Spin-Dependent Tunneling In III-V Semiconductors
Soline Richard
1
, Henri-Jean Drouhin
2
, Guy Fishman
1
, Nicolas Rougemaille
2
1
Institut d'Electronique Fondamentale, UMR 8622 CNRS, Université Paris Sud, 91405 Orsay Cedex, France
2
Laboratoire de Physique de la Matière Condensée, UMR 7643-CNRS,
Ecole Polytechnique, 91128 Palaiseau Cedex, France.
Abstract. We calculate evanescent waves in GaAs-like III-V semiconductors throughout the forbidden band gap taking
into account both the absence of inversion center and the spin-orbit coupling. We find that the evanescent energy bands
are spin-split and that the evanescent wave functions only exist in limited energy and wave-vector domains. Such tunnel
barriers can be used as solid-state spin injectors.
INTRODUCTION
Evanescent states in semiconductors have been
studied for a long time. For instance Chang [1]
considered semiconductors oriented in the [100], [111]
and [110] directions, with inversion center (O
h
group)
or without inversion center (T
d
group), but without
taking into account the spin-orbit coupling. Chang and
Schulman [2] performed a detailed calculation of the
band structure of silicon, which belongs to the O
h
group. Schuurmans and t'Hooft [3] studied
semiconductors belonging to the T
d
group but
explicitly discarded terms which lead to odd k terms so
that practically they studied GaAs and AlAs as if they
were belonging to the O
h
group. Briefly speaking,
calculations about evanescent waves taking into
account both the T
d
group symmetry and the spin-orbit
coupling have not been carried out. Here we calculate
the evanescent band structure in the fundamental gap
of GaAs-like III-V semiconductors including both the
spin-orbit coupling and the lack of inversion
symmetry, within a 30×30 k.p Hamiltonian framework
(H
30
). These properties enable the design of original
solid state spin injectors.
CALCULATION IN H
30
FORMALISM
We have calculated the H
30
eigenvalues for a GaAs
semiconducting barrier. The energy origin is set at the
top of the valence band. The most important is that our
parameters yield the γ value of 24 eV.ų,[4] a
parameter which characterizes the strength of the
D’yakonov-Perel’ field, responsible for the real
conduction band spin splitting .The result of the
calculation in the k = [iK, Q, 0] direction, where K and
Q are real, is plotted in Fig. 1 for Q/K = 3/7. These
directions are indexed by the angle θ they form with
respect to the imaginary K axis (tan θ = Q / K)
-1
-0.5
0
0.5
1
1.5
2
2.5
-0.2 -0.1 0 0.1 0.2
||k|| (unit of 2
π /a)
Energy (eV)
[iK,Q, 0] [K,Q, 0]
FIGURE 1. Evanescent states connecting the spin-split
conduction band to the upper valence bands throughout the
fundamental gap. Q/K = 3/7 and a is the cubic lattice
constant.
1345
Downloaded 26 Aug 2005 to 146.246.244.6. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jsp
CP772, Physics of Semiconductors: 27
th
International Conference on the Physics of Semiconductors,
edited by José Menéndez and Chris G. Van de Walle
© 2005 American Institute of Physics 0-7354-0257-4/05/$22.50