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doi:10.1016/j.jlu

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Journal of Luminescence 128 (2008) 1056–1058

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Excitonic quantum beat at the mini-Brillouin-zone boundaryin a GaAs/AlAs superlattice

Takayuki Hasegawaa,�, Kohji Mizoguchib, Masaaki Nakayamaa

aDepartment of Applied Physics, Graduate School of Engineering, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, JapanbDepartment of Physical Science, Graduate School of Science, Osaka Prefecture University, Gakuen, Naka-ku, Sakai, Osaka 599-8531, Japan

Available online 4 November 2007

Abstract

We have investigated excitonic quantum beats (QBs) at the mini-Brillouin-zone boundary (p-point) in a GaAs (6.8 nm)/AlAs (1.1 nm)

superlattice by using a femtosecond reflection-type electro-optic sampling technique. Photoreflectance spectroscopy was adopted to

characterize the optical transition energies of the heavy-hole (HH) and light-hole (LH) excitons at the mini-Brillouin-zone center (G-point) and the p-point. By systematically changing the pump-pulse energy in the energy region from the G-point exciton to the p-pointexciton, we have succeeded to observe the QB of the HH and LH excitons at the p-point in addition to the ordinary QB at the G-point.The observed frequencies agree with the values estimated from the energy difference between the relevant two excitons. The decay time of

the QB signal at the p-point is much shorter than that at the G-point. This behavior reflects a very fast relaxation process of the p-pointexcitons in the miniband dispersion.

r 2007 Elsevier B.V. All rights reserved.

Keywords: Superlattice; Miniband; Quantum beat; GaAs/AlAs

In a superlattice (SL) with sufficiently thin barriers, theelectronic states in individual quantum wells couple witheach other to form a miniband with a finite energy width.As a result of the miniband formation, there are two typesof critical-point transition: one is the transition at the mini-Brillouin-zone center (kz ¼ 0; G-point), and the other is thetransition at the mini-Brillouin-zone boundary (kz ¼ p/D;p-point), where D is a period of the SL [1]. Until now, thequantum beat (QB) between the heavy-hole (HH) andlight-hole (LH) excitons at the G-point have beenintensively investigated [2]; however, the observation ofthe QB between the p-point excitons peculiar to theminiband formation has not been reported until now. Thisis our motivation of the present work.

We have focused on the excitonic QB at the p point in aGaAs (6.8 nm)/AlAs (1.1 nm) SL at 10K. The excitonic QBwas observed by using a reflection-type electro-opticsampling (REOS) technique [3]. Photoreflectance (PR)spectroscopy was used to characterize the excitonic

e front matter r 2007 Elsevier B.V. All rights reserved.

min.2007.10.021

ing author. Tel./fax: +81 6 6605 2739.

ess: hasegawa@a-phys.eng.osaka-cu.ac.jp (T. Hasegawa).

transition energies at the G point and p point. Thisspectroscopy is much sensitive to detect optical transitionsat singular points of density of states [4,5]. From theenergies of the HH and LH excitons consisting of the firstquantized (n=1) subbands at the G and p points, H11(G),L11(G), H11(p), and L11(p), we can evaluate the frequen-cies of the relevant QBs. By systematically changing thepump-pulse energy in the energy region from the G-pointexciton to the p-point exciton, we have succeeded toobserve the QB of the H11(p) and L11(p) excitons inaddition to the usually-observed QB at the G point. Wediscuss the characteristics of the newly observed excitonicQB at the p point, comparing with those of the usual QB atthe G point.The sample used in the present work is a GaAs (6.8 nm)/

AlAs (1.1 nm) SL with 46 periods grown by molecular-beam epitaxy. In femtosecond time-domain REOS mea-surements, the laser source was a mode-locked Ti:sapphirepulse laser with a pulse duration of �70 fs and a repetitionrate of 80MHz. The pump laser was focused onto thesample surface with a spot diameter of �0.2mm. Thepump power was kept at �10mW: the power density of

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20

15

10

5

0

10-3

ΔReo

/R0

2.01.00.0

Time Delay (ps)

×2

×20 1.645eV

1.635 eV

1.618 eV

1.610 eV

1.600 eV

Fig. 2. Time-domain signals measured with the REOS at various pump

energies in the GaAs (6.8 nm)/AlAs (1.1 nm) SL at 10K.

FT I

nten

sity

(ar

b. u

nits

)

20151050

Frequency (THz)

1.645 eV

1.635 eV

1.618 eV

1.610 eV

1.600 eV

×3

×30

×150

×30000

Γ π

Fig. 3. FT spectra of the time-domain oscillatory signals shown in Fig. 2,

where the vertical dashed lines at 5.1 and 8.5THz indicate the expected

values of the frequencies of the excitonic QBs at the G- and p-points,

T. Hasegawa et al. / Journal of Luminescence 128 (2008) 1056–1058 1057

�0.4 mJ/cm2. In PR measurements, the probe beam wasproduced by combination of a halogen lamp (100W) and asingle monochromator with a resolution of 0.5 nm. Thepump beam was a 632.8 nm line of a He-Ne laser choppedat 630Hz. The PR spectrum was measured by a conven-tional lock-in technique. All the measurements wereperformed at 10K.

Fig. 1 shows the PR spectrum at 10K, where the arrowsindicate the transition energies calculated from the well-established Kronig-Penney model in a framework of aneffective-mass approximation including the band non-parabolicity of the electron and LH [6], and the labels ofG and p mean the transitions at the G and p points in theminiband dispersion, respectively. The transition energiesestimated from the line-shape analysis of the PR spectrumbased on the third derivative functional form [7] that isusually used are 1.597, 1.618, 1.618, and 1.653 eV for theH11(G), L11(G), H11(p), and L11(p) transitions, respec-tively. From this estimation, we expect that the frequenciesof the QB of the H11 and L11 excitons at the G- and p-points are �5.1 and �8.5 THz, respectively. It is noted thatthe frequency of the excitonic QB at the p-point is muchhigher than that at the G-point.

Fig. 2 shows the time-domain signals of the REOS atvarious pump energies, where the magnified oscillatorysignals at 1.635 and 1.645 eV, which are numericallyextracted from the original signals, are depicted in orderto make the oscillatory profile clear. In the pump-energyrange from 1.600 to 1.635 eV, the period of the oscillatorysignal is almost constant, though the oscillatory intensityremarkably changes with the pump energy. It is noted thatthe period of the oscillatory signal at 1.645 eV is clearlyshorter than that at the other pump energies. This behaviorsuggests the change of the sort of the QB.

In order to clarify the characteristics of the observedoscillation signals, we performed the Fourier transform(FT) of the time-domain signals. Fig. 3 shows the FTspectra of the time-domain oscillatory signals shown inFig. 2. In Fig. 3, the vertical dashed lines at 5.1 and 8.5 THzindicate the expected values of the frequencies of the QBsof the H11 and L11 excitons at the G- and p-points,respectively. In the pump energy range from 1.600 to

10

5

0

-5

Inte

nsity

(ar

b. u

nits

)

1.681.661.641.621.601.58

Photon Energy (eV)

H11L11

×20

(Γ) (π)

(Γ) (π)

Fig. 1. PR spectrum in the GaAs (6.8 nm)/AlAs (1.1 nm) SL at 10K. The

arrows indicate the calculated transition energies, and the labels of G and pmean the transitions at the G- and p-points in the miniband dispersion,

respectively.

respectively.

1.618 eV, which corresponds to the energy region betweenthe H11(G) and L11(G) excitons, the peak frequency of theFT spectrum almost agrees with the expected value of theQB of the H11(G) and L11(G) excitons. The oscillationintensity exhibits a maximum at 1.610 eV that correspondsto the center energy (1.608 eV) between the H11(G) andL11(G) excitons. Therefore, this FT peak is due to theexcitonic QB at the G-point. With a further increase ofpump energy, the profiles of the FT spectra changedrastically. At the pump energy of 1.635 eV, the FTspectrum becomes broader, and the high frequency tailreaches the expected frequency of the QB, 8.5 THz, at thep-point. At the pump energy of 1.645 eV, the FT spectrum,

ARTICLE IN PRESST. Hasegawa et al. / Journal of Luminescence 128 (2008) 1056–10581058

which exhibits a broad shape, has the peak around8.5 THz. It is noted that the pump energies of 1.635 and1.645 eV correspond to the energy region between theH11(p) and L11(p) excitons. The results described abovedemonstrate the observation of the excitonic QB at the p-point. In a pump energy region higher than 1.645 eV, wecould not observe the p-point QB. This is due to the factthat the simultaneous excitation of the H11(p) and L11(p)excitons is not achieved at the higher pump energy that isvery close to the L11(p)-exciton energy. In Figs. 2 and 3,the amplitude (intensity) of the excitonic QB at the p-pointis much weaker than that at the G-point. This is due to avery short decay time of the p-point QB in comparisonwith that of the G-point QB.

Finally, we briefly discuss the decay time of the excitonicQBs at the G- and p-points. In Fig. 2, it is clear that thedecay time of the QB at the p-point is shorter than that atthe G-point, which is related to the broader shape of the FTspectrum at 1.645 eV. The decay times estimated fromfitting the time-domain signals are �270 and �100 fs forthe G-point and p-point QBs at the 1.600 and 1.645 eV,respectively. In general, the excitons and carriers at a finitemomentum space have a very fast relaxation process, suchas phonon scattering, which results in the relaxationprocess of the excited states [2]. Thus, the shorter decaytime of the excitonic QB at the p-point is attributed toreflect the very fast relaxation process of the p-pointexcitons in the miniband dispersion.

In summary, we have succeeded to detect the excitonicQB at the p-point in the GaAs (6.8 nm)/AlAs (1.1 nm) SL byusing the femtosecond REOS technique at 10K in additionto the usually observed QB at the G-point. The energies ofthe HH and LH excitons at the G- and p-points, from whichwe estimate the frequencies of the relevant QBs, werecharacterized with PR spectroscopy. It is found that thedecay time of the QB at the p-point is much shorter thanthat at the G-point, which reflects the very fast relaxationprocess of the p-point excitons in the miniband dispersion.

This work was supported by the grant-in-aid forscientific research (no. 18340090) from Japan Society forthe Promotion of Science.

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