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A new technique for directly probing the intrinsic tristability and its temperature dependence in a resonant tunneling diode
Solid-State Electronics Vol, 37, Nos 4-6. pp. 961-964, 1994 Copyright © 1994 Elsevier Science Ltd
Pergamon
Printed in Great Britain. All rights reserved 0038-1101/94 $6.00+0.00
A NEW TECHNIQUE FOR DIRECTLY PROBING THE INTRINSIC TRISTABILITY AND ITS TEMPERATURE DEPENDENCE IN A RESONANT TUNNELING DIODE M. L. F. LERCHl, A. D. MART1N 1, P. E. SIMMONDS 1, U EAVES2 and M. L. LEADBEATER2 ~Department of Physics, University of Wollongong, Wollongong, NSW 2522, Australia and 2Department of Physics, University of Nottingham, Nottingham NG7 2RD, England Abstract--A new measurement technique employing a positively sloping load line has been used to probe the region of apparent bistability near a tunneling resonance in the electrical characteristic of a resonant tunneling diode. This technique is equivalent to using a voltage source and negative series resistance. The appearance of bistability is an artifact of the conventional measuring technique which uses a load line with negative slope. The complete characteristic is found to be a continuous Z shaped curve between 20 and 150 K, corresponding to tristability and in accordance with theoretical models based on the effects of charge accumulation in the central quantum well of the diode. The width of the tristable region passes through a maximum at 40 K and, at i 50 K, disappears as the resonance broadens. Above this temperature the resonance develops a region of negative differential resistance (NDR). As the device is cooled below 20 K additional structure develops in the central arm of the Z, with some portions of the characteristic exhibiting fivestable current states at temperatures below 15 K. At 4.2 K, the effect of an in plane magnetic field mimics that of increasing temperature.
INTRODUCTION
The occurrence of intrinsic bistability in the electrical characteristics ( I ( V ) curves) of semiconductor double-barrier structures (DBSs) has attracted considerable recent attention, both experimentally and theoretically. When a DBS device is biased, electron tunneling through the barriers and enclosed quantum well can show large resonances which occur when incoming electrons coincide in energy and transverse momentum with quantum states quasi-localized in the well. The characteristics in the vicinity of these resonances have regions of either negative differential resistance (NDR)[1] or apparent bistability[2-5] and devices which display both types of curve have been subject to detailed experimental study. In the bistable case there has been some initial debate as to the cause, since circuit oscillations in a region of NDR, or NDR together with a series resistance, can simulate this effect[6-8]. It is now clear that bistability which is intrinsic to the device has been realized experimentally in appropriately designed structures[3-5] and is caused by electrostatic feedback due to charge buildup in the well[2,5,9--i I]. This effect is particularly pronounced in devices with asymmetric barriers. The asymmetry facilitates the accumulation of free charge in the well when the device is biased so that the probability of tunneling into unoccupied well states through the emitter barrier greatly exceeds that of tunneling out through the thicker collector barrier[3-5]. The conventional technique for measuring the device characteristic uses a voltage source in series with the device together with some positive resistance. Although the resistance can be made
arbitrarily small, the interior of the bistability remains inaccessible to this technique. The appearance of bistability may therefore be an artifact of the conventional measuring technique and could conceal an important portion of the static characteristic which would indicate tristability or, possibly, more complex behaviour. Theoretical models, which include effects of charge accumulation in the well[9-11 ], predict a characteristic in the form of a continuous Z shaped curve provided that the tunneling resonance is sufficiently sharp. Such a characteristic should more correctly be called tristable[10]. The form of the characteristic in this region could yield useful information on the details of the tunneling process, particularly where there is substantial charge density in the well. In this paper we show that the interior of the bistability in one such device is indeed accessible to a measurement technique which employs a load line with positive slope, corresponding to a voltage source and a negative series resistance. The characteristic near the first tunneling resonance of the device under study is a continuous Z shaped curve between 150 and 20 K and develops additional structure as the device is cooled further. At 4.2 K, the effect of a small in plane magnetic (B < I T ) field mimics that of increasing temperature.
961
DEVICE STRUCTURE AND CHARACTERISTICS
The active region of the asymmetric device studied consists of a 5.8 nm GaAs quantum well, sandwiched between Al04Gao6 As barriers of different widths, 8.3 and 11.1 nm. Lightly doped GaAs spacer layers separate this region from the heavily doped n ÷ contact
M. L. F. LERCH et al.
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Fig. 1.1 (V) characteristics at 2 K of the asymmetric double barrier structure, measured using a conventional (near vertical) load line. Only the first resonance is shown in each bias direction. In forward bias the current switching directions observed using this measurement technique are indicated by arrows and delineate the region of apparent bistability. The broad peak near 0.9 V is associated with LO phonon assisted tunneling. Inset: Schematic conduction band energy diagram for the device under forward bias.
regions. An applied bias voltage causes an accumulation layer and associated two dimensional electron gas (2DEG) to form adjacent to the emitter barrier. Resonant tunneling occurs when this voltage brings one of the two quasi-bound states in the well into energy coincidence with the quasi-bound state in the emitter. Full details of the layer structure are given in Refs[4,5] and a schematic diagram of the conduction band edge under forward bias is shown in the inset to Fig. 1. The electrical characteristics have already been reported in detail and show two resonances in each bias direction[5]. Under reverse bias (electrons tunneling into the well through the thicker
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Fig. 2. (a) Schematic region of apparent bistability shown on an expanded voltage scale. The conventional load line corresponds to a voltage source Vm and a (small) positive series resistance R L. The gradient of the load line is - I / R k. Switching occurs at A and B as the load line is swept through the device characteristic by varying V~, and any part of the characteristic between A and B is inaccessible for any positive value of R L. The load line for a voltage source and a negative series resistance (an NOR supply) has a positive slope and can be used to probe the region between A and B provided that the slope of the load line is less than the slope of the device characteristic at Q (I/Rd). This is equivalent to the requirement that R k + R d < 0. (b) Circuit diagram for a NOR voltage supply. The output voltage is given by V D = I/1, + (R~ " R ~ / R , ) . I (i.e. VD increases as more current I is drawn from the supply). This is the equation of the NOR load line shown in Fig. 2(a). The circuit is equivalent to a voltage source V~ in series with a negative resistance R L = - R ~ R 3 / R 2.
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Fig. 3. Temperature dependence of the device characteristics measured near the peak of the resonance using the NOR supply. The onset of tristability and the development of more complex structure is shown as the temperature is lowered. Inset: Variation with temperature of the width, A V, of the voltage overhang and Vp, the voltage at the resonance peak.
963
The intrinsic tristability and its temperature dependence much broader and show apparent bistability. The characteristic due to the first resonance measured conventionally at 2 K is shown in Fig. 1. The region of apparent bistability near a bias of 0.7 V is studied in the present work. The charge buildup in the well which causes the extended voltage range of the first forward bias resonance (0.3-0.7V) has been confirmed by detailed magneto-capacitance and luminescence studies[5,14]. The fact that the device exhibits N D R under reverse bias (where no charge build up is detected) is in itself strong evidence in support of the intrinsic nature of this bistability. MEASUREMENT TECHNIQUE AND CIRCUIT STABILITY The measurements reported here (Figs 3 and 4) were taken using a voltage supply designed to have a negative output resistance (NOR), corresponding to a load line with positive slope. This enables the portion of the characteristic inside the region of apparent bistability to be probed (see Fig. 2(a)). An active circuit designed to meet the NOR requirement is shown in Fig. 2(b). Additional details of this circuit will be reported elsewhere. Provided that the device characteristic is continuous, the load line can be made to intersect any part of it inside the bistability at a point Q if [RL[ > e'h:l. Here Rd is the dynamic resistance dV/dl of the device at Q and - I/R L is the slope of the load line. Under these conditions the total circuit resistance RL + Ra < 0 and circuit oscillations can occur due to the exponential growth of any initial perturbation. Circuit analysis, based on dynamic circuit models of the NOR measuring circuit[l 5] and device[5,12,13], predicts a narrow range of values of R L and CL for which stability should occur. (CL is a capacitance which appears in parallel with RL in the NOR equivalent circuit. Both parameters are adjustable.) These values form an "island of stability" in RL--CL space. Stable measurements, for which no oscillations up to 400 MHz were observed, could be made with values of R L and CL close to those predicted, giving some confidence in the circuit models used. Varying R L or CL outside this range caused large amplitude oscillations at frequencies up to a few hundred kHz.
the peak of the first tunneling resonance close to a bias of 0.7 V are plotted for a number of temperatures between 160 and 4.2 K. For temperatures between about 150 and 20 K these results clearly demonstrate the continuous and tristable nature of the intrinsic device characteristic inside the region of apparent bistability as measured conventionally. The re-entrant form of the I (V) curve (resonance overhang) predicted in Ref.[10] (3DEG in the emitter) and Ref.[l 1] (2DEG in the emitter, corresponding to the present device) is reproduced qualitatively in the experimental data. As the temperature is reduced below 20 K the overhang region of the characteristic develops more complex behaviour. Between 20 and 4.2 K the resonance exhibits marked narrowing close to the current peak and an additional broader shoulder develops between the peak and foot. This coincides with a decrease both in the overall voltage width A V of the overhang and in the peak current. Very similar behaviour is observed for three different devices on two separate chips and is insensitive to (necessarily) small variations in the slope of the load line. Plots of the voltage width A V, together with bias at the current peak lip, against T are shown in the inset to Fig. 3. As expected, very similar data are obtained from conventional bistability width measurements[12] although switching between high and low current states in conventionally measured data occurs at bias voltages near the peak and foot of the resonance overhang. As the temperature is increased above 4.2 K, both AV and lip initially increase, with A V reaching its maximum value near 40 K. At still higher temperatures, broadening of the resonance causes a decrease in A V and the tristability vanishes near 150 K. Above this temperature the resonance exhibits NDR, an observation consistent with previous measurements[12]. ,
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MEASUREMENTS USING THE NOR CIRCUIT AND DISCUSSION Measurements made with the NOR circuit on the device characteristic outside the bistable region gave the same results as those obtained using conventional techniques and, for measurements obtained at 4.2 K, correspond closely to published data for an essentially identical device[4]. Adjusting the position of the load line by varying Vjn and Rj (see Fig. 2(b)) gave a smooth, continuous and reversible transition into the interior of the bistability. The results of these measurements are shown in Fig. 3, where the complete characteristics of the device near
B=0T 5
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i
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Fig. 4. Effect of an in plane (B_I_J) magnetic field on the device characteristic at 4.2 K. The field extends the range of the voltage overhang and has a similiar effect to that caused by increasing the temperature between 4.2 and 50 K, as shown in Fig. 3.
964
M . L . F . LERCH et al.
The detailed origin of the low temperature structure in the overhang region is unclear. The sharp corresponding reverse bias resonance displays no such satellite structure and quite separate LO phonon satellites lie at higher biases. The broad shoulder is possibly caused by an inelastic process due to some form of electron--electron interaction, for example electron shake-up or emission of a plasmon at k near kf in the well 2DEG. Either of these processes would be expected to give satellite structure separated by a few mV from the main emitter to well resonance voltage. Further experiments on different device structures would be required to establish that the complex characteristic observed here is an intrinsic feature of the tunneling process in devices displaying bistability. In the present asymmetric structure which exhibits strong charge build-up in the well at the first resonance, the peak-to-valley current ratio is significantly degraded relative to the sharp reverse bias resonance, and weak off-resonance and satellite tunnelling processes appear relatively enhanced. This is because the peak forward bias current is limited by the maximum carrier density, n ..... which can accumulate in the well at resonance ( E 0 = E I ) together with the low transmission probability of the wide collector barrier. This value of n . . . . . (2.2 x 1011 cm -2) occurs when the Fermi energies of the 2-D emitter and the well (and hence the sheet densities n e, n ..... respectively) are approximately equal, as has been confirmed experimentally[4,5]. Another feature of interest in Fig. 3 is the initial increase in A V and lip with temperature despite the obvious broadening of the re-entrant resonance curve (made evident by the new technique which exposes the full lineshape). This observation suggests that n ..... can be enhanced by thermal effects beyond its "resonance" value so that nw.max> he. It has been previously demonstrated that strong enhancement in the value of n ..... at resonance can be achieved by application of a quantising magnetic field (Bird) with consequent large increase in peak current and AV[14]. Alternatively, a smaller increase in n ..... and A V is obtainable by application of a small in-plane field (B_l_d). Results taken at B (,1_) = 0.5 and 1 T, at 4.2 K are shown in Fig. 4. The effect of the field is strikingly similar to that caused by an increase in temperature. This observation suggests a possible explanation for the temperature induced increase in Vp and overhang AV shown plotted in the inset to Fig. 3. The in-plane B field generally causes spreading and a shift in the resonance cut off to slightly higher emitter to well voltage[16]. At the new resonance cut off the levels Ej (well) and E0 (emitter) are misaligned with E~ lying at energy fiE below E o. This allows the stored charge density for B > 0 to exceed its maximum zero field value (i.e. n ...... > n¢) since, as mentioned above, n~.m,x corresponds to alignment of emitter and well Fermi levels. Field induced enhancement of the resonance overhang and increased Vp and peak current are expected, and observed (see Fig. 4),
since all three depend on n . . . . . (peak current is approximately ocn . . . . . ). F r o m the discussion in Ref.[16] we estimate a B field induced spreading 6 E ~ h 2k~Ak /m where Ak = eBLo~/h, k F is the emitter Fermi wavevector and Le~ ~ 18 nm, the effective emitter to well separation[4]. For B = 1 T, this yields r E ~ 1 meV corresponding to ~ 1 5 % increase in nw.,,ax, from which an increase in A V of ~ 65 meV is estimated, in good agreement with ~ 7 0 meV obtained experimentally. Since elevated temperature and applied magnetic field have similar effects on the characteristic there may be an underlying common mechanism in which thermal broadening of the resonance plays a role analogous to the field induced spreading. Acknowledgements--The expert technical assistance of Dale Hughes is gratefully acknowledged. This work was partially supported by the Australian Research Council and the U.K. Science and Engineering Research Council. REFERENCES
1. See, e.g., E. E. Mendez, in Physics and Applications of Quantum Wells and Superlattices (Edited by E. E. Mendez and K. von Klitzing), NATO ASI, Series B Physics, Vol. 170, p. 159. Plenum Press, New York (1988). 2. V. J. Goldman, D. C. Tsui and J. E. Cunningham, Phys. Ret,. Lett. 58, 1256 (19873. 3. A. Zaslavsky, V. J. Goldman, D. C. Tsui and J. E. Cunningham, Appl. Phys. Lett. 53, 1408 (19883. 4. M. L. Leadbeater, E. S. Alves, L. Eaves, M. Henini, O. H. Hughes, F. W. Sheard and G. A. Toombs, Semicond. Sei. Technol. 3, 1060 (19883. 5. M. L. Leadbeater, E. S. Alves, F. W. Sheard, L. Eaves, M. Henini, O. H. Hughes and G. A. Toombs, J. Phys.: Condens. Matter 1, 10605 (19893. 6. T. C. L. G. Sollner, Phys. Rev. Lett. 59, 1622 (1987); V. J. Goldman, Phys. Rev. Lett. 59, 1623 (1987). 7. T. J. Foster, M. L. Leadbeater, L. Eaves, M. Henini, O. H. Hughes, C. A. Payling, F. W. Sheard, P. E. Simmonds and G. A. Toombs, Phys. Rev. B 39, 6205 (1989). 8. W. D. Goodhue, T. C. L. G. Sollner, H. Q. Le, E. R. Brown and B. A. Vojac, Appl. Phys. Lett. 49, 1086 (1986); M. Tsuchiya and H. Sakaki, Appl. Phys. Lett. 49, 88 (1986). 9. F. W. Sheard and G. A. Toombs, Appl. Phys. Lett. 52, 1228 (19883. 10. D. D. Coon, K. M. S. V. Bandara and H. Zhao, Appl. Phys. Lett. 54, 2115 (19893. 11. F. W. Sheard and G. A. Toombs, Scmicond. Sci. Technol. 7, B460 (1992). 12. M. L. Leadbeater, Ph.D. thesis, Univ. of Nottingham (19903. 13. F. W. Sheard and G. A. Toombs, Solid-St. Electron. 32, 1443 (1989). 14. L. Eaves. M. L. Leadbeater, D. G. Hayes, E, S. Alves, F. W. Sheard, G. A. Toombs, P. E. Simmonds, M. S. Skolnick, M. Henini and O. H. Hughes, Solid-St. Electron. 32, II01 (1989). 15. A. D. Martin, M. L. F. Lerch, P. E. Simmonds, L. Eaves and M. L. Leadbeater 8th Int. Con£ on Hot Carriers in Semiconductors. Oxford. U.K. (19933. 16. M. L. Leadbeater, L. Eaves, P. E. Simmonds, G. A. Toombs, F. W. Sheard, P. A. Claxton, G. Hill and M. A. Pate, Solid-St. Electron. 31, 707 (I 988).
Pergamon
Printed in Great Britain. All rights reserved 0038-1101/94 $6.00+0.00
A NEW TECHNIQUE FOR DIRECTLY PROBING THE INTRINSIC TRISTABILITY AND ITS TEMPERATURE DEPENDENCE IN A RESONANT TUNNELING DIODE M. L. F. LERCHl, A. D. MART1N 1, P. E. SIMMONDS 1, U EAVES2 and M. L. LEADBEATER2 ~Department of Physics, University of Wollongong, Wollongong, NSW 2522, Australia and 2Department of Physics, University of Nottingham, Nottingham NG7 2RD, England Abstract--A new measurement technique employing a positively sloping load line has been used to probe the region of apparent bistability near a tunneling resonance in the electrical characteristic of a resonant tunneling diode. This technique is equivalent to using a voltage source and negative series resistance. The appearance of bistability is an artifact of the conventional measuring technique which uses a load line with negative slope. The complete characteristic is found to be a continuous Z shaped curve between 20 and 150 K, corresponding to tristability and in accordance with theoretical models based on the effects of charge accumulation in the central quantum well of the diode. The width of the tristable region passes through a maximum at 40 K and, at i 50 K, disappears as the resonance broadens. Above this temperature the resonance develops a region of negative differential resistance (NDR). As the device is cooled below 20 K additional structure develops in the central arm of the Z, with some portions of the characteristic exhibiting fivestable current states at temperatures below 15 K. At 4.2 K, the effect of an in plane magnetic field mimics that of increasing temperature.
INTRODUCTION
The occurrence of intrinsic bistability in the electrical characteristics ( I ( V ) curves) of semiconductor double-barrier structures (DBSs) has attracted considerable recent attention, both experimentally and theoretically. When a DBS device is biased, electron tunneling through the barriers and enclosed quantum well can show large resonances which occur when incoming electrons coincide in energy and transverse momentum with quantum states quasi-localized in the well. The characteristics in the vicinity of these resonances have regions of either negative differential resistance (NDR)[1] or apparent bistability[2-5] and devices which display both types of curve have been subject to detailed experimental study. In the bistable case there has been some initial debate as to the cause, since circuit oscillations in a region of NDR, or NDR together with a series resistance, can simulate this effect[6-8]. It is now clear that bistability which is intrinsic to the device has been realized experimentally in appropriately designed structures[3-5] and is caused by electrostatic feedback due to charge buildup in the well[2,5,9--i I]. This effect is particularly pronounced in devices with asymmetric barriers. The asymmetry facilitates the accumulation of free charge in the well when the device is biased so that the probability of tunneling into unoccupied well states through the emitter barrier greatly exceeds that of tunneling out through the thicker collector barrier[3-5]. The conventional technique for measuring the device characteristic uses a voltage source in series with the device together with some positive resistance. Although the resistance can be made
arbitrarily small, the interior of the bistability remains inaccessible to this technique. The appearance of bistability may therefore be an artifact of the conventional measuring technique and could conceal an important portion of the static characteristic which would indicate tristability or, possibly, more complex behaviour. Theoretical models, which include effects of charge accumulation in the well[9-11 ], predict a characteristic in the form of a continuous Z shaped curve provided that the tunneling resonance is sufficiently sharp. Such a characteristic should more correctly be called tristable[10]. The form of the characteristic in this region could yield useful information on the details of the tunneling process, particularly where there is substantial charge density in the well. In this paper we show that the interior of the bistability in one such device is indeed accessible to a measurement technique which employs a load line with positive slope, corresponding to a voltage source and a negative series resistance. The characteristic near the first tunneling resonance of the device under study is a continuous Z shaped curve between 150 and 20 K and develops additional structure as the device is cooled further. At 4.2 K, the effect of a small in plane magnetic (B < I T ) field mimics that of increasing temperature.
961
DEVICE STRUCTURE AND CHARACTERISTICS
The active region of the asymmetric device studied consists of a 5.8 nm GaAs quantum well, sandwiched between Al04Gao6 As barriers of different widths, 8.3 and 11.1 nm. Lightly doped GaAs spacer layers separate this region from the heavily doped n ÷ contact
M. L. F. LERCH et al.
962
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Fig. 1.1 (V) characteristics at 2 K of the asymmetric double barrier structure, measured using a conventional (near vertical) load line. Only the first resonance is shown in each bias direction. In forward bias the current switching directions observed using this measurement technique are indicated by arrows and delineate the region of apparent bistability. The broad peak near 0.9 V is associated with LO phonon assisted tunneling. Inset: Schematic conduction band energy diagram for the device under forward bias.
regions. An applied bias voltage causes an accumulation layer and associated two dimensional electron gas (2DEG) to form adjacent to the emitter barrier. Resonant tunneling occurs when this voltage brings one of the two quasi-bound states in the well into energy coincidence with the quasi-bound state in the emitter. Full details of the layer structure are given in Refs[4,5] and a schematic diagram of the conduction band edge under forward bias is shown in the inset to Fig. 1. The electrical characteristics have already been reported in detail and show two resonances in each bias direction[5]. Under reverse bias (electrons tunneling into the well through the thicker
10
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barrier) the resonances are sharp and exhibit NDR. Under forward bias the respective peak resonant currents are more than an order of magnitude larger,
T 160K
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Fig. 2. (a) Schematic region of apparent bistability shown on an expanded voltage scale. The conventional load line corresponds to a voltage source Vm and a (small) positive series resistance R L. The gradient of the load line is - I / R k. Switching occurs at A and B as the load line is swept through the device characteristic by varying V~, and any part of the characteristic between A and B is inaccessible for any positive value of R L. The load line for a voltage source and a negative series resistance (an NOR supply) has a positive slope and can be used to probe the region between A and B provided that the slope of the load line is less than the slope of the device characteristic at Q (I/Rd). This is equivalent to the requirement that R k + R d < 0. (b) Circuit diagram for a NOR voltage supply. The output voltage is given by V D = I/1, + (R~ " R ~ / R , ) . I (i.e. VD increases as more current I is drawn from the supply). This is the equation of the NOR load line shown in Fig. 2(a). The circuit is equivalent to a voltage source V~ in series with a negative resistance R L = - R ~ R 3 / R 2.
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Fig. 3. Temperature dependence of the device characteristics measured near the peak of the resonance using the NOR supply. The onset of tristability and the development of more complex structure is shown as the temperature is lowered. Inset: Variation with temperature of the width, A V, of the voltage overhang and Vp, the voltage at the resonance peak.
963
The intrinsic tristability and its temperature dependence much broader and show apparent bistability. The characteristic due to the first resonance measured conventionally at 2 K is shown in Fig. 1. The region of apparent bistability near a bias of 0.7 V is studied in the present work. The charge buildup in the well which causes the extended voltage range of the first forward bias resonance (0.3-0.7V) has been confirmed by detailed magneto-capacitance and luminescence studies[5,14]. The fact that the device exhibits N D R under reverse bias (where no charge build up is detected) is in itself strong evidence in support of the intrinsic nature of this bistability. MEASUREMENT TECHNIQUE AND CIRCUIT STABILITY The measurements reported here (Figs 3 and 4) were taken using a voltage supply designed to have a negative output resistance (NOR), corresponding to a load line with positive slope. This enables the portion of the characteristic inside the region of apparent bistability to be probed (see Fig. 2(a)). An active circuit designed to meet the NOR requirement is shown in Fig. 2(b). Additional details of this circuit will be reported elsewhere. Provided that the device characteristic is continuous, the load line can be made to intersect any part of it inside the bistability at a point Q if [RL[ > e'h:l. Here Rd is the dynamic resistance dV/dl of the device at Q and - I/R L is the slope of the load line. Under these conditions the total circuit resistance RL + Ra < 0 and circuit oscillations can occur due to the exponential growth of any initial perturbation. Circuit analysis, based on dynamic circuit models of the NOR measuring circuit[l 5] and device[5,12,13], predicts a narrow range of values of R L and CL for which stability should occur. (CL is a capacitance which appears in parallel with RL in the NOR equivalent circuit. Both parameters are adjustable.) These values form an "island of stability" in RL--CL space. Stable measurements, for which no oscillations up to 400 MHz were observed, could be made with values of R L and CL close to those predicted, giving some confidence in the circuit models used. Varying R L or CL outside this range caused large amplitude oscillations at frequencies up to a few hundred kHz.
the peak of the first tunneling resonance close to a bias of 0.7 V are plotted for a number of temperatures between 160 and 4.2 K. For temperatures between about 150 and 20 K these results clearly demonstrate the continuous and tristable nature of the intrinsic device characteristic inside the region of apparent bistability as measured conventionally. The re-entrant form of the I (V) curve (resonance overhang) predicted in Ref.[10] (3DEG in the emitter) and Ref.[l 1] (2DEG in the emitter, corresponding to the present device) is reproduced qualitatively in the experimental data. As the temperature is reduced below 20 K the overhang region of the characteristic develops more complex behaviour. Between 20 and 4.2 K the resonance exhibits marked narrowing close to the current peak and an additional broader shoulder develops between the peak and foot. This coincides with a decrease both in the overall voltage width A V of the overhang and in the peak current. Very similar behaviour is observed for three different devices on two separate chips and is insensitive to (necessarily) small variations in the slope of the load line. Plots of the voltage width A V, together with bias at the current peak lip, against T are shown in the inset to Fig. 3. As expected, very similar data are obtained from conventional bistability width measurements[12] although switching between high and low current states in conventionally measured data occurs at bias voltages near the peak and foot of the resonance overhang. As the temperature is increased above 4.2 K, both AV and lip initially increase, with A V reaching its maximum value near 40 K. At still higher temperatures, broadening of the resonance causes a decrease in A V and the tristability vanishes near 150 K. Above this temperature the resonance exhibits NDR, an observation consistent with previous measurements[12]. ,
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MEASUREMENTS USING THE NOR CIRCUIT AND DISCUSSION Measurements made with the NOR circuit on the device characteristic outside the bistable region gave the same results as those obtained using conventional techniques and, for measurements obtained at 4.2 K, correspond closely to published data for an essentially identical device[4]. Adjusting the position of the load line by varying Vjn and Rj (see Fig. 2(b)) gave a smooth, continuous and reversible transition into the interior of the bistability. The results of these measurements are shown in Fig. 3, where the complete characteristics of the device near
B=0T 5
i
i
0.70
i
i
0.75 Voltage (V)
i
!
0.80
Fig. 4. Effect of an in plane (B_I_J) magnetic field on the device characteristic at 4.2 K. The field extends the range of the voltage overhang and has a similiar effect to that caused by increasing the temperature between 4.2 and 50 K, as shown in Fig. 3.
964
M . L . F . LERCH et al.
The detailed origin of the low temperature structure in the overhang region is unclear. The sharp corresponding reverse bias resonance displays no such satellite structure and quite separate LO phonon satellites lie at higher biases. The broad shoulder is possibly caused by an inelastic process due to some form of electron--electron interaction, for example electron shake-up or emission of a plasmon at k near kf in the well 2DEG. Either of these processes would be expected to give satellite structure separated by a few mV from the main emitter to well resonance voltage. Further experiments on different device structures would be required to establish that the complex characteristic observed here is an intrinsic feature of the tunneling process in devices displaying bistability. In the present asymmetric structure which exhibits strong charge build-up in the well at the first resonance, the peak-to-valley current ratio is significantly degraded relative to the sharp reverse bias resonance, and weak off-resonance and satellite tunnelling processes appear relatively enhanced. This is because the peak forward bias current is limited by the maximum carrier density, n ..... which can accumulate in the well at resonance ( E 0 = E I ) together with the low transmission probability of the wide collector barrier. This value of n . . . . . (2.2 x 1011 cm -2) occurs when the Fermi energies of the 2-D emitter and the well (and hence the sheet densities n e, n ..... respectively) are approximately equal, as has been confirmed experimentally[4,5]. Another feature of interest in Fig. 3 is the initial increase in A V and lip with temperature despite the obvious broadening of the re-entrant resonance curve (made evident by the new technique which exposes the full lineshape). This observation suggests that n ..... can be enhanced by thermal effects beyond its "resonance" value so that nw.max> he. It has been previously demonstrated that strong enhancement in the value of n ..... at resonance can be achieved by application of a quantising magnetic field (Bird) with consequent large increase in peak current and AV[14]. Alternatively, a smaller increase in n ..... and A V is obtainable by application of a small in-plane field (B_l_d). Results taken at B (,1_) = 0.5 and 1 T, at 4.2 K are shown in Fig. 4. The effect of the field is strikingly similar to that caused by an increase in temperature. This observation suggests a possible explanation for the temperature induced increase in Vp and overhang AV shown plotted in the inset to Fig. 3. The in-plane B field generally causes spreading and a shift in the resonance cut off to slightly higher emitter to well voltage[16]. At the new resonance cut off the levels Ej (well) and E0 (emitter) are misaligned with E~ lying at energy fiE below E o. This allows the stored charge density for B > 0 to exceed its maximum zero field value (i.e. n ...... > n¢) since, as mentioned above, n~.m,x corresponds to alignment of emitter and well Fermi levels. Field induced enhancement of the resonance overhang and increased Vp and peak current are expected, and observed (see Fig. 4),
since all three depend on n . . . . . (peak current is approximately ocn . . . . . ). F r o m the discussion in Ref.[16] we estimate a B field induced spreading 6 E ~ h 2k~Ak /m where Ak = eBLo~/h, k F is the emitter Fermi wavevector and Le~ ~ 18 nm, the effective emitter to well separation[4]. For B = 1 T, this yields r E ~ 1 meV corresponding to ~ 1 5 % increase in nw.,,ax, from which an increase in A V of ~ 65 meV is estimated, in good agreement with ~ 7 0 meV obtained experimentally. Since elevated temperature and applied magnetic field have similar effects on the characteristic there may be an underlying common mechanism in which thermal broadening of the resonance plays a role analogous to the field induced spreading. Acknowledgements--The expert technical assistance of Dale Hughes is gratefully acknowledged. This work was partially supported by the Australian Research Council and the U.K. Science and Engineering Research Council. REFERENCES
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