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Electronic structure of self-assembled InAs quantum dots
Physica E 13 (2002) 208 – 211
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Electronic structure of self-assembled InAs quantum dots C. Bocka; ∗ , K.H. Schmidta , U. Kunzea , V.V. Khorenkob , S. Malzerb , G.H. D2ohlerb b Institut
a Lehrstuhl
f ur Werkstoe der Elektrotechnik, Ruhr-Universit at Bochum, D-44780 Bochum, Germany f ur Technische Physik I, Universit at Erlangen-N urnberg, Erwin-Rommel-Str. 1, D-91058 Erlangen, Germany
Abstract Electroluminescence (EL) is always related to carrier transport (i.e. current 4ow) into an active region. We used EL and transport measurements to study in detail the electronic structure in InAs quantum dots (QDs) embedded in the intrinsic GaAs region of a double hetero p–i–n diode. According to the position of the dot layer with respect to the n- and p-doped regions we independently investigated the QD levels of electrons and holes. From the di9erential capacitance the Coulomb blockade energy for electrons in the QD ground state and the energy splitting between the ground and :rst excited state in the conduction band system was extracted. Additionally the energy separation of the electron ground state from the GaAs conduction band edge was determined by the same technique. The energetic distance between the hole ground and :rst excited state can be estimated from the electroluminescence signal as well as from the di9erential conductance. ? 2002 Elsevier Science B.V. All rights reserved. PACS: 72.20; 72.20D; 73.61.Ey; 73.23Hk Keywords: Electronic structure; InAs quantum dots; Transport; Luminescence
The electronic structure of InAs quantum dots (QDs) is of great importance in perspective of the future device applications. Optical and transport measurements give experimental access to the energetic position of the zero-dimensional states in the dots. While optical spectra re4ect the hole combined with the electron system, capacitance spectroscopy allows to study the hole or the electron levels separately [1,2]. Besides capacitance measurements a few tunneling experiments are also done [3,4] to get information about zero-dimensional levels. p–i–n diode structures are predominately used either to study optical e9ects like the electro-optical :eld e9ect [5,6] or for applications like quantum dot lasers [7]. ∗ Corresponding author. Tel.: +49(0)234=32-23084; fax: +49(0)234=32-14166. E-mail address: [email protected] (C. Bock).
We used both optical and transport measurements to get information about the electronic structure. The samples were grown by molecular beam epitaxy on semi-insolating (1 0 0) GaAs substrate ◦ at a temperature of T = 585 C. A 400 nm n+ Al0:25 Ga0:75 As layer was grown, followed by an intrinsic GaAs region of a thickness t1 = 30 nm for sample A and t1 = 25 nm for sample B. The temper◦ ature was reduced to T = 490 C for the InAs islands growth. The dots were covered with t2 = 60 nm intrinsic GaAs in sample A and with t2 = 25 nm in sample B. The temperature was ramped up again to deposite a 300 nm p+ -Al0:25 Ga0:75 As. 20 nm p+ -GaAs formed the capping layer. In order to get information about the size, shape and density of the InAs islands the dots were also deposited on the surface under the same conditions as described before. With a scanning electron microscope (SEM) we determined an island
1386-9477/02/$ - see front matter ? 2002 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 6 - 9 4 7 7 ( 0 1 ) 0 0 5 2 1 - 5
C. Bock et al. / Physica E 13 (2002) 208 – 211
Fig. 1. Schematic of the conduction (EC ) and the valence band edge (EV ) of the investigated p–i–n structures at an applied forward bias of U ≈ 0:9 V.
diameter of 28 nm at a dot density of 5 × 1010 cm−2 . Ohmic contacts to the n- and p-type regions were prepared by alloying Au=Ge or Au=Zn, respectively. In our electrical experiments an AC voltage LU was added to the applied DC voltage and the di9erential conductance as well as the di9erential capacitance were measured using lock-in technique at a temperature of T = 4:2 K. For electroluminescence experiments the sample is mounted in a closed-cycle He-refrigerator with a base temperature of T = 30 K. The emitted light was dispersed by a 0:3 m spectrometer and detected with an InGaAs femtowatt receiver. Fig. 1 shows the schematic band diagram of the investigated structure at an applied forward bias of U ≈ 0:9 V. When the dots are positioned near the n-doped layer (sample A) the islands are charged with electrons before holes are able to tunnel into the dots giving rise to an EL as well as to an ohmic current signal. For U1 ≈ 0:86 V the QD ground state of the electrons comes into resonance with EFn and the charging process of the islands with the :rst electron results in a peak in the di9erential capacitance (labeled s1 in Fig. 2). Coulomb repulsion prevents the tunneling of a second electron into the dots. An additional bias is necessary to overcome the Coulomb blockade Energy EC; 00; e and to load the ground state of each dot with two electrons. In the third harmonic signal, represented by the dotted line in Fig. 2, each charg-
209
Fig. 2. Di9erential capacitance and conductance of sample B measured at T = 4:2 K with a modulation amplitude of 4 mV at a frequency of 433 Hz. The dotted line displays the curvature of the di9erential conductance measured with a modulation amplitude of 25 mV.
ing event is clearly re4ected by a minimum. From the voltage di9erence between the features s1 and s2 the Coulomb blockade energy of EC; 00; e ≈ 27 meV can be extracted. A third electron can tunnel into the dots when the :rst excited level of the islands is shifted below EFn and the Coulomb blockade energy of the ground state electrons minus the exchange energy is surpassed at U3 ≈ 1:105 V. According to Ref. [8] we roughly estimate the energetic distance between the ground and the :rst exited state in the conduction band E01; e ≈ 81 meV −1:25EC; 00; e ≈ 48 meV. Additionally, the energetic distance of the electron ground state from the GaAs conduction band edge can be extracted by LE0; GaAs; e ≈ e(Ubi − U1 )(t2 =(t1 + t2 )) ≈ 220 meV. When the dot layer is in the center of the intrinsic GaAs region (sample B) electrons as well as holes simultaneously tunnel into the ground state of the dots at U = 1:1 V. Consequently, there is no structure in the capacitive signal for U ¡ 1:1 V (Fig. 3). Since electrons and holes are injected into the islands at the same voltage, the EL signal appears immediately at the onset of the conductance (see inset of Fig. 3). The lineshape of the EL spectrum can be :tted by a single Gaussian curve re4ecting the size distribution of the InAs dots. At U2 = 1:144 V holes are injected into the :rst excited QD level resulting in another pronounced feature in the curvature of the ohmic
210
C. Bock et al. / Physica E 13 (2002) 208 – 211
Fig. 3. Curvature of the conductance signal measured on sample A at T = 4:2 K with a modulation amplitude of 4 mV and a modulation frequency of 233 Hz. The transport resonances are labeled with U1 –U5 . The inset displays the EL signal (T = 30 K) measured at U1 = 1:107 V and a Gaussian :t (boxed line) to the experimental data.
signal (Fig. 4). From a simple leverage law we estimate an energy distance between these two hole states of LE01; h ≈ e(U2 − U1 )=2 ≈ 22 meV. At the same voltage the EL spectrum becomes asymmetric and two Gaussians seperated by LE01; h ≈ 20 meV are necessary to :t the signal (Fig. 3). We attribute the high energy transition to a recombination process between electrons in the QD ground state and holes in the :rst excited level. Therefore the energy splitting between the Gaussian :ts re4ects the distance between the :rst two hole levels, which is in excellent agreement with our transport data. The structure labeled U3 ≈ 1:161 V results from the Coulomb-blocked electron transport into the QD s-shell in the conduction band. With a simple leverage law we determined the Coulomb blockade energy of LEC; 00; e ≈ e(U3 −U1 )=2 ≈ 27 meV for electrons in the QD ground state. This value coincides with the value determined from sample A. Due to the injection of the second electron into the s-shell the EL ground state transition strongly increases. The recombination process between p-electrons and holes of the :rst excited state seems to be very eOcient since a pronounced
Fig. 4. EL signal measured at T = 30 K and U2 = 1:144 V. Additionally, Gaussian :t (dashed lines) to the experimental data are shown.
transition appears in the EL spectra at an energy of LE11 ≈ 1:14 eV for U4 ¿ 1:255 V [9]. From the energy di9erence LE01 ≈ 70 meV of the two maxima in the EL spectra the quantization energy of the electrons LE01; e was extracted (LE01 ≈ LE01; e + LE01; h ). As already mentioned above we estimated a hole level splitting of LE01; h ≈ 20 meV from both the di9erential conductance and the EL signal, and therefore LE01; e ≈ 50 meV. This value :ts reasonably well to E01; e as determined by capacitance measurements on sample A. The second excited electron level is populated at U5 ≈ 1:306 V giving rise to another high-energy transition in the EL spectra at an energy LE22 ≈ 1:21 eV [9]. In conclusion, we studied the electronic structure of InAs QDs embedded in a GaAs matrix by a p–i–n diode structure by transport and optical spectroscopy. For electrons in the QD ground state a Coulomb blockade energy of EC; 00; e ≈ 27 meV and an energetic distance of E01; e ≈ 50 meV between the ground and :rst excited QD level of the electrons were determined from the di9erential capacitance. Additionally, the energetic distance LE0; GaAs; e ≈ 220 meV of the electron ground state from the GaAs conduction band edge was estimated with the same technique. From the asymmetry of the EL signal as well as from the ohmic transport signal an energy splitting of E01; h ≈ 20 meV was extracted for the hole system.
C. Bock et al. / Physica E 13 (2002) 208 – 211
Acknowledgements The authors gratefully acknowledge the :nancial support by the Deutsche Forschungsgemeinschaft. V.V. Khorenko acknowledges the support of Alexander von Humboldt Foundation. References [1] G. Medeiros-Riberio, et al., Appl. Phys. Lett. 66 (1995) 1767.
[2] [3] [4] [5] [6]
211
H. Drexler, et al., Phys. Rev. Lett. 73 (1994) 2252. I. Hapke-Wurst, et al., Phys. Rev. B 62 (2000) 12621. K.H. Schmidt, et al., submitted for publication. P.W. Fry, et al., Phys. Rev. Lett. 84 (2000) 733. F. Yang, et al., Superlattices Microstruct. 25 (1999) 419. [7] Z. Zou, et al., Appl. Phys. Lett. 75 (1999) 22. [8] R.J. Warburton, et al., Phys. Rev. B 58 (1998) 16221. [9] V.V. Khorenko, et al., Phys. Stat. Sol. B 224 (2001) 129.
www.elsevier.com/locate/physe
Electronic structure of self-assembled InAs quantum dots C. Bocka; ∗ , K.H. Schmidta , U. Kunzea , V.V. Khorenkob , S. Malzerb , G.H. D2ohlerb b Institut
a Lehrstuhl
f ur Werkstoe der Elektrotechnik, Ruhr-Universit at Bochum, D-44780 Bochum, Germany f ur Technische Physik I, Universit at Erlangen-N urnberg, Erwin-Rommel-Str. 1, D-91058 Erlangen, Germany
Abstract Electroluminescence (EL) is always related to carrier transport (i.e. current 4ow) into an active region. We used EL and transport measurements to study in detail the electronic structure in InAs quantum dots (QDs) embedded in the intrinsic GaAs region of a double hetero p–i–n diode. According to the position of the dot layer with respect to the n- and p-doped regions we independently investigated the QD levels of electrons and holes. From the di9erential capacitance the Coulomb blockade energy for electrons in the QD ground state and the energy splitting between the ground and :rst excited state in the conduction band system was extracted. Additionally the energy separation of the electron ground state from the GaAs conduction band edge was determined by the same technique. The energetic distance between the hole ground and :rst excited state can be estimated from the electroluminescence signal as well as from the di9erential conductance. ? 2002 Elsevier Science B.V. All rights reserved. PACS: 72.20; 72.20D; 73.61.Ey; 73.23Hk Keywords: Electronic structure; InAs quantum dots; Transport; Luminescence
The electronic structure of InAs quantum dots (QDs) is of great importance in perspective of the future device applications. Optical and transport measurements give experimental access to the energetic position of the zero-dimensional states in the dots. While optical spectra re4ect the hole combined with the electron system, capacitance spectroscopy allows to study the hole or the electron levels separately [1,2]. Besides capacitance measurements a few tunneling experiments are also done [3,4] to get information about zero-dimensional levels. p–i–n diode structures are predominately used either to study optical e9ects like the electro-optical :eld e9ect [5,6] or for applications like quantum dot lasers [7]. ∗ Corresponding author. Tel.: +49(0)234=32-23084; fax: +49(0)234=32-14166. E-mail address: [email protected] (C. Bock).
We used both optical and transport measurements to get information about the electronic structure. The samples were grown by molecular beam epitaxy on semi-insolating (1 0 0) GaAs substrate ◦ at a temperature of T = 585 C. A 400 nm n+ Al0:25 Ga0:75 As layer was grown, followed by an intrinsic GaAs region of a thickness t1 = 30 nm for sample A and t1 = 25 nm for sample B. The temper◦ ature was reduced to T = 490 C for the InAs islands growth. The dots were covered with t2 = 60 nm intrinsic GaAs in sample A and with t2 = 25 nm in sample B. The temperature was ramped up again to deposite a 300 nm p+ -Al0:25 Ga0:75 As. 20 nm p+ -GaAs formed the capping layer. In order to get information about the size, shape and density of the InAs islands the dots were also deposited on the surface under the same conditions as described before. With a scanning electron microscope (SEM) we determined an island
1386-9477/02/$ - see front matter ? 2002 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 6 - 9 4 7 7 ( 0 1 ) 0 0 5 2 1 - 5
C. Bock et al. / Physica E 13 (2002) 208 – 211
Fig. 1. Schematic of the conduction (EC ) and the valence band edge (EV ) of the investigated p–i–n structures at an applied forward bias of U ≈ 0:9 V.
diameter of 28 nm at a dot density of 5 × 1010 cm−2 . Ohmic contacts to the n- and p-type regions were prepared by alloying Au=Ge or Au=Zn, respectively. In our electrical experiments an AC voltage LU was added to the applied DC voltage and the di9erential conductance as well as the di9erential capacitance were measured using lock-in technique at a temperature of T = 4:2 K. For electroluminescence experiments the sample is mounted in a closed-cycle He-refrigerator with a base temperature of T = 30 K. The emitted light was dispersed by a 0:3 m spectrometer and detected with an InGaAs femtowatt receiver. Fig. 1 shows the schematic band diagram of the investigated structure at an applied forward bias of U ≈ 0:9 V. When the dots are positioned near the n-doped layer (sample A) the islands are charged with electrons before holes are able to tunnel into the dots giving rise to an EL as well as to an ohmic current signal. For U1 ≈ 0:86 V the QD ground state of the electrons comes into resonance with EFn and the charging process of the islands with the :rst electron results in a peak in the di9erential capacitance (labeled s1 in Fig. 2). Coulomb repulsion prevents the tunneling of a second electron into the dots. An additional bias is necessary to overcome the Coulomb blockade Energy EC; 00; e and to load the ground state of each dot with two electrons. In the third harmonic signal, represented by the dotted line in Fig. 2, each charg-
209
Fig. 2. Di9erential capacitance and conductance of sample B measured at T = 4:2 K with a modulation amplitude of 4 mV at a frequency of 433 Hz. The dotted line displays the curvature of the di9erential conductance measured with a modulation amplitude of 25 mV.
ing event is clearly re4ected by a minimum. From the voltage di9erence between the features s1 and s2 the Coulomb blockade energy of EC; 00; e ≈ 27 meV can be extracted. A third electron can tunnel into the dots when the :rst excited level of the islands is shifted below EFn and the Coulomb blockade energy of the ground state electrons minus the exchange energy is surpassed at U3 ≈ 1:105 V. According to Ref. [8] we roughly estimate the energetic distance between the ground and the :rst exited state in the conduction band E01; e ≈ 81 meV −1:25EC; 00; e ≈ 48 meV. Additionally, the energetic distance of the electron ground state from the GaAs conduction band edge can be extracted by LE0; GaAs; e ≈ e(Ubi − U1 )(t2 =(t1 + t2 )) ≈ 220 meV. When the dot layer is in the center of the intrinsic GaAs region (sample B) electrons as well as holes simultaneously tunnel into the ground state of the dots at U = 1:1 V. Consequently, there is no structure in the capacitive signal for U ¡ 1:1 V (Fig. 3). Since electrons and holes are injected into the islands at the same voltage, the EL signal appears immediately at the onset of the conductance (see inset of Fig. 3). The lineshape of the EL spectrum can be :tted by a single Gaussian curve re4ecting the size distribution of the InAs dots. At U2 = 1:144 V holes are injected into the :rst excited QD level resulting in another pronounced feature in the curvature of the ohmic
210
C. Bock et al. / Physica E 13 (2002) 208 – 211
Fig. 3. Curvature of the conductance signal measured on sample A at T = 4:2 K with a modulation amplitude of 4 mV and a modulation frequency of 233 Hz. The transport resonances are labeled with U1 –U5 . The inset displays the EL signal (T = 30 K) measured at U1 = 1:107 V and a Gaussian :t (boxed line) to the experimental data.
signal (Fig. 4). From a simple leverage law we estimate an energy distance between these two hole states of LE01; h ≈ e(U2 − U1 )=2 ≈ 22 meV. At the same voltage the EL spectrum becomes asymmetric and two Gaussians seperated by LE01; h ≈ 20 meV are necessary to :t the signal (Fig. 3). We attribute the high energy transition to a recombination process between electrons in the QD ground state and holes in the :rst excited level. Therefore the energy splitting between the Gaussian :ts re4ects the distance between the :rst two hole levels, which is in excellent agreement with our transport data. The structure labeled U3 ≈ 1:161 V results from the Coulomb-blocked electron transport into the QD s-shell in the conduction band. With a simple leverage law we determined the Coulomb blockade energy of LEC; 00; e ≈ e(U3 −U1 )=2 ≈ 27 meV for electrons in the QD ground state. This value coincides with the value determined from sample A. Due to the injection of the second electron into the s-shell the EL ground state transition strongly increases. The recombination process between p-electrons and holes of the :rst excited state seems to be very eOcient since a pronounced
Fig. 4. EL signal measured at T = 30 K and U2 = 1:144 V. Additionally, Gaussian :t (dashed lines) to the experimental data are shown.
transition appears in the EL spectra at an energy of LE11 ≈ 1:14 eV for U4 ¿ 1:255 V [9]. From the energy di9erence LE01 ≈ 70 meV of the two maxima in the EL spectra the quantization energy of the electrons LE01; e was extracted (LE01 ≈ LE01; e + LE01; h ). As already mentioned above we estimated a hole level splitting of LE01; h ≈ 20 meV from both the di9erential conductance and the EL signal, and therefore LE01; e ≈ 50 meV. This value :ts reasonably well to E01; e as determined by capacitance measurements on sample A. The second excited electron level is populated at U5 ≈ 1:306 V giving rise to another high-energy transition in the EL spectra at an energy LE22 ≈ 1:21 eV [9]. In conclusion, we studied the electronic structure of InAs QDs embedded in a GaAs matrix by a p–i–n diode structure by transport and optical spectroscopy. For electrons in the QD ground state a Coulomb blockade energy of EC; 00; e ≈ 27 meV and an energetic distance of E01; e ≈ 50 meV between the ground and :rst excited QD level of the electrons were determined from the di9erential capacitance. Additionally, the energetic distance LE0; GaAs; e ≈ 220 meV of the electron ground state from the GaAs conduction band edge was estimated with the same technique. From the asymmetry of the EL signal as well as from the ohmic transport signal an energy splitting of E01; h ≈ 20 meV was extracted for the hole system.
C. Bock et al. / Physica E 13 (2002) 208 – 211
Acknowledgements The authors gratefully acknowledge the :nancial support by the Deutsche Forschungsgemeinschaft. V.V. Khorenko acknowledges the support of Alexander von Humboldt Foundation. References [1] G. Medeiros-Riberio, et al., Appl. Phys. Lett. 66 (1995) 1767.
[2] [3] [4] [5] [6]
211
H. Drexler, et al., Phys. Rev. Lett. 73 (1994) 2252. I. Hapke-Wurst, et al., Phys. Rev. B 62 (2000) 12621. K.H. Schmidt, et al., submitted for publication. P.W. Fry, et al., Phys. Rev. Lett. 84 (2000) 733. F. Yang, et al., Superlattices Microstruct. 25 (1999) 419. [7] Z. Zou, et al., Appl. Phys. Lett. 75 (1999) 22. [8] R.J. Warburton, et al., Phys. Rev. B 58 (1998) 16221. [9] V.V. Khorenko, et al., Phys. Stat. Sol. B 224 (2001) 129.