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(AlGa)As Superlattices
JOURNAL
OF
LUMINESCENCE ELSEVIER
Journal of Luminescence
Photoluminescence
72-74
( 1997) 361-363
of Random GaAs/(AlGa)As
Superlattices
V. Capozzi a**,G.F. Lorussob, G. Pemaa, A. Bitz’ aDipartimento di Fisicu dell’ Univrrsitd di Buri, Via Anwndola 173. I-70126 Bwi, Italy blnstitut de Physique AppliquPe, EPFL. PH-Guhlens, CH-1015 Luusunnr, Switzerlrtnd ‘Institut de Miuo- et Optmktronique. EPFL. PH-Ecuhlens. CH-IOlS Lausunne, S~~itzerlund
Abstract
The photoluminescence (PL) spectra of disordered superlattices (d-SL) are discussed. The experimental the existence Kcywds:
of impurity-like Disordered
states and of disorder-induced
systems: Quantum wells; Electronic
results evidence
fine structures. states (localized)
Disorder-induced localization of carriers can have a strong influence on the electronic and optical properties of semiconductor materials. Very often, however, disorder is difficult to control, and its effects are then not completely understood. For these reasons, the development of the techniques for fabricating multilayered materials, as well as the possibility of technological applications [ 1J, strongly stimulated the investigations on disordered superlattices (d-SLs)
0.3
I
-l
r-7 $
F
0.2 EXTENDED STATES
u
1o-3
i? s ul
0.1 -
P-41. In this work we discuss the photoluminescence (PL) spectra of GaAs/Alo.jGao.,As d-SLs having randomly distributed well widths. The experimental results are compared with the numerical predictions obtained by means of the transfer matrix method [2, 31. The numerical analysis shows that the introduction of the disorder has two main effects. (I) The miniband containing extended states in the ordered case splits into sub-minibands of more or less localized states [2, 31. This effect is more evident in strongly d-SLs. (II) These sub-minibands show a disorder-induced
* Corresponding author. [email protected].
fax:
0039-80-544
2434;
e-mail:
0022-23 13/971$17.00 0 1997 Elsevier Science R.V. All rights reserved PII SOO22-23 13(97)00186-X
0.0 GROWTH
AXIS
Fig. I. Schematical picture of the conduction sub-miniband structure for a strongly d-SL, calculated by the transfer matrix method. k; 2 0 in the case of extended states, L: > I in the case of strongly localized states. L is the well width and Ii;, the localization length.
fine structure, which results more evident d-SLs [3].
in weakly
In Fig. 1, the numerical results for a strongly d-SL containing four different well widths (9, 27, 45 and
362
VI Capoxi
et cd /Journal
of’ Luminescence
63 ML, respectively) are reported. The barrier width is 9ML. The electron miniband splitting in four sub-minibands is evident. Furthermore, the subminibands at low energy are more localized than the highest one, which is almost extended. As in the case of bulk systems containing impurities or amorphous semiconductors, the disorder introduces localized states below a band of extended states. In order to confirm the numerical results reported in Fig. I, d-SLs were grown by means of molecular beam epitaxy at a temperature of 620°C on a (0 0 1)-oriented GaAs substrate. The samples have the following structure: upon the substrate there are a buffer layer of GaAs (0.3 pm thick), the SL (1 pm thick, about 200 periods) cladded between two Alo,3Gao.,As layers (each 1 pm thick) and a GaAs cap-layer (20 nm). The growth rates were 0.6 pm h-’ and the error on the layer thickness is about 1 ML. The design of the samples was confirmed by transmission electron microscopy, and the Al concentration was checked from the PL spectral position of the heavyhole exciton line of the AlGaAs cladding layer at 2 K. The PL spectra at 2 K were measured on samples immersed in superfluid helium. The samples were photoexcited by the 647nm line of a Kr-ion laser, and the emitted light was detected by a cooled optical multichannel analyzer. The dependence of the PL spectra on 7’ was investigated using a He closed-cycle cryostat, ranging from 8 to 300 K within 0.5 K of uncertainty. In this case, the samples were photoexcited by using the 514nm line of a Ar-ion laser, and detecting the signal by a cooled GaAs photomultiplier. The T dependence of the PL spectra of a d-SL is reported in Fig. 2. Here, the d-SL is the same one investigated in Fig. 1. The experimental spectra were fitted to a superposition of Lorentzian lines. The PL lines correspond to heavy-hole and light-hole excitonic recombinations in the different wells present in the d-SL. The semi-logarithmic plots of the PL intensity versus l/T were linear in the high T limits, thus indicating an Arrenhius dependence. This fact permitted to evaluate the activation energies of the two localized states at lower energy, which resulted to be 93 and 81 meV, respectively. These experimental results agree with the differences between extended and localized states reported in Fig. 1, thus supporting our numerical calculations.
72-74 11997) 361-363
1.52
1.53
T 3
100K
4 ir P $ li 1.51
1.46
1.48
1.52
1.50 1.52 ENERGYfeW
1.53
1.54
Fig. 2. Experimental PL spectra of a strongly d-SL at different T. The data were deconvoluted into a series of Lorentzian lines.
In Fig. 3, the PL spectrum of a weakly d-SL is compared with the numerical results for the joint density of states (JDOS) obtained by means of the transfer matrix method. In this case, the d-SL has four different well widths (9, 14, 19 and 24 ML, respectively). The barrier width is 9ML. The PL spectrum was measured at T = 1OOK and at an excitation intensity of 20 W/cm2. In order to have an easier comparison between the theoretical prediction and the experimental result, where excitonic effects are present, the derivative of the JDOS (i.e. the one-dimensional JDOS) has been reported in Fig. 3. Furthermore, the derivative of the JDOS was red shifted in order to take into account the dependence of the band gap on T. For this purpose, we used the Varshni semi-empirical relationship [5]: A,!&(T) = -cxT2/(/3 + T), being LXand fl materialdependent parameters related to the electron-phonon
V. Capozi
et al. /Journal
of Luminescence 72-74 11997) 361-363
experimental
,la)
100 K
363
interaction [6]. Also in this case, the main peaks correspond to excitonic transitions in the different wells in the d-SL. In contrast, the arrows indicate the disorder-induced fine structure, caused by the coupling between adjacent wells having the same widths in the d-SL [3]. The agreement between experimental and numerical results is good. We remark that no adjustable parameter has been used in our calculations.
References
1.56
1.58 ENERGY
1.60 (eV)
Fig. 3. (a) Experimental PL spectra of a weakly d-SL. (b) Derivative of the JDOS obtained by the transfer matrix method. The arrows point to the disorder-induced fine structure. No adjustable parameter was used.
[I] M.A. Sasaki. X. Wang and A. Wakahara, Appl. Phys. Lett. 64 (1994) 2016. [2] G.F. Lorusso. V. Capozzi, J.L. Staehli, C. Flesia. D. Martin and P. Favia, Phys. Rev. B 53 (1996) 1018. [3] G.F. Lorusso, V. Capozzi, J.L. Staehli. C. Flesia, D. Martin, P. Favia and G. Pema Semicond. Sci. Technol. 1 I (1996) 308. [4] G.F. Lorusso, F. Tassone, V. Capozzi, G. Perna and D. Martin, Solid State Commun. 98 (I 996) 705. [5] Y.P. Varshni, Physica 34 (1967) 149. [6] M. Guzzi and J.L. Staehli, Solid State Phen. 10 (1989) 22.
OF
LUMINESCENCE ELSEVIER
Journal of Luminescence
Photoluminescence
72-74
( 1997) 361-363
of Random GaAs/(AlGa)As
Superlattices
V. Capozzi a**,G.F. Lorussob, G. Pemaa, A. Bitz’ aDipartimento di Fisicu dell’ Univrrsitd di Buri, Via Anwndola 173. I-70126 Bwi, Italy blnstitut de Physique AppliquPe, EPFL. PH-Guhlens, CH-1015 Luusunnr, Switzerlrtnd ‘Institut de Miuo- et Optmktronique. EPFL. PH-Ecuhlens. CH-IOlS Lausunne, S~~itzerlund
Abstract
The photoluminescence (PL) spectra of disordered superlattices (d-SL) are discussed. The experimental the existence Kcywds:
of impurity-like Disordered
states and of disorder-induced
systems: Quantum wells; Electronic
results evidence
fine structures. states (localized)
Disorder-induced localization of carriers can have a strong influence on the electronic and optical properties of semiconductor materials. Very often, however, disorder is difficult to control, and its effects are then not completely understood. For these reasons, the development of the techniques for fabricating multilayered materials, as well as the possibility of technological applications [ 1J, strongly stimulated the investigations on disordered superlattices (d-SLs)
0.3
I
-l
r-7 $
F
0.2 EXTENDED STATES
u
1o-3
i? s ul
0.1 -
P-41. In this work we discuss the photoluminescence (PL) spectra of GaAs/Alo.jGao.,As d-SLs having randomly distributed well widths. The experimental results are compared with the numerical predictions obtained by means of the transfer matrix method [2, 31. The numerical analysis shows that the introduction of the disorder has two main effects. (I) The miniband containing extended states in the ordered case splits into sub-minibands of more or less localized states [2, 31. This effect is more evident in strongly d-SLs. (II) These sub-minibands show a disorder-induced
* Corresponding author. [email protected].
fax:
0039-80-544
2434;
e-mail:
0022-23 13/971$17.00 0 1997 Elsevier Science R.V. All rights reserved PII SOO22-23 13(97)00186-X
0.0 GROWTH
AXIS
Fig. I. Schematical picture of the conduction sub-miniband structure for a strongly d-SL, calculated by the transfer matrix method. k; 2 0 in the case of extended states, L: > I in the case of strongly localized states. L is the well width and Ii;, the localization length.
fine structure, which results more evident d-SLs [3].
in weakly
In Fig. 1, the numerical results for a strongly d-SL containing four different well widths (9, 27, 45 and
362
VI Capoxi
et cd /Journal
of’ Luminescence
63 ML, respectively) are reported. The barrier width is 9ML. The electron miniband splitting in four sub-minibands is evident. Furthermore, the subminibands at low energy are more localized than the highest one, which is almost extended. As in the case of bulk systems containing impurities or amorphous semiconductors, the disorder introduces localized states below a band of extended states. In order to confirm the numerical results reported in Fig. I, d-SLs were grown by means of molecular beam epitaxy at a temperature of 620°C on a (0 0 1)-oriented GaAs substrate. The samples have the following structure: upon the substrate there are a buffer layer of GaAs (0.3 pm thick), the SL (1 pm thick, about 200 periods) cladded between two Alo,3Gao.,As layers (each 1 pm thick) and a GaAs cap-layer (20 nm). The growth rates were 0.6 pm h-’ and the error on the layer thickness is about 1 ML. The design of the samples was confirmed by transmission electron microscopy, and the Al concentration was checked from the PL spectral position of the heavyhole exciton line of the AlGaAs cladding layer at 2 K. The PL spectra at 2 K were measured on samples immersed in superfluid helium. The samples were photoexcited by the 647nm line of a Kr-ion laser, and the emitted light was detected by a cooled optical multichannel analyzer. The dependence of the PL spectra on 7’ was investigated using a He closed-cycle cryostat, ranging from 8 to 300 K within 0.5 K of uncertainty. In this case, the samples were photoexcited by using the 514nm line of a Ar-ion laser, and detecting the signal by a cooled GaAs photomultiplier. The T dependence of the PL spectra of a d-SL is reported in Fig. 2. Here, the d-SL is the same one investigated in Fig. 1. The experimental spectra were fitted to a superposition of Lorentzian lines. The PL lines correspond to heavy-hole and light-hole excitonic recombinations in the different wells present in the d-SL. The semi-logarithmic plots of the PL intensity versus l/T were linear in the high T limits, thus indicating an Arrenhius dependence. This fact permitted to evaluate the activation energies of the two localized states at lower energy, which resulted to be 93 and 81 meV, respectively. These experimental results agree with the differences between extended and localized states reported in Fig. 1, thus supporting our numerical calculations.
72-74 11997) 361-363
1.52
1.53
T 3
100K
4 ir P $ li 1.51
1.46
1.48
1.52
1.50 1.52 ENERGYfeW
1.53
1.54
Fig. 2. Experimental PL spectra of a strongly d-SL at different T. The data were deconvoluted into a series of Lorentzian lines.
In Fig. 3, the PL spectrum of a weakly d-SL is compared with the numerical results for the joint density of states (JDOS) obtained by means of the transfer matrix method. In this case, the d-SL has four different well widths (9, 14, 19 and 24 ML, respectively). The barrier width is 9ML. The PL spectrum was measured at T = 1OOK and at an excitation intensity of 20 W/cm2. In order to have an easier comparison between the theoretical prediction and the experimental result, where excitonic effects are present, the derivative of the JDOS (i.e. the one-dimensional JDOS) has been reported in Fig. 3. Furthermore, the derivative of the JDOS was red shifted in order to take into account the dependence of the band gap on T. For this purpose, we used the Varshni semi-empirical relationship [5]: A,!&(T) = -cxT2/(/3 + T), being LXand fl materialdependent parameters related to the electron-phonon
V. Capozi
et al. /Journal
of Luminescence 72-74 11997) 361-363
experimental
,la)
100 K
363
interaction [6]. Also in this case, the main peaks correspond to excitonic transitions in the different wells in the d-SL. In contrast, the arrows indicate the disorder-induced fine structure, caused by the coupling between adjacent wells having the same widths in the d-SL [3]. The agreement between experimental and numerical results is good. We remark that no adjustable parameter has been used in our calculations.
References
1.56
1.58 ENERGY
1.60 (eV)
Fig. 3. (a) Experimental PL spectra of a weakly d-SL. (b) Derivative of the JDOS obtained by the transfer matrix method. The arrows point to the disorder-induced fine structure. No adjustable parameter was used.
[I] M.A. Sasaki. X. Wang and A. Wakahara, Appl. Phys. Lett. 64 (1994) 2016. [2] G.F. Lorusso. V. Capozzi, J.L. Staehli, C. Flesia. D. Martin and P. Favia, Phys. Rev. B 53 (1996) 1018. [3] G.F. Lorusso, V. Capozzi, J.L. Staehli. C. Flesia, D. Martin, P. Favia and G. Pema Semicond. Sci. Technol. 1 I (1996) 308. [4] G.F. Lorusso, F. Tassone, V. Capozzi, G. Perna and D. Martin, Solid State Commun. 98 (I 996) 705. [5] Y.P. Varshni, Physica 34 (1967) 149. [6] M. Guzzi and J.L. Staehli, Solid State Phen. 10 (1989) 22.