Collective behavior in the single-electron charging regime through classical molecular dynamics C. M. Carbonaro Istituto Nazionale di Fisica della Materia, Dipartimento di Scienze Fisiche, Universita ` degli Studi di Cagliari, Via Ospedale 72, I-09124 Cagliari, Italy R. Bertoncini Centro Richerche e Sviluppo, Studi Superiori in Sardegna, Casella Postale 1048, I-09123 Cagliari, Italy F. Meloni Istituto Nazionale di Fisica della Materia, D18-Dipartimento di Scienze Fisiche, Universita ` degli Studi di Cagliari, Via Ospedale 72, I-09124 Cagliari, Italy M. Rovere Istituto Nazionale di Fisica della Materia, Dipartimento di Fisica, Universita ` della Calabria, I-87036 Arcavacata di Rende, Italy Received 28 July 1995; revised manuscript received 28 November 1995 We studied a semiconductor quantum wire having a smooth and continuous double-barrier potential super- imposed along its length. The device is prepared at electron densities such that the interelectronic distance is bigger than the Bohr radius in GaAs. The strong Coulomb interaction between such carriers is accounted for exactly by classical molecular dynamics methods. We report the presence of charge-density-wave states as the main single-electron transport mechanism in this device. I. INTRODUCTION Mesoscopic devices with small capacitances have their operations dominated by charge-quantization phenomena whenever the charging energy associated with the addition of one electron into the structure exceeds the thermal energy. 1 These phenomena appear through periodic conductance oscillations as a function of carrier density, and are observed in devices such as metallic tunnel junctions, 2 silicon metal- oxide-semiconductor field-effect transistors 3 and GaAs/As x Ga 1 -x As heterojunctions. 4–6 Indeed, the possibility of ex- ploiting these phenomena in the fabrication of high- frequency oscillators and low-power nonvolatile memories with improved endurance characteristics 7 and operating at 1 electron/bit in contrast with the 10 4 or more of today’s flash-EEPROM’s has spurred many experimental as well as theoretical efforts towards a better understanding of the physics underlying them. In small metallic junctions, single-electron charging ef- fects have been successfully explained, within the semiclas- sical Coulomb-blockade model, by invoking tunneling through the discrete energy levels of an electron in a quan- tum well, and accounting for the Coulomb interaction by the macroscopic device capacitance. 1 In semiconductor structures, however, the various simpli- fications inherent in the Coulomb-blockade theory are no longer justified, and may lead to errors. 8 Unlike metallic sys- tems, the potential barriers in semiconductor structures are, in general, smooth and continuous, and electron transfer may be activated thermically, through a continuous energy spec- trum. This violates the basic requirement of the Coulomb- blockade formulation, for a discrete spectrum. Furthermore, in a semiconductor device, the number of carriers can be controlled by changing the gate voltage. 9 At very low electron densities, as the screening length increases, additional effects in the transport properties are likely to ap- pear because of the increased importance of the Coulomb interaction, which cannot, therefore, be accounted for by simple macroscopic-capacitance arguments. Indeed, below some critical density, an electron gas is expected to ‘‘crystal- lize’’ into a homogeneous ground state 10 whenever the Cou- lomb energy, which tends to localize electrons as far apart as possible from each other, dominates over the kinetic energy, which favors a smooth variation of the electron density. In semiconductor devices, therefore, as the interelectronic dis- tance becomes comparable to, or even larger than, the device relevant lengths, increased stability charge-density waves CDW or Wigner crystal WC states are expected. Forma- tion of CDW or WC has already been put forward to explain the periodic conductance oscillations in semiconductor devices. 4,5 The purpose of this paper is to analyze the low-density regime by evaluating the microscopic electron-electron cor- relations exactly. As shown by several authors, 11–14 this can be accomplished by classical molecular dynamics simula- tions, which, by operating in the full classical regime, also allow one to account for the nontunneling transfer occurring with the smooth potential barriers present in semiconductor structures. Indeed, along the lines of Ref. 14, we consider single-electron charging phenomena in semiconductor de- vices to be a pure classical effect that can be activated ther- mically, and does not depend on the availability of a quan- tized spectrum. The formation of WC or CDW states relies on charge discreteness, and can be detected by classical nu- PHYSICAL REVIEW B 15 APRIL 1996-I VOLUME 53, NUMBER 15 53 0163-1829/96/5315/101546/$10.00 10 154 © 1996 The American Physical Society