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Hybrid magneto-electric states in resonant tunnelling structures
Superlattices
and Microstructures.
HYBRID
MAGNETO-ELECTRIC
E. S. Alves,
527
Vol. 5, No. 4, 1989
STATES
M. L. Leadbeater,
IN RESOIUWI' TUNNELLIZ
STRUCTURES
L. Eaves, l4. Aenini, 0. H. Hughes
University of Nottingham, Department of Physics, Nottingham, NG7 2RD, U.K. A. Celeste and J. C. Portal SNCI-CNRS, 38042 Grenoble and LPS, INSA, 31077 Toulouse, France. G. Hill and W. A. Pate University of Sheffield, Dept. of Electronic & Electrical Engineering, Mappin Street, Sheffield, Sl 3JD, U.K. (Received 8 August 1988)
Double barrier resonant tunnelling structures with wide undoped quantum wells are used to study quantum ballistic transport in the presence of a magnetic field B. The structures are based on n-GaAs/(AlGa)As with well widths of 60 and 120 nm. At B=O, the wider well structure (120 nm) shows as many as 70 resonances in I(V). With B applied in the plane of the barriers (BlJ) these resonances evolve into hybrid maaneto-electric states. At sufficiently large B, the electron orbits no longer extend to the second barrier and tunnelling occurs into cycloidal interface states which are localised near the emitter barrier. A theoretical model for the observed resonances based on the quantisation of the hybrid and cycloidal orbits is presented. Ballistic path lengths of at least 400 nm are observed.
Resonant tunnelling structures have attracted considerable interest recently as promising high speed devices and as syetems whose electrical properties are controlled by fundamental quantummechanical processes. There have been several recent studies of the effect of a transverse magnetic field, BlJ , on tunnelling in semiconductor heterostructuresl-5. In a single-barrier system Snell et al reported the observation of tunnelling into interfacial Landau states. Here we present an investigation of the effect of a magnetic field (B1J 1 on resonant tunnelling in double barrier structures with wide quantum wells. The structures based on n(AlGa)As/GaAs were grown by molecular beam epitaxy. Structure 1 comprises the following layers in order of growth from the n+GaAs substrate: (i) 2pm, 2x10=cm-" n+GaAs buffer layer; (ii) 50 run, 2x10a6 cm-= n-GaAs; (iii) 2.5 nm undoped GaAs; 5.6 nm undoped (iv) (AlGa)As, [A1]=0.4; (v) 60 nm undoped GaAs; (vi) 5.6 nm undoped (AlGa)As, [A1]=0.4; (vii) 2.5 nm undoped GaAs; (viii) 50 nm, 2~10~~ cm-3 n-GaAs; (ix) 0749-6036/89/040527+04$02.00/0
0.5 mun, 2x101* cm-3 n+GaAs top contact. Structure 2 is the same as 1 except for the well (layer v), which is 120 XXII wide. Figures la and lb show the I(V) characteristics of the two structures at 4 K. In order to enhance the resonances the differential conductance (dI/dV) is also plotted. Structure 1 (60 run)shows 28 resonances. The first 12 resonances are ascribed to tunnelling into quasibound states of the well with energy E less than the height &, of the collector barrier. The others, at higher voltage, are "above-barrier" reson;f;sel;E;zz; caused by reflection of waves at the GaAs/(AlGa)As interfaoeg-e. The I(V) characteristics of structure 2 show 70 resonances, 23 corresponding to quasi-bound states of the well and 47 corresponding to above barrier states. The inset of Figure 1 is a schematic diagram of the electron potential energy in the device. The low doping in the regions adjacent to the barriers leads to the formation of a quasi-two-dimensional electron gas (2DEG) in the emitter contact. Resonant tunnelling occurs whenever the bound state of this 2DEG has 0 1989 Academic Press Limited
528
Superiattices
and Microstructures,
Vol. 5, No. 4, 7989
J I
Figure 1. Plots of I(V) and differential conducS~~~,~:~‘ at 4 X and B-0 for (a) (60 nm well) and (b) structure 2 The inset shows the variation electron potential through the double barrier structure under an applied voltage V.
the same energy as a state in the quantum well. The highest peak/valley ratio observed is only 1.75 (in structure 1) and this relatively low value is attributed to the close spacing of the energy levels causing overlap between neighbouring resonances. The beating apparent in the dI/dV curves at high voltages arises from the interference of electron waves scattered from the two interfaces of the collector barrier6s8. The existence of well-defined "standing wave" resonances implies that some electrons traverse distances of at least 240 nm (twice the well width) without scattering even when they are accelerated in the well up to high kinetic energy ('1 eV). These characteristics make the samples ideal for studying the effect of a confining potential (quantum well) on the electron eigenstates in crossed electric and magnetic fields, i.e. with the electric field perpendicular to the barriers (E//x ) and the magnetic field applied in the plane of the barriers (B//z ). The effect of a magnetic field is to bend the electron orbits in the well by the action of the Lorentz force. The electrons can tunnel through the emitter barrier into two distinct types magneto-electric of states: (a) "skipping" orbits which interact with the emitter barrier only - these corre-
Fiqure 2. Plot of the energy eigenvalues E,(k,) of the hybrid magneto-electric states in the 60 nm quantum well of structure 1 for V=lV and B=lOT. The parabola marked 6,.corresponds to the energies of the states in the accumulation layer. The inset shows the ballistic orbits corresponding to skipping (a) and traversing orbits (b).
spond to cycloidal motion under the action of cros;;dwh;c;nd 8; (b) "traversing" states the electron wave is repeatedly reflected off both barriers. The two types of orbit are shown in the inset of Figure 2. Note that electrons which tunnel into type (a) states travel parallel to the barrier interface (i.e. perpendicular to the electric field) and only contribute to the measured current if they undergo scattering. The transition from type (a) to type (b) orbits occurs when the diameter of-the -cyclotron orbit is greater than the width of the cuantum well. This changeover has recently been related to the quenching of the Hall effect in small structuress. It should be stressed that the skipping states observed in both structures 1 and 2 develop in an undoped region where there is a large electric field. They are therefore essentially different from the skipping states reported recently by Snell et alI in single-barrier heterostructures in which the electron orbits were in a heavily-doped n+ region where the electric field was practically zero. This leads to a different quantisation condition although tunnelling in both systems can be analysed using a transfer-Hamiltonian method similar to that outlined by Chan et alLo. The tunnelling process is governed by conservation of energy and of momentum components in the plane of the barrier (hk, and hk,=m*v,.-eBx).For electrons in the degenerate 2DEG in the accumulation layer, -hkr
Superlattices
and Microstructures,
529
Vol. 5, No. 4, 1989
Fermi wave vector. If the origin of coordinates is taken to be at the right hand side of the first barrier, the 2DEG is situated at x=-(b+a), where b is the barrier width and a is the mean distance of the 2DEG from the interface. Thus hk,=m'v,+fikowhere ko=eB(b+a)/h. Hence, neglecting the effect of the magnetic field on the quasi-bound state energy E. of the ZDEG, the energy of electrons in the emitter accumulation layer is given by E,(k,)=Eo + W&k,-ko)a
+ haks2 , 2m'
with ko-k+< k, cko+kr. The value of kf at a given S;;iasmay be determined from magneto-oscillations in the tunnel current or capacitance in the 6 //J configuration=O. The energies E,(k,) of the quantum-well states are determined by the conduction band profile under bias and the magnetic potential m"wo2(xX0)'/2, where wcl=eB/m*and Xo=m"E/eB1hk,/eB. They can be calculated using the WKB approximation . Figure 2 shows E,(k,) for structure 1 (with V=lV and B=lOT) in the simplified case of infinite barriers. The dashed curves mark the transitions between states which do and do not interact with the barriers. corresponds to skipping W;z; ,!a) the emitter barrier, (b) to hybrid states interacting with both bar~d~~x~t~~)ba:~i~5ipping states of the and region (d) corresponds to bulk states which interact with neither barrier. Electrons only tunnel into states in regions (a) and (b). The parabola labelled 6, represents the range of energies in the emitter contact. At low temperatures this is sharply cut off at k,-ko=fkt. The energy and momentum conservation conditions can be interpreted graphically by looking for intersections in the E-k, plane of the parabola 6, with the set of dispersion curves E,(k,) of the states in the well. As can be seen in Figure 2 this corresponds to a discrete set of k, values which are the only ones which can contribute to the tunnel current. Sweeping either the applied voltage or magnetic field causes intersections to enter or leave (when the parabola Eo+E~=E,(kofkr) ) leading to structure in the tunnel current. d21/dVZ characteristics of The structure 1 at several magnetic fields (B1J 1 are shown in Figure 3. Figure 4 presents a typical for I(B) curve structure 2. In order to enhance the resonant structure the second derivative is also plotted. The series of os-
Fiqure 3. Plot of d21/dV2 versus V for structure 1 (60 nm well) at 4 K for various magnetic fields, BlJ . For B > 2 T, a series of oscillations due to tunnelling into magnetically quantised interface states can be observed at low voltages. For the trace at 7 T, the critical voltage V, for the disappearance of the skipping orbits is indicated by an arrow.
B
(1)
Fiqure 4. Plots of I(B) and daI/dBz at V=600 mV. T=4 K for a '100 urn diameter mesa of structure 2, showing oscillatory structure due to tunnelling into magnetoelectric states.
530
Superlattices
cillations at low voltage in Figure 3 (7 and 10 T curves) is due to tunnelling into skipping states with ky=ko-ke (type (a-) orbits) and the oscillations at higher bias are due to hybrid magnetoelectric subbands (type (b) orbits). The largest skipping orbit observed in structure 2 corresponds to a ballistic path length of at least 400 nm. In the I(B) curve at V=600 mV, shown in Figure 4, three different series of oscillations can be observed: the two series from O-2T and 2-5T correspond to type (bt) orbits with k,=ko+kr respectively and the series above 6T corresponds to type (a-) orbits. The different tunnelling probability for fkr in the presence of a transverse fields means that only one k, value is observed at most values of V and B. Note that at high B (>15T at this voltage) the tunnel current is quenched as the large Lorentz force deflects electrons back into the emitter. The fan chart in Figure 5, for structure 1, shows the positions of the maxima in the current illustrating how the states evolve with magnetic field and applied voltage. The dashed lines define the regions in B-V space corresponding to the different types of orbit. In order to obtain more than qualitative agreement with the data, the outline theory presented here needs to be extended to include the effects of a finite barrier height and nonparabolicity of the conduction band, as well as a detailed calculation of the matrix elements for transitions between the emitter and the quantum well.
Vol. 5, No. 4, 1989
In conclusion, we have shown that high energy electrons travel ballistically over remarkably long distances (-400 run) in the wide quantum wells of double barrier structures based on nGaAs/(AlGa)As. In the presence of a quantising magnetic field applied parallel to the plane of the barriers electrons tunnel into two distinct types of hybrid magneto-electric states with conservation of energy and momentum. These hybrid states are closely related to those responsible for edge currents in the Quantum Hall effect and the quenching of the Hall voltage in narrow channels. Acknowledgment- This work is supported by SERC (U.K.), CNRS (France). One of us (ESA) is supported by CNPq (Brazil).
1.
2.
3.
4.
207 5.
6. 7. 8. Figure 5. Fan chart showina the oositions of the maxima in the cu&ent in B-V space for structure 1. The dashed lines define the regions corresponding to different types of orbit. The solid lines act as guides to the eyes.
and Microstructures,
9. 10
B.R. Snell, K.S. Chan, F.W. Sheard, L. Eaves, G.A. Toombs, D.K. Maude, J.C. Portal, S.J. Bass, P. Claxton, G. Hill and M.A. Pate, Phys. Rev. Lett. 59, 2806 (1987). R. A. Davies, D. J. Newson, T.G. Powell, M.J. Kelly and H.W. Myron, Semicond. Sci. Technol. 2, 61-64 (1987). M. L. Leadbeater, L. Eaves, P. E. Simmonds, G.A. Toombs, F.W. Sheard, P.A. Claxton, G. Hill and M.A. Pate, Solid State Electron. 2, 707 (1988). H. Bando, T. Nakagawa, H. Tokumoto, K. Ohta and K. Kajimura, Jap. J. of APP. Phys. 26 (Supl. 26-3), 765 (1987). L. Eaves, K. W. Stevens and F.W. Sheard. In M.J. Kelly and p_. Weisbuch (Ed.), The P&sics and Fabrication of Microstructures and Devices, Springer Proc. in Physics Springer-Verlag, Heidelberg, 13, p.343. M. Henini, E.S. Alves, L. Eaves, O.H. Hughes and M.L. Leadbeater, to be published. M. Heiblum, I.M. Anderson and C.M. Knoedler, App. Phys. Lett. 9, 207 (1986). R.C. Potter and A.A Lakhani, App. Phys. Lett. 52, 1349 (1988). C.W.J. Beenakker and H. van Houten, Phys. Rev. Lett. 60, 2406 (1988). K. S. Chan, L. Eaves, D.K. Maude, G-a. F.W. Sheard, B.R. Snell, . ____ Toombs , E.S.Alves, J.C. Portal and Solid State ElectmnS. Bass, ._ 3l, 711.(1988).
and Microstructures.
HYBRID
MAGNETO-ELECTRIC
E. S. Alves,
527
Vol. 5, No. 4, 1989
STATES
M. L. Leadbeater,
IN RESOIUWI' TUNNELLIZ
STRUCTURES
L. Eaves, l4. Aenini, 0. H. Hughes
University of Nottingham, Department of Physics, Nottingham, NG7 2RD, U.K. A. Celeste and J. C. Portal SNCI-CNRS, 38042 Grenoble and LPS, INSA, 31077 Toulouse, France. G. Hill and W. A. Pate University of Sheffield, Dept. of Electronic & Electrical Engineering, Mappin Street, Sheffield, Sl 3JD, U.K. (Received 8 August 1988)
Double barrier resonant tunnelling structures with wide undoped quantum wells are used to study quantum ballistic transport in the presence of a magnetic field B. The structures are based on n-GaAs/(AlGa)As with well widths of 60 and 120 nm. At B=O, the wider well structure (120 nm) shows as many as 70 resonances in I(V). With B applied in the plane of the barriers (BlJ) these resonances evolve into hybrid maaneto-electric states. At sufficiently large B, the electron orbits no longer extend to the second barrier and tunnelling occurs into cycloidal interface states which are localised near the emitter barrier. A theoretical model for the observed resonances based on the quantisation of the hybrid and cycloidal orbits is presented. Ballistic path lengths of at least 400 nm are observed.
Resonant tunnelling structures have attracted considerable interest recently as promising high speed devices and as syetems whose electrical properties are controlled by fundamental quantummechanical processes. There have been several recent studies of the effect of a transverse magnetic field, BlJ , on tunnelling in semiconductor heterostructuresl-5. In a single-barrier system Snell et al reported the observation of tunnelling into interfacial Landau states. Here we present an investigation of the effect of a magnetic field (B1J 1 on resonant tunnelling in double barrier structures with wide quantum wells. The structures based on n(AlGa)As/GaAs were grown by molecular beam epitaxy. Structure 1 comprises the following layers in order of growth from the n+GaAs substrate: (i) 2pm, 2x10=cm-" n+GaAs buffer layer; (ii) 50 run, 2x10a6 cm-= n-GaAs; (iii) 2.5 nm undoped GaAs; 5.6 nm undoped (iv) (AlGa)As, [A1]=0.4; (v) 60 nm undoped GaAs; (vi) 5.6 nm undoped (AlGa)As, [A1]=0.4; (vii) 2.5 nm undoped GaAs; (viii) 50 nm, 2~10~~ cm-3 n-GaAs; (ix) 0749-6036/89/040527+04$02.00/0
0.5 mun, 2x101* cm-3 n+GaAs top contact. Structure 2 is the same as 1 except for the well (layer v), which is 120 XXII wide. Figures la and lb show the I(V) characteristics of the two structures at 4 K. In order to enhance the resonances the differential conductance (dI/dV) is also plotted. Structure 1 (60 run)shows 28 resonances. The first 12 resonances are ascribed to tunnelling into quasibound states of the well with energy E less than the height &, of the collector barrier. The others, at higher voltage, are "above-barrier" reson;f;sel;E;zz; caused by reflection of waves at the GaAs/(AlGa)As interfaoeg-e. The I(V) characteristics of structure 2 show 70 resonances, 23 corresponding to quasi-bound states of the well and 47 corresponding to above barrier states. The inset of Figure 1 is a schematic diagram of the electron potential energy in the device. The low doping in the regions adjacent to the barriers leads to the formation of a quasi-two-dimensional electron gas (2DEG) in the emitter contact. Resonant tunnelling occurs whenever the bound state of this 2DEG has 0 1989 Academic Press Limited
528
Superiattices
and Microstructures,
Vol. 5, No. 4, 7989
J I
Figure 1. Plots of I(V) and differential conducS~~~,~:~‘ at 4 X and B-0 for (a) (60 nm well) and (b) structure 2 The inset shows the variation electron potential through the double barrier structure under an applied voltage V.
the same energy as a state in the quantum well. The highest peak/valley ratio observed is only 1.75 (in structure 1) and this relatively low value is attributed to the close spacing of the energy levels causing overlap between neighbouring resonances. The beating apparent in the dI/dV curves at high voltages arises from the interference of electron waves scattered from the two interfaces of the collector barrier6s8. The existence of well-defined "standing wave" resonances implies that some electrons traverse distances of at least 240 nm (twice the well width) without scattering even when they are accelerated in the well up to high kinetic energy ('1 eV). These characteristics make the samples ideal for studying the effect of a confining potential (quantum well) on the electron eigenstates in crossed electric and magnetic fields, i.e. with the electric field perpendicular to the barriers (E//x ) and the magnetic field applied in the plane of the barriers (B//z ). The effect of a magnetic field is to bend the electron orbits in the well by the action of the Lorentz force. The electrons can tunnel through the emitter barrier into two distinct types magneto-electric of states: (a) "skipping" orbits which interact with the emitter barrier only - these corre-
Fiqure 2. Plot of the energy eigenvalues E,(k,) of the hybrid magneto-electric states in the 60 nm quantum well of structure 1 for V=lV and B=lOT. The parabola marked 6,.corresponds to the energies of the states in the accumulation layer. The inset shows the ballistic orbits corresponding to skipping (a) and traversing orbits (b).
spond to cycloidal motion under the action of cros;;dwh;c;nd 8; (b) "traversing" states the electron wave is repeatedly reflected off both barriers. The two types of orbit are shown in the inset of Figure 2. Note that electrons which tunnel into type (a) states travel parallel to the barrier interface (i.e. perpendicular to the electric field) and only contribute to the measured current if they undergo scattering. The transition from type (a) to type (b) orbits occurs when the diameter of-the -cyclotron orbit is greater than the width of the cuantum well. This changeover has recently been related to the quenching of the Hall effect in small structuress. It should be stressed that the skipping states observed in both structures 1 and 2 develop in an undoped region where there is a large electric field. They are therefore essentially different from the skipping states reported recently by Snell et alI in single-barrier heterostructures in which the electron orbits were in a heavily-doped n+ region where the electric field was practically zero. This leads to a different quantisation condition although tunnelling in both systems can be analysed using a transfer-Hamiltonian method similar to that outlined by Chan et alLo. The tunnelling process is governed by conservation of energy and of momentum components in the plane of the barrier (hk, and hk,=m*v,.-eBx).For electrons in the degenerate 2DEG in the accumulation layer, -hkr
Superlattices
and Microstructures,
529
Vol. 5, No. 4, 1989
Fermi wave vector. If the origin of coordinates is taken to be at the right hand side of the first barrier, the 2DEG is situated at x=-(b+a), where b is the barrier width and a is the mean distance of the 2DEG from the interface. Thus hk,=m'v,+fikowhere ko=eB(b+a)/h. Hence, neglecting the effect of the magnetic field on the quasi-bound state energy E. of the ZDEG, the energy of electrons in the emitter accumulation layer is given by E,(k,)=Eo + W&k,-ko)a
+ haks2 , 2m'
with ko-k+< k, cko+kr. The value of kf at a given S;;iasmay be determined from magneto-oscillations in the tunnel current or capacitance in the 6 //J configuration=O. The energies E,(k,) of the quantum-well states are determined by the conduction band profile under bias and the magnetic potential m"wo2(xX0)'/2, where wcl=eB/m*and Xo=m"E/eB1hk,/eB. They can be calculated using the WKB approximation . Figure 2 shows E,(k,) for structure 1 (with V=lV and B=lOT) in the simplified case of infinite barriers. The dashed curves mark the transitions between states which do and do not interact with the barriers. corresponds to skipping W;z; ,!a) the emitter barrier, (b) to hybrid states interacting with both bar~d~~x~t~~)ba:~i~5ipping states of the and region (d) corresponds to bulk states which interact with neither barrier. Electrons only tunnel into states in regions (a) and (b). The parabola labelled 6, represents the range of energies in the emitter contact. At low temperatures this is sharply cut off at k,-ko=fkt. The energy and momentum conservation conditions can be interpreted graphically by looking for intersections in the E-k, plane of the parabola 6, with the set of dispersion curves E,(k,) of the states in the well. As can be seen in Figure 2 this corresponds to a discrete set of k, values which are the only ones which can contribute to the tunnel current. Sweeping either the applied voltage or magnetic field causes intersections to enter or leave (when the parabola Eo+E~=E,(kofkr) ) leading to structure in the tunnel current. d21/dVZ characteristics of The structure 1 at several magnetic fields (B1J 1 are shown in Figure 3. Figure 4 presents a typical for I(B) curve structure 2. In order to enhance the resonant structure the second derivative is also plotted. The series of os-
Fiqure 3. Plot of d21/dV2 versus V for structure 1 (60 nm well) at 4 K for various magnetic fields, BlJ . For B > 2 T, a series of oscillations due to tunnelling into magnetically quantised interface states can be observed at low voltages. For the trace at 7 T, the critical voltage V, for the disappearance of the skipping orbits is indicated by an arrow.
B
(1)
Fiqure 4. Plots of I(B) and daI/dBz at V=600 mV. T=4 K for a '100 urn diameter mesa of structure 2, showing oscillatory structure due to tunnelling into magnetoelectric states.
530
Superlattices
cillations at low voltage in Figure 3 (7 and 10 T curves) is due to tunnelling into skipping states with ky=ko-ke (type (a-) orbits) and the oscillations at higher bias are due to hybrid magnetoelectric subbands (type (b) orbits). The largest skipping orbit observed in structure 2 corresponds to a ballistic path length of at least 400 nm. In the I(B) curve at V=600 mV, shown in Figure 4, three different series of oscillations can be observed: the two series from O-2T and 2-5T correspond to type (bt) orbits with k,=ko+kr respectively and the series above 6T corresponds to type (a-) orbits. The different tunnelling probability for fkr in the presence of a transverse fields means that only one k, value is observed at most values of V and B. Note that at high B (>15T at this voltage) the tunnel current is quenched as the large Lorentz force deflects electrons back into the emitter. The fan chart in Figure 5, for structure 1, shows the positions of the maxima in the current illustrating how the states evolve with magnetic field and applied voltage. The dashed lines define the regions in B-V space corresponding to the different types of orbit. In order to obtain more than qualitative agreement with the data, the outline theory presented here needs to be extended to include the effects of a finite barrier height and nonparabolicity of the conduction band, as well as a detailed calculation of the matrix elements for transitions between the emitter and the quantum well.
Vol. 5, No. 4, 1989
In conclusion, we have shown that high energy electrons travel ballistically over remarkably long distances (-400 run) in the wide quantum wells of double barrier structures based on nGaAs/(AlGa)As. In the presence of a quantising magnetic field applied parallel to the plane of the barriers electrons tunnel into two distinct types of hybrid magneto-electric states with conservation of energy and momentum. These hybrid states are closely related to those responsible for edge currents in the Quantum Hall effect and the quenching of the Hall voltage in narrow channels. Acknowledgment- This work is supported by SERC (U.K.), CNRS (France). One of us (ESA) is supported by CNPq (Brazil).
1.
2.
3.
4.
207 5.
6. 7. 8. Figure 5. Fan chart showina the oositions of the maxima in the cu&ent in B-V space for structure 1. The dashed lines define the regions corresponding to different types of orbit. The solid lines act as guides to the eyes.
and Microstructures,
9. 10
B.R. Snell, K.S. Chan, F.W. Sheard, L. Eaves, G.A. Toombs, D.K. Maude, J.C. Portal, S.J. Bass, P. Claxton, G. Hill and M.A. Pate, Phys. Rev. Lett. 59, 2806 (1987). R. A. Davies, D. J. Newson, T.G. Powell, M.J. Kelly and H.W. Myron, Semicond. Sci. Technol. 2, 61-64 (1987). M. L. Leadbeater, L. Eaves, P. E. Simmonds, G.A. Toombs, F.W. Sheard, P.A. Claxton, G. Hill and M.A. Pate, Solid State Electron. 2, 707 (1988). H. Bando, T. Nakagawa, H. Tokumoto, K. Ohta and K. Kajimura, Jap. J. of APP. Phys. 26 (Supl. 26-3), 765 (1987). L. Eaves, K. W. Stevens and F.W. Sheard. In M.J. Kelly and p_. Weisbuch (Ed.), The P&sics and Fabrication of Microstructures and Devices, Springer Proc. in Physics Springer-Verlag, Heidelberg, 13, p.343. M. Henini, E.S. Alves, L. Eaves, O.H. Hughes and M.L. Leadbeater, to be published. M. Heiblum, I.M. Anderson and C.M. Knoedler, App. Phys. Lett. 9, 207 (1986). R.C. Potter and A.A Lakhani, App. Phys. Lett. 52, 1349 (1988). C.W.J. Beenakker and H. van Houten, Phys. Rev. Lett. 60, 2406 (1988). K. S. Chan, L. Eaves, D.K. Maude, G-a. F.W. Sheard, B.R. Snell, . ____ Toombs , E.S.Alves, J.C. Portal and Solid State ElectmnS. Bass, ._ 3l, 711.(1988).