1.4 Spin Injection into Silicon

One of the major criteria to realize the SpinFET device is to realize efficient spin injection in the conducting channel. The spin polarization can be achieved by optical spin excitation with circularly polarized light [88, 89]. Unlike e.g. GaAs, silicon is an indirect band gap semiconductor, so optical orientation or luminescence become ineffective for spin polarization or spin detection [62]. This is why the spin injection in silicon by optical means is a challenge. One of the straight forward methods of spin injection is rather by electrical means from a ferromagnetic electrode. An early exploration on spin injection through a ferromagnet/paramagnet interface and spin accumulation in a paramagnet was made by Johnson and Silsbee [90, 91, 92]. There is also some theoretical understanding regarding the transport of spin in silicon [93, 94]. However, due to a fundamental conductivity mismatch [95, 96, 97, 98] between a ferromagnetic metal contact and the semiconductor, the realization of the injection of a spin polarized current was not feasible. Even though there is a large spin imbalance between the majority and minority spins in a metal ferromagnet, both channels with up-spin and down-spin are equally populated in a semiconductor due to the relatively small density of states as compared to that for the minority spins in a ferromagnet. On the other hand, because of the comparatively larger resistance of the semiconductor in comparison to the metal, the voltage applied between the ferromagnetic metal and the semiconductor drops completely within the semiconductor. Henceforth, the properties of the contact are dominated by the non-magnetic semiconductor (silicon), and thus resulting in a current injection without spin polarization.

The use of a spin-dependent interface resistance between the ferromagnet and the semiconductor in the form of a tunnel barrier, is supposed to provide a solution to the above described conductivity mismatch problem [96, 97]. In this case, the influx of carriers from the ferromagnet into the semiconductor is reduced to such an extent that the majority spins supply just enough carriers to support the complete occupancy of the corresponding states in the semiconductor. Under such conditions the minority spin flow in semiconductors will be a fraction of that for the majority spins defined by the spin polarization in the ferromagnet. This ensures the existence of a spin polarized current and the spin injection into the semiconductor. However, in order to be able to properly detect the spin signal, the width of the tunnel barrier has to be precisely engineered [99]. Moreover, it drives the challenge to find an appropriate ferromagnetic semiconductor to ensure high quality interfaces without the tunnel barrier. An approach based on the use of hot electrons that do not suffer from the impedance mismatch problem, has been reported [8]. It was the first demonstration of the electrical spin injection, transport, and detection in undoped silicon at low temperature. The electrical spin injection into silicon from a ferromagnetic contact through an aluminium oxide tunnel barrier at low temperature has also been reported [100]. The vacuum tunneling is reported to preserve the spin-polarization properties of the electrons (92% spin polarized current) in GaAs at a temperature of around 100K [101]. Indeed, the introduction of a tunnel barrier, generally with defects, will cause charge trapping and eventually degrade the performance of the device. The use of ferromagnetic contacts made of semiconductors would be another possible solution. Unfortunately, no semiconductor with ferromagnetic properties at room temperature were known until recently. The existence of diluted magnetic semiconductor nanostructures having a Curie temperature above 400^∘C provides a promissing solution to the problem [102]. Another possibility to avoid the impedance mismatch problem is to employ half-metallic ferromagnets [103]. A half-metallic ferromagnet shows metallic properties with respect to one spin orientation, and acts like an insulator with respect to the other spin orientation. Some Heusler alloys and some transition metal oxides show this property [55]. Along with the above mentioned materials, the spin transport at room temperature in a doped-silicon channel has also been studied [104].

Regardless of the indisputable advantage in realizing the spin injection, detection, and transport in silicon at ambient temperature, several difficulties not explained within the theories are pending. According to the theory as explained in [44], the value of the voltage signal ΔV due to spin accumulation divided by the carrier current density (j) flowing through the injecting contact is proportional to = ²ρ_S with τs as the spin lifetime, and D_c as the diffusion coefficient. Because of the injection and detection, the tunnel spin polarization enters squared, and the silicon resistivity ρ_S multiplied with the spin diffusion length (Li = ) determines the additional area resistance of the contact due to spin accumulation under it. However, there is a several orders of magnitude discrepancy between the signal measured and the above mentioned theoretical value. The reasons for the discrepancies are heavily debated [44, 105, 106]. A spin signal much larger than the expected has been reported in germanium structures as well as for other semiconductors [107, 108, 109, 110]. Using single-layer graphene as the tunnel barrier can circumvent the conductivity mismatch issue, and the amplitude of the signal has been reported to be consistent with the spin accumulation in silicon [111]. An explanation based on the assumption that the resonant tunneling magneto-resistance effect and not the spin accumulation causes the electrically dependent spin signal has been proposed [105, 112]. On the other hand, an evidence that a proper account of space-charge effects at the interface may boost the spin injection signal by an order of magnitude was also presented [113].

In this work the semi-classical model of spin drift-diffusion in silicon is employed, when spin is injected in silicon from a ferromagnetic semiconductor. The effect of interface charge screening on spin injection efficiency is under scrutiny. It is noted that, the spin current increases while injected from a charge-depleted region in the ferromagnet, in comparison to when injected from a charge neutral or even a charge accumulated region. However, the spin injection efficiency is always limited by the bulk spin polarization of the magnetic material. This necessitates the further investigation of spin diffusion in silicon, when spin is injected through a charge neutral and a space-charge layer. However, in both cases, the spin current density can not be significantly higher than the spin current density at charge neutrality. Thus at a fixed boundary spin polarization, the maximum spin current in the bulk is always determined by its value at the charge neutrality condition - provided the charge current is kept fixed.