Effect of impurity correlation in modulation-doped quantum wires Doan Nhat Quang Center for Theoretical Physics, National Center for Natural Science and Technology, P. O. Box 429, Boho, Hanoi 10000, Vietnam Nguyen Huyen Tung and Tran Doan Huan Institute of Engineering Physics, Hanoi University of Technology, 1 Dai Co Viet Road, Hanoi, Vietnam Received 4 April 2000; revised manuscript received 28 June 2000; published 11 September 2001 A theory is given of the electronic properties of modulation-doped quantum wires which undergo a thermal treatment, taking into account the Coulomb interaction among ionized impurities in the sample preparation. It is pointed out that the correlation among impurities weakens their field and is enhanced when elevating the doping level, lowering the freezing temperature for impurity diffusion, and reducing the size of the impurity system. The screening of the ionic correlation by charge carriers in the sample growth is of minor importance. In the limiting case of a one-dimensional impurity system, the correlation may totally suppress the random field at any doping level, so that a finite electron mobility is governed by other scattering mechanisms than impurity doping, e.g., interface roughness and alloying. It is found that the ionic correlation changes the electron mobility of quantum wires as regards not only its magnitude but its dependence on the doping conditions as well. For impurity systems of a small size, the mobility may be increased by up to more than one order of magnitude at a doping level of 10 6 cm -1 . DOI: 10.1103/PhysRevB.64.125324 PACS numbers: 73.21.-b, 71.23.An I. INTRODUCTION Recently, there has been an increasing interest in semicon- ductor quantum wire QWR structures. These structures have opened up the potential for various device appli- cations. 1 In practice, intentional or unintentional doping is often inevitable in a wire, which determines its quality. The quasi-one-dimensional electron gas 1DEG in the wire is generally violently affected by disorder arising from impu- rity doping. The disorder has been shown to lead to remark- able changes in the observable properties of the wire, e.g., the electron mobility 1–5 and the density of states DOS. 6–9 It should be mentioned that all existing theories 1–9 of the disorder effect from impurity doping in QWR’s were estab- lished by assuming that the ionized impurities are absolutely randomly distributed in the sample. Nevertheless, it is well known 10–12 that the assumption of the random impurity dis- tribution fails to be valid at a high doping level, e.g., in heavily doped 3D bulk semiconductors, and in order to understand phenomena occurring in such a sample one has to invoke an impurity correlation. The effect is due to the Cou- lomb interaction among charged impurities in both the prepa- ration of a sample and the measurement of its observable properties during whose course they could move freely and interact to each other. In the sample preparation, this devel- ops during a sample growth and results in a correlation in realization of a given impurity configuration which is frozen after the growth. The effect is referred to as high-temperature ionic correlation. The situation is met when the sample un- dergoes a thermal treatment, e.g., prepared by molecular beam epitaxy 10–12 MBE or pulling from the melt. 13,14 Ob- viously, the correlation tends to drive the impurities to be uniformly distributed so that their configuration is of the lowest potential energy. Indeed, such ordered impurity distri- butions were experimentally observed by Headrick and co-workers 10 using x-ray diffraction. They reported corre- lated completely ordered B  3  3 two-dimensional struc- tures at the interface between Si111 and a -Si during MBE growth. Moreover, at a high doping level, the correlation effect is expected to significantly alter the doping profile as well as the characteristics of the impurity field seen by elec- trons. Experimentally, Schubert and co-workers 11,12 observed an apparent correlation-induced deviation from a  doping profile of the sample GaAs:Be grown by MBE. The effect is to be distinguished from the low-temperature ionic correla- tion that develops during a sample measurement and was well studied in Refs. 15 and 16. There, the ionic correlation is related to the migration of electrons between impurities at low temperatures changing the positions of charged impuri- ties if not all of the impurities are ionized. So far, a number of theories of heavily doped bulk semi- conductors have been established, starting from the assump- tion of the correlated impurity distribution. The theories were capable of explaining several experimental data, say, on the optical properties 13 and mobility. 14,17,18 In addition, the ionic correlation was shown to lead to an appreciable modification in the DOS of heavily doped materials. 19,20 It is well known that with a reduction of the dimension- ality of the electron system the effect of an interaction, e.g., disorder and many-body interactions, becomes generally stronger. So the influence of impurity correlation in a 1D structure is thought to likely be larger than that in 2D and 3D systems. Further, it is also believed that in the case of strictly one dimension, an interaction appears to exhibit some strik- ing behavior which is often of great physical interest. Thus far, this has been theoretically proved for 1D electron sys- tems. Indeed, in one dimension due to any small disorder all electronic states are exponentially Anderson localized, 21 whereas due to any small electron-electron interaction the 1D electrons make up a singular Tomonaga-Luttinger liquid. 22 So the ionic correlation in a 1D impurity system is thought to likely assume some peculiar property. Thus, the aim of this PHYSICAL REVIEW B, VOLUME 64, 125324 0163-1829/2001/6412/1253249/$20.00 ©2001 The American Physical Society 64 125324-1