Semiconductor structures with quantum dots are currently technique, was limited by the laser pulse duration. The the subject both of fundamental studies and of practical exciting circularly polarized light was obtained by passing applications. In the last few years much attention was linearly polarized lazer beam through a quarter-wave plate.
given to the study of the energy relaxation of carriers in The luminescence was registered along the growth axis (Oz) those structures [1–7]. Taking into account the spin of in back-scattering geometry.
carriers makes it possible to obtain additional information The results of polarization measurements in the different on the energy relaxation processes and the structure of the structures under study are qualitatively the same. Presented electron energy levels. In the present work, time resolved below are the results of experiments on sample 1. Fig. spectroscopy with picosecond resolution has been used for shows normalized luminescence spectra obtained under the first time to investigate spin dynamics in semiconductor excitation of carriers in the GaAs matrix. Spectrum 1 is quantum dots embedded in a semiconductor matrix. Spin recorded under continuous wave (cw) excitation with a polarization of carriers was created as a result of their pump density of 1 W/cm2. An increase of the cw excitaoptical orientation  by short ( 1ps) pulses of circularly tion intensity by two orders of magnitude did not change polarized light. It has been found that the spin polarization the shape and position of the spectrum. This indicates of electrons generated in the matrix or in the wetting layer, that spectrum 1 results from the emission of ground-state can survive their capture by the QDs and last a few hundreds electrons and holes. We associate the presence of two of picoseconds. This allowed us to observe quantum beats strongly overlapping lines in this spectrum with radiative of electron spin in a transverse magnetic field and thus to recombination of two groups of dots having different mean determine the magnitude of the transverse g-factor of quasizero-dimensional electrons in In0.5Ga0.5As/GaAs quantum dots.
The structures studied were grown by solid-source molecular beam epitaxy in Riber-32P machine on semi-insulating GaAs (100) substrates. Active region was inserted into the middle of a 0.2 µm thick undoped GaAs layer confined by AlAs(2nm)/GaAs(2nm) superlattices to prevent escape of non-equilibrium carriers to the sample surface and substrate.
In the first structure, denoted as 1, the active region consists of 6 planes of QDs separated by 50 thick GaAs spacers.
Each QD plane was formed by deposition of 4 monolayers (MLs) of In0.5Ga0.5As. In the structure 2 the active layer consists of 10 planes of 1.7 ML InAs QDs separated by 200 thick GaAs spacers. Sample 3 contains one plane of 2.7 ML InAs QDs. The growth temperature was set to be 485C for In-containing layers and 600C for the other Figure 1. Photoluminescence spectra of In0.5Ga0.5As/GaAs QDs parts of the structures .
(sample 1). T = 10 K. 1 — cw. excitation with Eexc = 1.610 eV A tunable Ti-sapphire laser producing 1.2-ps long light and power density 1 W/cm2; 2 and 3 — short pulse pumping with pulses with a repetition frequency of 82 MHz was used to power densities 0.1 and 1.6 MW/cm2, Eexc = 1.531 eV, time delay excite the investigated structures. The time resolution of the after excitation pulse equals 200 ps; 4 — cw photoluminescence excitation spectra at Edet = 1.248 eV.
experimental setup, based on the parametric up-conversion 872 V.K. Kalevich, M.N. Tkachuk, P. Le Jeune, X. Marie, T. Amand Figure 2. Luminescence circular polarization dependence on time delay at different detection energies Edet. Eexc = 1.531 eV, T = 10 K.
Solid lines show the exponential decay of the polarization degree with time constant S. S (ps): a — 290, b — 400, c — 211, d — 92.
sizes. Spectra 2 and 3 are registered under pulse excitation In our experiments the spin orientation of electrons and with pump densities of 0.1 and 1.6 MW/cm2 respectively. holes was created by cicularly polarized light. The recomAs seen from the comparison with spectrum 1, an increase bination radiation involving spin-oriented carriers also turns of the pulse excitation intensity results in a significant (up out to be circularly polarized. Therefore the luminescence to 50 meV) blue shift of the luminescence line. Such circular polarization degree = (I+ - I-)/(I+ + I-) transformation of the luminescence spectra of quantum dots can be used to measure the carriers spin polarization and their spin dynamics. Here I+ and I- denote the respective at high excitation levels has been observed before [4,6,7] intensities of the left-hand and right-hand circularly polarized and was due to the filling of the ground states of electrons luminescence components.
and holes and to the appearance of an intense light emission from the excited states. Indeed, as an estimate shows, at Fig. 2 shows the time dependences (t) measured at the maximum pump density of 1.6 MW/cm2 that we used, four different energies of recombination radiation quanta the number of photoexcited electron-hole pairs exceeds by Edet (marked by arrows in Fig. 1) under excitation into several times the number of quantum dots in the illuminated the GaAs barrier (Eexc = 1.531 eV) with pulse density region; this leads to population of the excited states, since of 1.6 MW/cm2. It can be seen from Fig. 2, a, b that at they cannot relax any more into the filled ground states. The the high-energy edge of the luminescence line the initial excited states, in turn, give rise to an intense luminescence value of is large (it reaches 80% at Edet = 1.363 eV) spectral component. Curve 4 in Fig. 1 represents the and slowly decreases with a characteristic time of about cw photoluminescence excitation spectrum recorded at a 300–400 ps. When going down to the low-energy part registration energy Edet = 1.245 eV (the position of the low- of the luminescence spectrum, the maximum value of energy maximum in spectrum 1). We, as well as the authors significantly decreases and the polarization decay time is of [4,7], assign the relatively broad band (1.42–1.48 eV) drastically reduced (Fig. 2, c, d). Thus, at Edet = 1.292 eV, near the edge of the fundamental absorption of GaAs to decreases from an initial value of (0) 22% down to the absorption of the wetting layer. 5% within 15 ps (Fig. 2, d).
Физика твердого тела, 1999, том 41, вып. Electron Spin Beats in InGaAs/GaAs Quantum Dots Let us first make some remarks regarding the nature of the slow decay of at large Edet. The rate of the change of is determined by the slowest of the spin relaxation processes in electrons and holes. Due to the strong spin-orbit interaction in the valence band, the spin relaxation time of holes is significantly shorter than that of electrons  and does not exceed a few picoseconds in bulk intrinsic semiconductors of the GaAs type . For this reason we think that the luminescence polarization is only determined by the spin polarization of electrons, while the slow change of is due to the large value of their spin relaxation time.
Quite surprising was the fact that at large Edet during some tens of picoseconds, the values of substantially exceed 50%, reaching 80% at Edet = 1.363 eV (Fig. 2, a).
Figure 3. Luminescence polarization oscillations in a transverse Since in investigated dots the holes participating in the magnetic field B = 3.5T. T = 1.7 K. The solid line is drawn on radiative recombination are heavy holes , the value of formula (2) with Larmor precession period equal to 76 ps.
is numerically equal to the spin polarization of electrons Pe: = Pe . At the same time, in accordance with the optical selection rules , the spin polarization of the electrons generated in bulk GaAs cannot exceed 50%.
The qualitative explanation of the appearance of values larger than 50% on the high energy side of the QDs spectra may be obtained in the following simple model. Suppose that the electrons, generated in the GaAs barrier with a spin polarization equal to 50%, are trapped by QDs with such polarization, while the holes lose entirely their polarization during their energy relaxation process. In dots analogous to ours, besides the ground levels there are excited levels of both holes and electrons [6,11–16]. By virtue of Pauli’s principle each level can locate no more than two electrons with opposite spins. As at Pe = 0.5 there are thrice as much electrons with spin -1/2 than electrons with spin +1/2, so with the increase of the concentration of photoexcited carriers leading to the saturation of the ground state, the highest electron levels will be populated predominantly by electrons with spin -1/2, which leads, at the limit, to the Figure 4. Spin beat frequency versus magnetic field.
100% polarization of the associated recombination radiation.
The scatter of the QD sizes, resultig in the inhomogeneous broadening of the luminescence line, diminishes this effect;
obeys the equation at the high-energy edge of the line, however, the value of may exceed 50%, which is just what we observe in dS S =(S) -, (1) our experiments. On the contrary, the radiation from the dt S ground state must be non-polarized, since two electrons where the first term on the right-hand side describes the occupying this state have opposite spins. This is also Larmor precession, and the second, spin relaxation. Since observed experimentally (see Fig. 2, d).
in our experiments a long-living luminescence polarization The long-living and large polarization of electrons can be is created by the electron polarization, = -2Sz, and in a used for the observation of their spin beats in transverse magnetic field directed perpendicular to the exciting beam, magnetic field and determination of the g-factor magnitude.
varies in time as Electron spin quantum beats set in under coherent excitation of the two electron spin levels by a short pulse of circularly (t) = e-t/S cos t. (2) polarized light and may be considered as a result of Larmor (0) precession of electron spins about the magnetic field B with a frequency = gµBB/, where g is the electron g-factor, µB It is easy to determine the magnitude of the electron gis the Bohr magneton . The pump pulse is substantially factor by measuring the beat frequency as a function of the shorter than the electron lifetime and spin relaxation time, magnetic field.
denoted and S, respectively. Therefore the motion of the The dependence (t) measured in a magnetic field average spin S of electrons excited during the pump pulse B = 3.5T at Edet = 1.355 eV is shown in Fig. 3. It Физика твердого тела, 1999, том 41, вып. 874 V.K. Kalevich, M.N. Tkachuk, P. Le Jeune, X. Marie, T. Amand can be seen that oscillates with time in agreement with  P. Le Jeune, X. Marie, T. Amand, J. Barrau, R. Planel. Proc.
24th Int. Conf. Phys. Semic. Jerusalem, Israel (1998). To be Eq. (2). The dependence of the spin beats frequency on published.
the magnetic field is presented on Fig. 4. It is quite linear.
 M. Grundman, O. Stier, D. Bimberg. Phys. Rev. B52, 16, Thus the modulus of the electron transverse g-factor of 11969 (1995).
In0.5Ga0.5As/GaAs QDs can be accurately deduced. We  C. Guasch, C.M. Sotomayor Torres, N.N. Ledentsov, D. Bimfind: |g| = 0.27 ± 0.03. Note that it is the g-factor of berg, V.M. Ustinov, P.S. Kop’ev. Superlattices and Microstrucelectrons in the excited state.
tures 21, 4, 509 (1997).
To conclude, electron spin orientation and its subsequent  R.J. Warburton, C. S. Durr, K. Karrai, J.P. Kottaus, dynamics in self-organized In(Ga)As/GaAs QDs have been G. Medeiros-Ribeiro, P.M. Petroff. Phys. Rev. Lett. 79, 26, studied for the first time using picosecond time-resolved 5282 (1997).
luminescence spectroscopy. It has been found that optical  E. Itskevich, I.A. Trojan, S.G. Lyapin, D. Mowbray, M.S. Skolorientation of electrons, excited in the matrix or in the nick, M. Hopkinson, L. Eaves, P.C. Main, M. Henini. Proc.
24th Int. Conf. Phys. Semic., Jerusalem, Israel (1998). To be wetting layer, can last after their capture by the QDs during published.
some hundred picoseconds. The saturation of electron  Craig Pryor. Phys. Rev. Lett. 80, 16, 3579 (1998); Craig Pryor.
ground states at high excitation intensity leads to electron Phys. Rev. B57, 12, 7190 (1998).
spin polarization in the excited states close to 100%, and to  O. Stier, M. Grundmann, D. Bimberg. Proc. 24th Int. Conf.
vanishing values in the ground state. Electron spin quantum Phys. Semic., Jerusalem, Israel (1998). to be published;
beats in transverse magnetic field are observed for the O. Stier, M. Grundmann, D. Bimberg. Phys. Rev. B, To be first time in semiconductor QDs, leading to determination published.
of the magnitude of the transverse electron g-factor in  A.P. Heberle, W.W. Ruhle, K. Ploog. Phys. Rev. Lett. 72, In0.5Ga0.5As/GaAs QDs.
24, 3887 (1994); R.M. Hannak, M. Oestreich, A.P. Heberle, W.W. Ruhle, K. Kohler. Solid State Commun. 93, 4, The authors are grateful to N.N. Ledentzov, V.M. Ustinov, (1995).
A.E. Zhukov and A.F. Tsatsul’nikov for supplying the samples and useful discussions, I.A. Merkulov and K.V. Kavokin for fruitful discussions.
Partial support of the Russian Fundamental Research Foundation (Grants 96-02-16941 and 98-02-18213) is acknowledged.
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