Determination of subband energy levels of double quantum well AlGaAs lasers by photoreflectance and self-excited electron Raman scattering

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Physica E 21 (2004) 793 – 797 www.elsevier.com/locate/physe

Determination of subband energy levels of double quantum well AlGaAs lasers by photore(ectance and self-excited electron Raman scattering Wataru Susakia;∗ , Soichiro Ukawaa , Ssatoshi Yokotaa , Nobuhito Ohnoa , Hideo Takeuchib , Yoshitugu Yamamotob , Ryo Hattorib , Akihiro Shimab , Yutaka Mihashib a Osaka

Electro-Communication University, Neyagawa 572-8530, Japan b Mitsubishi Electric Corp., Itami 664-8641, Japan

Abstract Subband energy levels of AlGaAs double quantum well (QW) layer structure with a separate con8nement scheme are determined by photore(ectance at room temperature. Also subband energy levels are compared with those determined by the self-excited electron Raman scattering of lasers fabricated from the same QW structure but with di9erent waveguide thickness outside the QWs. Electron subbands, heavy hole subbands, light hole subbands, determined both measurements, are in good agreement. ? 2003 Published by Elsevier B.V. PACS: 75.41.Xv; 72.45.Yu; 71.78Ag Keywords: Quantum well; Subband energy level; AlGaAs laser; Photore(ectance; Electron Raman scattering

1. Introduction It is a key issue to determine the subband energy levels of electrons and holes in quantum well (QW) lasers for design improvement of laser characteristics such as very low-temperature sensitive threshold current by complete con8nement of injected carriers in QWs. We have found the self-excited electronic Raman scattering (ERS) spectra at room temperature above threshold from InGaAs and InGaP QW lasers, and ∗

Corresponding author. Tel.: +81-72-824-1131; fax: +81-72-824-0014. E-mail address: [email protected] (W. Susaki). 1386-9477/$ - see front matter ? 2003 Published by Elsevier B.V. doi:10.1016/j.physe.2003.11.202

determined the subband levels of electrons and holes [1,2]. In this paper, subband energy levels of AlGaAs double quantum well (DQW) layer structure with a separate con8nement scheme are determined by photore(ectance and compared with those determined by the self-excited ERS of lasers fabricated from the same DQW structure but with di9erent waveguide thickness outside the DQWs. Subband energy levels determined by both measurements are in good agreement. 2. Layer structure and laser characteristics The layer structure of the DQW with a separate con8nement scheme is grown on GaAs substrate by

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MOVPE. Two 8 nm-Al0:1 Ga0:9 As-QWs are formed in Al0:35 Ga0:65 As waveguide/barrier layers. These layers are not intentionally doped and surrounded by n- and p-Al0:48 Ga0:52 As cladding layers (¿ 1 m). The thickness of Al0:48 Ga0:52 As waveguide layers is 12 nm. The barrier layer of Al0:35 Ga0:65 As waveguide adjacent to the surrounded by QWs is 8 nm thick. Lasers are fabricated from the same DQW structure but with thicker waveguide thickness (300 nm) outside the QWs. They have a 5 m loss-guide stripe and 900 m cavity length. Lasing wavelength and threshold current are 787:3 nm (1:574 eV) and 31 mA, respectively at 300 K. Fabrication and characteristics of the laser is described elsewhere [3].

mass in the direction of F and is an arbitrary phase factor. Table 1 shows the energy gaps and the e9ective masses of electrons and holes for Alx Ga1−x As. Electron e9ective mass m∗e (x) is calculated by following equations: m∗e (x) = 0:067 + 0:087x:

(2)

m∗hh; z (x),

m∗lh; z (x)

Heavy holes and light holes for growth direction are calculated by the following equations. Luttinger–Kohn parameters, 1 and 2 , for AlGaAs are postulated to be linearly interpolated between GaAs (x = 0) and AlAs (x = 1). m∗hh; z (x) = m0 =( 1 − 2 2 ); m∗lh; z (x) = m0 =( 1 + 2 2 ):

3. Photoreectance Photore(ectance of the layer is measured using a stabilized 532 nm SHG YAG laser modulated at 720 Hz by an optical chopper to modulate electric 8eld by generating photo-excited carriers in p-cladding layers. Carriers in the waveguides, the barrier, and QW layers and adjacent to regions of n- and p-cladding layers are depleted. It will be reasonable to assume that the electric 8eld F in the non-doped layers (waveguide/QW /barrier/QW/waveguide) is constant. The electric 8eld F is determined from Frantz– Keldish oscillation (FKO) frequencies in the waveguide layer and depleted cladding layers. The position of the mth extreme in the FKOs are given by [4]
 m = 43 {(2mr )1=2 (Em − Eg )3=2 =q˝F} + ; m = 0; 1; 2; 3; : : : ;

(1)

where Em is the photon energy of the mth extrema, Eg is the band gap, mr is the reduced interband e9ective

(3)

The reduced interband e9ective mass in the direction of F are calculated as 1=mrhh (x) = 1=m∗e (x) + 1=m∗hh; z (x):

(4)

Energy gap of Alx Ga1−x As (x ¡ 0:45) at 300 K is calculated by the following equation: Eg = 1:424 + 1:247x:

(5)

Fig. 1 shows the photore(ectance spectrum at room temperature. The FKOs are clearly observed in Al0:48 Ga0:52 As cladding layers and Al0:35 Ga0:65 As waveguide layers. The electric 8eld F is determined as 90 kV=cm from Eq. (1). The subband levels and wave functions are calculated by a 8nite di9erence numerical method of the SchrOodinger equation using the band o9set ratio PEC =PEG = 0:64 determined from the ERS as be described Section 2.3. It shows that the subband levels under electric 8eld F = 90 kV=cm are two electron subbands, e1 and e2, three heavy hole subbands hh1, hh2, hh3, two light hole subbands lh1 and lh2 in the QWs by numerical calculation. Also

Table 1 Energy gaps and e9ective masses of electrons, heavy holes, and light holes used for calculations Layer

x

Eg [meV]

m∗e (x)=m0

m∗hh; z (x)=m0

m∗lh; z (x)=m0

mrhh (x)=m0

1

2

QW Waveguide/barrier Cladding GaAs AlAs

0.10 0.35 0.48 0 1

1.549 1.860 1.985 1.424 2.16

0.076 0.097 0.109 0.067 0.15

0.348 0.384 0.403 0.333 0.478

0.114 0.165 0.135 0.094 0.902

0.060 0.077 0.086 0.056 0.28

6.51 5.65 5.22 6.85 3.45

1.96 1.60 1.42 2.1 0.68

W. Susaki et al. / Physica E 21 (2004) 793 – 797

795

Fig. 1. Photore(ectance of the DQW AlGaAs layers.

4. Self-excited ERS and band o set determination Self-excited Raman scattering spectra are observed from lasers above threshold [1,2]. Fig. 2 is the ERS spectra by changing the angles of the polarizer at 60 mA. The laser intensity at 1:574 eV is strongly TE polarized (angle 90◦ ). Some of the ERS spectra are clearly seen by changing the angle of the polarizer from 90◦ (TE) to 0◦ (TM). The ERS spectra are not observed at the angle 0◦ (TM). The ERS spectra are given by ER = EL + n1 (e2 − e1) + n2 (hh1 − hh2) + n3 (hh2 − hh3) + n4 (lh1 − lh2) + p1 ELO; GaAs + p2 ELO; AlAs ; n1 ; n2 ; n3 ; n4 ; p1 ; p2 = 0: ± 1; ±2; ±3; : : : ;

(6)

1.E+01 1.E+00 angle 0

1.E-01

angle 10 angle 22.5 angle 45 angle 90(TE)

1.E-02 intensity [a. u.]

because of the electric 8eld, there is an electric subband e2 near e2 in the QW for the layer structure shown in Fig. 1. This is because the energy in the waveguide is almost same to the e2 in the quantum well by built-in electric 8eld. Peaks are assigned as, A: e1–hh1, A0 : e1–lh1, B: e1-hh2, C: (e2 =e2)-hh1, C0 : (e2 =e2)-lh1, DFK1 is the 8rst FKO of D in the waveguide layers, and EFK1 and EFK2 are the 8rst and second FKO of E in the cladding layers. The (e2 =e2)-e1 is decreased from 105 to 91 meV, which shows a good agreement between both measurements.

1.E-03 1.E-04 1.E-05 1.E-06 1.E-07 1.E-08 1.E-09 1.3

1.4

1.5

1.6 1.7 1.8 photon energy [eV]

1.9

2

2.1

Fig. 2. Self-excited Raman scattering spectra of lasers at 60 mA.

where EL (=e1–hh1) is the lasing energy, ELO; GaAs and ELO; AlAs are the GaAs-like type and the AlAs-like type LO phonon energies, respectively. The electric 8eld F in QWs and waveguides/barrier is negligibly small by very high injected carriers at threshold in the laser. At threshold injected carrier densities are ∼ 5 × 1018 =cm3 , energy subband level e2 is below the electron quasi-Fermi levels, and hole subband level hh3 is above the hole quasi-Fermi level. This means anti-Stokes transitions are possibly observed in the self-excited ERS. Firstly, by using Eq. (1), (e2–e1) is determined to be 106 meV. We could estimate approximately the subband energy

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120

e2-e1 (meV)

115 110 105 100

Calculated Experimental

95 90 0.5

0.6 0.7 conduction band offset ratio

0.8

Fig. 3. Band o9set ratio determined from the self-excited Raman.

Table 2 Subband energy levels determined by the PR and the ERS

e2–e1 hh1–hh2 hh2–hh3 lh1–lh2 ELOGaAs ELOAlAs

PR

ERS

Calculated

91 33

105 32.5 52 77 35 41

105 33 57 77 35.6 45.5

di9erence (e2–e1) by calculating the SchrOodinger equation for the layer structure of Fig. 1. Fig. 3 shows the calculated values of (e2–e1) as a function of PEc =PEg . PEc =PEg is 0.64 for (e2–e1) = 105 meV. By setting PEc =PEg = 0:64, we calculate the subband energy levels with the e9ective masses shown in Table 1. Calculated subband energy levels are e1 = 42 meV, e2=147 meV, hh1=11 meV, hh2=44 meV, hh3 = 91 meV, lh1 = 28 meV, lh2 = 95 meV. On the other hand, there are two kinds of LO phonons to be considered, GaAs- and AlAs-like types. AlAs and GaAs type LO phonon energies are given as 44:63 + 8:78x − 3:32x2 (meV), 36:25 − 6:55x + 1:79x2 (meV), respectively. For x=0:1, LO phonon energies are AlAs type: ELOAlAs = 45:5 meV and GaAs type: ELOGalAs = 35:6 meV. Forbidden subband transitions such as e1– hh2 e2–hh1 and e2 –hh1 are possible due to the electric 8eld determined by the photo-re(ectance is and the ERS are summarized in Table 2. The discrepancy of e2–e1 is due to F in the layers. F is negligibly small because of extremely high-injected carrier density (∼ 5×1018 =cm3 ) at threshold in lasers.

However, in the PR measurements electrons could exist in both n- and p-side wells because of a large conduction band o9set under the built-in 8eld at zero bias, due to the built-in 8eld, holes are localized only in the p-side well. The electron–hole transition responsible for the PR occurs in the p-side well. In the well, there appear a electron energy level e2 originated from the n-side waveguide layer due to the energy of the conduction band edge of the layer become almost same to the e2 in the p-side well under the built-in 8eld by the numerical analysis of the SchrOodinger equation. 5. Conclusion The subband energy di9erence between the second electron subband level e2 and the 8rst electron subband level e1 is 91 meV. We have determined e2–e1 as 106 meV in ERS from lasers fabricated from the wafer. The discrepancy of e2–e1 is due to F in the layers. F is negligibly small because of extremely high-injected carrier density (∼ 5 × 1018 =cm3 ) at threshold in lasers. The subband levels and wave functions are calculated by a 8nite di9erence numerical method of the SchrOodinger equation using the band o9set ratio PEC =PEG = 0:64 determined from the ERS. The e2–e1 is decreased by the Stark shift from 105 to 91 meV, which is a good agreement between both measurements. Self-excited electronic Raman scattering (ERS) spectra with the eQciency of 10−4 ∼ 10−6 are observed above threshold in 780 nm-AlGaAs quantum well lasers at 300 K. They are assigned to electron intersubband transition between the 8rst and the second subbands in the quantum well accompanied with longitudinal optical phonon scattering. Conduction band o9set ratio is determined as 0.64 by comparing the experimental data to a numerical calculation by changing the ratio using SchrOodinger equation. Self-excitation by laser itself in the con8ned waveguide is a great advantage to realize eQcient stimulated ERS in quantum well lasers. Acknowledgements The authors gratefully acknowledge to Mr. T. Atsuta and Mr. K. Izawa for the self-excited ERS

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measurements in early stage of these works as their undergraduate studies. References [1] W. Susaki, et al., Proc. SPIE 4287 (2001) 176.

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[2] W. Susaki, et al., Proceedings of the International Symposium on Compound Semiconductors, Tokyo, 2001, pp. 227–230. [3] A. Shima, et al., Proc. SPIE 4248 (2001) 48. [4] H. Shen, M. Dutta, J. Appl. Phys. 62 (1995) 2151.