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$G. M. Zaslavsky, Chaos, fractional kinetics, and anomalous transport ...$

4sample potential. The variations of T and ΔT as a functionof E 0 are plotted in Fig.3(a). The transmission Tvaries over almost six orders of magnitude and clearly exhibitsthree regimes. In the low energy range, up to about80eV, T increases linearly with E 0 . In the intermediateenergy range, between 80eV and 350eV, the increase inT is more pronounced. Finally, above 350eV T steps upabruptly and goes beyond unity. The variation of the spindependent transmission ΔT also reveals three regimes inthe same three energy ranges. At low injection energyΔT is constant as was observed in all the previous similarexperiments. 9,10,12,14,18 However, beyond 80eV thespin-dependent transmission increases over four orders ofmagnitude. In the high energy range, the increase in ΔTis particularly spectacular as it is even faster than that ofthe transmission T . This is evidenced by the variation ofthe transmission spin asymmetry A C [Fig.3(b)] which unveilsa jump by an order of magnitude between 350eV and800eV injection energy. This feature is a strong deviationfrom the behavior of the transmission spin-asymmetry inthe low injection energy range which was expected, fromany previous studies performed at moderate injection energy,to show a constant decrease.III.THEORETICAL MODELA. Hot-electron transport through ametal/oxide/semiconductor junction.1. Overview of the model.In this section, we will first consider the caseof an unpolarized electron beam injected in ametal/oxide/semiconductor structure, where the metallayer is non-magnetic. The electron transport throughthe metallic layer is schematized in Fig.4. We assumethat it is governed by electron-electron scattering yieldinga secondary electron cascade. This results in the formationof an electron distribution mixing primary andsecondary electrons. The distribution F (ε) thatreachesthe metal/oxide/semiconductor junction, may be written:F (ε) =Mf(ε) (1)FIG. 3: (a) Variation of the transmission T (symbols x) andof the spin dependent transmission ΔT (symbols+) with theinjection energy E 0. The dashed line corresponds to a linearincrease in E 0, (b) Variation of the transmission spinasymmetry A C (symbols ) with the injection energy E 0.Thedashed line corresponds to a decrease proportional to 1/E 0.The right-hand vertical axis gives the corresponding value ofS = A C/P 0, the asymmetry for a 100% polarized incidentbeam. This quantity is analogous to the Sherman function inspin polarimetry.where f (ε) is the normalized distribution of electronsand M the multiplication factor related to the secondaryelectron cascade. Then, electron are transferred throughthe junction barrier into the semiconductor collector withan efficiency α (ε). The transmitted electrons collectedin the semiconductor form the current I C . The electronswhich can not cross the barrier accumulate in the metallicbase and contribute to the current I B , together withthe holes produced in the metal by the excitation of thesecondary electrons. Following these ideas, the electrontransmission T canbewritten:T = M∫+∞0α (ε) f (ε) dε (2)At the metal/semiconductor interface, the collection efficiencyα(ε) is known to be an increasing function ofthe collection energy ε above the barrier of the Schottkyjunction. 21 In the sample studied here, this tendency isreinforced by the presence of the oxide layer. Indeed, twobarriers have to be considered : the semiconductor bandbending barrier of height φ SC =0.78eV , 24 and the oxidelayer barrier of height φ Ox =4.5eV much larger than
5FIG. 4: Schematics of the electron relaxation process throughthe metal layer and of the transmission through the junctionbarrier. Incident electrons are injected into the Pd layer witha polarization ±P 0 and an energy E 0 with respect to the metalFermi level. They cross the distance z ball before their velocityis relaxed. At this point, their mean energy is E ball andthey cross the remaining distance z diff to the junction by a 3-dimensional diffusion-like transport process. In the magneticlayer, the relaxation is different for majority and minority spinelectrons leading to two different distributions at the junction.The current transmitted into the semi-conductor collector isthe sum of two contributions: the electrons transmitted abovethe semiconductor band-bending barrier φ SC with the transferefficiency α SC and the electrons transmitted above theα SC and the electrons transmitted above the oxide barrierφ Ox with the transfer efficiency α Ox oxide.φ SC . 24–26 We will therefore assume that α(ε) has a stepshape :i) for ε
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RésuméDRISS LAMINEEffet de filtre
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AbstractDRISS LAMINESpin filter eff
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RemerciementsRemerciementsJ’ai r
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Table des matièresTABLE DES MATIER
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Table des matières4.A. Notion de r
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PréambuleChapitre IPréambuleL’u
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PréambuleRougemaille03 : Rougemail
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Chapitre II - Concepts généraux a
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Chapitre III - Réalisation et cara
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Chapitre IV - Réalisation d’un t
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Chapitre V - Modélisation du trans
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Page 170 and 171: BibliographieHopster83 : Hopster et
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