectral range) from SiC structures with a natural superlattice. We attribute this emission to the electron Bloch oscillations in the SiC natural superlattice.
Theory of electron transitions in the Wannier-Stark ladder of silicon carbide natural superlattices
Parameters of minizone transport in silicon carbide polytypes
F t for the Bloch oscillation of electrons, (105V/cm)
F t for the Stark-phonon resonance, (106V/cm)
F t for complete localization of the first electron miniband, (106V/cm)
F t for resonance tunneling of electrons between the first and second (106V/cm)
The width of the first electron miniband E1 (meV)
The gap between the first and second minibands E1,2(meV)
Saturated velocity V s of electrons in the first miniband F∥C,(cm/s)
3.3 × 106
2.0 × 106
1.0 × 106
1.2 × 106
4.4 × 103
where L is the NSL thickness.
The samples suitable for THz electroluminescence experiments were chosen from a number of the prepared mesa-structures by means of analyzing their I-V characteristics at 300 K. The criterion for making this choice was the observation of a mobile high-field domain, which thereby confirmed the development of the WSL effect in the mesa-structure. The small mesa size contributed to a higher yield of high-quality structures. The diode structures selected in this way were used for investigations of the terahertz emission at liquid helium temperatures. Low temperatures are preferable for this kind of experiments because the intensity of electron scattering is reduced. Furthermore, the very low carrier density at helium temperatures and the small thickness of the n− layer contributed to a reduction in the probability of domain formation.
For the low-temperature experiments, the samples were placed on an insulating p-type SiC base. After silver wire bonding, the assembly was mounted on the cold finger of an optical cryostat, which was optimized for the THz spectral domain. The geometry of the available structures only permitted the observation of THz radiation though the substrate. Parabolic mirror optics were used to collect the THz emission in the direction normal to the substrate surface within a solid angle of ≈30° (Figure2b). Polarization of the emission was not expected in this geometry of the experiment, and therefore, all measurements were made in the regime of integrated polarization.
The sample under test was fed with a train of eight pulses, where each pulse in the train was 1 μ s in duration with a 950-μ s time interval between the pulses. It was paused in 7 μ s, after which the next train was begun. Thus, the repetition rate was about 75 Hz. Such a bias was used to minimize lattice heating effects. The duty cycle of the train was 50% at a frequency of 75 Hz. Such a bias was used to minimize lattice heating effects. The spectral measurements were performed with a spectral resolution of 0.6 meV using a Fourier spectrometer operating in the step-scan mode described elsewhere. To eliminate any influence of water vapor absorption, the internal volume of the spectrometer was evacuated down to a residual pressure level of 6 × 10−2 Torr. The THz emission signal was measured using a liquid-helium-cooled silicon bolometer and a lock-in amplifier.
Results and discussion
Taking into account the precise calibration of the detector used here with the emission of a black body source and also the measured attenuation factor of the experimental instrumentation, we can conclude that the spectrally integrated THz emission peak power for the SiC mesa-structure is about 10μ W at 46.2 W of peak pumping power (0.21 A, 220 V). The corresponding external quantum yield of the THz emission is about 0.01 THz photons/electron. Estimations of the internal quantum yield ( Equation 6) of the THz emission for the 6H-SiC structures studied here with a NSL thickness of 2μ m result in a value of. This value is in reasonable agreement with the experiment if the non-optimality of the experimental geometry is taken into account.
In Figure3, a set of THz electroluminescence spectra measured at different amplitudes of the bias voltage are demonstrated. It is seen that the THz emission spectrum consists practically of a single line, the maximum of which evidently shifts to higher frequencies with increases in the bias voltage. The shift in the emission maximum is in the order of 1.5 meV as the bias is varied from 200 to 255 V. The spectrally integrated THz emission power is about 26 μ W for the amplitude of the bias voltage of 255 V (see Figure3).
The experimental data allow the observed THz electroluminescence to be attributed to spontaneous radiation resulting from electron Bloch oscillations in a SiC natural superlattice. Using Equation 1 and the fact of the linear dependence of the emission peak position on the bias voltage for the 6H-SiC structures with NSL, the electric field strength F required for the BO can be estimated. The estimations give F in the order of 8.5 × 104V/cm (at 200 V), which is slightly less than the magnitude of F t for the BO regime obtained from high-field transport measurement data at 300 K on 6H-SiC (see above). However, the agreement between the electric fields is quite reasonable if an increase of the electron scattering time at 7 K compared to its value at 300 K and a corresponding decrease of the threshold field of the BO regime are taken into account. The value of the electric field F implies that only a small part (less than 10%) of the bias voltage drops on the base of the structure. The main voltage drops are on the top n+ layer for supporting of the impurity breakdown, on the substrate, and also partly on the contact regions. Nevertheless, the voltage drop on the n−layer (and hence the electric field F) is proportional to the total bias voltage, and this causes the observed linear dependence of the emission peak on the bias (Figure4). It is necessary to add that the experimental geometry used (Figure2b) was far from optimal since only a small fraction of the THz emission, mainly propagating along the substrate plane, can be collected in this configuration. Therefore, in the case of an optimal geometry (i.e., observation from the side facet of the structure or from the top and using a diffraction grating deposited on the n+ layer), the expected external quantum yield of the THz emission should be higher by some times.
It necessary to point out that Equation 5 also describes the I-V characteristic of the active region of the structure in a regime when the Wannier-Stark ladder states are well formed, and the electron transport is controlled by nonradiative transitions of electrons between the Wannier-Stark levels. In this case, the I-V characteristic should obey the I∝F5/2 dependence and not have a region of NDC. The sharp increase of the current (see Figure1) through the structure under the test excludes the existence of high field domains in the structure in the region of the temperatures and electric fields used in our experiment.
We have measured the polarization properties of the THz emission on specially designed n+ −n−−n+ structures allowing for the emission observation from a side facet. It was found that the emission is linearly polarized along the c-crystal axis (along the electric field), and the polarization degree attains 50% at least.
The previous results on the observation of Wannier-Stark quantization of electrons in silicon carbide NSLs obtained from transport experiments have given a hope of obtaining THz emission in this system. The new experimental data serve as evidence of the existence of steady-state THz radiation induced by Bloch oscillations. The intensive THz emission in the spectral range 1.5 to 2 THz has been found out. The previous papers[13, 14, 16–18] reported only three to four Bloch oscillation cycles, which were observed using ultrashort laser pulse excitations in different artificial superlattices, where the oscillations were damped after a few picoseconds. The properties of a NSL in SiC crystals allow study-state Bloch oscillations to be achieved under purely electrical excitation. In our opinion, the key factors enabling the achievement of the steady-state Bloch oscillations are the absence of heterointerfaces in SiC NSL and the possibility of electron transport along the sufficiently broad first miniband.
To summarize, THz emission due to electron Bloch oscillations in the steady-state regime has been observed for the first time. The experiments were performed on SiC structures with natural superlattice under electrical pumping. In combination with earlier reported high-field transport data[17, 18, 22–24] demonstrating the evolution of the fundamental stages of WSL in SiC natural superlattices, the presented results constitute substantial proof of the pronounced Wannier-Stark localization effect in solid-state objects. It is necessary to add that SiC with natural superlattices opens new possibilities for perspective research in the area of high-field transport phenomena. The discovered intensive THz electroluminescence with a variable frequency can find practical applications for electrically tunable THz emitters. The considerable variation of the emission frequency from 0.3 to 3 THz can be attained through the choice of SiC polytype with appropriate parameters for the superlattice: the highest emission frequency can be achieved with 4H-SiC, but for the lowest emission frequency, any polytype can be chosen from the row of 15R-SiC, 21R-SiC, 27R-SiC, 33R-SiC, and so on.
The authors would like to thank Pr’s N.S. Averkiev, Yu. L. Ivanov, V.V Kveder, and Dr. A.M. Monachov for their fruitful discussions, Dr. A.A. Maltsev for providing us with the necessary crystals with epitaxial layers, and Dr. A.G. Ostroumov for his help in the preparation of the experiment. This work was partially supported by the Russian Foundation of Basic Research and the Program of the Russian Academy of Sciences # 27.
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