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Coherent Spin-Valley Polarization Characteristics of Silicene Field Effect Transistor

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Coherent Spin-Valley Polarization Characteristics of Silicene Field Effect Transistor Journal of Multidisciplinary Engineering Science and Technology (JMEST) ISSN: 2458-9403 Vol. 4 Issue 2, February - 2017 Coherent Spin-valley polarization characteristics of silicene field effect transistor Ibrahim S. Ahmed, Mina D. Asham Adel H. Phillips Dept. of Basic Engineering Science Dept. of Engineering Physics and Mathematics Faculty of Engineering, Benha University Faculty of Engineering, Ain-Shams University Benha, Egypt Cairo, Egypt [email protected], [email protected] [email protected] Abstract—The quantum spin and valley power consumption, and increased integration transport characteristics in normal densities [23,24]. silicene/ferromagnetic silicene/ normal silicene Silicene is a monolayer of silicon atoms arranged junction are investigated under the effects of in a honeycomb lattice structure as similar as magnetic field and the frequency of the induced graphene. While, as in graphene, its low-energy ac-field. The spin and valley resolved dynamics near the two valleys at the corner of the conductances are deduced by solving the Dirac hexagonal Brillouin zone is described by the Dirac equation. Numerical calculations are performed theory, its Dirac electrons, due to a large spin-orbit and results show an oscillatory behavior to both (SO) interaction, are massive with a energy gap as spin and valley resolved conductances which due 1.55meV [17, 25]. Furthermore, due to the large ionic to resonant tunneling regime of the confined radius, silicene is buckled[10] such that the A and B states of ferromagnetic silicene. Spin and valley sublattices of honeycomb lattice shifted vertically with polarizations are calculated. Their values show respect to each other and sit in two parallel planes that spin and valley polarizations might be tuned with a separation of 0.46nm[25, 26]. The buckled by the applied gate voltage, or in other words, by structure of silicene allows tuning its band gap via an electric field. The present paper is very promising electric field applied perpendicular to its layer. These for spintronics application of silicene. features give many attractive properties to silicene [27-30]. Keywords—component; Normal/ferromagnetic/ To enhance the capability of conventional normal silicene junction; ac-field; magnetic field; electronics devices based on charge degree of spin-resolved conductance; valley-resolved freedom, spintronic devices based on spin degree of conductance; spin polarization; valley freedom have become more important [31]. More polarization. recently, valley degree of freedom based on two I. INTRODUCTION inquivalent Dirac points at K and K´has also attracted interests [32] as a pathway towards quantum In recent years new classes of materials called computing. The presence of large spin-orbit two-dimensional materials are synthesized [1-3]. The interaction and buckled atomic structure lead silicene first identified material in this new category was to be a candidate for these growing fields of graphene [3], which is a single atomic layer of carbon spintronics [33] and valleytronics [34]. Silicene also with a honeycomb structure. Since its discovery, in has stronger spin-orbit coupling which gives rise to the 2004, several studies have revealed the extraordinary spin-valley coupling [35]. There have been various properties of graphene, making it one of the most theoretical studies in spin valley transport at silicene promising materials for applications in electronics [4], junction, which helps the advancement in this area. optics [5], sensors [6], and energy storage [7]. The topics of those investigations are, for example, Besides the graphene, a large variety of these layered the electric field condition for the fully valley and spin materials have been studied such as boron nitride polarized transports [36], the mechanism of [8,9], dichalcogenides [10-12], germanene [13-15], magnetism opening different spin dependent band silicene [16-19], stanene [20], phosphorene [21,22]. gaps at K and K´ points which results in spin and Of this growing family of 2D materials, silicene has valley polarized transports [35]. emerged to replace, not only graphene, but also bulk The purpose of the present paper is to investigate silicon in the current electronics, because studies the spin and valley polarization characteristics of have shown that silicene has electronic properties normal / ferromagnetic/ normal silicene nanodevice. similar to those of graphene [15, 16]. Spintronics aims to exploit spin degrees of freedom instead of or in addition to charge degrees of freedom II. THE MODEL for information storage and logic devices. Compared In this section we shall derive both spin with conventional semiconductor devices, spintronic polarization and valley polarization equations for devices have the potential advantages of nonvolatility, silicene field effect transistor (SFET). This nanodevice increased data processing speed, decreased electric is modeled as follows: a ferromagnetic silicene is www.jmest.org JMESTN42352056 6701 Journal of Multidisciplinary Engineering Science and Technology (JMEST) ISSN: 2458-9403 Vol. 4 Issue 2, February - 2017 sandwiched between two normal silicenes and a i e metallic gate above the ferromagnetic silicene as aei() kxy x k y F z shown in the figure below. F eV in t Jeac . (5) IIi n n 1 e n i() kxy x k y F be z F And the eigenfunction in region III is: i() k x k y texy ei z F eVac in t (6) III Je n . n1 2EEFN EN n In Eqs.(4,5,6) “ eVac “ is the nth-order Bessel Jn n Fig. 1Regions I & III represent normal silicene and region II function of first kind [41,42]. The solution of Eq.(4,5,6) represents ferromagnetic silicene. must be generated by the presence of different subbands‘n’ in a quantum silicence nanodevice, which The transport of Dirac fermion carriers is come with phase factor exp(in t ) [41,42]. The influenced under the effect of both magnetic field and ac-field of frequency in mid infrared region. The Dirac angle is the incident angle on regions I & III and the equation is: angle is the incident angle on region II where they are expressed as: HE (1) kk tan11 (yy )and tan ( ) (7) Where H is the Hamiltonian and it is given as [36- kk 39]: xx The , E , , k , k´ , k and k´ are H(() v k k U h parameters F N F y y F F F x x y y z SOI z 0 (2) given by: eVac cos t ) FFF vk Where ħ is the reduced Planck’s constant, v - F EE (8) Fermi velocity, kx&ky are wave vectors, x,y,z are Pauli N F z SOI matrices, SOI is the intrinsic spin orbit coupling energy E U h F F z0 z SOI in silicene , h0 is the exchange energy of the ferromagnetic silicene, Vac is the amplitude of the ac- ky = kF sin and k’y= k’F sin (9) field with frequency . It is noted that =+1 for K- E 22 valley and = -1 for K´-valley and =+1 for spin up k F SOI (10) and = -1 for spin down. The parameter U in Eq.(2) is: F v F 1 (3) 2 2 U Vd eV sd eV g g B B EF U z h0 SOI 2 (11) kF Where Vd is the barrier height at each interface, Vsd v F is the bias voltage, Vg is the gate voltage, B – where EF is the Fermi energy. In Eqs.(4, 6) the magnetic field, g –Lande g-factor and B- Bohr rt& are the reflection and magneton. parameters zz The eigenfunctions in regions I, II, III are obtained transmission amplitudes. Applying the boundary by solving the Dirac equation Eq.(1) which are [36-40] conditions at the interfaces we get the tunneling : probability,(E), as : i() kxy x k y e i (12) e cos22 cos E 2EE E 2 2 2 FNN eV in t coskdx cos cos Jeac . (4) Ini() kxy x k y 2 n 1 re e i n sin21kd 2sin sin z F x 4 2EEFN E N The ratio γ is: Also the eigenfunction in region II is: www.jmest.org JMESTN42352056 6702 Journal of Multidisciplinary Engineering Science and Technology (JMEST) ISSN: 2458-9403 Vol. 4 Issue 2, February - 2017 k And the valley polarization [40,43] is: FF (13) kE FN GGGG KKKK (23) The wave vector k is: VP x GD 2 2 2 2 (14) ESULTS AND ISCUSSION kx kFF k sin III. R D Numerical calculations are performed for the The tunneling probability with the induction of ac-field transport characteristics parameters which are: the ac field E is given by[41,42]: valley resolved conductance (Eq.18), the spin resolved conductance (Eq.19), The Dirac fermion eV conductance for both spin & valley cases (Eqs. EJE 2 ac (15) ac field n n 20,21), and the spin & valley polarizations (Eqs. n1 22,23). The values of the following parameters are 5 According to the Landauer- Buttiker equation, the [37-41,44]: vF= 5.5x10 m/s, SOI= 3.9 meV, EF= conductance, G, is expressed as [40, 43]: 40meV, Vd= 60meV, Vac=0.25 V, Landé g-factor g=4, h0=0.2 eV (the exchange energy of the ferromagnetic e 2k W silicene), d=80 nm (length of the ferromagnetic G F 2 (16) silicene region or the channel) and W=20 nm (width of the model). EnF 2 f dE E FD cos d The features of the present results are: ac field E EF 2 - Figs. (2a,b,c, d) show the conductance, G, (Eq.16) versus the gate voltage, Vg,in case of both f FD where is the first derivative of the Fermi- parallel and anti-parallel spin alignments and for K E and K´ points at different values of the magnetic field. Dirac distribution function and is given by: As shown from these figures that an oscillatory behavior of the conductance with different peak f 1 E E n FD 4kT cosh2 F (17) heights are observed.
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