Journal of the Korean Physical Society, Vol. 39, No. 3, September 2001, pp. 522∼528 Manipulating Resonances and Electron Confinement in Quantum Barriers Chang Sub Kim ∗ Department of Physics, Chonnam National University, Kwangju 500-757 Arkady M. Satanin and Valerie B. Shtenberg Department of Theoretical Physics, Nizhny Novgorod University, N. Novgorod 603091, Russia Hyun-Woo Lee School of Physics, Korea Institute for Advanced Study, Seoul 130-012 (Received 9 November 2000) Coherent transport in the electron resonant-tunneling problem through GaAs/AlxGa1-xAs/ GaAs single-barrier structures is studied theoretically. Using the effective-mass envelope-function method, taking into account Γ-X intervalley mixing, and the multichannel Fabry-Perot scheme, we construct the scattering matrix of the system. Consequently, we show that the interaction between resonances can be manipulated by continuously tuning the pressure, which results in many inter- esting coherent effects. Also, we predict that a novel quantum state can be tamed, representing the confined two-dimensional electron gas in the barrier. I. INTRODUCTION It is well-known that a transition from a direct band- gap to an indirect band-gap structure occurs as the Al mole fraction x is increased in Al x Ga 1−x As semiconduc- tors [1,2]. Accordingly, when GaAs/Al x Ga 1−x As/GaAs single-barrier heterostructures are grown along [001] di- rection, the X valley can be brought close to the central Γ band in the sandwiched region artificially, and the X band minimum can even lie below Γ band edge. If such a structure is prepared as a tunneling diode, at least two electron waves become involved in the active propagating region. This situation is distinguishable from the typi- cal double-barrier structures where the Fermi energy is tuned in the range where only a single energy valley or channel is engaged for electron transport. The importance of the role of multi-valley states in res- onant tunneling was signaled in the early experiments, for instance those in Ref. [3], where the observed nega- tive differential resistance was attributed to the presence of a quasi-bound state associated with the X-point pro- file. Naturally, many research efforts followed to under- stand the complex feature of the multi-channel tunnel- ing problem in the similar single-barrier structures both theoretically and experimentally [4–11]. Since the bound levels supported by the X well interact with the Γ energy * E-mail: cskim@statphys.chonnam.ac.kr continuum, the resulting resonant structure turns out to be somewhat special: Instead of showing the symmetric Lorentzian shape that is usual in double-barrier struc- tures, what is known as the Fano structure, having the paired asymmetric peak and close-by antiresonance, ap- pears [12]. In most previous studies, however, attention was paid to the electron transmission or to the resonant-tunneling current for a prepared structure with fixed system pa- rameters. There were a few exemptions where a wide range of Al composition or the barrier width was con- sidered in studying transport through the single-barrier structures experimentally [2,9]. Even so, the resulting observations are still specific to the chosen Al composi- tions or the barrier widths since they cannot be varied continuously. On the other hand, it is anticipated that many interesting coherent interference effects may result in as the system is deformed continuously. In fact, the present authors have reported recently that the contin- uous tuning of the system parameters induces collision between resonances, which in turn brings about novel coherent effects in transmission resonances in different mesoscopic structures [13,14]. In this paper, we choose the pressure as a continu- ous external parameter and study the coherent interefer- ence effects that arise in multi-wave GaAs/Al x Ga 1−x As/ GaAs single-barrier structures. Since the electron wave- function varies slowly on the lattice constant scale, we use the envelope function approach generalized to include -522-