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Quantised current driven by surface acoustic waves
Materials Science and Engineering C 15 Ž2001. 97–100 www.elsevier.comrlocatermsec
Quantised current driven by surface acoustic waves J. Cunningham a,) , V. Talyanski a , J. Shilton a , M. Pepper a , D. Ritchie a , G. Jones a , C. Ford a , C. Smith a , A. Kristensen b, P. Lindelof b a
b
CaÕendish Laboratory, UniÕersity of Cambridge, UK Neils Bohr Institut, UniÕersitetsparken, Copenhagen, Denmark
Abstract A brief description is presented in our work on the quantised current driven through a GaAs chip by surface acoustic waves at GHz frequencies. The basic outline of the technique and factors affecting accuracy are discussed. q 2001 Published by Elsevier Science B.V. Keywords: Quantised current; Surface acoustic waves; GaAs chip
There has been considerable interest in single electron transport in semiconductors due to the prospects for both new devices and new fundamental studies of electronic behaviour w1x. In the former category, we can consider single electron memories and logic operations, opto-electronic devices and the possibility of quantum computing. In the latter category, the prospect of being able to make a direct measurement of the charge on the electron has aroused considerable interest. In our experiments, we have been moving single electrons about a chip at high frequencies, and as a first step have been attempting to use a single electron current to measure the charge on the electron. If this is successful, then it shows that the technique possesses an inherent accuracy to open up a number of applications. The fundamental quantum constants are e 2rh, erh and e where e is the fundamental charge, i.e. that on the electron, and h is Planck’s constant. The quantum Hall effect, in which a two-dimensional electron gas shows a quantised Hall resistance, directly gives the constant e 2rh. This quantity has the dimensions of ohms, which is why it is often present in two-dimensional electron phenomena, and it determines the value of the fine structure constant. The constant erh is found directly from the Josephson effect, which is the current produced by the tunneling of Cooper pairs between two superconductors separated by a thin insulating tunnel barrier. As both these constants are known to be better than one part in 10 7, the ratio gives the
)
Corresponding author.
0928-4931r01r$ - see front matter q 2001 Published by Elsevier Science B.V. PII: S 0 9 2 8 - 4 9 3 1 Ž 0 1 . 0 0 2 6 0 - 0
electron charge a very high accuracy and this is the value quoted in tables. Of course, the assumption must be that there are no higher order terms in either of these methods for determining these constants. If a direct method for the measurement of e was available, then this would allow the development of a current standard and also a cross-check of the Josephson and quantum Hall effects. This in turn would lead to a direct, high accuracy knowledge of Planck’s constant h. Thus, we see considerable benefits for the knowledge of fundamental physical quantities from the development of such a technique. However, the importance of such knowledge goes much further in that there are also numerous other benefits. As devices become smaller, the need for a current standard of absolute accuracy becomes very important. A method allowing the direct measurement of electron charge using a semiconductor also implies rigorous control and knowledge of the electron motion on a chip down to the single electron level and hence, a new range of possible device functions based on quantum principles become possible. Examples include the precise counting of numbers of electrons transferred from one device Žor gate. to another, the recombination of single electrons with holes leading to the generation of single photons with application in quantum cryptography and the manipulation of the spins of single electrons or pairs of electrons which could be the basis of quantum computing. If single electrons could be manipulated on chip at high frequencies, many of these suggestions could be turned into applications. It was realised in the late 1940s that if an electron was added to a small metal particle, which would have a small capacitance, then the capacitance charging energy due to
98
J. Cunningham et al.r Materials Science and Engineering C 15 (2001) 97–100
this process would be sufficient to prevent another electron arriving on the particle. Further charge movement occurred if a sufficient voltage could be applied to overcome the charging energy. This process, known as the Coulomb blockade, was first found in semiconductors in the 1960s and interest continues to the present. The aspect of the blockade most relevant for manipulating a single charge is tunneling into a quantum dot. Here, an electron tunnels through barriers into a conducting region. Because of the capacitive charging energy, further current is prevented until a voltage of erC is applied. As a result, the current–voltage relation is a series of spikes. If an ac voltage is applied to the entrance and exit barriers, then an electron can be transmitted at each cycle and a current flows given by I s ef. However, a particular problem is that the tunneling process is statistical and consequently, an electron is not transmitted at each cycle when the frequency is high. This phase slippage gives a deviation in the current from the exact quantised value, thus confining the operating frequency to a few megahertz w2x. In order to avoid the problems associated with tunneling, we have developed a technique for the manipulation of single electrons in the two-dimensional electron gas Ž2DEG., in the GaAs heterostructure, which is based on Surface Acoustic Waves ŽSAWs.. GaAs is a weakly piezoelectric material which transmits SAWs along the 110 direction. The SAWs, also known as Rayleigh waves Žor whispering gallery modes., are confined within a wavelength of the surface and then decayed in the bulk. They travel at the sound velocity Ž3.10 3 mrs. and are established by applying voltages to an interdigitated transducer fabricated on the surface of the chip. Typically, about 60 fingers are required to establish the necessary power and the wavelength is defined by the lithography and is twice the finger separation, which is 1 mm corresponding to a frequency of about 3 GHz. The SAWs comprise a series of moving minima in the conduction band and each one is a minimum in potential in which electrons can be trapped and dragged along to provide a current flow. This current is given by I s nef, where n is the number of electrons in each minimum and f is the frequency. In this work, the semiconductor system is a GaAs–AlGaAs heterostructure ˚ below the surface. with the electron gas about 1000 A In order to reduce the number of electrons in each well, it is necessary to apply techniques developed for the study of one- and zero-dimensional electron transport w3x. Here, a series of patterned gates are fabricated on the surface of the AlGaAs and the electron gas is squeezed into a desired shape. The simplest structure is that of two split gates, when a negative voltage is applied to the gates and the electron gas is narrowed until one-dimensional conduction is observed. The gates can either be fabricated from metal or by etching a highly doped n-type layer on the surface. If the gate is sufficiently short that transport is ballistic, then the conductance takes quantised values given by ie 2rh, where i is the number of occupied one-dimensional levels.
The technique works exceptionally well as the potential enclosing the electron gas is smooth, allowing the establishment of size quantisation. In the single electron work, the split gate voltage is sufficiently high to pinch-off the channel so that no current flows. However, when a SAW is established, this can drive a current through the channel and a current passes underneath the pair of split gates. By applying a negative voltage on the gates, it is possible to progressively reduce the value of n, the number of electrons in each minimum, to 4, 3, 2, 1, 0. As a result, the current decreases in a series of steps corresponding to the decrease in the integer value of n. An example of results taken at a frequency of 2.88 GHz and a temperature of 1.5 K is shown in Fig. 1a, where we see that below n s 7, distinct structure is forming at the integer values and plateaus are clear for n s 3, 2, 1. In Fig. 1b, the differential of Fig. 1a is shown, where it is clear that discrete numbers of electrons continue to be transferred up to 17 and beyond. The reason for the plateaus is that the electron energy levels in the wells are predominantly determined by the mutual repulsion of the electrons. As the well narrows, due to the gate voltage becoming increasingly negative, the mutual repulsion increases, giving a greater energy separation, which increases the range of gate voltage for which
Fig. 1. Ža. The acousto-electric current is shown as a function of the negative voltage applied to the split gates. The horizontal lines indicate the quantised current in units of ef. The frequency of the SAW is 2.87 GHz and the temperature is 1.3 K; the plateaus can be apparent up to a temperature of 20 K. Žb. The differential of the signal shown in Ža. is shown and it is clear that discrete electron transport is occurring throughout the range of gate voltage, although the process becomes increasingly indistinct with increasing number of electrons transferred.
J. Cunningham et al.r Materials Science and Engineering C 15 (2001) 97–100
only one electron is present. This gives a wide first plateau, which is very accurate because of a reduction in a principal source of error of a second electron being present in a well when only one is strictly allowed. Decreasing the power is equivalent to decreasing the depth of the SAW potential minima and results in less voltage being required to deplete the electrons. However, the plateau values are unaltered as these are independent of power. The role of temperature is to minimise the thermal energy, causing excitation of an electron from the minimum in potential. At present, it is possible to observe the effect up to 20 K. Fig. 2 shows an example of a plateau in which the deviation from flatness is seen to be better than about one part in 10,000 w4x. This device was fabricated using etched gates and here, the channel was completely depleted for zero applied gate voltage; thus, a positive voltage was necessary to widen the channel sufficiently for current flow. Although the flatness is encouraging, it is not sufficiently precise for ascertaining an accurate value and giving rise to applications. Hence, it is necessary to establish the causes of this error. Fig. 3a shows the form of the potential as the wave enters the channel; the pinched-off channel is a barrier normally preventing electrons drifting through. However, the minimum in SAW potential lowers this barrier and for the situation outlined in the figure allows only the electron in the lowest energy level to pass through. Those higher energy levels existing in the unperturbed SAW minima no longer exist in the modified potential and the electrons are ejected. We would therefore not expect any error due to an extra electron. High accuracy measurement of the first current plateau shows that the error is due to the current being slightly less
Fig. 2. The central portion of a plateau exhibited by an etched gate device is shown under the same operating conditions as the device in Fig. 1. The etched gate resulted in the channel being closed at zero gate voltage with a positive voltage being required for flow of the acousto-electric current. The central portion is seen to fall in a band of width 50 ppm.
99
Fig. 3. Ža. The potential at the entrance to the channel is illustrated. The electron enters and leaves via the two-dimensional electron gas on either side of the channel, forming a quasi one-dimensional barrier. The ejection of an electron is shown where W is the width of potential minimum formed and H is its depth. Žb. The experimental arrangement for the feeding back of the second, phase shifted SAW. The interdigitated transducer and split gate pattern are shown.
than that expected for one electron and implies that this ground state electron is tunneling out, when classically, it should be localised in the modified well. Such a phenomenon is well known in mesoscopic physics as being due to the non-adiabaticity, which occurs whenever an electron experiences a rapid change in potential, for example entering a narrow one-dimensional region from a twodimensional region. This can be minimised by grading a transition region in which the potential varies slowly, thus eliminating the back-tunneling. However, a particular difficulty is encountered if the channel is too long and that a charged defect may be present, which gives rise to noise in the current and can be sufficiently destructive to completely remove the plateau. On the other hand, a long graded channel, considerably longer than the wavelength, will be adiabatic and intrinsically more accurate than a short abrupt channel.
100
J. Cunningham et al.r Materials Science and Engineering C 15 (2001) 97–100
Fig. 4. This series of figures shows the effect of progressively shifting the phase of the second SAW through a complete cycle. As seen, the plateau is most pronounced and accurate in 11 and 12 and actually disappears for some values of phase. Due to phase shifts in the wiring, the absolute value of phase is not clear, only the change.
varies, which is clearly shown in Fig. 4. The phase is successively changed in the subset of figures that comprise Fig. 3b and the change of phase between the two SAWs drastically alters the shape of the plateau and can actually remove it w5x. The effect discussed here is a new macroscopic quantum phenomenon, which exploits the fact that charge comes in units of the fundamental electron charge in order to produce a quantised current. It is clear that the level of quantisation is high but further improvement is necessary before the value of charge can be established sufficiently, precisely to lead to applications. It is now a question of minimising the experimental problems such as the shape of the potential and elimination of defects and noise emanating from the semiconductor rather than limitations imposed by the basic physics. Higher temperature operation will also be necessary for some applications, which will mean increasing the confinement and searching for additional material systems.
References One way in which the non-adiabaticity can be simulated is by feeding back a small amplitude SAW in the opposite direction but at the same frequency to the SAW creating the current. In this way, a change of phase of the secondary SAW will alter the shape of the entrance potential; if this changes the back scattering probability, then it will alter the flatness of the plateau. Fig. 3b illustrates the way the second SAW is applied. As the phase between the main SAW and the secondary is varied, the plateau shape
w1x D.K. Ferry, S.M. Goodnick, Transport in Nanostructures. Cambridge Univ. Press, 1997. w2x H. Pothier, P. Lafarge, P.E. Orfila, C. Urbina, D. Esteve, M.H. Devoret, Physica B 169 Ž1991. 573. w3x T.J. Thornton, M. Pepper, H. Ahmed, D. Andrews, G.J. Davies, Phys. Rev. Lett. 56 Ž1986. 1198. w4x J. Cunningham, V.I. Talyanskii, J.M. Shilton, M. Pepper, A. Kristensen, P.E. Lindelof, Phys. Rev. B 62 Ž1999. 1564. w5x J. Cunningham, V.I. Talyanskii, J.M. Shilton, M. Pepper, M.Y. Simmons, D.A. Ritchie, Phys. Rev. B B60 Ž1999. 4850.
Quantised current driven by surface acoustic waves J. Cunningham a,) , V. Talyanski a , J. Shilton a , M. Pepper a , D. Ritchie a , G. Jones a , C. Ford a , C. Smith a , A. Kristensen b, P. Lindelof b a
b
CaÕendish Laboratory, UniÕersity of Cambridge, UK Neils Bohr Institut, UniÕersitetsparken, Copenhagen, Denmark
Abstract A brief description is presented in our work on the quantised current driven through a GaAs chip by surface acoustic waves at GHz frequencies. The basic outline of the technique and factors affecting accuracy are discussed. q 2001 Published by Elsevier Science B.V. Keywords: Quantised current; Surface acoustic waves; GaAs chip
There has been considerable interest in single electron transport in semiconductors due to the prospects for both new devices and new fundamental studies of electronic behaviour w1x. In the former category, we can consider single electron memories and logic operations, opto-electronic devices and the possibility of quantum computing. In the latter category, the prospect of being able to make a direct measurement of the charge on the electron has aroused considerable interest. In our experiments, we have been moving single electrons about a chip at high frequencies, and as a first step have been attempting to use a single electron current to measure the charge on the electron. If this is successful, then it shows that the technique possesses an inherent accuracy to open up a number of applications. The fundamental quantum constants are e 2rh, erh and e where e is the fundamental charge, i.e. that on the electron, and h is Planck’s constant. The quantum Hall effect, in which a two-dimensional electron gas shows a quantised Hall resistance, directly gives the constant e 2rh. This quantity has the dimensions of ohms, which is why it is often present in two-dimensional electron phenomena, and it determines the value of the fine structure constant. The constant erh is found directly from the Josephson effect, which is the current produced by the tunneling of Cooper pairs between two superconductors separated by a thin insulating tunnel barrier. As both these constants are known to be better than one part in 10 7, the ratio gives the
)
Corresponding author.
0928-4931r01r$ - see front matter q 2001 Published by Elsevier Science B.V. PII: S 0 9 2 8 - 4 9 3 1 Ž 0 1 . 0 0 2 6 0 - 0
electron charge a very high accuracy and this is the value quoted in tables. Of course, the assumption must be that there are no higher order terms in either of these methods for determining these constants. If a direct method for the measurement of e was available, then this would allow the development of a current standard and also a cross-check of the Josephson and quantum Hall effects. This in turn would lead to a direct, high accuracy knowledge of Planck’s constant h. Thus, we see considerable benefits for the knowledge of fundamental physical quantities from the development of such a technique. However, the importance of such knowledge goes much further in that there are also numerous other benefits. As devices become smaller, the need for a current standard of absolute accuracy becomes very important. A method allowing the direct measurement of electron charge using a semiconductor also implies rigorous control and knowledge of the electron motion on a chip down to the single electron level and hence, a new range of possible device functions based on quantum principles become possible. Examples include the precise counting of numbers of electrons transferred from one device Žor gate. to another, the recombination of single electrons with holes leading to the generation of single photons with application in quantum cryptography and the manipulation of the spins of single electrons or pairs of electrons which could be the basis of quantum computing. If single electrons could be manipulated on chip at high frequencies, many of these suggestions could be turned into applications. It was realised in the late 1940s that if an electron was added to a small metal particle, which would have a small capacitance, then the capacitance charging energy due to
98
J. Cunningham et al.r Materials Science and Engineering C 15 (2001) 97–100
this process would be sufficient to prevent another electron arriving on the particle. Further charge movement occurred if a sufficient voltage could be applied to overcome the charging energy. This process, known as the Coulomb blockade, was first found in semiconductors in the 1960s and interest continues to the present. The aspect of the blockade most relevant for manipulating a single charge is tunneling into a quantum dot. Here, an electron tunnels through barriers into a conducting region. Because of the capacitive charging energy, further current is prevented until a voltage of erC is applied. As a result, the current–voltage relation is a series of spikes. If an ac voltage is applied to the entrance and exit barriers, then an electron can be transmitted at each cycle and a current flows given by I s ef. However, a particular problem is that the tunneling process is statistical and consequently, an electron is not transmitted at each cycle when the frequency is high. This phase slippage gives a deviation in the current from the exact quantised value, thus confining the operating frequency to a few megahertz w2x. In order to avoid the problems associated with tunneling, we have developed a technique for the manipulation of single electrons in the two-dimensional electron gas Ž2DEG., in the GaAs heterostructure, which is based on Surface Acoustic Waves ŽSAWs.. GaAs is a weakly piezoelectric material which transmits SAWs along the 110 direction. The SAWs, also known as Rayleigh waves Žor whispering gallery modes., are confined within a wavelength of the surface and then decayed in the bulk. They travel at the sound velocity Ž3.10 3 mrs. and are established by applying voltages to an interdigitated transducer fabricated on the surface of the chip. Typically, about 60 fingers are required to establish the necessary power and the wavelength is defined by the lithography and is twice the finger separation, which is 1 mm corresponding to a frequency of about 3 GHz. The SAWs comprise a series of moving minima in the conduction band and each one is a minimum in potential in which electrons can be trapped and dragged along to provide a current flow. This current is given by I s nef, where n is the number of electrons in each minimum and f is the frequency. In this work, the semiconductor system is a GaAs–AlGaAs heterostructure ˚ below the surface. with the electron gas about 1000 A In order to reduce the number of electrons in each well, it is necessary to apply techniques developed for the study of one- and zero-dimensional electron transport w3x. Here, a series of patterned gates are fabricated on the surface of the AlGaAs and the electron gas is squeezed into a desired shape. The simplest structure is that of two split gates, when a negative voltage is applied to the gates and the electron gas is narrowed until one-dimensional conduction is observed. The gates can either be fabricated from metal or by etching a highly doped n-type layer on the surface. If the gate is sufficiently short that transport is ballistic, then the conductance takes quantised values given by ie 2rh, where i is the number of occupied one-dimensional levels.
The technique works exceptionally well as the potential enclosing the electron gas is smooth, allowing the establishment of size quantisation. In the single electron work, the split gate voltage is sufficiently high to pinch-off the channel so that no current flows. However, when a SAW is established, this can drive a current through the channel and a current passes underneath the pair of split gates. By applying a negative voltage on the gates, it is possible to progressively reduce the value of n, the number of electrons in each minimum, to 4, 3, 2, 1, 0. As a result, the current decreases in a series of steps corresponding to the decrease in the integer value of n. An example of results taken at a frequency of 2.88 GHz and a temperature of 1.5 K is shown in Fig. 1a, where we see that below n s 7, distinct structure is forming at the integer values and plateaus are clear for n s 3, 2, 1. In Fig. 1b, the differential of Fig. 1a is shown, where it is clear that discrete numbers of electrons continue to be transferred up to 17 and beyond. The reason for the plateaus is that the electron energy levels in the wells are predominantly determined by the mutual repulsion of the electrons. As the well narrows, due to the gate voltage becoming increasingly negative, the mutual repulsion increases, giving a greater energy separation, which increases the range of gate voltage for which
Fig. 1. Ža. The acousto-electric current is shown as a function of the negative voltage applied to the split gates. The horizontal lines indicate the quantised current in units of ef. The frequency of the SAW is 2.87 GHz and the temperature is 1.3 K; the plateaus can be apparent up to a temperature of 20 K. Žb. The differential of the signal shown in Ža. is shown and it is clear that discrete electron transport is occurring throughout the range of gate voltage, although the process becomes increasingly indistinct with increasing number of electrons transferred.
J. Cunningham et al.r Materials Science and Engineering C 15 (2001) 97–100
only one electron is present. This gives a wide first plateau, which is very accurate because of a reduction in a principal source of error of a second electron being present in a well when only one is strictly allowed. Decreasing the power is equivalent to decreasing the depth of the SAW potential minima and results in less voltage being required to deplete the electrons. However, the plateau values are unaltered as these are independent of power. The role of temperature is to minimise the thermal energy, causing excitation of an electron from the minimum in potential. At present, it is possible to observe the effect up to 20 K. Fig. 2 shows an example of a plateau in which the deviation from flatness is seen to be better than about one part in 10,000 w4x. This device was fabricated using etched gates and here, the channel was completely depleted for zero applied gate voltage; thus, a positive voltage was necessary to widen the channel sufficiently for current flow. Although the flatness is encouraging, it is not sufficiently precise for ascertaining an accurate value and giving rise to applications. Hence, it is necessary to establish the causes of this error. Fig. 3a shows the form of the potential as the wave enters the channel; the pinched-off channel is a barrier normally preventing electrons drifting through. However, the minimum in SAW potential lowers this barrier and for the situation outlined in the figure allows only the electron in the lowest energy level to pass through. Those higher energy levels existing in the unperturbed SAW minima no longer exist in the modified potential and the electrons are ejected. We would therefore not expect any error due to an extra electron. High accuracy measurement of the first current plateau shows that the error is due to the current being slightly less
Fig. 2. The central portion of a plateau exhibited by an etched gate device is shown under the same operating conditions as the device in Fig. 1. The etched gate resulted in the channel being closed at zero gate voltage with a positive voltage being required for flow of the acousto-electric current. The central portion is seen to fall in a band of width 50 ppm.
99
Fig. 3. Ža. The potential at the entrance to the channel is illustrated. The electron enters and leaves via the two-dimensional electron gas on either side of the channel, forming a quasi one-dimensional barrier. The ejection of an electron is shown where W is the width of potential minimum formed and H is its depth. Žb. The experimental arrangement for the feeding back of the second, phase shifted SAW. The interdigitated transducer and split gate pattern are shown.
than that expected for one electron and implies that this ground state electron is tunneling out, when classically, it should be localised in the modified well. Such a phenomenon is well known in mesoscopic physics as being due to the non-adiabaticity, which occurs whenever an electron experiences a rapid change in potential, for example entering a narrow one-dimensional region from a twodimensional region. This can be minimised by grading a transition region in which the potential varies slowly, thus eliminating the back-tunneling. However, a particular difficulty is encountered if the channel is too long and that a charged defect may be present, which gives rise to noise in the current and can be sufficiently destructive to completely remove the plateau. On the other hand, a long graded channel, considerably longer than the wavelength, will be adiabatic and intrinsically more accurate than a short abrupt channel.
100
J. Cunningham et al.r Materials Science and Engineering C 15 (2001) 97–100
Fig. 4. This series of figures shows the effect of progressively shifting the phase of the second SAW through a complete cycle. As seen, the plateau is most pronounced and accurate in 11 and 12 and actually disappears for some values of phase. Due to phase shifts in the wiring, the absolute value of phase is not clear, only the change.
varies, which is clearly shown in Fig. 4. The phase is successively changed in the subset of figures that comprise Fig. 3b and the change of phase between the two SAWs drastically alters the shape of the plateau and can actually remove it w5x. The effect discussed here is a new macroscopic quantum phenomenon, which exploits the fact that charge comes in units of the fundamental electron charge in order to produce a quantised current. It is clear that the level of quantisation is high but further improvement is necessary before the value of charge can be established sufficiently, precisely to lead to applications. It is now a question of minimising the experimental problems such as the shape of the potential and elimination of defects and noise emanating from the semiconductor rather than limitations imposed by the basic physics. Higher temperature operation will also be necessary for some applications, which will mean increasing the confinement and searching for additional material systems.
References One way in which the non-adiabaticity can be simulated is by feeding back a small amplitude SAW in the opposite direction but at the same frequency to the SAW creating the current. In this way, a change of phase of the secondary SAW will alter the shape of the entrance potential; if this changes the back scattering probability, then it will alter the flatness of the plateau. Fig. 3b illustrates the way the second SAW is applied. As the phase between the main SAW and the secondary is varied, the plateau shape
w1x D.K. Ferry, S.M. Goodnick, Transport in Nanostructures. Cambridge Univ. Press, 1997. w2x H. Pothier, P. Lafarge, P.E. Orfila, C. Urbina, D. Esteve, M.H. Devoret, Physica B 169 Ž1991. 573. w3x T.J. Thornton, M. Pepper, H. Ahmed, D. Andrews, G.J. Davies, Phys. Rev. Lett. 56 Ž1986. 1198. w4x J. Cunningham, V.I. Talyanskii, J.M. Shilton, M. Pepper, A. Kristensen, P.E. Lindelof, Phys. Rev. B 62 Ž1999. 1564. w5x J. Cunningham, V.I. Talyanskii, J.M. Shilton, M. Pepper, M.Y. Simmons, D.A. Ritchie, Phys. Rev. B B60 Ž1999. 4850.