Free induction decay and quantum beat of excitons in ZnSe

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CRYSTAL G R O W T H

ELSEVIER

Journal of Crystal Growth 138 (1994) 805-808

Free induction decay and quantum beat of excitons in ZnSe T. Saiki ,,a,b, K. Takeuchi a K. Ema a M. Kuwata-Gonokami K. Ohkawa c, T. Mitsuyu c

a

a Department of Applied Physics, Faculty of Engineering, The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113, Japan b KanagawaAcademy of Science and Technology, Sakado, Takatsu-ku, Kawasaki, Kanagawa 213, Japan c Central Research Laboratories, Matsushita Electric Company, Ltd., Moriguchi-shi, Osaka 570, Japan

Abstract

We study coherent transient phenomena of excitons using femtosecond time-resolved four-wave-mixing f i R FWM) in two types of high quality thin films of ZnSe; one is a homo-epitaxial film (1.2/xm thickness) and the other is a very thin (50 nm) hetero-epitaxial film on GaAs substrate. Free induction decay (FID) behavior of the third-order polarization is clearly observed. We obtained the same values of exciton dephasing time from the temporal measurements, the decay time of FID, and the frequency domain measurements, analyses of reflection spectra. This implies that the excitons in ZnSe films are homogeneous. In the thin film sample, we observe a beat signal in time-integrated and time-resolved FWM. Based on the perturbational calculation, we conclude that the beat originates from the quantum interference of heavy- and light-hole excitons.

1. Introduction

The development of tunable short pulse lasers enables us to study the coherent transient phenomena, such as free induction decay (FID), photon echo (PE) [1] and quantum beats (QB) [2-4], in semiconductors where the induced polarization decays much faster than in atoms. These phen o m e n a have so far been studied extensively in GaAs quantum wells. Although the growth technique of G a A s epitaxial layers has been well established, the strict control of inhomogeneous broadening of excitons is still difficult. This is because the binding energy of excitons in GaAs quantum well is so small that the small imperfection of the structures such as well width fluctua-

* Corresponding author.

tion causes the significant effect on the optical responses of excitons. Thus we often encounter the sample dependent p h e n o m e n a even qualitatively. On the other hand, the epitaxial growth technique of wide gap I I - V I semiconductors has been remarkably improved. In wide gap I I - V I semiconductors, the excitons are very stable and the resonant effects of excitons can be clearly observed. We observed a very large nonlinear phase shift at the exciton resonance in ZnSe films [5], which is then applied to the demonstration ot all optical serial to parallel conversion up to s u b - T b i t / s [6]. In this paper, we report the coherent transient nonlinear responses of excitons in high quality ZnSe films using high repetition rate tunable sub-picosecond pulses. We measure temporal responses of the third-order polarization in fourwave mixing. We use two types of thin film sam-

0022-0248/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSDI 0022-0248(93)E0453-E

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7". Saiki et al. /Journal of Crystal Growth 138 (1994) 805-808

pies, one is the homo-epitaxial ZnSe film, where we observe the FID behavior of excitons. The other is the very thin film grown on GaAs substrate, where we observed the QB signal of heavyand light-hole excitons. Based on these results, we discuss the intrinsic nature of the excitonic third-order nonlinearity.

Pulse 2 J ~ t .

Reference/~ Pulse ,J\ 2. E x p e r i m e n t s

Lens

Pulse 1.,~.

i Half Mirror

High quality ZnSe thin films samples are grown by molecular beam epitaxy method. One is a homo-epitaxial ZnSe film of 1.2 /zm thickness grown on ZnSe substrate (sample I) [7]. The other is a ZnSe film with thickness of 50 nm grown on GaAs substrate (sample II) [8]. In sample II, the valence band splits into a heavy- and a light-hole bands caused by the biaxial strain. In Fig. 1, we show the reflection spectra. A heavyand a light-hole exciton are clearly observed in sample II (Fig. lb). Sample I is free from any strain and we observe a single exciton band, as shown in Fig. la. We use the second harmonics of a CW passively mode-locked Ti:sapphire laser (Coherent Mira-900). This laser generates highrepetition rate pulses suitable for the detection of weak signals. The pulse duration is 100 fs and the spectral width is 13 meV. We use the spatially parametric type two-pulse degenerate four-wavemixing configuration as shown in Fig. 2. The

Fig. 2. Schematic drawing of the experimental configuration of TR-FWM and TI-FWM in reflection geometry.

sample is excited by two pulses with wave vectors k I and k 2. They are set to be co-polarized. The interval between two pulses, T, is positive when pulse 1 follows pulse 2. The third-order nonlinear signal in the direction 2 k ] - k 2 is detected in a reflection-type geometry [9]. We measure the temporal responses of the signal using the field correlation method. We denote this as time-resolved four-wave-mixing (TR-FWM) signal which is a function of the reference delay time, t. The temporal resolution is determined by the pulse width, about 150 fs. We define the time zero, t = 0, as the time when pulse 1 reaches the sample. All the experiments are performed at 10 K. The excitation density is estimated as 2 × 1015 cm -3. In this excitation density region, the intensity of the FWM signal shows a third-order power dependence of the input pulses.

3. R e s u l t s a n d d i s c u s s i o n

3.1. Sample I; observation of free induction decay of exciton (b) ~

heavy-hole

I

2.79

I

I

2.80 2.81 2.82 Photon Energy ( eV )

2.83

Fig. 1. Reflection spectra of sample ] (a) and of sample II (b).

Fig. 3 shows T R - F W M signals of sample I as a function of reference delay t at excitation delay T = 0 ps and 1 ps. The signals appear at the time when pulse 1 reaches the sample and the signals decay exponentially. The decay times are independent of the excitation delay T. We performed a third-order perturbational calculation based on the elementary excitation picture which we have recently applied to the

806

T. Saiki et al. /Journal

of Crystal Growth 138 (1994) 805-808

ples, one is the homo-epitaxial ZnSe film, where we observe the FID behavior of excitons. The other is the very thin film grown on GaAs substrate, where we observed the QB signal of heavyand light-hole excitons. Based on these results, we discuss the intrinsic nature of the excitonic third-order nonlinearity.

2. Experiments High quality ZnSe thin films samples are grown by molecular beam epitaxy method. One is a homo-epitaxial ZnSe film of 1.2 pm thickness grown on ZnSe substrate (sample I> [7]. The other is a ZnSe film with thickness of 50 nm grown on GaAs substrate (sample II) [S]. In sample II, the valence band splits into a heavy- and a light-hole bands caused by the biaxial strain. In Fig. 1, we show the reflection spectra. A heavyand a light-hole exciton are clearly observed in sample II (Fig. lb). Sample I is free from any strain and we observe a single exciton band, as shown in Fig. la. We use the second harmonics of a CW passively mode-locked Ti: sapphire laser (Coherent Mira-900). This laser generates highrepetition rate pulses suitable for the detection of weak signals. The pulse duration is 100 fs and the spectral width is 13 meV. We use the spatially parametric type two-pulse degenerate four-wavemixing configuration as shown in Fig. 2. The

(a)

Fig. 1. Reflection

spectra

2.81 Energy

of sample

sample is excited by two pulses with wave vectors k, and k,. They are set to be co-polarized. The interval between two pulses, T, is positive when pulse 1 follows pulse 2. The third-order nonlinear signal in the direction 2k, -k, is detected in a reflection-type geometry [93. We measure the temporal responses of the signal using the field correlation method. We denote this as time-resolved four-wave-mixing (TR-FWM) signal which is a function of the reference delay time, t. The temporal resolution is determined by the pulse width, about 150 fs. We define the time zero, t = 0, as the time when pulse 1 reaches the sample. All the experiments are performed at 10 K. The excitation density is estimated as 2 X 101” cm -3. In this excitation density region, the intensity of the FWM signal shows a third-order power dependence of the input pulses.

3.1. Sample Z; observation of free induction decay of exciton

w

2.80 Photon

of the experimental configuration in reflection geometry.

3. Results and discussion

“Is

2.79

Fig. 2. Schematic drawing of TR-FWM and TI-FWM

2.82

2.83

( eV ) I (a) and of sample

II (b).

Fig. 3 shows TR-FWM signals of sample I as a function of reference delay t at excitation delay T = 0 ps and 1 ps. The signals appear at the time when pulse 1 reaches the sample and the signals decay exponentially. The decay times are independent of the excitation delay T. We performed a third-order perturbational calculation based on the elementary excitation picture which we have recently applied to the

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T. Saiki et aL /Journal of Crystal Growth 138 (1994) 805-808

depth is the most important measure to distinguish the two types of beats. Third-order perturbational calculation predicts the 100% modulation depth for QB under the condition of equal spectral weights of heavy-hole exciton and lighthole exciton. In the case of CB, however, the modulation depth is 14% at the maximum within the possible range of T2 from the reflection spectrum, which is 0.9 < h / 2 7 r T 2 < 1.7 meV [11]. In Fig. 5a, we observe a modulation depth of more than 60%, which is much larger than the limit obtained from the CB regime. Fig. 5b shows the results of T R - F W M at various excitation delay T (indicated by the arrow in Fig. 5a). As the case depicted in Fig. 3, we again observe the free-induction-decay type responses. The signals start at t = 0 and the profiles are independent of T. The perturbational calculation of T R - F W M predicts that there is a qualitative difference between the two regimes. In the QB regime, the signal is promptly emitted when pulse 1 arrives, and the peak position is independent of T. In the CB regime, on the contrary, the rise and the peak time of the signals vary with T [3]. Our observations coincide with the behavior expected for QB. Thus, we conclude that the excitons in our thin film sample are also free from the inhomogeneous broadening effect, and the observed beating in Figs. 5a and 5b are the results of the quantum interferences of heavy- and light-hole excitons in ZnSe.

4. Conclusion We demonstrate the time-resolved FWM signal in high quality ZnSe films by using stable femtosecond optical pulses. FID behavior of the third-order polarization is clearly observed. We also observe the beat signal in time-integrated and time-resolved FWM. By perturbational calculation with the three-level system and two independent two-level systems, we conclude that the

origin of the beat is the quantum interference of heavy- and light-hole excitons, not the classical polarization interference. Our results assure that the excitons in ZnSe films have no inhomogeneity. Thus the ZnSe excitons are suitable for a rigorous comparison between experiments and theories especially to prove the various many body phenomena predicted by the theory, such as intrinsic photon echo [10].

5. Acknowledgments The authors are grateful to Professor E. Hanamura for enlightening discussions. This work is supported by a Grant-in-Aid for General Scientific Research and a Grant-in-Aid for Developmental Scientific Research from the Ministry of Education, Science and Culture, Japan.

6. References [1] S.T. Cundiff and D.G. Steel, IEEE J. Quantum Electron. QE-28 (1992) 2423. [2] K. Leo, E.O. G6bel, T.C. Damen, J. Shah, S. SchmittRink, W. Schiller, J.F. Miiller, K. Kfhler and P. Ganser, Phys. Rev. B 44 (1991) 5726. [3] M. Koch, J. Feldmann, G. von Plessen, E.O. G6bel, P. Thomas and K. K6hler, Phys. Rev. Lett. 69 (1992) 3631. [4] B.F. Feuerbacher, J. Kuhl, R. Eccleston and K. Ploog, Solid State Commun. 74 (1990) 1279. [5] T. Saiki, K. Takeuchi, M. Kuwata-Gonokami, K. Ohkawa and T. Mitsuyu, Appl. Phys. Lett 60 (1992) 192. [6] K. Ema, M. Kuwata-Gonokami and F. Shimizu, Appl. Phys. Lett. 59 (1991) 2799. [7] K. Ohkawa, T. Karasawa and T. Mitsuyu, J. Vac. Sci. Technol. B 9 (1991) 1934. [8] K. Ohkawa, T. Mitsuyu and O. Yamazaki, Phys. Rev. B 38 (1988) 12465. [9] T. Saiki, K. Takeuchi, M. Kuwata-Gonokami, T. Mitsuyu and K. Ohkawa, J. Crystal Growth 117 (1992) 802. [10] M. Lindberg, R. Binder and S.W. Koch, Phys. Rev. A 45 (1992) 1865. [11] K. Takeuchi, T. Saiki and M. Kuwata-Gonokami, 18th Int. Quantum Electronics Conf., Vienna, 1992.