Stimulated emission of Cr²⁺ ions in ZnS:Cr thin-film electroluminescent structures
First observation of stimulated Cr²⁺ emission in ZnS:Cr electroluminescent (EL) impact-excited thin-film waveguide structures is reported. The structures consist of the following thin films deposited on a glass substrate: a transparent In₂O₃:Sn electrode, an insulator SiO₂/Al₂O₃ layer (~270 nm),...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2009
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| Zitieren: | Stimulated emission of Cr²⁺ ions in ZnS:Cr thin-film electroluminescent structures / N.A. Vlasenko, P.F. Oleksenko, M.A. Mukhlyo, L.I. Veligura, and Z.L. Denisova // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2009. — Т. 12, № 4. — С. 362-365. — Бібліогр.: 9 назв. — англ. |
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irk-123456789-1188372017-06-01T03:06:10Z Stimulated emission of Cr²⁺ ions in ZnS:Cr thin-film electroluminescent structures Vlasenko, N.A. Oleksenko, P.F. Mukhlyo, M.A. Veligura, L.I. Denisova, Z.L. First observation of stimulated Cr²⁺ emission in ZnS:Cr electroluminescent (EL) impact-excited thin-film waveguide structures is reported. The structures consist of the following thin films deposited on a glass substrate: a transparent In₂O₃:Sn electrode, an insulator SiO₂/Al₂O₃ layer (~270 nm), an EL ZnS:Cr film (~600 nm), the same insulator layer, and an Al electrode. The stimulated character of the emission recorded through the edge of the structure is evidenced by the following. With increasing the applied voltage, a broad band with three waveguide mode maxima in the edge emission spectrum changes into an intensifying and narrowing band. The maximum of this band is the same as that of the Cr²⁺ emission band recorded through the face, i.e. through the In₂O₃:Sn electrode (1.75 and ~2.6 µm at the Cr concentrations (5-7)*10¹⁹ and (2- 3)*10²⁰ cm⁻³, respectively). The five-fold narrowing is observed when increasing the voltage by ~4% in the case of the lower Cr concentration. The voltage and frequency dependences of the edge emission are stronger than those for the face emission. A small manifestation of the gain occurrence in the ZnS:Cr TFELS is also observed in the face emission. The possibility to create a new type of electrically pumped lasers with the impact excitation mechanism is discussed. 2009 Article Stimulated emission of Cr²⁺ ions in ZnS:Cr thin-film electroluminescent structures / N.A. Vlasenko, P.F. Oleksenko, M.A. Mukhlyo, L.I. Veligura, and Z.L. Denisova // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2009. — Т. 12, № 4. — С. 362-365. — Бібліогр.: 9 назв. — англ. 1560-8034 PACS 78.45.+h, 78.60.Fi http://dspace.nbuv.gov.ua/handle/123456789/118837 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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First observation of stimulated Cr²⁺ emission in ZnS:Cr electroluminescent
(EL) impact-excited thin-film waveguide structures is reported. The structures consist of
the following thin films deposited on a glass substrate: a transparent In₂O₃:Sn electrode,
an insulator SiO₂/Al₂O₃ layer (~270 nm), an EL ZnS:Cr film (~600 nm), the same
insulator layer, and an Al electrode. The stimulated character of the emission recorded
through the edge of the structure is evidenced by the following. With increasing the
applied voltage, a broad band with three waveguide mode maxima in the edge emission
spectrum changes into an intensifying and narrowing band. The maximum of this band is
the same as that of the Cr²⁺ emission band recorded through the face, i.e. through the
In₂O₃:Sn electrode (1.75 and ~2.6 µm at the Cr concentrations (5-7)*10¹⁹ and (2-
3)*10²⁰ cm⁻³, respectively). The five-fold narrowing is observed when increasing the
voltage by ~4% in the case of the lower Cr concentration. The voltage and frequency
dependences of the edge emission are stronger than those for the face emission. A small
manifestation of the gain occurrence in the ZnS:Cr TFELS is also observed in the face
emission. The possibility to create a new type of electrically pumped lasers with the
impact excitation mechanism is discussed. |
| format |
Article |
| author |
Vlasenko, N.A. Oleksenko, P.F. Mukhlyo, M.A. Veligura, L.I. Denisova, Z.L. |
| spellingShingle |
Vlasenko, N.A. Oleksenko, P.F. Mukhlyo, M.A. Veligura, L.I. Denisova, Z.L. Stimulated emission of Cr²⁺ ions in ZnS:Cr thin-film electroluminescent structures Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Vlasenko, N.A. Oleksenko, P.F. Mukhlyo, M.A. Veligura, L.I. Denisova, Z.L. |
| author_sort |
Vlasenko, N.A. |
| title |
Stimulated emission of Cr²⁺ ions in ZnS:Cr thin-film electroluminescent structures |
| title_short |
Stimulated emission of Cr²⁺ ions in ZnS:Cr thin-film electroluminescent structures |
| title_full |
Stimulated emission of Cr²⁺ ions in ZnS:Cr thin-film electroluminescent structures |
| title_fullStr |
Stimulated emission of Cr²⁺ ions in ZnS:Cr thin-film electroluminescent structures |
| title_full_unstemmed |
Stimulated emission of Cr²⁺ ions in ZnS:Cr thin-film electroluminescent structures |
| title_sort |
stimulated emission of cr²⁺ ions in zns:cr thin-film electroluminescent structures |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/118837 |
| citation_txt |
Stimulated emission of Cr²⁺ ions in ZnS:Cr thin-film electroluminescent structures / N.A. Vlasenko, P.F. Oleksenko, M.A. Mukhlyo, L.I. Veligura, and Z.L. Denisova // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2009. — Т. 12, № 4. — С. 362-365. — Бібліогр.: 9 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
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| first_indexed |
2025-07-08T14:45:26Z |
| last_indexed |
2025-07-08T14:45:26Z |
| _version_ |
1837090400929579008 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 4. P. 362-365.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
362
PACS 78.45.+h, 78.60.Fi
Stimulated emission of Cr2+ ions in ZnS:Cr thin-film
electroluminescent structures
N.A. Vlasenko, P.F. Oleksenko, M.A. Mukhlyo, L.I. Veligura, and Z.L. Denisova
V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine
45, prospect Nauky, 03028 Kyiv, Ukraine
Abstract. First observation of stimulated Cr2+ emission in ZnS:Cr electroluminescent
(EL) impact-excited thin-film waveguide structures is reported. The structures consist of
the following thin films deposited on a glass substrate: a transparent In2O3:Sn electrode,
an insulator SiO2/Al2O3 layer (~270 nm), an EL ZnS:Cr film (~600 nm), the same
insulator layer, and an Al electrode. The stimulated character of the emission recorded
through the edge of the structure is evidenced by the following. With increasing the
applied voltage, a broad band with three waveguide mode maxima in the edge emission
spectrum changes into an intensifying and narrowing band. The maximum of this band is
the same as that of the Cr2+ emission band recorded through the face, i.e. through the
In2O3:Sn electrode (1.75 and ~2.6 µm at the Cr concentrations (5-7)1019 and (2-
3)1020 cm-3, respectively). The five-fold narrowing is observed when increasing the
voltage by ~4% in the case of the lower Cr concentration. The voltage and frequency
dependences of the edge emission are stronger than those for the face emission. A small
manifestation of the gain occurrence in the ZnS:Cr TFELS is also observed in the face
emission. The possibility to create a new type of electrically pumped lasers with the
impact excitation mechanism is discussed.
Keywords: stimulated emission, ZnS:Cr, impact electroluminescence, thin-film, optical
waveguide.
Manuscript received 24.06.09; accepted for publication 10.09.09; published online 30.10.09.
1. Introduction
There are two main mechanisms of the excitation of
electroluminescence (EL) in solids: 1) injection of
minority charged carriers and recombination with
majority ones; 2) impact excitation of luminescent
centers by hot electrons accelerated in a high electric
field ( 1 MV/cm). The former was realized in a wide
variety of light emitting diodes and semiconductor
lasers. However, the employment of this mechanism is
very complicated in the case of wide-gap
semiconductors and materials doped with transition
metals (TM) or rare earths (RE). First, it is difficult to
form a p-n junction. Second, some indirect process is
necessary to excite TM and RE ions with intraion
radiative transitions. This process includes the resonant
transfer of the excitation energy from some
recombination centres to TM and RE ions. At the same
time, intensive EL with the impact excitation mechanism
occurs in wide-gap semiconductors (ZnS, ZnSe, SrS,
etc.) doped with TM or RE [1]. In spite of this fact, there
is no any solid-state laser with the impact mechanism of
the EL excitation. Moreover, reliable publications on the
stimulated emission in the case of this EL mechanism
are absent. The reason of this is the difficulty to obtain a
sufficiently high electric field in bulk materials because
of the avalanche breakdown. That is why intensive
impact EL is only observed in thin-film structures of a
MISIM type (here M denotes an electrode, S is an EL
film, and I is an insulator layer) [1]. I layers in such thin-
film electroluminescent structures (TFELS) serve as a
ballast capacitance resistor preventing from the
breakdown. However, attainable optical gain is low in
TFELS for the onset of the marked stimulated emission
even at a high excitation level, if light is emitted from
the structure face, i.e. through a transparent In2O3:Sn
(ITO) electrode. This is related with a very small
thickness of EL film ( 1 m).
The possibility to obtain the high gain, when light
is laterally transferred in the EL film and emitted from
the structure edge, has been theoretically considered in
[2]. It is known [1] that TFELS with I layers that has the
refractive index lower than that of the EL film represent
a planar optical waveguide. Therefore, the main part of
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 4. P. 362-365.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
363
emission in such TFELS is transferred along the EL film
due to the total internal reflection on the S-I interfaces
and extracted through the edge. Edge TFEL structures
have been extensively investigated and developed in
1980-1990 for the creation of visible-light emitters with
very high luminance [1, 3]. However, stimulated
emission in such TFELS was not observed because of
the use non-laser EL materials (e.g., ZnS:Mn) as well as
of the high optical losses resulting from the scattering of
light on grain boundaries in EL polycrystalline films and
from the absorption of light by various lattice defects.
One can expect that these losses should be significantly
diminished in the near-infrared (NIR) and mean-infrared
(MIR) regions. The scattering decreases as n when the
wavelength () increases (n = 1 – 4 depending on the
size of scattering particles). The absorption by lattice
defects also decreases at > 1 m significantly. This has
been shown by studying the photodepolarization spectra
of TFELS [4,5].
The recent study [6] of ZnS:Er TFELS, which emit
in both the visible and NIR regions, has shown some
essential differences in characteristics of the emission
recorded through the face and the edge (hereafter the
former and the latter will be called “the face emission”
and “the edge emission”). The intensity of the NIR
bands in the EL spectrum (max = 0.985 and 1.535 m) is
higher relatively to the intensity of the green band
(max = 0.535 m) in the edge emission than in the face
emission. This confirms that optical losses in the NIR
region are lower in comparison with those in the visible
region. In addition, the main 1.535 m band, which
results from the I13/2 I15/2 transition in Er3+ ion,
narrows with increasing applied voltage (V) in the edge
emission, but its halfwidth in the face emission does not
change. This observation has been explained as a
manifestation of the occurrence of an optical
amplification of the emission propagating in the
waveguide. Observed narrowing of the 1.535 m band is
small (~1.7 times). Therefore, the gain is rather low in
the edge ZnS:Er TFELS studied. It is necessary to
enhance the gain for the irrefutable confirmation of the
possibility to obtain the stimulated emission in TFELS
with the impact excitation mechanism. There are two
ways for the gain enhancement. The first consists in
increasing the excitation level and decreasing the optical
losses in the edge ZnS:Er TFELS. The second more
feasible way is the use of laser materials with a lower
pumping threshold for EL films. Recently a low-
threshold optically pumped lasers have been created
using ZnS:Cr and ZnSe:Cr crystals [7, 8]. Attempts to
create lasers with electrical pumping in these crystals
were not successful, whereas the spontaneous NIR EL
emitted through the ITO electrode has been obtained [5].
In the present paper, we report on the first results of
studying edge ZnS:Cr TFELS. Characteristics of the
Cr2+ emission recorded from the edge and face of these
structures are compared. In the edge emission, some
peculiarities specific only to the stimulated emission
have been observed for the first time. The possibility to
create a new type of electrically pumped lasers has been
discussed.
2. Experimental details
The schematical view of the TFELS under study is
shown in Fig. 1. The waveguide TFELS of the MISIM
type consists of a glass substrate, ITO and Al electrodes,
SiO2/Al2O3 I layers and a ZnS:Cr film. The Al electrode
was in the form of a strip. The edge was made by cutting
the TFELS normally to the electrode strip. The
waveguide was 4 - 6 mm long, 1 - 2 mm wide and
0.6 - 0.65 m thick. The I layers and ZnS film were
deposited by electron-beam evaporation. Doping with Cr
of the ZnS film was performed by thermal co-
evaporation of chromium. The samples with the Cr
concentration (CCr) of (5-7)1019 and (2-3)1020 cm-3
were studied. EL was excited by sinusoidal voltage of 5-
20 kHz frequency ( f ). The emission spectrum of Cr2+
ions was measured by a MDR-12 monochromator with a
cooled PbS photoresistor.
3. Results and discussion
The EL spectrum of the ZnS:Cr TFELS with CCr of (5-
7)1019 cm-3 at increasing voltage of 20 kHz is shown in
Fig. 2 when the emission was recorded from the face and
edge. The photoluminescence (PL) spectrum of ZnS:Cr
crystals is also shown [7]. It is seen that the Cr2+
emission in the crystals and films occurs within the same
spectral region, but has some different spectral
distribution. The emission of the ZnS:Cr TFELS consists
of two bands. The maximum of the main band (at
1.75 m) is not far from the maximum of the PL
spectrum. The second band is located in the longwave
tail of the EL spectrum. This band becomes dominant
when the Cr concentration in the films increases (Fig. 3)
as well as when the ZnS:Cr crystals have some degree of
hexagonality [8]. Therefore, the longwave band of
ZnS:Cr is attributed to the emission of Cr2+ ions in a
low-symmetry crystal field [8, 9].
Fig. 1. Schematical view of waveguide ZnS:Cr TFELS.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 4. P. 362-365.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
364
Fig. 2. EL spectrum of face (a) and edge (b) Cr2+ emissions at
various voltages, V: 1 – 150, 2 – 151, 3 – 154, 4 – 157. f =
20 kHz. CCr = (5-7)1019 cm-3. Curve 5 in (a) is PL spectrum
of ZnS:Cr crystals [1].
2.4 2.6 2.8
96
98
100
1.8 2.0 2.2 2.4 2.6 2.8 3.0
0.0
0.2
0.4
0.6
0.8
1.0
I,
a
rb
.u
n
.
, m
1
2
, m
T
ra
ns
m
is
si
on
, %
Fig. 3. EL spectrum of face (1) and edge (2) emission for
ZnS:Cr TFELS with CCr of (2-3)1020 cm-3. V = 180 V. Curve
in insertion shows transmission of atmosphere on the length
between the sample and photodetector.
The EL spectrum of the face emission somewhat
changes with increasing V. The main band slightly
narrows and the relative intensity of the second band
first increases, but then decreases. On the contrary, the
behavior of the edge emission spectrum is essentially
different. At the threshold voltage of EL, there are three
maxima in the spectrum; the main maximum is not far
from that of the Cr2+ emission. These maxima are due to
the waveguide modes propagating at different angles (all
of them were condensed by a lens during measurements
of the spectrum). Spectral redistribution of this emission
takes place with increasing V. The waveguide-mode
maxima first decrease and then disappear. The most
intensive emission appears in the region that coincides
with the central part of the main Cr2+ emission band. The
emission in this region intensifies stronger than in other
regions of the spectrum with further increasing voltage.
In addition, the significant narrowing of the main Cr2+
emission band occurs. The voltage dependences of the
main band halfwidth for the face and edge emissions at
f = 20 kHz are compared in Fig. 4a. The halfwidth for
the former decreases only by ~20% when the voltage
increases by 6 V (i.e. by ~4%), whereas the halfwidth of
the edge emission decreases more than by a factor of
five. The halfwidth of the narrowest band obtained is
larger than the oscillation line width of the ZnS:Cr laser
only less than two-fold (80 and 50 nm, respectively).
The significant narrowing of the Cr2+ band in the edge
emission is also observed in the case of the higher Cr
concentration (Fig. 3). The most significant narrowing
takes place within the steep section of the voltage
dependence for the emission intensity (I) that is shown
in Fig. 4b. The narrowing of the band decreases on the
saturation section of the I(V) dependence. The saturation
is typical for TFELS of the MISIM type [1] and is due to
the voltage redistribution between the I layers and the
EL film, when the Ohmic resistance (R) of the latter
decreases and becomes commensurable with the
capacitive resistance of the I layers (the capacitive
resistance of the EL film and the I layers is almost the
same). The decrease of R is related with a significant
increase of the active current caused by the avalanche
multiplication of electrons.
It is seen from Fig. 4b that the voltage dependence
of the edge emission intensity is steeper than that of the
face emission. This is one essential peculiarity of the
edge emission more. The frequency dependence of the
intensity of the edge emission at a fixed voltage is also
steeper as compared with the I ( f ) dependence for the
face emission (Fig. 5). It should be noted that the
sublinear character of the I ( f ) dependence and a
decrease of I at f > 15 kHz are caused by growth of the
voltage drop at the transparent ITO electrode with
increasing the capacitive current passing through
TFELS. The resistance of the ITO electrode was rather
high (~300 Ohm/□) to diminish the optical absorption of
the Cr2+ emission by free electrons. The main band
halfwidth of the edge emission at a fixed voltage
diminishes when f becomes higher (Fig. 5), while the
face emission band does not change markedly.
As follows from the above results, there is an optical
amplification of the Cr2+ emission in the edge ZnS:Cr
TFELS. The gain is sufficiently high to generate a rather
intensive stimulated emission in these TFELS. The optical
amplification affects also the Cr2+ face emission, but
significantly more weakly because the passage length of
this emission is three orders of magnitude lower than that
of the edge emission. Some narrowing of the Cr2+ band in
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 4. P. 362-365.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
365
the face emission spectrum (Fig. 2) is a manifestation of
the amplification effect. In addition the influence of the
gain on the face emission is supported by the
nonmonotonic change of the intensity of the longwave
band relative to the main band intensity with increasing
the voltage. An initial increase of the relative intensity
results from the lower lifetime () of excited low-
symmetrical Cr2+ ions than of the high-symmetrical ones
[8]. The further relative decrease of the intensity of the
longwave band stems from a competitive effect of the
gain increase for the main band.
Fig. 4. Voltage dependence of: (a) Cr2+ band halfwidth for the
face (1) and edge (2) emissions; (b) maximum intensity of the
face (1) and edge (2) Cr2+ emissions. f = 20 kHz. CCr = (5-
7)1019 cm-3.
Fig. 5. Frequency dependence of the intensity for the face (1)
and edge (2) Cr2+ emissions as well as of the Cr2+ band
halfwidth for the edge emission (3). V = 156 V. CCr = (5-
7)1019 cm-3.
4. Conclusion
Thus, for the first time the stimulated emission is
obtained in ZnS:Cr at the electrical impact excitation. To
our knowledge, this is the first observation of the
impact-excited stimulated emission in solid states apart
of our observation of the rather insignificant effects of
the stimulated emission in the edge ZnS:Er TFELS [6].
The obtained results show the possibility of the creation
of new electrically pumped compact inexpensive lasers
based on edge TFELS doped with TM and RE, which
are especially actual for the NIR and MIR regions. One
can expect that the intensity and efficiency of these
lasers will be lower than those of injection lasers and
optically pumped ones due to thin active layers and low
efficiency of the impact excitation mechanism.
However, this will not prevent from a wide variety of
applications of new lasers, e.g. in medicine and spectral
chemical sensoring. Optimization of the waveguide
properties of the TFELS and using distributed feedback
optical coupling are needed to realize such lasers. It is
also expected that making the ZnS:Cr TFELS with the
Fabry-Perot cavity will result in the intensive stimulated
face Cr2+ emission, possibly, even in lasing.
References
1. Y.O. Ono, Electroluminescent Displays. World
Scientific, Singapore, 1995.
2. N.A. Vlasenko, S.I. Pekar and V.S. Pekar // Sov.
Phys. –JETP 37, p. 190 (1973).
3. M.R. Craven, W.M. Cranton R. Stevens,
C.B. Thomas // The Fourth Intern. Conf. on Sci.
and Techn. of Display Phosphors. Sept. 14-17,
Bend, Oregon, 1998, p. 279.
4. N.A. Vlasenko, L.I. Veligura, Z.L. Denisova,
M.A. Mukhlyo, Yu.A. Tsyrkunov, V.F. Zinchenko
// J. SID 14(7), p. 615 (2006).
5. L.I. Veligura, N.A. Vlasenko, Z.L. Denisova,
V.Yu. Goroneskul, Ya.F. Kononets, Yu.A. Tsyr-
kunov // Optoelektronika i Poluprovodnikovaya
Tekhnika 39, p. 124 (2004) (in Russion).
6. N.A. Vlasenko, P.F. Oleksenko, L.I. Veligura,
M.O. Mukhlyo, Z.L. Denisova, V. F. Zinchenko //
J. SID 15(11), p. 937 (2007).
7. S.B. Mirov, V.V. Fedorov, K. Graham,
I.S. Moskalev V.V. Badikov, V. Panyutin // Opt.
Lett. 27, p. 909 (2002).
8. I.T. Sorokina, E. Sorokin, S. Mirov, V. Fedorov,
V. Badikov, V. Panyutin, K.I. Shaffers // Opt. Lett.
27, p. 1040 (2002).
9. N.A. Vlasenko, P.F. Oleksenko, Z.L. Denisova,
M.O. Mukhlyo, L.I. Veligura // Phys. status solidi
(b) 245, p. 2550 (2008).
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