Microelectronic Engineering 51–52 (2000) 241–247 www.elsevier.nl / locate / mee Temperature and size dependence of fractal MCF in semiconductor billiards a, a,e b a c c * A.P. Micolich , R.P. Taylor , J.P. Bird , R. Newbury , T.M. Fromhold , C.R. Tench , a d d H. Linke , Y. Aoyagi , T. Sugano a School of Physics, University of New South Wales, Sydney, NSW , 2052, Australia b Center for Solid State Research, Arizona State University, Tempe, AZ 85287-6206, USA c School of Physics and Astronomy, University of Nottingham, Nottingham, NG72RD, UK d Nanoelectronics Materials Laboratory, RIKEN,2 -1 Hirosawa, Wako-shi, Saitama 351-01, Japan e Physics Department, University of Oregon, Eugene, OR 97403-1274, USA Abstract Fractal behaviour in the magneto-conductance fluctuations of mesoscopic systems has been predicted using semiclassical theory and observed experimentally in semiconductor billiards. Surface-gate billiards provide an ideal environment for investigations of fractal behaviour due to the ease with which parameters in the experimental system can be tuned. In this study we vary temperature and billiard size to investigate the classical and quantum limits of the semiclassical theory for fractal magneto-conductance fluctuations.  2000 Elsevier Science B.V. All rights reserved. Keywords: Fractal conductance fluctuations; Mesoscopic semiconductor billiards Modern semiconductor growth and fabrication technologies have allowed extensive investigations of low-dimensional electron systems in recent decades [1]. Lately, considerable interest has focused on semiconductor billiards, where material-induced length scales, such as the electron mean free path and the inelastic scattering length, exceed the electron confinement length and, as a consequence, phase-coherent ballistic transport effects are observed [1–4]. Sub-micron billiards can be defined in the two-dimensional electron gas (2DEG) of an AlGaAs / GaAs heterostructure using patterned metal gates deposited on the heterostructure surface. Application of a negative bias to these surface-gates leads to electrostatic depletion of the 2DEG in the regions directly below the gates and the formation of a billiard whose geometry closely resembles that of the patterned surface-gates [5]. At low temperatures, reproducible fluctuations in billiard conductance, due to electron quantum interference effects, are observed as a function of magnetic field [2–4]. These magneto-conductance fluctuations (MCF) provide an important probe of electron transport through the billiard. *Corresponding author. Fax: 161-2-9385-6060. E-mail address: mico@phys.unsw.edu.au (A.P. Micolich) 0167-9317 / 00 / $ – see front matter  2000 Elsevier Science B.V. All rights reserved. PII: S0167-9317(99)00484-0