- Email: [email protected]
AlGaAs-based quantum cellular automata cell
ARTICLE IN PRESS
Microelectronics Journal 39 (2008) 674–677 www.elsevier.com/locate/mejo
Realization of a GaAs/AlGaAs-based quantum cellular automata cell F. Perez-Martinez, K.D. Petersson, I. Farrer, D. Anderson, G.A.C. Jones, D.A. Ritchie, C.G. Smith Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, UK Available online 25 February 2008
Abstract We report on the experimental demonstration of a four-dot cell on a GaAs/AlGaAs substrate fabricated using electron beam lithographically defined gates. These surface metallic gates form a pair of double quantum dots, as well as a pair of quantum point contacts that act as non-invasive voltage probes. This device is used to realize a quantum cellular automata cell and, in further experiments, we employ it to investigate photon assisted tunneling. These results prove that the four-dot cell is a good building block candidate toward fulfilling the scalability DiVincezo criteria. r 2008 Elsevier Ltd. All rights reserved. PACS: 73.23.Hk; 73.63.Kv Keywords: QCA; Qubit; DQD; Quantum computation; PAT; Coulomb blockade
1. Introduction Investigation of zero-dimensional systems (quantum dots—QDs) has been a very active field of research in the last few years due to its many benefits when exploring quantum phenomena [1]. They have also found use as a transistor-less approach for solving the density problems that are starting to slow research in the microelectronics industry [2]. Moreover, a proposal exists to use QDs as building blocks for a quantum computer [3], which has propelled intense research by many groups and the creation of a worldwide effort to create a test bed for quantum computation experiments [4]. The natural evolution of the research of QDs in semiconductors led to the study of groups of QDs [5]. To date, extensive literature exists in the use of double quantum dots (DQDs) [6], as well as some effort into higher order dot systems (for example, see Ref. [7–9]). In this paper we report the realization of a device consisting of four QDs that, when measured at cryogenic temperatures, show evidence of being able to operate in the few electron Corresponding author. Tel.: +44 1223 766130; fax: +44 1223 337271.
E-mail address: [email protected] (F. Perez-Martinez). URL: http://www.sp.phy.cam.ac.uk/ (F. Perez-Martinez). 0026-2692/$ - see front matter r 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.mejo.2008.01.005
regime. As a proof of principle, we tune our system to operate as a Quantum Cellular Automata (QCA).1 By means of a high frequency setup, we show this device can also be employed in microwave ðmWÞ experiments.
2. Fabrication and experiment An electron micrograph of the four-dot cell is shown in Fig. 1. The QDs are defined by means of metallic surface gates. LtðbÞ , MtðbÞ and RtðbÞ form the top (bottom) DQD system. LtðbÞ and RtðbÞ control the coupling to StðbÞ and DtðbÞ , the ohmic contacts to the top (bottom) electron reservoirs. The coupling between DQDs is controlled with gates C. In addition, DtðbÞ and Lt ðRb Þ define the top (bottom) non-invasive voltage probe used to detect charge movements in the main four-dot system by using both direct current and lock-in measurements through the ohmic contacts SQPCtðbÞ and DQPCtðbÞ [11]. These quantum point contacts (QPCs) were also employed to determine the absolute electron occupancy of the dots (see Fig. 2). 1 QCAs consist of four QDs located in the corners of an imaginary square. When two electrons are added to the cell, they will be forced to occupy opposite positions due to coulomb repulsion, thus defining two possible states that in turn can be used to encode binary information [10].
ARTICLE IN PRESS F. Perez-Martinez et al. / Microelectronics Journal 39 (2008) 674–677
Fig. 1. Electron micrograph of a device similar to the one measured.
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top and the bottom electron reservoirs. Next, gates LtðbÞ and RtðbÞ were used to define a large QD in the top (bottom) section of the cell. Direct transport measurements with an AC signal of 10 mV were employed to measure such a configuration. At the same time, gate MtðbÞ allowed for the formation of the top (bottom) DQD, thus forming the top (bottom) half-cell. After this was accomplished, detection was achieved using the top (bottom) QPC by defining gates DtðbÞ and Lt ðRb Þ and probing its corresponding ohmic contacts with an AC signal of 100 mV keeping the same frequencies used for the direct transport measurements. Electron reservoirs to the half-cells were grounded when sensing through the QPCs. We note that sometimes we employed one of the gates forming one halfcell to define a QPC to detect the opposite half-cell, as this setup is easier to compensate (Fig. 2 was obtained with this approach). Electron numbers in the top (bottom) DQD were controlled by varying the voltage applied to the plungerbarriers gates LtðbÞ and RtðbÞ for the left- and right- hand dots, respectively. Due to the inherent design layout, compensation of the gates defining the non-invasive voltage probes was needed when operating in this configuration. The result of the electron number mapping for the bottom cell is shown in Fig. 2. fpb ; qb } refers to the absolute number of electrons in the {left, right} QDs for the bottom DQD. Similar results were obtained for the other half-cell (not shown). Point A in the inset of Fig. 2 shows the last electron during source–drain bias spectroscopy of dot qb . We also employed gates Dt and Db to perform the same electron mapping measurements, where we obtained similar results.
3. Results Fig. 2. (Color online) Honeycomb diagram for the bottom half-cell from the numerical differential of a non-invasive measurement through gates C and Lt . Absolute electron numbers are indicated as fpb ; qb }. A best-fit plane is subtracted to compensate for gate coupling. Inset: Numerical differential of the signal through the QPC during source–drain bias spectroscopy of dot qb . Point A indicates the last electron.
The device was fabricated using a GaAs/AlGaAs heterostructure (T569) with a high mobility two-dimensional electron gas (2DEG) 97 nm below the surface. The ungated 2DEG had a mobility at 1:3 K of 1:55 106 cm2 =V s and a carrier concentration in the dark of 1:4 1011 =cm2 . Wet etching was used to define a center mesa, and evaporation of an alloy of Au/Ge/Ni followed by rapid thermal annealing was used to ohmic-contact the electron gas underneath. Optical and electron beam lithography (EBL) with subsequent evaporation of Ti/Au and lift-off were employed to create the surface gates as pictured in Fig. 1. During a part of the experiment, we had high frequency wires connected to gates Lt and Rb . In order to define the QDs, we initially split the device in half by biasing gate C to prevent current flow between the
QCA operation is demonstrated by driving an electron in the input sequence fpb ; qb þ 1g ! fpb þ 1; qb g, that is, by pushing an electron from the bottom-right QD into the bottom-left QD (continuous arrow in Fig. 3a). This input sequence (input polarization voltage Db ) is achieved by carefully biasing gates Lb and Rb . If the top cell is properly set up, the electrostatic repulsion between half-cells will drive an electron from the top-left QD into the top-right QD, therefore forcing the output sequence fpt þ 1; qt g ! fpt ; qt þ 1g ðDt —output polarization voltage, see dashed arrow in Fig. 3b). Measurements across the QPCs when the polarization voltage Db of the input (i.e. bottom) cell is applied are shown in Fig. 3 for two cases. In Fig. 3c the output cell (i.e. top) is defined at point A as indicated in Fig. 3b, which is at a considerable distance from the triple point of the top DQD. Because of this, the transfer of the electron in the input cell does not have any effect on the output cell, that is, QCA operation is not realized in this configuration. The bottom (top) detector does (does not) show the electron transfer between adjacent QDs.
ARTICLE IN PRESS 676
F. Perez-Martinez et al. / Microelectronics Journal 39 (2008) 674–677
Fig. 3. (a) Diagram of the area around the triple point for (a) input dots and (b) output dots. The corresponding polarization voltage is indicated with an arrow. (c) At point A, QCA operation is not realized, as the output dots are too far away from the triple point. (d) Output cell biased in position B. As we sweep across Db in the input cell, we induce transfer of an electron in the output cell. This is detected by the output-cell QPCt . QCA operation is thus demonstrated. We used QPCb and QPCt for the non-invasive measurements in (c) and (d). A best-fit background is subtracted from both plots to compensate for gate coupling.
However, when the output cell is biased at point B (i.e. near a triple point, see Fig. 3b), the input sequence driven by voltage Db does produce the output sequence, as can be seen by looking at the QPC signals in Fig. 3d, where now both detectors show an electron hopping between adjacent QDs. QCA operation is therefore realized. These results were obtained at a base temperature of 60 mK. In another experiment, we shine high frequency photons through RF wiring connected to gate Rb . Microwaves induce transitions between dots when the photon frequency matches the energy separation between charge states. The tunnel barriers to the reservoirs were, however, too opaque for current to be measured. We hence employed charge sensing for direct measurement of microwave-induced charge state repopulation. This one-photon PAT event is shown with the white arrows in Fig. 4, which is a scan of the triple point corresponding to the f1; 1g2f0; 2g transi-
tion with a 20 GHz continuous wave (cw) applied to gate Rb . These features do not appear in the absence of high frequency signals (see Fig. 2). The number of excess electrons in the right-hand dot is shown in the inset of Fig. 4. The traces were obtained by scanning through the polarization voltage D (i.e. detuning, black arrow in Fig. 4) and show results for 15 and 20 GHz cws. The dips and peaks marked with the small vertical arrows indicate the evolution of the resonances as a function of frequency and polarization voltage, which is consistent with the expected behavior of PAT [12], in other words, increasing photon frequency moves the photon event further away from the triple point. Moreover, increasing the power of the cw showed the appearance of further resonances, that is, two-photon events (not shown). The results outlined above were obtained at a base temperature of 8 mK.
ARTICLE IN PRESS F. Perez-Martinez et al. / Microelectronics Journal 39 (2008) 674–677
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20 GHz. The results prove a viable multi-dot quantum system that can be used for quantum computation experiments for both the spin and charge-based paradigms. Acknowledgments The authors thank S.J. Chorley for useful discussions. This work was partially supported by EPSRC. F. PerezMartinez acknowledges support from CONACYT, the C. T. Taylor Fund and the Cambridge Philosophical Society. References
Fig. 4. (Color online) The triple point in the f1; 1g2f0; 2g transition with a 20 GHz cw applied to gate Rb . White arrows denote resonances due to photons (PAT). A best-fit plane was subtracted to compensate for gate coupling. Inset: Polarization D (detuning) for two different photon energies. Frequency dependance is observed and is consistent with PAT behavior.
4. Conclusions In summary, we have realized a four-dot system which we used to demonstrate QCA operation in a GaAs/ AlGaAs heterostructure. Measurements were done using non-invasive voltage probes which also helped us to determine absolute electron occupancy. The stability, ease of fabrication and setup of this design should allow easy scaling into more complex QCA logic [13]. In another experiment, we performed high frequency measurements, where we observed charge state repopulation at 15 and
[1] L.P. Kouwenhoven, et al., Electron Transport in Quantum Dots, in: L.L. Sohn, L.P. Kouwenhoven, G. Scho¨n (Eds.), Mesoscopic Electron Transport NATO ASI Series E, vol. 345, Kluwer Academic publisher, Dordrecht, 1997, p. 657. [2] C.S. Lent, P.D. Tougaw, W. Porod, G.H. Bernstein, Nanotechnology 4 (1993) 49. [3] D. Loss, D.P. DiVincenzo, Phys. Rev. A 57 (1998) 120. [4] QIST Expert Panel, A Quantum Information Science and Technology Roadmap: Quantum Computation, December, 2002. [5] M. Kemerink, L.W. Molenkamp, Appl. Phys. Lett. 65 (1994) 1012. [6] W.G. van der Wiel, S. De Franceschi, J.M. Elzerman, T. Fujisawa, S. Tarucha, L.P. Kouwenhoven, Rev. Mod. Phys. 75 (2003) 1. [7] F.R. Waugh, M.J. Berry, D.J. Mar, R.M. Westervelt, K.L. Campman, A.C. Gossard, Phys. Rev. Lett. 75 (1995) 705. [8] N.J. Craig, J.M. Taylor, E.A. Lester, C.M. Marcus, M.P. Hanson, A.C. Gossard, Science 304 (2004) 565. [9] A. Vidan, R.M. Westervelt, M.Stopa.M. Hanson, A.C. Gossard, Appl. Phys. Lett. 85 (2004) 3602. [10] C.G. Smith, Science 284 (1999) 274. [11] M. Field, C.G. Smith, M. Pepper, D.A. Ritchie, J.E.F. Frost, G.A.C. Jones, D.G. Hasko, Phys. Rev. Lett. 70 (1993) 1311. [12] J.R. Petta, A.C. Johnson, C.M. Marcus, M.P. Hanson, A.C. Gossard, Phys. Rev. Lett. 93 (2004) 186802. [13] A.O. Orlov, R. Kummamuru, R. Ramasubramaniam, C.S. Lent, G.H. Bernstein, G.L. Snider, Surf. Sci. 532 (2003) 1193.
Microelectronics Journal 39 (2008) 674–677 www.elsevier.com/locate/mejo
Realization of a GaAs/AlGaAs-based quantum cellular automata cell F. Perez-Martinez, K.D. Petersson, I. Farrer, D. Anderson, G.A.C. Jones, D.A. Ritchie, C.G. Smith Cavendish Laboratory, University of Cambridge, J J Thomson Avenue, Cambridge CB3 0HE, UK Available online 25 February 2008
Abstract We report on the experimental demonstration of a four-dot cell on a GaAs/AlGaAs substrate fabricated using electron beam lithographically defined gates. These surface metallic gates form a pair of double quantum dots, as well as a pair of quantum point contacts that act as non-invasive voltage probes. This device is used to realize a quantum cellular automata cell and, in further experiments, we employ it to investigate photon assisted tunneling. These results prove that the four-dot cell is a good building block candidate toward fulfilling the scalability DiVincezo criteria. r 2008 Elsevier Ltd. All rights reserved. PACS: 73.23.Hk; 73.63.Kv Keywords: QCA; Qubit; DQD; Quantum computation; PAT; Coulomb blockade
1. Introduction Investigation of zero-dimensional systems (quantum dots—QDs) has been a very active field of research in the last few years due to its many benefits when exploring quantum phenomena [1]. They have also found use as a transistor-less approach for solving the density problems that are starting to slow research in the microelectronics industry [2]. Moreover, a proposal exists to use QDs as building blocks for a quantum computer [3], which has propelled intense research by many groups and the creation of a worldwide effort to create a test bed for quantum computation experiments [4]. The natural evolution of the research of QDs in semiconductors led to the study of groups of QDs [5]. To date, extensive literature exists in the use of double quantum dots (DQDs) [6], as well as some effort into higher order dot systems (for example, see Ref. [7–9]). In this paper we report the realization of a device consisting of four QDs that, when measured at cryogenic temperatures, show evidence of being able to operate in the few electron Corresponding author. Tel.: +44 1223 766130; fax: +44 1223 337271.
E-mail address: [email protected] (F. Perez-Martinez). URL: http://www.sp.phy.cam.ac.uk/ (F. Perez-Martinez). 0026-2692/$ - see front matter r 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.mejo.2008.01.005
regime. As a proof of principle, we tune our system to operate as a Quantum Cellular Automata (QCA).1 By means of a high frequency setup, we show this device can also be employed in microwave ðmWÞ experiments.
2. Fabrication and experiment An electron micrograph of the four-dot cell is shown in Fig. 1. The QDs are defined by means of metallic surface gates. LtðbÞ , MtðbÞ and RtðbÞ form the top (bottom) DQD system. LtðbÞ and RtðbÞ control the coupling to StðbÞ and DtðbÞ , the ohmic contacts to the top (bottom) electron reservoirs. The coupling between DQDs is controlled with gates C. In addition, DtðbÞ and Lt ðRb Þ define the top (bottom) non-invasive voltage probe used to detect charge movements in the main four-dot system by using both direct current and lock-in measurements through the ohmic contacts SQPCtðbÞ and DQPCtðbÞ [11]. These quantum point contacts (QPCs) were also employed to determine the absolute electron occupancy of the dots (see Fig. 2). 1 QCAs consist of four QDs located in the corners of an imaginary square. When two electrons are added to the cell, they will be forced to occupy opposite positions due to coulomb repulsion, thus defining two possible states that in turn can be used to encode binary information [10].
ARTICLE IN PRESS F. Perez-Martinez et al. / Microelectronics Journal 39 (2008) 674–677
Fig. 1. Electron micrograph of a device similar to the one measured.
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top and the bottom electron reservoirs. Next, gates LtðbÞ and RtðbÞ were used to define a large QD in the top (bottom) section of the cell. Direct transport measurements with an AC signal of 10 mV were employed to measure such a configuration. At the same time, gate MtðbÞ allowed for the formation of the top (bottom) DQD, thus forming the top (bottom) half-cell. After this was accomplished, detection was achieved using the top (bottom) QPC by defining gates DtðbÞ and Lt ðRb Þ and probing its corresponding ohmic contacts with an AC signal of 100 mV keeping the same frequencies used for the direct transport measurements. Electron reservoirs to the half-cells were grounded when sensing through the QPCs. We note that sometimes we employed one of the gates forming one halfcell to define a QPC to detect the opposite half-cell, as this setup is easier to compensate (Fig. 2 was obtained with this approach). Electron numbers in the top (bottom) DQD were controlled by varying the voltage applied to the plungerbarriers gates LtðbÞ and RtðbÞ for the left- and right- hand dots, respectively. Due to the inherent design layout, compensation of the gates defining the non-invasive voltage probes was needed when operating in this configuration. The result of the electron number mapping for the bottom cell is shown in Fig. 2. fpb ; qb } refers to the absolute number of electrons in the {left, right} QDs for the bottom DQD. Similar results were obtained for the other half-cell (not shown). Point A in the inset of Fig. 2 shows the last electron during source–drain bias spectroscopy of dot qb . We also employed gates Dt and Db to perform the same electron mapping measurements, where we obtained similar results.
3. Results Fig. 2. (Color online) Honeycomb diagram for the bottom half-cell from the numerical differential of a non-invasive measurement through gates C and Lt . Absolute electron numbers are indicated as fpb ; qb }. A best-fit plane is subtracted to compensate for gate coupling. Inset: Numerical differential of the signal through the QPC during source–drain bias spectroscopy of dot qb . Point A indicates the last electron.
The device was fabricated using a GaAs/AlGaAs heterostructure (T569) with a high mobility two-dimensional electron gas (2DEG) 97 nm below the surface. The ungated 2DEG had a mobility at 1:3 K of 1:55 106 cm2 =V s and a carrier concentration in the dark of 1:4 1011 =cm2 . Wet etching was used to define a center mesa, and evaporation of an alloy of Au/Ge/Ni followed by rapid thermal annealing was used to ohmic-contact the electron gas underneath. Optical and electron beam lithography (EBL) with subsequent evaporation of Ti/Au and lift-off were employed to create the surface gates as pictured in Fig. 1. During a part of the experiment, we had high frequency wires connected to gates Lt and Rb . In order to define the QDs, we initially split the device in half by biasing gate C to prevent current flow between the
QCA operation is demonstrated by driving an electron in the input sequence fpb ; qb þ 1g ! fpb þ 1; qb g, that is, by pushing an electron from the bottom-right QD into the bottom-left QD (continuous arrow in Fig. 3a). This input sequence (input polarization voltage Db ) is achieved by carefully biasing gates Lb and Rb . If the top cell is properly set up, the electrostatic repulsion between half-cells will drive an electron from the top-left QD into the top-right QD, therefore forcing the output sequence fpt þ 1; qt g ! fpt ; qt þ 1g ðDt —output polarization voltage, see dashed arrow in Fig. 3b). Measurements across the QPCs when the polarization voltage Db of the input (i.e. bottom) cell is applied are shown in Fig. 3 for two cases. In Fig. 3c the output cell (i.e. top) is defined at point A as indicated in Fig. 3b, which is at a considerable distance from the triple point of the top DQD. Because of this, the transfer of the electron in the input cell does not have any effect on the output cell, that is, QCA operation is not realized in this configuration. The bottom (top) detector does (does not) show the electron transfer between adjacent QDs.
ARTICLE IN PRESS 676
F. Perez-Martinez et al. / Microelectronics Journal 39 (2008) 674–677
Fig. 3. (a) Diagram of the area around the triple point for (a) input dots and (b) output dots. The corresponding polarization voltage is indicated with an arrow. (c) At point A, QCA operation is not realized, as the output dots are too far away from the triple point. (d) Output cell biased in position B. As we sweep across Db in the input cell, we induce transfer of an electron in the output cell. This is detected by the output-cell QPCt . QCA operation is thus demonstrated. We used QPCb and QPCt for the non-invasive measurements in (c) and (d). A best-fit background is subtracted from both plots to compensate for gate coupling.
However, when the output cell is biased at point B (i.e. near a triple point, see Fig. 3b), the input sequence driven by voltage Db does produce the output sequence, as can be seen by looking at the QPC signals in Fig. 3d, where now both detectors show an electron hopping between adjacent QDs. QCA operation is therefore realized. These results were obtained at a base temperature of 60 mK. In another experiment, we shine high frequency photons through RF wiring connected to gate Rb . Microwaves induce transitions between dots when the photon frequency matches the energy separation between charge states. The tunnel barriers to the reservoirs were, however, too opaque for current to be measured. We hence employed charge sensing for direct measurement of microwave-induced charge state repopulation. This one-photon PAT event is shown with the white arrows in Fig. 4, which is a scan of the triple point corresponding to the f1; 1g2f0; 2g transi-
tion with a 20 GHz continuous wave (cw) applied to gate Rb . These features do not appear in the absence of high frequency signals (see Fig. 2). The number of excess electrons in the right-hand dot is shown in the inset of Fig. 4. The traces were obtained by scanning through the polarization voltage D (i.e. detuning, black arrow in Fig. 4) and show results for 15 and 20 GHz cws. The dips and peaks marked with the small vertical arrows indicate the evolution of the resonances as a function of frequency and polarization voltage, which is consistent with the expected behavior of PAT [12], in other words, increasing photon frequency moves the photon event further away from the triple point. Moreover, increasing the power of the cw showed the appearance of further resonances, that is, two-photon events (not shown). The results outlined above were obtained at a base temperature of 8 mK.
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20 GHz. The results prove a viable multi-dot quantum system that can be used for quantum computation experiments for both the spin and charge-based paradigms. Acknowledgments The authors thank S.J. Chorley for useful discussions. This work was partially supported by EPSRC. F. PerezMartinez acknowledges support from CONACYT, the C. T. Taylor Fund and the Cambridge Philosophical Society. References
Fig. 4. (Color online) The triple point in the f1; 1g2f0; 2g transition with a 20 GHz cw applied to gate Rb . White arrows denote resonances due to photons (PAT). A best-fit plane was subtracted to compensate for gate coupling. Inset: Polarization D (detuning) for two different photon energies. Frequency dependance is observed and is consistent with PAT behavior.
4. Conclusions In summary, we have realized a four-dot system which we used to demonstrate QCA operation in a GaAs/ AlGaAs heterostructure. Measurements were done using non-invasive voltage probes which also helped us to determine absolute electron occupancy. The stability, ease of fabrication and setup of this design should allow easy scaling into more complex QCA logic [13]. In another experiment, we performed high frequency measurements, where we observed charge state repopulation at 15 and
[1] L.P. Kouwenhoven, et al., Electron Transport in Quantum Dots, in: L.L. Sohn, L.P. Kouwenhoven, G. Scho¨n (Eds.), Mesoscopic Electron Transport NATO ASI Series E, vol. 345, Kluwer Academic publisher, Dordrecht, 1997, p. 657. [2] C.S. Lent, P.D. Tougaw, W. Porod, G.H. Bernstein, Nanotechnology 4 (1993) 49. [3] D. Loss, D.P. DiVincenzo, Phys. Rev. A 57 (1998) 120. [4] QIST Expert Panel, A Quantum Information Science and Technology Roadmap: Quantum Computation, December, 2002. [5] M. Kemerink, L.W. Molenkamp, Appl. Phys. Lett. 65 (1994) 1012. [6] W.G. van der Wiel, S. De Franceschi, J.M. Elzerman, T. Fujisawa, S. Tarucha, L.P. Kouwenhoven, Rev. Mod. Phys. 75 (2003) 1. [7] F.R. Waugh, M.J. Berry, D.J. Mar, R.M. Westervelt, K.L. Campman, A.C. Gossard, Phys. Rev. Lett. 75 (1995) 705. [8] N.J. Craig, J.M. Taylor, E.A. Lester, C.M. Marcus, M.P. Hanson, A.C. Gossard, Science 304 (2004) 565. [9] A. Vidan, R.M. Westervelt, M.Stopa.M. Hanson, A.C. Gossard, Appl. Phys. Lett. 85 (2004) 3602. [10] C.G. Smith, Science 284 (1999) 274. [11] M. Field, C.G. Smith, M. Pepper, D.A. Ritchie, J.E.F. Frost, G.A.C. Jones, D.G. Hasko, Phys. Rev. Lett. 70 (1993) 1311. [12] J.R. Petta, A.C. Johnson, C.M. Marcus, M.P. Hanson, A.C. Gossard, Phys. Rev. Lett. 93 (2004) 186802. [13] A.O. Orlov, R. Kummamuru, R. Ramasubramaniam, C.S. Lent, G.H. Bernstein, G.L. Snider, Surf. Sci. 532 (2003) 1193.