Therefore, at the resonant magnetic field Bres = 3.424 T and In - polarization, the polarized effect of the miT = 1.6 K all electrons lie in the N = 0 Landau level crowave heating plays the main role at high magnetic fields and most of them populate the lower spin state (+1/2) by (B > 3T) and the non-polarized effect at low magnetic thermalization because of the long lifetime ( = 2.7 µs) fields (B < 1T). For 1
magnetic field strength. In + polarization, only the nonFor the - polarized luminescence of the trion, there is a polarized effect plays a role and the ODMR background small electron population in the (-1/2) state and a strong signals decline slowly to zero due to the suppression of the exciton population in the (-1) state. Microwave resonant microwave heating. Since the polarized ODMR background absorption increases the electron population in the (-1/2) (at B > 3T) is due to the microwave heating of excess state and enhances the formation probability of the (-3/2) electrons and electrons which are bound to impurities can X-. Therefore, we observed a positive electron ODMR not be heated by microwaves, the ODMR measurements signal detected on the X- emission and simultaneously a prove clearly the attribution of the PL line to X- and not to negative electron ODMR signal detected on the X emission since the enhanced formation of X- is in expense of X. an impurity bound exciton.
In + polarization, there exists a strong electron popula- 2.3. T r i o n s f o r m e d w i t h t h e l i g h t h o l e tion in the (+1/2) state and a small exciton population in exci t on. A fingerprint of X- is the strong polarization the (+1) state. The formation probability of the (+3/2) X- of its resonance in external magnetic fields. When the therefore in not sensitive to changes of the (+1/2) electron excess electrons are strongly polarized by the external population. Thus, the sharp electron ODMR line can not be magnetic field, excitation of the X- singlet state is allowed Физика твердого тела, 1999, том 41, вып. Exciton-Electron Interaction in Quantum Wells with a Two Dimensional Electron Gas of Low Density 3. Combined Exciton-Cyclotron Resonance In external magnetic fields, besides the trion line, another new line appears in the PLE and reflectivity spectra, which can not be attributed to the normal magneto-exciton peaks.
This line is attributed to a combined exciton-cyclotron resonance (ExCR) and is a supplementary example for new features observable in semiconductor quantum wells containing an electron gas of low density . An incident photon creates an exciton in the ground state and simultaneously excites one of the resident electrons from the lowest to first (ExCR1) or to the second (ExCR2) Landau level. As can be seen from Fig. 6 the energetic positions of these ExCR lines are in the range of the Coulomb bound states, but they behave very differently. For instance, the intensity of the ExCR line increase strongly for larger ne, whereas the magnetoexciton lines are insensitive to this parameter. Furthermore, Fig. shows that the ExCR lines shift linearly in magnetic fields with a slope of 1.2 meV/T (ExCR1) or 2.9 meV/T (ExCR2), Figure 5. Reflectivity spectra of a 10 nm respectively, which is comparable to the electron cyclotron ZnSe/Zn0.89Mg0.11S0.18Se0.82 quantum well at 1.6 K and 7 T energies in CdTe/(Cd,Mg)Te QWs. An extrapolation of for + (solid) and - (dashed) lines. The insert shows the these shifts to zero field meets approximately the energy of radiative damping (oscillator strength) for the exciton and the the 1s state of the heavy-hole exciton (1s-hh). This linear trion.
shift of the ExCR lines, as opposed to the quadratic one of the heavy-hole excitons (1s, 2s, and 3s states also displayed in Fig. 6), shows that the free electrons contribute to the observed process. Theoretically the shift of the ExCR lines for one defined polarization only. In contrast to the in an external magnetic field behave like N· c,e(1+me/M), CdTe/(Cd,Mg)Te structures discussed so far the g factor where me is the electron and M = me + mh is the exciton of the electron in ZnSe/(Zn,Mg)(S,Se) QWs is positive (ge = 1.1). Therefore, the allowed transition for X- formed with the heavy-hole exciton in these structures is the polarization, whereas + is the allowed polarization for the trion formed with the light hole exciton. Such a behavior is demonstrated for a 10 nm ZnSe/Zn0.89Mg0.11S0.18Se0.QW with ne 4·1010 cm-2 in Fig. 5. The resonance indeed appear in opposite circular polarization of the reflected light.
Furthermore, from Fig. 5 the binding energy of the trion can be determined. At B = 7 T the binding energy of X- formed with the heavy hole exciton is 4.6 meV, and 3.8 meV for Xformed with the light hole exciton.
We have fitted all experimentally observed resonances in the frame of a model of a nonlocal dielectric response .
In the insert of Fig. 5 we have plotted the dependencies of the exciton and trion radiative damping as a function of the magnetic field. It is obvious that the exciton radiative damping constant 0 (i. e. the exciton oscillator strength) shows no dependence on the magnetic field strength for both circular polarizations. The trion oscillator strength, in contrary to the excitonic one, decrease with the magnetic field for the + polarization and increases for the polarization. This different behavior of 0 for + and - polarizations is due to the singlet structure of the trion ground state, where the two electrons involved have opposite Figure 6. Fan chart of an 8 nm CdTe/Cd0.7Mg0.3Te quantum well.
spins. In the presence of a magnetic field the background Open symbols represent + and closed symbols - polarization electrons are polarized and the trions could be created by respectively. The lines represent calculation for the exciton 1 s, 2 s photons of one polarization only. and 3 state applying the model described in ref. .
6 Физика твердого тела, 1999, том 41, вып. 836 W. Ossau, D.R. Yakovlev, C.Y. Hu, V.P. Kochereshko, G.V. Astakhov, R.A. Suris, P.C.M. Christianen...
mass, c,e is the cyclotron energy and N an integer (details This work has been supported in part by the European of the theoretical consideration are in ref. ). Applying Commission TMR program Access to Large Scale Facilities, the experimentally obtained mass values me = 0.11m0 contract ERB FMGE CT950079, the Volkswagen Foundaand mhh = 0.48m0 gives 1.24 meV/T very close to the tion and the mutual grant of Russian Foundation for Basic experimental value. Research and the Deutsche Forschungsgemeinschaft N 9802-04089 and Os98/5.
The ExCR line is strongly - polarized, when the spin of the free electron gas is parallel to the free electron gas polarization in the external field direction. As a References photon creates an electron with the same spin orientation as the background electron. In this case the exciton angular  K. Kheng, R.T. Cox, Y. Merle d’Aubigne, F. Bassani, K. Samimomentum in the final state is (-1), and the recombination nadayar, S. Tatarenko. Phys. Rev. Lett. 71, 1752 (1993).
of such a photon is dipole allowed. On the other hand,  D.R. Yakovlev, V.P. Kochereshko, W. Ossau, G. Landwehr, a + polarized photon leads to a final state exciton with P.C.M. Christianen, J.C. Maan, T. Wojtowicz, G. Karczewski, J. Kossut. Proc. of the 24th Int. Conf. Phys. Semicond.
a magnetic moment of 2, whose recombination is dipole Jerusalem (1998), in press.
forbidden. Such excitons can recombine only after a spin  D.R. Yakovlev, V.P. Kochereshko, R.A. Suris, H. Schenk, flip of either the electron or the hole caused by scattering W. Ossau, A. Waag, G. Landwehr, P.C.M. Christianen, processes, and therefore their contribution to the PL intensity J.C. Maan. Phys. Rev. Lett. 79, 3974 (1997).
is much weaker.
 C.Y. Hu, W. Ossau, D.R. Yakovlev, G. Landwehr, T. WojtoIn addition, it can be seen in Fig. 6 that for magnetic wicz, G. Karczewski, J. Kossut. Phys. Rev. B58, Rfield above 11 T the ExCR1 line exhibits a strong bowing (1998).
and splitting into two components. In this field range the  V.P. Kochereshko, D.R. Yakovlev, W. Ossau, G. Landwehr, LO-phonon energy equals the cyclotron energy resulting in T. Wojtowicz, G. Karczewski, J. Kossut. J. Crystal Growth a resonant polaron coupling , which can be established 184/185, 826 (1998).
 W. Ossau, V.P. Kochereshko, D.R. Yakovlev, R.A. Suris, from the typical anticrossing behavior caused by the mixing D. Turchinovich, G. Landwehr, T. Wojtowicz, G. Karczewski, of electron and phonon states. The observation of a resonant J. Kossut. Phys. Low-Dim. Struct. 1/2, 205 (1998).
polaron coupling via the ExCR line also evidences the  V.P. Kochereshko, D.R. Yakovlev, A.V. Platonov, W. Ossau, participation of 2D electrons in the ExCR process.
A. Waag, G. Landwehr, R.T. Cox. Proc. 23rd Int. Conf. Phys.
Semicond. Berlin, Germany (1996). P. 1943. World Scientific, Singapore (1996) / Ed. by M. Scheffler and R. Zimmermann.
4. Additional Features Correlated with the  A.A. Sirenko, T. Ruf, M. Cardona, D.R. Yakovlev, W. Ossau, 2DEG A. Waag, G. Landwehr. Phys. Rev. B56, 2114 (1997).
 K. Kheng, R.T. Cox, V.P. Kochereshko, K. Saminadayar, Besides the linearly blue shift of the ExCR line observed S. Tatarenko, F. Bassani, A. Franciosi. Superlattices and in PLE and reflectivity the PL spectra of QWs with an Microstructures 15, 253 (1994).
 R. Romestain, C. Weisbuch. Phys. Rev. Lett. 45, 2067 (1980).
electron gas of low density exhibit lines that are correlated  B.C. Cavenett, E.J. Pakulis. Phys. Rev. B32, 8449 (1985).
with shake-up processes . We observe a series of low  The electron Zeeman splitting energy E = 0.25 meV energy satellites related to the excitation of the 2DEG . In at B = 3 T, is in the same range as the thermal energy emission the transition energy of the photon is lowered by kT 0.14 meV at T = 1.6 K. This means that the electron energy conservation. The shake-up process excites, similar population between two spin states is very sensitive to the to the ExCR mechanism, inter Landau level transitions electron temperature.
giving rise to a red shifted PL lines with an energy separation  K. Seeger. Semiconductor Physics. Springer-Verlag, Wien from the trion energy of about -N c,e.
(1973). Ch. 11.
Besides all of these above discussed elastic scattering  B. Kowalski, P. Omling, B.K. Meyer, D.M. Hofmann, C. Wetprocesses we would like to mention inelastic and spin- zel, V. Hrle, F. Scholz, P. Sobkowicz. Phys. Rev. B49, R(1994).
dependent scattering processes, where the photo-generated  E.L. Ivchenko, A.V. Kavokin, V.P. Kochereshko, G.R. Pozina, excitons loses their energy by scattering to an ortho-exciton I.N. Uraltsev, D.R. Yakovlev, R.N. Bichnell-Tassius, A. Waag, state and the simultaneous excitation to an upper Zeeman G. Landwehr. Phys. Rev. B46, 7713 (1992).
sublevel. Details of these scattering processes are published  R.J. Nicholas, S. Sasaki, N. Miura, F.M. Peeters, J.M. Shi, elsewhere .
G.Q. Hai, J.T. Devreese, M.J. Lawless, D.E. Ashenford, B. Lunn. Phys. Rev. B50, 7596 (1994).
 K.J. Nash, M.S. Skolnick, M.K. Saker, S.J. Bass. Phys. Rev.
Acknowledgment Lett. 70, 3115 (1993).
 N.A. Gippius, A.L. Yablonskii, A.B. Dzyubenko, The authors would like to thank T. Wojtowicz, G. KarS.G. Tikhodeev, L.V. Kulik, V.D. Kulakovskii, A. Forchel. J.
czewski and J. Nrnberger for providing the excellent Appl. Phys. 83, 5410 (1998).
structures. Without them these studies would not have been possible.
Физика твердого тела, 1999, том 41, вып.