Spin-dependent tunnelling through an indirect double-barrier structure

We use the transfer matrix method to study the quantum tunnelling through an indirect-band-gap double-barrier like the GaAs/AlAs/GaAs/AlAs/GaAs heterostructures along the [001] axis, which is described by the tight-binding model. The X-valley quasi-bound state gives rise to the Fano resonance different from the direct double-barrier transition in a resonance-tunnelling diode. The quantitative calculations demonstrate that a relatively high spin-polarization of the transmission probability can be achieved as compared with the single-barrier tunnelling case. Moreover the extension to the multi-barrier device is provided and leads to an important observation that the spin polarization increases with the number of barriers.