Physica E 42 (2010) 2648–2651

Contents lists available at ScienceDirect

Physica E

1386-94

doi:10.1

� Corr

E-m

journal homepage: www.elsevier.com/locate/physe

Upconversion of photoluminescence due to subband resonancesin a GaAs/AlAs multiple quantum well structure

Takayuki Hasegawa a,�, Satoshi Okamoto b, Masaaki Nakayama b

a Department of Material Science, University of Hyogo, Koto, Kamigori, Ako-gun, Hyogo 678-1297, Japanb Department of Applied Physics, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan

a r t i c l e i n f o

Article history:

Received 12 August 2009

Received in revised form

3 October 2009

Accepted 6 October 2009Available online 14 October 2009

Keywords:

Upconversion

Photoluminescence

Subband resonance

Multiple quantum well

GaAs/AlAs

77/$ - see front matter & 2009 Elsevier B.V. A

016/j.physe.2009.10.003

esponding author. Tel.: +8179158 0372.

ail address: t_hase@sci.u-hyogo.ac.jp (T. Hase

a b s t r a c t

We have investigated the upconversion of photoluminescence (PL) due to subband resonances in a

simple GaAs(15.3 nm)/AlAs(4.5 nm) multiple quantum well embedded in a p–i–n diode structure. The

systematic measurements of the PL spectra and the calculated results of the interband transition

energies as a function of electric field strength reveal that the PL bands from the electron subbands with

n=3 (E3) and n=4 (E4) sharply appear under the first-nearest-neighbor resonance conditions between

the E1 and E3 subbands and the E1 and E4 subbands, respectively, owing to the carrier injection to the

E3 and E4 subbands from the E1 subband. This result indicates that the resonant tunneling due to the

subband resonance is a dominant mechanism for the carrier population in the higher lying subbands.

Utilizing these subband resonances, we have demonstrated the upconversion of PL from the E3 and E4

subbands under the excitation condition of the fundamental interband transition between the E1 and

the n=1 heavy-hole subbands.

& 2009 Elsevier B.V. All rights reserved.

1. Introduction

In semiconductor quantum well (QW) structures, electric fieldeffects on subband states have attracted great interest infundamental physics and optoelectronic applications. One of theprominent phenomena on the subband states under application ofelectric field in multiple QW (MQW) structures is a resonanttunneling between spatially separated subbands [1–3]. If anelectrostatic potential difference between adjacent QWs justagrees with an energy spacing between the first (n=1) and higherlying quantized (nZ2) subbands, the n=1 subband state in agiven QW resonantly couples with the higher lying subband in theQW on the lower potential side, which results in the resonanttunneling between the relevant subband states. Under thesubband resonance condition, the resonant tunneling causes acarrier injection to the higher lying subband from the n=1subband. From the viewpoint of photoluminescence (PL), thesubband resonance leads to an upconversion of PL from the higherlying subband owing to the carrier injection from the n=1subband to the higher lying subband, which is also called anti-Stokes PL [4–8]. Although the upconversion of PL due to thesubband resonance was investigated [7,8], asymmetric double QWstructures were typically used to achieve an efficient carrierinjection for the upconversion. It is noted that little has beenknown about the upconversion of PL in a simple MQW structure.

ll rights reserved.

gawa).

In this work, we have investigated the upconversion of PL dueto subband resonances in a simple GaAs(15.3 nm)/AlAs(4.5 nm)MQW embedded in a p–i–n diode structure, where the intrinsiclayer consists of the MQW. The electric-field-strength dependenceof energies of various optical transitions between the electronsubbands and the heavy-hole (HH) subbands was calculated usinga transfer-matrix (TM) method with Airy functions [9]. From thesystematic PL measurements as a function of electric fieldstrength under the excitation energy higher than the E4-relatedtransition energy, we found that the PL band from the E3 (E4)subband sharply appears under the first-nearest-neighbor sub-band resonance condition between the E1 and E3 (E4) subbands.On the basis of this finding, we have demonstrated the upconver-sion of PL from the E3 and E4 subbands under the excitationcondition of the fundamental interband transition between the E1subband and the n=1 HH subband.

2. Experimental

The sample used in this work was GaAs(15.3 nm)/AlAs(4.5 nm)MQW with 20 periods embedded in a p–i–n diode structuregrown on an n-type (0 0 1) GaAs substrate by molecular-beamepitaxy, where the n (p) layer is a Si (Be)-doped Al0.5Ga0.5As layerwith a thickness of 0.8mm (0.2mm). The value of electric fieldstrength F was evaluated from F=(Vb�Va)/Li, where Vb is the built-in voltage that is 1.3 V in the present case, Va is an applied biasvoltage, and Li is the total thickness of the undoped layers. In PLmeasurements, the light sources were 633 nm line of a He–Ne

T. Hasegawa et al. / Physica E 42 (2010) 2648–2651 2649

laser and a continuous-wave Ti:sapphire laser. The excitationpower density was �4 W/cm2 in both the excitation sources. ThePL emitted from the sample was detected with a cooled multi-channel detector attached to a 32 cm single monochromator. Thespectral resolution was 0.3 nm. All the optical measurements wereperformed at 5 K using a closed-cycle He cryostat.

3. Results and discussion

First, we describe the calculated results of the electric-field-strength dependence of the interband transition energies usingthe TM method with Airy functions [9] in order to clarify theprofiles of subband resonances. In the TM calculation, themodeled MQW consists of 9 sets of GaAs(15.6 nm)/AlAs(4.8 nm)sandwiched by semi-infinite Al0.5Ga0.5As layers. The thicknessesof the QW and barrier layers were slightly changed from thedesigned values [GaAs(15.3 nm)/AlAs(4.5 nm)] in order to adjustthe calculated results to experimental transition energies. Inthis TM calculation, we used the band parameters according toRef. [10].

Fig. 1 shows the calculated transition energies of the variousinterband transitions as a function of electric field strength, wherethe notation of Ene(m)HH nh indicates the interband transitionbetween the neth electron subband and the nhth HH subband, m

in the parentheses is the distance between QWs having theelectron and HH subbands in units of MQW period, and the sign of+ indicates the QW in the higher potential side. In Fig. 1, the low-energy shift of the Ene(0)HH1 transition with an increase inelectric field strength is due to the quantum-confined Stark effect[11]. The quantum-confined Stark effect causes the symmetrybreaking of the envelope functions of electron and hole states. Thesymmetry breaking of the envelope functions leads to the changesof interband transition energies and the transition oscillator

E1(0)HH1

E2(0)HH1

E3(0)HH1

E4(0)HH1

E1(+1)HH1

Ene

rgy

(eV

)

E1(+1)-E3(0)

E1(+1)-E4(0)

0 50 100 150 200 2501.4

1.5

1.6

1.7

1.8

1.9

Electric Field (kV/cm)

Fig. 1. Calculated results of the interband transition energies as a function of

electric field strength, where the notation of Ene(m)HH nh indicates the interband

transition between the Ene subband and the nhth HH subband. m in the

parentheses is the distance between QWs having the electron and HH subbands

in units of MQW period, and the sign of + indicates the QW in the higher potential

side.

strengths in addition to the appearances of the optical transitionsbetween electron and hole subbands with different quantumnumbers (neanh). Note that the optical transition in neanh isusually forbidden. The energy crossings indicated by the circlesmean the occurrence of the first-nearest-neighbor subbandresonances between the electron subbands with differentquantum numbers: the subband resonances of E1(+1)–E3(0)and E1(+1)–E4(0) in this case. It is expected that the carrierinjection from the E1(+1) subband to the E3(0) and E4(0)subbands occurs at �80 and �150 kV/cm, respectively.

Fig. 2 shows the PL spectra as a function of electric fieldstrength with a step of �5 kV/cm at the excitation energy of1.959 eV, where the intensities of the PL spectra in the energyregion higher than 1.60 eV are magnified by a factor of 100 inorder to make them clear. The identification of the interbandtransition is based on the calculated results of the electric-field-strength dependence of the transition energy shown in Fig. 1.Note that the E2(0)HH1-PL band could not be observed becausethe tail of the strong E1(0)HH1-PL band hides the E2(0)HH1-PLband. In Fig. 2, the E1(0)HH1-PL band appears in a wide range ofelectric field strength, while the E3(0)HH1-PL and E4(0)HH1-PLbands in the energy region higher than 1.60 eV sharply appear at�89 and �143 kV/cm, respectively. In addition, the E3(0)HH1-PL band appears again at �143 kV/cm. Thus, the electric-field-strength dependence of the E3(0)HH1-PL and E4(0)HH1-PLbands is considerably different from that of the E1(0)HH1-PLband.

Hereafter, we discuss the electric-field-strength dependence ofthe PL intensities from the viewpoint of the subband resonancediscussed in Fig. 1. Fig. 3 shows the integrated intensities of theE1(0)HH1-PL, E3(0)HH1-PL, and E4(0)HH1-PL bands as a function ofelectric field strength. From Fig. 1, the TM calculation predicts thatthe subband resonances of E1(+1)–E3(0) and E1(+1)–E4(0) occur at�80 and �150 kV/cm, respectively. These subband resonances

PL I

nten

sity

(ar

b. u

nits

)

1.65 1.7 1.75 1.8

F (kV/cm)

E1(0)HH1E4(0)HH1

E3(0)HH10

100

50

150

200

250

1.45 1.5 1.55 1.6

Photon Energy (eV)

Fig. 2. PL spectra as a function of electric field strength with a step of �5 kV/cm in

the GaAs(15.3 nm)/AlAs(4.5 nm) MQW at the excitation energy of 1.959 eV at 5 K,

where the intensities of PL spectra in the energy region higher than 1.60 eV are

magnified by a factor of 100 in order to make them clear.

PL I

nten

sity

(ar

b. u

nits

)

E3(0)HH1(×200)

E4(0)HH1

(×100)

E1(0)HH1

(offset +3)

0 100 150 200 250

0

3

6

9

12

Electric Field (kV/cm)

50

Fig. 3. Integrated intensities of the PL bands shown in Fig. 2 as a function of

electric field strength, where the offset value of 3 is added to the result of the

E1(0)HH1-PL band, and the intensities of the E3(0)HH1-PL and E4(0)HH1-PL bands

are magnified by factors of 200 and 100, respectively. Photon Energy (eV)PL

Int

ensi

ty (

arb.

uni

ts)

Exc.laser

0

110meV

190meV

E4(0)HH1

E3(0)HH1

250

50

100

150

200

F (

kV/c

m)

1.5 1.55 1.6 1.65 1.7 1.75 1.8

Fig. 4. PL spectra as a function of electric field strength with a step of �5 kV/cm in

the GaAs(15.3 nm)/AlAs(4.5 nm) MQW at 5 K and the excitation laser spectrum.

The excitation energy corresponds to the E1(0)HH1 transition energy.

T. Hasegawa et al. / Physica E 42 (2010) 2648–26512650

cause the carrier injection to the E3(0) and E4(0) subbands from theE1(+1) subband, which leads to the appearance of the E3(0)HH1-PLand E4(0)HH1-PL bands. Furthermore, the subband resonances ofE1(+1)–E3(0) and E1(+1)–E4(0) result in the decrease of theintensity of the E1(0)HH1-PL band because of the reduction of thecarrier population in the E1 subband. This scenario is consistentwith the electric-field-strength dependence of the PL intensitiesshown in Fig. 3, namely, the peaky profiles of the intensities of theE3(0)HH1-PL and E4(0)HH1-PL bands associate with the dip profilesof the intensity of the E1(0)HH1-PL band. The dip profile of theE1(0)HH1-PL band at �50 kV/cm seems to be due to the E1(+1)–E2(0) resonance expected from Fig. 1. The E2(0)HH1-PL band ishidden by the tail of the strong E1(0)HH1-PL band. The calculatedelectric field strengths at which the subband resonances occurslightly deviate from the observed results. This deviation may bedue to some inhomogeneity of the internal electric field. Thegradual decrease of the intensity of the E1(0)HH1-PL band with anincrease in electric field strength seems to be due to a decrease ofthe transition probability resulting from the quantum-confinedStark effect. Note that the E3(0)HH1-PL band reaches maximumagain under the E1(+1)–E4(0) resonance condition. This behaviorsuggests the occurrence of the relaxation of carriers from the E4subband to the E3 subband, which makes the carrier population inthe E3 subband.

The experimental results shown in Figs. 2 and 3 indicate that thesubband resonances of E1(+1)–E3(0) and E1(+1)–E4(0) are adominant mechanism for the carrier population in the E3 and E4subbands. Therefore, we expect that the upconversion-PL bandsrelated to the E3(0)HH1 and E4(0)HH1 transitions appear byadjusting the excitation energy to the E1(0)HH1 transition energyunder the E1(+1)–E3(0) and E1(+1)–E4(0) resonance conditions.Fig. 4 shows the PL spectra as a function of electric field strengthwith a step of �5 kV/cm and the excitation laser spectrum. Notethat the excitation energy corresponds to the E1(0)HH1 transitionenergy. In Fig. 4, it is evident that the E3(0)HH1-PL and E4(0)HH1-PL bands appear in the energy region higher than the excitationenergy. This result clearly demonstrates the occurrence of theupconversion of PL. The origins of the appearance of the E3(0)HH1-PL and E4(0)HH1-PL bands are due to the E1(+1)–E3(0) andE1(+1)–E4(0) resonances, respectively, discussed above. The

upconversion energies observed in Fig. 4 are �110 and �190 meVfor the E3(0)HH1-PL and E4(0)HH1-PL bands, respectively. Theseenergies are higher than the typical value of upconversion energy inasymmetric double QW structures [7,8]. Consequently, utilizing thesubband resonances of E1(+1)–E3(0) and E1(+1)–E4(0), wedemonstrate the upconversion of PL that corresponds to theappearance of the E3(0)HH1-PL and E4(0)HH1-PL bands under theexcitation of the fundamental E1(0)HH1 transition.

4. Conclusions

We have investigated the upconversion of PL due to subbandresonances in the simple GaAs(15.3 nm)/AlAs(4.5 nm) MQWstructure under applied electric field conditions. In addition, theinterband transition energies as a function of electric fieldstrength were calculated using the TM method in order to clarifythe profiles of the subband resonances. Under the first-nearest-neighbor subband resonance conditions of E1(+1)–E3(0) andE1(+1)–E4(0), we have found that the E3(0)HH1-PL andE4(0)HH1-PL bands sharply appear under the excitation conditionof the fundamental E1(0)HH1 transition, respectively. This factdemonstrates the occurrence of the upconversion of PL. Themechanism of the upconversion of PL is the efficient carrierinjection to the E3 and E4 subbands from the E1 subband owing tothe resonant tunneling resulting from the subband resonances.Thus, the subband resonances dominate the upconversion of PL inthe MQW.

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