Superlattices and Microstructures. Vol. 5, No. 3, 7989 375 COHERENT VERSUS INCOHERENT RESONANT TUNNELING AND IMPLICATIONS FOR FAST DEVICES Serge Luryi AT&T Bell Laboratories, Murray Hill, NJ 07974, USA (Received 8 August 1988) Physics of resonant tunneling (RT) in quantum-well structures is reviewed, emphasizing the difference between the truly coherent tunneling, analogous to the resonant transmission through a Fabri-Perot Ctalon in optics, and the sequential processes, in which the phase of electron wave function is destroyed between two tunneling steps. Several proposals and experimental demonstrations of three-terminal RT configurations are also discussed. In addition to a negative differential resistance in their output circuit, most RT transistors exhibit a negative transconductance, a feature which can lead to the implementation of various high-speed junctiona logic devices. 1. Introduction Resonant tunneling (RT) in double-barrier (DB) quantum-well (QW) structures had been originally proposed and discussed as an electron wave phenomenon analogous to the resonant transmission of light through a Fabry-Perot &talon. A discussion of the historical development of these ideas and references to the early work can be found in my recent review.’ Considering an electron at energy E incident on a one-dimensional DBQW structure (Fig. l), one finds that when E matches one of the energy levels Ei in the QW, then the amplitude of the electron de Broglie waves in the QW builds up due to multiple scattering and the waves leaking in both directions cancel the reflected waves and enhance the transmitted ones. Near the resonance one has 4TrT’z 2 T(E) = (T, +T2)2 (E-E,)2 + y2 where T, and T2 are the transmission coefficients of the two barriers at the energy E =Ei and y E h/r is the lifetime width of the resonant state [quasi-classically, y = Ei(TI +T,)]. In the absence of scattering, a system of two identical barriers ( T 1 = T2 ) is completely transparent for electrons entering at resonant energies, and for different barriers the peak transmission is proportional to the ratio T,i,/ T,, , where Tmin and T,, are respectively the smallest and the largest of the 0749%6036/89/030375+08 $02.00/O coefficients T1 and T2. The total transmission coefficient, plotted against the incident energy has a number of sharp peaks, as shown in Fig. 1. For a one-dimensional system, the connection between the transmission coefficient and the electrical resistance R of the DBQW system clad by two electron reservoirs at different chemical potentials, maintained by an external bias, is established by the well-known Landauer formula, R-’ = (e2/ri) T(EF), which can also be extended to the three-dimensional case via its multi-channel generalizations. A lucid discussion of this approach to RT can be found in the recent paper? by Biittiker. Several years ago, I had argued3 that the experimentally observed negative differential resistance (NDR) in DBQW diodes can be understood without invoking a coherent Fabry- Perot transmission resonance - but rather as a two-step process in which electrons first tunnel from the emitter electrode into the quasi-bound state in the QW, and then from the well into the collecting electrode. Between these two steps the electron phase memory may be completely lost. For a detailed discussion of the sequential mechanism of operation of RT diodes the reader is referred to the review.’ In three-dimensional DBQW diodes, the NDR arises solely as a consequence of the dimensional confinement of states in a QW, and the conservation of energy and lateral momentum in 0 1989 Academic Press Limited