Simulations of the tunneling current as a function of voltage and temperature for a Zener diode
where both sides are ferromagnetic have been performed. The current is evaluated as a function
of the applied bias, the magnetization, and the temperature on the diode. The tunneling
magnetoresistance is also analyzed. Mn doped GaAs parameters were used to simulate a highly
asymmetric doped diode, which leads to a large difference on the magnetization values between the
p and n sidesThis work was supported by Spanish Government Grant Nos. TIN2007-67537-C03-01 and TEC2010-17320 and by Xunta de Galicia Grant Nos. DXIDI09TIC001CT and INCITE08PXIB206094PRS

Aldegunde Villar, Manuel Alejo

Comesaña Figueroa, Enrique

García Loureiro, Antonio Jesús

Applied Physics Letters

English

E. Comesaña

M. Aldegunde

A. J. Garcia-Loureiro

Crossref

Spin-polarized transport in a full magnetic pn tunnel junction

Repositorio Institucional da Universidade de Santiago de Compostela

Reuse of AIP Publishing content is subject to the terms at: <a href="https://publishing.aip.org/authors/rights-and-permissions">https://publishing.aip.org/authors/rights-and-permissions</a>. Downloaded to: 193.144.79.182 on 13 November 2018, At: 00:41Spin-polarized transport in a full magnetic pn tunnel junctionE. Comesaña, M. Aldegunde, and A. J. Garcia-LoureiroCitation: Appl. Phys. Lett. 98, 192507 (2011); doi: 10.1063/1.3586770View online: https://doi.org/10.1063/1.3586770View Table of Contents: http://aip.scitation.org/toc/apl/98/19Published by the American Institute of PhysicsSpin-polarized transport in a full magnetic pn tunnel junctionE. Comesaña,1,a M. Aldegunde,2 and A. J. Garcia-Loureiro11Departamento de Electrónica e Computación, Universidade de Santiago de Compostela,15782 Santiago de Compostela, Spain2Centro de Supercomputación de Galicia (CESGA), 15705 Santiago de Compostela SpainReceived 18 November 2010; accepted 13 April 2011; published online 11 May 2011Simulations of the tunneling current as a function of voltage and temperature for a Zener diodewhere both sides are ferromagnetic have been performed. The current is evaluated as a functionof the applied bias, the magnetization, and the temperature on the diode. The tunnelingmagnetoresistance is also analyzed. Mn doped GaAs parameters were used to simulate a highlyasymmetric doped diode, which leads to a large difference on the magnetization values between thep and n sides. © 2011 American Institute of Physics. doi:10.1063/1.3586770The recent progress in developing semiconductor mate-rials that show ferromagnetic characteristics at room tem-peratures is leading to a growing interest to replace chargewith spin in signal processing devices. Spintronics is moti-vated by the belief that spin signal processing may yieldadvantages in terms of processing speed, power consump-tion, or device density.Dilute magnetic semiconductors DMSs are showinggood characteristics at rising temperatures and are being de-veloped to achieve spin control at room temperature. In anoptimally doped DMS the density of carriers is approxi-mately half that of the density of magnetic ions which isusually between x=5% and x=15%. The well establishedDMSs occur with one type of carrier. One of the most inves-tigated materials is the III–V material GaMnAs in whichthe Mn ion provides a localized spin S=5 /2 and also con-tributes a hole.1 The holes are degenerate and strongly polar-ized at low temperatures.2 The ferromagnetic III–V dopedmaterials are all p type but there is much effort to find acompatible n type ferromagnetic semiconductor.3 Magneticproperties have been seen in a number of magnetically dopedoxides, particularly ZnO, TiO2, and SnO2 Refs. 4–6 all ofwhich occur as n type semiconductors.A pn junction of two highly degenerated semicon-ductors makes a Zener tunneling diode, which has manyapplications7 and adding magnetic functionality would en-able more devices such as magnetic switching of microwavedevices. Also the understanding of the behavior of theferromagnetic pn junction is cornerstone to the study ofmore complicated spin-based devices, such as magnetic bi-polar transistors8 or spin field-effect transistors.9 Zener tun-neling has been observed in a ferromagnetic-nonmagneticGaMnAs/GaAs heterostructure,10 and a high spin polariza-tion is observed optically.11 The voltage dependence of thetunneling current in a spin-polarized Zener diode is wellfitted by the theory of a nonmagnetic diode.2 We aredeveloping analytical12 and numerical models13 to study thetransport in ferromagnetic Zener diodes. Our numericalsimulator solves self-consistently drif-diffusion model equa-tions, which has been extensively used to study spintronicdevices.14–16 Using these models we have predicted the de-pendence of the tunneling current on the mean magnetizationof the system and we have evaluated the tunneling magne-toresistance TMR for different values of the applied biasand temperatures in a theoretical both-sided ferromagneticdiode.The current through a tunneling diode has threecomponents;7 the tunneling current, the excess current, andthe diffusion current. The tunneling current is expected torise to a maximum at low voltage, about the lowest of thedistances between the Fermi level and the conduction bandin the n-side n /qe and the valence band in the p-sidep /qe. Then it falls to zero when bias increases over n+p /qe, see Fig. 1. This fall in the I-V curve is known asnegative resistance region NRR and is produced by theoverlapping of the density of carrier functions in both p andn sides.17 The last two components become important forhigher voltages out of the range of interest in this letter.In this letter, we show the results obtained for a fullferromagnetic GaAs diode from our numerical simulator.This numerical implementation intends to be more accuratethan the analytical model because it takes into account theexact change in the tunneling barrier with the band splittingand the applied bias, see, for example, Fig. 2b. While theanalytical model was developed for temperatures near 0 K,the numerical simulator also allows us to run simulations atdifferent temperatures. This letter offers a detailed analysisof the tunneling current and the effect of temperature andbias on the TMR, thanks to the improvement of the bandspin-splitting model by adding the dependence of the spon-taneous magnetization with the temperature.The tunneling of carriers through the band gap is animportant part of the carrier transport in highly doped pnaElectronic mail: enrique.comesana@usc.es.TotalCurrentPeakCurrentValleyCurrent ExcessCurrentDiffusionCurrentTunnelingCurrentIIIV V ~V VPVP V TnEVn+p+ECEFε pεEgap(a) (b)FIG. 1. Color online a Tunnel diode band diagram and b typical I-Vcharacteristic, showing the three contributions to the total current; tunnel,excess, and diffusion currents.APPLIED PHYSICS LETTERS 98, 192507 20110003-6951/2011/9819/192507/3/$30.00 © 2011 American Institute of Physics98, 192507-1junctions. There are two tunneling mechanisms; the directtransition from band to band and the trap assisted tunneling.The basic principles of the band to band tunneling were ex-plained by Kane.17 The tunneling probability, , is ob-tained from the WKB approximation. The tunneling densityof current is described as follows:17Jtun =q    fu + t − f l + t  tddt,1where t=memh /22 is the two-dimensional density ofstates related to the two transversal wave vectors, and f l andfu are the Fermi–Dirac functions evaluated using the pseudo-Fermi level of the majority carrier in the classical turningpoints. The tunneling current can be added to the electronand hole continuity equations as the nonlocal generation-recombination term Rtun=dJtun /dF with F the electricfield.The effect of the exchange interaction between thecharge carriers and the localized magnetic moments on theenergy band structure and the transport properties can beestimated by using a perturbation theory.18 The correction ofthe band energies due to the exchange potential can be writ-ten asEk	 = Ebe0 +2k22m−2	↑ − 	↓ , 2where =xJexchSz	 is the band splitting. In the mean fieldapproximation, the average spin polarization of the magneticmoments, Sz	, is given by xSz	=xSBSy, where x is the Mnions concentration and BSy is the Brioullin function for thespin S.Figure 2b shows the calculated band splitting of theband edge for GaMnAs using this approach of the ex-change interaction with Jexchpd =1.4 eV, m=0.5m0, TC=110 K, and S=5 /2. The band splitting disappears for tem-peratures over TC at B=0 and rises to a maximum value forlow temperatures.When the bands edges are spin-split, there are two dif-ferent characteristic energies for the occupations for eachspin n	=EFn−EC	 =EFp−ECn /2 and p	=EV	−EFp=EV−EFpp /2 with 	= ↑ ,↓. The tunneling occurs betweenthe two majority and the two minority bands or, if the rela-tive magnetization of the layer is reversed, between the ma-jority and the minority bands, see Fig. 2. We call these cur-rents antiparallel current IapV, Fig. 2c, and parallelcurrent IpV, Fig. 2d, respectively. The tunneling recombi-nation term is reevaluated for each spin-band obtaining fourrecombination terms related with the e↑−h↓ and the e↓−h↑recombinations.To calculate the spin splitting we assume that the totalcarrier concentration remains constant when the spin is po-larized, n0=n↑+n↓ and p0=p↑+p↓, where n0 and p0 are theelectron and hole concentrations with no spin polarization. Inthis letter we have made the assumption that the spin polar-ization ratio, defined as P= n↑−n↓ /n0 or P= p↑−p↓ /p0both are equivalent, is conserved in each device region, avalid approximation as long as the spin coherence lengthseveral micro meter is much larger than the depletion re-gion width several nano meter in our devices. Therefore,the band splitting in the depletion region will drop smoothlyas the carrier concentration decreases. To study the ferromag-netic and the antiferromagnetic interactions between the pand n sides, which correspond to the antiparallel and parallelconfigurations, we considered that the spin flip occurs in thedepletion region, in the point where the carrier concentrationreaches its minimum, because in that point the carrier medi-ated exchange interaction has to be weaker.If a Zener diode with both sides ferromagnetic is takenaround a hysteresis loop it should show TMR TMR= IpV− IapV / IpV+ IapV because the magnetizations wouldbe parallel at large fields and antiparallel at intermediate fieldvalue. We made calculations choosing doping levels of Nd=21018 cm−3 in the n-side and Na=31020 cm−3 in thep-side, in a constant profile for each side. These doping lev-els lead to the typical carrier concentration levels inGa0.9Mn0.1As magnetic semiconductors, which exhibit aCurie temperature of around 110 K. The voltage dependenceof Ip, Iap and the TMR are shown in Fig. 3a for a tempera-ture of 77 K. The simulations results are analyzed between 0P NDOS FM P DOS FM NEqVADOS FM P DOS FM NP NqVAERange of allowedenergies fortunneling processesx = ux = lupperlowerεTunnelingprocessat energy εεε0 50 100−0.1−0.0500.050.1E E(a)(b)(c) (d)FIG. 2. Color online a Schematic representation of a tunneling process atenergy . The figure shows the classical turning points, the Fermi pseudolev-els and the range of allowed energies. b Temperature dependence of theband edge in GaMnAs, TC=110 K. Schematic of the spin-split bands forthe antiparallel c and parallel d configuration. The arrows show the tun-nel recombination processes.30 50 70 90 1100.15 V0.17 V0.18 V0.20V0.22V0.25V0.30V0.35VTemperature (K)0.020.04J tot(A/cm2 )00.51TMRParallel currentAntiparallel currentNon−magnetic diodeParallel currentAntiparallel current0 0.1 0.2 0.3 0.4 0.500.20.40.630K60K80K90K100K105K108 K110 KVoltage (V)TMR(a)(b)(c) (d)FIG. 3. Color online a Current density and TMR dependence on the biasvoltage for 77 K. b Current density and TMR dependence on the devicetemperature at 0.35 V. c TMR variation with the temperature for differentcharacteristic biases. d TMR variation with the bias for differenttemperatures.192507-2 Comesaña, Aldegunde, and Garcia-Loureiro Appl. Phys. Lett. 98, 192507 2011and 0.4 V, the range in which the tunneling current in thenonmagnetic diode is expected to be nonzero. Larger biasvalues are not considered because the ferromagnetism effectsare only important for low biases.19,20 It is worth noting thatthe antiparallel current is higher than the parallel current forvery low biases 0.15 V. In this case the tunneling cur-rent is controlled by the carriers with higher energy, whichhave similar distributions in the parallel and antiparallel con-figurations, and the antiparallel configuration leads to highertunneling probabilities for low voltages. Also, the apparentlyhigh values of the TMR for biases larger 0.4 V are unphysi-cal because the other current components will become morerelevant, hiding the effect of the ferromagnetism on the tun-neling current.To analyze the dependence of the TMR on the tempera-ture, the calculations were repeated for different tempera-tures between 30 and 110 K. Figure 3b shows the evolutionof the tunneling current in the parallel and antiparallel con-figurations and the corresponding TMR for different tem-peratures. The tunneling current corresponds to a bias of 0.35V, chosen in the middle of the NRR as we expect the TMRmaximum value in this range.12 The TMR shows saturationat low temperatures around 60% and it falls down and dis-appears as the temperature goes near and further of the Curietemperature 110 K. This is what we expect from thechange in the band splitting with the temperature, Fig. 2b.The TMR tends to saturate its value in the NRR, this canbe seen in Figs. 3c and 3d, where the TMR is almostconstant for biases in the NRR. Figure 3c also shows howthe TMR in the NRR acts an upper bound in the TMR evo-lution for low biases. In Fig. 3d we observe that the TMRsignal is stronger for higher voltages in the NRR; however,we have to find a tradeoff between this increase and thedegradation of the TMR at high biases associated to othercurrent components. It is also worth mentioning that the par-allel current always becomes larger than the antiparallel cur-rent at the same bias, VA0.15 mV. At this voltage, theenergy overlapping between the carrier distributions in the pand n sides reaches its maximum in the parallel configurationand therefore the lowest energy carriers start to dominate thetunneling current. In this moment, the parallel configurationbegins to generate larger currents than the antiparallel one.The results derived here will act as a guide to whatshould be expected in an experiment. They also intend to bea temperature and voltage parametrization of the behavior ofa future device based on a ferromagnetic pn junction. TheTMR becomes more intense for growing voltages and satu-rates in the NRR and also at low temperatures. Study of thevoltage dependence of the tunneling current will give de-tailed information on the relative size of the spin polarizationof the carriers in each band.This work was supported by Spanish Government GrantNos. TIN2007-67537-C03-01 and TEC2010- 17320 andby Xunta de Galicia Grant Nos. DXIDI09TIC001CT andINCITE08PXIB206094PR.1T. Jungwirth, J. Sinova, J. Mašek, J. Kučera, and A. H. MacDonald, Rev.Mod. Phys. 78, 809 2006.2H. Holmberg, N. Lebedeva, S. Novikov, P. Kuivalainen, M. Malfait, andV. V. Moshchalkov, Phys. Status Solidi A 204, 791 2007.3J. Mašek, J. Kudrnovský, F. Máca, B. L. Gallagher, R. P. Campion, D. H.Gregory, and T. Jungwirth, Phys. Rev. Lett. 98, 067202 2007.4A. Ney, V. Ney, S. Ye, K. Ollefs, T. Kammermeier, T. Kaspar, S. Cham-bers, F. Wilhelm, and A. Rogalev, Phys. Rev. B 82, 041202R 2010.5A. Serrano, E. Pinel, A. Quesada, I. Lorite, M. Plaza, L. Pérez, F. Jiménez-Villacorta, J. de La Venta, M. Martín-González, J. Costa-Krämer, J.Fernandez, J. Llopis, and M. García, Phys. Rev. B 79, 144405 2009.6A. Espinosa, M. García-Hernández, N. Menéndez, C. Prieto, and A. deAndrés, Phys. Rev. B 81, 064419 2010.7S. M. Sze and K. K. Ng, Physics of Semiconductor Devices, 3rd ed.Wiley, New York, 2006.8J. Fabian, I. Žutić, and S. Das Sarma, Appl. Phys. Lett. 84, 85 2004.9H. Ohno, D. Chiba, F. Matsukura, T. 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Spin-polarized transport in a full magnetic pn tunnel junction

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