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Effect of vertical electric fields on exciton fine structure of GaAs natural quantum dots
ARTICLE IN PRESS
Physica E 40 (2008) 2069–2071 www.elsevier.com/locate/physe
Effect of vertical electric fields on exciton fine structure of GaAs natural quantum dots S. Marceta,b, T. Kitaa,b, K. Ohtanib, H. Ohnoa,b, a
Semiconductor Spintronics Project, Exploratory Research for Advanced Technology, Japan Science and Technology Agency, Kitamemachi 1-18, Aoba-ku, Sendai 980-0023, Japan b Laboratory for Nanoelectronics and Spintronics, Research Institute of Electrical Communication, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan Available online 29 September 2007
Abstract The effect of vertical electric fields on the neutral exciton of GaAs ‘‘natural’’ quantum dots is investigated. A Stark effect with a quadratic field dependence up to 2 meV was observed and reveals a displacement of the excitonic wave function. The luminescencequenching limits the applied electric field range. No significative change on the fine structure splitting of the neutral exciton has been observed, suggesting that the lateral potential induced by the vertical electric field is too weak to modify the in-plane anisotropy of the exciton wave function. r 2007 Elsevier B.V. All rights reserved. PACS: 78.55.Cr; 71.35.Cc; 78.67.Hc Keywords: Quantum dots; GaAs; Fine structure splitting; Spectroscopy
1. Introduction Semiconductor quantum dots (QDs) have been proposed for a source of polarization entangled photon pair [1]. Biexciton radiative decay emits a pair of photons with polarization determined by the spin of the intermediate exciton. However, entanglement state cannot be realized if the two exciton states are not degenerate having the fine structure splitting (FSS), because in this case the polarization of the photon can be determined by its energy. This FSS results from the elongated shape and strain leading to in-plane anisotropy of the QDs. One way to overcome this is to reduce the anisotropy by a modification of the wave functions of the single particles, hole and electron, using an external perturbation. The FSS of InAs self-assembled QDs has been tuned to 0 by external in-plane magnetic [2] and electric [3,4] fields. Here we investigate the influence of Corresponding author. Laboratory for Nanoelectronics and Spintronics, Research Institute of Electrical Communication, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan. Tel./fax: +81 22 217 5555. E-mail address: [email protected] (H. Ohno).
1386-9477/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2007.09.106
a vertical electric field on the exciton photoluminescence (PL) and the FSS of GaAs QDs. Because of an easier integration in devices, we apply in our study an electric field in order to control the anisotropy. In our structures, where the bias voltage is applied between a metal mask and the substrate, a vertical electric field also induces a lateral potential that may influence the in-plane anisotropy. 2. Sample structure and experimental setup The sample consists of a GaAs quantum well (QW) of 14 monolayer thick sandwiched between two 25 nm thick Al0:3 Ga0:7 As barriers and covered by a 50 nm thick GaAs cap layer. It was grown by molecular beam epitaxy on a n-GaAs:Si substrate, used as a backside electrode. The socalled ‘‘natural’’ QDs are formed in the one monolayer wider islands naturally formed during the 2 min growth interruption at each interface of the QW. Electron beam lithography and metal lift-off were used to open 200 nm apertures in a metal mask consisting of 80 nm of Ti and 20 nm of Au, forming a Schottky contact and used as the top electrode. The PL was excited and observed through
ARTICLE IN PRESS S. Marcet et al. / Physica E 40 (2008) 2069–2071
the same hole with a He–Ne laser and an excitation power of 100 W cm2 . The PL was detected with a 1.5 m double spectrometer with a resolution of 10 meV and a Si CCD camera. 3. Results and discussion The excitonic PL of a single QD was measured under a vertical electric field up to 55 kV cm1 (Fig. 1). A Stark shift up to 2 meV and a broadening of the line, from 70 meV at 5:5 kV cm1 to 150 meV at 40 kV cm1 , with a decrease of the intensity due to the electric field were observed. The spatial separation of electron and hole due to the electric field leads to a reduction of the oscillator strength and a drop of the luminescence intensity. The tunneling of the carriers out of the dot reduces the lifetime of the exciton in the QDs and thus leads to a broadening of the emission line. The photocurrent is very small, below 1 mA but increases drastically when the emission intensity abruptly drops above 35 kV cm1 . Above 45 kV cm1 and below 225 kV cm1 , the PL is quenched due to the carriers escaping out of the QDs, limiting the applied electric field range. The energy shift due to the Stark effect is not centered around 0 because of the Schottky barrier height. The energy shift has a quadratic field dependence E ¼ E 0 pF þ bF 2 with E 0 the energy at F ¼ 0; p the permanent dipole moment, b the polarizability and F the electric field [5]. p and F are defined as p ¼ er where e is the electronic charge and r the separation between the center of gravity of the electron and hole wave functions and F ¼ ðV g V 0g Þ=d, where V g is the applied gate voltage, V 0g ¼ 0:92 V the Schottky barrier height and d the distance between the sample surface and the n-doped layer. V 0g was measured from the photocurrent induced by light above the Al0:3 Ga0:7 As barriers. V 0g ¼ 0:92 V was determined, where the current changes sign for flat bands. We found p ¼ 1:3 e A˚ and b ¼ 0:73 meV ðkV=cm1 Þ2 . p is one order
of magnitude smaller with that in InAs self-assembled QDs [5] whereas b is of the same order of magnitude. In InAs self-assembled QDs, a negative value of p reveals a permanent dipole moment with the hole confined at the base of the QDs, below the electron [5]. This separation is explained by the In composition inhomogeneity and the QD shape with a larger base. The absence of such inhomogeneities in our QDs explains the small value of p. Fig. 2 shows the linear polarization, lying along the crystal axis [1 1 0] and ½1 1 0 [6], of the excitonic transition. The small energy shift of the two lines, due to the exciton state splitting, gives the FSS, measured in our sample to be 60 meV. This value depends on the amount of a symmetry of the QD shape and is of the same order of magnitude than the splitting of 25 meV measured by Gammon et al. in natural GaAs QDs [6]. Although a small change of the FSS with applied bias voltage can be observed in Fig. 3, no clear 400
Photoluminescence [arb. unit]
2070
300
T = 5K λex = 632.8 nm Vg = 0.4 V
FSS
200 70 μeV 100
0 1640.8
1640.9 1641.0 Energy [meV]
1641.1
1641.2
Fig. 2. Linearly polarized excitonic photoluminescence for V g ¼ 0:4 V and T ¼ 5 K. The signal is detected for linear polarizations parallel to [1 1 0] and ½1 1 0.
Energy splitting [μeV]
80
T=5 K λex = 632.8 nm
70
60
50
40
30 0.4 Fig. 1. Photoluminescence energy and intensity (gray scale) at 5 K as a function of the emitted photon energy and applied vertical bias voltage.
0.6
0.8 1.0 1.2 Bias voltage [V]
1.4
1.6
Fig. 3. FSS as a function of the vertical applied bias voltage at T ¼ 5 K.
ARTICLE IN PRESS S. Marcet et al. / Physica E 40 (2008) 2069–2071
dependence was observed. Moreover, the trend is very weak compared to the modification induced by an in-plane electric field on InAs self-assembled QDs: about 100 meV for a few kV cm1 range [3,4] but is of the same order of magnitude than reported with a vertical electric field [7]. Due to a different device structure, a weak lateral component is present in our sample and might induce the observed FSS modification. Thus, a vertical electric field does not modify significantly the FSS in the applied electric field range.
Acknowledgments
4. Conclusion
References
In summary, we have investigated the vertical electric field influence on the excitonic photoluminescence of GaAs QDs. A Starkshift with a permanent dipole moment p ¼ 1:3 e A˚ and a polarizability b ¼ 0:73 meV ðkV cm1 Þ2 is observed and evidences a displacement of the excitonic wave function. At high electric field, the line is broadened and suppressed above 45 kV cm1 , limiting the amplitude of the field that can be applied in our structure. The absence of significative change in the FSS as a function of the vertical electric field tends to show that the displacement of the wave function, with the Stark effect is rather along the vertical direction. The lateral potential is thus too weak to induce a significative modification of the in-plane
2071
anisotropy of the exciton wave function. Improved devices with lateral electric field are necessary to enhance the wave function lateral displacement and control the FSS [3,4,7].
The authors thank Dr. Y. Ohno and S. Matsuzaka for technical help.
[1] O. Benson, C. Santori, M. Pelton, Y. Yamamoto, Phys. Rev. Lett. 84 (2000) 2513. [2] R.M. Stevenson, R.J. Young, P. Atkinson, K. Cooper, D.A. Ritchie, A.J. Shields, Nature 439 (2006) 179. [3] B.D. Gerardot, S. Seidl, P.A. Dalgarno, R.J. Warburton, D. Granados, J.M. Garcian, K. Kowalik, O. Krebs, K. Karrai, A. Badolato, P.M. Petroff, Appl. Phys. Lett. 90 (2007) 041101. [4] K. Kowalik, O. Krebs, A. Lemaıˆ re, S. Laurent, P. Senellart, P. Voisin, J.A. Gaj, Appl. Phys. Lett. 86 (2005) 041907. [5] R.J. Warburton, C. Schulhauser, D. Haft, C. Scha¨flein, K. Karrai, J.M. Garcia, W. Schoenfeld, P.M. Petroff, Phys. Rev. B 65 (2002) 113303. [6] D. Gammon, E.S. Snow, B.V. Shanabrook, D.S. Katzer, D. Park, Phys. Rev. Lett. 76 (1996) 3005. [7] K. Kowalik, O. Krebs, P. Senellart, A. Lemaıˆ tre, B. Eble, A. Kudelski, J. Gaj, P. Voisin, Phys. Stat. Sol. (c) 3 (2006) 3890.
Physica E 40 (2008) 2069–2071 www.elsevier.com/locate/physe
Effect of vertical electric fields on exciton fine structure of GaAs natural quantum dots S. Marceta,b, T. Kitaa,b, K. Ohtanib, H. Ohnoa,b, a
Semiconductor Spintronics Project, Exploratory Research for Advanced Technology, Japan Science and Technology Agency, Kitamemachi 1-18, Aoba-ku, Sendai 980-0023, Japan b Laboratory for Nanoelectronics and Spintronics, Research Institute of Electrical Communication, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan Available online 29 September 2007
Abstract The effect of vertical electric fields on the neutral exciton of GaAs ‘‘natural’’ quantum dots is investigated. A Stark effect with a quadratic field dependence up to 2 meV was observed and reveals a displacement of the excitonic wave function. The luminescencequenching limits the applied electric field range. No significative change on the fine structure splitting of the neutral exciton has been observed, suggesting that the lateral potential induced by the vertical electric field is too weak to modify the in-plane anisotropy of the exciton wave function. r 2007 Elsevier B.V. All rights reserved. PACS: 78.55.Cr; 71.35.Cc; 78.67.Hc Keywords: Quantum dots; GaAs; Fine structure splitting; Spectroscopy
1. Introduction Semiconductor quantum dots (QDs) have been proposed for a source of polarization entangled photon pair [1]. Biexciton radiative decay emits a pair of photons with polarization determined by the spin of the intermediate exciton. However, entanglement state cannot be realized if the two exciton states are not degenerate having the fine structure splitting (FSS), because in this case the polarization of the photon can be determined by its energy. This FSS results from the elongated shape and strain leading to in-plane anisotropy of the QDs. One way to overcome this is to reduce the anisotropy by a modification of the wave functions of the single particles, hole and electron, using an external perturbation. The FSS of InAs self-assembled QDs has been tuned to 0 by external in-plane magnetic [2] and electric [3,4] fields. Here we investigate the influence of Corresponding author. Laboratory for Nanoelectronics and Spintronics, Research Institute of Electrical Communication, Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan. Tel./fax: +81 22 217 5555. E-mail address: [email protected] (H. Ohno).
1386-9477/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physe.2007.09.106
a vertical electric field on the exciton photoluminescence (PL) and the FSS of GaAs QDs. Because of an easier integration in devices, we apply in our study an electric field in order to control the anisotropy. In our structures, where the bias voltage is applied between a metal mask and the substrate, a vertical electric field also induces a lateral potential that may influence the in-plane anisotropy. 2. Sample structure and experimental setup The sample consists of a GaAs quantum well (QW) of 14 monolayer thick sandwiched between two 25 nm thick Al0:3 Ga0:7 As barriers and covered by a 50 nm thick GaAs cap layer. It was grown by molecular beam epitaxy on a n-GaAs:Si substrate, used as a backside electrode. The socalled ‘‘natural’’ QDs are formed in the one monolayer wider islands naturally formed during the 2 min growth interruption at each interface of the QW. Electron beam lithography and metal lift-off were used to open 200 nm apertures in a metal mask consisting of 80 nm of Ti and 20 nm of Au, forming a Schottky contact and used as the top electrode. The PL was excited and observed through
ARTICLE IN PRESS S. Marcet et al. / Physica E 40 (2008) 2069–2071
the same hole with a He–Ne laser and an excitation power of 100 W cm2 . The PL was detected with a 1.5 m double spectrometer with a resolution of 10 meV and a Si CCD camera. 3. Results and discussion The excitonic PL of a single QD was measured under a vertical electric field up to 55 kV cm1 (Fig. 1). A Stark shift up to 2 meV and a broadening of the line, from 70 meV at 5:5 kV cm1 to 150 meV at 40 kV cm1 , with a decrease of the intensity due to the electric field were observed. The spatial separation of electron and hole due to the electric field leads to a reduction of the oscillator strength and a drop of the luminescence intensity. The tunneling of the carriers out of the dot reduces the lifetime of the exciton in the QDs and thus leads to a broadening of the emission line. The photocurrent is very small, below 1 mA but increases drastically when the emission intensity abruptly drops above 35 kV cm1 . Above 45 kV cm1 and below 225 kV cm1 , the PL is quenched due to the carriers escaping out of the QDs, limiting the applied electric field range. The energy shift due to the Stark effect is not centered around 0 because of the Schottky barrier height. The energy shift has a quadratic field dependence E ¼ E 0 pF þ bF 2 with E 0 the energy at F ¼ 0; p the permanent dipole moment, b the polarizability and F the electric field [5]. p and F are defined as p ¼ er where e is the electronic charge and r the separation between the center of gravity of the electron and hole wave functions and F ¼ ðV g V 0g Þ=d, where V g is the applied gate voltage, V 0g ¼ 0:92 V the Schottky barrier height and d the distance between the sample surface and the n-doped layer. V 0g was measured from the photocurrent induced by light above the Al0:3 Ga0:7 As barriers. V 0g ¼ 0:92 V was determined, where the current changes sign for flat bands. We found p ¼ 1:3 e A˚ and b ¼ 0:73 meV ðkV=cm1 Þ2 . p is one order
of magnitude smaller with that in InAs self-assembled QDs [5] whereas b is of the same order of magnitude. In InAs self-assembled QDs, a negative value of p reveals a permanent dipole moment with the hole confined at the base of the QDs, below the electron [5]. This separation is explained by the In composition inhomogeneity and the QD shape with a larger base. The absence of such inhomogeneities in our QDs explains the small value of p. Fig. 2 shows the linear polarization, lying along the crystal axis [1 1 0] and ½1 1 0 [6], of the excitonic transition. The small energy shift of the two lines, due to the exciton state splitting, gives the FSS, measured in our sample to be 60 meV. This value depends on the amount of a symmetry of the QD shape and is of the same order of magnitude than the splitting of 25 meV measured by Gammon et al. in natural GaAs QDs [6]. Although a small change of the FSS with applied bias voltage can be observed in Fig. 3, no clear 400
Photoluminescence [arb. unit]
2070
300
T = 5K λex = 632.8 nm Vg = 0.4 V
FSS
200 70 μeV 100
0 1640.8
1640.9 1641.0 Energy [meV]
1641.1
1641.2
Fig. 2. Linearly polarized excitonic photoluminescence for V g ¼ 0:4 V and T ¼ 5 K. The signal is detected for linear polarizations parallel to [1 1 0] and ½1 1 0.
Energy splitting [μeV]
80
T=5 K λex = 632.8 nm
70
60
50
40
30 0.4 Fig. 1. Photoluminescence energy and intensity (gray scale) at 5 K as a function of the emitted photon energy and applied vertical bias voltage.
0.6
0.8 1.0 1.2 Bias voltage [V]
1.4
1.6
Fig. 3. FSS as a function of the vertical applied bias voltage at T ¼ 5 K.
ARTICLE IN PRESS S. Marcet et al. / Physica E 40 (2008) 2069–2071
dependence was observed. Moreover, the trend is very weak compared to the modification induced by an in-plane electric field on InAs self-assembled QDs: about 100 meV for a few kV cm1 range [3,4] but is of the same order of magnitude than reported with a vertical electric field [7]. Due to a different device structure, a weak lateral component is present in our sample and might induce the observed FSS modification. Thus, a vertical electric field does not modify significantly the FSS in the applied electric field range.
Acknowledgments
4. Conclusion
References
In summary, we have investigated the vertical electric field influence on the excitonic photoluminescence of GaAs QDs. A Starkshift with a permanent dipole moment p ¼ 1:3 e A˚ and a polarizability b ¼ 0:73 meV ðkV cm1 Þ2 is observed and evidences a displacement of the excitonic wave function. At high electric field, the line is broadened and suppressed above 45 kV cm1 , limiting the amplitude of the field that can be applied in our structure. The absence of significative change in the FSS as a function of the vertical electric field tends to show that the displacement of the wave function, with the Stark effect is rather along the vertical direction. The lateral potential is thus too weak to induce a significative modification of the in-plane
2071
anisotropy of the exciton wave function. Improved devices with lateral electric field are necessary to enhance the wave function lateral displacement and control the FSS [3,4,7].
The authors thank Dr. Y. Ohno and S. Matsuzaka for technical help.
[1] O. Benson, C. Santori, M. Pelton, Y. Yamamoto, Phys. Rev. Lett. 84 (2000) 2513. [2] R.M. Stevenson, R.J. Young, P. Atkinson, K. Cooper, D.A. Ritchie, A.J. Shields, Nature 439 (2006) 179. [3] B.D. Gerardot, S. Seidl, P.A. Dalgarno, R.J. Warburton, D. Granados, J.M. Garcian, K. Kowalik, O. Krebs, K. Karrai, A. Badolato, P.M. Petroff, Appl. Phys. Lett. 90 (2007) 041101. [4] K. Kowalik, O. Krebs, A. Lemaıˆ re, S. Laurent, P. Senellart, P. Voisin, J.A. Gaj, Appl. Phys. Lett. 86 (2005) 041907. [5] R.J. Warburton, C. Schulhauser, D. Haft, C. Scha¨flein, K. Karrai, J.M. Garcia, W. Schoenfeld, P.M. Petroff, Phys. Rev. B 65 (2002) 113303. [6] D. Gammon, E.S. Snow, B.V. Shanabrook, D.S. Katzer, D. Park, Phys. Rev. Lett. 76 (1996) 3005. [7] K. Kowalik, O. Krebs, P. Senellart, A. Lemaıˆ tre, B. Eble, A. Kudelski, J. Gaj, P. Voisin, Phys. Stat. Sol. (c) 3 (2006) 3890.