Cd1 − vMgyTe single quantum wells in magneti fields

Superlattices and Microstructures, Vol. 25, No. 1/2, 1999 Article No. spmi.1998.0663 Available online at http://www.idealibrary.com on

Excitonic magnetic polaron dynamics of MBE grown CdTe/Cd1−x Mnx Te, Cd1−x Mnx Te/Cd1−y Mgy Te single quantum wells in magnetic fields M UKUL C. D EBNATH , I ZURU S OUMA , E IJI S HIRADO , T OSHIO S ATO , J INXI S HEN , YASUO O KA Research Institute for Scientific Measurements, Tohoku University, Sendai 980-8577, Japan and CREST, Japan Science and Technology Corporation, Kawaguchi 332-0012, Japan (Received 26 October 1998) Excitonic lifetimes in Cd1−x Mnx Te, Cd1−x Mgx Te epilayers and CdTe/Cd1−x Mnx Te, Cd1−x Mnx Te/Cd1−y Mg y Te single quantum wells with different well widths and Mn, Mg compositions are investigated. The excitonic lifetimes are found to reduce drastically by applying external magnetic fields to samples with giant Zeeman splittings. The observed phenomenon is interpreted in terms of the PL decay time contribution from the long-life dark excitons which can convert to excitons for recombinations by a spin-flip process. We attribute the lifetime reduction to the depletion of dark excitons due to their crossing over the exciton energies for dipole allowed transitions in magnetic fields. c 1999 Academic Press

Key words: transient photoluminescence, magnetic polaron, diluted magnetic semiconductor.

1. Introduction The strong exchange interaction between the spins of carriers and magnetic ions in diluted magnetic semiconductors is of considerable current interest. This interaction leads to novel spin-dependent phenomena including giant Zeeman splitting of the band states, large Faraday rotation, and magnetic polaron effects [1, 2]. Our attention focuses on the dynamics of the exciton spin properties, and also the dynamics of the excitonic magnetic polaron (EMP), where the exchange interaction between the magnetic ions and the photoexcited carriers contributes significantly to the polaron binding energy [3, 4]. Generally speaking, after laser excitations, especially under nonresonant excitation, the photo-excited carriers will lose their phase and spin memories within several hundred femto-seconds. When the Coulomb force binds electrons and holes to form excitons, exciton spins can take all kinds of configurations, namely, both for allowed and dipole forbidden transitions [5]. The excitons with spin configurations for dipole forbidden transitions, so called dark excitons, can live relatively long, since they are energetically lower than the excitons for allowed transitions in a zero magnetic field due to the electron–hole exchange interaction. These dark excitons can recombine with the assistance of a spin-flip process. They can also relax to lower energy states for nonradiation recombinations. To distinguish from the dark excitons, we will call excitons with spin configurations for dipole allowed transitions 0749–6036/99/010383 + 06

$30.00/0

c 1999 Academic Press

384

Superlattices and Microstructures, Vol. 25, No. 1/2, 1999

Table 1: Field dependence of PL decay time. Samples

τ (B = 0 T) (ns)

τ (B = 6.5 T) (ns)

Cd0.8 Mn0.2 Te Cd0.88 Mn0.12 Te/Cd0.82 Mg0.18 Te (L W = 22 nm) Cd0.88 Mn0.12 Te/Cd0.82 Mg0.18 Te (L W = 3.7 nm) CdTe/Cd0.76 Mn0.24 Te (L W = 2.7 nm) Cd0.86 Mg0.14 Te

0.37 0.26 0.29 0.1 0.24

0.12 0.084 0.18 0.076 0.28

τ (B = 6.5 T) /τ (B = 0 T) (ns) 0.32 0.32 0.62 0.76 1.16

PL intensity

Energy (eV) 1.938 1.879 1.824 3000 Cd Mn Te/Cd Mg Te 0.88 0.12 0.82 0.18 2000 1000 0

1.771

1.722

T= 4.2 K, B= 0 T

0

Time

1

2

3

4

Fig. 1. A transient PL image in the Cd0.88 Mn0.12 Te/Cd0.82 Mg0.18 Te SQWs. The transitions around 1.867 and 1.797 eV correspond to the emissions from the wells with widths 3.7 and 22 nm, respectively.

as bright excitons. As the lifetime of the dark excitons is longer than the bright excitons, so they serve as a reservoir for bright excitons. The spin-flip scattering of the dark excitons will obviously increase the apparent PL decay time of the bright excitons. For semimagnetic semiconductors, however, the relative energy positions between the dark and bright excitons can change due to the giant Zeeman splitting in magnetic fields. It may reduce the thermal occupation of the dark excitons greatly and, therefore, shorten the apparent PL decay time drastically in magnetic fields. To test the above assumption, we will present our time-resolved PL results on the Cd1−x Mnx Te epilayers, Cd1−x Mnx Te/Cd1−y Mg y Te and CdTe/Cd1−x Mnx Te single quantum wells and Cd1−y Mg y Te epilayers with decreasing Zeeman splitting of the band-edge transitions. We will show that the reduction of the apparent PL lifetime is only determined by the Zeeman splitting and hence the Mn2+ content within the exciton radius.

2. Sample parameters and experimental setup Cd1−x Mnx Te, Cd1−y Mg y Te epilayers and CdTe/Cd1−x Mnx Te, Cd1−x Mnx Te/Cd1−y Mg y Te single quantum wells (SQWs) were grown by MBE method on a (100)-oriented GaAs substrate with x varying from 12

Peak energy (eV)

Superlattices and Microstructures, Vol. 25, No. 1/2, 1999

1.80

Cd0.88Mn0.12Te/Cd0.82Mg0.18Te

1.79 1.78

385

Lw= 22 nm

1E= 41 meV

1.77

Peak energy (eV)

1.76 1.86

Cd0.88Mn0.12Te/Cd0.82Mg0.18Te

1.85 1.84

1E= 30 meV

Lw= 3.7 nm

1.83

Peak energy (eV)

1.82

1.76

T= 4.2 K CdTe/Cd0.76Mn0.24Te

1.75 1.74 1.73

1E= 7 meV

Lw= 2.7 nm

1.72 0

2

4 B (T)

6

8

Fig. 2. Zeeman energy shift of Cd0.88 Mn0.12 Te/Cd0.82 Mg0.18 Te SQWs with 22 nm wells (open circles), 3.7 nm wells (filled circles) and a CdTe/Cd0.76 Mn0.24 Te SQW with a 2.7 nm well (filled triangle).

to 24% and y from 14 to 18%. Before growing the epilayers and the SQWs, a 20 nm-thick ZnTe buffer and a 600 nm-thick CdTe buffer are introduced to release the lattice strain and lattice mismatch. On top of the buffer layer, a 1 µm-thick Cd1−x Mnx Te or Cd1−y Mg y Te layer was deposited. SQWs were separated by 30 nm-thick barriers, so that coupling between the adjacent wells is negligible. Two SQWs samples are used in this study, one is a CdTe/Cd0.76 Mn0.24 Te SQW with a 2.7 nm-thick well and the other is Cd0.88 Mn0.12 Te/Cd0.82 Mg0.18 Te SQWs with 3.7 nm- and 22 nm-thick well. For the wide well, the exciton wavefunction is totally confined in the well, while for the narrow well, the wavefunction penetrates into the barriers. Time-resolved photoluminescence (TRPL) was carried out in the Faraday configuration with samples mounted strain-free in a superconducting magnetic cryostat with fields up to 7 T. Samples were immersed in a liquid helium bath. They were excited by a frequency doubled laser pulse at 395 nm from a mode-locked titanium-sapphire laser (repetition rate 76 MHz and pulse width 120 fs), pumped by an argon ion laser. The spectra were taken by a Hamamatsu streak camera C4334 with 5 ps time resolution.

3. Results and discussion Figure 1 shows a typical TRPL image in Cd0.88 Mn0.12 Te/Cd0.82 Mg0.18 Te SQWs taken by the streak camera. The emission peaks around 1.857 and 1.797 eV are due to the recombination of heavy hole excitons in quantum wells with well widths 3.7 and 22 nm, respectively. A series of TRPL spectra is taken as a function of the magnetic fields of the samples listed in Table 1. The peak shift of the time-integrated spectra as a function of

386

Superlattices and Microstructures, Vol. 25, No. 1/2, 1999

B =0 T B = 6.5 T

A

Cd0.88Mn0.20Te

PL intensity (a.u.)

B

Cd0.88Mn0.12Te/Cd0.82Mg0.18Te Lw= 22 nm

C

Cd0.88Mn0.12Te/Cd0.82Mg0.18Te Lw= 3.7 nm

D

CdTe/Cd0.76Mn0.24Te Lw= 2.7 nm

E Cd0.86Mg0.14Te –0.2 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Time (ns) Fig. 3. PL intensity decay of the Cd0.8 Mn0.2 Te, the Cd0.88 Mn0.12 Te/Cd0.82 Mg0.18 Te SQWs, the CdTe/Cd0.76 Mn0.24 Te SQW and the Cd0.86 Mg0.14 Te epilayer both with (dashed line) and without (solid line) a magnetic field. The dashed lines in B, indicate the two, exponential PL decay.

the external magnetic fields is plotted in Fig. 2 for the two SQW samples. The Zeeman shift originates from the exchange interaction between the photo-excited carriers and the Mn ions within an exciton effective Bohr orbit. At the magnetic field of 6.5 T, the red shift of the 22 nm, wide well of sample Cd0.88 Mn0.12 Te/Cd0.82 Mg0.18 Te reaches 41 meV, while the 3.7 nm well reaches only 30 meV due to the penetration of the carrier wavefunction into the nonmagnetic barrier material. In the CdTe/Cd0.76 Mn0.24 Te SQWs, the central part of the excitonic wavefunction locates in the nonmagnetic CdTe well, so that the exchange interaction contribution to the Zeeman splitting becomes small. Still due to the strong confinement within a very narrow well width of L W = 2.7 nm, the carrier wavefunction penetrates into the magnetic barriers. The influence of Mn ion spins in the barrier layer can still be detected as a 7 meV spectral red shift although this is much less pronounced. Figure 3 shows the PL intensity decay under the nonresonant excitation for the Cd0.80 Mn0.20 Te epilayer, the Cd0.88 Mn0.12 Te/Cd0.82 Mg0.18 Te SQWs, the CdTe/Cd0.76 Mn0.24 Te SQW and the Cd0.86 Mg0.14 Te epilayer. The best-fit one-exponential decay times, both with and without a magnetic field, are listed in Table 1. Except for the CdTe/Cd0.76 Mn0.24 Te SQW sample, where the band-edge excitons are in the binary CdTe compound well so that the lifetime is relatively short due to fewer band-edge fluctuations, all other samples show relatively the same exciton lifetime in a zero magnetic field. Experimentally, we found that the exciton lifetime reduces drastically by applying a magnetic field when their Zeeman splitting is large in both the Cd0.80 Mn0.20 Te

Superlattices and Microstructures, Vol. 25, No. 1/2, 1999

387

A –1/2

1/2

1/2 C

2 1

4

–1/2 1

3 V –3/2

3/2

2

–3/2

4 3 3/2

B 1, 4 2, 3

4 ex.

B =0 T

3 2 1 B >0 T

Fig. 4. Schematic diagram of Zeeman splitting for carriers A, in a one-particle picture and B, the corresponding excitonic spin splitting in a two-particle picture in magnetic fields for a quantum well sample. The spin splitting of excitons in a zero magnetic field denoted as ex. in B, is due to the electron–hole exchange interaction. The solid transition line denotes the allowed transition while the dashed line denotes the dipole forbidden transition.

epilayer and Cd0.88 Mn0.12 Te/Cd0.82 Mg0.18 Te SQWs, whereas the reduction of the exciton lifetime is not so obvious for the CdTe/Cd0.76 Mn0.24 Te SQW. The reduction of the exciton lifetime for the Cd0.86 Mg0.14 Te epilayer is almost not detectable, instead an increase of the exciton lifetime is observed. This lifetime increase may be related to an increase of the carrier localization in the magnetic fields. Compared with the Zeeman shift in Fig. 2, we can only conclude that the reduction rate of the excitonic lifetime is only determined by the Zeeman splitting of the excitons in the magnetic fields. The above experimental results can be qualitatively understood with the schematic diagram shown in Fig. 4. As is well known, the carriers lose their spin memories after laser excitation in an extremely short time. Therefore, the Coulomb force binds electrons and holes with all possible spin configurations to form excitons which are denoted as transitions from 1 to 4 in Fig. 4, among which the spin combination of 2 and 3 are for forbidden dipole transitions. The excitons with spin configurations of 2 and 3 form dark excitons with a binding energy lower than the excitons with spin configurations of 1 and 4 for allowed transitions due to electron–hole exchange interaction [5]. Therefore, the thermal occupation of these dark excitons is larger than that of bright excitons of 1 and 4; it serves as a large exciton reservoir. These dark excitons will convert to bright excitons if the spin of the electron, or of the hole, is flipped by spin scattering. This spin-flip process converts the long life dark excitons to bright excitons, so that the apparent bright exciton lifetime is prolonged. The assumption of the additional supplement of the bright excitons from the dark excitons might be corroborated by the fine behavior of the PL intensity decay. For all samples we have measured, we found that the exciton decay time can be much better fitted by a two-exponential decay function than a one-exponential decay function, which can be easily identified by the nonlinear PL intensity decay curve in a log scale shown in Fig. 3. In magnetic fields, however, due to the giant Zeeman splitting, the dark excitons raise their energies. They locate energetically higher than the excitons with the spin configuration of 1 in Fig. 4. Therefore, thermodynamically, the exciton reservoir, which may be densely populated in a zero magnetic field, no longer exists. The apparent lifetime of excitons will be reduced, compared with the results given in Table 1. The above qualitative analysis explains our experimental results quite reasonably, however, it still faces one

388

Superlattices and Microstructures, Vol. 25, No. 1/2, 1999

quantitative challenge. Since the inter-cross of exciton states between 1 and 2 in Fig. 4 should happen in rather low magnetic fields, less than 1 T. However, the experiments show that the exciton lifetime reduces in even higher magnetic fields, similar to the behavior of the spectral shift due to giant Zeeman splitting. Therefore, we believe that a detailed discussion of the lifetime reduction should include the excitonic magnetic polaron effect. In the frame of formation of the magnetic polarons, the carrier spins will polarize the Mn spins and reduce the system energy. Therefore, a spin flip of a photo-excited carrier will be accompanied by the spin flip of the surrounding Mn spins. As a result, a carrier with its spin correlated to the spin of Mn is hard to flip. This might explain the gradual evolution of the exciton lifetime reduction in semi-magnetic materials in magnetic fields.

4. Conclusion We have measured the exciton lifetime in a Cd0.80 Mn0.20 Te epilayer, Cd0.88 Mn0.12 Te/Cd0.82 Mg0.18 Te SQWs, CdTe/Cd0.76 Mn0.24 Te SQWs and Cd0.86 Mg0.14 Te epilayer structures. We have found that the lifetime reduces strongly in a magnetic field for samples with giant Zeeman splittings. The observed phenomena are attributed to the spin flip of dark excitons which have a dense population in a zero magnetic field, while deplete in a high magnetic field due to the cross over of their energies above the energy of the excitons for dipole allowed transitions.

References [1] }J. K. Furdyna, J. Appl. Phys. 64, R29 (1988). [2] }Y. Oka and K. Yanata, J. Lumin. 70, 35 (1996). [3] }D. R. Yakovlev, W. Ossau, L. Landwehr, R. N. Bicknekk-Tassius, A. Waag, S. Schmeusser, and I. N. Uraltsev, Solid State Commun. 82, 29 (1992). [4] }G. Mackh, W. Ossau, D. R. Yakovlev, A. Waag, and G. Landwehr, Phys. Rev. B49, 10248 (1994). [5] }K. Cho, S. Suga, W. Dreybrodt, and F. Willmann, Phys. Rev. B11, 1512 (1974).