Exciton tunnelling and resonances in semimagnetic double-quantum-well structures

Exciton tunnelling and resonances in semimagnetic double-quantum-well structures

,. . . . . . . . ELSEVIER CRYSTAL GROWTH Journal of Crystal Growth 159 (1996) 1014-- 1017 Exciton tunnelling and resonances in semimagnetic double...

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ELSEVIER

CRYSTAL GROWTH

Journal of Crystal Growth 159 (1996) 1014-- 1017

Exciton tunnelling and resonances in semimagnetic double-quantum-well structures K. H i e k e a, , , W . H e i m b r o d t a, T h . P i e r b H . - E . G u m l i c h b W . W . R i i h l e c, J.E. N i c h o l l s a B. L u n n d a Humboldt Universitht zu Berlin, Institutffe Physik, lnvalidenstrasse 110, Unter den Linden 6, D-10099 Berlin, Germany b Technische Universit~tt Berlin, lnstitutffir Festki6rperphysik, Berlin, Germany ¢ Max-Planck Institutffir Festkfrperforschung, Stuttgart, Germany a University of Hull, Department of Engineering, Design and Manufacture/Applied Physics Department, Hull, UK

Abstract We present a study of tunnelling processes between C d T e / C d M n T e quantum wells by means of steady-state and time-resolved spectroscopy. The energy difference of the involved states and the barrier height can be controlled by an external magnetic field and resonances of the heavy-hole and exciton levels can be achieved. The heavy-hole (hh) resonance is essential for the type and direction of the transfer process. An efficient transfer of excitons is possible even without emission of LO phonons.

1. Introduction

Asymmetric double-quantum-well structures (ADQWs) consisting of CdTe/CdMnTe are useful to study the tunnelling through a potential barrier, because the giant Zeeman effect [1] leads to a remarkable splitting of the band-gap energy of the CdMnTe layers in an external magnetic field allowing to modify the tunnelling processes dramatically. Two possibilities exist to exploit the magneto-optical effects: (1) In samples with CdTe wells the height of the CdMnTe barrier is decreased in a magnetic field. We have shown [2,3] that tunnelling then becomes much more efficient. Both, transfer of whole excitons or

* Corresponding author. Fax: +49 30 2803 486; E-mail: [email protected] physik.hu-beflin.de.

electrons and heavy-holes (hh) separately, occur. The independent transfer of electrons and hh dominates when the barrier is very thin (e.g., 2.5 nm). In this case spatially indirect excitons are formed as an intermediate state. (2) The magnetic field changes the energy difference between the involved states and causes resonances if the wide well, too, contains some Mn [4,5]. This configuration clarifies (i) the role of the energy relaxation in the transfer processes between these two states and (ii) what happens if hh or exciton energies are resonant. Beyond a resonance the transfer direction is reversed. In this paper we will focus on point (2). Recently, other authors published studies, where transfer of direct excitons by emission of LO phonons or via 1 s-2s resonant states was suggested to be the dominant mechanism [5,6]. We demonstrate here that exciton transfer occurs even when these two chan-

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K. Hieke et aL /Journal of Crystal Growth 159 (1996) 1014-1017

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nels are not possible. The resonance between the hh states of the wells is identified as an important feature which controls the transfer processes.

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The samples are grown by MBE on InSb(100) substrates. The A D Q W consists of a wide magnetic Cd~ _rMnyTe well (MW), a Cd~ _~Mn~Te inner bartier, and a narrow nonmagnetic CdTe well (NMW) and is embedded between Cdt_xMnxTe cladding layers. The thicknesses of the magnetic well ( M W ) / barrier/ nonmagnetic well (NMW) are LM/B/NM= 8 . 5 / 7 / 4 . 5 nm (sample (a)) a n d LM/B/NM = 1 0 / 2 / 5 nm (sample (b)). The Mn concentrations are (a) x = 0.13, y = 0.035; and (b) x = 0.105, y = 0.04. The sample parameters are determined by X-ray rocking curve measurements and confirmed by the exciton energy positions. We performed optical spectroscopy in the cw domain (photoluminescence (PL) and PL excitation (PLE)) at T = 1.8 K and time-resolved PL (TRPL) with picosecond excitation at T = 7 K. The external magnetic field ( 0 - 1 3 T) was applied in Faraday configuration. A comparison between experimental data requires a careful consideration of the temperature because it influences the magnitude of the Zeeman splitting [ 1].

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Fig. I. The hh exciton energies as obtained by cw PLE measurements versus magnetic field of the sample (a) with LB = 7 nm barrier thickness and x = 0.13 (T = 1.8 K). Solid (open) squares and triangles refer to o'+ (o'-) polarisation. Inset: schematic drawing of the energy levels and possible transfer directions at 0 and 10 T (o-+).

assumed to be in the valence band. From the calculations we conclude that the resonance of the hh states of the magnetic and nonmagnetic wells occurs at Bch" = 1.4 T. We have analyzed the cw PL intensities to obtain information about the transfer process. The dependence of the integrated intensity ratio between the magnetic and nonmagnetic well 1M/INM on the magnetic field is plotted in Fig. 2. At 1.5 T there is a distinct minimum in this ratio because the hh of both wells are in resonance and therefore an efficient

3. Results Fig. i shows a plot of the hh exciton energies of sample (a) as function of the magnetic field. The Zeeman shift of the barrier hh exciton is 60 meV at l0 T. The experimental points at 1661 meV and 1680 meV (0 T) are identified as direct excitons located in the nonmagnetic and magnetic well, respectively. As the Zeeman splitting for the excitons in the M W is larger than for those in the N M W we find a resonance of the exciton energies at Bc xc -- 2.9 T in the cr÷ polarised branch. For comparison we have included the calculated curves in Fig. 1. The calculations use the transfer matrix formalism [7] for electrons and holes and include exciton binding energies calculated according to [8]. 30% of the total potential offset are

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K. Hieke et al./ Journal of Crystal Growth 159 (1996) 1014-1017

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transfer becomes possible. Between 2.5 and 4.5 T, the PL lines are not clearly separated and therefore the ratio IM/INM is not defined. We have measured the temporal evolution of the PL intensities after ps excitation of excitons in both wells (Elaser = 1.7 eV) to study the dynamics of the tunnelling processes in sample (a). The decay and rise times which we obtain by a curve-fit procedure are shown in Fig. 3. In the inset the PL energies at 7 K are plotted for comparison. At 0 T the decay time "/'NM of the nonmagnetic well PL is 200 ps and of the magnetic well r M - - 6 0 ps. The shorter decay time of PL M indicates that a fast transfer process MW--* NMW competes with the radiative recombination in the MW. The arriving particles populate the NMW additionally therefore the rise time r~M is r considerably longer than TM . r As the rise time rNM equals the decay time z M, we conclude that the tunnelling particles are complete excitons rather then independent electrons and holes which would tunnel with different time constants. At B ~ = 4.5 T which is the position of the hh resonance at 7 K the situation changes: ~'M starts to increase and "/'NMr is decreasing. The reason is that the transfer of direct excitons MW ~ NMW becomes less efficient beyond the hh resonance because the lowest energy hh state is now localised in the MW. At high fields, the decay and rise times of both wells are nearly equal to each other. This shows that no remarkable transfer

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e (Testa) Fig. 4. PL rise and decay times of the magnetic ( • , I ) and nonmagnetic ( A []) well of the sample (b) versus magnetic field from TRPL measurements (T = 7 K). The times of free hh excitons are clearly resolved only beyond the exciton resonance a t 2 T therefore we give only the decay and rise time of bound NMW excitons at 0 T for comparison. Inset: PL energies at 7 K (from TRPL).

NMW ~ MW does compete to the radiative recombination. For comparison we have plotted the PL decay times of sample (b) in Fig. 4. The inset shows the corresponding PL energies. At B < 2 T the PL M is only a high-energy shoulder at PLNM. The hh and exciton energy resonances in this sample occur at Bchh = 1 and B~xc = 2 T, respectively. We focus here on the decay times at higher magnetic fields. The r > rNM, r indicate that a facts, that rNM < r M and r M transfer process NMW ~ MW takes place. We suggest that in this sample at high fields hh transfer dominates instead of exciton transfer as r ~ ~ rNM while the electrons are delocalised over both wells.

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4. Discussion The schematic drawings in inset of Fig. 1 show that the energetically lowest hh state of the whole structure is localised in the nonmagnetic (magnetic) well below (above) the critical field B chh. The hh tend to be transferred from MW ~ NMW (NMW MW) below (above) B~hh to populate the energetically favourable state. The electrons tend to tunnel from MW ~ NMW. However, the wavefunctions become delocalised with increasing magnetic field and a fast interband relaxation becomes possible

K. Hieke et al. /Journal of Crystal Growth 159 (1996) 1014-1017

which is not necessarily connected with a spatial transfer. In the sample (a) with L B = 7 nm we observe exciton transfer MW -o NMW with a tunnelling time of T~xc ---90 ps at B < Bchh. The transfer of whole excitons is preferred against independently travelling particles because the barrier is too thick to form indirect excitons. The binding energy of a "crossed" exciton which would be a necessary intermediate state was calculated to be only 4 meV (compared to 20 meV for direct excitons) and thus such an exciton would have higher energy than both direct ones. When B > B hh the transfer of direct excitons MW NMW becomes less efficient. Even if the whole exciton would gain energy as long as B < B~xc the hh lose energy in this transfer which inhibits such a transfer process. The corresponding increase of ~'u starts exactly at B = B h" as we have checked also with other samples. At high fields the electronic wavefunctions are delocalised and no spatial transfer of electrons will occur. Therefore, the measured NMW decay times ~'r~M are determined mainly by the hh transfer which tends to go in the direction NMW ~ MW. The hh transfer times are dependent on the geometrical parameters of the sample, as the comparison of Figs. 3 and 4 shows. At 7 nm barrier thickness (a) the transfer time is much longer than the exciton recombination times thus the measured decay times are determined by the recombination and are equal for the NMW and MW. On the other hand, for the sample (b) with 2 nm barrier the hh transfer time has the order of 150-200 ps and influences the NMW decay time. It has already been proofed by other authors [9] for G a A s / G a A I A s DQWs that tunnelling of hh can be dominating in spite of their large effective mass if the barrier is thin enough. It is worth mentioning that we observe fast decay times (~'M = 60 ps) for the MW even if transfer by LO phonon emission or transfer via the 2s exciton of the lower energy well is possible. For comparison,

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other authors [5,6] have reported that these mechanisms allow rapid transfer (~'M --- 25 ps) and determine the critical field at which the increase of ~'r~ starts by the condition E~ - ENM < ELO = 21.4 meV or EM(lS)< ENM(2S). We have shown here that in absence of these mechanisms, when exciton transfer assisted by acoustical phonons or impurity scattering is possible, the hh resonance at B hh defines the critical field at which the increase of r M starts. The exciton transfer is then inhibited due to the reversed direction of hh transfer. In conclusion, we have demonstrated an efficient transfer of carriers and excitons through a single CdMnTe barrier between two quantum wells without emission of LO phonons. An external magnetic field causes resonances of the hh energies at a critical field B hh and at higher fields the exciton transfer MW --->NMW is suppressed. The hh resonance controis the decay times of the luminescence of the magnetic and nonmagnetic well.

References [1] J.K. Furdyna, J. Appl. Phys. 64 (1988) R29. [2] Th. Pier, K. Hieke, B. Henninger, W. Heimbrodt, O. Goede, H.-E. Gumlich, J.E. NichoUs, M. O'Neill, S.J. Weston and B. Lunn, J. Crystal Growth 138 (1994) 889. [3] K. Hieke, W. Heimbrodt, I. Lawrence, W.W. R~hle, Th. Pier, H.-E. Gumlich, D.E. Ashenford and B. Lunn, Solid Sta~ Commun. 93 (1995) 257. [4] I. Lawrence, G. Feuillet, H. Tuffigo, C. Bodin, J. Cibert, P. Peyla and A. Wasiela, Superlattices and Microstructures 12 (1992) 119. [5] I. Lawrence, S. Haacke, H. Mariette, W.W. Riihle, H. UlmerTuffigo, J. Cibert and G. Feuillet, Phys. Rev. Lett. 73 (1994) 2131. [6] S. Haacke, N.T. Pelekanos, H. Mariette, M. Zigone, A.P. Heberle and W.W. Riihle, Phys. Rev. B 47 (1993) 16643. [7] L.R. Ram-Mohan, K.H. Yoo and R.L. Aggarwal, Phys. Rev. B 38 (1988) 6151. [8] R.P. Leavitt and J.W. Little, Phys. Rev. B 42 (1990) 11774. [9] A.P. Heberle, X.Q. Zhou, A. Takeuchi, W.W. Ri~hle and K. KShler, Semicond. Sci. Technol. 9 (1994) 519.