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Probing ordering in self-assembled nanostructures by Raman scattering interferometry
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Physica E 17 (2003) 533 – 536 www.elsevier.com/locate/physe
Probing ordering in self-assembled nanostructures by Raman scattering interferometry M. Cazayousa;∗ , J. Groenena , J. Braultb , M. Gendryb , U. Denkerc , O.G. Schmidtc a Laboratoire
Physique des Solides, Universite Paul Sabatier, UMR 5477-IRSAMC, 118 rte de Narbonne, F-31062 Toulouse Cedex 4, France b Laboratoire d’Electronique-LEOM, UMR 5512, Ecole Centrale Lyon, 36 av G. de Collongue, F-69131 Ecully Cedex, France c Max Planck Institut f3 ur Festkorperforschung, Heisenbergstrasse 1, D-70174 Stuttgart, Germany
Abstract Raman scattering interferences are shown to provide a means of probing self-organization in quantum dot multilayers. These interferences result from the interaction between acoustic phonons and con4ned electronic states. The degree of alignment in Ge/Si quantum dot multilayers has been derived from the interference contrast. Clear evidence of the staggered arrangement is found in the Raman spectra of InAs/InAlAs quantum wires. ? 2002 Elsevier Science B.V. All rights reserved. PACS: 78.30.−j; 63.20.Kr; 81.07.Ta; 81.15.Hi Keywords: Raman scattering; Interferences; Self-organization; Quantum dots
1. Introduction
2. Experiments and simulations
Self-organization in quantum dot (QD) multilayers has been the scope of various studies in recent years [1–4]. Ordering is usually evidenced by means of transmission electron microscopy (TEM) [1,3]. X-ray diBraction is an interesting alternative, as it is non-destructive and has an improved statistical accurancy [4]. In this paper, we show that Raman scattering interferences (RSI) provides a means of probing self-organization in QD multilayers. Examples with diBerent types of ordering are provided.
Self-assembled Ge/Si QD and InAs/InAlAs quantum wire (QW) multilayers were grown by molecular beam expitaxy. Details on growth can be found in Refs. [3,5], respectively. Samples A and B contain 4ve Ge QD layers capped by a 100 nm Si layer (the spacings are t = 12:5 and 100 nm, respectively). Ge islands have a plano convex lens shape with a mean height h = 6 nm and width w = 85 nm. The QD density is 4 × 109 cm−2 . Sample C contains 4ve InAs QW layers, with h = 4:8 nm and width w = 18 nm and InAlAs spacings of 15 nm. Raman scattering was performed at room temperature in backscattering geometry in vacuum in order to avoid the air related Raman peaks. Scattered light was detected by a T800 Coderg triple spectrometer
∗ Corresponding author. Tel.: +33-11-335-6155-6185; fax: +33-11-335-6155-6233. E-mail address: [email protected] (M. Cazayous).
1386-9477/03/$ - see front matter ? 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S1386-9477(02)00861-5
534
M. Cazayous et al. / Physica E 17 (2003) 533 – 536
Fig. 1. Schematic view of the structure used in the simulations. QDs are modelled by disks. t is the interlayer spacing.
coupled to a photomultiplier. Spectra were excited with an argon laser, in resonance with the E1 transitions of the QDs. Resonant Raman spectra were simulated using the model presented in Ref. [7]. In this model we consider the deformation potential interaction between acoustic phonons and con4ned electronic states (Fig. 1). QDs are modelled by disks. Various QD in-plane distributions were simulated. Acoustic wave reLections at the interfaces and sample surface are included. 3. Results and discussion Due to the lack of translational invariance, the usual wave vector conservation law breaks down: acoustic phonons become Raman active [6]. According to the three-dimensional electronic con4nement, acoustic phonons with both qz and q wave vector components do contribute. Notice however that, according to the QD height/width ratio, the phonons which contribute signi4cantly do have small q wave vector components [7]. The coherent sum of the scattering probability amplitudes yields RSI [6]. Such interferences are shown in Fig. 2. Well de4ned oscillations are observed. Their period scales inversely with the interlayer spacing and
Fig. 2. Experimental spectra (A and B) and simulated ones with random distributions (0%) and with vertical correlations (100%). t equals 12.5 and 100 nm, respectively.
their envelope is determined by the electronic con4nement [6]. Let us now discuss the ordering eBects. Simulations were performed considering a random in-plane distribution in the 4rst layer with no correlation in the next layers (0%) and with perfect vertical correlation (100%). We de4ne a normalized Raman interference contrast: CRaman = (C exp − C ran )=(C cor − C ran ), where C exp is the experimental contrast, C ran the contrast calculated with random QD distribution, and C cor the contrast calculated with vertically correlated QDs. The RSI contrast depends much on the QDs spatial distribution. Strong contrast is observed for 100% and a weak contrast remains for 0%. Fig. 3 shows the RSI contrast as a function of both the ordering and the QD density. The residual contrast observed for random distributions (0%) depends much on the density, whereas it does not for perfect vertical correlation (100%). For a given QD density, the RSI contrast increases progressively with the vertical correlation degree. One can use these calculations to derive the degree of correlation from the experimental spectra. One can normalize the experimental contrast
M. Cazayous et al. / Physica E 17 (2003) 533 – 536
Fig. 3. Raman interference contrast as a function of vertical correlation and QD density.
with respect to the simulated ones with ordered (100%) and random (0%) distributions. Spectrum A is similar to the 100% one. The contrast in spectrum B is in between the two extreme cases. The normalized contrast is 98% and 17% for A and B, respectively. These values compare well with the degree of
535
alignment obtained by TEM [3]. The degree of vertical alignment can thus be derived from the RSI. Let us now consider another type of spatial arrangement. The InAs/InAlAs structures present a staggered arrangement (see Fig. 4) of InAs quantum wires (QW) [5]. Fig. 4 represents the experimental spectrum (C) compared to simulated spectra with vertically and staggered arrangements (C1 and C2 , respectively). C1 and C2 both display RSI. Notice that C1 displays doublets whereas C2 does not. The RSI period of C1 is therefore twice larger than the one of C2 . This means that the period in the QW arrangement is twice smaller. This is consistent with the diBerence of the periodicity when the two arrangements are compared (Fig. 4). The simulated spectrum C2 compares well with the experimental one C. RSI provide thus a clear signature in reciprocal space of the staggered QW arrangement. 4. Conclusion We have shown that one can probe ordering in QD multilayers by means of RSI. We emphasize that these
Fig. 4. Experimental spectrum (C) and simulated spectra considering vertical alignment (C1 ) and staggered vertical organisation (C2 ). Both vertical aligned and staggered arrangements are schematised.
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M. Cazayous et al. / Physica E 17 (2003) 533 – 536
RSI provide 3D sampling and are relevant for probing ordering over length scales ranging from a few to a few hundreds of nanometers. References [1] Q. Xie, A. Madhukar, P. Chen, N.P. Kobayashi, Phys. Rev. Lett. 75 (1995) 2542. [2] G. Springholz, M. Pinczolits, P. Mayer, V. Holy, G. Bauer, H.H. Kang, L. Salamanca-Riba, Phys. Rev. Lett. 84 (2000) 4669.
[3] O. Kienzle, F. Ernst, M. RPuhle, O.G. Schmidt, K. Eberl, Appl. Phys. Lett. 74 (1999) 269. [4] J. Stangl, T. Roch, G. Bauer, I. Kegel, T.H. Metzger, O.G. Schmidt, K. Eberl, O. Kienzle, F. Ernst, 77 (2000) 3953. [5] J. Brault, M. Gendry, O. Marty, M. Pitaval, J. Olivares, G. Grenet, G. Hollinger, Appl. Surf. Sci. 162–163 (2000) 584. [6] M. Cazayous, J.R. Huntzinger, J. Groenen, A. Mlayah, S. Christiansen, H.P. Strunk, O.G. Schmidt, K. Eberl, Phys. Rev. B 62 (2000) 7243. [7] M. Cazayous, J. Groenen, J.R. Huntzinger, A. Mlayah, O.G. Schmidt, Phys. Rev. B 64 (2001) 033306.
Physica E 17 (2003) 533 – 536 www.elsevier.com/locate/physe
Probing ordering in self-assembled nanostructures by Raman scattering interferometry M. Cazayousa;∗ , J. Groenena , J. Braultb , M. Gendryb , U. Denkerc , O.G. Schmidtc a Laboratoire
Physique des Solides, Universite Paul Sabatier, UMR 5477-IRSAMC, 118 rte de Narbonne, F-31062 Toulouse Cedex 4, France b Laboratoire d’Electronique-LEOM, UMR 5512, Ecole Centrale Lyon, 36 av G. de Collongue, F-69131 Ecully Cedex, France c Max Planck Institut f3 ur Festkorperforschung, Heisenbergstrasse 1, D-70174 Stuttgart, Germany
Abstract Raman scattering interferences are shown to provide a means of probing self-organization in quantum dot multilayers. These interferences result from the interaction between acoustic phonons and con4ned electronic states. The degree of alignment in Ge/Si quantum dot multilayers has been derived from the interference contrast. Clear evidence of the staggered arrangement is found in the Raman spectra of InAs/InAlAs quantum wires. ? 2002 Elsevier Science B.V. All rights reserved. PACS: 78.30.−j; 63.20.Kr; 81.07.Ta; 81.15.Hi Keywords: Raman scattering; Interferences; Self-organization; Quantum dots
1. Introduction
2. Experiments and simulations
Self-organization in quantum dot (QD) multilayers has been the scope of various studies in recent years [1–4]. Ordering is usually evidenced by means of transmission electron microscopy (TEM) [1,3]. X-ray diBraction is an interesting alternative, as it is non-destructive and has an improved statistical accurancy [4]. In this paper, we show that Raman scattering interferences (RSI) provides a means of probing self-organization in QD multilayers. Examples with diBerent types of ordering are provided.
Self-assembled Ge/Si QD and InAs/InAlAs quantum wire (QW) multilayers were grown by molecular beam expitaxy. Details on growth can be found in Refs. [3,5], respectively. Samples A and B contain 4ve Ge QD layers capped by a 100 nm Si layer (the spacings are t = 12:5 and 100 nm, respectively). Ge islands have a plano convex lens shape with a mean height h = 6 nm and width w = 85 nm. The QD density is 4 × 109 cm−2 . Sample C contains 4ve InAs QW layers, with h = 4:8 nm and width w = 18 nm and InAlAs spacings of 15 nm. Raman scattering was performed at room temperature in backscattering geometry in vacuum in order to avoid the air related Raman peaks. Scattered light was detected by a T800 Coderg triple spectrometer
∗ Corresponding author. Tel.: +33-11-335-6155-6185; fax: +33-11-335-6155-6233. E-mail address: [email protected] (M. Cazayous).
1386-9477/03/$ - see front matter ? 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S1386-9477(02)00861-5
534
M. Cazayous et al. / Physica E 17 (2003) 533 – 536
Fig. 1. Schematic view of the structure used in the simulations. QDs are modelled by disks. t is the interlayer spacing.
coupled to a photomultiplier. Spectra were excited with an argon laser, in resonance with the E1 transitions of the QDs. Resonant Raman spectra were simulated using the model presented in Ref. [7]. In this model we consider the deformation potential interaction between acoustic phonons and con4ned electronic states (Fig. 1). QDs are modelled by disks. Various QD in-plane distributions were simulated. Acoustic wave reLections at the interfaces and sample surface are included. 3. Results and discussion Due to the lack of translational invariance, the usual wave vector conservation law breaks down: acoustic phonons become Raman active [6]. According to the three-dimensional electronic con4nement, acoustic phonons with both qz and q wave vector components do contribute. Notice however that, according to the QD height/width ratio, the phonons which contribute signi4cantly do have small q wave vector components [7]. The coherent sum of the scattering probability amplitudes yields RSI [6]. Such interferences are shown in Fig. 2. Well de4ned oscillations are observed. Their period scales inversely with the interlayer spacing and
Fig. 2. Experimental spectra (A and B) and simulated ones with random distributions (0%) and with vertical correlations (100%). t equals 12.5 and 100 nm, respectively.
their envelope is determined by the electronic con4nement [6]. Let us now discuss the ordering eBects. Simulations were performed considering a random in-plane distribution in the 4rst layer with no correlation in the next layers (0%) and with perfect vertical correlation (100%). We de4ne a normalized Raman interference contrast: CRaman = (C exp − C ran )=(C cor − C ran ), where C exp is the experimental contrast, C ran the contrast calculated with random QD distribution, and C cor the contrast calculated with vertically correlated QDs. The RSI contrast depends much on the QDs spatial distribution. Strong contrast is observed for 100% and a weak contrast remains for 0%. Fig. 3 shows the RSI contrast as a function of both the ordering and the QD density. The residual contrast observed for random distributions (0%) depends much on the density, whereas it does not for perfect vertical correlation (100%). For a given QD density, the RSI contrast increases progressively with the vertical correlation degree. One can use these calculations to derive the degree of correlation from the experimental spectra. One can normalize the experimental contrast
M. Cazayous et al. / Physica E 17 (2003) 533 – 536
Fig. 3. Raman interference contrast as a function of vertical correlation and QD density.
with respect to the simulated ones with ordered (100%) and random (0%) distributions. Spectrum A is similar to the 100% one. The contrast in spectrum B is in between the two extreme cases. The normalized contrast is 98% and 17% for A and B, respectively. These values compare well with the degree of
535
alignment obtained by TEM [3]. The degree of vertical alignment can thus be derived from the RSI. Let us now consider another type of spatial arrangement. The InAs/InAlAs structures present a staggered arrangement (see Fig. 4) of InAs quantum wires (QW) [5]. Fig. 4 represents the experimental spectrum (C) compared to simulated spectra with vertically and staggered arrangements (C1 and C2 , respectively). C1 and C2 both display RSI. Notice that C1 displays doublets whereas C2 does not. The RSI period of C1 is therefore twice larger than the one of C2 . This means that the period in the QW arrangement is twice smaller. This is consistent with the diBerence of the periodicity when the two arrangements are compared (Fig. 4). The simulated spectrum C2 compares well with the experimental one C. RSI provide thus a clear signature in reciprocal space of the staggered QW arrangement. 4. Conclusion We have shown that one can probe ordering in QD multilayers by means of RSI. We emphasize that these
Fig. 4. Experimental spectrum (C) and simulated spectra considering vertical alignment (C1 ) and staggered vertical organisation (C2 ). Both vertical aligned and staggered arrangements are schematised.
536
M. Cazayous et al. / Physica E 17 (2003) 533 – 536
RSI provide 3D sampling and are relevant for probing ordering over length scales ranging from a few to a few hundreds of nanometers. References [1] Q. Xie, A. Madhukar, P. Chen, N.P. Kobayashi, Phys. Rev. Lett. 75 (1995) 2542. [2] G. Springholz, M. Pinczolits, P. Mayer, V. Holy, G. Bauer, H.H. Kang, L. Salamanca-Riba, Phys. Rev. Lett. 84 (2000) 4669.
[3] O. Kienzle, F. Ernst, M. RPuhle, O.G. Schmidt, K. Eberl, Appl. Phys. Lett. 74 (1999) 269. [4] J. Stangl, T. Roch, G. Bauer, I. Kegel, T.H. Metzger, O.G. Schmidt, K. Eberl, O. Kienzle, F. Ernst, 77 (2000) 3953. [5] J. Brault, M. Gendry, O. Marty, M. Pitaval, J. Olivares, G. Grenet, G. Hollinger, Appl. Surf. Sci. 162–163 (2000) 584. [6] M. Cazayous, J.R. Huntzinger, J. Groenen, A. Mlayah, S. Christiansen, H.P. Strunk, O.G. Schmidt, K. Eberl, Phys. Rev. B 62 (2000) 7243. [7] M. Cazayous, J. Groenen, J.R. Huntzinger, A. Mlayah, O.G. Schmidt, Phys. Rev. B 64 (2001) 033306.