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Physica E 10 (2001) 86–90
www.elsevier.nl/locate/physe
Theoretical and experimental considerations on the spin !eld
e"ect transistor
A. Bournel ∗ , V. Delmouly, P. Dollfus, G. Tremblay, P. Hesto
Institut d’Electronique Fondamentale, CNRS UMR 8622, Universite Paris Sud, Bât. 220, F-91405 Orsay, Cedex, France
Abstract
We propose a study of the spin !eld e"ect transistor (spin-FET), as a structure for the investigation of the physics of
spin polarized transport in ferromagnet=semiconductor structures and as a device for fast electronics. From Monte Carlo
simulation of spin-polarized transport in the channel of this device, we develop in a !rst part theoretical considerations about
the scaling of the spin-FET. In particular, we point out that the magnetization of the ferromagnetic source contact has to
be perpendicular to ferromagnet=semiconductor interface. In a second part, we present a study of the magnetic properties of
c 2001 Elsevier Science
ultrathin Co layers deposited on GaAs with the aim of obtaining a perpendicular magnetization. B.V. All rights reserved.
PACS: 71.70.Ej; 73.40.Kp; 73.30.Gw; 75.70.Ak
Keywords: Spin; Semiconductors; Magnetic thin !lms
1. Introduction
Recently, the spin-related properties of charge
carriers in III–V semiconductors have generated a
growing interest, leading to propositions of magnetoelectronics devices. The Rashba spin-orbit coupling
[1] appearing in the triangular quantum well formed
in a modulation-doped heterostructure makes feasible
the control of the electron spin orientation through
the con!ning electric !eld [2]. This mechanism leads
to the concept of the spin !eld e"ect transistor,
∗
Corresponding author. Tel.: +33-1-69-15-40-25; fax: +33-169-15-40-20.
E-mail address: [email protected] (A. Bournel).
the spin-FET [3]. The spin-FET consists of a high
electron mobility transistor (HEMT) where ferromagnetic source-drain contacts act as spin polarizer and
spin analyzer. The drain current is modulated magnetically by the gate voltage VG through the Rashba
coupling, in addition to the classical !eld e"ect
control.
In this paper, we develop considerations about the
scaling of the spin-FET from Monte Carlo (MC) simulation of spin-polarized transport in a semiconductor
2D electron gas (2DEG). Moreover, we present our
recent experimental results regarding magnetic properties of ferromagnet=semiconductor contacts usable
for the spin-FET.
c 2001 Elsevier Science B.V. All rights reserved.
1386-9477/01/$ - see front matter PII: S 1 3 8 6 - 9 4 7 7 ( 0 1 ) 0 0 0 5 9 - 5
A. Bournel et al. / Physica E 10 (2001) 86–90
87
2. Spin-polarized transport in a 2DEG
In a modulation-doped heterostructure, the Rashba
spin-orbit coupling originates from the lack of symmetry of the conduction band perpendicularly to the heterointerface. This coupling induces a spin precession
vector R , about which the electron spin precesses.
For a 2DEG formed in the xz-plane, we have [4]
R =
2a46 Ey
(−kz ux + kx uz )
˜
(1)
where a46 is a constant depending on 2DEG material, Ey the con!ning electric !eld, ux(z) a unitary
vector along x(z)-axis, and k = kx ux + kz uz the electron wave vector. As R depends strongly on k,
the electron=crystal scattering events randomize the
R -direction. So, during the motion of one electron,
its spin orientation becomes progressively incoherent.
The spin polarization of the electron population may
be thus relaxed. Such spin relaxation phenomenon
is denoted as the D’yakonov–Perel’ mechanism [5].
However, this mechanism is not eHcient in a spin-FET
with a 1DEG because the wave vector component
kz vanishes. In this case, the R -direction remains
always the same and the spin rotation angle related
to the Rashba precession varies proportionally to the
distance x along the channel [6,7]. If the term proportional to kx appearing in R carries the information,
the term proportional to kz is perturbing for the spin
in a 2DEG. Nevertheless, the use of a 1D-channel
makes the realization of the spin-FET very tricky.
Using a MC technique, it is possible to calculate
both easy and accurately the e"ect of scatterings on
spin precession in a 2DEG. A particle MC transport
model is based on a microscopic description of conduction phenomena: the current results of the collective motion of individual particles. The MC approach
taking into account the spin precession is described
in detail in a previous work [7]. For symmetric GaAs
quantum wells, we deduced spin relaxation times from
MC simulation in very good agreement with experimental results indeed [8].
Fig. 1 shows the variations of the spin polarization P along an In0:53 Ga0:47 As 2D-channel of in!nite width W at 77 K, for electrons injected with a
spin S parallel to the gate length L (SL) or to the
channel width (SW ). The electric !eld Ey perpendicular to the 2DEG is equal to 240 kV=cm, and the
Fig. 1. Spin polarization variation along an In0:53 Ga0:47 As
2D-channel for electrons injected with a spin orientation parallel
to the gate length L (SL) or to the channel width (SW ). Data
from MC simulation at 77 K for a 2D-channel with an in!nite
width W . Con!ning electric !eld Ey =240 kV=cm, driving electric
!eld Ex = 0:5 kV=cm.
driving electric !eld Ex to 0:5 kV=cm. For SL, the
spin polarization oscillates clearly along the channel,
but the spin coherence of electrons injected in the
channel is lost for x greater than about 2 m. We
quantify more precisely this phenomenon by !tting the
variations of the spin polarization using the following
expression
∗
2m a46 Ey x
x
exp
−
;
(2)
P(x) = cos
˜2
Ls
where m∗ is the electron e"ective mass and Ls is de!ned as the spin di"usion length. The sine law in
Eq. (2) corresponds to P-variations in a 1DEG [7].
At 77 K; Ls is equal to 750 nm. Such spin transport
properties are suHcient to experimentally characterize the Rashba precession at 77 K, but not to design a
device having electrical characteristics exploitable for
application. In fact, Ls has to be higher than 1:4 m in
an In0:53 Ga0:47 As 2DEG to obtain signi!cant negative
transconductance e"ects [6].
However, the spin relaxation can be reduced if
the channel width W is reduced to a value less than
500 nm. In Fig. 2, we plot the spin di"usion length
Ls for SL as a function of the inverse of standard
deviation Kz of the electron lateral displacements
Kz in the lateral z-direction during one free-Light, at
77 and 300 K and for Ey = 300 kV=cm. We deduce
both Ls and Kz from MC simulation in channels of
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A. Bournel et al. / Physica E 10 (2001) 86–90
Fig. 2. Spin di"usion length Ls in In0:53 Ga0:47 As 2D-channels, for
injected spin parallel to L, against the inverse of the standard deviation Kz of electron displacements in the lateral z-direction during
one free-Light. Data from MC simulation for W values ranging
between 50 nm and the in!nite, Ey =300 kV=cm; Ex =0:5 kV=cm.
Fig. 3. Spin polarization along a short width 2D-channel in
In0:53 Ga0:47 As, from MC simulation using two types of electron
reLections against the channel lateral boundaries. Solid lines: spec.
= specular reLections and di". = di"usive reLections. Dashed
line: 1D-channel. Ey = 240 kV=cm; Ex = 0:5 kV=cm; W = 100 nm;
T = 77 K.
width ranging between 50 nm and the in!nite. For W
higher than 500 nm; Ls varies weakly with W and
remains equal to about 750 nm at 77 K and 250 nm at
300 K. But for lower W values, the scatterings tend
to lose their spin-randomizing e"ect and Ls increases
strongly with decreasing W at both temperatures. At
300 K, the spin coherence is conserved over a distance as long as 2 m for W lower than 100 nm and
even 11 m for W = 50 nm. As shown in Fig. 2, the
Ls -increase is strongly correlated to the reduction of
Kz with decreasing W . The following considerations
can qualitatively explain this tendency. The spin relaxation is due to the kz -term appearing in Eq. (1).
During a free-Light of duration tf , perturbing variation of spin orientation varies roughly as kz tf , that
is as Kz. If scatterings are non correlated events, the
noise for the spin polarization during a great number
of free-Lights is additive, and its magnitude depends
2
on Kz 2 = Kz
since Kz = 0.
As shown in Fig. 2, it is not necessary to design a 1D-channel to obtain spin di"usion length
higher than 1:4 m: a 2D-channel with a 100 nm
width is suHcient. It should also be mentioned that
the roughness of the lateral channel boundaries has
no signi!cant inLuence on the spin relaxation. In
Fig. 3, we plot P(x)-variations obtained by considering specular (spec.) or di"usive (di".) reLec-
tions of the electrons against the lateral boundaries
in a 2D-channel of 100 nm width at 77 K. Both results are very close to the variations obtained in a
1D-channel (dashed line in Fig. 3).
If the spin of injected electrons is parallel to the
channel width (SW in Fig. 1), the spin polarization does not oscillate against the distance. In this
case, the spin orientation of electrons reaching drain
cannot be controlled by the gate voltage. The injected
spin indeed is parallel to the informative term of R
(in kx uz ) and normal to the perturbing term (in kz ux ),
which yields an ine"ective spin precession. For a good
device operation, the magnetic moment of the ferromagnetic source contact must be perpendicular to
the ferromagnet=semiconductor interface, which is of
great importance for practical application.
3. Magnetic properties of
ferromagnet=semiconductor contact
The shape anisotropy leads to an easy magnetization axis along the largest dimension of the source
contact that is along the width of the spin-FET.
However, thanks to surface anisotropy, it may be
possible to obtain a perpendicular magnetization by
designing ferromagnetic contact of thickness t along
A. Bournel et al. / Physica E 10 (2001) 86–90
the gate length direction lower than a critical thickness tc [9]. The best candidate to obtain perpendicular
anisotropy is the hexagonal-closed-packed (HCP) Co.
However, tc is lower than 2 nm in the case of HCP
Co. In this part, we report some magnetic properties
of ultrathin Co layers deposited on GaAs (1 0 0) with
the aim of obtaining a perpendicular magnetization.
For Co layers directly deposited on clean GaAs,
compounds of Co, Ga and As are formed [10], which
could be detrimental to the magnetic properties of the
ferromagnetic layer. Moreover, Co is known to grow
epitaxially on GaAs and a body-centered-cubic (BCC)
phase appears on the !rst nanometers which yields an
in-plane anisotropy [11]. To circumvent these diHculties and recover a HCP phase, we study a procedure proposed in the case of Fe=GaAs contacts [12].
We oxidize GaAs before Co deposition to prevent interdi"usion, which is likely to improve the magnetic
quality. Moreover, the use of an amorphous layer for
Co deposition favors growth with HCP phase. However, the oxide thickness must be low enough to allow
tunnel e"ect.
The oxide layer is grown by UV-ozone exposure of
GaAs. The oxide thickness tox , ranging between 0 and
9 nm, is determined by ellipsometry and Auger electron spectroscopy. The Co thickness tCo , deposited by
sputtering, is determined by alternative gradient force
magnetometer (AGFM) measurements and ranges between 1 and 2 nm.
We use magneto-optic Kerr e"ect (MOKE) to
characterize perpendicular magnetization. A typical
curve of the Kerr rotation signal as a function of perpendicular applied magnetic !eld is plotted in Fig. 4
for an oxide thickness of 4 nm and a Co thickness of
1:5 nm. Such a curve, without signi!cant hysteresis, is
characteristic of in plane easy magnetization axis.
However, the saturation !eld Hsat values remain reasonable. By plotting Hsat as a function of 1=tCo , the
!rst order magnetic anisotropy constant K1b can be
determined [9]. We evaluate that K1b is equal to
0:65 × 106 erg=cm3 for Co deposited on non oxidized GaAs and 1:6 × 106 erg=cm3 for tox = 3:7 nm,
while K1b = 4:5 × 106 erg=cm3 for bulk HCP Co. If
the Co structural quality is signi!cantly improved by
the oxide layer, it remains far from that of a perfect
HCP Co, which explains the in-plane anisotropy of
our layers.
89
Fig. 4. Kerr signal as a function of perpendicular applied magnetic
!eld H . Oxide thickness tox = 4 nm, Co thickness tCo = 1:5 mn.
4. Conclusion
In a spin-FET with a 2D-channel of in!nite width,
the electron=crystal scatterings lead to a signi!cant
D’yakonov-Perel’ spin relaxation mechanism. This
mechanism vanishes with the decrease of the channel width W and the spin di"usion length exceeds
1 m for W lower than 100 nm at room or liquid
nitrogen temperature. However, the spin orientation
injected by the source contact has to be parallel
to the transistor length L, that is perpendicular to
ferromagnet=semiconductor interface, in order to obtain an e"ective gate-controlled spin precession in the
spin-FET channel.
In this connection, the thickness of the source contact along L-direction has to be ultrathin and the use of
HCP Co seems appropriate. We show that the structural quality of the ultrathin Co layers deposited on
oxidized GaAs is higher than that of layers directly
deposited on GaAs. Nevertheless, their quality is not
good enough to obtain a perpendicular magnetization.
The use of magnetic bi- or multilayers could enhance
the perpendicular anisotropy [13], but it yet complicates the spin-FET realization.
Finally, the validity of the concept of spin-selective
injection=collection in a spin-FET has not been
demonstrated till now. In fact, Schmidt et al. have
recently pointed out that this concept is not valid
in the case of ohmic contacts [14]. However their
model does not take into account any interfacial
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A. Bournel et al. / Physica E 10 (2001) 86–90
spin-dependent properties, while such properties are
essential in magnetic tunnel junctions [15]. Further
investigations seem necessary in the case of tunnel or
Schottky ferromagnet=semiconductor junctions.
Acknowledgements
The authors would like to acknowledge P. Bruno
from Max Planck Institut fNur Mikrostrukturphysik
(Halle) for valuable discussions on spin polarized
transport, P. Beauvillain and C. Chappert from Institut d’Electronique Fondamentale (Orsay) for the
interpretation of magnetic measurements.
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