Trions in quantum-well structures with two-dimensional electron gas
D. B. Turchinovich and V. P. Kochereshko
A. F. Ioffe Physicotechnical Institute, Russian Academy of Sciences, 194021 St. Petersburg, Russia
D. R. Yakovlev
A. F. Ioffe Physicotechnical Institute, Russian Academy of Sciences, 194021 St. Petersburg, Russia;
Physikalisches Institut der Universita ¨t Wu ¨rzburg, 97074 Wu ¨rzburg, Germany
W. Ossau and G. Landwehr
Physikalisches Institut der Universita ¨t Wu ¨rzburg, 97074 Wu ¨rzburg, Germany
T. Wojtowicz, G. Karczewski, and J. Kossut
Institute of Physics, Polish Academy of Sciences, PL02608 Warsaw, Poland
Fiz. Tverd. Tela St. Petersburg 40, 813–815 May 1998
A study has been made of bound exciton–electron complexes trions and unbound
exciton–electron states combined exciton–cyclotron resonance from reflectance spectra
obtained from modulation-doped CdTe/CdMgTe quantum-well structures. It has been established
that the contribution of trions to dielectric permittivity is comparable to that of excitons.
An analysis is made of the magnetic-field dependence of the parameters describing the contribution
to dielectric permittivity due to exciton-cyclotron-resonance states. © 1998 American
Institute of Physics. S1063-78349801005-3
The exciton–electron interaction processes have been
considered to be sufficiently well studied until recently.
Their analysis reduced to two main mechanisms: 1 destruc-
tion by free electrons of the exciton states through k -space
filling and screening of the electron–hole Coulomb interac-
tion in the exciton, and 2 enhancement of exciton damping
due to exciton–electron scattering. Both these mechanisms
lead to destruction of exciton states and suppression of exci-
ton lines in optical spectra. It has recently been found that in
the case of a low free-electron density in semiconductor
quantum wells QW exciton-electron interaction results in
the formation of a bound exciton-electron complex trion.
1,2
Such trion states were observed to exist in II–VI and III–V
semiconductor QWs.
2,3
Unbound resonant exciton–electron
states, i.e. the exciton cyclotronresonance ExCR, were de-
tected in the presence of a magnetic field.
4
This work deals
with a study of reflectance spectra from modulation-doped
CdTe/Cd
0.7
Mg
0.3
Te QW structures containing a low-density
two-dimensional electron gas.
We studied CdTe/Cd
0.7
Mg
0.3
Te heterostructures grown
by molecular-beam epitaxy on 100-oriented GaAs sub-
strates. Structures with a single 80-Å thick CdTe QW were
doped with iodine at a distance of 100 Å from the QW. The
electron density in the QW was 10
9
cm
-2
in an undoped
structure and was as high as 10
11
cm
-2
in a doped one.
In the absence of a magnetic field, the reflectance spectra
of undoped QW structures contained only one free-exciton
line ( X ) whereas modulation-doped structures exhibit two
lines, namely, X , which corresponds to the free exciton, and
X
-
, due to the trion Fig. 1. The trion reflectance line is
shifted toward long wavelengths by 3 meV relative to the
exciton line. The amplitude of the X
-
line grows with elec-
tron density in the QW, while that of the exciton line, de-
creases. In the modulation-doped structure the exciton line is
substantially broadened as a result of exciton–electron scat-
tering and screening by free carriers. For high doping levels,
the exciton line is not observed at all, and the spectrum is
dominated by the X
-
line. This implies that the trion state
provides the major contribution to the dielectric permittivity
of doped QWs.
No changes were observed in the reflectance spectra of
the undoped structure as the magnetic field was increased.
Fig. 1a and 1b shows reflectance spectra of the modulation-
doped quantum-well structure in magnetic fields from zero to
7.5 T obtained in two circular polarizations,
+
and
-
. The
+
spectrum exhibits three reflectance lines corresponding,
respectively, to the exciton ( X ), trion ( X
-
), and exciton–
cyclotron resonances ExCR. Viewed in this polarization,
the amplitude of the trion reflectance line falls off with in-
creasing magnetic field to disappear altogether at 4.5 T,
whereas that of the exciton line grows. The
-
spectrum
exhibits only the X and X
-
lines, and the amplitudes of both
resonances increase slightly with magnetic field. The maxi-
mum of the ExCR line shifts linearly with increasing mag-
netic field toward higher energy with a slope close to the
electron cyclotron energy. Approximation of this line to zero
magnetic field yields the exciton resonance energy. The ori-
gin of this exciton–cyclotron resonance line is assigned to
the following process: the incident photon creates an exciton
with asimultaneous transition of the additional electron be-
tween the Landau levels.
4
All the observed transitions are strongly polarized in a
PHYSICS OF THE SOLID STATE VOLUME 40, NUMBER 5 MAY 1998
747 1063-7834/98/40(5)/3/$15.00 © 1998 American Institute of Physics