- Email: [email protected]
GaAs quantum dots
PERGAMON
Solid State Communications 110 (1999) 657–660
Room temperature photoreflectance of MOCVD-grown InAs/GaAs quantum dots G. Se˛k a,*, J. Misiewicz a, K. Ryczko a, M. Kubisa a, F. Heinrichsdorff b, O. Stier b, D. Bimberg b a
Institute of Physics, Wrocl⁄aw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wrocl⁄aw, Poland b Institute of Solid State Physics, Technical University Berlin, Hardenbergstrasse 36, D10623 Berlin, Germany Received 20 January 1999; accepted 18 March 1999 by H. Eschrig
Abstract Photoreflectance spectroscopy results are reported for InAs/GaAs self-organised quantum dots grown by low-pressure MOCVD. Quantum dot-related optical transitions have been observed for the first time at room temperature. Good agreement between experiment and theory based on a recent 8-band k·p theory has been obtained. q 1999 Elsevier Science Ltd. All rights reserved. Keywords: A. Semiconductors; A. Nanostructures; D. Electronic states (localized)
Most of the previous reports on InAs/GaAs quantum dots (QDs), which present a basis for novel lasers, deal with structures grown by MBE [1–5]. The development of QD structures of similar quality by metalorganic chemical vapor deposition (MOCVD) was originally hindered by various mechanisms, particular in the growth process. In particular, the growth of the dot layers with high lateral density was originally accompanied by the tendency towards formation of large plastically relaxed clusters, indicating the greater influence of growth kinetics (e.g. long-range adatom surface migration) than in MBE. These clusters not only decreased the optical quality of the dot layers and may even exclude their application in QD lasers, but also made vertical stacking of device quality QDs impossible. In most of the original studies of MOCVD InxGa12xAs/GaAs QDs, ternary InxGa12xAs with x in the range of 30–70% was used for the dot * Corresponding author.
growth [6–8]. Recently parameters for the growth of binary InAs/GaAs QDs were assessed [9–12] and stacked QD layers leading to excellent room temperature lasers were grown [13]. Despite the proven value of modulation spectroscopy, particularly contactless modes such as photoreflectance (PR), in studying two-dimensional (2D) systems [14,15], there has been very little work done on 1D and 0D nanostructures. In PR (contactless form of electromodulation) modulation of the built-in electric field in the sample is caused by photoexcited electron–hole pairs created by a pump source (laser or other light source) which is chopped at frequency fm. This procedure results in sharp derivative-like spectral features in the region of intersubband transitions. In reduced-dimensional systems, it has been shown that PR produces a lineshape that is the first derivative of the unmodulated optical constants [14,15]. To the best of our knowledge no modulation spectroscopy results have been presented so far for InAs
0038-1098/99/$ - see front matter q 1999 Elsevier Science Ltd. All rights reserved. PII: S0038-109 8(99)00144-1
658
G. Se˛k et al. / Solid State Communications 110 (1999) 657–660
Fig. 1. Room temperature photoreflectance spectrum of InAs/GaAs quantum dot structure. FDGL: fit according to the first derivative of Gaussian profile. Experimental transition energies are indicated by arrows.
MOCVD-grown QDs. Only contactless electroreflectance [16] investigation for MBE-grown InAs/GaAs QDs has been reported. Till now no photoreflectance signal related to InAs QDs has been observed. There are papers on photoreflectance measurements of MOCVD-grown structures with InAs dots but no QD-related features have been shown [17,18]. In this work we present, for the first time, results of room temperature photoreflectance spectroscopy for an InAs/GaAs QD structure grown by metalorganic epitaxy, demonstrating the excellent quality of the sample. The structure studied here has been grown by low-pressure (20 mbar) MOCVD on (001) Tedoped GaAs substrate. The QD system has been obtained by deposition of 1.65 ML (monolayer) of InAs (nominal thickness) on a 100 nm GaAs buffer layer. The strong lattice mismatch between the two compounds induces the formation of InAs pyramids. The QDs are covered by 1 nm of In0.3Ga0.7As, not directly by GaAs, enhancing the optical quality of the QDs [13]. Then a 25 nm GaAs layer follows. The whole structure is cladded between two 25 nm Al0.3Ga0.7As layers and capped with 20 nm of GaAs. More details of the growth conditions have been described elsewhere [13]. On the basis of transmission electron microscopy (TEM) measurements the base length of the dots is 10–12 nm, and the base height is 2.5–3 nm. In this study we have used a standard PR apparatus
with a thermoelectrically cooled Ge photodiode as a detector. The 488 nm line of the Ar 1 laser chopped at a frequency of 30 Hz has been used as a pump beam. More details have been described elsewhere [19]. The room temperature photoreflectance spectrum of the investigated QD structure is presented in Fig. 1. We can see three groups of features related to QDs, WL (InAs wetting layer) and GaAs band gap, respectively. The low energy features labelled QD1, QD2 and QD3 originate from the QDs, while in the midenergy region of the spectrum the resonances designated WL1 and WL2 correspond to the 11H and 11L transitions in the step-shaped quantum well formed by the InAs wetting layer and In0.3Ga0.7As layer covering the QDs. The notation mnH(L) denotes a transition between the mth conduction and nth valence subbands of heavy (H) or light (L) holes, respectively. On the high energy side of the spectrum an additional oscillation-like feature is attributed to the Franz–Keldysh oscillations related to the GaAs band gap bulk-like transition. The photoreflectance (electromodulation) signals from bound states such as those in quantum dots or quantum wells can be fit to the first derivative of either a Lorentzian or a Gaussian lineshape, depending on the nature of the broadening [14,15]. A very good fit has been obtained for all QD and WL features using the first derivative of a Gaussian lineshape (FDGL). This observation proves again the well-known fact
G. Se˛k et al. / Solid State Communications 110 (1999) 657–660 Table 1 Transition energies in InAs/GaAs QD structure from PR measurements (experiment) and from calculations (theory) Transition
Experiment (eV)
Theory (eV)
QD1, e0 ! h0 QD2, e2 ! h1 QD3, e1 ! h3 WL1, 11H WL2, 11L
1.113 1.190 1.257 1.285 1.353
1.135 1.260 1.274 1.280 1.366
that the broadening in our structure is inhomogeneous and is due to fluctuations in the size and composition of the nanostructures. The complete values of the experimental energies are presented in Table 1. WL transition energies obtained from calculations based on an envelope function approximation [20] are included in Table 1. To interpret the three observed QD transitions we compare them with recent theoretical results for buried, pyramid-shaped, InAs QDs on GaAs (001) bounded by {101} facets [21,22]. The electronic structure and optical properties were modelled using 8-band k·p theory, assuming low temperature (6.5 K) and a pyramid base width of 20 lattice constants (GaAs), i.e. 11.3 nm, and accounting for the present strain distribution, piezoelectricity, valence band mixing, and conduction-band–valence-band coupling. Extrapolation of these results to room temperature yields the transitions displayed in Table 1. The energies refer to (actually inexisting) direct electron–hole recombination. Since the exciton ground state binding energy is 25 meV, the actually predicted ground state transition energy is 1.110 eV, which is very close to the observed one. The listed theoretical energies of the excited states transitions also need to be corrected somewhat downwards due to excitonic effects. The transitions occur between the three existing bound electron states (e0, e1, e2) and those hole states (h0, h1, h3) which have the same ‘‘parity’’, i.e. a similar wave function shape, as the respective electrons: the electron ground-state (e0) has an s-like envelope and the two excited states (e1, e2) have plike envelopes whose nodal planes are (110) and (1 2 10), respectively. The second excited hole state (h2) has a different shape, due to the impact of the piezoelectric field, and yields no significant oscillator
659
strength with electron states (e0, e1, e2), hence it is not seen in the present spectrum. In the case of the e2–h1 transition the calculated energy deviates from the experimental one. This is probably due to the fact that the calculation proceeds from slightly different structural properties than present in reality. Nevertheless, we conclude that the three transition lines attributed to the QD are good fingerprints of the three bound electron states, which exist for the present QD size. Our experimental results are also in good agreement with the ones reported previously by Aigouy [16] from contactless electroreflectance measurements for similar, MBE-grown, QDs. The transition energies obtained by us are slightly shifted in cpmparison to those presented in Ref. [16], but this is probably due to the presence of In0.3Ga0.7As layer in our structure that changes the strain distribution around the dots. In summary, we have performed a PR investigation at room temperature of the InAs/GaAs QD structure. This is the first report, to our knowledge, on modulation spectroscopy investigation of MOCVD-grown InAs quantum dots. Calculations of the QD transition energies have been made on the base of 8-band k·p theory and agree well with the measured transitions. The spectrum reveals the existence of three bound electron states in our QDs.
References [1] J.Y. Marzin, J.M. Ge´rard, A. Izrae¨l, D. Barrier, G. Bastard, Phys. Rev. Lett. 73 (1994) 716. [2] D. Bimberg, M. Grundmann, N.N. Ledentsov, S.S. Ruvimov, P. Werner, U. Richter, J. Heydenreich, V.M. Ustinov, P.S. Kopev, Z.I. Alferov, Thin Solid Films 267 (1995) 32. [3] N.N. Ledentsov, M. Grundmann, N. Kirstaedter, O. Schmidt, R. Heitz, J. Bo¨hrer, D. Bimberg, V.M. Ustinov, V.A. Shchukin, A.Y. Egorov, A.E. Zhukov, S. Zaitsev, P.S. Kopev, Z.I. Alferov, S.S. Ruvimov, A.O. Kosogov, P. Werner, U. Go¨sele, J. Heydenreich, Solid State Electron. 40 (1996) 785. [4] D. Bimberg, N.N. Ledentsov, M. Grundmann, N. Kirstaedter, O.G. Schmidt, M.H. Mao, V.M. Ustinov, A.Y. Egorov, A.E. Zhukov, P.S. Kopev, Z.I. Alferov, S.S. Ruvimov, U. Go¨sele, J. Heydenreich, Phys. Stat. Sol. (b) 194 (1996) 159. [5] D. Bimberg, N.N. Ledentsov, M. Grundmann, N. Kirstaedter, O.G. Schmidt, M.H. Mao, V.M. Ustinov, A.Y. Egorov, A.E. Zhukov, P.S. Kopev, Z.I. Alferov, S.S. Ruvimov, U. Go¨sele, J. Heydenreich, Jpn. J. Appl. Phys. 35 (1996) 1311.
660
G. Se˛k et al. / Solid State Communications 110 (1999) 657–660
[6] J. Oshinowo, M. Nishioka, S. Ishida, Y. Arakawa, Appl. Phys. Lett. 65 (1994) 1421. [7] K. Mukai, N. Ohtsuka, M. Sugawara, S. Yamazaki, Jpn. J. Appl. Phys. 33 (1994) L1710. [8] F. Heinrichsdorff, A. Krost, M. Grundmann, D. Bimberg, A. Kosogov, P. Werner, Appl. Phys. Lett. 68 (1996) 3284. [9] F. Adler, M. Geiger, A. Bauknecht, F. Scholz, H. Schweizer, M.H. Pilkuhn, B. Ohnesorge, A. Forchel, J. Appl. Phys. 80 (1996) 4019. [10] F. Heinrichsdorff, A. Krost, N. Kirstaedter, M.H. Mao, M. Grundmann, D. Bimberg, A.O. Kosogov, P. Werner, Jpn. J. Appl. Phys. 36 (1997) 4129. [11] F. Adler, M. Geiger, A. Bauknecht, F. Scholz, H. Schweizer, Phys. Stat. Sol. (a) 164 (1997) 431. [12] F. Adler, M. Geiger, A. Bauknecht, D. Haase, P. Ernst, A. Do¨rnen, F. Scholz, H. Schweizer, J. Appl. Phys. 83 (1997) 1631. [13] F. Heinrichsdorff, M.H. Mao, N. Kirstaedter, A. Krost, D. Bimberg, A.O. Kosogov, P. Werner, Appl. Phys. Lett. 71 (1997) 22. [14] O.J. Glembocki, B.V. Shanbrook, Semiconductors and Semimetals, in: D.G. Seiler, C.L. Littler (Eds.), Academic Press, New York, 1992, p. 221.
[15] F.H. Pollak, in: M. Balkanski (Ed.), Handbook on Semiconductors, North Holland, Amsterdam, 1994, pp. 527. [16] L. Aigouy, T. Holden, F.H. Pollak, N.N. Ledentsov, W.M. Ustinov, P.S. Kopev, D. Bimberg, Appl. Phys. Lett. 70 (1997) 3329. [17] A. Patene´, M. Grassi-Alessi, F. Intonti, A. Polimeni, M. Capizzi, F. Martelli, M. Geddo, A. Bosacchi, S. Franchi, Phys. Stat. Sol. (a) 164 (1997) 493. [18] M. Geddo, M. Capizzi, A. Patene´, F. Martelli, J. Appl. Phys. 84 (1998) 3374. [19] J. Misiewicz, K. Jezierski, P. Sitarek, P. Markiewicz, R. Korbutowicz, M. Panek, B. S´ciana, M. Tl⁄aczal⁄a, Adv. Mater. Opt. Electron. 5 (1995) 321. [20] G. Bastard, Wave mechanics applied to semiconductor heterostructures, Les Editions de Physique, Paris, 1992, p. 31. [21] O. Stier, M. Grundmann, D. Bimberg, Proceedings of the 24th International Conference on Physics of Semiconductors, World Scientific, Singapore, 1998, p. 138. [22] O. Stier, M. Grundmann, D. Bimberg, Phys. Rev. B 58 (1998) 10557.
Solid State Communications 110 (1999) 657–660
Room temperature photoreflectance of MOCVD-grown InAs/GaAs quantum dots G. Se˛k a,*, J. Misiewicz a, K. Ryczko a, M. Kubisa a, F. Heinrichsdorff b, O. Stier b, D. Bimberg b a
Institute of Physics, Wrocl⁄aw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wrocl⁄aw, Poland b Institute of Solid State Physics, Technical University Berlin, Hardenbergstrasse 36, D10623 Berlin, Germany Received 20 January 1999; accepted 18 March 1999 by H. Eschrig
Abstract Photoreflectance spectroscopy results are reported for InAs/GaAs self-organised quantum dots grown by low-pressure MOCVD. Quantum dot-related optical transitions have been observed for the first time at room temperature. Good agreement between experiment and theory based on a recent 8-band k·p theory has been obtained. q 1999 Elsevier Science Ltd. All rights reserved. Keywords: A. Semiconductors; A. Nanostructures; D. Electronic states (localized)
Most of the previous reports on InAs/GaAs quantum dots (QDs), which present a basis for novel lasers, deal with structures grown by MBE [1–5]. The development of QD structures of similar quality by metalorganic chemical vapor deposition (MOCVD) was originally hindered by various mechanisms, particular in the growth process. In particular, the growth of the dot layers with high lateral density was originally accompanied by the tendency towards formation of large plastically relaxed clusters, indicating the greater influence of growth kinetics (e.g. long-range adatom surface migration) than in MBE. These clusters not only decreased the optical quality of the dot layers and may even exclude their application in QD lasers, but also made vertical stacking of device quality QDs impossible. In most of the original studies of MOCVD InxGa12xAs/GaAs QDs, ternary InxGa12xAs with x in the range of 30–70% was used for the dot * Corresponding author.
growth [6–8]. Recently parameters for the growth of binary InAs/GaAs QDs were assessed [9–12] and stacked QD layers leading to excellent room temperature lasers were grown [13]. Despite the proven value of modulation spectroscopy, particularly contactless modes such as photoreflectance (PR), in studying two-dimensional (2D) systems [14,15], there has been very little work done on 1D and 0D nanostructures. In PR (contactless form of electromodulation) modulation of the built-in electric field in the sample is caused by photoexcited electron–hole pairs created by a pump source (laser or other light source) which is chopped at frequency fm. This procedure results in sharp derivative-like spectral features in the region of intersubband transitions. In reduced-dimensional systems, it has been shown that PR produces a lineshape that is the first derivative of the unmodulated optical constants [14,15]. To the best of our knowledge no modulation spectroscopy results have been presented so far for InAs
0038-1098/99/$ - see front matter q 1999 Elsevier Science Ltd. All rights reserved. PII: S0038-109 8(99)00144-1
658
G. Se˛k et al. / Solid State Communications 110 (1999) 657–660
Fig. 1. Room temperature photoreflectance spectrum of InAs/GaAs quantum dot structure. FDGL: fit according to the first derivative of Gaussian profile. Experimental transition energies are indicated by arrows.
MOCVD-grown QDs. Only contactless electroreflectance [16] investigation for MBE-grown InAs/GaAs QDs has been reported. Till now no photoreflectance signal related to InAs QDs has been observed. There are papers on photoreflectance measurements of MOCVD-grown structures with InAs dots but no QD-related features have been shown [17,18]. In this work we present, for the first time, results of room temperature photoreflectance spectroscopy for an InAs/GaAs QD structure grown by metalorganic epitaxy, demonstrating the excellent quality of the sample. The structure studied here has been grown by low-pressure (20 mbar) MOCVD on (001) Tedoped GaAs substrate. The QD system has been obtained by deposition of 1.65 ML (monolayer) of InAs (nominal thickness) on a 100 nm GaAs buffer layer. The strong lattice mismatch between the two compounds induces the formation of InAs pyramids. The QDs are covered by 1 nm of In0.3Ga0.7As, not directly by GaAs, enhancing the optical quality of the QDs [13]. Then a 25 nm GaAs layer follows. The whole structure is cladded between two 25 nm Al0.3Ga0.7As layers and capped with 20 nm of GaAs. More details of the growth conditions have been described elsewhere [13]. On the basis of transmission electron microscopy (TEM) measurements the base length of the dots is 10–12 nm, and the base height is 2.5–3 nm. In this study we have used a standard PR apparatus
with a thermoelectrically cooled Ge photodiode as a detector. The 488 nm line of the Ar 1 laser chopped at a frequency of 30 Hz has been used as a pump beam. More details have been described elsewhere [19]. The room temperature photoreflectance spectrum of the investigated QD structure is presented in Fig. 1. We can see three groups of features related to QDs, WL (InAs wetting layer) and GaAs band gap, respectively. The low energy features labelled QD1, QD2 and QD3 originate from the QDs, while in the midenergy region of the spectrum the resonances designated WL1 and WL2 correspond to the 11H and 11L transitions in the step-shaped quantum well formed by the InAs wetting layer and In0.3Ga0.7As layer covering the QDs. The notation mnH(L) denotes a transition between the mth conduction and nth valence subbands of heavy (H) or light (L) holes, respectively. On the high energy side of the spectrum an additional oscillation-like feature is attributed to the Franz–Keldysh oscillations related to the GaAs band gap bulk-like transition. The photoreflectance (electromodulation) signals from bound states such as those in quantum dots or quantum wells can be fit to the first derivative of either a Lorentzian or a Gaussian lineshape, depending on the nature of the broadening [14,15]. A very good fit has been obtained for all QD and WL features using the first derivative of a Gaussian lineshape (FDGL). This observation proves again the well-known fact
G. Se˛k et al. / Solid State Communications 110 (1999) 657–660 Table 1 Transition energies in InAs/GaAs QD structure from PR measurements (experiment) and from calculations (theory) Transition
Experiment (eV)
Theory (eV)
QD1, e0 ! h0 QD2, e2 ! h1 QD3, e1 ! h3 WL1, 11H WL2, 11L
1.113 1.190 1.257 1.285 1.353
1.135 1.260 1.274 1.280 1.366
that the broadening in our structure is inhomogeneous and is due to fluctuations in the size and composition of the nanostructures. The complete values of the experimental energies are presented in Table 1. WL transition energies obtained from calculations based on an envelope function approximation [20] are included in Table 1. To interpret the three observed QD transitions we compare them with recent theoretical results for buried, pyramid-shaped, InAs QDs on GaAs (001) bounded by {101} facets [21,22]. The electronic structure and optical properties were modelled using 8-band k·p theory, assuming low temperature (6.5 K) and a pyramid base width of 20 lattice constants (GaAs), i.e. 11.3 nm, and accounting for the present strain distribution, piezoelectricity, valence band mixing, and conduction-band–valence-band coupling. Extrapolation of these results to room temperature yields the transitions displayed in Table 1. The energies refer to (actually inexisting) direct electron–hole recombination. Since the exciton ground state binding energy is 25 meV, the actually predicted ground state transition energy is 1.110 eV, which is very close to the observed one. The listed theoretical energies of the excited states transitions also need to be corrected somewhat downwards due to excitonic effects. The transitions occur between the three existing bound electron states (e0, e1, e2) and those hole states (h0, h1, h3) which have the same ‘‘parity’’, i.e. a similar wave function shape, as the respective electrons: the electron ground-state (e0) has an s-like envelope and the two excited states (e1, e2) have plike envelopes whose nodal planes are (110) and (1 2 10), respectively. The second excited hole state (h2) has a different shape, due to the impact of the piezoelectric field, and yields no significant oscillator
659
strength with electron states (e0, e1, e2), hence it is not seen in the present spectrum. In the case of the e2–h1 transition the calculated energy deviates from the experimental one. This is probably due to the fact that the calculation proceeds from slightly different structural properties than present in reality. Nevertheless, we conclude that the three transition lines attributed to the QD are good fingerprints of the three bound electron states, which exist for the present QD size. Our experimental results are also in good agreement with the ones reported previously by Aigouy [16] from contactless electroreflectance measurements for similar, MBE-grown, QDs. The transition energies obtained by us are slightly shifted in cpmparison to those presented in Ref. [16], but this is probably due to the presence of In0.3Ga0.7As layer in our structure that changes the strain distribution around the dots. In summary, we have performed a PR investigation at room temperature of the InAs/GaAs QD structure. This is the first report, to our knowledge, on modulation spectroscopy investigation of MOCVD-grown InAs quantum dots. Calculations of the QD transition energies have been made on the base of 8-band k·p theory and agree well with the measured transitions. The spectrum reveals the existence of three bound electron states in our QDs.
References [1] J.Y. Marzin, J.M. Ge´rard, A. Izrae¨l, D. Barrier, G. Bastard, Phys. Rev. Lett. 73 (1994) 716. [2] D. Bimberg, M. Grundmann, N.N. Ledentsov, S.S. Ruvimov, P. Werner, U. Richter, J. Heydenreich, V.M. Ustinov, P.S. Kopev, Z.I. Alferov, Thin Solid Films 267 (1995) 32. [3] N.N. Ledentsov, M. Grundmann, N. Kirstaedter, O. Schmidt, R. Heitz, J. Bo¨hrer, D. Bimberg, V.M. Ustinov, V.A. Shchukin, A.Y. Egorov, A.E. Zhukov, S. Zaitsev, P.S. Kopev, Z.I. Alferov, S.S. Ruvimov, A.O. Kosogov, P. Werner, U. Go¨sele, J. Heydenreich, Solid State Electron. 40 (1996) 785. [4] D. Bimberg, N.N. Ledentsov, M. Grundmann, N. Kirstaedter, O.G. Schmidt, M.H. Mao, V.M. Ustinov, A.Y. Egorov, A.E. Zhukov, P.S. Kopev, Z.I. Alferov, S.S. Ruvimov, U. Go¨sele, J. Heydenreich, Phys. Stat. Sol. (b) 194 (1996) 159. [5] D. Bimberg, N.N. Ledentsov, M. Grundmann, N. Kirstaedter, O.G. Schmidt, M.H. Mao, V.M. Ustinov, A.Y. Egorov, A.E. Zhukov, P.S. Kopev, Z.I. Alferov, S.S. Ruvimov, U. Go¨sele, J. Heydenreich, Jpn. J. Appl. Phys. 35 (1996) 1311.
660
G. Se˛k et al. / Solid State Communications 110 (1999) 657–660
[6] J. Oshinowo, M. Nishioka, S. Ishida, Y. Arakawa, Appl. Phys. Lett. 65 (1994) 1421. [7] K. Mukai, N. Ohtsuka, M. Sugawara, S. Yamazaki, Jpn. J. Appl. Phys. 33 (1994) L1710. [8] F. Heinrichsdorff, A. Krost, M. Grundmann, D. Bimberg, A. Kosogov, P. Werner, Appl. Phys. Lett. 68 (1996) 3284. [9] F. Adler, M. Geiger, A. Bauknecht, F. Scholz, H. Schweizer, M.H. Pilkuhn, B. Ohnesorge, A. Forchel, J. Appl. Phys. 80 (1996) 4019. [10] F. Heinrichsdorff, A. Krost, N. Kirstaedter, M.H. Mao, M. Grundmann, D. Bimberg, A.O. Kosogov, P. Werner, Jpn. J. Appl. Phys. 36 (1997) 4129. [11] F. Adler, M. Geiger, A. Bauknecht, F. Scholz, H. Schweizer, Phys. Stat. Sol. (a) 164 (1997) 431. [12] F. Adler, M. Geiger, A. Bauknecht, D. Haase, P. Ernst, A. Do¨rnen, F. Scholz, H. Schweizer, J. Appl. Phys. 83 (1997) 1631. [13] F. Heinrichsdorff, M.H. Mao, N. Kirstaedter, A. Krost, D. Bimberg, A.O. Kosogov, P. Werner, Appl. Phys. Lett. 71 (1997) 22. [14] O.J. Glembocki, B.V. Shanbrook, Semiconductors and Semimetals, in: D.G. Seiler, C.L. Littler (Eds.), Academic Press, New York, 1992, p. 221.
[15] F.H. Pollak, in: M. Balkanski (Ed.), Handbook on Semiconductors, North Holland, Amsterdam, 1994, pp. 527. [16] L. Aigouy, T. Holden, F.H. Pollak, N.N. Ledentsov, W.M. Ustinov, P.S. Kopev, D. Bimberg, Appl. Phys. Lett. 70 (1997) 3329. [17] A. Patene´, M. Grassi-Alessi, F. Intonti, A. Polimeni, M. Capizzi, F. Martelli, M. Geddo, A. Bosacchi, S. Franchi, Phys. Stat. Sol. (a) 164 (1997) 493. [18] M. Geddo, M. Capizzi, A. Patene´, F. Martelli, J. Appl. Phys. 84 (1998) 3374. [19] J. Misiewicz, K. Jezierski, P. Sitarek, P. Markiewicz, R. Korbutowicz, M. Panek, B. S´ciana, M. Tl⁄aczal⁄a, Adv. Mater. Opt. Electron. 5 (1995) 321. [20] G. Bastard, Wave mechanics applied to semiconductor heterostructures, Les Editions de Physique, Paris, 1992, p. 31. [21] O. Stier, M. Grundmann, D. Bimberg, Proceedings of the 24th International Conference on Physics of Semiconductors, World Scientific, Singapore, 1998, p. 138. [22] O. Stier, M. Grundmann, D. Bimberg, Phys. Rev. B 58 (1998) 10557.