Active solid-state devices (e.g. – transistors – solid-state diode – Field effect device – Having insulated electrode
Reexamination Certificate
2003-01-27
2004-08-17
Nelms, David (Department: 2818)
Active solid-state devices (e.g., transistors, solid-state diode
Field effect device
Having insulated electrode
C257S068000, C257S071000, C257S296000, C257S298000, C257S326000, C438S003000, C438S240000
Reexamination Certificate
active
06777731
ABSTRACT:
BACKGROUND OF THE INVENTION
Field of the Invention
The present invention relates to a magnetoresistive tunnel element having a first electrode, a second electrode, and a tunnel barrier disposed between the two electrodes, a first interface being fashioned between the tunnel barrier and the first electrode, and a second interface being fashioned between the tunnel barrier and the second electrode and the magnetoresistive tunnel element having a quantum mechanical barrier height within the tunnel barrier and also an electrical conductivity. It furthermore relates to a magnetoresistive memory cell having a magnetoresistive tunnel element, and to a memory device having magnetoresistive memory cells.
The core of a magnetoresistive memory cell based on the tunnel effect is of a magnetoresistive tunnel element (magnetic tunnel junction element, MTJ element). Such an MTJ element includes two ferromagnetic layers (electrodes hereinafter) on both sides of a nonferromagnetic or dielectric tunnel barrier.
In a magnetoresistive memory cell, the material of the first electrode is typically a hard-magnetic material, for instance, a cobalt-iron alloy. This first electrode, then, functions with a magnetization that is constant in terms of magnitude and direction as reference layer.
The second electrode made of a soft-magnetic material, typically, a nickel-iron alloy, then forms a memory layer. The magnetization of the memory layer is oriented in the same direction as or in the opposite direction to the magnetization of the reference layer, in a manner corresponding to a data content of the memory cell. The memory cell, thus, has two distinguishable magnetization states (unidirectional, oppositely directed) in accordance with its data content.
The frequency of a passage of electrons from one electrode to the other (quantum mechanical tunneling probability) is dependent on the spin polarization of the electrons in the two electrodes. The tunneling probability is higher in the case of unidirectional magnetization of the two electrodes than in the case of oppositely directed magnetization of the two electrodes. From the conductivity of the MTJ element, it is possible to deduce the orientation of the magnetization of the memory layer relative to the magnetization of the reference layer and, thus, the data content of the memory cell.
A magnetoresistive memory cell usually has further components in addition to the MTJ element. In present concepts, by way of example, the reference layer is provided as a partial layer of an artificial antiferromagnet and the magnetization of the reference layer is, thereby, stabilized. Compared with individual hard-magnetic layers, ferromagnetic or antiferromagnetic systems that are coupled to such an extent through the Rudermann-Kittel-Kasuya-Yoshida (RKKY) interaction have an improved thermal and long-term data stability and are less sensitive to interference magnetic fields.
The tunneling probability in an MTJ element is dependent on the thickness of the tunnel barrier (barrier length), the solid-state properties of the material of the tunnel barrier and the two electrodes (barrier height), the state densities of the electrons in the two electrodes, and on a measurement voltage U
m
applied between the two electrodes.
Specifically, in accordance with the Bardeen formalism for a tunneling current I between two electrodes on both sides of a tunnel barrier, a dependence on an external field &Dgr;F results from the summation of the individual occupation states—regulated by the Fermi distribution f(E)—in the two electrodes &ngr;, &mgr;:
I
(
Δ
F
)
=
2
π
e
ℏ
-
∑
μ
∑
v
|
T
μ
,
v
|
2
f
(
E
μ
)
(
l
-
f
(
E
v
)
)
δ
(
E
μ
-
E
v
-
Δ
F
)
(
1
)
where:
T
&mgr;,&ngr;
: matrix element between an occupation state &PSgr;&mgr; of the first electrode and an occupation state &PSgr;
&ngr;
of the second electrode,
E: energy of an occupation state &PSgr;,
f(E): Fermi function.
By introducing the electron state densities N(E), it is possible to convert the formula (1) into an integral form:
I
(
Δ
F
)
=
2
π
e
ℏ
∫
E
L
.
μ
∞
ⅆ
E
μ
∫
E
L
,
v
∞
ⅆ
E
v
N
μ
(
E
μ
)
N
v
(
E
v
)
&AutoLeftMatch;
|
&AutoLeftMatch;
T
μ
,
v
|
2
f
(
E
μ
)
(
1
-
f
(
E
v
)
)
δ
(
E
μ
-
E
v
-
Δ
F
)
(
2
)
where E
L
: conduction band minimum of the electrodes.
For small voltages, the matrix elements and the state densities are regarded as virtually independent of impulse and energy of the electrons and are in each case extracted before the integral. Furthermore, the product of two Fermi functions at the critical temperature of 300 K yields a virtually rectangular window. Under these assumptions, with
R
T
=
ℏ
e
2
N
μ
N
v
|
T
μ
,
v
|
2
(
3
)
the following results for the tunneling current I(&Dgr;F):
I
(
Δ
F
)
=
e
R
T
∫
E
L
∞
ⅆ
Ef
(
E
)
(
l
-
f
(
E
-
Δ
F
)
)
(
4
)
I
(
Δ
F
)
=
e
Δ
F
e
2
R
T
(
l
-
exp
(
-
Δ
E
k
B
T
)
)
(
5
)
In such a case, the matrix element, which can be interrupted as transmission probability for electrons from an initial occupation state through the tunnel barrier to a final occupation state, is proportional to a state density at the Fermi edge, D(E, U
m
). For an arbitrary profile of the potential barrier &PHgr;(z) within the tunnel barrier in dependence on the spatial variable z, the following relationship results according to J. G. Simmons, “Generalized Formula for the Electric Tunnel Effect between Similar Electrodes Separated by a Thin Insulating Film”, J. Appl. Phys., Vol. 34, No. 6, 1793-1803, 1963:
|
T
μ
,
v
|
2
∝
D
(
E
,
V
)
=
exp
(
-
2
∫
0
d
[
2
m
ℏ
2
(
E
F
,
μ
+
Φ
(
z
)
-
E
)
]
ⅆ
z
)
(
6
)
According to the approximation according to Wentzel, Kramers and Brillouin (WBK approximation) for simple tunnel barriers without taking account of image potentials, the following results for a matrix element:
&LeftBracketingBar;
T
μ
,
v
&RightBracketingBar;
2
∝
D
(
E
,
V
)
≈
exp
(
-
2
d
2
m
ℏ
2
(
E
F
,
μ
+
Φμ
-
Φ
v
2
-
|
e
V
2
|
-
E
)
)
(
7
)
Inserted into the derived formula for the tunneling current I, the latter can be developed into a series having the form
I
(
U
m
)=
aU
m
+bU
m
2
+. . . .
The magnetoresistive effect, that is to say the dependence of the tunneling current on the relative magnetic polarization, results from the spin-dependent state densities of the electrons, and also the influenceability of the spin-dependent state densities by a magnetic field.
Furthermore, from formula (5) including formula (7), a polarity-independent or virtually polarity-independent current-voltage behavior results at customary tunnel barriers.
Methods for producing tunnel barriers have been described in many places.
P. Rottlander et al. “Tantalum oxide as an alternative low height tunnel barrier in magnetic junctions” in Applied Physics Letters, Vol. 78, No. 21, May 21, 2001, describe a tunnel barrier made of oxidized tantalum (TaOx) with a barrier height of about 0.4 eV.
N. F. Gillies et al. describe in “Magnetic tunnel junctions with tantalum oxide barriers displaying a magnetoresistance ratio of up to 10% at room temperature” in Applied Physics Letters, Vol. 78, No. 22, May 28, 2001, the dependence of barrier height and barrier length on the oxidation time of a tantalum layer having a thickness of 0.8 nm.
For Zns tunnel barriers, barrier heights of 0.58 eV are specified, e.g., in N. G
Greenberg Laurence A.
Huynh Andy
Infineon - Technologies AG
Mayback Gregory L.
Nelms David
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