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Effect of impurity correlation in modulation-doped quantum wires

Mathematics and Statistics

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Effect of impurity correlation in modulation-doped quantum wires

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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 mobility1 - 5 and the density of states (DOS).6 - 9

It should be mentioned that all existing theories1 - 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 known10 - 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 epitaxy10 - 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-workers10 using x-ray diffraction. They reported corre-lated completely ordered B 3 size 12{ sqrt {3} } {} x 3 size 12{ sqrt {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-workers11,12 observed an apparent correlation-induced deviation from a δ size 12{δ} {} 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 properties13 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 thispaper is to supply an estimate of the effect from high-temperature ionic correlation in the sample preparation on the electronic properties of the 1D structure based on QWR’s and to explore the behavior of correlated-impurity systems in one dimension.

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