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Asymmetric carrier transport in InGaAs quantum wells and wires grown on tilted InP substrates
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Physica E 17 (2003) 169 – 171 www.elsevier.com/locate/physe
Asymmetric carrier transport in InGaAs quantum wells and wires grown on tilted InP substrates A.F.G. Montea;∗ , S.W. da Silvaa , J.M.R. Cruza , P.C. Moraisa , A.S. Chavesb a Instituto
de F sica, NFA, Universidade de Bras lia, Bras lia DF, 70919-970, Brazil de F sica, Universidade de Minas Gerais, Belo Horizonte MG, Brazil
b Departamento
Abstract The in1uence of the interface morphology upon the electron–hole transport in intrinsic In0:53 Ga0:47 As=InP quantum structures was investigated by scanning the photoluminescence PL intensity pro6le on the sample surface. The results suggest that the carrier di7usion is very sensitive to both the roughness of the interfaces and the presence of 6nite-width terraces. It was found that the carrier density pro6le shows asymmetric di7usion normal to the terraces whereas it shows symmetric expansion along the terraces. ? 2002 Elsevier Science B.V. All rights reserved. PACS: 73.21.Fg; 73.21.Hb; 68.35.Fx Keywords: Quantum well; Quantum wire; Fractal di7usion; Asymmetric di7usion
1. Introduction Experimental results of spatially resolved imaging in In0:53 Ga0:47 As=InP heterostructures are presented and discussed focusing the investigation of the carrier di7usion. It has been shown that carrier di7usion in quantum well (QW) layers with the normal oriented along the [0 0 1] direction is clearly distinct from di7usion in QWs grown on tilted substrates (2◦ o7 towards [1 1 1]). In the 6rst case carrier di7usion is axially symmetric, whereas in the second case it is asymmetric, showing a tail along the [1 1 0] direction. We carried out studies on In0:53 Ga0:47 As quantum wires
∗ Corresponding author. Tel.: +55-61-7233940; fax: +55-612726026. E-mail address: [email protected] (A.F.G. Monte).
F (one (QWRs) with thickness varying from 3 to 12 A to four monolayers), whereas the lateral dimension F varies from about 80 –180 A. 2. Results and discussion Samples used in this study were grown by vapour levitation epitaxy (VLE), which has been described in detail elsewhere [1]. Sn-doped InP substrates oriented 2◦ o7 the (1 0 0) toward the (1 1 1) were used. The InP substrate as well as the epitaxial InP surface, upon which the In0:53 Ga0:47 As was grown, are not perfectly planar and have steps of monolayer height F The growth rates were about 2 and (a0 = 2:93 A). F 0:5 A=s for the InP and In0:53 Ga0:47 As layers, respectively. Using extremely short In0:53 Ga0:47 As growth times (0.5, 1, and 2 s), it was possible to grow
1386-9477/03/$ - see front matter ? 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S1386-9477(02)00736-1
170
A.F.G. Monte et al. / Physica E 17 (2003) 169 – 171
Growth
T = 13K
PL intensity (arb. units)
time 0.5s
M=1
1s
M=1
2s
M=2
10s
M=4
-80
- 40 0 40 Distance (µm)
80
Fig. 1. Carrier density pro6les taken from di7erent In0:53 Ga0:47 As= InP quantum structures as quoted by the In0:53 Ga0:47 As growth times.
uniform QWRs having a few monolayers high and suf6ciently narrow lateral width. Longer In0:53 Ga0:47 As growth times (¿ 10 s) allows the growth of very thin QWs instead of QWRs. The samples were mounted in a temperaturecontrolled optical cryostat and excited using an Ar + -ion laser (ex =514:5 nm). The laser beam was focused down to a spot of 2 m in diameter. Band-pass 6lters are used to select the PL emission from the luminescent region. Fig. 1 shows the variation observed on the spatial carrier distribution as obtained from the In0:53 Ga0:47 As=InP samples as a function of the growth times. It is quite clear the e7ect of the width of the In0:53 Ga0:47 As terraces upon the asymmetric carrier distribution. The carrier distribution observed from the 10 s sample is highly asymmetric with a shoulder on the right-hand side of the main feature. The e7ect of the asymmetry in the di7usion pro6le is reduced as the sample growth time decreases from 10 to 0:5 s. The carrier distribution is almost symmetric for the 0:5 s sample.
The relationship between growth time and lateral wire width is the most important factor to understand the asymmetry observed on the carrier di7usion pro6le. According to Worlock et al. [2], the lateral wire width in these samples are around 80, F for 0.5, 1, and 2 s growth times, 100, and 180 A respectively. The number of monolayers height (M) increases with the growth time, as quoted in Fig. 1. Wire coupling is ignored for the 0:5 s sample, which presents only one monolayer in thickness and about F of lateral width. In the 1 s sample, which is one 80 A monolayer height but presenting a wider terrace, the asymmetry is slightly observed. For the 2 s sample, which is two monolayers height, the wires are coupled together and the asymmetry is large. In the 10 s sample the wires are completely merged in a QW structure. The carrier di7usion can be modeled using two distinct regimes. One regime is the normal di7usion, which follows the di7usion equation given by the Fick’s law [3]. The other regime is the anomalous diffusion described by the LLevy’s statistics [4]. It has been shown that the solution of the di7usion equation in a symmetrical medium can be described by a Gaussian distribution, whereas the solution in an asymmetrical medium is described by a true LLevy distribution [5].
3. Conclusion In summary, it is revealed that the carrier di7usion normal to the wires has an asymmetric component superimposed to a symmetric one. However, the carrier expansion along the wire direction shows a symmetric pro6le. This indicates that carrier mobility in In0:53 Ga0:47 As=InP tilted structures is very sensitive to the interface roughness and terrace widths. Combination of asymmetric and symmetric di7usion along different directions could be a key aspect in the design of mesoscopic devices.
Acknowledgements The authors would like to thank 6nancial support from CNPq-Brazil and TWAS-Italy.
A.F.G. Monte et al. / Physica E 17 (2003) 169 – 171
References [1] H.M. Cox, S.G. Hummel, V.G. Keramidas, J. Crystal Growth 79 (1986) 900. [2] J.M. Worlock, F.M. Peeters, H.M. Cox, P.C. Morais, Phys. Rev. B 44 (1991) 8923.
171
[3] Y. Chen, S.S. Prabhu, S.E. Ralph, D.T. McIntur7, Appl. Phys. Lett. 72 (1998) 439. [4] A.S. Chaves, Phys. Lett. A 239 (1998) 13. [5] A.F.G. Monte, S.W. da Silva, J.M.R. Cruz, P.C. Morais, A.S. Chaves, Phys. Lett. A 268 (2000) 430.
Physica E 17 (2003) 169 – 171 www.elsevier.com/locate/physe
Asymmetric carrier transport in InGaAs quantum wells and wires grown on tilted InP substrates A.F.G. Montea;∗ , S.W. da Silvaa , J.M.R. Cruza , P.C. Moraisa , A.S. Chavesb a Instituto
de F sica, NFA, Universidade de Bras lia, Bras lia DF, 70919-970, Brazil de F sica, Universidade de Minas Gerais, Belo Horizonte MG, Brazil
b Departamento
Abstract The in1uence of the interface morphology upon the electron–hole transport in intrinsic In0:53 Ga0:47 As=InP quantum structures was investigated by scanning the photoluminescence PL intensity pro6le on the sample surface. The results suggest that the carrier di7usion is very sensitive to both the roughness of the interfaces and the presence of 6nite-width terraces. It was found that the carrier density pro6le shows asymmetric di7usion normal to the terraces whereas it shows symmetric expansion along the terraces. ? 2002 Elsevier Science B.V. All rights reserved. PACS: 73.21.Fg; 73.21.Hb; 68.35.Fx Keywords: Quantum well; Quantum wire; Fractal di7usion; Asymmetric di7usion
1. Introduction Experimental results of spatially resolved imaging in In0:53 Ga0:47 As=InP heterostructures are presented and discussed focusing the investigation of the carrier di7usion. It has been shown that carrier di7usion in quantum well (QW) layers with the normal oriented along the [0 0 1] direction is clearly distinct from di7usion in QWs grown on tilted substrates (2◦ o7 towards [1 1 1]). In the 6rst case carrier di7usion is axially symmetric, whereas in the second case it is asymmetric, showing a tail along the [1 1 0] direction. We carried out studies on In0:53 Ga0:47 As quantum wires
∗ Corresponding author. Tel.: +55-61-7233940; fax: +55-612726026. E-mail address: [email protected] (A.F.G. Monte).
F (one (QWRs) with thickness varying from 3 to 12 A to four monolayers), whereas the lateral dimension F varies from about 80 –180 A. 2. Results and discussion Samples used in this study were grown by vapour levitation epitaxy (VLE), which has been described in detail elsewhere [1]. Sn-doped InP substrates oriented 2◦ o7 the (1 0 0) toward the (1 1 1) were used. The InP substrate as well as the epitaxial InP surface, upon which the In0:53 Ga0:47 As was grown, are not perfectly planar and have steps of monolayer height F The growth rates were about 2 and (a0 = 2:93 A). F 0:5 A=s for the InP and In0:53 Ga0:47 As layers, respectively. Using extremely short In0:53 Ga0:47 As growth times (0.5, 1, and 2 s), it was possible to grow
1386-9477/03/$ - see front matter ? 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S1386-9477(02)00736-1
170
A.F.G. Monte et al. / Physica E 17 (2003) 169 – 171
Growth
T = 13K
PL intensity (arb. units)
time 0.5s
M=1
1s
M=1
2s
M=2
10s
M=4
-80
- 40 0 40 Distance (µm)
80
Fig. 1. Carrier density pro6les taken from di7erent In0:53 Ga0:47 As= InP quantum structures as quoted by the In0:53 Ga0:47 As growth times.
uniform QWRs having a few monolayers high and suf6ciently narrow lateral width. Longer In0:53 Ga0:47 As growth times (¿ 10 s) allows the growth of very thin QWs instead of QWRs. The samples were mounted in a temperaturecontrolled optical cryostat and excited using an Ar + -ion laser (ex =514:5 nm). The laser beam was focused down to a spot of 2 m in diameter. Band-pass 6lters are used to select the PL emission from the luminescent region. Fig. 1 shows the variation observed on the spatial carrier distribution as obtained from the In0:53 Ga0:47 As=InP samples as a function of the growth times. It is quite clear the e7ect of the width of the In0:53 Ga0:47 As terraces upon the asymmetric carrier distribution. The carrier distribution observed from the 10 s sample is highly asymmetric with a shoulder on the right-hand side of the main feature. The e7ect of the asymmetry in the di7usion pro6le is reduced as the sample growth time decreases from 10 to 0:5 s. The carrier distribution is almost symmetric for the 0:5 s sample.
The relationship between growth time and lateral wire width is the most important factor to understand the asymmetry observed on the carrier di7usion pro6le. According to Worlock et al. [2], the lateral wire width in these samples are around 80, F for 0.5, 1, and 2 s growth times, 100, and 180 A respectively. The number of monolayers height (M) increases with the growth time, as quoted in Fig. 1. Wire coupling is ignored for the 0:5 s sample, which presents only one monolayer in thickness and about F of lateral width. In the 1 s sample, which is one 80 A monolayer height but presenting a wider terrace, the asymmetry is slightly observed. For the 2 s sample, which is two monolayers height, the wires are coupled together and the asymmetry is large. In the 10 s sample the wires are completely merged in a QW structure. The carrier di7usion can be modeled using two distinct regimes. One regime is the normal di7usion, which follows the di7usion equation given by the Fick’s law [3]. The other regime is the anomalous diffusion described by the LLevy’s statistics [4]. It has been shown that the solution of the di7usion equation in a symmetrical medium can be described by a Gaussian distribution, whereas the solution in an asymmetrical medium is described by a true LLevy distribution [5].
3. Conclusion In summary, it is revealed that the carrier di7usion normal to the wires has an asymmetric component superimposed to a symmetric one. However, the carrier expansion along the wire direction shows a symmetric pro6le. This indicates that carrier mobility in In0:53 Ga0:47 As=InP tilted structures is very sensitive to the interface roughness and terrace widths. Combination of asymmetric and symmetric di7usion along different directions could be a key aspect in the design of mesoscopic devices.
Acknowledgements The authors would like to thank 6nancial support from CNPq-Brazil and TWAS-Italy.
A.F.G. Monte et al. / Physica E 17 (2003) 169 – 171
References [1] H.M. Cox, S.G. Hummel, V.G. Keramidas, J. Crystal Growth 79 (1986) 900. [2] J.M. Worlock, F.M. Peeters, H.M. Cox, P.C. Morais, Phys. Rev. B 44 (1991) 8923.
171
[3] Y. Chen, S.S. Prabhu, S.E. Ralph, D.T. McIntur7, Appl. Phys. Lett. 72 (1998) 439. [4] A.S. Chaves, Phys. Lett. A 239 (1998) 13. [5] A.F.G. Monte, S.W. da Silva, J.M.R. Cruz, P.C. Morais, A.S. Chaves, Phys. Lett. A 268 (2000) 430.