The two-dimensional electron-hole liquid (EHL) in 2- and 4-nm-thick SiGe layers of Si/Si0.91Ge0.09/Si heterostructures is discovered and its properties are studied by photoluminescence (PL) spectroscopy in the near-infrared and visible spectral ranges at low temperatures. It is shown that the PL in the visible range observed at high excitation levels originates from two-electron recombination transitions in the EHL. For the SiGe layer thickness d = 2 nm, the barrier formed by this layer for electrons in the conduction band is tunnel-transparent, and the EHL is spatially direct. For d = 4 nm, this barrier is nontransparent, and the EHL has dipolar character, with holes being confined in the SiGe layer and electrons occupying Si layers. It is found that the binding energy and the critical temperature of the dipolar EHL is substantially less than the spatially direct. The binding energy of free biexcitons in the tunnel-transparent SiGe layer is determined

Burbaev, T.M.

Kozyrev, D.S.

Sibeldin, N.N.

Skorikov, M.L.

SocioEconomic Challenges Journal (Sumy State University)

PROCEEDINGS OF THE INTERNATIONAL CONFERENCE  
NANOMATERIALS: APPLICATIONS AND PROPERTIES 
Vol. 3 No 1, 01NTF01(3pp) (2014) 
 
 
2304-1862/2014/3(1)01NTF01(3) 01NTF01-1  2014 Sumy State University 
Two-dimensional Electron-hole Liquid in Systems of Spatially Direct and Indirect Excitons 
in Si / SiGe Heterostructures 
 
T.M. Burbaev *, D.S. Kozyrev, N.N. Sibeldin, M.L. Skorikov 
 
Lebedev Physical Institute of the Russian Academy of Sciences, 53, Leninskii Pr., 119991 Moscow, Russia 
 
(Received 11 March 2014; published online 29 August 2014) 
 
The two-dimensional electron-hole liquid (EHL) in 2- and 4-nm-thick SiGe layers of Si/Si0.91Ge0.09/Si 
heterostructures is discovered and its properties are studied by photoluminescence (PL) spectroscopy in 
the near-infrared and visible spectral ranges at low temperatures. It is shown that the PL in the visible 
range observed at high excitation levels originates from two-electron recombination transitions in the 
EHL. For the SiGe layer thickness d  2 nm, the barrier formed by this layer for electrons in the conduc-
tion band is tunnel-transparent, and the EHL is spatially direct. For d  4 nm, this barrier is nontranspar-
ent, and the EHL has dipolar character, with holes being confined in the SiGe layer and electrons occupy-
ing Si layers. It is found that the binding energy and the critical temperature of the dipolar EHL is sub-
stantially less than the spatially direct. 
The binding energy of free biexcitons in the tunnel-transparent SiGe layer is determined. 
 
Keywords: Electron-hole liquid, Biexciton, Quasi-two-dimensional layers, Heterostructures, Photolumine-
scence. 
 
 PACS numbers: 73.20.Mf, 78.67.De 
 
 
                                                          
* burbaev@sci.lebedev.ru 
1. INTRODUCTION 
 
It is well known that, at low temperatures, the 
ground state of a nonequilibrium electron-hole system 
with sufficiently high density in bulk silicon and ger-
manium corresponds to metallic electron-hole liquid 
(EHL), into which excitons condense [1-5]. In bulk ma-
terials, the spatial distribution of nonequilibrium elec-
trons and holes coincide. In contrast, in type-II  
Si / Si1 – xGex / Si heterostructures, systems where elec-
trons and holes are spatially separated can be pre-
pared. In these structures, a strained Si1 – xGex layer 
clad between thick Si layers forms a deep potential well 
for holes in the valence band and a relatively low barri-
er for electrons in the conduction band. Electrons, 
which are attracted to quantum-confined holes, can 
also penetrate into the barrier. Varying the thickness d 
of the SiGe layer, one can obtain systems with either 
spatially direct excitons (for small d) or spatially indi-
rect (dipolar) excitons (Fig. 1). Here, we investigated 
multiparticle excitations in such systems using the 
spectroscopy of photoluminescence (PL) in the near-
infrared (NIR) and visible spectral ranges. 
 
2. EXPERIMENTAL 
 
Strained-layer SiGe structures were grown by mo-
lecular-beam epitaxy on Si (001) substrates. Thickness-
es of the buffer and the cap Si layers were 100 nm and 
100-200 nm, respectively. The PL spectra in the NIR 
spectral range were recorded for the sample tempera-
tures Т = 260 K and excitation levels P  0.05-
300 W/cm2. A He-Cd laser was used as the PL excita-
tion source and the recombination radiation was ana-
lyzed by a grating monochromator and detected by a 
liquid-nitrogen-cooled Ge pin photodiode. 
 
 
 
Fig. 1 – Schematic band diagrams of Si/Si1 – xGex/Si 
heterostructures with the SiGe layer thickness d   4 (а) and 
(b) 2 nm. Dashed lines show the electron-density distribution 
along the growth axis and the heavy-hole quantum-
confinement level for each structure 
 
Also, spectra of the PL in the visible range were rec-
orded. This PL results from the so-called two-electron 
transitions, i.e., from simultaneous recombination of two 
electrons and two holes accompanied by the emission of 
a single photon whose energy equals the total energy of 
the four recombining particles [6, 7]. These measure-
ments were carried out for T  15 K and P  0.3-
150 W/cm2. A Ti-sapphire laser tuned to   0.75 m was 
used as the PL excitation source. The recombination 
radiation was analyzed by a grating spectrometer and 
detected by a liquid-nitrogen-cooled CCD matrix. A com-
parison of one- and two-electron spectra makes for more 
reliable identification of different components in the con-
ventional (one-electron) PL spectra, since lines in the 
two-electron spectra cannot originate from species con-
taining less than two electron-hole pairs. 
 
 T.M. BURBAEV, D.S. KOZYREV, ET AL. PROC. NAP 3, 01NTF01 (2014) 
 
 
01NTF01-2 
3. RESULTS AND DISCUSSION 
 
Figure 2 presents the NIR PL spectra for two struc-
tures in which the Si1 – xGex layer has the same composi-
tion (x  0.09) but different thicknesses d  4 nm (sample 
#4, Fig. 2a) and 2 nm (sample #2, Fig. 2b). The figure 
shows the most intense components of the PL, resulting 
from the simultaneous emission of a photon and a TO 
phonon. At low excitation levels (Fig. 2a, curves 1-5; 
Fig. 2b, curves 1-4), the exciton PL lines are observed in 
the short-wavelength part of the spectrum. Excitons are 
free at high temperatures. In structure #4, dipolar exci-
tons are free for T ≥ 23 K; in structure #2, spatially di-
rect excitons are free for T ≥ 12 K. With decreasing tem-
perature, excitons become localized in the wells of the 
random lateral potential originating from the composi-
tional inhomogeneity in the SiGe layer plane and at het-
erointerfaces; the exciton localization is accompanied by 
a red shift of the corresponding PL lines, as indicated in 
Fig. 2a. In addition, a decrease in the temperature 
brings about the appearance of the biexciton PL lines on 
the red side of the exciton lines. Thus, the PL of localized 
dipolar biexcitons is observed in structure #4, while the 
PL of free spatially direct biexcitons is observed in struc-
ture #2 for T ≥ 12 K. The dependence of the biexciton PL 
intensity on the excitation level is linear in the first case 
and close to quadratic in the second case. At high excita-
tion levels and low temperatures, the spectra are domi-
nated by the emission from the EHL, which is spatially 
direct in structure #2 (Fig. 2b, curve 5) and indirect in 
structure #4 (Fig. 2a, curves 6, 7). 
It is known that independence of the PL line shape 
from the excitation level is a signature of the EHL lumi-
nescence. According to Fig. 2a, the normalized shapes of 
the PL spectra of sample #4 recorded at T  1.8 K for two 
pump powers differing by a factor of 2 (curves 6, 7) coin-
cide. The shape and position of the PL lines recorded for 
the same pump level in the temperature range of 1.8-6 K 
also coincide with those of curves 6 and 7. The dipolar 
EHL in structure #4 is composed by heavy holes in the 
quantum well formed in the valence band by the SiGe 
layer and electrons from Δ4 valleys of the conduction 
band of Si, which are bound to the holes by Coulomb 
attraction and occupy triangular potential wells formed 
at Si / SiGe heterointerfaces owing to the band bending 
at high excitation levels. In this case, the calculated lu-
minescence line is described by two-dimensional density 
of states both for heavy holes and Δ4 electrons (Fig. 2a, 
dashed line). The calculated profile of the luminescence 
line of spatially direct EHL in structure #2 is shown in 
Fig. 2b (curve 5, solid line) [1]. The difference between 
the EHL luminescence line shape in structures #2 and 
#4 originates from the difference in the energy depend-
ences of the electron density of states  (  Е1/2 for #2 
and   const for #4). In addition, the ratio Fe / Fh of the 
electron and hole Fermi energies, which affects the 
shape of the EHL luminescence line, is different in the 
two cases. Comparing the energy separation between the 
EHL and FE lines in Figs. 2a and 2b, one can see that 
the binding energy in the dipolar EHL is considerably 
lower than in the spatially direct EHL. 
The variation of the PL spectra of structures #4 and 
#2 in the visible range with increasing excitation level 
is shown in Fig. 3. The visible-range PL originates from 
simultaneous recombination of two holes in the valence 
 
 
Fig. 2 – Modification of the NIR PL spectra of structures (a) #4 
and (b) #2 with decreasing temperature T and increasing 
pump power P. 
(a) Curves 1-5: T varies between 26 and 6 K, P  0.12 W/cm2. 
Curves 6 and 7 (shown overlapping by circles and solid line, 
respectively): T  1.8 K, P  85 and 170 W/cm2, respectively; 
dashed line shows the calculated spectrum of the dipolar EHL 
luminescence. 
(b): Curves 1-4: T varies between 21 and 12 K, P  2 W/cm2. Curve 
5 (circles): T  1.8 K, P  4 W/cm2; solid line shows the calculated 
spectrum of the spatially direct EHL luminescence [8]. 
FE, FBiE, LBiE, and EHL stand for free excitons, free biexci-
tons, localized biexcitons, and electron-hole liquid, respective-
ly. Normalized spectral curves are shown in all cases 
 
band in the SiGe layer and two electrons from the oppo-
site valleys in the conduction band. Thus, the PL result-
ing from these so-called two-electron transitions occurs 
at photon energies approximately a factor of 2 higher 
than the energies of no-phonon (NP) single-electron 
transitions in the NIR range. Narrow lines in Fig. 3 cor-
respond to the biexciton luminescence, and wide lines, to 
the EHL luminescence. At low excitation levels, biexci-
tons in structure #4 are observed in the temperature 
range of 1.8-23 K. As the temperature decreases to 1.8 K, 
they become localized; similarly to the NIR PL spectra, 
this is accompanied by a red shift of the biexciton PL 
line. The dipolar EHL appears at higher excitation lev-
els. The shape and position of the corresponding PL line 
become independent of the excitation level as the latter 
is raised still further and hardly depend on temperature 
for T  1.8-6 K. 
The modification of the visible-range PL spectra of 
structure #2 with increasing pump level at T  15 K is 
shown in Fig. 3b. At low excitation levels, a narrow PL 
line of free biexcitons (FWHM  4 meV) is clearly 
observed. At high excitation levels, the spectra are 
dominated by a broad (FWHM  20 meV) PL line of the 
EHL. Similarly to the NIR spectra, the shape of this 
line ultimately becomes independent of the excitation 
level (compare curves 3 and 4), which is a feature 
characteristic of the EHL luminescence. In this case, 
the EHL is spatially direct, and its binding energy and 
critical temperature are considerably higher than those 
 TWO-DIMENSIONAL ELECTRON-HOLE LIQUID… PROC. NAP 3, 01NTF01 (2014) 
 
 
01NTF01-3 
for the dipolar EHL. At 15 K, the EHL line shape is to a 
large extent determined by temperature effects. At 1.8 K 
(curve 5, circles), the lineshape is determined only by the 
behavior of (Е) and the electron and hole Fermi 
energies in the EHL. Here, the solid line shows the 
numerical convolution of the corresponding spectrum 
 
 
 
Fig. 3 – Modification of the visible-range PL spectra with 
increasing pump power. 
(a) Structure #4. T  1.8 K, P  (2) 3.8, (3) 13, (4) 108, and (5) 
180 W/cm2; curves 4 (circles) and 5 (solid line) are shown 
overlapping. Curve 1 (dashed line) shows the biexciton PL 
spectrum observed for T  23 K and P  3.5 W/cm2. 
(b) Structure #2. T  15 K, P  (1) 0.5, (2) 1.0, (3) 85, and (4) 
150 W/cm2; curves 3 (circles) and 4 (solid line) are shown 
overlapping. Curve 5 (dashed line) shows the PL spectrum 
recorded for T  1.8 K and P  260 W/cm2; the solid line shows 
the numerical convolution of the experimental spectrum 5 
(Fig. 2b). 
Normalized spectral curves are shown in all cases 
 
recorded in the NIR range (Fig. 2b, curve 5). Good 
agreement between the experimentally determined 
shape of the visible PL line and the convolution of the 
EHL luminescence line recorded in the NIR range 
indicates that the nature of the PL lines in the two 
cases is the same. Thus, we observe the single-electron 
and two-electron recombination radiation of the 
spatially direct quasi-two-dimensional EHL in the NIR 
and visible PL spectra, respectively. 
Combining data from the NIR and visible PL spec-
tra, one can determine the binding energy of free biex-
citons EM: 
 
 EM  2[hNIR(FE-NP)]  hVIS(FBiE),  
 
where hNIR and hVIS are photon energies of the NIR 
and visible PL corresponding to the excited states indi-
cated in parentheses. It is convenient to reference all 
energies to the EHL luminescence energy and to use 
intense TO-phonon components of the NIR spectrum as 
follows: 
 
EM  2[hNIR(FE-TO)  hNIR(EHL-TO)]   
 [hVIS(FBiE)  hVIS(EHL)]. 
 
Taking the required photon energies from the spectra 
in Figs. 2 and 3, we obtain EM  2.0 ± 0.5 meV. The value 
of the binding energy of quasi-two-dimensional free biex-
citons thus obtained exceeds noticeably the free-
biexciton binding energy in the three-dimensional case 
(in bulk uniaxiallystrained Si, EM ≈ 1.3-1.4 meV [9]). 
 
AKNOWLEDGEMENTS 
 
We are grateful to L.V. Keldysh and A.P. Silin for 
interest in this study and useful discussions; 
D.V. Shepel’ and V.A. Tsvetkov for help with experi-
mental work; D.N. Lobanov and A.V. Novikov for grow-
ing the Si / SiGe heterostructures. 
This study was supported by the Russian Founda-
tion for Basic Research (projects nos. 13-02-00853, 13-
02-904 67), and Programs of fundamental studies of the 
Russian Academy of Sciences. 
 
 
REFERENCES 
 
1. L.V. Keldysh, Proceedings of 9th International Conference 
on the Physics of Semiconductors, Moscow, 1968 (Lenin-
grad: Nauka: 1969). 
2. T.M. Rice, J.C. Hensel, T.G. Fillips, G.A. Thomas, Solid 
State Physics 32, (New York: Academic Press: 1977). 
3. The Electron-Hole Drops in Semiconductors, in: Modern Prob-
lems in Condensed Matter Sciences, 6, (Eds. by C.D. Jeffries, 
L.V. Keldysh), (Amsterdam: North-Holland: 1983). 
4. L.V. Keldysh, N.N. Sibeldin, Ibid, 16, (Eds. by 
W. Eisenmenger, A.A. Kaplyanskii) (1986). 
5. N.N. Sibeldin. Electron-Hole Liquid in Semiconductors, in: 
Problems of Condensed Matter Physics: Quantum Coher-
ence Phenomena in Electron-Hole and Coupled Matter-
Light System, (Eds. by A.L. Ivanov, S.G. Tikhodeev), In-
ternational Series of Monographs on Physics 139, p.227, 
(Oxford University Press: 2008). 
6. K. Betzler, R. Conradt, Phys. Rev. Lett. 28, 1562 (1972). 
7. T.W. Steiner, L.C. Lenchyshyn, M.L.W. Thewalt, 
J.P. Noel, N.L. Rowell, D.C. Houghton, Solid State Com-
mun. 89, 429 (1994). 
8. D. Shepel, T. Burbaev, N. Sibeldin, M. Skorikov, phys. 
status solidi c 8, 1186 (2011). 
9. V.D. Kulakovskii, V.G. Lysenko, V.B. Timofeev, Sov. Phys. 
Usp. 28, 735 (1985). 
 


English

Two-Dimensional Electron-Hole Liquid in Systems of Spatially Direct and Indirect Excitons in Si/SiGe Heterostructures

Electronic Sumy State University Institutional Repository

PROCEEDINGS OF THE INTERNATIONAL CONFERENCE  NANOMATERIALS: APPLICATIONS AND PROPERTIES Vol. 3 No 1, 01NTF01(3pp) (2014)   2304-1862/2014/3(1)01NTF01(3) 01NTF01-1  2014 Sumy State University Two-dimensional Electron-hole Liquid in Systems of Spatially Direct and Indirect Excitons in Si / SiGe Heterostructures  T.M. Burbaev *, D.S. Kozyrev, N.N. Sibeldin, M.L. Skorikov  Lebedev Physical Institute of the Russian Academy of Sciences, 53, Leninskii Pr., 119991 Moscow, Russia  (Received 11 March 2014; published online 29 August 2014)  The two-dimensional electron-hole liquid (EHL) in 2- and 4-nm-thick SiGe layers of Si/Si0.91Ge0.09/Si heterostructures is discovered and its properties are studied by photoluminescence (PL) spectroscopy in the near-infrared and visible spectral ranges at low temperatures. It is shown that the PL in the visible range observed at high excitation levels originates from two-electron recombination transitions in the EHL. For the SiGe layer thickness d  2 nm, the barrier formed by this layer for electrons in the conduc-tion band is tunnel-transparent, and the EHL is spatially direct. For d  4 nm, this barrier is nontranspar-ent, and the EHL has dipolar character, with holes being confined in the SiGe layer and electrons occupy-ing Si layers. It is found that the binding energy and the critical temperature of the dipolar EHL is sub-stantially less than the spatially direct. The binding energy of free biexcitons in the tunnel-transparent SiGe layer is determined.  Keywords: Electron-hole liquid, Biexciton, Quasi-two-dimensional layers, Heterostructures, Photolumine-scence.   PACS numbers: 73.20.Mf, 78.67.De                                                             * burbaev@sci.lebedev.ru 1. INTRODUCTION  It is well known that, at low temperatures, the ground state of a nonequilibrium electron-hole system with sufficiently high density in bulk silicon and ger-manium corresponds to metallic electron-hole liquid (EHL), into which excitons condense [1-5]. In bulk ma-terials, the spatial distribution of nonequilibrium elec-trons and holes coincide. In contrast, in type-II  Si / Si1 – xGex / Si heterostructures, systems where elec-trons and holes are spatially separated can be pre-pared. In these structures, a strained Si1 – xGex layer clad between thick Si layers forms a deep potential well for holes in the valence band and a relatively low barri-er for electrons in the conduction band. Electrons, which are attracted to quantum-confined holes, can also penetrate into the barrier. Varying the thickness d of the SiGe layer, one can obtain systems with either spatially direct excitons (for small d) or spatially indi-rect (dipolar) excitons (Fig. 1). Here, we investigated multiparticle excitations in such systems using the spectroscopy of photoluminescence (PL) in the near-infrared (NIR) and visible spectral ranges.  2. EXPERIMENTAL  Strained-layer SiGe structures were grown by mo-lecular-beam epitaxy on Si (001) substrates. Thickness-es of the buffer and the cap Si layers were 100 nm and 100-200 nm, respectively. The PL spectra in the NIR spectral range were recorded for the sample tempera-tures Т = 260 K and excitation levels P  0.05-300 W/cm2. A He-Cd laser was used as the PL excita-tion source and the recombination radiation was ana-lyzed by a grating monochromator and detected by a liquid-nitrogen-cooled Ge pin photodiode.    Fig. 1 – Schematic band diagrams of Si/Si1 – xGex/Si heterostructures with the SiGe layer thickness d   4 (а) and (b) 2 nm. Dashed lines show the electron-density distribution along the growth axis and the heavy-hole quantum-confinement level for each structure  Also, spectra of the PL in the visible range were rec-orded. This PL results from the so-called two-electron transitions, i.e., from simultaneous recombination of two electrons and two holes accompanied by the emission of a single photon whose energy equals the total energy of the four recombining particles [6, 7]. These measure-ments were carried out for T  15 K and P  0.3-150 W/cm2. A Ti-sapphire laser tuned to   0.75 m was used as the PL excitation source. The recombination radiation was analyzed by a grating spectrometer and detected by a liquid-nitrogen-cooled CCD matrix. A com-parison of one- and two-electron spectra makes for more reliable identification of different components in the con-ventional (one-electron) PL spectra, since lines in the two-electron spectra cannot originate from species con-taining less than two electron-hole pairs.   T.M. BURBAEV, D.S. KOZYREV, ET AL. PROC. NAP 3, 01NTF01 (2014)   01NTF01-2 3. RESULTS AND DISCUSSION  Figure 2 presents the NIR PL spectra for two struc-tures in which the Si1 – xGex layer has the same composi-tion (x  0.09) but different thicknesses d  4 nm (sample #4, Fig. 2a) and 2 nm (sample #2, Fig. 2b). The figure shows the most intense components of the PL, resulting from the simultaneous emission of a photon and a TO phonon. At low excitation levels (Fig. 2a, curves 1-5; Fig. 2b, curves 1-4), the exciton PL lines are observed in the short-wavelength part of the spectrum. Excitons are free at high temperatures. In structure #4, dipolar exci-tons are free for T ≥ 23 K; in structure #2, spatially di-rect excitons are free for T ≥ 12 K. With decreasing tem-perature, excitons become localized in the wells of the random lateral potential originating from the composi-tional inhomogeneity in the SiGe layer plane and at het-erointerfaces; the exciton localization is accompanied by a red shift of the corresponding PL lines, as indicated in Fig. 2a. In addition, a decrease in the temperature brings about the appearance of the biexciton PL lines on the red side of the exciton lines. Thus, the PL of localized dipolar biexcitons is observed in structure #4, while the PL of free spatially direct biexcitons is observed in struc-ture #2 for T ≥ 12 K. The dependence of the biexciton PL intensity on the excitation level is linear in the first case and close to quadratic in the second case. At high excita-tion levels and low temperatures, the spectra are domi-nated by the emission from the EHL, which is spatially direct in structure #2 (Fig. 2b, curve 5) and indirect in structure #4 (Fig. 2a, curves 6, 7). It is known that independence of the PL line shape from the excitation level is a signature of the EHL lumi-nescence. According to Fig. 2a, the normalized shapes of the PL spectra of sample #4 recorded at T  1.8 K for two pump powers differing by a factor of 2 (curves 6, 7) coin-cide. The shape and position of the PL lines recorded for the same pump level in the temperature range of 1.8-6 K also coincide with those of curves 6 and 7. The dipolar EHL in structure #4 is composed by heavy holes in the quantum well formed in the valence band by the SiGe layer and electrons from Δ4 valleys of the conduction band of Si, which are bound to the holes by Coulomb attraction and occupy triangular potential wells formed at Si / SiGe heterointerfaces owing to the band bending at high excitation levels. In this case, the calculated lu-minescence line is described by two-dimensional density of states both for heavy holes and Δ4 electrons (Fig. 2a, dashed line). The calculated profile of the luminescence line of spatially direct EHL in structure #2 is shown in Fig. 2b (curve 5, solid line) [1]. The difference between the EHL luminescence line shape in structures #2 and #4 originates from the difference in the energy depend-ences of the electron density of states  (  Е1/2 for #2 and   const for #4). In addition, the ratio Fe / Fh of the electron and hole Fermi energies, which affects the shape of the EHL luminescence line, is different in the two cases. Comparing the energy separation between the EHL and FE lines in Figs. 2a and 2b, one can see that the binding energy in the dipolar EHL is considerably lower than in the spatially direct EHL. The variation of the PL spectra of structures #4 and #2 in the visible range with increasing excitation level is shown in Fig. 3. The visible-range PL originates from simultaneous recombination of two holes in the valence   Fig. 2 – Modification of the NIR PL spectra of structures (a) #4 and (b) #2 with decreasing temperature T and increasing pump power P. (a) Curves 1-5: T varies between 26 and 6 K, P  0.12 W/cm2. Curves 6 and 7 (shown overlapping by circles and solid line, respectively): T  1.8 K, P  85 and 170 W/cm2, respectively; dashed line shows the calculated spectrum of the dipolar EHL luminescence. (b): Curves 1-4: T varies between 21 and 12 K, P  2 W/cm2. Curve 5 (circles): T  1.8 K, P  4 W/cm2; solid line shows the calculated spectrum of the spatially direct EHL luminescence [8]. FE, FBiE, LBiE, and EHL stand for free excitons, free biexci-tons, localized biexcitons, and electron-hole liquid, respective-ly. Normalized spectral curves are shown in all cases  band in the SiGe layer and two electrons from the oppo-site valleys in the conduction band. Thus, the PL result-ing from these so-called two-electron transitions occurs at photon energies approximately a factor of 2 higher than the energies of no-phonon (NP) single-electron transitions in the NIR range. Narrow lines in Fig. 3 cor-respond to the biexciton luminescence, and wide lines, to the EHL luminescence. At low excitation levels, biexci-tons in structure #4 are observed in the temperature range of 1.8-23 K. As the temperature decreases to 1.8 K, they become localized; similarly to the NIR PL spectra, this is accompanied by a red shift of the biexciton PL line. The dipolar EHL appears at higher excitation lev-els. The shape and position of the corresponding PL line become independent of the excitation level as the latter is raised still further and hardly depend on temperature for T  1.8-6 K. The modification of the visible-range PL spectra of structure #2 with increasing pump level at T  15 K is shown in Fig. 3b. At low excitation levels, a narrow PL line of free biexcitons (FWHM  4 meV) is clearly observed. At high excitation levels, the spectra are dominated by a broad (FWHM  20 meV) PL line of the EHL. Similarly to the NIR spectra, the shape of this line ultimately becomes independent of the excitation level (compare curves 3 and 4), which is a feature characteristic of the EHL luminescence. In this case, the EHL is spatially direct, and its binding energy and critical temperature are considerably higher than those  TWO-DIMENSIONAL ELECTRON-HOLE LIQUID… PROC. NAP 3, 01NTF01 (2014)   01NTF01-3 for the dipolar EHL. At 15 K, the EHL line shape is to a large extent determined by temperature effects. At 1.8 K (curve 5, circles), the lineshape is determined only by the behavior of (Е) and the electron and hole Fermi energies in the EHL. Here, the solid line shows the numerical convolution of the corresponding spectrum    Fig. 3 – Modification of the visible-range PL spectra with increasing pump power. (a) Structure #4. T  1.8 K, P  (2) 3.8, (3) 13, (4) 108, and (5) 180 W/cm2; curves 4 (circles) and 5 (solid line) are shown overlapping. Curve 1 (dashed line) shows the biexciton PL spectrum observed for T  23 K and P  3.5 W/cm2. (b) Structure #2. T  15 K, P  (1) 0.5, (2) 1.0, (3) 85, and (4) 150 W/cm2; curves 3 (circles) and 4 (solid line) are shown overlapping. Curve 5 (dashed line) shows the PL spectrum recorded for T  1.8 K and P  260 W/cm2; the solid line shows the numerical convolution of the experimental spectrum 5 (Fig. 2b). Normalized spectral curves are shown in all cases  recorded in the NIR range (Fig. 2b, curve 5). Good agreement between the experimentally determined shape of the visible PL line and the convolution of the EHL luminescence line recorded in the NIR range indicates that the nature of the PL lines in the two cases is the same. Thus, we observe the single-electron and two-electron recombination radiation of the spatially direct quasi-two-dimensional EHL in the NIR and visible PL spectra, respectively. Combining data from the NIR and visible PL spec-tra, one can determine the binding energy of free biex-citons EM:   EM  2[hNIR(FE-NP)]  hVIS(FBiE),   where hNIR and hVIS are photon energies of the NIR and visible PL corresponding to the excited states indi-cated in parentheses. It is convenient to reference all energies to the EHL luminescence energy and to use intense TO-phonon components of the NIR spectrum as follows:  EM  2[hNIR(FE-TO)  hNIR(EHL-TO)]    [hVIS(FBiE)  hVIS(EHL)].  Taking the required photon energies from the spectra in Figs. 2 and 3, we obtain EM  2.0 ± 0.5 meV. The value of the binding energy of quasi-two-dimensional free biex-citons thus obtained exceeds noticeably the free-biexciton binding energy in the three-dimensional case (in bulk uniaxiallystrained Si, EM ≈ 1.3-1.4 meV [9]).  AKNOWLEDGEMENTS  We are grateful to L.V. Keldysh and A.P. Silin for interest in this study and useful discussions; D.V. Shepel’ and V.A. Tsvetkov for help with experi-mental work; D.N. Lobanov and A.V. Novikov for grow-ing the Si / SiGe heterostructures. This study was supported by the Russian Founda-tion for Basic Research (projects nos. 13-02-00853, 13-02-904 67), and Programs of fundamental studies of the Russian Academy of Sciences.   REFERENCES  1. L.V. Keldysh, Proceedings of 9th International Conference on the Physics of Semiconductors, Moscow, 1968 (Lenin-grad: Nauka: 1969). 2. T.M. Rice, J.C. Hensel, T.G. Fillips, G.A. Thomas, Solid State Physics 32, (New York: Academic Press: 1977). 3. The Electron-Hole Drops in Semiconductors, in: Modern Prob-lems in Condensed Matter Sciences, 6, (Eds. by C.D. Jeffries, L.V. Keldysh), (Amsterdam: North-Holland: 1983). 4. L.V. Keldysh, N.N. Sibeldin, Ibid, 16, (Eds. by W. Eisenmenger, A.A. Kaplyanskii) (1986). 5. N.N. Sibeldin. Electron-Hole Liquid in Semiconductors, in: Problems of Condensed Matter Physics: Quantum Coher-ence Phenomena in Electron-Hole and Coupled Matter-Light System, (Eds. by A.L. Ivanov, S.G. Tikhodeev), In-ternational Series of Monographs on Physics 139, p.227, (Oxford University Press: 2008). 6. K. Betzler, R. Conradt, Phys. Rev. Lett. 28, 1562 (1972). 7. T.W. Steiner, L.C. Lenchyshyn, M.L.W. Thewalt, J.P. Noel, N.L. Rowell, D.C. Houghton, Solid State Com-mun. 89, 429 (1994). 8. D. Shepel, T. Burbaev, N. Sibeldin, M. Skorikov, phys. status solidi c 8, 1186 (2011). 9. V.D. Kulakovskii, V.G. Lysenko, V.B. Timofeev, Sov. Phys. Usp. 28, 735 (1985).  

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Two-Dimensional Electron-Hole Liquid in Systems of Spatially Direct and Indirect Excitons in Si/SiGe Heterostructures

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