Bias dependence of the collector current

One of the main advantage of MTTs over SVTs is the possibility to study the transport over a given range of electronic energies. As described in section (2.1), the injected electrons will have an energy ditribution centered around eV where V is the voltage applied across the tunnel barrier. MTTs can thus be used as spectroscopic tools to probe the energy dependence of the transport properties of hot electrons in metals and semiconductors. The evolution of the collected current with V however is quite complex as several physical processes ruling the transport in a MTT depend explicitly on the energy of the electrons. The question as to how big an influence those different processes have on the evolution of the collector current with the emitter bias voltage is therefore addressed here. Figure 2.9 shows the collector current in the parallel case calculated within our simulation scheme for a MTT structure consisting of GaAs/Ni(30)/Au(30)/Ni(30)/Al2O3/Au in the parallel case. We can see that between V =φ_B/e (here 0,75V) and V = 1.2V, I_col increases by several orders of magnitude. The reason for this is twofold: the emitter current I_em across the tunnel barrier increases strongly with increasing voltage and the phase space matching the energy and wavevector conditions for collection in the semiconductor scales with√

E. To distinguish between both effects, one can use the transfer ratio α =Icol/Iem. Its energy dependence is plotted in the inset of the left panel in fig 2.9. We can see that α increases by more than 3 orders of magnitude when the energy is varied between 0,8V and 1,2V. By comparing this value with the increase of the collector current within the same voltage range, we can see that the increase of the collector current with the emitter voltage is mostly due to the augmentation of the phase space in the semiconductor. The GaAs bandstructure is

2.5. Transport properties of the magnetic tunnel transistor

Figure 2.9: Simulated emitter voltage dependence of the collector current in the parallel case for a GaAs/Ni(30)/Au(30)/Ni(30)/Al₂O₃/Au MTT at 11K and without interface scattering:

(left) collector current versus emitter voltage. The inset depicts the evolution of the transfer ratio α

(right) emitter voltage dependence of the contribution of each GaAs valley to the collector current

usually approximated by taking into account three valleys centered at the Γ, L, and X points. The energy separations between the valleys taken here are d_ΓL = 0.29eV and d_ΓX = 0.48eV and the Schottky barrier height in the Γ valley is Φ_B = 0.75eV. The right panel in figure 2.9 shows the current collected through each valley. We can see that at low energies, for E < Φ_B+d_ΓL, all the electrons transit in the Γ valley as it is the only valley accessible. As E is increased, states in the L valleys become accessible. However, this is limited to electrons with a high wavevector component parallel to the interface. Due to the fact that the electrons are strongly forward focused due to the tunnel emission, only few electrons will be able to reach the L valleys. Contrary to theLvalleys which is centered around zone edges, one of theX valleys is centered around the interface Brillouin zone center. As the effective mass and thus the density of states is much higher in the X than in the Γ valley, as soon as the electrons energy allows it, the electrons will preferentially transit through the X valley. We can indeed see that from E = Φ_B +d_ΓX on, most of the current is collected in the central X valley. It is to be noted that all the physical processes described so far are spin independent. Consequently, the qualitative features of the collector current in the antiparallel case would be the same.

The differences betweenI_col^P and I_col^AP are created during the transit through the spin valve base and can be investigated through the study of the magneto current ratio defined as

M CR= I_col^P −I_col^AP I_col^AP .

This ratio will be determined by the relative magnitude of the spin dependent at-tenuation length in the ferromagnetic layers. As the emitter bias voltage is varied,

Figure 2.10: Simulation results showing the influence of the base material on the MCR

the hot electrons will probe a different part of the ferromagnets’ band structures and their group velocities and relaxation times will vary. Consequently, the magnitude of the MCR will depend on the emitter bias. Furthermore, since the variation of the attenuation lengthλ↑(↓) with the electrons energies is related to the material’s band-structure, it is expected that the bias dependence of the MCR will vary qualitatively and quantitatively with the choice of ferromagnetic materials. From the values pub-lished by Zhukov and coworkers[37], it can be seen for instance that the evolution of λ↑/λ↓ is qualitatively different for Fe and Ni. As a result, the bias dependence of the MCR is different for those two materials. As an example figure 2.10 shows the simulated emitter bias dependence of the MCR for two MTTs where only one of the ferromagnetic layer differ. We can see that the MTT with a Ni/Au/Ni spin valve base shows a constant decrease of the MCR whereas the one with a Ni/Au/Fe base shows a maximum at about 1.5V. This is in good agreement with an experimental study published in the case of MTTs with a FeCo/Cu/NiFe base[50]. It is to be noted that in the simulation scheme used here, the energy loss caused by any inelas-tic scattering event (electron-electron scattering or spontaneous spin wave emission) is assumed to be high enough for the scattered electron not to be able to overcome the Schottky barrier. Thus the simulation doesn’t take into account the contribu-tion of secondary electrons to the collector current The existence of a maximum in the M CR(V) curve in those simulations is therefore only due to the variation with the energy of the majority and minority attenuation lengths. This non monotonic variation of M CR(V) has been found in other theoretical investigations[51] but the underlying physical reason was to be found in the interplay between electron elec-tron scattering and SSW emission resulting in a spin asymmetry of the secondary electron emission probability.

2.5. Transport properties of the magnetic tunnel transistor