Conductance in Co/Al2O3/Si/Al2O3 permalloy with asymmetrically doped barrier

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by  R. Guerrero

Conductance in Co|Al2O3|Si|Al2O3 Permalloy with asymmetrically doped barrier
R. Guerrero,1 F. G. Aliev,1 R. Villar,1 T. Santos,2 J. Moodera,2 V. K. Dugaev,3 and J. Barnaś4
1Dpto. de Fisica de la Materia Condensada, C-III,
Universidad Autonoma de Madrid, 28049, Madrid, Spain
2Francis Bitter Magnet Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
3Department of Physics, Rzeszów University of Technology,
al. Powstańców Warszawy 6, 35-959 Rzeszów, Poland,
and Department of Physics and CFIF, Instituto Superior Técnico,
TU Lisbon, av. Rovisco Pais, 1049-001 Lisbon, Portugal
0 4Department of Physics, Adam Mickiewicz University, Umultowska 85,
1 61-614 Poznań, Poland; and Institute of Molecular Physics,
0 Polish Academy of Sciences, Smoluchowskiego 17, 60-197 Poznań, Poland
2 (Dated: January 14, 2010)

n We report on dependence of conductance and tunnelling magnetoresistance on bias voltage at
a different temperatures down to 2K in Co|Al2O3(10Å)|Si(δ)|Al2O3(2Å)|Permalloy magnetic tunnel
J
junctions. Complementary low frequency noise measurements are used to understand the conduc-

4 tance results. The obtained data indicate the breakdown of the Coulomb blockade for thickness of
1 the asymmetric silicon layer exceeding 1.2Å. The crossover in the conductance, the dependence of
the tunnelling magnetoresistance with the bias voltage and the noise below 80K correspond to 1
] monolayercoverage. Interestingly,thezerobiasmagnetoresistanceremainsnearlyunaffectedbythe
r
e presenceofthesiliconlayer. TheproposedmodelusesLarkin-Matveevapproximationoftunnelling
h through a single impurity layer generalized to 3D case and takes into account the variation of the
t barriershapewiththebiasvoltage. Themaindifferenceisthelocalization ofalltheimpuritylevels
o
within a single atomic layer. In the high thickness case, up to 1.8Å, we have introduced a phe-
.
t nomenological parameter, which reflects the number of single levels on the total density of silicon
a
m atoms.
- PACSnumbers:
d
n
o I. INTRODUCTION [5], nonmagnetic [6] (even superconducting [6, 7]) quan-
c
tum dots (QD), would add a new degree of freedom to
[
spin polarized tunnelling and strongly enhance the ver-
The discovery of large tunnelling magnetoresistance
1 satilityofspintronicdevicesbasedonspinpolarizedtun-
(TMR) at room temperature [1, 2] has strongly renewed
v
nelling. Tunnelling in such hybrid, but non magnetic
5 the interest in spin tunnelling phenomena. Up to very
devices, has been intensively studied during the last two
1 recently the main efforts were concentrated on the in-
decadesandespeciallyinsingleelectrontransistorswhere
4 crease of tunnelling magnetoresistance values by using
2 ferromagnetic electrodes with the highest possible spin thegateelectrodeisattachedtoquantumdotsseparated
. bytwobarrierseachwithametalliccontact(emitterand
1 polarization(halfmetallicferromagnetism),searchingfor
collector)[8].
0 new types of insulating barriers (including the so called
0 spin filters [3]), or a combination of both approaches, Recent theoretical studies of hybrid spintronic devices
1
where the ferromagnetic/insulatorinterfacedesign could with two ferromagnetic leads contacting single or dou-
:
v alsoplayanimportantrolefor spinpolarizedtunnelling. ble quantum dots have revealed plenty of new interest-
Xi The last approach has recently provided an enormous ing phenomena related with the interplay between mag-
progressintheTMRvaluesatroomtemperatures. Ithas netic tunnelling processes and spin/chargeaccumulation
r
a been demonstrated that in epitaxial Fe/MgO/Fe mag- on quantum dots. From the experimental side, some
netic tunnel junctions (MTJ), where there exist condi- few groupshave demonstratedthat Coulombinteraction
tions for coherent propagation of specific spin orbitals mayindeedplayanimportantrolenotonlyin ferromag-
fromone ferromagneticelectrode to the other one,TMR netic granular systems [9] (as occurs in the correspond-
has reached experimentally values up to 410% [4]. This ing nonmagnetic analogs),but also in ferromagnetic sin-
fact, supported by theoretical calculations predicting a gle electron tunnelling devices constructed either from a
TMR of more than 1000% have further increased both 2D electrongas [10] or when a single metallic nanoparti-
the fundamentalandtechnologicalinterestinspinpolar- cle is contacted by ferromagnetic electrodes [11]. It has
ized tunnelling. alsobeenreportedthatinultrasmallnanoparticles,with
Another possible research direction, which remains a diameter between 5-10nm, their electronic structures
howeverpoorlyexplored,is relatedto tunnelling incom- (i.e. quantum effects) may also influence spin polarized
plex (hybrid) junctions. Indeed, the manipulation of the tunnelling[12]. Otherinterestingexamplesofspinpolar-
barrier by doping with magnetic or nonmagnetic impu- izedtunnellinginhybridstructuresincludeferromagnetic
rities, or inserting magnetic, for example see reference leadscontactingcarbonnanotubes[13]oraC60molecule
2
[14]. nelling rates from one of the electrodes to the central
Actually,fromthetechnologicalpointofview,itiseas- particle, and from the island to the other electrode. As
ier to attach ferromagnetic leads via tunnelling barriers soon as conductance and spin current polarization are
to an array instead of to a single quantum dot. This modified, a modificationof the dependence onvoltageof
method, despite the evident drawback due to some dis- the tunnelling magnetoresistance may be expected. In-
tributioninQDsizesandthecorrespondingchargingen- deed, when the bias voltage is increased, the number of
ergies,addsevidentversatilitytothedesignoftheexper- allowed two steps processes is also increased.
iment, allowing continuous tuning between two different Previously to this work, Jansen et al. [23] studied
regimes: (i) weak doping regime where QDs are substi- MTJs with Si nanoparticles up to 1.8Å introduced in
tuted by impurities and (ii) strong doping regime. In a symmetric position. They observed gradual suppres-
thesecondregimeonewouldexpecttheQDchargingen- sionoftunnellingmagnetoresistance. Inthepresentwork
ergy to reduce continuously with the average dot size, Si particles were introduced asymmetrically inside the
allowing sequential electron transport through an other- barrier. While symmetric doping effectively separates
wise blocked channel (Coulomb blockade) in addition to the barrier into two parts with similar tunneling rates,
direct tunnelling. the asymmetric doping is expected to affect weakly the
Therefore, the knowledge of different mechanisms af- largest tunneling rate minimizing the influence of the
fecting the conductance, and especially its dependence nonmagnetic Si doping (at least for relatively weak dop-
on the applied bias, could be an important instrument ing levels).
for a comparative analysis of noise and transport. We This work presents an experimen-
should, however, note that the bias dependence of con- tal study of electron transport in
ductivity and TMR in real magnetic tunnel junctions, is Co(100Å)/Al2O3(10Å)/Si(δ)/Al2O3(2Å)/Py(100Å)
still poorly understood. The most accepted model [15], hybrid magnetic tunnel junctions, where the largest
which does not take into accountthe possible defects in- barrieris5timeslargerthanthe shortone. We observed
side the barrier, predicts an attenuation of the polariza- acontinuoustransitionbetweenthe weak(Si impurities)
tion due to the decrease of the difference between the and strong (array of Si quantum dots) regimes. In order
height of the barrier and the bias voltage. However, the to discriminate the different conductance regimes, we
observed reduction in conductivity usually exceeds the study the temperature and bias dependence of both the
predicted effect. conductivity and TMR as a function of Si doping.
Two theories have been developed in order to explain
the anomalous reductionin TMR. The firstone explores
the existence of impurity states, which reduce the spin II. EXPERIMENTAL DETAILS.
currentpolarizationandinfluencetheconductanceofthe
junctionsatlowbias[16]. Thesecondoneinvolvesinelas- Detailsofsamplepreparationhavebeenpublishedpre-
tic tunnelling as the main origin of unpolarized current viously[23]. Forsilicondoped samples,the tunnel barri-
[17]. This point of view has been also supported by the ers were deposited in two steps. After deposition of the
measurement of inelastic tunnelling in magnetic tunnel underlyingCoelectrode,afirsttunnelbarrierwasformed
junctions [18]. Later on Ding et al [19] have also de- by deposition and subsequent oxidation of 10 Å of Al.
tected a tunnelling magnetoresistance in vacuum based Subsequently, sub-monolayeramounts ofSi (δ in the fol-
magnetictunneljunctionswithareduceddependenceon lowing)weredepositedontheAl O surface,followedby
2 3
the bias voltage. These results indicate a possible in- a secondAl layerdeposition (2 Å) and oxidation,result-
fluence of the impurity states on the polarization of the ing ina “δ-doped” Al O |Si|Al O tunnel barrier. After
2 3 2 3
tunnel current. thedepositionofthe barrier100Åofpermalloywerede-
For the nonmagnetic tunnel junctions with (nonmag- posited, in order to form the second magnetic layer. All
netic) nanoparticles inside the barrier the presence of a the samples thicknesses were measured using a quartz
zero bias anomaly was first reported and explained by monitor. The quality of the Al layersand the Al O has
2 3
Giaever [20]. The main mechanism responsible for the been previously tested in Ref. [24, 25]. In the following
appearance of the threshold voltage is Coulomb block- the positive bias voltage corresponds to the application
ade, which controls two steps tunnelling. In this model of the voltage in the top electrode, while the negative to
the threshold voltage is distributed from 0 V to a max- application of the voltage in the bottom one.
imum voltage Vs. In the doped tunnel junctions Vs is Measurements were performed using a computer con-
given by the size of the doping particles, which deter- trolled system [26], which allows to detect the dynamic
mines a charging energy,given by the capacitance of the resistance, the DC value of the current and the voltage,
particles. This providessome distributioninthe popula- and the noise in the device under study. Biasing of the
tion of electrons inside the particles. samples was done at a constant current, applied using a
Thetwostepstunnellinginamagnetictunneljunction calibrated source. It also allowed to modulate the ap-
has beenlater treatedusing the othermethod developed plied current. A square waveform was used in order to
by Glazman and Matveev [21, 22]. This theory states detect the transfer function of the line and the dynamic
that the current is defined, in each particle, by the tun- resistance of the junctions. The voltage response of the
3

20(a) 1.5 0.20(b) 120 100 a T=2K. bT= 300K.
width(¯)11112468 01..50 Height(eV) Assymetry(eV) 000...011505 G(S) 10246800000-0.2 -0.1 V0(.V0) 0.1 0.2 R(K) 10
10 0.00 10.0 0.4 0.8 1.2 1.6 2.00.0 0.4 0.8 1.2 1.6 2.0
8 0.0 0.4 0.8 1.2 1.6 2.00.0 0.0 0.4 0.8 1.2 1.6 2.0 (¯) (¯)
(¯) (¯)
FIG. 2: Resistance of the MTJ’s at low temperature, graph
FIG. 1: Barrier parameters evaluated using the BDR model. (a) and room temperature, graph (a), as a function of the Si
The graph (a) shows the barrier width and height in the left thickness (δ(Å)). The lines in the graphs are guides to the
andtherightaxis,respectively,asfunctionoftheSithickness. eyes.
In the graph (b) is shown the asymmetry also as function of
the Si thickness. In the inset we present the typical depen-
dence on voltage of the conductance at room temperature. of the barrier, it clearly diminishes when the silicon is
The dashed line is a parabolic fit used to extract theparam- introduced inside the barrier. At present we have no
eters plotted in thegraph (a) and (b). clear explanation for this reduction. One of the possible
reasons could be some decrease of the work function of
the aluminium oxide. This explanation, however, con-
deviceswasamplifiedbyusingDCcoupledlownoiseam-
tradicts the observedvariationof the barrierasymmetry
plifiers. The amplified signal was recorded in an analog-
(Fig. 1), which decreases with the thickness of the Si
digital converter.
layer. Thedisagreementbetweenthedepositedthickness
The measurement of the noise uses the same biasing
andtheobtainedparametersusingtheBDRmodelcould
technique and the same low noise amplifiers, which were
be attributed either to the simplification made by the
placed in the top part of a cryostat. The pre-amplified
model, which assums a trapezoidal barrier, a parabolic
signals are further amplified by additional low-noise am-
band structure and the WKB approximation, or to de-
plifiers(StanfordResearchSR560). Aspectrumanalyzer
fects inside the barrier that should diminish the barrier
SR780 calculates the cross-correlation spectrum of the
height. However the obtained results present evidence
voltagenoise,containingthermal,shotand1/f contribu-
that the Si layer affects the barrier properties beyond
tions. Theobtaineddynamicresistanceallowstoconvert
the errors committed in the estimation procedure.
the voltage noise into the current noise. Extrinsic noise,
ThetunnellingresistanceofthestudiedSidopedMTJs
introduced by the amplifiers and the currentsource,was
measuredatT =2KandT =300K,inthezerobiaslimit,
removed by using the data extracted from a careful cal-
is plotted in Fig. 2. The observed enhancement of the
ibration performed on resistors at low temperatures. In
resistancewhen the temperature is loweredrules out the
the experiments we measured 9 different samples, 2 of
presence of pinholes even for the highest silicon thick-
eachSithickness,exceptforδ=0.6Åwhereweonlychara-
ness [28, 29]. There is an increase of the resistance for
terized 1.
δ ≥1.5Å,bothatroomandlowtemperatures,whereasat
lower concentrations the resistance trend is to decrease.
This factindicatesa changeofthe regimein the conduc-
III. CONDUCTANCE, ZERO BIAS ANOMALY
tance,whichwillbefurtherconfirmedinthedependence
AND TUNNELLING MAGNETORESISTANCE
of the conductance on the bias voltage and the TMR.
At room temperature the dependence of the conduc-
tance on the bias voltage fits well to a parabolic func-
A. Dependence of the conductance on the voltage
tion (see inset to Fig. 1b). The parabolic depen-
at low temperatures
denceoftheconductance,beingduetodirecttunnelling,
wasexplainedwithintheBrinkman-Dynes-Rowell(BDR)
model [27], which describes the tunnelling conductance Whileatroomtemperatureconductanceisaparabolic
as a function of the parameters of a trapezoidal barrier: function of the bias, at low temperatures (below 100 K),
the width, the averageheightandthe difference between the dependence of conductance on the bias changes sub-
the sides of the barrier, such difference being known as stantially. On the one hand, all MTJs at low biases
asymmetry. (V.30 mV) present a peak in the resistance. Usually
The results of the fits are plotted in Fig. 1, showing such a peak is called zero bias anomaly (ZBA). On
in general an increase of the barrier width with Si dop- the other hand, high bias conductance regimes (above
ing. However, the increase of the width does not corre- 100 mV) show a strong variation with silicon thickness.
spond with the deposited Si thickness. As to the height Toshowmoreclearlythequalitativechangeofconduc-
4
tance regime with Si doping we present the bias depen- Wehaveobservedthatgenerally,forallMTJsstudied,
dence of the normalized conductance the low bias conductance varies linearly with tempera-
tureatlowtemperatures(T<20K).WithintheCoulomb
R(100mV−R(0mV) blockade model this could be attributed to a variation
ZBA(%)=100× (1)
R(100mV) in the thermally activated population of electrons inside
the islands [30], which determines the slope of the con-
The dependence of ZBA vs. Si thickness, plotted in ductance at zero bias. In brief, the conductance at zero
Fig. 4, shows that the resistance peak, being weakly bias and low temperatures could be expressed as
dependentonδforlowSithickness,stronglyincreasesfor
thehighdopingregion. Thecrossoverregioncorresponds
to the thickness of approximately δ=1.2 Å. ∞ −eVCh kB
Theexperimentaldatapresentedabovemaybeunder- G(0,T)∝Z n(VCh)e kBT dVCh ∼n(VCh ∼0) e T
0
stoodwithinthetwo-stepmodelasfollows. Iftheforma- (2)
tion of silicon islands starts for a Si thickness δ=1.2 Å, where eV is the charging energy needed to intro-
Ch
then the enhanced resistance peak (ZBA) could be at- duce an electron in the metallic layer. At V =0 V the
tributed to the appearance of a new energy scale in the number of charged islands is given by the exponential
electron transport through the barrier, related with the term. Then,atlowtemperatures,theconductanceispro-
finite electron capacitance of the silicon islands, being portional to the number of charged particles in thermal
practically absent for the small Si thickness range. This equilibriumn(0). Althoughthetemperaturedependence
hypothesisissupportedbytheplotofthenormalizedbias of conductivity of the different MTJs studied varies in
voltage dependence of the conductance, Fig. 3. Clearly nearly two ordersof magnitude, the normalized(to 2 K)
in the conductance of the junctions with higher Si dop- low temperature slope in the linear dependence of con-
ing levels there is a crossover at a certain voltage. At ductivity vs. temperature was found to be much weakly
higher voltage the dependence of the conductance be- dependentonthesiliconthickness,withanaveragevalue
comes less pronounced, whereas the junctions with low of (5±3)×10−4 K−1 but with a rather large dispersion
dopingmaintainthesamebehavior,asexpectedinanon- (Fig. 5).
doped tunnel junction with electrontransportdue to di-
rect tunneling.
The change of the conductance regime is also evident
B. Tunneling magnetoresistance
from comparison of the lower bias conductance for un-
doped MTJs and those with highest Si doping (corre-
The dependence of the tunnelling magnetoresistance
sponding to δ=1.8 Å). As can be seen in the (b) graph
on Si thickness is shownin figure 6. This plot represents
in Fig. 3, both curves show structure in G(V) at low
the zero bias tunnelling magnetoresistance, obtained by
bias close to V=30 mV. The similarity of these weak
using the following definition of TMR
anomalies both for the undoped and doped MTJs in-
dicate their common origin, most probably related with
electron conduction mechanisms through the aluminium
oxide barrier.

100
100 (¯) 80 AP
a 01.2 1.4 b %) P
G(0) 1.8 A( 60
G(V)/ 10 1. 2 ZB 40
(¯)
1.8
1.0 0 20
1
-1.0 -0.5 0.0 0.5 1.0-0.2 -0.1 0.0 0.1
V(V) V(V) 0 0.0 0.4 0.8 1.2 1.6 2.0
(¯)
FIG. 3: Dependence of the conductance on the bias voltage
at T=2 K. The curves are normalized by the conductance
measured at 0mV in each curve. The plot (a) presents data FIG. 4: Dependence of the quantity ZBA (defined in the
up tohigh bias, where a mechanism related to theformation text) on silicon thickness at T=2 K in the parallel (P) and
ofSiislandsbecomesimportant(seethetext). Thegraph(b) theantiparallel (AP) magnetic state. The increased ZBA at
presents the low bias behavior, showing the presence of the higherdopinglayersreflectsadifferentbehavior,relatedwith
same zero bias anomaly at V.30mV. theformation of Siislands.
5
Indeed, forsmallSithickness,only directtunnelling is
possible,dueto Coulombblockade. Thisweaklychanges
1.2 1.002
TMRatlowtemperaturesfor smallbias,whichdoesnot
-1 mK) 0.9 a 2K) b activatepossiblespinmixingduetothespinflipprocesses
n( 0.6 T)/G(1.001 introduced by the Si. The Coulomb blockade is sup-
G( pressedforthe dopingrangeofδ ≥1.5Å,asindicatedby
0.3
conductancevs. voltagemeasurements(Fig. 3), opening
0.00.0 0.4 0.8 1.2 1.6 2.0 1.0002 4 6 8 new conductance channels relatedto two-steptunnelling
¯ T(K) via the array of Si dots. The newly opened conductance
channels create also a source of unpolarized current due
FIG. 5: The graph (a) plots the slope of the temperature to spinmixing andloose ofspinmemoryof the electrons
dependenceoftheconductancenormalizedbyitsvalueatthe tunnelling through the array of Si dots. Suppression of
lowesttemperature.Thegraph(b)showsthelowtemperature
Coulomb blockade just for the Si thickness bigger than
linear dependenceof theconductanceon temperature.
1.2Å could be due to activation of a segregation process
of Si atoms to nanometer scale dots, acting as a real ca-
pacitance. This is contrary to the behaviour in low Si
thickness junctions, where seems reasonable to suppose

that Si could be more homogenously diluted inside the
30
Al O barrier in form of impurities and defects. In fact,
2 3
two step tunnelling could, in principle, affect the con-
ductance for both regimes discussed above. This is due
%) 20 to the unavoidablepresence of defects inside the barrier,
( evenwithout Si doping [31], whichmix the spincurrents
R
M and are a source of an unpolarized current. Therefore,
T thisimpliesthepresenceofafinitecharacteristicspin-flip
10
300K time on the defects and on the silicon layer both for the
80K
low and the high Si thickness regimes [32].
2K
TheanalysisofbiasdependenceofTMRwhichfollows
0 further supports our hypothesis. In order to analyze the
0.0 0.4 0.8 1.2 1.6 2.0
bias dependence of TMR as a function of Si thickness,
(¯)
we have found the voltage needed to suppress a TMR
to its half (zero bias) value (i.e. to TMR(0 V)/2). This
FIG. 6: Dependence of the tunnelling magnetoresistance on parameter, called VTMR/2 is shown in Fig.7, plotted as
the silicon thickness (δ(Å)) at three different temperatures. a function of the silicon thickness. Evidently, there is
Whilepresenceofsiliconreducessignificantlythepolarization a crossover from a nearly constant VTMR/2 regime be-
atroomtemperature,decreasingthevalueoftheTMRratio, low δ =1.2 Å, to a strongly decreasing one VTMR/2 as
for temperatures below 80K the presence of the silicon layer a function of δ, for Si thicknesses above one monolayer.
seems not to affect the spin polarization, for δ ≤1.2Å˙. Some The low Si doping regime with nearly constant VTMR/2
small influenceappears at δ>1.2 Å.
provesthe presenceoftwo steptunnelling throughlocal-
ized states, with character and density of states nearly
unchanged up to Si thickness of 1.2 Å.
When δ ≥ 1.2 seems that the effective capacitance
R −R
AP P corresponding to localized states inside the barrier is re-
TMR(%)=100× (3)
RP duced,increasingdramaticallythenumberofstatesavail-
able inside the barrierfor tunnelling. The new transport
where R and R are the resistance in the antiparallel
AP P
channels serve as a source of unpolarized current, which
and the parallel states, respectively.
explains the much stronger voltage dependence of TMR
We have analyzed zero bias TMR vs. Si thickness for
for large Si doping.
three different temperatures (300 K, 80 K, 2 K). The
influence of the silicon doping on TMR is strongest at
roomtemperature,suppressingTMRinnearlyoneorder
ofmagnitudeforthehighestSithickness(1.8Å).Thelow IV. THEORETICAL MODEL
temperature TMR values, however, remain nearly unaf-
fected by the silicon. The step-like reduction of TMR To account for the above discussed experimental fea-
at low temperatures (of about 10% at 77 K and 2 K) turesofelectronictransportintunneljunctions,wecalcu-
was observed for a Si thickness of δ ≥1.2 Å. This appar- latenowtheoreticallytransportcharacteristicsasafunc-
entreductionofthetunnellingmagnetoresistancemaybe tionofbiasvoltageV usingthemodelofrectangulartun-
directly linked to variation of the ZBA with Si content neling barrier with a thin layer of impurities (Si atoms)
(shown in Fig. 4). which create a number of impurity levels inside the bar-
6
A. Impurity-mediated tunneling
Asthedensityofimpuritiesgrows,anadditionalmech-
anismoftunnelingthroughtheimpuritylevelsinsidethe
barrier becomes more effective than the direct tunnel-
ing. In the frame of the Larkin-Matveev [22] model, the
resonanttunneling throughthe structure is described by
the transition probabilities w . More specifically, w
kp kp
is the probability of transition from the state described
by the wavevectorp on the left side of the barrierto the
statecorrespondingtothewavevectorkontherightside
(from now on we drop the spin index σ referring to the
tunneling in different spin channels), and is given by the
formula
2
2π T T
ki ip
w = δ(ε −ε ), (5)
FIG. 7: Voltage needed to reduce the tunnelling magnetore- kp ~ (cid:12)(cid:12)(cid:12)Xi εp−εi+iΓi(cid:12)(cid:12)(cid:12) p k
(cid:12) (cid:12)
sistance to 1/2 of its value at zero bias at T∼2K. This value whereT andT (cid:12)arethematrixele(cid:12)mentsfortransitions
pi ik
quantifies the dependence of the magnetoresistance on the between the states of the correspondingleads and of the
bias voltage. A low value of VTMR/2 means a strong depen- i-th impurity, whereas Γi is the width of the impurity
dence on bias voltage, while a high value means a weak one. level associated with tunneling from the localized level
We observe a diminished value of VTMR/2 when the ZBA through the barrier. The sum in Eq. (5) runs over all
starts to increase (see Fig. 4 ).
impurities. The i factor is the imaginary unit.
An important point is that the matrix elements T
pi
andT include aphasefactordepending onthe location
ik
rier. In the limit of low density of Si levels, the current of the impurity inside the barrier,
is due to direct tunneling in each spin channel, and the 1 ~2
current density can be calculated from the formula Tki = S1/2 e−ikl·Ri ekz(zi−L/2) m (2πκ)1/2, (6)
1 ~2
e [2m(ε−Vlσ)]1/2/~ Tip = S1/2 eipl·Ri e−pz(zi+L/2) m (2πκ)1/2, (7)
j(V)= dε k dk |t |2
4π2~ Z Z l l kσ where S is the junction area, Ri and zi are the in-plane
Xσ 0 and out-of-plane components of the i-th impurity posi-
× ε−~2kl2/2m−Vrσ 1/2[f(ε)−f(ε−eV)], (4) tion, k ≡ (kl,ikz) (and similarly for p), while κ is the
(cid:18)ε−~2k2/2m−V (cid:19) inverse localization length of the impurity wavefunction.
l lσ
We assume that the impurities are randomly distributed
in the plane, i.e. R is a random variable, whereas z is
i i
where kl is the in-plane wavevector component of an the same for all impurities.
electron incident on the barrier, tkσ is the transmis- Assuming that the energy level εi and the level width
sion amplitude for an electron with wavevector k and Γ do not depend onthe position R, and averagingover
i i
spin σ, while Vlσ and Vrσ are the spin-dependent en- Ri in the plane, we obtain the following formula for the
ergy band edges on the left and right sides of the junc- electric current:
tion, respectively, which depend on the applied voltage
as Vlσ = Vlσ0 +eV/2 and Vr = Vrσ0 −eV/2 (here Vlσ0 j(V)= 2πe | iTkiTip|2
and V are the corresponding band edges at zero volt- S~ (εP−ε)2+Γ2
rσ0 Xσ Xk,p k i i
age). Apart from this, the integration in Eq. (4) is over
the electronenergy ǫ, and f(ε) is the Fermi-Dirac distri- ×δ(εk−εp)[f(εk)−f(εk−eV)]. (8)
bution function.
After calculatingthe average| T T |2,onefinds that
To calculate the tunneling probability for a nonzero i ki ip
the current density j in the rePsonance-impurity channel
voltage applied to the system we use a semiclassical ap-
consists of two terms, and can be written as
proximationfor the wavefunctioninside the barrier with
a slope of potential. This is justified in case when the 2πe n|T |2|T |2
j(V)= ki ip [1+nδ(k −p )]
wvaarviaelteionngtohf tλhe∼ba~r/r(ie2rmhVei)g1h/t2,V0wihsicshmarlelsatrtictthsetehleectbrioans ~ Xσ Xk,p (εk−εi)2+Γ2i l l
0
voltage to |eV| ≪ m1/2V3/2L/~, where L is the barrier ×δ(εk−εp)[f(εk)−f(εk−eV)].
0
(9)
width.
7
n=1.0 1013cm-2 n=1.0 1013cm-2
40 1.0 1014 1.0 1014
) 2.0 1014 1.3 2.0 1014
-1m 34..00 11001144 34..00 11001144
c 30 )
1 0
- G( 1.2
40 20 V)/
1
( G(
S 1.1
G/ 10
0 1.0
-0.4 -0.2 0.0 0.2 0.4 -0.4 -0.2 0.0 0.2 0.4
V(V) V(V)
FIG. 8: Total conductance per unit area, G/S, calculated FIG. 9: Reduced conductance, G(V)/G(0), as a function of
as a function of the bias voltage for indicated areal impurity bias voltage V for indicated density of Si atoms. The other
concentrations. The other parameters are described in the parameters as in Fig. 8
text.
tal data (Fig. 2), however,reveala rather sharp increase
ThefirstterminEq.(9)islinearinthe2Dimpurityden-
of the resistance to much higher values when the den-
sity n and describes the transitions through completely
sityncrossesacriticalvaluen correspondingtonearly
cr
isolated single levels. Such transitions do not conserve
complete filling of one atomic layer with Si atoms. The
the in-plane components of p and k. The second term
resultsforTMRpresentedinFigs.6and7alsoshowthat
in Eq.(9) is nonlinear in n and describes the electron
the physics of tunneling is substantially different for the
transitions through the impurity plane. For such transi-
density of Si atoms corresponding to complete filling of
tions the corresponding in-plane components of electron
the plane.
wavevectorsare conserved.
We assume that the physical reasonof such transition
In our calculations we include all three channels. The
is related to a dramatic increase of the role of Coulomb
total conductance per unit area, G/S, is presented in
interactionintheconductancethroughtheSilevels. This
Fig. 8 for parallel magnetic configuration and for indi-
effect can be also described by the decrease of the num-
cated impurity concentrations. The width of the tun-
ber of active levels, which are able to transmit electrons
nel barrier is taken as L = 1.2 nm, and the Si atoms
through the barrier. Indeed, if some Si atoms form a
are located within the plane of z = −0.4 nm, mea-
i small cluster, then the cluster of several atoms acts as
sured from the center of the barrier. The energy struc-
a single level for transmission because the Coulomb in-
ture corresponds to the majority and minority bands in
teraction prevents two or more electrons to occupy the
Co, E = 4.5 eV and E = 0.66 eV, respectively.
F↓ F↑ samecluster. ThuswecanassumethatEq.(9)describes
The height of the barrier is assumed to be V = 1 eV.
0 the conductance as a function of the density of effective
In turn, in Fig. 9 we show the reduced conductance,
levels, n → n , corresponding to the number of im-
ef
G(V)/G(V =0).
purity clusters. As the density of Si atoms approaches
It should be noted that the conductance as well as
the critical value n , the value of n decreases rapidly.
cr ef
thereducedconductanceareslightlyasymmetric withre-
If n > n and the density of Si atoms keeps growing
cr
spect to bias reversal, see Fig. 8 and Fig. 9. This asym-
then it corresponds to increasing thickness of the layer
metry is here associated with tunneling through single
completely filled with the Si atoms. In such a case the
impurity levels which are located asymmetrically within
Coulomb interaction is suppressed as there are no small
the barrier. In our calculations we assumed that the im-
clusters anymore, and the conductance can be described
purities are located in the barrier close to the interface
using a model of three-layer structure with well-defined
betweenthebarrierandoneoftheelectrodes–likeinex-
propertiesof eachofthe layers. One canexpect that the
perimentsdiscussedabove. Suchanasymmetryofimpu-
properties of the Si layer in such a structure are close to
rity position with respect to the center of tunnel barrier
those of layered amorphous Si.
leads to the asymmetry of the conductance G(V).
It should be emphasized that the direct tunneling is
also suppressed in the vicinity of n ∼ n . This is re-
cr
lated to the Coulomb repulsion of electrons transmitted
B. Role of Coulomb interaction
through the barrier from the charged impurity clusters,
sothatthe electronscantunnel throughthe barrieronly
When the density of impurity levels n grows, the con- in those areas, which are free from the impurity clusters
ductance calculated within the model described above orislands. Onecandescribethisbyalocalincreaseofthe
andincludingbothdirectandimpurity-mediatedtunnel- tunneling barrier in the areas filled with clusters. This
ingincreasesmonotonically(seeFig.8). Theexperimen- effectively leads to an increase of the average tunneling
8
3.5 n=1.0 1013cm-2
2.4 1.0 1014
3.0 2.0 1014
) 3.0 1014
m 2.2 4.0 1014
c 2.5 )
0 2.0
(
4 2.0 G
-0 )/ 1.8
1 V
( 1.5 ( 1.6
G
S
1.0 1.4
R
0.5 1.2
1.0
0.0 0.05 0.1 0.15 -0.4 -0.2 0.0 0.2 0.4
(nm) V(V)
FIG.10: Variationoftheresistanceperunitsquareasafunc- FIG. 11: Reduced conductance in the model with Coulomb
tion of Si layer thickness. repulsion and the DOS of amorphous Si layer taken into ac-
count.
barrier.
Usingtheabovedescribedideaswehavecalculatedthe findthedependencepresentedinFig.11. Thecalculated
resistanceasafunctionofδ,takingintoaccountallthree dependence shown in Fig. 11 is in reasonable qualitative
channels of conductivity as described above, but instead agreement with the experimental curves Fig. 3,a.
ofthenumberofimpuritiesnweputinEqs.(8),(9)anef-
fectivenumberoflevelsn ,whichweassumedtochange
ef
rapidly from n = n at n < n ≃ 1.1 × 1014 cm−2 V. DISCUSSION
ef cr
to a constant value 1013 cm−2. We also corrected the
contribution due to direct tunneling making it strongly Severalattempts have been made previously trying to
dependent on n in the vicinity of the transition point understand the possible role of Coulomb blockade in the
n = ncr. More specifically, we reduced this contribution tunnelling current and magnetoresistance for ferromag-
for n > ncr by modeling the dependence of the tunnel netic leads contacting a quantum dot [35, 36]. These
barrier V0 on n: for n < ncr we take V0 = const inde- works predict an oscillation in TMR(V) with a period
pendent of n but for n > ncr we assume that this value given by the charging voltage. Experimentally, for tun-
increases by 0.6 eV, which corresponds to suppression of nellingthroughanarrayofdots,theoscillatorybehaviour
the directtunneling due tothe ’screening’fromthe large has beenreportedonly for the magnetic tunnelling junc-
impurity clusters within the Si layer. The results for the tions with a barrier doped with cobalt nanoparticles.
resistance as a function of δ are presented in Fig. 10. As Those junctions had rather small ferromagnetic elec-
onecannote,thetheoreticalcurveisqualitativelysimilar trodes area A=0.5×0.5 µm2 with the conduction almost
to the experimental one. completely blocked at low bias [9], and TMR oscillat-
Further improvement of the model can be made by ing with the period predicted theoretically. Other ex-
taking into accountthe dependence of the impurity den- periments, which also studied spin dependent electron
sity of states ν on energy in the vicinity of the Fermi transport through arrays of dots doping the barrier of
level, ε = µ. One can assume that the function ν(ε) magnetic tunnel junctions, have reached conclusions in
has a minimum near ε = µ in accordance with the respecttoconductancesimilartothosereportedhere,i.e
shape of the density of states (DOS) in amorphous Si observation of a non-oscillating increase of the conduc-
(see, for example, Refs. [33, 34]). The DOS profile tivity with bias, when Coulomb blockade is suppressed
in the vicinity of the minimum at ε = µ in amor- by the applied voltage [5, 6, 10, 37].
phous a-Si can be approximately presented as a sum The above cited reports employed different devices
of the DOS tails related to the conduction and valence in order to study spin dependent tunnelling through a
bands, ν(ε) ≃ ν0 e−(ε−µ+∆)/ε0 +e(ε−µ−∆)/ε0 , where medium controlled by Coulomb blockade, and two of
∆ ≃ 0.25 eV−1atom(cid:0)−1, and ε0 ≃ 100 meV. In t(cid:1)he vicin- them specifically Ref. [5] and Ref. [9] used qualitatively
ity of the minimum at ε = 0 one can use the parabolic similarmagnetictunneljunctiondevices. Inthesepapers
approximation a granular film, consisting of nanometer size cobalt par-
ticles (with radius close to ∼2.5 nm) was embedded in a
(ε−µ)2 matrix of aluminium oxide. This array of Co dots was
ν(ε)≃ν(µ) 1+ (10)
(cid:18) 2ε2 (cid:19) deposited on top of the aluminium oxide barrier (2.7nm
0
in the first case [5] and 1-2 nm in the second one [9])and
where ν(µ)=2ν e−∆/ε0. wascoveredby the secondaluminiumoxidebarrier. The
0
After substituting the constant DOS ν(µ) by the ap- topbarrierwasdifferent in the studies mentioned above.
proximate function (10) with ε = 100 meV, we finally While the firstpaper[5]useda ∼1.5nmthick secondary
0
9
RTN has been previously reported for nonmagnetic
-10 tunnel junctions and some other devices such as field ef-
10
z) fect transistors or quantum dots connected to metallic
H -11
2 V/10 a leads [38]. As to the tunnel junctions, RTN has been
S(1V0-12 1/f usuallyattributedtoresistancefluctuationsduetoasin-
gle or few fluctuators [39]. The RTN was usually found
10-13 for rather small area (below 1µm2) junctions and low
101 102 103 104 temperatures, because in this case the tunnel resistance
V(u.a.)24 t=1 26 sf(Hz) b c islsatarcgtoeenflttruuoncltnleuedaltbjiuoynnacstfoieofwntshfl,euarcsetusiinastttianhngecedp.erfIeenscettnsht,epsctrauosdveyid,oifnthgraettwohbeor--
0
servation of RTN could not be described by the above
3 3
0 1x10 2x10 models,involvingdirectinfluence ofsingle orfew defects
time(u.a.)
fluctuations on the resistance. A non-uniform current
distribution, induced by pin-holes, which are a source of
FIG. 12: Typical random telegraph noise process. The plot
”hotspots” justbeforetheMTJsarebrokendownbythe
(a)showsthepowerspectrumoftheprocess. Itisdominated
intensity of current, would neither explain the observed
by a Lorentzian added to a 1/f noise background (straight
lineinthegraph). Thegraph(b)ofthefigureshowsatypical voltagedependenceoftheRTN.Indeed,ourexperimental
time series. The two states fluctuation is clearly seen in the data,particularlythe current-voltagecharacteristicsand
histogram (shown in (c)). The histogram shows the number thetemperaturedependenceoftheconductanceshowab-
of counts at a certain bin of voltage. Two peaks correspond sence of pinholes and the above mentioned ”hot spots”.
to two states of different conductance. As discussedabove,for thick enoughsiliconlayersδ ≥
1.2 Å the effective capacitance of the Si dots becomes
smallenoughtobreakdowntheCoulombblockadeabove
barrier,thelaterworkdidnotuseanyaluminabarrierto a certain bias voltage. This increases the electron popu-
coverthe Co nanoparticles,whichprobably produced an lationoftheislandduetothetwostepstunnellingevents
uncontrolled secondary barrier. Another difference is re- and enhances the tunnelling conductance.
latedtothejunctionsarea. Inthefirststudyaratherbig It is evident that in the system under study the ca-
(4.5×10−2 mm2) area MTJ was used, while the second pacitanceoftheSidotsand,correspondingly,theSidots
work studied Coulomb blockade controlled spin depen- population, should be distributed over the MTJ area,
dent tunnelling in MTJ’s with much smaller area junc- providingapossiblevariationofthe localtunnelling cur-
tion. All different studies of the spin dependent trans- rent as a function of the spatial coordinate. In addition,
port in MTJ’s with nanoparticle doped barrier,with the the two-level systems situated close to the Si dots seem
exception ofYakushiji et al., [9], reporteda staircasede- to introduce also time dependent fluctuations or RTN
pendence of the IVs presumably due to single electron in the tunnelling current through these dots. The un-
charging effects, and did not show any conductance os- avoidable dependence of the tunnelling current on the
cillation. coordinatemayenhance the effective contributionto the
Although our samples have a silicon δ layer inside the overallconductancefromonlyafewfluctuators,resulting
barrier, instead of a magnetic δ layer introduced in the in a noise contribution additionalto 1/f due to effective
previous reports, the observed behaviour of the conduc- ”amplification” ofsomeconductance fluctuationsrespon-
tancevs. voltageisingeneralsimilartothedatareported sibleforRTNfromthesefewdefects. Thisisrepresented
forspintunnellingthrougharraysofmagneticnanoparti- schematically in the Fig. 13: the change in the charge
cles[5],withexceptionofthedependenceofTMRonbias in the defect yields two states with different tunneling
voltage which is smoother (VTMR/2 ∼0.5 V, [5]) than in rates (τ), hence different conductance. The origin of the
our samples. different times lies in the different levels inside the dots,
whicharedeterminedbythecapacitance,thusbythe lo-
A further confirmation of the role of the Coulomb
cal environment. Of course, in our tunnel junction there
blockadeinoursamplescouldbeobservedinthenoiseat
aremanydefects,butatlowtemperaturesthereareonly
low frequency in the studied samples. Whereas for low
several of them active because the trapping-detrapping
Si doping (δ < 1.2 Å), the power spectrum at low tem-
process uses to be thermally activated.
peratures is ”white” (i.e. nearly frequency independent)
andcorrespondswelltotheshotnoiseexpectedfordirect
tunnellinginatunneljunction(orfortwo-steptunnelling
VI. CONCLUSIONS
through strongly asymmetric barriers), for δ ≥1.5 Åa
randomtelegraphnoise(RTN),Fig. 12,contributionbe-
comes evident for bias voltages above a critical value. Toconclude,wehavecarriedoutanextensivestudyof
The appearance of RTN for δ ≥1.2 Åmight be under- electrontransportinCo|Al O |Pymagnetictunneljunc-
2 3
stood as a consequence of the suppression of Coulomb tions asymmetrically doped with Si. Our experimental
blockade. data suggest that the observed behaviours of conduc-
10
electron population, even though their capacitances are
characterized by rather narrow size distributions, giving
risetosomedistributionofthe maximumthresholdvolt-
age suppressing Coulomb blockade ±V . This leads to
ch
the observed zero bias anomaly in our samples. On the
other hand, the variation of the electron population in
each particle may explain the suppression of the pre-
dicted [35] Coulomb oscillations, which could be present
only for a constant equilibrium electron population in Si
particles across the junction area. One of the ways to
reachamoreuniformelectronpopulationintheSiparti-
clescouldbethereductionoftheareaofthejunctionsas
in Ref. [9], implying tunnelling through a smaller array
ofnanoparticleswithasizedistributionnarrowerthanin
the present case.
FIG. 13: Schematic explanation of the noise observed at low Acknowledgments
temperatures. The presence of traps in our barrier modifies
the levels inside our dot. This effect leads to two resistance
This work was supported by funds from the Span-
statesdependingonwhatisthestateofthedefect. Thiseffect
ish Comunidad de Madrid (Grant No. P2009/MAT-
invisibleat lowtemperaturesbecauseonlyfew processes are
activated, hence the noise is RTN type as is clearly seen in 1726) and Spanish MICINN (Grants No. MAT2006-
Fig. 12. 07196, No. MAT2009- 10139, Consolider Grant No.
CSD2007-00010). As a part of the European Science
Foundation EUROCORES Programme Grant No. 05-
tance vs Si doping are closely related, clearly indicat- FONE-FP-010-SPINTRA, work was supported by funds
ing a suppression of the Coulomb blockade regime for Si fromtheSpanishMEC(MAT2006-28183-E),PolishMin-
layer thicknesses above about one monolayer. Although istry of Science and Higher Education as a research
no staircase behavior of the conductance was observed project in years 2006Ű2009, and the EC Sixth Frame-
for the regime of suppressed Coulomb blockade, as in work Programme, under Contract No. ERAS-CT-2003-
some other systems [9], the observed behavior of tun- 980409. The work was also supported by ESF-AQDJJ
nelling conductance is rather similar to the one reported programme,FCT GrantPTDC/FIS/70843/2006inPor-
longtimeagobyGiaever[20], whichwassuccessfullyex- tugal, and by the Polish Ministry of Science and Higher
plained as due to the presence of a large amount of par- Education as a research project in years 2007Ű2010
ticles inside the barrier. For a fixed bias voltage applied (V.K.D.). Work in MIT is supported by NSF Grant No.
in equilibrium, these particles might have very different DMR-0504158and ONR Grant No. N00014-06-1-0235.
[1] T. Miyazaki and N. Tezuka, Journal of magnetism and Journal of Physics D-AppliedPhysics 35, 2422 (2002).
magnetic materials 139, L231 (1995). [10] K. Ono, H. Shimada, S. ichi Kobayashi, and Y. Ootuka,
[2] J.Moodera,L.Kinder,R.Wong,andR.Meservey,Phys- JournalofthePhysicalSocietyofJapan65,3449(1996).
ical Review Letters 74, 3273 (1995). [11] A. Bernand-Mantel, P. Seneor, N. Lidgi, M. Muñoz,
[3] P.LeClair, J. K. Ha,H. J. M. Swagten, J. T. Kohlhepp, V.Cros, S.Fusil,K.Bouzehouane,C.Deranlot,A.Vau-
C.H.vandeVin,andW.J.M.deJonge,AppliedPhysics res, F. Petroff, and A. Fert, Applied Physics Letters 89,
Letters 80, 625 (2002). 062502 (2006).
[4] S. Yuasa, A. Fukushima, H. Kubota, Y. Suzuki, and [12] M.M.DeshmukhandD.C.Ralph,Phys.Rev.Lett.89,
K.Ando,Applied Physics Letters 89, 042505 (2006). 266803 (2002).
[5] L. F. Schelp, A. Fert, F. Fettar, P. Holody, S. F. Lee, [13] A.Jensen,J.R.Hauptmann,J.Nygrd,andP.E.Linde-
J. L. Maurice, F. Petroff, and A. Vaurès, Phys. Rev. B lof, Physical Review B 72, 035419 (2005).
56, R5747 (1997). [14] A. N. Pasupathy, R. C. Bialczak, J. Martinek, J. E.
[6] J.H.Shyu,Y.D.Yao,C.D.Chen,andS.F.Lee,Journal Grose, L.A.K.Donev,P.L.McEuen,and D.C.Ralph,
of Applied Physics 93, 8421 (2003). Science 306, 86 (2004).
[7] S. Takahashi, H. Imamura, and S. Maekawa, Physical [15] J. Slonczewski, Physical Review B 39, 6995 (1989).
ReviewLetters 82, 3911 (1999). [16] A. M. Bratkovsky,Phys.Rev.B 56, 2344 (1997).
[8] S. Maekawa, Concepts in Spin Electronics (Oxford Uni- [17] S.Zhang,P.M.Levy,A.C.Marley,andS.S.P.Parkin,
versity Press, NewYork,2006). Physical ReviewLetters 79, 3744 (1997).
[9] K. Yakushiji, S. Mitani, K. Takanashi, and H. Fujimori, [18] J.S.Moodera, J.Nowak,andR.J.M.vandeVeerdonk,