- Email: [email protected]
Al0.3Ga0.7As multiple-quantum-wells
Solid State Communications, Vol. 71, No. 12, pp. 1137-1140, 1989. Printed in Great Britain.
0038-1098/89 $3.00 + ,00 Pergamon Press plc
ANISOTROPY OF QUANTUM-SIZE EFFECTS IN (0 0 1)- AND (l 1 I)-ORIENTED GaAs/A103Ga0vAs MULTIPLE-QUANTUM-WELLS M. Nakayama, I. Kimura and H. Nishimura Department of Applied Physics, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka 558, Japan and T. Komatsu and Y. Kaifu Department of Physics, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka 558, Japan (Received 25 April 1989 by J. Kanamori)
We have investigated the anisotropy of quantum-size effects in (0 0 1)and (1 1 1)-oriented GaAs/A103Ga0.TAs multiple-quantum-wells (MQW's) with the GaAs layer thickness ranging from 15 to 150 A and the fixed AIGaAs layer thickness of 200A by using photoluminescence and photoluminescence-exciton spectroscopy at 4.2 K. The light-hole-exciton energy is not affected by the quantization direction whole over the thickness range of the GaAs layer, while the heavy-hole-exciton energy of the (1 1 1)-MQW is lower than that of the (0 0 1)-MQW with the same structure. The energy difference increases from ~ 2 to ~ 24 meV as the GaAs layer thickness decreases from 150 to 15 A, which is consistent with the results calculated on the basis of an effective-mass approximation assuming the heavy-hole effective-mass anisotropy of mh~, (O01):mhh (1 1 1) = 0.34:0.9 for GaAs.
THE electronic and optical properties of GaAs/ A103xGa~ _~As quantum-well (QW) structures have been studied intensely over last fifteen years; however, only several works [1-7] have been reported for non(0 0 1)-oriented QW structures because of the difficulty of the crystal growth. Hayakawa et al. reported a low threshold-current behaviour in (1 1 1)-oriented GaAs/ Al0.3~Ga~__~As QW lasers [1]; this suggests that non(00 1)-oriented QW structures are very valuable for optical devices. It is well known that the valence band structures of zinc-blende-type semiconductors are anisotropic [8]; therefore, determination of the effective-mass anisotropy is very important in device applications. Measurements of the energies of heavyhole and light-hole excitons in the non-(0 0 l)-oriented QW structures by photoluminescence (PL) and photoluminescence-excitation (PLE) spectroscopies enable us to determine the anisotropy. The results obtained in the previous works, where only a few samples were used, indicate the anisotropy of the heavy-hole effective-mass of GaAs: mhh (0 0 1) : mhh (1 1 1) = 0.34 : 0.9 by Hayakawa et al. [2], 0.34 : 0.7 by Molenkamp et al. [5], and 0.34:0.75 by Shanabrook et al. [7]. Thus, the heavy-hole effective-mass anisotropy is some ambiguous. Until now, there has been no report on a systematic study for the effective-mass anisotropy using
non-(0 0 1)-oriented QW structures with a wide range of the individual layer thickness. In the present work, we have measured PL and PLE spectra of (001) and (1 1 l)-oriented GaAs/ Al03Ga0vAs MQW's with the GaAs layer thickness ranging from 15 to 150 A. and the fixed A1GaAs layer thickness of 200A. The heavy-hole and light-hole exciton energies in the (00 1) and (1 1 1) MQW's have been obtained as a function of the GaAs layer thickness. From the systematic experimental data of the exciton energies, we discuss the effective-mass anisotropy on the basis of an effective-mass approximation. The GaAs/A103Ga0.TAs MQW's used in this work were grown by molecular-beam epitaxy (MBE, Riber 2300-R&D) on (00 1)- and 0.5 ° misoriented-(1 I 1)B GaAs substrates at ~720°C, where the (00 1) and (1 1 1)B substrates were mounted on a Mo-block [simultaneous growth of the (00 1)- and (1 1 I)-MQW's]. The details of the crystal growth are described in [1]. All the MQW's consist of forty periods of undoped GaAs and Al0.3Ga0.yAs layers: the GaAs layer thicknesses (L~) are 15, 30, 50, 100, and 150A, and the A10.3Ga0vAs layer thickness (L~) is fixed as 200A. The MQW's are sandwiched by the 1.4#m-thick A103Ga0.vAs cladding layers. The individual layer thicknesses are estimated from the crystal growth rate;
1137
1138
A N I S O T R O P Y OF Q U A N T U M - S I Z E E F F E C T S
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Fig. 1. Photoluminescence (dashed lines) and photoluminescence-excitation (solid lines) spectra of the (00 1)- and (1 1 l)-oriented GaAs/Alo.~Gao.7As MQW's with the .- 50-A thick GaAs layers at 4.2 K.
Fig. 2. Photoluminescence (dashed lines) and photoluminescence-excitation (solid lines) spectra of the (00 l)and (I 11)-oriented GaAs/A10.~Gao,As M Q W ' s with the -- 15-A thick G a A s layers at 4,2 K.
therefore, they contain some uncertainty of ~ 10%. For the A1 concentration, the uncertainty is 0.3 _+ 0.02. For PL and PLE measurements, the light source was a 100-W halogen lamp. We used a 50-cm singletype monochromator for the PL excitation and a 25-cm double-type tk~r the eL detection. Although measurements of PL and PLE spectra were performed at a wide temperature range from 4.2 to - 300 K, we sho~ only the spectra at 4.2 K. where the samples were hnmersed in liquid-helium, because the spectra were measured with the highest resolution. In the PI, and P I E measurements, the typical resolutions were -, 3 and - 8 A, respectively. Figure I shows the PL (dashed lines) and PLE (5olid Hnes) spectra of the (00 I)- and (1 I I)-GaAs/ Al0~Ga,~As MQW's with the - 5 0 - A thick GaAs layers at 4.2K. The PL bands correspond to the recombination o[' the heavy-hole excitons labeled as e,-h/,E involving then = I electrons and n = [ heavy holes. In the PLE spectra, the lower- and higherenergy bands are identified as the transition of the heavy-hole excitons and that of the light-hole excitons (e, -lh, ) involving the n -- l electrons and n = I light holes, respectively. Comparing the exciton energies of the (00 I)-MQW with those of the (1 I I)-MQW in Fig. 1, it is obvious that the light-hole-exciton energy does not depend on the quantization direction, while the heavy-hole-exciton energy of the (1 1 1FMQW is 16-meV lower than that of the (00 I)-MQW. This indicates lhe anisotropy of the heavy-hole effectivemass and the isotropy of the electron and light-hole effective-masses.
Until now, there has been no report tbr non(00 l)-oriented M Q W ' s with very thin G a A s layers. Figure 2 shows the PL (dashed lines) and PLE (solid lines) spectra of the (0 0 1)- and ( I 1 I )-GaAs/Al0 ~Ga, :As MQW's with the ~ 15-,)k thick GaAs layers at 4.2 K. Two PL bands appear in each PL spectrum. In suci] a very thin well width, one-monolayer change of the well width induces remarkable shifts of the subband energies. "Ihe energy shift of the e~ hhT exciton in the (00 I)-MQW is estimated to be ,- 20nleV on the basis of the effective-mass approximation [9]. The parameters used in this calculation are taken from [9J: the energy gap of G a , \ s atl.d A10~Ga,:As are 1.519 and 1.895 eV, the conduction-band offseFratio is 0.65, the electron and heavy-,hole etfective-masses of GaAs (Al0 ~(~'a. ..As) are 0.0665 (0.0827) and 0.34 (0.35t in units of the flee-electron mass, and the electronnonparaboiidty factor is 4,9 x 10 I~ m-'. The calculated ~aluc ahnost agrees with the energy difference between the two PL bands in each PL spectrum. The MBE-growth mechanisms at high temperatures ("-680c'C) reported by ,loyce eta/. [10] suggest that the interfaces of A]GaAs on GaAs have large terraces (-.200-A widtht with one-monolayer thickness, whereas the terrace width of the interfaces of GaAs on AIGaAs is significantly smaller f - 35 A). The above estimation and the growth mechanisms indicate that the two PL bands in each PL spectrum are identified as two e~-hh~ bands originating from large temtces with one-monolayer thickness at the AI, ~Ga,~As GaAs interlaces. The PI,E spectrum of the (I 1 I)-MQW in Fig. 2
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1139
A N I S O T R O P Y OF Q U A N T U M - S I Z E E F F E C T S
Vol. 71, No. 12
50
100 Lz (A)
Fig. 3. Difference between the energy of the n = 1 heavy-hole exciton in the (001)-oriented GaAs/ Al0.3Ga07As MQW [E~hh(00 1)] and that in the (1 1 1)MQW [E~hh(l 1 1)] obtained from the PLE spectra at 4.2 K as a function of the GaAs layer thickness (L~): the closed circles are the experimental results in the present work, and the open circle is that in Ref. [6]. The solid and dashed lines indicate the Lz dependence of Ethh(0 0 l)-Emh (111) calculated using the effectivemass approximation: the solid line in mhh(11 1) = 0.9 and the dashed line in mhh(l 11) = 0.7. consists of four PLE bands. From the above discussion, it is evident that the two PLE bands on the lowerenergy (higher-energy) side correspond to the e~-hh~ and eL-hh~ (e~-lhl and el-lh~) band resulting from the one-monolayer difference of the well width. In the PLE spectrum of the (0 01)-MQW, the eL-hh~ band overlaps the e~-lh~ one. The energies of the light-hole excitons in the (1 1 1)-MQW are almost equal to those in the (00 1)-MQW; this indicates that the effective masses of electrons and light holes are isotropic even in this high confinement-energy condition ( ~ 0.2eV for electrons and ,~ 0.1 eV for light holes). For the heavy-hole excitons, the energy difference is ~ 24 meV, which increases in comparison with the value of 1 6 m e V i n L : ~ 50A. Figure 3 shows the difference between the energy of the eL-hh] exciton in the (00 1)-oriented GaAs/ A103Ga0vAs MQW [EJhh(O01)] and that in the (1 1 I)MQW [Ejhh(11 1)], which are obtained from the PLE spectra, as a function of the GaAs layer thickness (L:). The close circles indicate the experimental results in the present work, and the value of the open circle is taken from Ref. [6]. The exciton binding energy must be taken into account to estimate the effective-mass anisotropy from the observed exciton energies. According to Hayakawa et al. [3], the exciton binding energy in (1 l l)-QW's is ~ 10% larger than that in (001)QW's; this suggests that the influence of the bindingenergy difference is minor (below ~ 1.5 meV) on the value ofElhh(00 l)--ELhh(1 11). As described above, the effective mass of electrons is isotropic; therefore, the
~
50
1~o
15o
Lz (~,)
Fig. 4. Stokes shift [E~hh(PLE)-E~hh(PL)] at 4.2 K as a function of the GaAs layer thickness (L:): the closed circles for the (lll)-oriented-GaAs/Al03Ga0.7As MQW's and the open circles for the (00 I)-MQW's. energy difference of E~hh(O0 l)-E~hh(11 l) is due to the anisotropy of the heavy-hole effective-mass. The solid and dashed lines show the Lz dependence of E~hh(OO1)-E~hh(lll ) calculated using the effectivemass approximation: mhh(111) = 0.9 [2] (solid line) and 0.7 [5] (dashed line) for GaAs. For m,h(1 1 1) of A10,3Ga0,TAS, it is obtained by multiplying mhh(O01) of Al0,3Ga0.vAs by the anisotropy factor [rnhh(lll)/ mhh(O0 l)] of GaAs. From Fig. 3, it is evident that mh~(11 1) = 0.9 is appropriate, besides it is the best fit value. The anisotropy factor of 2,65 is consistent with the value of 2.7 obtained from the k • p analysis [8]. Finally, we discuss the Stokes shift of the PL band corresponding to the energy difference between the el-hhl PLE and PL bands [Ethh(PLE)-EI~h(PL)], which occurs below --~ 50 K. Figure 4 shows the Stokes shift as a function of the GaAs layer thickness (L:): the closed circles for the (1 1 I)-MQW's and open circles for the (0 0 1)-MQW's. According to [11] and [12], the Stokes shift is due to the localization nature of the excitons resulting from random-potential fluctuations (disorder) at the interfaces. As L, decreases, the confinement energy of excitons increases; therefore, the influence of the potential fluctuations on the exciton energies increases, which is the reason for the L~ dependence of the Stokes shift in Fig. 4. In L: below 30A, the Stokes shift in the (1 1 1)-MQW is obviously smaller than that in the (0 0 1)-MQW. This suggests that the heavy-hole excitons in the (1 1 1)-MQW's are less affected by the potential fluctuations relative to those in the (0 0 I)-MQW's because of the heavy-hole effective-mass anisotropy. In summary, we have measured the energies of the n = l heavy-hole and light-hole excitons in the (001)- and ( l l l ) - o r i e n t e d GaAs/AIo3Gao7As MQW's as a function of the GaAs layer thickness from 15 to 150 A,. The light-hole-exciton energies are
ll40
A N I S O T R O P Y OF Q U A N T U M - S I Z E EFFECTS
isotropic whole over the thickness range of the GaAs layer, while the heavy-hole-exciton energies are anisotropic. The difference between the energy of the heavy-hole exciton in the (0 0 I)-MQW and that in the (1 1 1)-MQW increases from ~ 2 to ~ 24meV as the GaAs layer thickness decreases from 150 to 15/~. On the basis of the effective-mass approximation, we have determined the heavy-hole effective-mass anisotropy as mhh(00 l):mht,(l I 1) = 0.34:0.9 from the systematic experimental data. Furthermore, the localization nature of the heavy-hole excitons at low temperatures is affected by the heavy-hole effective-mass anisotropy.
Acknowledgements - We would like to thank K. Takahashi of Sharp Corporation for supplying the samples. We are also grateful to T. Hayakawa of Eastman Kodak (Japan) Ltd. for his fruitful discussions. REFERENCES T. Hayakawa, M. Kondo, T. Suyama, K. Takahashi, S. Yamamoto & T. Hijikata, Jpn. J. Appl. Phys. 26, L302 (1987).
2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.
Vol. 71, No. 12
T. Hayakawa, K. Takahashi, M. Kondo, T. Suyama, S. Yamamoto & T. Hijikata, Phys. Rev. Lett. 60, 349 (1988). T. Hayakawa, K. Takahashi, M. Kondo, T. Suyama, S. Yamamoto & T. Hijikata, Phys. Rev. B38, 1526 (1988). T. Hayakawa, K. Takahashi, T. Suyama, M. Kondo, S. Yamamoto & T. Hijikata, Jpn. J. Appl. Phys. 27, L300 (1988). L.W. Molenkamp, R. Eppenga, G.W. Hooft, P. Dawson, C.T. Foxson & K.J. Moore, Phys. Rev. B38, 4314 (1988). L.W. Molenkamp, G.E.W. Bauer, R. Eppenga & C.T. Foxon, Phys. Rev. B38, 6147 (1988). B.V. Sbanabrook, O.J. Glembocki, D.A. Broido & W.I. Wang, Phys. Rev. B39, 3411 (1989). P. Lawaetz, Ph),s. Rev. B4, 3460 (1971). D.F. Nelson, R.C. Miller, C.W. Tu & S.K. Sputz, Phys. Rev. B36, 8063 (1987). B.A. Joyce, P.J. Dobson & J.H. Neave, Sur/i Sci. 174, 1 (1986). J. Hagarty, L. Goldner & M.D. Sturge, Phys. Rev. B30, 7346 (1984). Y. Masumoto, S. Tarucha & H. Okamoto, Surf. Sci. 174, 283 (1986).
0038-1098/89 $3.00 + ,00 Pergamon Press plc
ANISOTROPY OF QUANTUM-SIZE EFFECTS IN (0 0 1)- AND (l 1 I)-ORIENTED GaAs/A103Ga0vAs MULTIPLE-QUANTUM-WELLS M. Nakayama, I. Kimura and H. Nishimura Department of Applied Physics, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka 558, Japan and T. Komatsu and Y. Kaifu Department of Physics, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka 558, Japan (Received 25 April 1989 by J. Kanamori)
We have investigated the anisotropy of quantum-size effects in (0 0 1)and (1 1 1)-oriented GaAs/A103Ga0.TAs multiple-quantum-wells (MQW's) with the GaAs layer thickness ranging from 15 to 150 A and the fixed AIGaAs layer thickness of 200A by using photoluminescence and photoluminescence-exciton spectroscopy at 4.2 K. The light-hole-exciton energy is not affected by the quantization direction whole over the thickness range of the GaAs layer, while the heavy-hole-exciton energy of the (1 1 1)-MQW is lower than that of the (0 0 1)-MQW with the same structure. The energy difference increases from ~ 2 to ~ 24 meV as the GaAs layer thickness decreases from 150 to 15 A, which is consistent with the results calculated on the basis of an effective-mass approximation assuming the heavy-hole effective-mass anisotropy of mh~, (O01):mhh (1 1 1) = 0.34:0.9 for GaAs.
THE electronic and optical properties of GaAs/ A103xGa~ _~As quantum-well (QW) structures have been studied intensely over last fifteen years; however, only several works [1-7] have been reported for non(0 0 1)-oriented QW structures because of the difficulty of the crystal growth. Hayakawa et al. reported a low threshold-current behaviour in (1 1 1)-oriented GaAs/ Al0.3~Ga~__~As QW lasers [1]; this suggests that non(00 1)-oriented QW structures are very valuable for optical devices. It is well known that the valence band structures of zinc-blende-type semiconductors are anisotropic [8]; therefore, determination of the effective-mass anisotropy is very important in device applications. Measurements of the energies of heavyhole and light-hole excitons in the non-(0 0 l)-oriented QW structures by photoluminescence (PL) and photoluminescence-excitation (PLE) spectroscopies enable us to determine the anisotropy. The results obtained in the previous works, where only a few samples were used, indicate the anisotropy of the heavy-hole effective-mass of GaAs: mhh (0 0 1) : mhh (1 1 1) = 0.34 : 0.9 by Hayakawa et al. [2], 0.34 : 0.7 by Molenkamp et al. [5], and 0.34:0.75 by Shanabrook et al. [7]. Thus, the heavy-hole effective-mass anisotropy is some ambiguous. Until now, there has been no report on a systematic study for the effective-mass anisotropy using
non-(0 0 1)-oriented QW structures with a wide range of the individual layer thickness. In the present work, we have measured PL and PLE spectra of (001) and (1 1 l)-oriented GaAs/ Al03Ga0vAs MQW's with the GaAs layer thickness ranging from 15 to 150 A. and the fixed A1GaAs layer thickness of 200A. The heavy-hole and light-hole exciton energies in the (00 1) and (1 1 1) MQW's have been obtained as a function of the GaAs layer thickness. From the systematic experimental data of the exciton energies, we discuss the effective-mass anisotropy on the basis of an effective-mass approximation. The GaAs/A103Ga0.TAs MQW's used in this work were grown by molecular-beam epitaxy (MBE, Riber 2300-R&D) on (00 1)- and 0.5 ° misoriented-(1 I 1)B GaAs substrates at ~720°C, where the (00 1) and (1 1 1)B substrates were mounted on a Mo-block [simultaneous growth of the (00 1)- and (1 1 I)-MQW's]. The details of the crystal growth are described in [1]. All the MQW's consist of forty periods of undoped GaAs and Al0.3Ga0.yAs layers: the GaAs layer thicknesses (L~) are 15, 30, 50, 100, and 150A, and the A10.3Ga0vAs layer thickness (L~) is fixed as 200A. The MQW's are sandwiched by the 1.4#m-thick A103Ga0.vAs cladding layers. The individual layer thicknesses are estimated from the crystal growth rate;
1137
1138
A N I S O T R O P Y OF Q U A N T U M - S I Z E E F F E C T S
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Vol. 71, No. 12
170
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Fig. 1. Photoluminescence (dashed lines) and photoluminescence-excitation (solid lines) spectra of the (00 1)- and (1 1 l)-oriented GaAs/Alo.~Gao.7As MQW's with the .- 50-A thick GaAs layers at 4.2 K.
Fig. 2. Photoluminescence (dashed lines) and photoluminescence-excitation (solid lines) spectra of the (00 l)and (I 11)-oriented GaAs/A10.~Gao,As M Q W ' s with the -- 15-A thick G a A s layers at 4,2 K.
therefore, they contain some uncertainty of ~ 10%. For the A1 concentration, the uncertainty is 0.3 _+ 0.02. For PL and PLE measurements, the light source was a 100-W halogen lamp. We used a 50-cm singletype monochromator for the PL excitation and a 25-cm double-type tk~r the eL detection. Although measurements of PL and PLE spectra were performed at a wide temperature range from 4.2 to - 300 K, we sho~ only the spectra at 4.2 K. where the samples were hnmersed in liquid-helium, because the spectra were measured with the highest resolution. In the PI, and P I E measurements, the typical resolutions were -, 3 and - 8 A, respectively. Figure I shows the PL (dashed lines) and PLE (5olid Hnes) spectra of the (00 I)- and (1 I I)-GaAs/ Al0~Ga,~As MQW's with the - 5 0 - A thick GaAs layers at 4.2K. The PL bands correspond to the recombination o[' the heavy-hole excitons labeled as e,-h/,E involving then = I electrons and n = [ heavy holes. In the PLE spectra, the lower- and higherenergy bands are identified as the transition of the heavy-hole excitons and that of the light-hole excitons (e, -lh, ) involving the n -- l electrons and n = I light holes, respectively. Comparing the exciton energies of the (00 I)-MQW with those of the (1 I I)-MQW in Fig. 1, it is obvious that the light-hole-exciton energy does not depend on the quantization direction, while the heavy-hole-exciton energy of the (1 1 1FMQW is 16-meV lower than that of the (00 I)-MQW. This indicates lhe anisotropy of the heavy-hole effectivemass and the isotropy of the electron and light-hole effective-masses.
Until now, there has been no report tbr non(00 l)-oriented M Q W ' s with very thin G a A s layers. Figure 2 shows the PL (dashed lines) and PLE (solid lines) spectra of the (0 0 1)- and ( I 1 I )-GaAs/Al0 ~Ga, :As MQW's with the ~ 15-,)k thick GaAs layers at 4.2 K. Two PL bands appear in each PL spectrum. In suci] a very thin well width, one-monolayer change of the well width induces remarkable shifts of the subband energies. "Ihe energy shift of the e~ hhT exciton in the (00 I)-MQW is estimated to be ,- 20nleV on the basis of the effective-mass approximation [9]. The parameters used in this calculation are taken from [9J: the energy gap of G a , \ s atl.d A10~Ga,:As are 1.519 and 1.895 eV, the conduction-band offseFratio is 0.65, the electron and heavy-,hole etfective-masses of GaAs (Al0 ~(~'a. ..As) are 0.0665 (0.0827) and 0.34 (0.35t in units of the flee-electron mass, and the electronnonparaboiidty factor is 4,9 x 10 I~ m-'. The calculated ~aluc ahnost agrees with the energy difference between the two PL bands in each PL spectrum. The MBE-growth mechanisms at high temperatures ("-680c'C) reported by ,loyce eta/. [10] suggest that the interfaces of A]GaAs on GaAs have large terraces (-.200-A widtht with one-monolayer thickness, whereas the terrace width of the interfaces of GaAs on AIGaAs is significantly smaller f - 35 A). The above estimation and the growth mechanisms indicate that the two PL bands in each PL spectrum are identified as two e~-hh~ bands originating from large temtces with one-monolayer thickness at the AI, ~Ga,~As GaAs interlaces. The PI,E spectrum of the (I 1 I)-MQW in Fig. 2
3 0 t /"X
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..~ 20i [,;I'~,",',,\ ,,~
--
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0
1139
A N I S O T R O P Y OF Q U A N T U M - S I Z E E F F E C T S
Vol. 71, No. 12
50
100 Lz (A)
Fig. 3. Difference between the energy of the n = 1 heavy-hole exciton in the (001)-oriented GaAs/ Al0.3Ga07As MQW [E~hh(00 1)] and that in the (1 1 1)MQW [E~hh(l 1 1)] obtained from the PLE spectra at 4.2 K as a function of the GaAs layer thickness (L~): the closed circles are the experimental results in the present work, and the open circle is that in Ref. [6]. The solid and dashed lines indicate the Lz dependence of Ethh(0 0 l)-Emh (111) calculated using the effectivemass approximation: the solid line in mhh(11 1) = 0.9 and the dashed line in mhh(l 11) = 0.7. consists of four PLE bands. From the above discussion, it is evident that the two PLE bands on the lowerenergy (higher-energy) side correspond to the e~-hh~ and eL-hh~ (e~-lhl and el-lh~) band resulting from the one-monolayer difference of the well width. In the PLE spectrum of the (0 01)-MQW, the eL-hh~ band overlaps the e~-lh~ one. The energies of the light-hole excitons in the (1 1 1)-MQW are almost equal to those in the (00 1)-MQW; this indicates that the effective masses of electrons and light holes are isotropic even in this high confinement-energy condition ( ~ 0.2eV for electrons and ,~ 0.1 eV for light holes). For the heavy-hole excitons, the energy difference is ~ 24 meV, which increases in comparison with the value of 1 6 m e V i n L : ~ 50A. Figure 3 shows the difference between the energy of the eL-hh] exciton in the (00 1)-oriented GaAs/ A103Ga0vAs MQW [EJhh(O01)] and that in the (1 1 I)MQW [Ejhh(11 1)], which are obtained from the PLE spectra, as a function of the GaAs layer thickness (L:). The close circles indicate the experimental results in the present work, and the value of the open circle is taken from Ref. [6]. The exciton binding energy must be taken into account to estimate the effective-mass anisotropy from the observed exciton energies. According to Hayakawa et al. [3], the exciton binding energy in (1 l l)-QW's is ~ 10% larger than that in (001)QW's; this suggests that the influence of the bindingenergy difference is minor (below ~ 1.5 meV) on the value ofElhh(00 l)--ELhh(1 11). As described above, the effective mass of electrons is isotropic; therefore, the
~
50
1~o
15o
Lz (~,)
Fig. 4. Stokes shift [E~hh(PLE)-E~hh(PL)] at 4.2 K as a function of the GaAs layer thickness (L:): the closed circles for the (lll)-oriented-GaAs/Al03Ga0.7As MQW's and the open circles for the (00 I)-MQW's. energy difference of E~hh(O0 l)-E~hh(11 l) is due to the anisotropy of the heavy-hole effective-mass. The solid and dashed lines show the Lz dependence of E~hh(OO1)-E~hh(lll ) calculated using the effectivemass approximation: mhh(111) = 0.9 [2] (solid line) and 0.7 [5] (dashed line) for GaAs. For m,h(1 1 1) of A10,3Ga0,TAS, it is obtained by multiplying mhh(O01) of Al0,3Ga0.vAs by the anisotropy factor [rnhh(lll)/ mhh(O0 l)] of GaAs. From Fig. 3, it is evident that mh~(11 1) = 0.9 is appropriate, besides it is the best fit value. The anisotropy factor of 2,65 is consistent with the value of 2.7 obtained from the k • p analysis [8]. Finally, we discuss the Stokes shift of the PL band corresponding to the energy difference between the el-hhl PLE and PL bands [Ethh(PLE)-EI~h(PL)], which occurs below --~ 50 K. Figure 4 shows the Stokes shift as a function of the GaAs layer thickness (L:): the closed circles for the (1 1 I)-MQW's and open circles for the (0 0 1)-MQW's. According to [11] and [12], the Stokes shift is due to the localization nature of the excitons resulting from random-potential fluctuations (disorder) at the interfaces. As L, decreases, the confinement energy of excitons increases; therefore, the influence of the potential fluctuations on the exciton energies increases, which is the reason for the L~ dependence of the Stokes shift in Fig. 4. In L: below 30A, the Stokes shift in the (1 1 1)-MQW is obviously smaller than that in the (0 0 1)-MQW. This suggests that the heavy-hole excitons in the (1 1 1)-MQW's are less affected by the potential fluctuations relative to those in the (0 0 I)-MQW's because of the heavy-hole effective-mass anisotropy. In summary, we have measured the energies of the n = l heavy-hole and light-hole excitons in the (001)- and ( l l l ) - o r i e n t e d GaAs/AIo3Gao7As MQW's as a function of the GaAs layer thickness from 15 to 150 A,. The light-hole-exciton energies are
ll40
A N I S O T R O P Y OF Q U A N T U M - S I Z E EFFECTS
isotropic whole over the thickness range of the GaAs layer, while the heavy-hole-exciton energies are anisotropic. The difference between the energy of the heavy-hole exciton in the (0 0 I)-MQW and that in the (1 1 1)-MQW increases from ~ 2 to ~ 24meV as the GaAs layer thickness decreases from 150 to 15/~. On the basis of the effective-mass approximation, we have determined the heavy-hole effective-mass anisotropy as mhh(00 l):mht,(l I 1) = 0.34:0.9 from the systematic experimental data. Furthermore, the localization nature of the heavy-hole excitons at low temperatures is affected by the heavy-hole effective-mass anisotropy.
Acknowledgements - We would like to thank K. Takahashi of Sharp Corporation for supplying the samples. We are also grateful to T. Hayakawa of Eastman Kodak (Japan) Ltd. for his fruitful discussions. REFERENCES T. Hayakawa, M. Kondo, T. Suyama, K. Takahashi, S. Yamamoto & T. Hijikata, Jpn. J. Appl. Phys. 26, L302 (1987).
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