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The intensive terahertz electroluminescence induced by Bloch oscillations in
SiC natural superlattices
Nanoscale Research Letters 2012, 7:560 doi:10.1186/1556-276X-7-560
Vladimir I Sankin (Sankin@mail.ioffe.ru)
Alexandr V Andrianov (email@example.com)
Alexey G Petrov (firstname.lastname@example.org)
Alexey O Zakhar`in (Alex.Zaharin@mail.ioffe.ru)
Ala A Lepneva (Sankin@mail.ioffe.ru)
Pavel P Shkrebiy (email@example.com)
9 July 2012
19 September 2012
9 October 2012
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The intensive terahertz electroluminescence
induced by Bloch oscillations in SiC natural
1A.F. Ioffe Physico-Technical Institute, 26 Politekhnicheskaya, St. Petersburg, 194021, Russia
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.
terahertz emission; natural superlattice; Bloch oscillations; Wannier-Stark localization; transport in high
78.66 Fd; 73.20.Dx
The possibility of oscillating motion of electrons in crystals at high field bias has attracted great interest since it
was predicted [1,2]. The Bloch oscillations (BO) with frequency (ν)
ν = eFa/h,(1)
where e, h, and a are the electron charge, the Plank constant, and the crystal lattice period, respectively, originate
from the acceleration of electrons in an electric field and their Bragg reflection at the Brillouin zone boundary.
One important condition must be satisfied to achieve the BO regime, namely:
eFl ≥ E1
orF ≥ Ft=E1
where l is the electron mean free path, E1is the width of the allowed electron band (the subscript 1 corresponds
to the bottom electron band), and Ftis 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 Ft≈ 110 ± 25 kV/cm, Ft≈ 150 ± 30 kV/cm
and Ft≈ 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
Theory of electron transitions in the Wannier-Stark ladder of silicon carbide natural superlattices
The internal quantum yield of the THz emission due to optical transitions between Wannier-Stark levels in the
natural superlattice of 6H-SiC was estimated. The band diagram of the 6H-SiC NSL depicted in Figure 1 was
used for these estimations.
Figure 1 Schematic diagram of Wannier-Stark states. Schematic diagram of Wannier-Stark states in a 6H-SiC
natural superlattice at a modest uniform electric field. The solid and dotted curves depict the envelope wave
functions corresponding to different steps in the ladder. The thick short lines correspond to the electron
Wannier-Stark levels confined within the first well (dashed lines).
The values for the quantum well width and the energy width of the first electron miniband were taken to be
consistent with the experimental data [17,18,22,23] on high-field transport in SiC natural superlattices, which
have demonstrated the evolution of the fundamental stages of WSL in these systems (the transition from a
relatively small field regime of Bloch oscillations to large field regimes: the Stark-phonon resonances between
Wannier-Stark ladder levels, the full localization of the lowermost miniband, and inter-miniband resonance
transitions between the first and second minibands). The most important results of these transport studies are
summarized in Table 1.
Table 1 Parameters of minizone transport in silicon carbide polytypes
of the first
The width of
in the first
F ∥ C,(cm/s)
3.3 × 106
2.0 × 106
1.0 × 106
1.2 × 106
4.4 × 103
1.8  1.9 260 
Parameters of minizone transport in silicon carbide polytypes. Here, Ftis the threshold field, and (Est.) means an approximate estimation
made on the basis of the experimental value of E1for the 6H-SiC polytype and taking into account the fact that E1∝ k2
d is the NSL period. F, electric field. Ft, threshold electric field.
d, where kd= ¯ h/d and
Using the tight-binding approximation developed for such systems by Bouchard and Luban , the amplitude
of the electron wave function can be expressed by the transfer integrals between the nearest quantum wells V1:
where Jnis the Bessel function of the first kind, order n, and ul(z) is the wave function of the electron with the
energy El= leFd in the ground state of the quantum well. Taking into account Equation 3, it is straightforward
to calculate the probability of an optical transition of an electron between two adjacent quantum wells:
where c/n is the speed of light in SiC,¯ hω = eFd is the energy of the emitted quantum, and m is the electron
effective mass. We suppose that the electric field is insufficient for the inter-miniband resonant tunneling of the
electrons, and the major nonradiative process is the transition between the nearest Wannier-Stark states with the
emission of the longwave acoustic phonons. The corresponding probability of the nonradiative process is
where ? is the deformation potential constant, s is the speed of sound, and ρ is the SiC material density. The
formula (5) is applicable only for a low electric field, which satisfies eFd ≪2πs¯ h
determining the strong dependence of τ−1
wave vectors to small values in the weak electric fields. Secondly, the electron wave function involves many
quantum wells, in this work (E1
d. There are two factors
nonradon the electric field. Firstly, the conservation laws limit the phonon
eFd≈ 40), and the contributions ul(z) from different quantum wells partly
compensate each other. The internal quantum yield, η, of the THz emission is
where L is the NSL thickness.
The samples studied in this work were unipolar 6H-SiC n+− n−− n+diode structures. The n−epitaxial layer
(the base of the diode) was grown by the sublimation on-axis method  on a 6H-SiC (0001) Lely substrate,
which had Nd− Na≈ 2 × 1018cm−3and a thickness of 200 µm. The base had a donor concentration of
1015cm−3< Nd− Na< 1016cm−3, and the thickness was varied in the interval of 2 to 4 µm. The 6H-SiC
polytype of the epitaxial layer and its acceptable doping homogeneity were confirmed by X-ray diffraction,
photoluminescence microscopy, and C-V measurements. The latter measurements were done using auxiliary
Schottky barriers created on the n−layer surface. The top n+layer with Nd−Na≈ 1020cm−3was fabricated on
the n−epitaxial layer by ion implantation of nitrogen with subsequent annealing. Finally, the cylindrical
mesa-structures with a diameter of 50 µm (S = 2.0 × 10−5cm2) and cruciform mesa-structures
(S = 3 × 10−5cm2) (Figure 2a) were made by dry etching after photolithography. For a contact, a sputtered and
annealed (900◦C) nickel film with a thickness of 0.2 µm was used. A common contact area was located on the
upper surface of the substrate. Insulator layers were created by proton implantation on the mesa-periphery and
on the upper surface of the substrate. In accordance with the aforementioned property of the 6H polytype of SiC
crystals, such a diode structure was a natural supperlattice as a whole.
Figure 2 General view of the structures. (a) General view of the structures used for THz measurements. (b)
Geometry of the experiment.
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◦(Figure 2b). 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 µs in duration
with a 950-µs time interval between the pulses. It was paused in 7 µs, 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 × 10−2Torr. The
THz emission signal was measured using a liquid-helium-cooled silicon bolometer and a lock-in amplifier.
Results and discussion
An intensive THz signal was detected at bias voltages exceeding 190 to 195 V. The existence of such a threshold
voltage for the THz emission can be explained by the impurity breakdown in the top n+-SiC layer, which is
required for injection of electrons into the NSL. Upon reaching the breakdown of the top layer of the structure,
the bias voltage becomes redistributed, and some part of it starts to drop to the base of the structure (n−layer).
At the same time, the intensity of the THz emission begins to grow almost linearly with increases in current. The
I-V characteristic of the 6H-SiC n+− n−− n+diode structures and the dependence of the intensity of THz
emission on the current are demonstrated in Figure 3 (insert). The current is practically absent at voltages below
≈180 V due to extremely small carrier concentration in the active region of the structure at helium temperatures,
and the current appears only as a result of the electron injection from the top n+layer.
Figure 3 Spectra of the THz emission. Spectra of the THz emission from the cruciform SiC mesa-structure at
several bias voltages. T ≈ 7 K. The spectra werre corrected for the spectral response of the measurement system,
normalized to the emission maximum, and vertically shifted for clarity. The scaling factors are shown in the
graph. The figure insert demonstrates the dependencies of the THz emission intensity and the voltage drop on the
current through the structure.
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 10 µW 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 2 µm result in a value of
agreement with the experiment if the non-optimality of the experimental geometry is taken into account.
nonrad≈ 2,666.6 × (1.8 × 105s−1/1.3 × 1010s−1) ≈ 0.04. This value is in reasonable
In Figure 3, 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 µW for the amplitude of the bias voltage of 255 V (see Figure 3).
As seen from Figure 4, the shift of the THz emission peak versus the bias voltage can be well approximated by
linear law with a gradient of ≈32 µeV/V. It is important to note that the FWHM of the emission line is almost
constant and equal to ≈2.9 meV (0.7 THz) as the bias voltage varies from 200 to ≈240 V (Figure 3). The shape
of the emission spectrum at high bias voltages (255 V and higher) is caused by the superposition of two emission
bands. The first of them pertains to the above mentioned series of Bloch emissions at about 6 to 7 meV. The
maximum of the second emission band is at about 13 meV. The manifestation of this band can be seen on spectral
line at 255-V voltages. We tentatively attribute this band at ≈13 meV to the optical transition of electrons over
the next Wannier-Stark ladder state in the high-field-biased NSL of SiC. We have to note that a more detailed
theoretical analysis is required for precise interpretation of the experimental findings. At this moment, it is
important to underline that similar spectra have been observed for 4H- and 8H-SiC NSL structures, and its
spectral features correlate with aforementioned miniband widths and periods of NSL in 4H-, 6H-, and 8H-SiC.
Figure 4 Dependencies of the peak position on the bias voltage. Dependences of the peak position of the THz
emission line and the emission line width on the bias voltage. The solid line corresponds to a linear fit of the
experimental emission maximum (Emax) versus bias voltage (V) with a gradient of ≈32 µeV/V. The dashed line
is a guide for the eye.
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 Ftfor 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 (Figure 4). It is necessary to add that the experimental geometry used (Figure 2b) 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 ∝ F5/2dependence and not have a region of NDC. The sharp increase of the current (see Figure 1)
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 declare that they have no competing interests.
VS conceived, designed, and coordinated the study, determined the directions of investigations, and wrote the
manuscript. AA determined the technology of THz optical investigations and wrote the manuscript. AP carried
out the theoretical analysis of THz transition physics in Bloch oscillation regime and wrote the manuscript. AZ
carried out the optical measurements. AL carried out the electrical measurements of the experimental structures.
PS carried out all cycles of electrical contact fabrication to experimental structures. All authors read and
approved the final manuscript.
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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