AlAs multiple quantum wells

AlAs multiple quantum wells

ARTICLE IN PRESS Journal of Luminescence 108 (2004) 195–199 Enhancement of coherent LO phonons by quantum beats of excitons in GaAs/AlAs multiple qu...

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ARTICLE IN PRESS

Journal of Luminescence 108 (2004) 195–199

Enhancement of coherent LO phonons by quantum beats of excitons in GaAs/AlAs multiple quantum wells O. Kojima*, K. Mizoguchi, M. Nakayama Department of Applied Physics, Graduate School of Engineering, Osaka City University, Sugimoto 3-3-138, Sumiyoshi-ku, Osaka 558-8585, Japan

Abstract We have investigated the dynamical properties of the coherent GaAs-like longitudinal optical (LO) phonon and the quantum beat of excitons in GaAs/AlAs multiple quantum wells with different splitting energies of the heavy-hole and light-hole excitons by using a reflection-type pump–probe technique. It has been found that the coherent GaAs-like LO phonon in the multiple quantum well is remarkably enhanced as the splitting energy approaches to the LO phonon energy of GaAs. The pump-energy dependence of the intensity of the coherent GaAs-like LO phonon is similar to that of the excitonic quantum beat in the multiple quantum wells with the splitting energy nearly equal to the LO phonon energy of GaAs. We conclude that the enhancement of the coherent LO phonon is induced by the coupling of the excitonic quantum beat with the coherent GaAs-like LO phonon through the longitudinal polarization. r 2004 Elsevier B.V. All rights reserved. PACS: 63.20.Kr; 73.21.Fg; 78.47.+P Keywords: Quantum beat; Coherent phonon; Quantum-confined Stark effect; Pump–probe technique; GaAs/AlAs multiple quantum wells

1. Introduction Coherent phonons in multiple quantum wells (MQWs) and superlattices (SLs) have been extensively studied, for a review see Refs. [1,2]. In MQWs and SLs, the electronic and optical properties are controllable by changing the structural parameters. Dekorsy et al. [3] observed an enhancement of the amplitude of the coherent longitudinal optical (LO) phonon by tuning the frequency of the Bloch oscillation to that of the *Corresponding author. Tel./fax: +81-6-6605-2739. E-mail address: [email protected] (O. Kojima).

coherent LO phonon in GaAs/AlGaAs SLs. It is known that the longitudinal polarization from the excitonic quantum beat is induced by the quantum-confined Stark effect (QCSE) [4,5], and that the LO phonons also have longitudinal polarization. When the splitting energy of the heavy-hole (HH) and light-hole (LH) excitons (DEHH–LH) is tuned to the LO phonon energy (ELO), we can expect that the coherent LO phonons will be enhanced by the coupling with the excitonic quantum beat through the longitudinal polarization. In this work, we have investigated the dynamical properties of the coherent GaAs-like LO phonon and the quantum beat of the HH and LH excitons in three samples of GaAs/AlAs

0022-2313/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jlumin.2004.01.042

ARTICLE IN PRESS O. Kojima et al. / Journal of Luminescence 108 (2004) 195–199

MQWs with different HH–LH splitting energies by using a reflection-type pump–probe technique. We have found that the coherent LO phonon is markedly enhanced in the sample with DEHH–LH nearly equal to ELO. We discuss the enhancement of the coherent LO phonon in terms of the coupling of the coherent LO phonon with the excitonic quantum beat, which is demonstrated by the pumpenergy dependence of the coherent oscillations.

10K (18,18) MQW

δ (∆R/R0 )/δt (arb. units)

196

Pump Energy = 1.690 eV (25,25) MQW

3. Results and discussion Fig. 1 shows the oscillatory profiles in the time derivatives of the time-resolved reflectivity changes

x 100 Pump Energy = 1.653 eV

(35,35) MQW

2. Experiment The samples are three (GaAs)m/(AlAs)m MQWs with m=18, 25, and 35 grown on a (0 0 1) GaAs substrate by molecular-beam epitaxy, where the subscript m denotes the thicknesses of the constituent layers in monolayer units (0.283 nm). Hereafter, we will identify these samples by ‘‘(m,m) MQW’’. The splitting energies of the HH and LH excitons, which were determined by photoluminescence excitation spectroscopy, are 38, 27 and 15 meV in the (18,18), (25,25), and (35,35) MQWs, respectively. It is noted that DEHH–LH in the (18,18) MQW is nearly equal to the GaAs ELO value of 36.5 meV. The quantum beat of the HH and LH excitons and the coherent GaAs-like LO phonon were measured at 10 K by a reflection-type pump– probe technique. The laser source was a modelocked Ti:sapphire pulse laser delivering 100-fs pulses at a repetition rate of 82 MHz. The pump and probe beams were orthogonally polarized to each other in order to minimise the pump–beam contribution to the probe beam. The pump-power density was kept at about 0.2 mJ/cm2. Assuming that the excitonic absorption coefficient is about 1  104 cm 1 [6], the photoexcited carrier density is estimated to be 4.5  1015 cm 3. The time-domain signals were extracted by numerically differentiating the time-resolved reflectivity changes in order to subtract a slowly varying background resulting from the relaxation of photoexcited carriers.

x 25

x 500 Pump Energy = 1.570 eV

0.0

1.0

2.0 3.0 Time Delay (ps)

4.0

Fig. 1. Oscillatory profiles extracted using time derivatives of the time-resolved reflectivity changes at 10 K in the (18,18), (25,25), and (35,35) MQWs. The pump energy corresponds to the center energy between the HH and LH excitons in each sample.

in the (18,18), (25,25), and (35,35) MQWs at 10 K. The energy of the laser pulse was tuned to the center energy between the HH and LH excitons in each sample. The oscillatory profiles observed in all the samples consist of two components. One is a strong oscillatory component occurring within 1.5 ps and the other is a weak oscillatory component lasting over 4.0 ps. The periods of the strong component are 109, 153, and 275 fs for the (18,18), (25,25), and (35,35) MQWs, respectively, while that of the weak component is 113 fs for each sample. Although the amplitude of the strong component is almost the same for each sample, that of the weak component depends remarkably on the sample structure. The decay time of the strong component, obtained by fitting with a damped harmonic oscillation, is almost the same in each sample. Since the periods of the strong and weak components in the (18,18) MQW are very close to each other, the weak component seemingly extends the tail of the strong component. In order to clarify the origin of each oscillatory component, we divided the time-domain signals into two time ranges, (0.2–1.5 ps) and (1.5–4.0 ps) and performed the Fourier transform (FT) of each. In Fig. 2, the solid curves show the FT spectra of the time-domain signals in the time

ARTICLE IN PRESS O. Kojima et al. / Journal of Luminescence 108 (2004) 195–199

FT Intensity (arb. units)

x 50 (25,25) MQW

Pump Energy = 1.653 eV

x 1000

(35,35) MQW

Pump Energy = 1.570 eV

x 40000

0

2

4

6 8 10 Frequency (THz)

12

14

Fig. 2. FT spectra of the time-domain signals shown in Fig. 1 for two time ranges: (0.2–1.5 ps) (solid lines) and (1.5–4.0 ps) (broken lines) in the (18,18), (25,25), and (35,35) MQWs.

range from 0.2 to 1.5 ps. The peak frequencies are 9.2, 6.5, and 3.6 THz, corresponding to DEHH–LH in the (18,18), (25,25), and (35,35) MQWs, respectively. Therefore, the strong components in Fig. 1 are attributed to the quantum beats of the HH and LH excitons. The broken curves in Fig. 2 show the FT spectra of the time-domain signals in the time range from 1.5 to 4.0 ps. The peak frequency in each sample has the constant value of 8.8 THz, corresponding to ELO of GaAs. Thus, the weak components in Fig. 1 arise from the coherent GaAs-like LO phonon. The intensity associated with the coherent LO phonon varies with DEHH–LH, while that of the excitonic quantum beat is almost constant. The ratio of the FT intensity of the coherent LO phonon to the excitonic quantum beat in the (18,18) MQW and that in the (25,25) MQW are, respectively, about 650 and 35 times larger than that in the (35,35) MQW. Thus, the enhancement factor of the coherent LO phonon is increased as DEHH–LH approaches to ELO. Oscillatory structure is seen in the FT spectra of the excitonic quantum beats for the (18,18) and (25,25) MQWs. Since in these cases the coherent LO phonon signal is not negligible in

the time region of the excitonic quantum beat, the overlap of the two signals creates the oscillatory structure in the FT spectrum. In order to investigate the origin of the remarkable enhancement of the coherent LO phonon in the (18,18) MQW, the oscillatory profiles were observed at various pump energies. We performed the time-partition FT of the timedomain signals for the two time ranges already cited. Fig. 3 (a) shows the integrated intensities of the FT bands of the excitonic quantum beat and the coherent LO phonon as a function of pump energy in the (35,35) MQW with DEHH–LH { ELO. The intensity of the excitonic quantum beat reaches a peak at the center energy between the HH and LH excitons, while that of the coherent LO phonon shows a broad peak around the LH exciton energy. In Fig. 3(b), the integrated intensities of the FT bands of the excitonic quantum beat and the coherent LO phonon are

FT intensity (arb. units)

[0.2 - 1.5 ps] [1.5 - 4.0 ps]

HH

LH

x 10000 1.56

1.58 1.60 Photon Energy (eV) HH

1.62

(18,18) MQW

Quantum Beat

LH

Coherent LO phonon

1.66

(b)

(35,35) MQW Quantum Beat

Coherent LO phonon

(a) FT intensity (arb. units)

(18,18) MQW Pump Energy = 1.690 eV

197

x 500

1.68

1.70

1.72

Photon Energy (eV)

Fig. 3. Integrated intensities of the FT bands of the excitonic quantum beat and of the coherent LO phonon as a function of pump energy in (a) the (35,35) MQW and (b) the (18,18) MQW. The dotted lines indicate the HH and LH exciton energies for each sample.

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plotted as a function of pump energy in the (18,18) MQW with DEHH LH EELO : The intensities of both the excitonic quantum beat and the coherent LO phonon reach a peak at the center energy between the HH and LH excitons. It should be noted that the pump-energy dependence of the FT intensity of the coherent LO phonon in the (18,18) MQW is considerably different from that in the (35,35) MQW. The intensity of the excitonic quantum beat in each of these MQWs exhibits a similar pumpenergy dependence. It is well known that the excitonic quantum beat is strongest at the center energy between the HH and LH excitons. For the pump-energy dependence of the coherent LO phonon, if the photoexcited carriers do participate in the generation of the coherent LO phonon, the intensity will be resonantly enhanced at the exciton energies. The resonance profile of the coherent LO phonon in the (35,35) MQW indicates some contribution of the photoexcited carriers to the generation process. However, there is no resonance effect around the HH exciton energy. The conclusive reason for the absence of the HHexciton resonance remains an open question. One of the possible reasons may be the difference in the Bloch function forms of the HH and LH. The LH Bloch function has a growth-direction component, while the HH Bloch function has only an in-plane component. The growth-direction component of the LH Bloch function may cause resonance enhancement of the coherent LO phonon. On the other hand, the pump-energy dependence of the coherent LO phonon in the (18,18) MQW cannot be explained by this resonance effect, because the intensity of the coherent LO phonon reaches a peak at the center energy between the HH and LH excitons, which is similar to the pump-energy dependence of the excitonic quantum beat. This fact suggests that the coherent LO phonon couples with the excitonic quantum beat. Finally, we discuss the coupling mechanism. Under an electric field along the growth direction of the MQW, a longitudinal polarization is induced by the excitonic quantum beat [4,5]. The origin of this longitudinal polarization is attributed to the QCSE resulting in symmetry breaking of the envelope functions [7]. In general, there is a

built-in electric field because of pinning of the Fermi level at the surface in a semiconductor. Thus, it is expected that longitudinal polarization is induced by the excitonic quantum beat, even though there is no applied electric field in these samples. Since the coherent LO phonon in the MQW also has longitudinal polarization along the growth direction, the excitonic quantum beat will couple with the coherent LO phonon via the longitudinal polarization where the energies of two coherent oscillations approach each other. In summary, the excitonic quantum beat acts as a driving force to the coherent LO phonon under the coupling conditions leading to the enhancement of the coherent LO phonon. 4. Conclusions We have investigated the coherent GaAs-like LO phonon and the quantum beat of the HH and LH excitons in the (GaAs)m/(AlAs)m MQWs with m=18, 25, and 35 by using a reflection-type pump–probe technique. We find that the amplitude of the coherent GaAs-like LO phonon in the MQW is markedly enhanced with as DEHH–LH approaches ELO. Moreover, the pump-energy dependence of the intensity of the coherent LO phonon in the (18,18) MQW with DEHH LH EELO is similar to that of the excitonic quantum beat, with the intensity strongest at the center energy between the HH and LH excitons. These results demonstrate that the enhancement of the coherent LO phonon is induced by the coupling between the excitonic quantum beat and the coherent LO phonon. Acknowledgements This work was partially supported by a Grantin-Aid for the Scientific Research (No. 15340102) from the Ministry of Education, Culture, Sports, Science, and Technology of Japan.

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