- Email: [email protected]
GaAs quantum dots
Solid State Communications 128 (2003) 213–217 www.elsevier.com/locate/ssc
Radiative recombination lifetime of excitons in self-organized InAs/GaAs quantum dots A. Mellitia,*, M.A. Maaref a, F. Hassenb, M. Hjirib, H. Maaref b, J. Tignonc, B. Sermaged a
Unite´ de Recherche de Physique des Semiconducteurs, Institut Pre´paratoire aux Etudes Scientifiques et Technologiques, La Marsa 2070, Tunisia b Laboratoire de Physique des Semiconducteurs, Faculte´ des Sciences de Monastir, Monastir, Tunisia c Laboratoire de Physique de la Matie`re Condense´e, Ecole Normale Supe´rieure, 24 rue Lhomond, 75231 Paris cedex 05, Paris, France d Laboratoire de Photonique et de Nanostructures, CNRS, Route de Nozay, 91460 Marcoussis, France Received 22 May 2003; accepted 26 August 2003 by T.T.M. Palstra
Abstract We report an investigation of the exciton dynamics in self-organized InAs/GaAs quantum dots (QD’s) grown by molecularbeam epitaxy on (001)-oriented GaAs substrate. We have combined continuous wave and time resolved luminescence as a function of temperature to obtain quantitative information on the recombination processes in the dots. We have found that the excitonic radiative lifetime of two monolayers InAs QD’s is almost independent of temperature. q 2003 Elsevier Ltd. All rights reserved. PACS: 78.67.HC; 81.16.Nd; 78.55.Ap; 81.07.Ta Keywords: A. InAs/GaAs; A. Quantum dots; D. Decay time; D. Radiative lifetime; E. Photoluminescence; E. Temperature
1. Introduction The quest for high performance optoelectronic devices has promoted a growing interest for zero-dimensional semiconductor quantum dots (QD’s). In these systems, indeed, the strong localization of the electronic wave function leads to an atomic-like electronic density of states and to the possible realization of novel and improved photonic and electronic devices [1– 3]. Furthermore, the self-aggregation of defect-free QD’s during the epitaxial deposition of strained semiconductor layers [4] has stimulated a large number of experimental works. QD injection-laser prototypes, made from InAs/GaAs heterostructures, have now characteristics as good as quantum well based devices [5]. In order to assess QD for application in photonic devices parameters such as carrier radiative lifetime must be measured. A systematic study of this * Corresponding author. Tel.: þ216-989-996-46; fax: þ 216-717465-51. E-mail address: [email protected] (A. Melliti). 0038-1098/$ - see front matter q 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2003.08.020
parameter in quantum boxes formed naturally along the axis of a V-shaped GaAs/AlGaAs quantum wires by means of time and spatially resolved resonant photoluminescence (PL) has been reported by Bellessa et al. [6]. They have found that the radiative recombination rate varies linearly with the length of the box. Heitz et al. [7] have investigated by time resolved PL spectroscopy the recombination in selforganized InAs/GaAs luminating at about 1.1 eV. They have found that the radiative lifetime is around 1 ns at 1.8 K. As regards the excited states in self-assembled InAs/ GaAs QD’s Raymond et al. [8] have proposed a model that allows to calculate the radiative rates at low temperature. The calculated rates decline from 109 to 1.4 £ 108 s21 as higher energy states are probed. On the other hand, using PL spectroscopy and a Monte Carlo model Buckle et al. [9] have shown that the radiative decay time of the emission from the ground, first excited, second excited and third excited states are about 1, 3.7, 4, and 1.4 ns at 6 K. Weaker values of radiative lifetime have been reported for selfassembled AlInAs/AlGaAs QD’s (500 ps) [10] and single CdSe/ZnSe QD (290 ps) [11].
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In this paper, we investigate the effect of the temperature on the excitonic radiative lifetime in self-organized InAs/GaAs QD’s by time resolved (TR) and continuous wave (CW) PL. The sizes of these structures are not uniform. The carriers diffuse from small QD’s to larger ones [12 – 19]. This process causes the refilling of large QD’s at high temperature during the decay. Consequently, the direct determination of the radiative lifetime of these QD’s is impossible. To avoid this problem, we have limited the study of this process to the small QD’s. We have calculated the radiative lifetime using the rate equation model [12]. The decay constant of the ground state has been modeled correctly by this model [12,20].
2. Sample growth and experimental details The InAs QD’s embedded in GaAs were grown on an (001)-oriented GaAs substrate by using a molecular beam epitaxy system. An undoped GaAs buffer layer was grown on the substrate at 580 8C. The self-organized coherent InAs islands were formed at 520 8C by deposition of nominally ˚ thick layers of two monolayers grown between two 200 A GaAs. The temperature was then increased to 580 and a ˚ GaAs cap layer was grown. The morphology of the 300 A InAs islands, grown under the same conditions as an uncapped sample, were investigated in air by contact mode by atomic force microscopy using a digital Nanoscope III system. The results show two main size distributions (larger 20 nm diameter and smaller 14 nm diameter QD’s). The QD’s density was estimated as 3 £ 1010 cm22 The CWPL emission was spectrally resolved by a monochromator blazed at 1 m. The excitation source was a frequency-doubled Nd: vanadate laser emitting at 2.33 eV (into the GaAs barrier) with an excitation power density of the order of 5 W cm22. The luminescence was detected with a silicon avalanche photodiode. The sample was held in a closed cycle He cryostat. TRPL measurements were made using a closed cycle He cryostat and mode-locked Ti-saphir laser giving nearly Fourier-transform limited pulse in the range of 1 – 1.5 ps with a repetition rate of 82 MHz. Its energy was tuned to 1.46 eV (into the wetting layer (WL)). The excitation power density is of the order of 80 W cm22. The emission is spectrally dispersed using a monochromator. Next, temporal analysis is performed by a synchro scan streak camera. Finally, the signal is detected using a charge-coupled device. The time resolution lies around 5 ps.
3. Results and discussion Fig. 1 shows a broad CWPL band associated to the luminescence of QD’s at different temperatures. The PL band obtained at 10 K is centered around 1.24 eV. The
Fig. 1. QD’s PL bands at different temperatures.
luminescence results from the radiative recombination on the ground and excited states of two QD’s size distributions [16]. Fig. 2 shows the TRPL decays measured at different
Fig. 2. Each figure shows PL decay obtained at different temperatures for a particular emitting state (solid line), (a) and (b) correspond, respectively, to emitting states of energies 1.128 and 1.299 eV at 10 K. The detection energy is redshifted as the temperature increases to account for the energy band-gap-shift with temperature. The dotted lines show fit curves.
A. Melliti et al. / Solid State Communications 128 (2003) 213–217
temperatures and at detection energies corresponding to the low and high-energy sides of the QD’s PL spectra. Each detection energy corresponds to a particular emitting state. As the temperature varies from 10 K toward higher values, the detection energies are redshifted to take into account the energy band-gap-shift with temperature. For the first order of approximation, the band gap shift is estimated using the formula described in Ref. [21]. For the low energy detection ðE1 ¼ 1:179 eVÞ (Fig. 2(a)), the PL decay can be well fitted by a monoexponential for low temperatures (,90 K) and high temperatures (.200 K). In the intermediate temperature range, the PL intensity is initially constant over a few hundred of picoseconds. This result may be due to two processes: the refilling of the large QD’s by carriers escaped from small QD’s and the state blocking caused by the effects of Pauli exclusion [9]. For the high-energy detection ðE3 ¼ 1:318 eVÞ (Fig. 2(b)) we have not observed the PL intensity saturation vs. time. This behavior indicates that the recapture by small QD’s is weak. On the other hand, for the high-energy detection, the PL decay is fitted by two exponentials. We attribute the two components to the superposition of excited states PL of large QD’s and ground states PL of smaller ones. Fig. 3 shows the PL decay times for various emission energies plotted vs. sample temperature. The luminescence decay times were determined by fitting the experimental decay curves at a particular emission energy to a single exponential over a time windows selected to avoid the possible influence of excited state emission. The arrows in the inset indicate the positions of detection energies within
215
the QD’s PL band. We remark that the decay time associated to the high-energy extremity of the PL band ðE3 ¼ 1:318 eVÞ is almost constant (750 ps) up to 100 K. Then it decreases with temperature. For lower detection energies, the decay time curves show a maximum. The greater maximal value is obtained for E1 ( ¼ 1.179 eV). We note that the maximal decay times and the PL saturation vs. time (shown in Fig. 2(a)) are obtained in the same temperature range. The model developed in Ref. [12] explains the behavior of decay time corresponding to a given detection energy. At sufficiently high temperature, the small QD’s experience a relatively large rate of thermal emission of electron-hole pairs back into the WL, leading to a reduction of the PL decay time for these QD’s. Meanwhile, recapture from the WL causes the repopulation of the other lower-energy QD’s and leads to an increase of their PL decay time. At higher temperatures, thermally activated emission ultimately begins to cause a decrease of the PL decay times of the lower-energy QD states. This model allows us to interpret the variation as a function of temperature of the decay time corresponding to a given energy detection, but it does not explain its increase as the detection energy vary from E0 ( ¼ 1.16 eV at 10 K) to E1 ( ¼ 1.179 eV at 10 K). We note that the variation of the decay time of QD’s corresponding to the high-energy extremity of the PL spectra (HEQD’s), that does not increase at low temperatures, indicates that the recapture has no significant effect on the evolution of the population of these QD’s. We have analyzed our results using the rate equation deduced from the model developed in Ref. [12]: dn 1 1 ¼ cMJ 2 þ n ð1Þ dt tr te Where n is the population of QD’s excitons, c is the capture rate coefficient, M is the number of WL excitons per unit area, JðEÞ is the normalized density of ground states of QD’s excitons, it is related to the inhomogeneous broadening of QD’s PL band, tr and te correspond, respectively, to the radiative lifetime and to the time for thermal emission to the WL. We neglect the recapture of carriers by HEQD’s. This approximation is supported by the fact that for these QD’s:
Fig. 3. PL decay times vs. temperature. Solid lines provide a guide to the eye. The values of E0 ¼ 1:16 eV; E1 ¼ 1:179 eV; E2 ¼ 1:227 eV and E3 ¼ 1:318 eV represent the detection energies at what the PL is measured at 10 K. As one moves along each line from 10 K toward higher temperatures, the energy detection is redshifted to account for the energy-band-gap shift with temperature. The arrows in the inset indicate the positions of the detection energies within the PL band obtained at 10 K for pulsed excitation.
† The decay does not present a saturation vs. time (Fig. 2(b)) † The decay time does not increase with temperature (Fig. 3) † The value of JðEÞ is small. Using this approximation, the rate equation of excitons in these QD’s is given in the case of pulsed excitation by: dn 1 1 1 þ ð2Þ <2 n¼2 n tr te t dt solution of this equation corresponding to RTPL
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measurements is given by n ¼ n0 expð2t=tÞ: The decay time corresponding to energy close to E3 can be directly interpreted as t: For a continuous excitation, n is given by: n ¼ cJM t: The CWPL intensity (IPL) can be written as: IPL ¼ cJM t=tr Considering two detection energies corresponding to HEQD’s (E01 ¼ 1:31 eV and E0 s2 ¼ 1:32 eV) we obtain the following equations: IPL ðE1 Þ t t JðE01 Þ ¼ r2 1 IPL ðE2 Þ tr1 t2 JðE02 Þ
ð3Þ
1 1 1 ¼ þ t1 tr1 te1
ð4Þ
1 1 1 ¼ þ t2 tr2 te2
ð5Þ
radiative lifetime with decreasing QD size is connected with a reduction of confinement effects [20]. The flat temperature dependence of the exciton radiative lifetime is expected [13,22]. Indeed, the density of states consists of a series of d functions. Increasing, the temperature cannot redistribute excitons within a band of adjacent states since these do not exist.
4. Conclusion
Where t1 ðt2 Þ; tr1 ðtr2 Þ and te1 ðte2 Þ are, respectively, the decay time, the radiative lifetime and the thermal emission time corresponding to E01 ðE02 Þ: te1 and te2 are related by the relationship [12]: 0 E 2 E01 te1 ¼ te2 exp 2 ð6Þ 2kb T To estimate J we have used the CWPL band obtained with excitation power of 0.5 W cm22 and at 10 K, to avoid the excited states contribution and the influence of inter-dots diffusion. The Eqs. (3)– (6) allow to calculate the radiative lifetime from the CWPL and RTPL measurements. The values of tr are presented in Fig. 4. We note that tr is of the order of 800 ps and is almost independent of temperature. The calculated value of tr is smaller than that measured by Heitz et al. [7] and Buckle et al. [9] (1 ns). The QD’s studied by Heitz and Buckle are larger than those studied here. Indeed, the transition energy of QD’s studied by Heitz and Buckle are 1.1 and 1.13 eV, respectively, and those of QD’s studied here are 1.31 and 1.32 eV. The decrease of the
Fig. 4. Radiative recombination time (tr1 and tr2 ) corresponding to E01 ¼ 1:31 eV (circles) and E02 ¼ 1:32 eV (squares).
We have determined the radiative lifetime of small QD’s ˚ ) using CWPL and TRPL measurements. (diameter ¼ 140 A We have found that the excitonic radiative lifetime is of the order of 800 ps and is almost independent of temperature. On the other hand, we have observed that for intermediate temperature range, the PL intensity of large QD’s remains constant over a few hundred of picoseconds. We have attributed this behavior to two processes: the refilling of the large QD’s by carriers escaped from small QD’s and the state blocking caused by the effects of Pauli exclusion.
References [1] G. Bryant, Phys. Rev. B 37 (1988) 8763. [2] S. Schmitt-Rink, D. Miller, D. Chemla, Phys. Rev. B 35 (1987) 8113. [3] T. Takagahara, Phys. Rev. B 36 (1987) 9293. [4] D. Leonard, K. Pond, P.M. Petroff, Phys. Rev. B 50 (1994) 11687. [5] D. Bimberg, M. Grundmann, N. Ledentsov, MRS Bull. 23 (1998) 31. [6] J. Bellessa, V. Voliotis, R. Grousson, X.L. Wang, M. Ogura, H. Hatsuhata, Phys. Rev. B 58 (1998) 9933. [7] R. Heitz, M. Veit, N.N. Ledentsov, A. Hoffmann, D. Bimberg, V.M. Ustinov, P.S. Kop’ev, Zh.I. Alferov, Phys. Rev. B 56 (1997) 10435. [8] S. Raymond, X. Guo, J.L. Merz, S. Fafard, Phys. Rev. B 59 (1999) 7624. [9] P.D. Buckle, P. Dawson, S.A. Hall, X. Chen, M.J. Steer, D.J. Mowbray, M.S. Skolnick, M. Hopkinson, J. Appl. Phys. 86 (1999) 2555. [10] S. Raymond, S. Fafard, S. Charbonneau, R. Leon, D. Leonard, P.M. Petroff, J.L. Merz, Phys. Rev. B 52 (1995) 17238. [11] G. Bacher, R. Weigand, J. Seufert, V.D. Kulakovskii, N.A. Gippius, A. Forchel, K. Leonardi, D. Hommel, Phys. Rev. Lett. 83 (1999) 4417. [12] W. Yang, R.R. Lowe-Webb, H. Lee, P.C. Sercel, Phys. Rev. B 56 (1997) 13314. [13] H. Yu, S. Lycett, C. Roberts, R. Murray, Appl. Phys. Lett. 69 (1996) 4087. [14] A. Fiore, P. Borri, W. Langbein, J.M. Hvam, U. Oesterle, R. Houdre´, R.P. Stanley, M. Llegems, Appl. Phys. Lett. 76 (2000) 3430. [15] M. Hjiri, F. Hassen, H. Maaref, Mater. Sci. Engng B 69–70 (2000) 514.
A. Melliti et al. / Solid State Communications 128 (2003) 213–217 [16] M. Hjiri, F. Hassen, H. Maaref, Mater. Sci. Engng B 88 (2002) 255. [17] M. Hjiri, F. Hassen, H. Maaref, Mater. Sci. Engng B 74 (2000) 253. [18] S. Sanguinetti, M. Henini, M.G. Alessi, M. Capizzi, P. Frigeri, S. Franchi, Phys. Rev. B 60 (1999) 8276. [19] L. Brusaferri, S. Sanguinetti, E. Grilli, M. Guzzi, A. Bignazzi,
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F. Bogani, L. Carraresi, M. Colocci, A. Bosacchi, P. Frigeri, S. Franchi, Appl. Phys. Lett. 69 (1996) 3354. [20] D. Bimberg, M. Grundmann, N.N. Ledentsov, Quantum dot Heterostructures, Wiley, Chichester, 1999, p. 251. [21] S. Adachi, Physical Properties of III – V Semiconductor Compounds, Wiley, New York, 1992, p. 104. [22] G. Wang, S. Fafard, D. Leonard, J.E. Bowers, J.L. Merz, P.M. Petroff, Appl. Phys. Lett. 64 (1994) 2815.
Radiative recombination lifetime of excitons in self-organized InAs/GaAs quantum dots A. Mellitia,*, M.A. Maaref a, F. Hassenb, M. Hjirib, H. Maaref b, J. Tignonc, B. Sermaged a
Unite´ de Recherche de Physique des Semiconducteurs, Institut Pre´paratoire aux Etudes Scientifiques et Technologiques, La Marsa 2070, Tunisia b Laboratoire de Physique des Semiconducteurs, Faculte´ des Sciences de Monastir, Monastir, Tunisia c Laboratoire de Physique de la Matie`re Condense´e, Ecole Normale Supe´rieure, 24 rue Lhomond, 75231 Paris cedex 05, Paris, France d Laboratoire de Photonique et de Nanostructures, CNRS, Route de Nozay, 91460 Marcoussis, France Received 22 May 2003; accepted 26 August 2003 by T.T.M. Palstra
Abstract We report an investigation of the exciton dynamics in self-organized InAs/GaAs quantum dots (QD’s) grown by molecularbeam epitaxy on (001)-oriented GaAs substrate. We have combined continuous wave and time resolved luminescence as a function of temperature to obtain quantitative information on the recombination processes in the dots. We have found that the excitonic radiative lifetime of two monolayers InAs QD’s is almost independent of temperature. q 2003 Elsevier Ltd. All rights reserved. PACS: 78.67.HC; 81.16.Nd; 78.55.Ap; 81.07.Ta Keywords: A. InAs/GaAs; A. Quantum dots; D. Decay time; D. Radiative lifetime; E. Photoluminescence; E. Temperature
1. Introduction The quest for high performance optoelectronic devices has promoted a growing interest for zero-dimensional semiconductor quantum dots (QD’s). In these systems, indeed, the strong localization of the electronic wave function leads to an atomic-like electronic density of states and to the possible realization of novel and improved photonic and electronic devices [1– 3]. Furthermore, the self-aggregation of defect-free QD’s during the epitaxial deposition of strained semiconductor layers [4] has stimulated a large number of experimental works. QD injection-laser prototypes, made from InAs/GaAs heterostructures, have now characteristics as good as quantum well based devices [5]. In order to assess QD for application in photonic devices parameters such as carrier radiative lifetime must be measured. A systematic study of this * Corresponding author. Tel.: þ216-989-996-46; fax: þ 216-717465-51. E-mail address: [email protected] (A. Melliti). 0038-1098/$ - see front matter q 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2003.08.020
parameter in quantum boxes formed naturally along the axis of a V-shaped GaAs/AlGaAs quantum wires by means of time and spatially resolved resonant photoluminescence (PL) has been reported by Bellessa et al. [6]. They have found that the radiative recombination rate varies linearly with the length of the box. Heitz et al. [7] have investigated by time resolved PL spectroscopy the recombination in selforganized InAs/GaAs luminating at about 1.1 eV. They have found that the radiative lifetime is around 1 ns at 1.8 K. As regards the excited states in self-assembled InAs/ GaAs QD’s Raymond et al. [8] have proposed a model that allows to calculate the radiative rates at low temperature. The calculated rates decline from 109 to 1.4 £ 108 s21 as higher energy states are probed. On the other hand, using PL spectroscopy and a Monte Carlo model Buckle et al. [9] have shown that the radiative decay time of the emission from the ground, first excited, second excited and third excited states are about 1, 3.7, 4, and 1.4 ns at 6 K. Weaker values of radiative lifetime have been reported for selfassembled AlInAs/AlGaAs QD’s (500 ps) [10] and single CdSe/ZnSe QD (290 ps) [11].
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In this paper, we investigate the effect of the temperature on the excitonic radiative lifetime in self-organized InAs/GaAs QD’s by time resolved (TR) and continuous wave (CW) PL. The sizes of these structures are not uniform. The carriers diffuse from small QD’s to larger ones [12 – 19]. This process causes the refilling of large QD’s at high temperature during the decay. Consequently, the direct determination of the radiative lifetime of these QD’s is impossible. To avoid this problem, we have limited the study of this process to the small QD’s. We have calculated the radiative lifetime using the rate equation model [12]. The decay constant of the ground state has been modeled correctly by this model [12,20].
2. Sample growth and experimental details The InAs QD’s embedded in GaAs were grown on an (001)-oriented GaAs substrate by using a molecular beam epitaxy system. An undoped GaAs buffer layer was grown on the substrate at 580 8C. The self-organized coherent InAs islands were formed at 520 8C by deposition of nominally ˚ thick layers of two monolayers grown between two 200 A GaAs. The temperature was then increased to 580 and a ˚ GaAs cap layer was grown. The morphology of the 300 A InAs islands, grown under the same conditions as an uncapped sample, were investigated in air by contact mode by atomic force microscopy using a digital Nanoscope III system. The results show two main size distributions (larger 20 nm diameter and smaller 14 nm diameter QD’s). The QD’s density was estimated as 3 £ 1010 cm22 The CWPL emission was spectrally resolved by a monochromator blazed at 1 m. The excitation source was a frequency-doubled Nd: vanadate laser emitting at 2.33 eV (into the GaAs barrier) with an excitation power density of the order of 5 W cm22. The luminescence was detected with a silicon avalanche photodiode. The sample was held in a closed cycle He cryostat. TRPL measurements were made using a closed cycle He cryostat and mode-locked Ti-saphir laser giving nearly Fourier-transform limited pulse in the range of 1 – 1.5 ps with a repetition rate of 82 MHz. Its energy was tuned to 1.46 eV (into the wetting layer (WL)). The excitation power density is of the order of 80 W cm22. The emission is spectrally dispersed using a monochromator. Next, temporal analysis is performed by a synchro scan streak camera. Finally, the signal is detected using a charge-coupled device. The time resolution lies around 5 ps.
3. Results and discussion Fig. 1 shows a broad CWPL band associated to the luminescence of QD’s at different temperatures. The PL band obtained at 10 K is centered around 1.24 eV. The
Fig. 1. QD’s PL bands at different temperatures.
luminescence results from the radiative recombination on the ground and excited states of two QD’s size distributions [16]. Fig. 2 shows the TRPL decays measured at different
Fig. 2. Each figure shows PL decay obtained at different temperatures for a particular emitting state (solid line), (a) and (b) correspond, respectively, to emitting states of energies 1.128 and 1.299 eV at 10 K. The detection energy is redshifted as the temperature increases to account for the energy band-gap-shift with temperature. The dotted lines show fit curves.
A. Melliti et al. / Solid State Communications 128 (2003) 213–217
temperatures and at detection energies corresponding to the low and high-energy sides of the QD’s PL spectra. Each detection energy corresponds to a particular emitting state. As the temperature varies from 10 K toward higher values, the detection energies are redshifted to take into account the energy band-gap-shift with temperature. For the first order of approximation, the band gap shift is estimated using the formula described in Ref. [21]. For the low energy detection ðE1 ¼ 1:179 eVÞ (Fig. 2(a)), the PL decay can be well fitted by a monoexponential for low temperatures (,90 K) and high temperatures (.200 K). In the intermediate temperature range, the PL intensity is initially constant over a few hundred of picoseconds. This result may be due to two processes: the refilling of the large QD’s by carriers escaped from small QD’s and the state blocking caused by the effects of Pauli exclusion [9]. For the high-energy detection ðE3 ¼ 1:318 eVÞ (Fig. 2(b)) we have not observed the PL intensity saturation vs. time. This behavior indicates that the recapture by small QD’s is weak. On the other hand, for the high-energy detection, the PL decay is fitted by two exponentials. We attribute the two components to the superposition of excited states PL of large QD’s and ground states PL of smaller ones. Fig. 3 shows the PL decay times for various emission energies plotted vs. sample temperature. The luminescence decay times were determined by fitting the experimental decay curves at a particular emission energy to a single exponential over a time windows selected to avoid the possible influence of excited state emission. The arrows in the inset indicate the positions of detection energies within
215
the QD’s PL band. We remark that the decay time associated to the high-energy extremity of the PL band ðE3 ¼ 1:318 eVÞ is almost constant (750 ps) up to 100 K. Then it decreases with temperature. For lower detection energies, the decay time curves show a maximum. The greater maximal value is obtained for E1 ( ¼ 1.179 eV). We note that the maximal decay times and the PL saturation vs. time (shown in Fig. 2(a)) are obtained in the same temperature range. The model developed in Ref. [12] explains the behavior of decay time corresponding to a given detection energy. At sufficiently high temperature, the small QD’s experience a relatively large rate of thermal emission of electron-hole pairs back into the WL, leading to a reduction of the PL decay time for these QD’s. Meanwhile, recapture from the WL causes the repopulation of the other lower-energy QD’s and leads to an increase of their PL decay time. At higher temperatures, thermally activated emission ultimately begins to cause a decrease of the PL decay times of the lower-energy QD states. This model allows us to interpret the variation as a function of temperature of the decay time corresponding to a given energy detection, but it does not explain its increase as the detection energy vary from E0 ( ¼ 1.16 eV at 10 K) to E1 ( ¼ 1.179 eV at 10 K). We note that the variation of the decay time of QD’s corresponding to the high-energy extremity of the PL spectra (HEQD’s), that does not increase at low temperatures, indicates that the recapture has no significant effect on the evolution of the population of these QD’s. We have analyzed our results using the rate equation deduced from the model developed in Ref. [12]: dn 1 1 ¼ cMJ 2 þ n ð1Þ dt tr te Where n is the population of QD’s excitons, c is the capture rate coefficient, M is the number of WL excitons per unit area, JðEÞ is the normalized density of ground states of QD’s excitons, it is related to the inhomogeneous broadening of QD’s PL band, tr and te correspond, respectively, to the radiative lifetime and to the time for thermal emission to the WL. We neglect the recapture of carriers by HEQD’s. This approximation is supported by the fact that for these QD’s:
Fig. 3. PL decay times vs. temperature. Solid lines provide a guide to the eye. The values of E0 ¼ 1:16 eV; E1 ¼ 1:179 eV; E2 ¼ 1:227 eV and E3 ¼ 1:318 eV represent the detection energies at what the PL is measured at 10 K. As one moves along each line from 10 K toward higher temperatures, the energy detection is redshifted to account for the energy-band-gap shift with temperature. The arrows in the inset indicate the positions of the detection energies within the PL band obtained at 10 K for pulsed excitation.
† The decay does not present a saturation vs. time (Fig. 2(b)) † The decay time does not increase with temperature (Fig. 3) † The value of JðEÞ is small. Using this approximation, the rate equation of excitons in these QD’s is given in the case of pulsed excitation by: dn 1 1 1 þ ð2Þ <2 n¼2 n tr te t dt solution of this equation corresponding to RTPL
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measurements is given by n ¼ n0 expð2t=tÞ: The decay time corresponding to energy close to E3 can be directly interpreted as t: For a continuous excitation, n is given by: n ¼ cJM t: The CWPL intensity (IPL) can be written as: IPL ¼ cJM t=tr Considering two detection energies corresponding to HEQD’s (E01 ¼ 1:31 eV and E0 s2 ¼ 1:32 eV) we obtain the following equations: IPL ðE1 Þ t t JðE01 Þ ¼ r2 1 IPL ðE2 Þ tr1 t2 JðE02 Þ
ð3Þ
1 1 1 ¼ þ t1 tr1 te1
ð4Þ
1 1 1 ¼ þ t2 tr2 te2
ð5Þ
radiative lifetime with decreasing QD size is connected with a reduction of confinement effects [20]. The flat temperature dependence of the exciton radiative lifetime is expected [13,22]. Indeed, the density of states consists of a series of d functions. Increasing, the temperature cannot redistribute excitons within a band of adjacent states since these do not exist.
4. Conclusion
Where t1 ðt2 Þ; tr1 ðtr2 Þ and te1 ðte2 Þ are, respectively, the decay time, the radiative lifetime and the thermal emission time corresponding to E01 ðE02 Þ: te1 and te2 are related by the relationship [12]: 0 E 2 E01 te1 ¼ te2 exp 2 ð6Þ 2kb T To estimate J we have used the CWPL band obtained with excitation power of 0.5 W cm22 and at 10 K, to avoid the excited states contribution and the influence of inter-dots diffusion. The Eqs. (3)– (6) allow to calculate the radiative lifetime from the CWPL and RTPL measurements. The values of tr are presented in Fig. 4. We note that tr is of the order of 800 ps and is almost independent of temperature. The calculated value of tr is smaller than that measured by Heitz et al. [7] and Buckle et al. [9] (1 ns). The QD’s studied by Heitz and Buckle are larger than those studied here. Indeed, the transition energy of QD’s studied by Heitz and Buckle are 1.1 and 1.13 eV, respectively, and those of QD’s studied here are 1.31 and 1.32 eV. The decrease of the
Fig. 4. Radiative recombination time (tr1 and tr2 ) corresponding to E01 ¼ 1:31 eV (circles) and E02 ¼ 1:32 eV (squares).
We have determined the radiative lifetime of small QD’s ˚ ) using CWPL and TRPL measurements. (diameter ¼ 140 A We have found that the excitonic radiative lifetime is of the order of 800 ps and is almost independent of temperature. On the other hand, we have observed that for intermediate temperature range, the PL intensity of large QD’s remains constant over a few hundred of picoseconds. We have attributed this behavior to two processes: the refilling of the large QD’s by carriers escaped from small QD’s and the state blocking caused by the effects of Pauli exclusion.
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