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Observation of impurity effects on conductance quantization
Superlattices
and Nlicrostructures,
OBSERVATION
OF IMPURITY
EFFECTS
J. Faist, P. G&ret
IEM
Research
349
Vol. 7, No. 4, 1990
Division,
Zurich
ON CONDUCTANCE
and H. Rothuizen
Research Switzerland
(Received
QUANTIZATION
Laboratory,
8803 Riischlikon,
July 30. 1990)
We report the experimental observation of impurity-induced conductance dips in quantized channels as predicted by previous theorical studies. Our experiments use quantum point contacts on a two-dimensional The electron gas in a modulation-doped GaAs/AIGaAs heterostructure. electron gas has a sheet density of 1.2 x 10” crnd2 and a mobility of Our data, which are qualitatively 4.6 x lO%m*/Vs, measured at 50 mK. very similar to those calculated using a two-dimentional Anderson model. strongly suggest that we are observing both the erosion of conductance in the presence of an impurity-induced quantization, and localization random potential.
Conductance measurements (van Wees et al.,’ Wharam et al.*) with quantum point contacts (QPC) on a two-dimensional (Z-D) electron gas in modulation-doped GaAslAlGaAs heterostructures have demonstrated the existence of plateaux at integer multiples of the elementary conductance G, = q’/nA. The plateaux observed in those experiments are fairly flat and well defined, pointing to nearly ideal conditions for their observation. Following this discovery, it is now of great interest to understand how various factors such as the potential distribution in the constriction affect the quantization. Impurity potentials are, in this respect, of particular interest and have therefore attracted widespread interest among theoreticians. For example, it has been shown3 that attractive impurities, in particular, exhibit a clear signature in the form of a deep dip appearing at the end of each conductance plateau, followed by a sharp rise to the next plateau as the channel width is increased. Using a somewhat different approach, other theoreticians4 have studied the cross-over from ballistic to diffusive transport in quantized channels as a function of disorder produced by a random, attractive impurity potential. Their results show a rounding of the conductance steps with increasing disorder, loss of the quantization in units of G,, and the occur-
rence of pronounced conductance dips at each new channel opening. The present contribution reports the first experimental observation of impurity-induced conductance dips in quantized channels as predicted by the authors cited above. Our data, which also exhibit a strong erosion of the plateaux and a loss of exact quantization, are qualitatively very similar to the results computed by Masek, Lipavsky and Kramer4 and by Kander, lmry and Sivan4 and indicate that we are dealing with the random impurity potential case studied by these authors. The QPCs used in our experiments are fabricated on a modulation-doped AIGaAs/GaAs heterostructure using a planar doping technique and a 70 nm spacer layer. The distance between the 2-D gas and the surface is 170 nm. After illumination D gas with a sheet deksity* of 1.2 x loli ,“,-sand mobility of 4.6 x 10 cm /Vs (measured at 50 mK) is obtained at the GaAslAlGaAs interface. This sheet density corresponds to a Fermi wavelength 1, of 72 nm, a value significantly larger than that published in ather reports.lB*S5XsThe device, which is sketched in the inset of Fig. 1, is fabricated by means of electronbeam lithography. Two 100 nm long Ti/Pt gates facing each other at a distance of 300 nm
0 1990 Academic Press Limited
350
Superlattices
AV= 0.8
and Microstructures,
0.4
Vol. 7, No. 4, 1990
0 -0.4
-0.8
V
./ /
4’
-4.00
-3.60
-3.20
- 2.80
-2.40
- 2.00
vg(V) Fig. 1. Point-contact conductance G (in units of Go) as a function of the average gate voltage Vg. A voltage of Vg + AVIZ and Vs - AV/2 is applied to each of the two gates defming the constriction. Curves for voltages offsets AV equal to +0.8, 0.4, V are displayed. Inset: sample 0, - 0.4, -0.8 layout. The gates in the constriction region are 100 nm long and 300 nm apart.
define the constriction. The electrostatically voltage probes are located about three electron mean free paths (~7.5 pm) from the constriction, so that the carrier distributions are nearly equilibrated. The resistance measurements are performed in the mixing chamber of a dilution refrigerator at a temperature below 35 mK. An a.c. current of 2 nA rms amplitude is driven through the sample and the resistance is measured in a four-probe fashion as a function of the two gate potentials. Our measurement setup includes one additional degree of freedom and applies different potentials to the two gates, namely Vg + AV/2 and Vg - AV/2. Performing the measurements with different values of AV steers the channel laterally and thus allows the inhomogeneities in the channel potential to be probed. Our experimental results are displayed in Fig. 1 where the normalized conductance of the QPC is plotted as a function of the average gate voltage V for different voltage offsets AV. The characterISI.ICS are overall fairly smooth, except for two sin.“
gular regions near the quantized values G, and 2 x G,. The main features of these regions are a noticeable conductance dip, followed by a very jump towards the average sharp positive conductance line. We observe moreover that the characteristics in Fig. 1 evolve smoothly as AV is varied and the confined beam is steered laterally across the channel. For large negative values of AV, in particular, the conductance maxima disappear. Although the characteristics shown in Fig. 1 are reproducible, they are fairly sensitive to sample handling. We have found, for example, that temperature cycling or passing a current of 2 PA though the sample may change the characteristics in an (experimentally) irreversible manner. This type of sensitivity can be regarded in turn as an indirect indication that the reported behavior is indeed associated with impurity effects. V;ith reference to recent theoretical investigalions,3,4 our observations strongly suggest that we are dealing here with conductance quantization in the presence of an impurity-induced potential.
Superlattices
and Microstructures,
351
Vol. 7, No, 4, 1990
The calculations by Chu and Sorbello3, Tekman and Ciraci,3 for example, have shown that an attractive impurity located in an otherwise quantized channel gives rise, as in our case, to conductance dips followed by a sharp step to the next plateau as a new channel is opened. Closer still to our present experimental findings are the recent results of Masek, Lipavsky and Kramer’. and of Kander, lmry and Sivan.4 Calculating the influence of a random impurity potential on quantization. these authors find that the step quantization in units of G, is lost with increasing disorder. There are no plateaux to speak of and what remains is basically a regular sequence of conductance dips and steps associated with each channel opening. These theoretical results are qualitatively very similar to those reported here. This indicates that the singularities we observed are probably related to a disorder-induced localization which sets in when a new channel is opened, as suggested by Kander, lmry and Sivan? since the longitudinal kinetic energy in a barely opened channel is small, this channel is localized and reflects many of the incoming electrons, including those of the foregoing channel which have scattered into the newly opened one. This results in a conductance dip each time a new channel is opened. To our knowledge, the singularities in the conductance characteristics of QPCs described in this contribution have not been previously reported, at least not for this type of experiment where the conductance is measured as a function of the gate voltage. Conductance fluctuations in QPCs have been reported by Hirayama et al.5 in a situation where the conductance of the wire was measured as a function of time while being subjected to a weak illumination. Subsequent measurements by the same authors6 on structures covered by a gate electrode did not verify such an effect, however, suggesting that the conductance fluctuations they had previously observed were due to the trapping and detrapping of electrons. Localization effects are not unexpected in QPCs fabricated on a low-n, 2-D gas, since the QPC characteristics scale with /1, Our sample has an estimated background impurity concentration” of 5 x 1014 cm*--3, which corresponds to an average impurity spacing of cfi 5 120 nm. We have strong evidence that these impurities result from an unintentional (residual) Be-doping which acts as an attractive impurity in the GaAs. The main scattering process for such an impurity concentration and electron sheet density is due to the residual impurities in the channel and spacer layer.7 The background impurity concentration of the structure used by van Wees et al.’ can also be estimated’,8 from the published mobility and electron density approximatively data,’ angl should be 2 x 1014 cmleading to a value of d,- 171 nm.
The ratio I,ldi, which gives a qualitative indication of the strength of the localization effect in the QPC, is thus equal to 0.6 in our case. This value is much larger than our estimated value of 0.24 for a device exhibiting nearly perfect quantization.’ The remote impurity doping layer may also contribute to the localization effects if the amplitude of the potential fluctuations due to the discreteness of the dopants is comparable to the energy level sepaAn estiration in the one-dimensional channel. mate of these potential fluctuations using a unscreened coulomb potential for a 2-D structure with comparable characteristics9 yields 2 meV. This value is comparable to our estimate (3 meV) of the subband energy separation calculated using a parabolic potential. AcknowlegementThe authors are grateful to H.P. Meier for providing the MBE-grown samples, to P. Vettiger for stimulating discussions on processing, and to H.-P. Dietrich and U Deutsch for technical support. One of us (H.R.) would like to thank S.J. Wind and W.W. Molzen of IBM Yorktown for valuable help with the e-beam lithography. After submitting this work, we have been made aware of recent experiments by B.J van Wees et al (submitted to Phys. Rev. B) which provide further evidence for impurity effects on conductance quantization.
REFERENCES
1 B.J. van Wees, H. van Houten. C.W.J. Beenakker, J.G. Williamson, L.P. Kouwenhoven, D. van der Marel, C.T. Foxon, Physical Review Letters 60, 848 (1988) 7 D.A. Wharam, T.J. Thonton, R. Newbury. M. Pepper, J.E.F. Frost, D.G. Hasko, D.C. Peacock, D.A. Ritchie, and G.A. Jones, Journal of Physics C: Solid State Physics 21, L209 (1988) 3 D. van de Mare1 and E.G. Haanappel, Physical Review B 39, 7811 (1989); C.S. Chu and R.S. Sorbello, Physical Review B 40, 5941 (1989); E. Tekman and S. Ciraci, to appear in Physical Review B, (1990) 4 J. Masek. P. Lipavsky and B. Kramer, J. Phys.: Condens. Matter 1, 6395 (1989); Song He and S. Das Sarma, Solid State Electronics 32, 1695 (1989); I. Kander, Y. Imry, and U. Sivan, preprint 5 Y. Hirayama, T. Saku, Y. Horikoshi, Physical Review B 39, 5535 (1989); ibid, Journal of Applied Physics 26, L701 (1989) 6 Y. Hirayama and T. Saku, Applied Physics Letters 54, 2556 (1989) 7 F. Stern, Applied Physics Letters 43. 974 (1983) 8 K. Hirakawa and H. Sakaki, Physical Review B 33, 8291 (1986) 9 E.F. Shubert. L. Pfeiffer, K.W. West, and A. Izabelle, Applied Physics Letters 54, 1350 (1989)
and Nlicrostructures,
OBSERVATION
OF IMPURITY
EFFECTS
J. Faist, P. G&ret
IEM
Research
349
Vol. 7, No. 4, 1990
Division,
Zurich
ON CONDUCTANCE
and H. Rothuizen
Research Switzerland
(Received
QUANTIZATION
Laboratory,
8803 Riischlikon,
July 30. 1990)
We report the experimental observation of impurity-induced conductance dips in quantized channels as predicted by previous theorical studies. Our experiments use quantum point contacts on a two-dimensional The electron gas in a modulation-doped GaAs/AIGaAs heterostructure. electron gas has a sheet density of 1.2 x 10” crnd2 and a mobility of Our data, which are qualitatively 4.6 x lO%m*/Vs, measured at 50 mK. very similar to those calculated using a two-dimentional Anderson model. strongly suggest that we are observing both the erosion of conductance in the presence of an impurity-induced quantization, and localization random potential.
Conductance measurements (van Wees et al.,’ Wharam et al.*) with quantum point contacts (QPC) on a two-dimensional (Z-D) electron gas in modulation-doped GaAslAlGaAs heterostructures have demonstrated the existence of plateaux at integer multiples of the elementary conductance G, = q’/nA. The plateaux observed in those experiments are fairly flat and well defined, pointing to nearly ideal conditions for their observation. Following this discovery, it is now of great interest to understand how various factors such as the potential distribution in the constriction affect the quantization. Impurity potentials are, in this respect, of particular interest and have therefore attracted widespread interest among theoreticians. For example, it has been shown3 that attractive impurities, in particular, exhibit a clear signature in the form of a deep dip appearing at the end of each conductance plateau, followed by a sharp rise to the next plateau as the channel width is increased. Using a somewhat different approach, other theoreticians4 have studied the cross-over from ballistic to diffusive transport in quantized channels as a function of disorder produced by a random, attractive impurity potential. Their results show a rounding of the conductance steps with increasing disorder, loss of the quantization in units of G,, and the occur-
rence of pronounced conductance dips at each new channel opening. The present contribution reports the first experimental observation of impurity-induced conductance dips in quantized channels as predicted by the authors cited above. Our data, which also exhibit a strong erosion of the plateaux and a loss of exact quantization, are qualitatively very similar to the results computed by Masek, Lipavsky and Kramer4 and by Kander, lmry and Sivan4 and indicate that we are dealing with the random impurity potential case studied by these authors. The QPCs used in our experiments are fabricated on a modulation-doped AIGaAs/GaAs heterostructure using a planar doping technique and a 70 nm spacer layer. The distance between the 2-D gas and the surface is 170 nm. After illumination D gas with a sheet deksity* of 1.2 x loli ,“,-sand mobility of 4.6 x 10 cm /Vs (measured at 50 mK) is obtained at the GaAslAlGaAs interface. This sheet density corresponds to a Fermi wavelength 1, of 72 nm, a value significantly larger than that published in ather reports.lB*S5XsThe device, which is sketched in the inset of Fig. 1, is fabricated by means of electronbeam lithography. Two 100 nm long Ti/Pt gates facing each other at a distance of 300 nm
0 1990 Academic Press Limited
350
Superlattices
AV= 0.8
and Microstructures,
0.4
Vol. 7, No. 4, 1990
0 -0.4
-0.8
V
./ /
4’
-4.00
-3.60
-3.20
- 2.80
-2.40
- 2.00
vg(V) Fig. 1. Point-contact conductance G (in units of Go) as a function of the average gate voltage Vg. A voltage of Vg + AVIZ and Vs - AV/2 is applied to each of the two gates defming the constriction. Curves for voltages offsets AV equal to +0.8, 0.4, V are displayed. Inset: sample 0, - 0.4, -0.8 layout. The gates in the constriction region are 100 nm long and 300 nm apart.
define the constriction. The electrostatically voltage probes are located about three electron mean free paths (~7.5 pm) from the constriction, so that the carrier distributions are nearly equilibrated. The resistance measurements are performed in the mixing chamber of a dilution refrigerator at a temperature below 35 mK. An a.c. current of 2 nA rms amplitude is driven through the sample and the resistance is measured in a four-probe fashion as a function of the two gate potentials. Our measurement setup includes one additional degree of freedom and applies different potentials to the two gates, namely Vg + AV/2 and Vg - AV/2. Performing the measurements with different values of AV steers the channel laterally and thus allows the inhomogeneities in the channel potential to be probed. Our experimental results are displayed in Fig. 1 where the normalized conductance of the QPC is plotted as a function of the average gate voltage V for different voltage offsets AV. The characterISI.ICS are overall fairly smooth, except for two sin.“
gular regions near the quantized values G, and 2 x G,. The main features of these regions are a noticeable conductance dip, followed by a very jump towards the average sharp positive conductance line. We observe moreover that the characteristics in Fig. 1 evolve smoothly as AV is varied and the confined beam is steered laterally across the channel. For large negative values of AV, in particular, the conductance maxima disappear. Although the characteristics shown in Fig. 1 are reproducible, they are fairly sensitive to sample handling. We have found, for example, that temperature cycling or passing a current of 2 PA though the sample may change the characteristics in an (experimentally) irreversible manner. This type of sensitivity can be regarded in turn as an indirect indication that the reported behavior is indeed associated with impurity effects. V;ith reference to recent theoretical investigalions,3,4 our observations strongly suggest that we are dealing here with conductance quantization in the presence of an impurity-induced potential.
Superlattices
and Microstructures,
351
Vol. 7, No, 4, 1990
The calculations by Chu and Sorbello3, Tekman and Ciraci,3 for example, have shown that an attractive impurity located in an otherwise quantized channel gives rise, as in our case, to conductance dips followed by a sharp step to the next plateau as a new channel is opened. Closer still to our present experimental findings are the recent results of Masek, Lipavsky and Kramer’. and of Kander, lmry and Sivan.4 Calculating the influence of a random impurity potential on quantization. these authors find that the step quantization in units of G, is lost with increasing disorder. There are no plateaux to speak of and what remains is basically a regular sequence of conductance dips and steps associated with each channel opening. These theoretical results are qualitatively very similar to those reported here. This indicates that the singularities we observed are probably related to a disorder-induced localization which sets in when a new channel is opened, as suggested by Kander, lmry and Sivan? since the longitudinal kinetic energy in a barely opened channel is small, this channel is localized and reflects many of the incoming electrons, including those of the foregoing channel which have scattered into the newly opened one. This results in a conductance dip each time a new channel is opened. To our knowledge, the singularities in the conductance characteristics of QPCs described in this contribution have not been previously reported, at least not for this type of experiment where the conductance is measured as a function of the gate voltage. Conductance fluctuations in QPCs have been reported by Hirayama et al.5 in a situation where the conductance of the wire was measured as a function of time while being subjected to a weak illumination. Subsequent measurements by the same authors6 on structures covered by a gate electrode did not verify such an effect, however, suggesting that the conductance fluctuations they had previously observed were due to the trapping and detrapping of electrons. Localization effects are not unexpected in QPCs fabricated on a low-n, 2-D gas, since the QPC characteristics scale with /1, Our sample has an estimated background impurity concentration” of 5 x 1014 cm*--3, which corresponds to an average impurity spacing of cfi 5 120 nm. We have strong evidence that these impurities result from an unintentional (residual) Be-doping which acts as an attractive impurity in the GaAs. The main scattering process for such an impurity concentration and electron sheet density is due to the residual impurities in the channel and spacer layer.7 The background impurity concentration of the structure used by van Wees et al.’ can also be estimated’,8 from the published mobility and electron density approximatively data,’ angl should be 2 x 1014 cmleading to a value of d,- 171 nm.
The ratio I,ldi, which gives a qualitative indication of the strength of the localization effect in the QPC, is thus equal to 0.6 in our case. This value is much larger than our estimated value of 0.24 for a device exhibiting nearly perfect quantization.’ The remote impurity doping layer may also contribute to the localization effects if the amplitude of the potential fluctuations due to the discreteness of the dopants is comparable to the energy level sepaAn estiration in the one-dimensional channel. mate of these potential fluctuations using a unscreened coulomb potential for a 2-D structure with comparable characteristics9 yields 2 meV. This value is comparable to our estimate (3 meV) of the subband energy separation calculated using a parabolic potential. AcknowlegementThe authors are grateful to H.P. Meier for providing the MBE-grown samples, to P. Vettiger for stimulating discussions on processing, and to H.-P. Dietrich and U Deutsch for technical support. One of us (H.R.) would like to thank S.J. Wind and W.W. Molzen of IBM Yorktown for valuable help with the e-beam lithography. After submitting this work, we have been made aware of recent experiments by B.J van Wees et al (submitted to Phys. Rev. B) which provide further evidence for impurity effects on conductance quantization.
REFERENCES
1 B.J. van Wees, H. van Houten. C.W.J. Beenakker, J.G. Williamson, L.P. Kouwenhoven, D. van der Marel, C.T. Foxon, Physical Review Letters 60, 848 (1988) 7 D.A. Wharam, T.J. Thonton, R. Newbury. M. Pepper, J.E.F. Frost, D.G. Hasko, D.C. Peacock, D.A. Ritchie, and G.A. Jones, Journal of Physics C: Solid State Physics 21, L209 (1988) 3 D. van de Mare1 and E.G. Haanappel, Physical Review B 39, 7811 (1989); C.S. Chu and R.S. Sorbello, Physical Review B 40, 5941 (1989); E. Tekman and S. Ciraci, to appear in Physical Review B, (1990) 4 J. Masek. P. Lipavsky and B. Kramer, J. Phys.: Condens. Matter 1, 6395 (1989); Song He and S. Das Sarma, Solid State Electronics 32, 1695 (1989); I. Kander, Y. Imry, and U. Sivan, preprint 5 Y. Hirayama, T. Saku, Y. Horikoshi, Physical Review B 39, 5535 (1989); ibid, Journal of Applied Physics 26, L701 (1989) 6 Y. Hirayama and T. Saku, Applied Physics Letters 54, 2556 (1989) 7 F. Stern, Applied Physics Letters 43. 974 (1983) 8 K. Hirakawa and H. Sakaki, Physical Review B 33, 8291 (1986) 9 E.F. Shubert. L. Pfeiffer, K.W. West, and A. Izabelle, Applied Physics Letters 54, 1350 (1989)