THz emitter based on intracenter

Terahertz emitters based on intracenter transitions in semiconductors
James Kolodzey * and Jay Prakash Gupta
University of Delaware, 140 Evans Hall, Newark, DE, USA 19716-3130;
ABSTRACT
Terahertz emitters are important for fundamental studies in an interesting frequency regime and for applications ranging
from medical diagnostics to see-through imaging. A simple approach to THz emission from semiconductors is based on
intracenter optical transitions in dopants and impurities in semiconductors. The centers can be excited either electrically
or optically, and the THz emission occurs when carriers in the dopant upper energy states relax toward the ground state.
Both n–type and p–type dopants as well as deep impurities can be used for THz emission from many host
semiconductors including silicon, SiC, and GaN. Unlike with conventional p–n junction devices, the centers for THz
emission must be occupied and not thermally ionized, which suggests the need for deep energy levels and/or low
temperature operation. Significant center occupation at elevated temperatures favors the wide bandgap semiconductors
such as SiC and GaN, in which the dopant ionization energy can greatly exceed the thermal energy kBT at room
temperature. For example, electrically pumped THz emitters fabricated from nitrogen-doped SiC can operate at
temperatures to about 250 K in pulse mode. The SiC emission spectra had peaks from 5 to 12 THz (20 to 50 meV), and
these surface-emitting devices produced a peak power density of 30 milliwatt–cm–2
at 77 K, which is suitable for a wide
range of high power THz applications. We report the characteristics and limitations of electrically pumped dopant-
transition THz emitters, and their performance in several semiconductor systems.
Keywords: Terahertz emitters, Terahertz properties, radiative transitions, wide bandgap semiconductors, dopants and
impurities in semiconductors, impurity transitions
1. INTRODUCTION
The study of Terahertz (THz) emission from semiconductor devices is important because it can give new insights into
fundamental principles, reveal internal device behavior, and enable novel commercial applications 1
. There are many
families of THz emitters based on semiconductor devices, including electronic multipliers, electrooptic mixers, quantum
cascade lasers, and the intracenter transition devices. The THz emitters that are based on intracenter radiative transitions
in doped semiconductors have simple device structures, can emit high powers (milliwatts), operate to above 200 K, and
are the topic of this report.
1.1 Impurity centers in semiconductors
Radiative transitions between the energy states of dopant centers (both shallow and deep) in semiconductors can produce
photons with energies in the range from 4.1 to 50 meV (1–12.2 THz). Dopant-based THz emitters are not yet well
understood, the previous reports have tended to be empirical, and the basic operating mechanism has not been widely
discussed. Unlike other THz emitters such as quantum cascade lasers, the dopant-based THz emitters have not been used
for practical or commercial applications. This report will review the operating principles of intracenter transition–based
devices, describe their characteristics and limitations, and give some examples of their operation and performance.
*kolodzey@udel.edu; phone: 1 302 831-2405; fax: 1 302 831-4316; www.eecis.udel.edu/~kolodzey/
Invited Paper
Terahertz Emitters, Receivers, and Applications IV, edited by Manijeh Razeghi, Alexei N. Baranov, John M. Zavada,
Proc. of SPIE Vol. 8846, 88460E · © 2013 SPIE · CCC code: 0277-786X/13/$18 · doi: 10.1117/12.2024447
Proc. of SPIE Vol. 8846 88460E-1
Downloaded From: http://proceedings.spiedigitallibrary.org/ on 11/05/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx

1.2 Terahertz emission from intracenter optical transitions
Terahertz emission from bulk semiconductors can originate from the oscillations of charge instabilities, the
recombination and electrons and holes, and the radiative transitions in impurities and dopants 2
. Complex interactions
that produce THz emission can also occur in multilayers and quantum confined structures, but these will not be
discussed here. Since the energy of THz photons is typically less than about 50 meV (12.2 THz), narrow bandgap
semiconductors would need to be used for the mechanism of electron-hole recombination via interband transitions,
which have the accompanying problem of high thermal leakage currents. Intraband transitions in quantum wells require
devices to have thousands of complex layers as in the THz quantum cascade laser, which is limited in operating
temperature to about 200 K in pulse mode 3
. On the other hand, the radiative intracenter transitions in semiconductor
dopants may provide an important approach to THz devices. For example, the well-known gallium-doped germanium
(Ge:Ga) extrinsic photoconductor can detect in the far infrared to wavelengths as long as 200 µm (1.5 THz) at low
temperatures, based on the mechanism of hole ionization from Ga acceptors by THz photons 4
. The dopant-based THz
emitters described here are similar to the Ge:Ga detector, but they operate by the recapture of electrons or holes from the
conduction or valence bands to high energy states in donors or acceptors, with subsequent radiative transitions from
excited states to the dopant ground state 5,6
. For efficient THz emission, the thermal energy kBT must not be sufficiently
high to re-excite the carrier out of the dopant states back into the bands. For this condition to be satisfied, either the
operating temperature must be low or the dopant energy must be deep. The operation and performance of electrically
pumped THz emitters based on intracenter optical transitions are described below.
2. OPERATING MECHANISM OF INTRACENTER THZ EMITTERS
2.1 Impurity energy levels
Dopant-based THz emitters are made from either n-type or p-type bulk semiconductor host crystals, containing suitable
impurity centers (donors or acceptors) that have relatively deep ionization energy, and that can be excited by an applied
current. The doping concentration must be sufficiently high to have many atomic sources for powerful emission, but not
high enough to produce impurity band conduction that may dissipate the carriers. In order to undergo transitions, the
dopants must be neutral and occupied by the charge carriers (freeze-out condition), which implies low operating
temperatures or deep levels (>kBT), as discussed below. Either electron or hole transitions can produce THz emissions 5,6
.
The dopant center energy levels Eimp are hydrogenic in character, and for the simple case of an isotropic energy spectrum
of electrons, are given by 7
:
Eimp = −
m*e4
8εs
2
h2
l2
(1)
where m* is the effective mass, e is the magnitude of the electron charge, εs is the semiconductor host permittivity, h is
Planck’s constant, l is the level quantum number, and the donor levels are referenced to the bottom of the conduction
band at E = 0. The spacing of energy levels depends on the dielectric function and the anisotropy of the effective
masses, but is otherwise similar for different dopants as shown in Figs. 1 and 2 for silicon, with the level designations
based on the irreducible representations 8
. The dopant ground state energy (dopant ionization energy EI) depends on the
chemical nature of the impurity and the semiconductor host crystal. For instance, typical values of ionization energies
for different crystals and dopants are: 45 meV (Si:B and Si:P), 50–100 meV (4H– and 6H–SiC:N, with nitrogen
substituting for carbon), and 210 meV (GaN:Mg). In SiC, the ionization energies have a range of values because the
donor atoms can reside on either the deeper cubic lattice sites, or the shallower hexagonal sites, and the energies depend
on the SiC polytype 9
. In multiple valley semiconductors such as Si and SiC, the ground state of the dopants can be split
by valley-orbit interactions, such as for the 1s(A), 1s(T2), and the 1s(E) states in Fig. 1, which are due to the asymmetric
Coulomb potential in the immediate vicinity of the donor site 7
.

>a
E
a
W
20
10
0
-10
-20
-30
-40
-50
-3x10
i
3p+
2p,_
2p0
1s(E)
1 s(T2)
1s(A)
0
k (cm')
3x107
Conducthn Band
3
2 Ypo/-
2p0
hv
1s(E)
1s(T2)
1s(A)
Figure 1. Left panel shows the energies of impurity states in the reciprocal lattice (k) space of phosphorus doped silicon with
respect to the conduction band minimum at E = 0, revealed by low temperature far-infrared absorption studies. Vertical
arrows indicate possible THz emitting transitions. Right panel shows energy schemes with electron transition paths. Lateral
arrows show nonradiative transitions, the vertical arrows show possible radiative transitions, and the wavy line indicates
photon emission. The leftmost upward arrow is a pumping transition from the donor ground state to the conduction band.
THz emission occurs when an electron (or hole) occupying the dopant makes an allowed radiative transition from an
upper to a lower state, such as from a p state to an s state, as in Fig. 1. The charge carriers can be excited to the higher
dopant states either by optical pumping, or an electrical current as described here. Electrical excitation is the most
convenient method, but is also challenging because in the dopant freeze-out condition, the electrical conductivity of the
host semiconductor is so low that there is little current to produce excitation of the dopant states to make them available
for THz emission. At low temperatures, the applied voltage must be sufficiently high to enable the electric field-assisted
ionization of the dopants and produce significant conduction (a process known as thermal breakdown). Depending on
the amplitude of the applied voltage, it can take time (e.g. several sequential pulses) for sufficient carriers to be ionized
from the dopants to enable conduction and to excite the other dopants.
Carriers in excited dopant states must relax to lower levels without thermally re-exciting into other higher levels or the
bands, which places another constraint on the thermal energy kBT versus the depth of these levels. This requirement is
equivalent to having the upper dopant levels separated by greater than kBT from the conduction or valence band edges.
Shallow dopants are too easily ionized by kBT, and these carriers will not be available for transitions. In addition, the
high applied currents that are needed for high output powers can heat the semiconductor, which depopulates the dopant
states if they are too shallow.
2.2 THz emission spectra
Fig. 2 shows the energy levels of the valance band and the acceptor states for boron doped silicon. Fig. 3 shows an
emission spectrum for B acceptors in Si at low temperature, measured by Fourier Transform Infrared Spectroscopy
(FTIR). The main emission peaks had transition assignments based on the known absorption spectrum associated with
Fig. 2, with remarkable agreement between absorption and emission energies 8
. Transitions between the higher levels of
the dopant states are not typically observed in absorption spectroscopy, which involves transitions from the ground state.
Interestingly, the emission spectroscopy can reveal the energies of the upper levels by observing transitions between
excited states, which are not always observable by absorption from the ground state.

Pan ground state
Pan valence band
Pin ground state
pm valence band
15
10
5
14.1 µW/cm
6.84µW /cm'
1
12.63µW /cm'
5.48µW /cm'
0
500 400 300 200 100
Wave Number (cm -1)
Figure 2. The impurity band structure in acceptor doped silicon, showing the p3/2 and p½ valence band with associated
impurity states. The Γ designations are the irreducible representations 8
. Hole energy increases downward. The downward
arrows represent the absorption lines from infrared absorption measurements. Δ is the spin–orbit splitting at k=0. The p3/2
valence band comprises the heavy hole (mj=±3/2) and the light hole (mj=±1/2) bands.
Figure 3. A typical electroluminescence spectrum of a boron doped silicon device at a temperature of 77 K, taken with an
FTIR spectrometer 10
. The emission peaks corresponded to the intra-center transitions from the 1Γ8
–
state at 230 cm–1
(7
THz), the 2Γ8
–
state at 270 cm–1
(8 THz), and the mixed states of 1Γ6
–
+ 1Γ7
–
at 320 cm–1
(9.5 THz), to the ground state
1Γ8
+
, with level designations as in Fig. 2. A convenient conversion relation is: 100 cm–1
~ 100 µm ~ 3 THz ~ 12.3 meV.
The spectral power was calibrated by a known blackbody source.
3. THEORY OF DOPANT EMITTER EXCITATION
The section reviews the electrical excitation of the neutral dopants, the emitted THz power efficiency and its dependence
on applied current and temperature.

3.1 Impurity center excitation and transition rates
The emitted THz power can be described by rate equations, similar to those reported for the emission from excited states
in Er-doped semiconductors 11
. This simplified theory given here assumes that the dopant is occupied by a carrier
(freeze-out state), and is a two state system with excited and ground states. The emitted THz power, Pout, is proportional
to the photon energy, hν, and the total number of photons, n, emitted per time, with Pout = hνdn/dt. Assuming a uniform
semiconductor emitter with volume, V, and a density N of impurity centers that are occupied by the appropriate carrier,
with density N* of these centers in the excited state, with upper state lifetime τ, then dn/dt = ηintVN*/τ, where ηint is the
internal quantum efficiency of emitted photons per electron transition. For these calculations, it is assumed that all the
impurities are occupied, which requires low temperatures or deep levels. The excited state density increases with the
applied current density J, the capture (or collision) cross section σ of carriers by an unexcited center; and decreases as
the states relax:
dN *
dt
=
σ J
e
N − N *( )−
N *
τ
(2)
In steady state, the density of excited centers is:
N* = N
τσ J / e
1+τσ J / e
(3)
which contributes to the photon emission rate and where the τσ product can be extracted by fitting to emission data. The
emitted THz power is given by:
Pout =
ηinthvVN
τ
τσ J / e
1+τσ J / e
!
"#
$
%& (4)
and has two limiting regimes; for high currents with τσJ/e >>1, and low currents when τσJ/e << 1. In the high current
regime the emitted power is given by a saturated value:
Psat =
ηinthvVN
τ
(5)
that, interestingly, does not depend on the applied current. Presumably at the high current limit, all states are excited and
higher currents cannot excite more states, so that the limiting factor for transitions is the state lifetime.
In the low current regime:
Pout =
ηinthvVNσ J
e
(6)
in which the power is linearly proportional to the applied current, which supplies the charge carriers that produce the
excitations. Interestingly, the low power equation does not depend on the lifetime of the excited states, presumably
because at low currents in steady state, most states are unexcited and the emission rate is limited by the supply of
carriers, not the lifetime of the states.
Typical parameters for the devices studied here include: volume 120 µm × 190 µm × 380 µm = 8.7×10–6
cm3
, a doping
density of 5×1015
cm–3
, and a photon energy hν = 34.5 meV (8.4 THz), To extract the other device parameters, such as
transition lifetime and capture cross section, Eqn. (4) can be fit to the experimental data from the THz emitters.

400
300
ó
200
E 100 Temperature = 78K
0
0 1 2 3
Current (A)
4
10
80 100 120 140 160 180
Temperature (K)
Current =3A -
3.2 Effects of heating and temperature on THz emission
A more comprehensive model of the output power should includes the effects of current heating, which would make the
dopant states ionize and become unavailable for THz emitting transitions 10,12
. The extent of device heating can be
included in the power equation (in the linear current regime) as extra terms that decrease the emitted power in proportion
to the current squared, and including an activation energy Ea, which describes the center ionization. Heuristically, an
equation for output power that includes current heating is:
Pout =ηinthvVN
σ
e
J − AJ2
( ) 1+ Bexp −
Ea
kT
"
#
$
%
&
'
(
)
*
+
,
-
−1
(7)
where A is a constant that describes the decrease in output power with Joule heating, and B and Ea are constants that
describe the occupation of the centers and their ionization energy.
Figure 4. The dependence of the emitted THz power on applied pumping current and device heat sink temperature of
terahertz emitting device based on nitrogen doped 6H–SiC. Left panel shows that the output power increased with applied
current, but began to saturate at higher currents above 1 A in accord with the predictions of Eqns. (4) and (7). Right panel
shows that at applied current of 3 A, the output power decreased with temperature, which is in accord with Eqn. (7).
An external quantum efficiency, ηext, can be defined as the number of emitted photons per injected electron, such that
ηext = (P/hν)/(J/e), giving the following dependence:
ηext =ηintVNσ 1− AJ[ ] 1+ Bexp −
Ea
kT
"
#
$
%
&
'
(
)
*
+
,
-
−1
(8)
with the same constants as in Eqn. 7. Eqn. (8) indicates that the external quantum efficiency decreases with increasing
current and with increasing temperature, in agreement with the data of Figs. 4 and 5.
Experimental data on the variation of the external quantum efficiency with applied current is shown for a nitrogen-doped
6H–SiC in Fig. 5, where the indicated current is the peak value of the applied pulses, which typically had a 10 % duty
cycle. The data in Fig. 5 shows that the external quantum efficiency exceeded 1 % at low temperatures. At high values
of current, above 1 A, the power decreased with increasing temperature, which qualitatively supports the heating model.
The curve-fitting of Eqns. (7) and (8) to experimental data versus current and temperature can be used to extract
important parameters such as the state capture cross section, the internal quantum efficiency (emitted photons per center
transition), and the center activation energy.

;, 2.0
U
.5 1.5
E 1.0
ó, 0.5
000
_90K,
210K_ - - - - .
- --
1 2 3 4 5
Current (A)
Figure 5. External quantum efficiency (emitted photons per injected electron) versus peak current for N-doped 6H–SiC
device operating at heat sink temperature from 77 K to 210 K. The trends versus current and temperature are in reasonable
agreement with the predictions of Eqns. (7) and (8). The wall-plug efficiency (THz power output divided by electrical
power input) for this device was about 2x10–6
at 77 K.
Eqns. (4) and (7) suggest ways to increase the THz output power of dopant emitters. The power increases with current,
as long as heating does not depopulate the excited states. The THz power will increase if the impurities have a shorter
state lifetime. Power increases with the density of impurity centers, but if the density is too high, an impurity band will
form, and the carriers will conduct to other centers rather than enter an excited state of the initial center. Impurities with
a deeper ionization energy will render the heating term less influential and will give higher output powers as well as
higher temperature operation. For the best performance of a THz dopant-based emitter, it is important to optimally
select a deep center with short lifetime, and a host semiconductor with high thermal conductivity to reduce localized
heating.
3.3 Impurity center current excitation
The structure of the THz emitting devices consisted of a bulk resistor region and two metal–semiconductor Schottky
contacts, as in Fig. 6 13
. At low temperatures, most of the carriers occupied the dopant ground states so that the
resistivity was high, and the two back-to-back Schottky contacts limited the current. When the electric field was above 1
kV/cm, however, the current conduction increased dramatically. For instance, at 4 K, boron doped silicon devices can
conduct current more than 1A at 100V. Simulations suggested that the current conduction at low biases mainly depended
on the leakage current from the reverse biased contact, and current conduction at high bias was caused by impurity
impact ionizations, with good agreement between experimental data and calculations.

W sc
M
Figure 6. Energy band diagram of the THz emitter structure with Schottky battier metal contacts; prior to applied bias
(dashed lines), and after applied bias (solid lines). The J symbols represent the applied current; Vext is the external bias
voltage (with positive bias applied to the left side, relative to the right); ΔΦB represents the Schottky barrier heights, σLeak is
a leakage conductivity past the Schottky barriers; and W represents the space charge depletion width 13
.
4. THZ EMITTER PERFORMANCE RESULTS
THz emitters were fabricated from samples of doped silicon carbide. This section describes their fabrication, emitted
spectrum and output power versus applied current.
4.1 Aluminum doped SiC emitter fabrication
Impurity-center THz emitters were fabricated from a 625 µm thick double-sided polished p-type 6H–SiC wafer, which
was predominantly doped with Al acceptors. In 6H–SiC, the Al acceptor is a deep level with an ionization energy of 239
meV on the hexagonal h–site, and 249 meV on the cubic k–site at 4 K.
Figure 7. Micrograph of SiC THz emitter. Upper mesh pattern is the top electrical contact with fine Au wire bonds
extending toward the bottom. Below the mesh, the dual shaded horizontal region is the 6H–SiC material. The device
surface size is 1mm x 2 mm.
For device fabrication, the samples were RCA cleaned, followed by contact photolithography to define a mesh-shaped
metal contact pattern in photoresist with 80 µm lines and spaces, for a 50% fill factor, as shown in Fig. 7. The metal
contacts on both the top and back sides were deposited by the e-beam evaporation of Ti/Au (10 nm/300 nm). After the
photoresist lift-off to pattern the metallic contacts, the samples were cut into dice, with the metal mesh covering the
whole top surface as shown in Fig. 7. For measurement, the devices were mounted onto a copper block heat sink using
low temperature conductive epoxy with high electrical and thermal conductivity. The copper block was attached to the
cold finger of a cryostat that used liquid nitrogen cooling (for T > 77 K), with a high density polyethylene (HDPE)
optical window. All temperatures reported in this paper were that of the heat sink measured with a platinum resistor. The
actual device temperature can be as much as 50K higher than the heat sink, depending on the device structure and the
packaging.

500 400 300 200
Wavenumber (cm')
100
340
330
3 320
W 310
300
0.5 1.0 1.5
Current (A)
2.0
4.2 Aluminum doped SiC emitter performance
The THz emission spectra were measured using a ThermoNicolet Nexus 870 Fourier Transform Infra-Red (FTIR)
spectrometer equipped with a liquid helium-cooled silicon bolometer (IRLabs) detector 13
. A pulse generator was used to
electrically drive the devices with submicrosecond pulse trains. The current was measured using an inductive current
probe and an oscilloscope. A lock-in amplifier was used to synchronously detect the signals from the bolometer.
The emission spectrum of a 6H–SiC:Al emitter at 78 K is shown in Fig. 8 for different applied currents. As the current
increased, the output power increased, and the spectrum changed, which was attributed to differences in the occupation
of the excited levels. The THz peak output power versus peak applied current is shown in Fig. 9, calibrated by a known
black body emitter. The peak emitted intensity from the top surface was about 30 milliwatts–cm–2
. Note that at
comparable operating temperatures and applied currents, the SiC device with deeper acceptor ionization energy near 240
meV, had a much higher output power than a Si:B emitter with acceptor ionization energy of only 45 meV.
Figure 8. Electroluminescent (EL) emission spectra from an Al-doped 6H–SiC device at different pumping currents, from
0.5 A at lower intensities, up to 2 A at higher intensities. The emission peaks centered around 200–250 cm–1
had a spectral
intensity of about 2.5µW/cm–1
, depending on pumping current. The peak around 400–450 cm–1
had a spectral intensity of
around 1.5µW/cm–1
, depending on pumping current. The applied current pulses were 100 ns in duration.
Figure 9. Calibrated emitted THz power versus pumping current at 78K, for a top emission patterned Al-doped 6H–SiC
device with spectrum shown in Fig. 8.

4.3 Emitter operating temperature range
Materials that have deeper ionization energy than the typical dopants in silicon may be able to achieve higher operating
temperatures. For example, Lv et al. 14
reported a 150 K operating temperature from nitrogen-doped 4H–SiC devices,
which had an ionization energy of 52.1meV for the h–site (hexagonal) and 91.8meV for the k–site (cubic) 15
. This
device produced an output power of ~ 80 µW at an applied peak current of 3 A at a temperature of 80 K. The average
photon energy was about 37 meV, so the photon emission rate was 1.3x1016
photons/s. On the other hand, nitrogen
donors in the 6H polytype of SiC have the even deeper ionization energy of 81meV for the h–site, 137.6meV for the k1–
site, and 142.4meV for the k2–site, so devices made from nitrogen doped 6H–SiC may have even higher operating
temperatures 16
.
Using the constraint that the dopant ionization energies must exceed kBT for efficient transitions, the maximum operating
temperatures of THz dopant emitters can be estimated. For example, for boron acceptors in Si (ionization energy 45
meV), the maximum operating temperature was observed to be about 118 K (kBT = 10 meV) 10
. In addition, for nitrogen
in 6H–SiC (ionization energy near 100 meV for hexagonal site), the maximum operating temperature was observed to be
above 210 K (kBT = 20 meV). These observations imply that the ground state must be greater than about 5 kBT from the
band edge to avoid thermal degradation of the THz emission. Using this factor of 5 for a device to operate at room
temperature, the dopant ionization energy must be greater than 5x26 meV = 130 meV, which is available with certain
impurities in the wide bandgap semiconductors SiC and GaN. The larger ionization energy enables impurity states to be
occupied at higher temperatures. In addition, more complex device structures may be able to provide higher
performance. For example, the use of p–n junctions in dopant–based THz emitters may allow higher emission
efficiencies 17
.
5. CONCLUSIONS
Based on experiment and theory, dopant–based THz emitting devices that operate by intracenter transitions can have
significant output power, depending on the choice of materials, operating temperature, and current. For example, Al
doped 6H–SiC devices emitted a peak intensity from the top surface of about 30 milliwatts–cm–2
. Compared to shallow
dopants in conventional semiconductors, the wide bandgap semiconductors can have deep impurity levels that are
significantly occupied at relatively higher temperatures, which gives advantages to SiC and GaN for high power, high
temperature THz emission. The emission data appeared to follow qualitatively simple device models, which implied
that higher temperature operation should be possible using deeper dopants. Higher output powers may be also be
possible by using higher densities of centers (but without impurity band conduction), and short radiative lifetimes of the
dopant states. The optimum THz emitter for room temperature operation will require the identification of deep dopants
in suitable wide gap semiconductors.
ACKNOWLEDGMENTS
Special thanks to T. Adam, A. Andrianov, M.S. Kagan, S. Kim, P.-C. Lv, M.A. Odnoblyudov, G. Pomrenke, S.K. Ray,
R.T. Troeger, G. Xuan, I.N. Yassievich, and J. Zavada for valuable discussions. Thanks to W.T. Kolodzey for reviewing
the manuscript. This work was supported by NSF Award No. ECCS-1306149.
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