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

10energy is due to the increasing portion of electrons whichmay surmount the barrier φ Ox and be collected with ahigh efficiency α Ox . This is even more clearly evidencedwhen analyzing the variation of the transmission spinasymmetry A C . Indeed, for a single step barrier of heightφ and collection efficiency α above φ, averysimpleapproximatedexpression of A C can be obtained:A C = ΔT2T ≈ P φ0(33)E 0We have deduced this simple approximation from theexpressions of T and ΔT of Eqs.(2) and (29) and from theexpressions of the energy distributions given by Eqs.(4)and (30). We have also considered that A p (ε) ≈ 1and1−2A Ep
11IV.CONCLUSIONWe have studied spin-polarized electron transport ina ferromagnetic metal/oxide/semiconductor junction asa function of the injection energy. We have observedan increase in the electron transmission and in the spindependenttransmission over several orders of magnitude.Theriseinthetransmittedcurrentcomesfromtothemultiplication by secondary electron excitation and fromthe increase in the mean energy of the electron distributionreaching the junction barrier. The increase in themean electron energy is related to the increase in the distancecrossed by electrons in the metal layer before theirvelocity is relaxed. Indeed, the electrons are scatteredforward as long as their mean velocity is not randomized.A diffusion-like transport then takes place which favorsenergy relaxation. When the injection energy becomessignificantly larger than the Fermi energy, the distancenecessary for the relaxation the electron velocity startsto increase. This reduces the remaining distance towardsthe metal/oxide interface that electrons have to cross ina three-dimensional random diffusion regime. Therefore,energy relaxation is reduced and the mean electron energyat the junction increases.This latter effect is reinforced by the two-step structureof the metal/oxide/semiconductor junction: the lowbarrier φ SC of the semiconductor band bending and thehigher barrier φ Ox of the oxide layer. This junctionstructure induces a transition between two transmissionregimes : at low injection energy, the current collectedin the semiconductor is dominated by electrons transmittedabove φ SC after crossing the oxide layer with apoor efficiency, and at high injection energy, the transmissionexhibits a stiff increase due to hot electrons whichovercome φ Ox with a transmission efficiency of the orderof unity. At the transition between these two transmissionregimes the spin-dependent component of the transmittedcurrent also exhibits a large increase, over morethan three orders of magnitude, which is even more pronouncedthan the transmission increase. As a result, thetransmission asymmetry surges by about a factor 10 atthe transition between the two regimes. A simple analysisof the spin-polarized electron transmission shows thatthe transmission spin asymmetry A C is in fact mainlygiven by the ratio of the electron exit energy, which isdetermined by the barrier height φ, to the electron injectionenergy : A C ≈ P 0 φ/E 0 . Therefore, the experimentaljump in asymmetry is related to the rise in the mean electrontransmission energy from φ SC to φ Ox . This appearsas a simple rule for the determination of the transmissionspin-asymmetry which may be very useful, in particularfor the design of optimized spin detector based on thinmagnetic spin-filter.This rule holds as long as the exit energy of the transmittedelectrons remains close to the barrier height.But when the mean electron transmission energy becomessignificantly higher than the barrier height, thespin-selectivity of the junction dramatically decreases.As a consequence, the spin-filtering effect vanishes andmay even be counterbalanced by the effect of the spindependentsecondary electron multiplication. Then, thetransmission spin-asymmetry should become negative.Single barrier junction with transfer efficiency varyingslowly versus energy would be appropriate structures toevidence the predicted negative spin-dependent transmission.But in the present experiment, this effect is notobserved since it is masked by the transmission regimeabove the oxide barrier. This is a major result for devicesusing spin-filtering effects through a ferromagneticmetal base. Indeed, because of the presence of the oxidebarrier with height φ Ox and transfer efficiency α Ox closeto1aboveφ Ox , the spin-selectivity of the magnetic layeris fully exploited even at high injection energy. This isdemonstrated by the fact that, over the whole probed injectionenergy range, the measured spin-dependent transmissionis well described with the simple approximationA p (ε) ≈ 1, which corresponds to spin-selectivity of 100%.Therefore, high transmission (much larger than unity)and high spin-filtering efficiency (close to 100%) are obtainedtogether when operating at high injection energy.Of course, not only the primary electrons are efficientlyspin-filtered, as demonstrated in the present work, butalso the secondary electrons. 29 In the configuration ofthe present experiment, we can only measure the transmissionasymmetry related to the primary electron polarization.Therefore, the polarization of the secondaryelectrons can not be evidenced since its orientation isdetermined by that of the magnetic layer magnetizationand not by the primary electron polarization. To evidencethe spin-filtering of secondary electrons one shouldeither use a spin-valve structure or measure the polarizationof the transmitted electrons. This has two importantconsequences. First, even for unpolarized injected electrons,the amplified transmitted current must be highlyspin-polarized parallel to the majority spins in the ferromagneticlayer. Therefore the electron multiplicationprocess by the secondary electron cascade can be an efficienttool for the study of highly spin-polarized electroninjection from a ferromagnetic metal into a semiconductor.Second, transistor-like devices exhibiting largemagneto-current asymmetry together with current gainlarger than unity can be envisage when using a spin valvestructure as metallic base with a controlled base-collectorbarrier shape. The price to pay is to design a devicewhich emitter-base junction may be operated at high injectionenergy.AcknowledgmentsThe authors thank D. Paget and A. Rowe for fruitfuldiscussions and a critical reading of the manuscript.
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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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