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SEMICONDUCTORS AND NANOSTRUCTURES 2009Two-dim<strong>en</strong>sional weak localization in polycrystalline granular SnO 2 filmsThe ph<strong>en</strong>om<strong>en</strong>on of quantum interfer<strong>en</strong>ce in disorderedconductors is well known and its effects on the electricalconductance are widely used to determine the inelasticscattering time of charge carriers, and thus, the mechanismsof inelastic scattering. Because of the promin<strong>en</strong>teffects of weak localization in 2D systems they became anobject of int<strong>en</strong>sive studies. However, the reduced dim<strong>en</strong>sionalityand the pres<strong>en</strong>ce of disorder lead not only to <strong>en</strong>hancem<strong>en</strong>tof interfer<strong>en</strong>ce effects, but also to the necessityto take into account the electron-electron interaction. It appearedthat such characteristics as d<strong>en</strong>sity of states, temperatureand magnetic field dep<strong>en</strong>d<strong>en</strong>cies of electrical conductancecould be <strong>des</strong>cribed only if one takes into accountthe effects of electron-electron interaction in a disorderedlow-dim<strong>en</strong>sional system [Altshuler and Aronov, Modernproblems in cond<strong>en</strong>sed matter sci<strong>en</strong>ces Vol 10, Efros andPollak. ed., North Holland 1985]. Moreover, the dephasingmechanisms in weak localization are strongly relatedto interaction effects; inelastic electron-phonon scattering,quasi-elastic electron-electron scattering with small <strong>en</strong>ergytransfer. The interplay of interfer<strong>en</strong>ce and interaction effectsremains a puzzling problem that is still far from beingsolved.(2006)] where the weak localization model is ext<strong>en</strong>ded beyondthe diffusion limit. In the frame of this model, onlysmall closed loops are believed to give contribution to theeffect of weak localization at such high magnetic fields, theminimum number of collisions in each loop being 3. Onecan suppose that relative to electron-electron interaction effects,these triangles should be easier to study rather thanany complicated electronic path with a large number of collision.As in many materials the dephasing in the weak localizationeffect was found to be due to electron-electroninteractions, the study of these materials in high magneticfields should provide important information about these interactions(single electron’s wave function interfer<strong>en</strong>ce is<strong>des</strong>troyed, so the interaction effects should give the maincontribution to magnetoconductance).In our SnO 2 polycrystalline films the low transverse magneticfield dep<strong>en</strong>d<strong>en</strong>ce of the conductance is positive andcan be <strong>des</strong>cribed in the frame of a 2D weak localizationmodel, the phase breaking mechanism being electronelectronscattering with small <strong>en</strong>ergy transfer.In figure 64, the dep<strong>en</strong>d<strong>en</strong>ce of the magnetoconductance onthe normalized magnetic field B/B ϕ , measured on the samesample, are pres<strong>en</strong>ted over the full range of applied magneticfield up to 50 T. Here, B ϕ is the value of magnetic fieldat which the flux of magnetic field through an area <strong>en</strong>closedby the electron’s paths becomes equal to the flux quantumh/2e. From both the inset, where the curves are pres<strong>en</strong>tedin linear coordinates, and from the main part of figure 64,one can see that at high fields the curves exhibit differ<strong>en</strong>tbehaviour and no longer overlap any more. We thus suggestthe necessity to take into account the anisotropy ofthe scattering pot<strong>en</strong>tial in order to <strong>des</strong>cribe the observedresults. Differ<strong>en</strong>t particularities of single scattering ev<strong>en</strong>tsmay have influ<strong>en</strong>ce at differ<strong>en</strong>t temperatures in this highfield region.The experim<strong>en</strong>tal curves in figure 64 resemble those derivedby Zduniak et al. [Phys. Rev. B 56, 1996 (1997)]and by German<strong>en</strong>ko et al. [Phys. Rev. B 73, 233301Figure 64: The magnetic field dep<strong>en</strong>d<strong>en</strong>cies of magnetoconductanceas a function of normalized magnetic field. Inset shows fielddep<strong>en</strong>d<strong>en</strong>cies of magnetoresistance in linear coordinates measuredon the same sample.The analysis of high-field magnetoresistance data, obtainedon our samples of SnO 2 polycrystalline thin films, will provideanother one possibility to justify the mechanism ofelectron-electron interaction in disordered systems. The advantageof our samples is in highly controllable degree ofdisorder, which provi<strong>des</strong> possibility to tune the range of occurr<strong>en</strong>ceof quantum interfer<strong>en</strong>ce under applied magneticfields.T. A. Dauzh<strong>en</strong>ka, J. GalibertV. K. Ks<strong>en</strong>evich (Belarus State University, Dept Phys. SC & Nanoelectronics, BY-Minsk), I.A. Bashmakov (BelarusState Univ. Research Institute of Physicochemical Problems, BY-Minsk)48

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