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AlAs superlattices and quantum wire-like structures
Physica E 2 (1998) 368—371
Optical properties of the (3 1 1) oriented GaAs/AlAs superlattices and quantum wire-like structures A. Milekhin!, Yu. Yanovskii!, V. Preobrazhenskii!, B. Semyagin!, Yu. Pusep",*, J.C. Galzerani" ! Institute of Semiconductor Physics, 630090, Novosibirsk, Russian Federation " Departamento de Fisica, Universidade Federal de SaJ o Carlos, 13565-905, SaJ o Carlos, SP, Brazil
Abstract Optical vibrational modes in the (3 1 1)-oriented GaAs/AlAs superlattices and structures with quantum wires were investigated by the FTIR spectroscopy. A splitting of the fundamental TO vibrational mode localized in the GaAs quantum wire into two ones with a different polarization was observed. The dispersion of the transverse optical GaAs phonons in the (3 1 1) direction was obtained. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: Superlattice; Quantum wire; Infrared spectroscopy
Progress of the Molecular Beam Epitaxy (MBE) technology make it possible to grow the perfect GaAs/AlAs superlattices (SL’s) on high-index GaAs surfaces, such as (0 1 1) [1], (1 1 2) [2,3], (3 1 1) [2—4]. Lowering of the symmetry of these SL’s in comparison with the (1 0 0)-oriented GaAs/AlAs SL’s leads to optical anisotropy in the plane of the SL layers [2—6]. Anisotropy of optical and electronic properties can be explained by the surface corrugation which became the highest for the (3 1 1) A_ -oriented SL’s [2,3]. Thus, the surface corrugation allows to fabricate GaAs/AlAs quantum wire-like structures (QWR’s) during direct MBE growth.
* Corresponding author. Fax: #55 (016) 272-6835; e-mail: [email protected].
Although there have been a number of reports on the electronic properties, only few studies of the optical properties, particular in infrared, have been carried out [7—10]. In this paper the vibrational spectrum of the (3 1 1)A-oriented GaAs/AlAs superlattices and quantum wire-like structures has been studied by means of the FTIR spectroscopy. The samples under investigations were the (GaAs) /(AlAs) periodical structures (where n"8, n m 10, 12, 28 and m"12, 16, 24, number of monolayers in the corresponding layer) grown on the (3 1 1)A and (3 1 1)B-oriented GaAs surface. Thickness of the GaAs and AlAs layers was determined from RHEED experiments using SL’s grown in the same process on (1 0 0) GaAs substrates. The number of monolayers m and n were calculated for (GaAs) /(AlAs) SL’s with abrupt interfaces n m
1386-9477/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved PII: S 1 3 8 6 - 9 4 7 7 ( 9 8 ) 0 0 0 7 7 - 0
A. Milekhin et al. / Physica E 2 (1998) 368—371
without taking into account a surface corrugation. The layer structure was repeated 100 times for all the SL’s under investigations. The infrared reflection spectra were recorded using the FTIR spectrometer Bruker IFS-113V equipped with an Oxford Instruments cryostat at a temperature 79 K. The resolution was 0.5 cm over the entire spectral range. The IR reflection spectra taken at normal incidence of light together with the p-polarized spectra obtained at oblique incidence (h+70°) were analyzed. The reflection spectra of the structures with QWR’s were measured at normal incidence of light when the vector of electric polarization was directed along and normal to the quantum wire direction. Lowering of the symmetry in the (3 1 1) SL’s in comparison with SL’s grown along the (1 0 0) direction, complicates identification of phonon modes propagating along the (3 1 1) direction in the (3 1 1) SL’s where confined optical modes of pure transverse (AA) and mixed longitudinal/transverse (A@) character arise [8]. Moreover, the lateral corrugation in the (3 1 1)A superlattices can lead to the splitting of the optical confined modes. The splitting of LO confined modes in the GaAs layers was explained by phonon localization in the wide and narrow parts of the layers [7]. According to selection rules all the modes (A@ and AA) can be active in the infrared spectra of the (3 1 1)A-oriented GaAs/AlAs SL’s due to their non-vanished dipole momentum. The wave number of the AA confined modes in the long-period SL’s (when the influence of the surface corrugation is negligible) can be defined as usual q "mp/(n#d)d m
369
(0 1 !1) directions the splitting value becomes negligible small up to wave numbers q+0.3. The IR reflection spectra of SL’s recorded at normal incidence of the light on the sample show the possibility to study the TO confined phonons while LO phonons are active in the p-polarized IR spectra due to the Berreman effect. As a rule only odd confined optical modes are revealed in IR spectra of SL’s due to their non-zero dipole momenta. The p-polarized reflection spectra of the (1 0 0), (3 1 1)A and (3 1 1)B-oriented GaAs/AlAs SL’s in the spectral range of LO phonons of AlAs are presented in Fig. 1. The structural features in the spectra marked by arrows correspond to the LO confined modes localized in the AlAs layers. As can be seen from Fig. 1, the frequencies of the fundamental vibrational modes of all SL’s are decreasing
(1)
where n is the number of monolayers, d"a/J11 is the thickness of one monolayer in the (3 1 1) direction, a is the lattice parameter in the (1 0 0) direction and m is the number of confined mode. The parameter d describes the penetration of confined modes into neighboring layers. The identification of the mixed confined modes with small wave numbers becomes easier due to mainly LO or TO polarization of corresponding confined modes [11]. Moreover, in spite of the degeneracy lifting of the TO modes polarized along the (!2 3 3) and
Fig. 1. The IR reflection spectra of samples measured with the p-polarized light in the spectral range of the LO phonons of AlAs: (a) the (1 0 0) SL’s: (GaAs) (AlAs) (curve 1), (GaAs) 17 15 7 (AlAs) (curve 2), (GaAs) (AlAs) (curve 3), (b, c) the (3 1 1)A 9 4 4 and (3 1 1)B SL’s respectively: (GaAs) (AlAs) (curve 1), 28 24 (GaAs) (AlAs) (curve 2), (GaAs) (AlAs) (curve 3). 12 17 9 9
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A. Milekhin et al. / Physica E 2 (1998) 368—371
with the decrease of the AlAs layer thickness according to the dispersion law of AlAs phonons. Moreover, the reflection spectra reveal the LO 3 modes that confirms a high crystalline quality of samples. The alteration of vibrational modes position is caused by the different localization length in SL’s. Figs. 2 and 3 present the reflection spectra of the (3 1 1)A (solid lines) and the (3 1 1)B (dashed lines) SL’s which reveal only the fundamental TO modes localized in the AlAs and GaAs layers, respectively. The frequencies of the TO modes localized in the GaAs layers of the SL’s are placed near the “reststrahlen band” of the bulk GaAs. To determine the frequencies of these TO modes highly accurately we analyzed the derivative of the reflection dR/dl (Fig. 3). The minima indicated by arrows corres-
Fig. 2. The IR reflection spectra of the (3 1 1)A (solid line) and (3 1 1)B (dashed line) SL’s measured at a normal incidence in the spectral range of the TO phonons of AlAs: (GaAs) (AlAs) 28 24 (curve 1), (GaAs) (AlAs) (curve 2), (GaAs) (AlAs) (curve 3). 12 17 9 9
pond to the TO confined modes. The experimental reflection spectra of the long-period (3 1 1)A and (3 1 1)B SL’s (solid and dashed curves labelled as 1 in Fig. 3) presents the odd confined modes up to the TO mode. The alteration of vibrational modes 5 position in different SL’s is caused by the different localization lengths only. Using the frequencies of confined modes taken from the IR reflection spectra and relation (1) the dispersion of the TO phonons of GaAs in the (3 1 1) direction was obtained. The penetration parameter d was taken as 1 [11]. The experimental frequencies of the TO confined modes as a function of wave number are shown in Fig. 4 by triangles. The Raman data taken from [5] are given by circles. The dispersion of the TO phonons of GaAs in (3 1 1) SL’s obtained from IR spectra is in rather good agreement with Raman data presented in Fig. 4 by circles. At smaller thickness of the GaAs layers (4—6 ml) strong evidence of the wire-like behavior of the vibrational spectrum of the (3 1 1)A oriented structures was found. The polarized IR reflection spectra of these structures measured at normal incidence of light are presented in Fig. 5. The direction of the polarization vector with respect to the wire
Fig. 3. The IR reflection spectra of the (3 1 1)A SL’s measured at a normal incidence in the spectral range of the TO phonons of GaAs: (GaAs) /(AlAs) (curve 1), (GaAs) /(AlAs) (curve 2). 24 12 12 12
A. Milekhin et al. / Physica E 2 (1998) 368—371
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direction is shown in the inset. The curves 1, 3 and 2, 4 correspond to the IR spectra polarized along the [!2 3 3] and [0 1 !1] directions, respectively. As one can see from Fig. 5, the fundamental confined vibrational modes of the GaAs propagating normal to the layers are split into two modes with the different electric polarization. The highfrequency modes (TO modes) have the electric M polarization perpendicular to the wire direction, while the electric polarization of the low-frequency modes (TO modes) is directed parallel to the wire , direction. The TO mode is assigned to the bulk " GaAs TO phonon of the substrate. This work was supported by Russian Science Foundation under grant No. 95-02-0443 and Russian Ministry of Higher Education under grant No. CI-249-96/231 P 2-5. Fig. 4. The dispersion of the TO phonons in GaAs measured in the (3 1 1) SL’s (triangles). The dispersion of the TO phonons in the (0 0 1) direction is presented by solid line. The Raman data taken from Ref. [5] are shown by circles.
Fig. 5. The IR reflection spectra of the (3 1 1)A SL’s measured at a normal incidence with the polarized light in the spectral range of the TO phonons of GaAs: (GaAs) /(AlAs) (curves 1 and 2), 8 16 (GaAs) /(AlAs) (curves 3 and 4). The direction of the electric 10 16 polarization with respect to the quantum wire direction is shown in the inset.
References [1] L.N. Pfeiffer, K.W. West, H. Stormer et al., Appl. Phys. Lett. 56 (1990) 1697. [2] R. Notzel, N. Ledentsov, L. Daweritz et al., Phys. Rev. Lett. B 27 (1991) 3507. [3] R. Notzel, N.N. Ledentsov, L. Daweritz et al., Phys. Rev. B 45 (1992) 3507. [4] R. Notzel, L. Daweritz, K. Ploog, Phys. Rev. B 46 (1992) 4736. [5] C. Jouanin, A. Hallaoui, D. Bertho, Phys. Rev. B 50 (1994) 1645. [6] D. Gershoni, I. Brener, G.A. Baraff et al., Phys. Rev. B 44 (1991) 1930. [7] S.W. da Silva, Yu.A. Pusep, J. Galzerani et al., Phys. Rev. B 53 (1996) 1927. [8] Z.V. Popovich, E. Richter, J. Spitzer et al., Phys. Rev. B 49 (1994) 7577. [9] Yu.A. Pusep, S.W. da Silva, J. Galzerani et al., Phys. Rev. B 51 (1995) 5473. [10] P. Castrillo, L. Colombo, Phys. Rev. B 49 (1994) 10362. [11] A. Milekhin, Yu. Pusep, D. Lubyshev et al., Proc. 22nd Internat. Symp. on Compound Semiconductors, Cheju Island, Korea, 1995, published in Compound Semiconductors, Institute of Phys. Conf. Ser., 1996, No. 145, Chapter 3, IOP Publishing, Bristol, p. 437.
Optical properties of the (3 1 1) oriented GaAs/AlAs superlattices and quantum wire-like structures A. Milekhin!, Yu. Yanovskii!, V. Preobrazhenskii!, B. Semyagin!, Yu. Pusep",*, J.C. Galzerani" ! Institute of Semiconductor Physics, 630090, Novosibirsk, Russian Federation " Departamento de Fisica, Universidade Federal de SaJ o Carlos, 13565-905, SaJ o Carlos, SP, Brazil
Abstract Optical vibrational modes in the (3 1 1)-oriented GaAs/AlAs superlattices and structures with quantum wires were investigated by the FTIR spectroscopy. A splitting of the fundamental TO vibrational mode localized in the GaAs quantum wire into two ones with a different polarization was observed. The dispersion of the transverse optical GaAs phonons in the (3 1 1) direction was obtained. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: Superlattice; Quantum wire; Infrared spectroscopy
Progress of the Molecular Beam Epitaxy (MBE) technology make it possible to grow the perfect GaAs/AlAs superlattices (SL’s) on high-index GaAs surfaces, such as (0 1 1) [1], (1 1 2) [2,3], (3 1 1) [2—4]. Lowering of the symmetry of these SL’s in comparison with the (1 0 0)-oriented GaAs/AlAs SL’s leads to optical anisotropy in the plane of the SL layers [2—6]. Anisotropy of optical and electronic properties can be explained by the surface corrugation which became the highest for the (3 1 1) A_ -oriented SL’s [2,3]. Thus, the surface corrugation allows to fabricate GaAs/AlAs quantum wire-like structures (QWR’s) during direct MBE growth.
* Corresponding author. Fax: #55 (016) 272-6835; e-mail: [email protected].
Although there have been a number of reports on the electronic properties, only few studies of the optical properties, particular in infrared, have been carried out [7—10]. In this paper the vibrational spectrum of the (3 1 1)A-oriented GaAs/AlAs superlattices and quantum wire-like structures has been studied by means of the FTIR spectroscopy. The samples under investigations were the (GaAs) /(AlAs) periodical structures (where n"8, n m 10, 12, 28 and m"12, 16, 24, number of monolayers in the corresponding layer) grown on the (3 1 1)A and (3 1 1)B-oriented GaAs surface. Thickness of the GaAs and AlAs layers was determined from RHEED experiments using SL’s grown in the same process on (1 0 0) GaAs substrates. The number of monolayers m and n were calculated for (GaAs) /(AlAs) SL’s with abrupt interfaces n m
1386-9477/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved PII: S 1 3 8 6 - 9 4 7 7 ( 9 8 ) 0 0 0 7 7 - 0
A. Milekhin et al. / Physica E 2 (1998) 368—371
without taking into account a surface corrugation. The layer structure was repeated 100 times for all the SL’s under investigations. The infrared reflection spectra were recorded using the FTIR spectrometer Bruker IFS-113V equipped with an Oxford Instruments cryostat at a temperature 79 K. The resolution was 0.5 cm over the entire spectral range. The IR reflection spectra taken at normal incidence of light together with the p-polarized spectra obtained at oblique incidence (h+70°) were analyzed. The reflection spectra of the structures with QWR’s were measured at normal incidence of light when the vector of electric polarization was directed along and normal to the quantum wire direction. Lowering of the symmetry in the (3 1 1) SL’s in comparison with SL’s grown along the (1 0 0) direction, complicates identification of phonon modes propagating along the (3 1 1) direction in the (3 1 1) SL’s where confined optical modes of pure transverse (AA) and mixed longitudinal/transverse (A@) character arise [8]. Moreover, the lateral corrugation in the (3 1 1)A superlattices can lead to the splitting of the optical confined modes. The splitting of LO confined modes in the GaAs layers was explained by phonon localization in the wide and narrow parts of the layers [7]. According to selection rules all the modes (A@ and AA) can be active in the infrared spectra of the (3 1 1)A-oriented GaAs/AlAs SL’s due to their non-vanished dipole momentum. The wave number of the AA confined modes in the long-period SL’s (when the influence of the surface corrugation is negligible) can be defined as usual q "mp/(n#d)d m
369
(0 1 !1) directions the splitting value becomes negligible small up to wave numbers q+0.3. The IR reflection spectra of SL’s recorded at normal incidence of the light on the sample show the possibility to study the TO confined phonons while LO phonons are active in the p-polarized IR spectra due to the Berreman effect. As a rule only odd confined optical modes are revealed in IR spectra of SL’s due to their non-zero dipole momenta. The p-polarized reflection spectra of the (1 0 0), (3 1 1)A and (3 1 1)B-oriented GaAs/AlAs SL’s in the spectral range of LO phonons of AlAs are presented in Fig. 1. The structural features in the spectra marked by arrows correspond to the LO confined modes localized in the AlAs layers. As can be seen from Fig. 1, the frequencies of the fundamental vibrational modes of all SL’s are decreasing
(1)
where n is the number of monolayers, d"a/J11 is the thickness of one monolayer in the (3 1 1) direction, a is the lattice parameter in the (1 0 0) direction and m is the number of confined mode. The parameter d describes the penetration of confined modes into neighboring layers. The identification of the mixed confined modes with small wave numbers becomes easier due to mainly LO or TO polarization of corresponding confined modes [11]. Moreover, in spite of the degeneracy lifting of the TO modes polarized along the (!2 3 3) and
Fig. 1. The IR reflection spectra of samples measured with the p-polarized light in the spectral range of the LO phonons of AlAs: (a) the (1 0 0) SL’s: (GaAs) (AlAs) (curve 1), (GaAs) 17 15 7 (AlAs) (curve 2), (GaAs) (AlAs) (curve 3), (b, c) the (3 1 1)A 9 4 4 and (3 1 1)B SL’s respectively: (GaAs) (AlAs) (curve 1), 28 24 (GaAs) (AlAs) (curve 2), (GaAs) (AlAs) (curve 3). 12 17 9 9
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A. Milekhin et al. / Physica E 2 (1998) 368—371
with the decrease of the AlAs layer thickness according to the dispersion law of AlAs phonons. Moreover, the reflection spectra reveal the LO 3 modes that confirms a high crystalline quality of samples. The alteration of vibrational modes position is caused by the different localization length in SL’s. Figs. 2 and 3 present the reflection spectra of the (3 1 1)A (solid lines) and the (3 1 1)B (dashed lines) SL’s which reveal only the fundamental TO modes localized in the AlAs and GaAs layers, respectively. The frequencies of the TO modes localized in the GaAs layers of the SL’s are placed near the “reststrahlen band” of the bulk GaAs. To determine the frequencies of these TO modes highly accurately we analyzed the derivative of the reflection dR/dl (Fig. 3). The minima indicated by arrows corres-
Fig. 2. The IR reflection spectra of the (3 1 1)A (solid line) and (3 1 1)B (dashed line) SL’s measured at a normal incidence in the spectral range of the TO phonons of AlAs: (GaAs) (AlAs) 28 24 (curve 1), (GaAs) (AlAs) (curve 2), (GaAs) (AlAs) (curve 3). 12 17 9 9
pond to the TO confined modes. The experimental reflection spectra of the long-period (3 1 1)A and (3 1 1)B SL’s (solid and dashed curves labelled as 1 in Fig. 3) presents the odd confined modes up to the TO mode. The alteration of vibrational modes 5 position in different SL’s is caused by the different localization lengths only. Using the frequencies of confined modes taken from the IR reflection spectra and relation (1) the dispersion of the TO phonons of GaAs in the (3 1 1) direction was obtained. The penetration parameter d was taken as 1 [11]. The experimental frequencies of the TO confined modes as a function of wave number are shown in Fig. 4 by triangles. The Raman data taken from [5] are given by circles. The dispersion of the TO phonons of GaAs in (3 1 1) SL’s obtained from IR spectra is in rather good agreement with Raman data presented in Fig. 4 by circles. At smaller thickness of the GaAs layers (4—6 ml) strong evidence of the wire-like behavior of the vibrational spectrum of the (3 1 1)A oriented structures was found. The polarized IR reflection spectra of these structures measured at normal incidence of light are presented in Fig. 5. The direction of the polarization vector with respect to the wire
Fig. 3. The IR reflection spectra of the (3 1 1)A SL’s measured at a normal incidence in the spectral range of the TO phonons of GaAs: (GaAs) /(AlAs) (curve 1), (GaAs) /(AlAs) (curve 2). 24 12 12 12
A. Milekhin et al. / Physica E 2 (1998) 368—371
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direction is shown in the inset. The curves 1, 3 and 2, 4 correspond to the IR spectra polarized along the [!2 3 3] and [0 1 !1] directions, respectively. As one can see from Fig. 5, the fundamental confined vibrational modes of the GaAs propagating normal to the layers are split into two modes with the different electric polarization. The highfrequency modes (TO modes) have the electric M polarization perpendicular to the wire direction, while the electric polarization of the low-frequency modes (TO modes) is directed parallel to the wire , direction. The TO mode is assigned to the bulk " GaAs TO phonon of the substrate. This work was supported by Russian Science Foundation under grant No. 95-02-0443 and Russian Ministry of Higher Education under grant No. CI-249-96/231 P 2-5. Fig. 4. The dispersion of the TO phonons in GaAs measured in the (3 1 1) SL’s (triangles). The dispersion of the TO phonons in the (0 0 1) direction is presented by solid line. The Raman data taken from Ref. [5] are shown by circles.
Fig. 5. The IR reflection spectra of the (3 1 1)A SL’s measured at a normal incidence with the polarized light in the spectral range of the TO phonons of GaAs: (GaAs) /(AlAs) (curves 1 and 2), 8 16 (GaAs) /(AlAs) (curves 3 and 4). The direction of the electric 10 16 polarization with respect to the quantum wire direction is shown in the inset.
References [1] L.N. Pfeiffer, K.W. West, H. Stormer et al., Appl. Phys. Lett. 56 (1990) 1697. [2] R. Notzel, N. Ledentsov, L. Daweritz et al., Phys. Rev. Lett. B 27 (1991) 3507. [3] R. Notzel, N.N. Ledentsov, L. Daweritz et al., Phys. Rev. B 45 (1992) 3507. [4] R. Notzel, L. Daweritz, K. Ploog, Phys. Rev. B 46 (1992) 4736. [5] C. Jouanin, A. Hallaoui, D. Bertho, Phys. Rev. B 50 (1994) 1645. [6] D. Gershoni, I. Brener, G.A. Baraff et al., Phys. Rev. B 44 (1991) 1930. [7] S.W. da Silva, Yu.A. Pusep, J. Galzerani et al., Phys. Rev. B 53 (1996) 1927. [8] Z.V. Popovich, E. Richter, J. Spitzer et al., Phys. Rev. B 49 (1994) 7577. [9] Yu.A. Pusep, S.W. da Silva, J. Galzerani et al., Phys. Rev. B 51 (1995) 5473. [10] P. Castrillo, L. Colombo, Phys. Rev. B 49 (1994) 10362. [11] A. Milekhin, Yu. Pusep, D. Lubyshev et al., Proc. 22nd Internat. Symp. on Compound Semiconductors, Cheju Island, Korea, 1995, published in Compound Semiconductors, Institute of Phys. Conf. Ser., 1996, No. 145, Chapter 3, IOP Publishing, Bristol, p. 437.