A PERSPECTIVE OF RESONANT TUNNELING

L. L. Chang

IBM Thomas J. Watson Research Center Yorktown Heights, New York 10598, U.S.A.

Abstract - We provide a perspective of the development of resonant tunneling over the last two decades. The work starts with a consideration of different semiconduc­tor materials, proceeds to discuss the effects of band structure and electron dynam­ics, continues to describe systems of multiple barriers and low dimensional electrons, and ends with a summary of device applications. The emphasis is on major exper­imental observations, which serve as cornerstones of this field.

INTRODUCTION

Resonant tunneling refers to the process of resonant enhancement of electron tunneling by intermediate energy states. The simplest case is that of a single poten­tial well sandwiched between two potential barriers, usually called a double-barrier structure. The current flows between two outside electrodes through the structure, and resonance occurs when incoming electrons coincide in energy with the quantum states created in the well. Indeed, the first observation of resonant tunneling came from a double-barrier made of GaAs-GaAlAs grown by molecular beam epitaxy.1 This experiment in fact also served as the first demonstration that prescribed, man­made quantum states can be formed in ultra thin semiconductor heterostructures. Subsequent measurements followed immediately both to substantiate the resonant energies by use of different well widths2 and to extend resonant transport to superlattices.3

The idea of resonant tunneling, of course, has a much longer history. The Kronig-Penny model of a one-dimensional crystal contains a series of potential bar­riers and wells, in which resonant transmission results in allowed and forbidden en­ergy bands. The situation of a double-barrier was considered theoretically by use of both WKB approximation4 and transfer matrix formalism,5.6 describing various topics related to resonant conditions, linewidths and lifetimes. But it was recognized all along that, while the physics involved in resonant tunneling was undoubtedly in-

ResoniJnl Tunneling in Semiconductors Edited by L.L. Chang et ai .. Plenum Press, New York. 1991

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teresting, the main challenge lay in its experimental realization. Vertical transport perpendicular to the heterostructure layers usually demands the utmost in material and structural perfection, particularly at the interfaces. The stringent requirements in fact were largely responsible for the relatively few activities in this area,? even af­ter its initial observation. In comparison, parallel transport and optical experiments are generally more forgiving in terms of interface defects.

With continuous progress in materials and ever expanding interest in quantum heterostructures, the pace in resonant tunneling eventually accelerated and indeed exploded. Much improved current-voltage characteristics were achieved, and reso­nance was demonstrated in structures made of different materials and configurations. The observation of fast tunneling response was of particular importance,S as it aroused great interest in high-frequency devices and, related to that, earnest dis­cussions of the mechanisms of resonant tunneling.9 The report of resonance of holes in the valence band led to a large number of investigations of band-structure effects on the tunneling process. to Research efforts also expanded in different directions, including multiple-barrier structures, low-dimensional systems, optical and dynamic studies, and device schemes for various applications. The field of resonant tunneling has been established as a result of all these efforts, and today it is being enthusi­astically pursued worldwide in both academic and industrial laboratories. In view of the voluminous publications in the literature, we can only give here a brief account of some of the most important developments.

MATERIALS AND CONFIGURATIONS

Research activities in quantum heterostructures started with the material sys­tem of GaAs-GaAlAs. The current-voltage characteristics of a double-barrier, as shown in Fig. 1, demonstrate not only the formation of quantum states but their manifestation in controlling the transport properties. t Resonant electron trans­mission occurs when its energy coincides with that of the state, resulting in destruc­tive wave interference and perfect electron penetration. The inherent width of the resonant peak r 0 is governed by fjj 'To' where 'To is the lifetime associated with the state. To calculate the current, the transmission coefficient is integrated over the Fermi energy in the electrode, subject to the conservations of energy and parallel momentum. The Fermi energy is usually wide in comparison with the inherent width of the quantum state so that, under applied voltages, the current starts with the state coinciding with the Fermi level and ceases when the state is aligned with the con­duction band edge. In Fig. 1, the two resonances associated with the two states are clearly observable, as indicated at (a) and (c). That the two barriers are similar lead to symmetrical characteristics with voltages at resonance equal to twice that of the state energies.

One of the important features of double-barrier tunneling is its flexibility in terms of structural parameters, materials and configurations. For GaAs-GaAlAs, extensive investigations were carried out by varying both the well and barrier widths and compositions. Sharp negative-resistance characteristics were observed even at room temperature. 11 Double-barriers of a variety of materials beyond GaAs were also achieved, including in particular InGaAs wells because of its desirable wave­length in communication applications. Different barrier materials were used for dif­ferent purposes, such as GaSbAs as mentioned earlier,? and InP, GaAlAs and

0.3 0.9

dl/dV-

0.2 0.6

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-0.2 (b)~ 0.68

-0.3 (e) Jir\ -0.9

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Figure 1. Tunneling characteristics of a GaAs-GaAlAs double-barrier to identify the quantum states at resonance as shown in (a) and (c). (After Ref. 1)

InAlAS. 12•13 Direct energy gap with a relatively light electron mass in the last alloy made it desirable to produce a large peak-to-valley current ratio, an important con­sideration for device performance. More recently, the interesting polytype heterostructure of InAs-GaSb-AlSb was explored for double-barrier tunneling. 14

With InAs well and GaSb electrodes, the unusual situation of band-gap separation of these two semiconductors 7 leads to extremely sharp negative-resistance. The transport process is a combination of resonance and interband tunneling.

While square quantum well is used in most experiments, obviously it can as­sume any shape in principle as long as proper quantum states can be created for tunneling enhancement. One interesting example is a parabolic well. The energy spacings of the states are equal in this case, and a large number of resonances were detected. 15 Another interesting configuration in which resonant tunneling was ob­served relates to a doping heterostructure. 16 In a p-n-p structure, electrons flow be­tween the valence band in the p-regions with the resonant levels provided by the n-Iayer in the conduction band. This represents another case of resonance involving interband tunneling.

BAND STRUCTURE EFFECTS

While the tunneling behavior can simply be modelled with parameters such as a barrier height and an effective mass for energies associated with the fundamental gap for both the wells and barriers, the effect of the band structure must in general be taken into account. The first example of such an effect dealt with the complex valence band in connection with hole tunneling. Figure 2 shows the conductance of a GaAs-AlAs double-barrier under a magnetic field. lO The primary origin of the carriers can be identified by studying the temperature dependence, as the light holes usually result in a more pronounced current. The application of a magnetic field is also helpful for this identification, since it varies the energy of the resonant states,

3

4

which is inversely proportional to the mass. It is clear from Fig. 2 that the various resonant features depend on the magnetic field in a complex manner, indicating the strong effect of band mixing between the heavy and light holes.

This initial experiment generated great interest in studies in hole tunneling both theoretically and experimentally. The Si-SiGe system represented a notable case that was extensively pursued under lattice-matched as well as strained conditions,17·18 Theoretical calculations were carried out to include the mixing effect,19,20 and the results, by summing all the incoming states and outgoing channels of the heavy and light holes, largely reproduced the observed tunneling spectra. Meanwhile, the field of resonant magneto-tunneling was opened up for both electrons and holes. With a magnetic field perpendicular to the layers, Landau levels were created for states both in the well and the electrodes. The conservation of parallel momentum in this case translates into that of the Landau level index, leading to an oscillating current in re­flection of the density of states.21 The field was also applied in the parallel direction with the effect of reducing the magnitude of the peak current and increasing its broadening.22 The most significant result was that it provided a way to deduce the energy-momentum dispersion which, in the case of holes, showed directly the mixed states in the layer plane.22,23

The effect of the band structure also comes into play when critical valleys other than the r - valley become important in influencing the tunneling process. A specific example is the use of high AI-composition in GaAlAs so that the X- valley provides the lowest barrier in energy. A similar situation can be realized with the application of a hydrostatic pressure. Experiments of this kind led to conclusions regarding the nature of the resonant state and non-resonant current in terms of the different val­leys.24 At higher voltages in the current characteristics, additional resonant states may be formed and brought into the energy range of interest for tunneling. In this connection, X- states above the barrier and r - states in the continuum were ob­served,17, 25 We should point out that the effect of r -X mixing and interaction is rather complex. It is a topic of broad interest that requires vigorous treatment,26,27

~ B=OT z ~ g o z o u

-0.5 -1.0 VOLTS

-1.5

T=1.5K

-2.0

Figure 2. Tunneling conductance of holes in a GaAs-AlAs double-barrier under a perpendicular magnetic field with respect to the layers. (After Ref. 10)

particularly in areas involving interface problems, indirect materials and short-period heterostructures.

DYNAMIC EFFECTS

Tunneling is usually considered an extremely fast process. The time it takes for electrons to tunnel through a barrier, a subject of extensive discussion in the litera­ture,28 can be much faster than picoseconds in typical cases. With a double-barrier, the lifetime of the states is the crucial parameter, which is expected to be related to the accumulation and escape time of carriers in the well. Experimentally, the initial experiment of mixing and detection with infrared lasers indicated that a double­barrier can respond to frequencies in the terahertz range.8 This is illustrated in Fig. 3 where the response at the high frequency is shown to compare favorably with that derived from the dc characteristic. Subsequent measurements of microwave oscil­lations further demonstrated frequency operations beyond tens of gigahertz.29 More recently, direct switching experiment by electro-optic sampling revealed a rise time of a few picoseconds.3o All these results are consistent with theoretical estimates of the limit in the frequency domain,31,32 pointing to the capability of double-barrier diode as one of the fastest high-speed electronic devices.

The original observation of the high-frequency response also promoted the question with regard to the origin of the negative resistance or, more generally, the mechanism of resonant tunneling.9 In the presence of scattering, the electrons may not be able to tunnel coherently, analogous to the situation of a Fabry-Perot resonator, but suffer severe scattering events to lose their phase memory and tunnel through the two barriers in sequence. The relevant parameter is the scattering time 'T s relative to the lifetime 'To' as mentioned earlier. Since in any resonant process the inverse resonant width sets the time scale, sequential transmission becomes impor­tant when 'T s < 'To or r s > r 0' 33 where r s is given by Ii! 'T s' similar to r 0 defined be­fore. In GaAs systems, sequential tunneling usually plays an essential role; the

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-0.48 -0.24 o VOLTS

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Figure 3. Current response of a GaAs-GaAlAs double-barrier measured from both dc and ac conditions to show the general agreement. (After Ref. 8)

5

6

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Figure 4. Temporal evolution of photoluminescence decay of GaAs-AlAs double­barriers with different well widths and measured at different temperatures. (After Ref. 37)

coherent part tends to prevail only in structures with thin barriers and, of course, low scattering rate. The tunneling current near resonance, obtained usually at relatively high voltages by integrating over the wide Fermi energy, is insensitive to the scat­tering process as long as the width of the resonant state is small.34,35 The question of coherent versus sequential tunneling has been extensively discussed in the litera­ture.36

Unlike earlier experiments which were largely confined in transport properties, recent work shifted to optical as well as electro-optical measurements, particularly time-resolved measurements to probe directly the dynamic behavior of the tunneling process. The first work of this kind, as shown in Fig. 4, was to generate photo­carriers in a quantum well and monitor the time decay of the photoluminescence.37 With structures of thin barriers, the electron escape time at low temperatures was shown to vary exponentially with the barrier thickness, consistent with that expected from the width of the resonant state. A large number of experiments have since been performed, including luminescence, photocurrent and absorption. Usually, an asymmetrical double quantum well was used to create states at proper energies. By applying an electric field to change the alignment of the states and observing simul­taneously the decay rates of relevant luminescence, tunneling rates at or off reso­nance can be obtained under proper conditions.38,39 The results must be analyzed with care because of the complexity of the process, which involves carrier relaxation and recombination, and tunneling of both electrons and holes.

Relevant to the process of tunneling, as mentioned above, is carrier accumu­lation or build-up inside the well. The initial observation of this phenomenon came from that of the bistability in the current-voltage characteristic,40 as shown in Fig. 5, where the bistability is marked by arrows. It arises as a result of dynamic electron storage in the well, leading to the creation of a space-charge layer. The electrostatic feedback then produces a hysteresis whose width depends on the magnitude of the

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...... 0.6 « E ~

!z 0.4 IIJ a: a: a 0.2

0.01---­o 0.2 0.4

VOLTS 0.6

Figure 5. Current-voltage characteristic of a GaAs-GaAlAs double-barrier to illus­trate the intrinsic bistability as indicated by arrows. (After Ref. 40)

accumulated electronic charge. That the bistability is intrinsic to the double-barrier tunneling was confirmed by use of asymmetrical barriers for its enhancement or re­duction.40,41 Recently, both photoluminescence and magneto-photoluminescence were used to investigate these effects.42,43 By examining the integrated intensity and line shape as a function of voltage, both the accumulated charge and the time scale were deduced; the latter being consistent again with that from the width of the res­onant state.

MULTIPLE-BARRIER SYSTEMS

Resonant tunneling in a double-barrier structure represents the simplest case, as mentioned earlier. Similar resonance with a triple-barrier, for example, was in­vestigated both theoretically and experimentally.6,44 The voltage distribution in these situations, however, may be complex and has to be properly taken into account. For a multiple-barrier system like a superlattice, resonant transport of electrons was ob­served at the very early stage,3 as shown in Fig. 6. There are two important points in connection with this result. One is the presence of the initial negative-resistance, which arises as the field gradually induces Stark localization, resulting in a reduction in current. The subband conduction breaks down in the limit when the energy dif­ference per period becomes comparable to the band width, eFd ~ r o' The other point relates to the subsequent oscillation in current or conductance versus the ap­plied voltage. Since the breakdown in band conduction is expected to occur in a lo­calized region, caused by fluctuations and defects, a high-field domain is created in the region. With increasing voltages, other domains are successively formed and expanded in space, giving rise to a periodic current as electrons proceed via tunneling and relaxation, as schematically indicated in the inset of Fig. 6. The presence of the high-field domains was recently observed and identified from photocurrent spectroscopy.45

A variety of configurations based on a similar process have been investigated. An interesting case was the introduction of a distinctly different barrier, separating two superlattice regions between which tunneling occurs.46 Recent experiments demonstrated further the remarkable observation of Stark states that form the finite

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Figure 6. Current and conductance characteristics of a GaAs-AlAs superlattice where electron transport proceeds from subband conduction (a) to localized tunneling (b) and (c). (After Ref. 2)

superlattice subband at rather low fields.47 Also, resonant tunneling was shown in double-barrier structures in which a superlattice was used instead of an alloy as the barrier.48 In a separate development, the multiple-barrier structure was incorporated in a p-i-n junction, where resonant transport was observed for optically generated carriers.49 Measurements of photocurrents exhibited well-defined peaks at energies corresponding to tunneling between ground and excited states in adjacent quantum wells.

It is worth noting the relation between the localization-induced negative­resistance with that predicted originally on the basis of electron deceleration due to energy dispersion. 50 The condition for it to occur in this case, as electrons scatter toward the superlattice zone boundary, can be written as eFd ~ f. with f. = lihs as defined earlier. The negative-resistance observed at the very beginning of the superlattice was interpreted on this basis.51 The negative differential velocity ob­tained from microwave experiments was also explained similarly. 52 Very recently, it was argued that the two mechanisms for current reduction are physically equivalent. 53

LOW-DIMENSIONAL SYSTEMS

Tunneling in double-barriers usually proceeds between three-dimensional electrodes through a resonant state which is two-dimensional in nature. Under proper interface and bias conditions, a two-dimensional layer may be formed in the space-charge region of the emitter electrode adjacent to the barrier. Tunneling be­tween two regions of two-dimensional systems shows a rather peculiar behavior: Electrons can flow only at a singular voltage to satisfy the conservation of parallel momentum. This voltage corresponds to the energy difference between the two states, and it becomes zero for a symmetrical structure. With a double barrier of

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GaAs-AlAs under hydrostatic pressure, a sharp feature near zero bias was observed, which was interpreted as tunneling between two-dimensional states in AlAs through GaAs as defined by the X-valley potential profile. 54 Further studies under a magnetic field were carried out in specially designed structures having the barrier sandwiched between an inversion and accumulation layer.55 Tunneling between different Landau levels was detected, violating the momentum conservation. Increased electron scat­tering by the field, applied perpendicularly to the layer plane in this case, was pre­sumably the cause for this violation. There is currently a growing interest in tunneling between electron systems of different dimensionalities. In general, singularities in the current-voltage characteristic will be present for systems lower than three-dimensional, if the law of parallel momentum conservation is strictly fol­lowed. For three-dimensional electrodes, the tunneling current as a function of voltage also shows a variety of behaviors, depending on the resonant state being two-, one- or zero-dimensional in nature. 56

One of the most remarkable observations involving low-dimensional systems was that of tunneling in resonance with states in a zero-dimensional structure or quantum dot. 57 Recent advancement in lithography and etching techniques has made it possible to provide additional energy confinement in the lateral directions in the plane to form both quantum wires and dots. Figure 7 shows the current-voltage characteristics of a single dot as a function of temperature. The arrows indicate the peak voltage positions corresponding to the additional levels from lateral quantization. The peaks arise as the one-dimensional states in the emitter align with the zero-dimensional states in the well, involving both momentum conserving and non-conserving transitions. But the most prominent peak, which persists even at the high temperatures as seen in Fig. 7, is due to the ground states resonance with mo­mentum conservation.

Laterally confined structures have drawn great attention lately. Metallized patterns with properly applied gate voltages, instead of etching, create conducting

Figure 7. Tunneling characteristics of a GaAs-GaAlAs quantum dot as a function of temperature to show resonance with zero-dimensional states, as indicated by ar­rows. (After Ref. 57)

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and depleted regions in the plane of a two-dimensional electron system,58 where transport can be studied under various conditions of energy quantization, geometric restrictions, ballistic injection and electron focussing. Using a dual gate, a surface double-barrier was formed, and negative-resistance characteristics were observed and interpreted on the basis of resonant tunneling. 59 Additional features appeared under illumination, which were ascribed to possible resonance with impurity-related deep states. Indeed, similar resonance was also detected in tunneling through a single barrier.60 The resonance in this case was postulated to be due to bound states in the barrier associated with isolated coulombic sites. In a separate experiment, a square dot region was surrounded by a thin gate from the outside electrodes. The conductance under proper conditions exhibits resonant features, reflecting the zero­dimensional energy states.61

DEVlCESTRUCTURES

The combination of the fast tunneling process and the presence of a negative­resistance led immediately to possibilities of device applications. Indeed, the earlier observation of the extremely rapid response of a double-barrier paved the way for the demonstration of quantum-well oscillators.8,29 High-frequency oscillators still remain perhaps the most advanced and the best developed device, utilizing resonant tunneling. With a proper choice of the structural parameters and a better under­standing in circuit modelling, the frequency of the fundamental oscillation has reached beyond a few hundred gigahertz with a power in excess of a fraction of a microwatt. 62 These numbers were further improved recently with the use of more desirable materials, such as InGaAs-AlAs and InAs-AlSb. They provide a low series resistance, a high current density and a high peak-to-valley ratio; all being favorable to the performance of double-barrier oscillators.

It is always desirable, for device applications, to have three-terminal operation. There have been various schemes in which a resonant-tunneling double-barrier structure can be incorporated into different regions in a transistor. The first exper­imental demonstration of this kind was to institute such a structure between the emitter and the base,63 as shown in Fig. 8. Electrons are injected from the emitter

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120 ~ .:( EMITTER BASE =1. ~ 80 :t COLLECTOR

40

0.1 0.2 0.3 0.4 0.5 VeE (V)

Figure 8. Collector current as a function of emitter-base voltage in a GaAs-GaAlAs transistor structure where a double-barrier is incorporated to control electron in­jection. (After Ref. 63)

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to the base by resonant tunneling to result in a peaked collector current character­istic, which depends primarily on the base voltage with respect to the emitter. Fre­quency multiplication and logic function were shown to be possible in circuits with this device. Another example was to have the double-barrier in the base region of a bipolar transistor,64 exhibiting common-emitter characteristics with large current in logic swings and negative-resistance effect.65 The resonant tunneling diode has also been integrated with a field-effect transistor.66 The negative-resistance now appears in the source-drain curve, that is controllable with a gate bias. In general, a three­terminal transistor with a double-barrier can be used as amplifiers, signal processors, switching and logic devices, and it can perform these functions with fewer number of devices.

Instead of its incorporation in a transistor structure, a three-terminal device can also be implemented in a double-barrier itself by attaching a third electrode to the quantum well between the two barriers. It is interesting in this connection to observe the similarity between a double-barrier structure and what has long been known as a hot-electron transistor. The latter device has many variations; its heterojunction version with a tunneling emitter has essentially the same configuration as a double­barrier, with the exception that the barriers are typically asymmetric and the width of the quantum-well base is relatively thick. Such structures have been exper­imentally realized with a good transfer efficiency.67 As the base width shrinks, reso­nant tunneling with both bound and virtue states in the well has been observed.68

CONCLUDING REMARKS

It has been nearly twenty years since the first observation of the phenomenon of resonant tunneling. The field has attracted extensive interest, particularly in re­cent years, which led to a multi-disciplinary effort in research with a coverage of materials, physics and devices. In this work, we have given but a brief summary re­view, focussing on some of the key observations that highlight the development of the field, as we know it today.

The field has clearly grown out of its infant stage and reached a degree of ma­turity. In the coming period, while most of the areas will continue to expand, four are expected to provide the most thrust: new materials and configurations, including semiconductors with unusual properties and band structures; low-dimensional, small structures, in accordance with intensive current interest in mesoscopic systems; dy­namic processes and properties, which lie in the very heart of resonant tunneling where many issues still remain; and device inventions and implementations, which will draw increasingly large attention as the field becomes more matured and estab­lished. Resonant tunneling will continue to offer tremendous scientific and techno­logical opportunities.

ACKNOWLEDGEMENT

I would like to express my thanks to many of my colleagues at ffiM, in partic­ular, L. Esaki and E. E. Mendez with whom I have been working together on reso­nant tunneling over the years, and to many of my colleagues outside, who have made available to me their preprints related to this work. I would like also to acknowledge the sponsorship of this work by the Army Research Office.

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36. M. Buttiker, "Coherent and Sequential Tunneling in Series Barriers", IBM J. Res. Develop., 32,63 (1988); also this volume.

37. M. Tsuchiya, T. Matsusue and H. Sakaki, "Tunneling Escape Rate of Electrons from Quantum Well in Double Barrier Heterostructures", Phys. Rev. Lett., 59, 2356 (1987).

38. T. B. Norris, N. Vodjdani, B. Vinter, C. Weisbuch and G. A. Mourou, "Charge-Transfer-State Photoluminescence in Asymmetric Coupled Quantum Wells", Phys. Rev. B40, 1392 (1989).

39. D. Y. Oberli, J. Shah, T. C. Darnen, C. W. Tu, T. Y. Chang, D. A. B. Miller, J. E. Henry, R. F. Kopf, N. Sauer and A. E. DiGiovanni, "Direct Measurement of Resonant and Nonresonant Tunneling Times in Asymmetric Coupled Quantum Wells", Phys. Rev. B40, 3028 (1989).

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40. V. J. Goldman, D. C. Tsui and J. E. Cunningham, "Observation of Intrinsic Bistability in Resonant Tunneling Structures", Phys. Rev. Lett. 58, 1256 (1987); also Solid State Electron. 31,731 (1988).

41. M. L. Leadbeater, E. S. Alves, L. Eaves, M. Henin, O. H. Hughes, F. W. Sheard and G. A. Toombs, "Charge Build-Up and Intrinsic Bistability in an Asymmetric Resonant-Tunneling Structure", Semicond. Sci. Technol. 3, 1060 (1988).

42. J. F. Young, B. M. Wood, G. C. Aers, R. W. S. Devine, H. C. Liu, D. Landheer, M. Buchanan, A. L. Springthorpe and P. Mandeville, "Determination of Charge Accumulation and Its Characteristic Time in Double-Barrier Resonant Tunneling Structures Using Steady-State Photoluminescence", Phys. Rev. Lett. 60,2085 (1988).

43. D. G. Hayes, M. S. Skolnick, P. E. Simmonds, L. Eaves, D. P. Halliday, M. L. Leadbeater, M. Henini and O. H. Hughes, "Optical Investigation of Charge Accumulation and Bistability in an Asymmetric Double-Barrier Resonant Tunneling Heterostructure", Surf. Sci., 228, 373 (1990).

44. T. Nakagama, H. Imamoto, T. Kojima and K. Ohta, "Observation of Resonant Tunneling in AlGaAs/GaAs Triple Barrier Diodes", Appl. Phys. Lett. 49, 73 (1986).

45. H. T. Grahn, H. Schneider and K. v. Klitzing, "Optical Detection of High-Field Domains in GaAs/ AlAs Superlattices", Appl. Phys. Lett. 54, 1757 (1989).

46. R. A. Davies, M. J. Kelly and T. M. Kerr, "Tunneling Between Two Strongly Coupled Superlattices", Phys. Rev. Lett. 55, 1114 (1985).

47. R. J. Aggarwal, M. A. Reed, W. R. Frensley, Y. C. Kao and J. H. Luscombe, "Tunneling pectroscopic Study of Finite Superlattices", Appl. Phys. Lett. 57, 707 (1990).

48. M. A. Reed and J. W. Lee, "Resonant Tunneling in Double Superlattice Barrier Heterostructures", Superlattices and Microstructures, 3, 111 (1987).

49. F. Capasso, K. Mohammed and A. Y. Cho, "Sequential Resonant Tunneling Through a Multiquantum-Well Superlattice", Appl. Phys. Lett. 45,478 (1986).

50. L. Esaki and R. Tsu, "Superlattice and Negative Differential Conductivity in Semiconductors", IBM J. Res. Develop. 14,65 (1970).

51. L. L. Chang, L. Esaki, W. E. Howard and R. Ludeke, "The Growth of a GaAs-GaAlAs Superlattice", J. Vac. Sci. Technol. 10, 11 (1973).

52. A. Sibille, J. F. Palmier, H. Wang and F. Mollot, "Observation of Esaki-Tsu Negative Differential Velocity in GaAs/ AlAs Superlattices", Phys. Rev. Lett. 64,52 (1990).

53. F. Beltram, F. Capasso, D. L. Sivco, A. L. Hutchinson, S. G. Chu and A. Y. Cho, "Scattering-Controlled Transmission Resonances and Negative Differential Conductance by Field-Induced Localization in Superlattices", Phys. Rev. Lett. 64,3167 (1990).

54. E. E. Mendez and L. L. Chang, "Tunneling Between Two-Dimensional Electron Gas", Surf. Sci. 229, 173 (1990).

55. W. Demmerle, J. Smoliner, G. Berthold, E. Goruik, G. Weimann and W. Schlapp, "Magneto-Tunneling Between Barrier-Separated 2D Electron Gas Systems", Surf. Sci. 229, 169 (1990).

56. H. C. Liu and G. C. Aers, "Theory of the Vertical Transport Through One, Two and Three Dimensionally Confined Quantum Wells", Solid State Commun. 67, 1131 (1988); also J. Appl. Phys. 65,4908 (1989).

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57. M. A. Reed, J. N. Randall, R. J. Aggarwal, R. J. Matyi, T. M. Moore and A. E. Wetsel, "Observations of Discrete Electronic States in a Zero-Dimensional Semiconductor Nanostructure", Phys. Rev. Lett. 60,535 (1988).

58. T. J. Thornton, M. Pepper, H. Ahmed, D. Andrews and G. J. Davies, "One­Dimensional Conduction in the 2D Electron Gas of a GaAs-AlGaAs Heterojunction", Phys. Rev. Lett. 56, 1198 (1986).

59. s. Y. Chou, D. R. Allee, R. F. W. Pease and J. S. Harris, "Observation of Electron Resonant Tunneling in a Lateral Dual-Gate Resonant Tunneling Field-Effect Transistor", Appl. Phys. Lett. 55 177 (1989).

60. T. E. Kopley, P. L. McEuen and R. G. Wheeler, "Resonant Tunneling Through Simple Electronic States and Its Suppression in a Magnetic Field", Phys. Rev. Lett. 61, 1654 (1988).

61. C. G. Smith, M. Pepper, H. Ahmed, J. E. F. Frost, D. G. Hasko, D. C. Peacock, D. A. Ritchie and G. A. C. Jones, "The Transition From One- to Zero­Dimensional Ballistic Transport", J. Phys. C21, L893 (1988).

62. E. R. Brown, W. D. Goodhue and T. C. L. G. Sollner, "FundamentaIOscil­lations up to 200 GHz in Resonant Tunneling Diodes and New Estimates of Their Maximum Oscillation Frequency from Stationary-State Tunneling Theory", J. Appl. Phys. 64, 1519 (1988); also T. C. L. G. Sollner, et al. in this volume.

63. N. Tokoyama, K. Inamura, S. Muto, S. Hiyamizu and H. Nishi, "A New Func­tional, Resonant-Tunneling Hot Electron Transistor", Jpn. J. Appl. Phys. 24, L853 (1985).

64. F. Capasso and R. A. Kiehl, "Resonant Tunneling Transistor with Quantum Well Base and High Energy Injection: A new Negative Differential Resistance Device", J. Appl. Phys. 58, 1366 (1985).

65. F. Capasso, S. Sen, A. C. Gossard, A. L. Hutchinson and J. H. English, "Quantum-Well Resonant Tunneling Bipolar Transistor Operating at Room Temperature", IEEE Electron Device Lett. 7, 573 (1986).

66. T. K. Woodward, T. C. McGill and R. D. Burnham, "Experimental Realization of a Resonant Tunneling Transistor", Appl. Phys. Lett. 50,451 (1987).

67. N. Yokoyama, S. Inamura, T. Ohshima, H. Nishi, S. Muto, K. Kondo and S. Hiyamizu, "Tunneling Hot Electron Transistor Using GaAs/ AIGaAs Heterojunctions", Jpn. J. Appl. Phys. 23, L311 (1984).

68. M. Heiblum, M. V. Fischetti, W. P. Dumke, D. J. Frank, I. M. Anderson, C. M. Knoedler and L. Osterling, "Electron Interference Effects in Quantum Wells: Observation of Bound and Resonant States", Phys. Rev. Lett. 58, 816 (1987).

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