Resonant interband tunneling spin filter

We propose an InAs/GaSb/AlSb-based asymmetric resonant interband tunneling diode as a spin filter. The interband design exploits large valence band spin–orbit interaction to provide strong spin selectivity, without suffering from fast hole spin relaxation. Spin filtering efficiency is also enhanced by the reduction of tunneling through quasibound states near the zone center, where spin spitting vanishes and spin selectivity is difficult. Our calculations show that, when coupled with an emitter or collector capable of lateral momentum selectivity, the asymmetric resonant interband tunneling diode can achieve significant spin filtering in conventional nonmagnetic semiconductor heterostructures under zero magnetic field.

We propose an InAs/GaSb/AlSb-based asymmetric resonant interband tunneling diode as a spin filter.The interband design exploits large valence band spin-orbit interaction to provide strong spin selectivity, without suffering from fast hole spin relaxation.Spin filtering efficiency is also enhanced by the reduction of tunneling through quasibound states near the zone center, where spin spitting vanishes and spin selectivity is difficult.Our calculations show that, when coupled with an emitter or collector capable of lateral momentum selectivity, the asymmetric resonant interband tunneling diode can achieve significant spin filtering in conventional nonmagnetic semiconductor heterostructures under zero magnetic field.© 2002 American Institute of Physics.͓DOI: 10.1063/1.1524700͔A major research area in spintronics ͑spin-based elec-tronics͒ is the development of efficient spin polarized current sources. 1 An interesting candidate is the Rashba effect resonant tunneling spin filter made of nonmagnetic semiconductor heterostructures. 2 The device uses structural inversion asymmetry ͑SIA͒ to create spin splitting, 3 and exploits the fact that the spin of a resonantly transmitted electron aligns with that of the quasibound state traversed 4,5 to achieve spin filtering.As illustrated in Fig. 1 of Ref. 6, spin directions of quantum well states are perpendicular to the growth direction (z axis͒ and to the in-plane wave vector k ʈ , 7 and, when plotted along with the constant energy contours of two spinsplit subbands in the k ʈ plane, appear as counterclockwise ͑CCW͒ and clockwise ͑CW͒ pinwheels ͓see also Fig. 4͑b͔͒.This poses major challenges for the resonant tunneling spin filter.Within a given spin-split subband, which we label as CCW or CW, states opposite in k ʈ have opposite spins.Thus, the ensemble of electrons resonantly transmitted through a given subband yields no net spin polarization.To solve this problem, Voskoboynikov and co-workers 2 proposed the use of a small lateral ͑perpendicular to the growth direction͒ E-field in the source region to create an anisotropic lateral momentum distribution. 2Also, at a given k ʈ , states in the two spin-split subbands have opposite spins.While we exploit this property for spin filtering, we also require adequate resolution between the spin-split states.But this can be difficult, since the Rashba spin splitting is linearly proportional to k ʈ near ͑and vanishes at͒ the zone center. 3o improve spin filtering efficiency, Koga and coworkers recently introduced a spin-blockade mechanism to provide much stronger discrimination between the CCW and CW current components. 8In this work we propose the resonant interband tunneling 9 spin filter, which demonstrates large disparity between the transmission probabilities associated with the CCW and CW subbands, and significant reduction in zone center contributions. Our device structure consists of an asymmetric composite InAs-GaSb well, surrounded by AlSb barriers and InAs electrodes.With appropriate layer widths, it can operate in either, under moderate bias, the intraband resonant tunneling regime ͓Fig.1͑a͔͒ in which electrons traverse conduction subband states in InAs, or, under low bias, the resonant interband tunneling 9 regime ͓Fig.1͑b͔͒ where electrons traverse valence subband states in GaSb.In the interband design we exploit the strong spin-orbit interaction in valence bands for enhanced spin filtering, but collect electrons in the InAs conduction band to avoid fast spin relaxation in the valence bands. 10,11igure 2 shows spin-dependent transmission coefficient spectra calculated within the effective bond orbital model 12 using the multiband quantum transmitting boundary method. 13We intentionally align the spin axis of the incident electrons with that of the resonances probed (y axis, here͒.Figure 2͑a͒ shows that in the intraband tunneling case, the resonant transmission probabilities through the two spin-split nϭ1 conduction subband states ͑cb1͒ are approximately equal.Figure 2͑b͒ shows that in the interband tunneling case, transmission peak strength ͑height times width͒ through the highest heavy hole ͑hh1͒ states is much larger (Ϸ16 times) for the ϩy than the Ϫy spin polarization.This pronounced difference is a key property that we use to improve spinfiltering efficiency.We have confirmed the same strong spin dependence in a k•p calculation.To understand its origin, we examine the properties of hh1 transmission resonances in Fig. 3.As spinorbit interaction increases with k ʈ , both the T max ͑peak height͒ and ⌬E ͑peak width͒ differences between the ϩy and the Ϫy spin channels also increase.However, the large difference in T max is the primary source for the spindependence in peak strengths.A possible physical explanation of this result is provided by the analysis of double barrier resonant tunneling structures by Ricco and Azbel, 14 which states that the peak transmission coefficient T max is given by the ratio between the transmission probability of the strong barrier and that of the weak barrier.T max ϭ1 is achieved only in symmetric structures, in which left and right barrier have equal strengths.In our case, the GaSb valance band quantum well is confined to the left by the AlSb barrier, and to the right by the combination of the ͑effectively thicker͒ InAs-AlSb barrier.Apparently, for the Ϫy spin, spin-orbit interaction strengthens the left barrier and weakens the right ͑recall that spin-orbit interaction is proportional to ٌV, which has opposite signs at the two quantum well interfaces͒, effectively making the double barrier structure more symmetric, and thereby increasing T max .The opposite is true for the ϩy spin.Thus as spin-orbit interaction increases with k x , the difference between the transmission peak strengths of the two spin channels also increases.
Figure 3 shows that near the zone center, hh1 peak strengths are exceedingly weak due to the narrow hh1 resonance peak widths.This reduces contributions due to resonant tunneling through quasibound states near the zone center, where spins are difficult to resolve.Away from the zone center, the transmission resonance width ⌬E increases rapidly due to hole mixing. 15The calculated tunneling escape times (ϭប/⌬E) for k x Ͼ0.0075(2/a) are shorter than 10 fs.The fast resonant tunneling process allows us to avoid significant spin relaxation while electrons transit the GaSb valence subbands.
Figure 4 illustrates the operating principles of the interband resonant tunneling spin filter.Figure 4͑a͒ shows the valence subband structure of the spin-split quasibound states, together with the conduction band structure for the bulk InAs emitter.The shaded region represents the emitter states available for resonant tunneling.The tilt in the top of the shaded region is the result of modification to the emitter Fermi level due to the applied lateral E-field, as described by the relaxation time approximation. 16We use the same doping level in the emitter and in the collector.The dotted line represents the collector Fermi level.At a bias of 0.02 V, the occupied states in the collector block the light hole ͑lh1͒ and hh2 states, so that resonant interband tunneling takes place only through the hh1 states.Note that by setting the incident reservoir Fermi level below the hh1 band edge, we have another method of removing zone center contributions.
In Fig. 4͑a͒, the overlap between the hh1 quasibound states and the available emitter states fulfills energy and inplane momentum conservation conditions for resonant tunneling.Its k ʈ -space representation is shown as the shaded areas in Fig. 4͑b͒.The lateral E-field results in opposite net spins in the resonantly transmitted currents for each of the two spin-split hh1 subbands.However, strong spin-dependent tunneling allows the lower hh1 subband to dominate, yielding net spin in the total transmitted current.
Figure 5 shows the computed current densities and current polarizations as functions of lateral E-field for a resonant interband tunneling spin filter operating at a fixed transverse biasing voltage.Note that the lateral E-field is much smaller than the transverse E-field. Figure 5͑a͒ shows the contributions from each of the spin-split subband bands separately.As a result of spin-dependent tunneling, J CW is more than an order of magnitude larger than J CCW .In Fig. 5͑b͒ we analyze the spins of transmitted electrons along the y axis, and record separately current densities for spin up and spin down as J ϩy and J Ϫy , respectively.Figure 5͑c͒ shows the current polarization P. For a modest value of E x ϭ70 V/cm, we can obtain ͉P͉Ͼ50%.A similar device structure, highly optimized for intraband operation, yields Ϸ7%.These theoretical results demonstrate that the interband tunneling concept can be used to improve the efficiency of the resonant tunneling spin filter 2 significantly.

a͒
FIG.1.Schematic energy band diagrams of the resonant intraband and interband tunneling spin filters.

FIG. 2 .
FIG. 2. Transmission coefficients of an asymmetric resonant tunneling diode operating in ͑a͒ the intraband and ͑b͒ the interband modes.