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Ballistic Transport
Solid-State Electronics Vol. 31, No. 3/4, pp. 617 618, 1988
0038-1101/88 $3.00+0.00 Pergamon Journals Ltd
Printed in Great Britain
Ballistic Transport
M. Heiblum IBM, Thomas J. Watson Research Center, Yorktown Heights, N. Y. 10598
"Ballistic transport" is defined as the smooth motion of carriers without any elastic or inelastic scattering events. In a solid, one can almost completely remove inelastic events by staying as close as possible to equilibrium at 0 K. This is simply due to the absence of empty states the carriers can scatter into. The nature of the transport is then determined, indirectly, via low field mobility measurements and quantum interference effects (such as reproducible voltage fluctuations). However, when transport far from equilibrium takes place, as occurring in high speed devices, "hot carriers" can scatter inelastically due to the abundance of empty states at lower energies. Here, the realization of ballistic transport is more difficult, however, it turns out that it is easier to detect it directly and unambiguously. To do just that, a "well prepared" hot electron distribution is needed. Such a distribution can be easily prepared with a tunnel junction injector, placed at the input of a thin transport region where ballistic transport is to occur. This injected distribution has a bell shape some 60 meV wide for a case of a tunnelling barrier injector with a 0.3 eV barrier height and about 10 nm barrier thickness (the case in a GaAs-A1GaAs-GaAs injector structure). At the end of the transport region a spectrometer analyzes the energy distribution of the current. By comparing the output and input distributions one can say: (a) Whether the distributions had broadened after traversing longer transport regions - indicative of the existence of small angle elastic scatterings, (b) Whether the detected distribution peaks moved to lower energies - indicative of inelastic or large angle elastic scatterings, and lastly in the case of ballistic transport, (c) The fraction of the injected current that traversed the transport region ballistically. We have utilized the Tunnelling Hot Electron Transfer Amplifier (THETA) device to inject and energy analyze hot electrons. Heavily n type doped transport regions - the base of the THETA devices - with thickness in the range 30-110 nm, were confined between the tunnel injector barrier on one side and a thick A1GaAs spectrometer barrier (60-100 nm thick) on the other side. By performing spectroscopy (changing the barrier height of the spectrometer barrier via an external voltage and thus scanning through the electron distribution) in devices with 30 nm base width, we have measured ballistic distributions, 60 meV wide, with peaks at energies near the Fermi level of the injector (emitter). Spectroscopy done in devices with longer transport regions (up to 80 nm) resulted with similar distribution widths, however, with smaller fractions of ballistic electrons arriving at the end of the transport regions. The largest ballistic fractions measured were about 75%, traversing devices with 30 nm wide base and n type doped to a level of 7 x 10 '7 cm-< Since the distributions didn't get any broader in devices with longer transit regions, it is reasonable to believe that small angle elastic scattering are absent. The scattered electrons thermalized most likely by some inelastic processes involving the equilibrium electrons in the base (such as electron-electron and electron-plasmons). The confinement of the thin transport regions (between the injector and spectrometer barriers) quantizes the residing equilibrium and the traversing non-equilibrium electrons in the base, thus modifying the kinematics (via possible interference effects) and the dynamics (the scattering processes) of the electrons traversing the base. Even though a detailed study of the dynamics was not done yet, it is reasonable to believe that the quasi two dimensional behavior of the electron gas in the base, with wave vector mostly in the plane of the layer, will lead to a smaller scattering cross section with the traversing hot electrons with their wave vector mostly perpendicular to the base layer. Indeed we find mean free paths in the range of 80-100 nm for hot electrons with 0.25 eV kinetic energy; mfp's considerably greater than simple calculations done for bulk material predict. Kinematically (ignoring scattering), the ballistic electrons are reflected back by strong potential changes and interfere coherently among themselves. These effects are prominent when the the width of the confined transport regions are on the same order of magnitude as the ballistic electron wavelength. Then, new energy subbands are formed in the region, and these are observable when the energy separation betwezn adjacent subbands is not much smaller than the energy width of the ballistic distributions. We have observed in the THETA devices resonances in the injected hot electron currents and in the transfer ratios of the devices as a function of the injection energy. Particularly interesting were the observations of "virtual states" in the thin transport region (the states in the continuum energy range, the range above the potential height of the confining barriers). This effect is interesting since it indicates, by itself, the existence of ballistic motion. Otherwise, the scattering would most probably 'smear'
617
618
the weak enhancement in the density of states due to these unbound virtual states, and "wash out" completely the resonances in the currents. It is also interesting since at this energy range (greater than 0.3 eV) it is most difficult to study the properties of the F electrons since electrons share their population between a few energy valleys. Since tile coherent effects we observed are due only to the ballistic F electrons, we were able to "map" the F band and found a constant, first order, nonparabolicity parameter (which different from the ones commonly used), which accounted for our results in a variety of devices at the energy range of 0-0.4 eV. Other modes of spectroscopy were also utilized in the TItETA devices. One was the observation of electron transfer into the L valleys, and the other the measurement of barrier heights (in most cases equal to the band discontinuities). The fact that the L electrons have a barrier at the base-collector barrier interface has manifested itself in a clear reduction in the transfer ratios of the devices when the injection energies exceeded the F to L energy splitting (which is about 0.29 eV). This intervalley transfer was verified by the application of hydrostatic pressure on the devices and the observation of an onset of transfer occurring at lower injection energies satisfying AErL= --5.5 m e V / k b a r . In a similar fashion, the onset of the collector current (or that of the transfer coefficient) at a particular injection energy gave the potential height of the collector barrier relative to the Fermi level in the base. If we ignore possible unintentional negative charges in the collector barrier, we find a conduction band discontinuity equal to hEc~-9OOx, where A E c is the band discontinuity in meV and x < 0.37 is the A1 mole fraction in the alloy AI~Gal_~As that forms the potential barrier. The THETA device, in addition to its value in studying transport effects of hot electrons, can be a very fast device due to its short transit time, the potentially low base resistance (which can be selectively doped), and the absence of minority carriers storage effects in the base. Its main drawback today is the the relatively low transfer ratio a, or in other words, the small fraction of ballistic electrons arriving at the collector. So far we have measured a's as high as 0.9 in GaAs devices at low temperatures (with doped base). We believe that higher a's, at least 0.95, can be achieved. Provided the base could carry a sufficiently high current density (1 x 105 a/cm2), the THETA device could be a competitive high speed device. Work was done with the collaboration of I. Anderson, E. Calleja, W. Dumke, M. Fischetti, C. Knoedler, M. Nathan, L. Osterling, D. Thomas, and G. Wilson.
For an extensive list of references and a farther elaboration on the subject see: Heiblum, M. and M. V. Fischetti (1987). Ballistic Electron Transport in Hot Electron Transistors, in F. Capasso (Ed.) Topics in Current Physics, Springer-Verlag. To be published; Heiblum, M. (1986). Ballistic Transport and Electron Spectroscopy in Tunnelling Hot Electron Transfer Amplifiers (THETA), in B. K~illb~ick and H Beneking (Eds.) Electronics and Photonics~ Vol. 22, Springer-Verlag, New York. pp. 11-18.
0038-1101/88 $3.00+0.00 Pergamon Journals Ltd
Printed in Great Britain
Ballistic Transport
M. Heiblum IBM, Thomas J. Watson Research Center, Yorktown Heights, N. Y. 10598
"Ballistic transport" is defined as the smooth motion of carriers without any elastic or inelastic scattering events. In a solid, one can almost completely remove inelastic events by staying as close as possible to equilibrium at 0 K. This is simply due to the absence of empty states the carriers can scatter into. The nature of the transport is then determined, indirectly, via low field mobility measurements and quantum interference effects (such as reproducible voltage fluctuations). However, when transport far from equilibrium takes place, as occurring in high speed devices, "hot carriers" can scatter inelastically due to the abundance of empty states at lower energies. Here, the realization of ballistic transport is more difficult, however, it turns out that it is easier to detect it directly and unambiguously. To do just that, a "well prepared" hot electron distribution is needed. Such a distribution can be easily prepared with a tunnel junction injector, placed at the input of a thin transport region where ballistic transport is to occur. This injected distribution has a bell shape some 60 meV wide for a case of a tunnelling barrier injector with a 0.3 eV barrier height and about 10 nm barrier thickness (the case in a GaAs-A1GaAs-GaAs injector structure). At the end of the transport region a spectrometer analyzes the energy distribution of the current. By comparing the output and input distributions one can say: (a) Whether the distributions had broadened after traversing longer transport regions - indicative of the existence of small angle elastic scatterings, (b) Whether the detected distribution peaks moved to lower energies - indicative of inelastic or large angle elastic scatterings, and lastly in the case of ballistic transport, (c) The fraction of the injected current that traversed the transport region ballistically. We have utilized the Tunnelling Hot Electron Transfer Amplifier (THETA) device to inject and energy analyze hot electrons. Heavily n type doped transport regions - the base of the THETA devices - with thickness in the range 30-110 nm, were confined between the tunnel injector barrier on one side and a thick A1GaAs spectrometer barrier (60-100 nm thick) on the other side. By performing spectroscopy (changing the barrier height of the spectrometer barrier via an external voltage and thus scanning through the electron distribution) in devices with 30 nm base width, we have measured ballistic distributions, 60 meV wide, with peaks at energies near the Fermi level of the injector (emitter). Spectroscopy done in devices with longer transport regions (up to 80 nm) resulted with similar distribution widths, however, with smaller fractions of ballistic electrons arriving at the end of the transport regions. The largest ballistic fractions measured were about 75%, traversing devices with 30 nm wide base and n type doped to a level of 7 x 10 '7 cm-< Since the distributions didn't get any broader in devices with longer transit regions, it is reasonable to believe that small angle elastic scattering are absent. The scattered electrons thermalized most likely by some inelastic processes involving the equilibrium electrons in the base (such as electron-electron and electron-plasmons). The confinement of the thin transport regions (between the injector and spectrometer barriers) quantizes the residing equilibrium and the traversing non-equilibrium electrons in the base, thus modifying the kinematics (via possible interference effects) and the dynamics (the scattering processes) of the electrons traversing the base. Even though a detailed study of the dynamics was not done yet, it is reasonable to believe that the quasi two dimensional behavior of the electron gas in the base, with wave vector mostly in the plane of the layer, will lead to a smaller scattering cross section with the traversing hot electrons with their wave vector mostly perpendicular to the base layer. Indeed we find mean free paths in the range of 80-100 nm for hot electrons with 0.25 eV kinetic energy; mfp's considerably greater than simple calculations done for bulk material predict. Kinematically (ignoring scattering), the ballistic electrons are reflected back by strong potential changes and interfere coherently among themselves. These effects are prominent when the the width of the confined transport regions are on the same order of magnitude as the ballistic electron wavelength. Then, new energy subbands are formed in the region, and these are observable when the energy separation betwezn adjacent subbands is not much smaller than the energy width of the ballistic distributions. We have observed in the THETA devices resonances in the injected hot electron currents and in the transfer ratios of the devices as a function of the injection energy. Particularly interesting were the observations of "virtual states" in the thin transport region (the states in the continuum energy range, the range above the potential height of the confining barriers). This effect is interesting since it indicates, by itself, the existence of ballistic motion. Otherwise, the scattering would most probably 'smear'
617
618
the weak enhancement in the density of states due to these unbound virtual states, and "wash out" completely the resonances in the currents. It is also interesting since at this energy range (greater than 0.3 eV) it is most difficult to study the properties of the F electrons since electrons share their population between a few energy valleys. Since tile coherent effects we observed are due only to the ballistic F electrons, we were able to "map" the F band and found a constant, first order, nonparabolicity parameter (which different from the ones commonly used), which accounted for our results in a variety of devices at the energy range of 0-0.4 eV. Other modes of spectroscopy were also utilized in the TItETA devices. One was the observation of electron transfer into the L valleys, and the other the measurement of barrier heights (in most cases equal to the band discontinuities). The fact that the L electrons have a barrier at the base-collector barrier interface has manifested itself in a clear reduction in the transfer ratios of the devices when the injection energies exceeded the F to L energy splitting (which is about 0.29 eV). This intervalley transfer was verified by the application of hydrostatic pressure on the devices and the observation of an onset of transfer occurring at lower injection energies satisfying AErL= --5.5 m e V / k b a r . In a similar fashion, the onset of the collector current (or that of the transfer coefficient) at a particular injection energy gave the potential height of the collector barrier relative to the Fermi level in the base. If we ignore possible unintentional negative charges in the collector barrier, we find a conduction band discontinuity equal to hEc~-9OOx, where A E c is the band discontinuity in meV and x < 0.37 is the A1 mole fraction in the alloy AI~Gal_~As that forms the potential barrier. The THETA device, in addition to its value in studying transport effects of hot electrons, can be a very fast device due to its short transit time, the potentially low base resistance (which can be selectively doped), and the absence of minority carriers storage effects in the base. Its main drawback today is the the relatively low transfer ratio a, or in other words, the small fraction of ballistic electrons arriving at the collector. So far we have measured a's as high as 0.9 in GaAs devices at low temperatures (with doped base). We believe that higher a's, at least 0.95, can be achieved. Provided the base could carry a sufficiently high current density (1 x 105 a/cm2), the THETA device could be a competitive high speed device. Work was done with the collaboration of I. Anderson, E. Calleja, W. Dumke, M. Fischetti, C. Knoedler, M. Nathan, L. Osterling, D. Thomas, and G. Wilson.
For an extensive list of references and a farther elaboration on the subject see: Heiblum, M. and M. V. Fischetti (1987). Ballistic Electron Transport in Hot Electron Transistors, in F. Capasso (Ed.) Topics in Current Physics, Springer-Verlag. To be published; Heiblum, M. (1986). Ballistic Transport and Electron Spectroscopy in Tunnelling Hot Electron Transfer Amplifiers (THETA), in B. K~illb~ick and H Beneking (Eds.) Electronics and Photonics~ Vol. 22, Springer-Verlag, New York. pp. 11-18.