Microelectronic Engineering 23 (1994) 31-39 Elsevier 31 zyxwvutsrq Quantum transport in nanostructures: from electron waveguide to electron box H. van Hout8ena aPhilips Research Laboratories, Professor Holstlaan 4 5656 AA Eindhoven, The Netherlands zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Mesoscopic physics refers to phenomena occurring in a size regime intermediate between that of individual atoms or molecules, and that of macroscopic materials. This review provides an introduction to a sub-class of mesoscopic physics, dealing with quantum transport through nanostructures. The dual wave- and particle-nature of the conduction electrons is discussed, and illustrated by the examples of the electron waveguide and the electron box. 1. INTRODUCTION The low-temperature conductance of sub- micron sized structures in semiconductors or in met,als may reveal t,he dual wave-particle nature of conduction electrons. Ballist,ic electron wave propagation may be studied in short. and clean quant,um wires! known as quantum point con- t,acts. A quantum point, cont,act behaves as an electron waveguide, as evidenced most. clearly by the quantization of its conductance in units of e’/h. This effect shows up as steps and plateaux in the conductance versus gate voltage, each step corresponding t,o the addition of one propagating mode t,o the elect.ron waveguide. The discret,eness of the electron charge e -a typical particle characteristic- shows up in tun- neling through very small islands. The capaci- t,ance c’ of t#he island with respect, t,o its environ- ment can be so small that, the elementary charg- ing energy e2/C associat,ed with the tunneling of a single electron may easily exceed thermal fluc- t,uations in the energy of order zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA kT. As a result,, the charge on such an island is quantized. One speaks of an electron box. The conductance of t.he electron box, coupled by two tunnel junc- t,ions t,o source and drain, and by a capacitor to a gate elect,rode, oscillat#es periodically as the gate voltsage is varied, each peak corresponding to a single electron added t#o t,he island. This phe- nomenon is known as t#he Coulomb-blockade os- cillations, because in the mimima of the conduc- tance t,ransport, is blocked by Coulomb int,erac- tion effects. An electron box in semiconductors is also referred to as a quantum box, because the quantum mechanical confinement of the electron waves in the box gives rise to a discrete energy spectrum. The amplitude and temperature de- pendence of the Coulomb blockade oscillations re- veals the dual wave and particle aspects of single electron tunneling through a quantum box. The present article is only intended t,o intro- duce a few key concepts and results. Comprehen- sive reviews may be found elsewhere [l-5]. 2. NANOSTRUCTURES Mesoscopic transport, physics has been ex- plored in nanostructures defined in metals or in semiconductors, fabricat#ed using advanced mul- tilayer growth methods, and lateral patterning techniques such as elect,ron beam lithography. A variet,y of techniques has been used[l) 21, and here we can only mention a few. Metallic wires may be defined in a thin film de- posited on an insulating substrate, using electron- beam lithography for pattern definition, and lift,- off or subtractive etching for pattern transfer. Small metallic point contacts have also been made using semiconductor membranes with small holes, met,allized on bot,h sides[6]. Low-capacitance metallic tunnel junct,ions have been made pri- marily by an ingenious shadow-evaporation tech- nique[7], using aluminum as the preferred metal, and aluminum oxide as the tunnel oxide. An ideal model system for the study of quant,um transport has been provided by semi- conductor nanostructures, defined in t’he two- 0167-9317/94/$07.00 0 1994 - Elsevier Science B.V. All rights reserved.