Stimulated Terahertz Stokes Emission of Silicon Crystals Doped with Antimony Donors
S.G. Pavlov and H.-W. Hu ¨bers
Institute of Planetary Research, German Aerospace Center (DLR), 12489 Berlin, Germany
J.N. Hovenier and T.O. Klaassen
Kavli Institute of Nanoscience Delft, Delft University of Technology, 2600 GA Delft, The Netherlands
D.A. Carder, P.J. Phillips, and B. Redlich
FOM-Institute for Plasma Physics, 3439 MN Nieuwegein, The Netherlands
Institute of Crystal Growth, Max-Born-Strasse 2, 12489 Berlin, Germany
R.Kh. Zhukavin and V.N. Shastin
Institute for Physics of Microstructures, Russian Academy of Sciences, 603950 Nizhny Novgorod, Russia
(Received 21 June 2005; published 26 January 2006)
Stimulated Stokes emission has been observed from silicon crystals doped by antimony donors when
optically excited by radiation from a tunable infrared free electron laser. The photon energy of the emis-
sion is equal to the pump photon energy reduced by the energy of the intervalley transverse acoustic (TA)
g phonon in silicon (?2:92 THz). The emission frequency covers the range of 4.6–5.8 THz. The laser
process occurs due to a resonant coupling of the 1s?E? and 1s?A1? donor states (separation ?2:97 THz)via
the g-TA phonon, which conserves momentum and energy within a single impurity center.
DOI: 10.1103/PhysRevLett.96.037404PACS numbers: 78.47.+p, 41.60.Cr, 42.65.Es, 71.55.Cn
In the past few years, significant progress has been made
towards silicon based lasers. Silicon is an indirect band gap
semiconductor. Therefore, it is difficult to realize an effi-
cient process for light amplification. This fact compels the
search for nontraditional approaches for light generation.
In the near infrared region, numerous approaches (see
Ref.  for a review) to overcome this difficulty, such as
silicon nanocrystals [2,3], Si=SiO2 and Si=SiGe 
superlattices, porous silicon , erbium-doped silicon
, and silicon light-emitting diodes , have been at-
tempted. Recently, the first silicon lasers operating at 1:540
and 1:675 ?m based on stimulated Raman scattering have
been reported [9,10]. The Raman effect in silicon occurs
via scattering of photons by optical phonons of the crystal.
The strongest Stokes emission is due to the threefold
degenerate short-wavelength optical modes at the center
of the Brillouin zone of silicon .
The first silicon laser was realized by infrared optical
excitation of group-V donor centers embedded in a silicon
host lattice [12,13]. For this type of laser, the interaction
between phonons and electrons is essential. Except zone-
centered optical phonons, intervalley acoustic and optical
phonons have been found to play a decisive role in energy
and momentum relaxation for nonequilibrium charge car-
riers insilicon [14,15].Strongresonantintervalleyphonon-
impurity interaction has been observed in absorption spec-
tra of Bi donors in silicon . When the phonon energy
does not exactly coincide with the energy between two
impurity states, the contributions from the electronic im-
purity state and the phonon-related part form a ‘‘mixed’’
state, as in silicon doped by Ga . These interactions
play an important role in the formation of population
inversion between excited states, eventually leading to
lasing on particular intracenter transitions in Si:Bi  as
well as in Si:As . A different situation occurs in silicon
doped by antimony (Si:Sb). The energy of the transverse
acoustic g-TA intervalley phonon and the energy between
the 1s?E? and 1s?A1? states are almost equal (?12 and
12.27 meV, respectively). This enhances the nonradiative
electronic relaxation between these states. Terahertz intra-
center laser emission in Si:Sb has been observed when the
crystal was excited by radiation from a pulsed CO2laser
. The population inversion is formed due to a cascade-
type capture of photoexcited electrons from the conduction
band into excited donor states, following their accumula-
tion in the relatively long-living 2p0state. The intracenter
Si:Sb laser operates at low lattice temperature (T < 15 K).
The emission spectrum consists of a single line at 5.15 THz
[2p0! 1s?T2? transition] . In this Letter, we report on
a laser with variable emission frequency in the terahertz
spectral region, based on Si:Sb optically excited by a
frequency tunable infrared free electron laser.
Silicon crystals doped with antimony at a concentration
of ND? 4 ? 1015cm?3were grown by the float zone
technique in the ?111? direction. The investigated Si:Sb
sample is a rectangular parallelepiped of 8 ? 7 ? 5 mm3.
Four facets were polished to form a resonator on total
internal reflection modes. The free electron laser (FEL)
generates ?6 ?slong macropulses at a 5Hz repetition rate
in the range 31–43 meV. Each macropulse consists of a
PRL 96, 037404 (2006)
27 JANUARY 2006
© 2006 The American Physical Society
train of micropulses with duration between 3 and 10 ps
separated by 1 ns.The spectrum of the emission pulse has a
Lorentzian shape with a full width at half maximum
(FWHM) of 0.1–0.2 meV. The silicon crystals were cooled
to ?5 K in a continuous flow liquid helium (lHe) cryostat
and optically excited by the FEL radiation. The power on
the sample was controlled by a step attenuator. The largest
facet of the sample ?h111i? was irradiated (inset in Fig. 1).
The emission was detected by a lHe cooled Ge:Ga detector
with a rise time of ?50 ns. FEL radiation was blocked by a
room-temperature crystalline quartz filter in front of the
detector (cutoff energy >31 meV). The emission was
spectrally analyzed by a Fourier transform spectrometer
with a resolution of ?0:5 cm?1(0.06 meV).
At a certain pump power, a pronounced threshold is
observable abovewhich the output power of the Si:Sb laser
increases byseveral ordersofmagnitude (Fig.1). This is an
indication of a laser process. The higher the impurity state,
which is optically populated, the higher the laser threshold.
It is important to note that laser emission appears not only
when the pump transition ends in one of the excited donor
states but also when the pump frequency does not corre-
spond to any transition frequency between the 1s?A1?
ground state and an excited state of an impurity atom
(33.45meV curve in Fig.1).Inthis case, the laser threshold
is the highest, but the signal does not exhibit any pro-
nounced saturation with increasing pump power as ob-
served when pumping into the odd-parity excited donor
The spectra measured for pump photon energies in the
range 31–40 meV show two types of lines with different
properties (Fig. 2). The frequency of one line does not
depend on the pump frequency, and its frequency corre-
sponds to the 2p0! 1s?E? intracenter transition of Si:Sb
as determined byspectroscopy .The other line changes
its frequency proportional to the pump photon energy from
19.2 to 24.1 meV (4.6–5.8 THz). Its linewidth is signifi-
cantly broader (FWHMS? 0:18–0:76 meV) than that of
the intracenter line (FWHMI? 0:12–0:20 meV). For di-
rect pumping into one of the excited donor states such as
2p0, 2s, 2p?, both lines appear simultaneously. When
pumped into the 2p0 state, their energies differ by
0.37 meV. This is another indication that the lines are of
different origin. The relation between the energies of the
pump and the emitted light is
@!S? @!P? ?12:10 ? 0:02? meV:
The energy of the emitted photon @!Sdiffers from the
pump photon energy @!Pby a constant value of 12:10 ?
0:02 meV, which is close to the energy of the intervalley
g-TA phonon in silicon h?g?TA. Magnetophonon reso-
nance technique gives h?g?TAvalues of 11.3 meV (for
magnetic field direction h111i), 12 meV ?h110i?, and
12.2 meV ?h100i? for pure silicon at a lattice temperature
of 65 K . Intervalley scattering in n-silicon involving
the transfer of an electron in a ?100?-type direction to the
equivalent valley (g scattering) is an umpklapp process, in
which the sum of the wave vector qgof the g phonon and
the change of thewavevector of the electron ?k is equal to
a principal vector of the reciprocal
Momentum conservation for this process can be written as
?k ? K001? qg:
Intervalley phonons can accelerate the intracenter relaxa-
tion of an electron if the energy of the phonon coincides
pumping by FEL photon :
33.45 meV (B)
Si:Sb emission intensity (a.u.)
FEL photon flux density (photon cm
pump photon energy are shown in the left corner (inset: sketch of
Typical Si laser thresholds. The pumped Sb states or
pump photon energy (meV
emission photon energy (meV)
emission frequency (THz)
frequencies (same symbols as in Fig. 1). The accuracy of the
central wavelength of the FEL pump pulse is <0:01 meV and
the FWHM is ?0:1–0:2 meV. The instrumental resolution for
the emission spectra is ?0:06 meV. The dip in the emission
spectrum (when pumped in the 2s state) is due to atmospheric
absorption at ?21:8 meV.
Emission spectra from Si:Sb taken at different pump
PRL 96, 037404 (2006)
27 JANUARY 2006
with the energy gap between a pair of particular impurity
states. In the resonant intracenter interaction, the ?k wave
vector is reduced to the wave vector connecting the ex-
trema of two opposite valleys in the conduction band, so
that, in the reduced Brillouin zone, the intracenter relaxa-
tion due to scattering on a g phonon occurs as a ‘‘vertical’’
transition (no change of the momentum of an electron is
required). Equations (1) and (2) describe the energy and
momentum conservation for the observed emission
(Fig. 3). We call this emission process Brillouin-type (B)
lasing since it involves acoustic g-TA phonons in contrast
to Raman silicon lasers [9,10] where an optical phonon is
employed. The specific feature of this emission is that the
photon scattering occurs at the antimony donor center. The
laser transition corresponds to Stokes scattering compo-
nent and originates always from the pumped state (virtual
or excited donor) and terminates about 0.3 meV below the
1s?E? level. We assume that this is an indication for a
mixed 1s?E? state with an electronic part 1sEL?E? and a
phonon-related part 1sPH?E?, which is induced by strong
interaction with the g-TA phonon, similar as in Si:Ga .
Momentum conservation is obtained because the ump-
klapp scattering process of Eq. (2) cancels the large mo-
mentum of the emitted g-TA phonon [qg?TA? 3:4?
107cm?1? !P?n=c?, !S?n=c?; here n is the refractive
index of silicon and c is the velocity of light (see Fig. 3)].
No emission was observed when pure (residual doping
?1013cm?3) silicon crystals were optically pumped.
Therefore, the presence of antimony impurity centers is
mandatory for the Brillouin-type lasing. Since no absorp-
tion of FEL radiation was registered at photon frequencies
corresponding to pumping in between the 2p0and 2p?
states, only a pair of principle electronic states taking part
in the g-TA phonon-assisted electron relaxation, i.e.,
1sPH?E? and 1s?A1? states, can be involved in this laser
mechanism, while pumping and emission occur via a
virtual state (dashed line in Fig. 3, on the right). On the
contrary, for intracenter lasing, pumping occurs exclu-
sively in the dipole-allowed optical transitions terminating
in the odd-parity donor excited states. At least three donor
levels, always including the long-living 2p0state and the
short-living 1sEL?E? state, are involved in the I-laser
mechanism (Fig. 3, on the left).
One may systemize the observed laser emission as fol-
lows. There are three different cases: pure intracenter
emission (I), pure Brillouin-type emission (B), and simul-
taneousemissionofboth (I ? B).I lasing issimilar towhat
was observed for Si:P under intracenter pumping.
Photoexcited electrons accumulate in the long-living 2p0
state, which is the upper laser level for all pump photon
energies. In contrast to the Si:P laser, the lower laser level
is the 1s?E? state independent of the pump transition .
Brillouin-type lasing has a different nature. Pure B
emission occurs when the Si:Sb crystal is pumped with a
photon energy out of resonance with an excited impurity
state. It occurs for pump photon energies between 31 meV,
the smallest available energy in the experiment, and
36 meV. Above 36 meV, the pump process is apparently
not efficient enough to maintain laser emission. B lasing
has a lower efficiency than I lasing and requires peak pump
intensities of ?5–50 kWcm?2for pure Brillouin-type las-
ing compared to ?0:1–10 kWcm?2for I lasing. With
respect to I emission, the pure B emission is relatively
unstable and delayed by about 1:5 ?sec (Fig. 4). Above
the laser threshold, B emission grows rapidly with the
pump intensity and does not saturate (Fig. 1). For direct
pumping into an excited state, the absorption length of the
pump radiation is ?0:5 mm due to the large optical cross
section for intracenter donor transitions (?1014cm2).
Therefore, the gain volume of the I laser is much smaller
than the Si:Sb crystal. In contrast, the Brillouin-type emis-
sion uses the entire volume due to the smaller cross section
at frequencies out of resonance with donor transitions. The
g-TA phonon dispersion is determined mainly by
momentum-space localization of the 1s?E? state, which is
much larger that the free-spectral range of the Si:Sb laser
(?0:04–0:09 cm?1). Hence, the Brillouin-type gain al-
ways overlaps with a number of eigenmodes of the Si:Sb
laser resonator. One can estimate the gain of the Brillouin-
type laser using the method described in Ref.  and
scaling the magnitude of the scattering susceptibility
from the infrared to the terahertz frequency range. Tak-
ing the measured Brillouin linewidth of 0.2 meV at
and the Brillouin-type (B laser) mechanisms in Si:Sb. The two
parts of the graph represent two opposite equivalent valleys of
the silicon conduction band. Gray bold arrows are for stimulated
emission; hollow up arrows indicate optical pump transitions.
Diagonal arrows indicate intervalley phonons. Curved arrows are
for cascade relaxation of electrons due to intravalley acoustic
phonon-assisted transitions. Donor states are labeled as in
Ref. ; 1sEL?E? and 1sPH?E? represent the electronic (black
thin line) and phonon-related (graded gray rectangle) contribu-
tions, respectively, in the mixed 1s?E? donor state [separation of
the 1sEL?E? and 1sPH?E? states is not to scale].
Schematic energy diagram of the intracenter (I laser)
PRL 96, 037404 (2006)
27 JANUARY 2006
!S? 3:32 ? 1013sec?1, one calculates a gain per unit Download full-text
pump intensity of ?S? 1:7 ? 10?3cmMW?1at a lattice
temperature of 77 K. Another way to estimate the gain is
from the exponential intensity increase at the very start of
the B emission. For a pump energy of @!P? 33:45 meV,
this yields 7:4 ? 10?3cmMW?1, somewhat larger than
the previous value. The difference might be caused by an
enhanced scattering of pump photons due to the resonance
of the g-TA phonon with the interstate energy gap 1s?E? ?
1s?A1?, also known as resonant Brillouin scattering .
Simultaneous intracenter and Brillouin-type emission
(I ? B) appears for excitation into the 2p0 state, the
2s?E? state, and the 2p?state. In these cases, scattering
of pump photons is enhanced by both incoming
[!P: 1s?A1? ! ex:st:] and outgoing [!P: ex:st: ! 1s?E?]
resonance with impurity states. Excitation into higher
states yields only I emission. In the case of resonant
pumping into the 2p0state, I- as well as B-laser emission
have the lowest pump threshold (Fig. 1), with B emission
much stronger than I emission and without any delay
(Fig. 4). Pumping into donor states higher than 2p0in-
volves intracenter relaxation of electrons into the 2p0state
and, thus, is less efficient. In this case, B emission appears
always with a significant delay after I emission. The time
delay of B lasing with respect to I lasing is caused by the
comparatively low gain of the Brillouin-type process. I
lasing is dominating due to its larger optical cross section
[??1–7? ? 10?15cm2], which results in a gain of
?1 cm?1at moderate pump intensities. The power of
Brillouin-type emission decreases with increasing pump
photon energy, where the intracenter transitions contribute
more (or solely) to the laser emission. This is apparently
due to high density of the impurity states above 3p0and the
dominating role of intracenter relaxation over scattering
In summary, we have shown that Brillouin-type stimu-
lated Stokes emission based on resonant scattering by
intervalley transverse acoustic g phonons is realized in
silicon doped by antimony donors.The emission frequency
can be varied over a wide range between 4.6 and 5.8 THz
by changing the pump laser frequency. The low gain of this
laser mechanism, ?10?3cm?1at a pump intensity of
100 kWcm?2, results in a few microsecond delay for the
buildup of the laser signal. The multivalley structure of
excited donor states in silicon allows for the compensation
of the large phonon momentum needed for the laser emis-
sion within a single Coulomb center.
This work was supported by the Deutsche Forschungs-
gemeinschaft and the Russian Foundation for Basic
Research (05-02-16734). We gratefully acknowledge the
supportbythe Stichting voorFundamenteel Onderzoek der
Materie (FOM) and the FELIX staff.
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Si:Sb emission signal (a.u.)
the corresponding pump Sb states. The flat top of the emission
pulse when pumped in the 2p0impurity state is due to saturation
of the Ge:Ga detector. The FEL macropulse (gray) is recorded
using a fast infrared photodetector.
Typical silicon laser emission pulses (black lines) with
PRL 96, 037404 (2006)
27 JANUARY 2006