transport facilities - technology accessibilitypleclair.ua.edu/capabilities.pdf · 2011-09-08 ·...

THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGYAn NSF Science and Engineering Center

Quantum Design PPMS T: 350mK -- 400K H: 0 -- 7T

Transport facilities

magnetoresistancehall effectimpedance spectroscopytunneling spectroscopy:

inelastic tunneling spectroscopy (IETS)spin polarization (Meservey-Tedrow)

Radiant ferroelectric tester

custom electronicsI(V,T)dI/dV(V,T)d2I/dV2(V,T) Z(ω,θ,H,T)


Examples ...Magnetoresistance

I(V)

dI/dV (V)


• thin film SC in a field (~2-3T) Zeeman split quasiparticle DOS

• dI/dV ~ Nsc Nfm

• asymmetry = spin polarizationrobust, microscopic theory

“directly” gives spin imbalance of tunneling current

Meservey-Tedrow tunneling


Co / Al2O3 / Al

spin polarization of Co films

onset of ferromagnetism:Ni on Bi

Examples ...

The University of Alabama

Inelastic Tunneling Spectroscopy (IETS)

• tunneling electrons excite vibrational modes– see Raman & IR modes– no strong selection rules

• tells us – the molecule is still there– it participates in transport

• when eV ≥ hv– stepped increase in dI/dV– new set of final states available

• example: studying model catalysts– CO on Rh/Al2O3 -- CO vibrations

“tunneling energy loss spectroscopy”

detail: tiny signals … challenging

d2I/dV2

dI/dV

Vhv

Vhv

Lambe & Jaklevic, Phys. Rev. 165, 821 (1968)


IETS: we really have transport through the molecule, it is intact

Al/Al2O3/X-benzoic acid/Co, T = 2K


0.05 0.10 0.15 0.20 0.35 0.40

0.0

0.4

0.8

1.2

1.6400 800 1200 1600 2800 3200

!as

ym

CO

O-

& ! C

Car

rin

g o

ut-

of-

pla

ne

" C

X

! C

Har

eV (cm-1)d

2I

/ d

V2 (

a.u

.)

eV (meV)

4-iodobenzoic

4-chlorobenzoic

" C

H

! C

X

Al-

OH

!sy

m C

OO

- +

! C

Car

# C

H # C

H +

Al-

O

! C

Car

! C

=O

ν: stretchβ: in-‐plane bendγ: out-‐of-‐plane bend

indexing - compare with ATR-FTIRaromatic is intactchemisorbed benzoate ion

absence of C=O, presence of COO-


0.10 0.15 0.200

1

2

3

4800 1200 1600

γ(O

-H)

γ(C

-H)

eV (cm-1)In

tens

ity (a

.u.)

eV (meV)

ν(C

-C) ar

ν as(C

OO

− ), ν

(C-C

) ar

ν(C

-X) ν s

(CO

O- )

ν(C

-C) ar

γ(C

-H),

Al-O

ν(C

=O)

β(C

-H)

Al/Al2O3/4-iodobenzoic/Co

IETS

ATR-FTIR

But … what is the state of the I substituent?aromatic-halogen modes insensitiveprobe with XPS


Impedance spectroscopy of thin films


How?• apply ac voltage, measure current & phase

• gives Z(ω)

• model system with an equivalent circuit

• each component physically meaningful

• probing dielectric/spectral function

• ac lock-in techniques or ‘impedance analyzer’

• complementary: dI/dV vs V at fixed freq


physical realizations• lossy capacitor

• tunnel junction

• imperfect dielectric

• cell walls, to an extent

• electrochemistry ...

impedance spectroscopy

magneto-dielectric measurements


Example: MgO-MTJ

• high-frequency operation for MRAM, reader

• MTJ is like a capacitor too ...

• what is C doing?

• significant magnetocapacitance

Frequency-dependent magnetoresistance and magnetocapacitanceproperties of magnetic tunnel junctions with MgO tunnel barrier

P. Padhan,a! P. LeClair, and A. Guptab!

Center for Materials for Information Technology, University of Alabama, Tuscaloosa, Alabama 35487

K. Tsunekawa and D. D. DjayaprawiraElectron Device Equipment Division, Canon Anelva Corporation, 5-8-1 Yotsuya, Fuchu-shi, Tokyo 183-8508, Japan

!Received 19 January 2007; accepted 28 February 2007; published online 4 April 2007"

The frequency-dependent impedance of magnetic tunnel junctions !MTJs" with MgO barriers wasinvestigated. The capacitance of the MTJs switches from high to low when the relative electrodemagnetizations change from parallel to antiparallel, opposite the resistance change. Additionally, forparallel magnetizations, the capacitance varies with temperature though resistance remainsapproximately constant. The low frequency resistance and the tunneling magnetoresistance are inagreement with dc values. The capacitance is found to be larger than the expected !geometrical"capacitance, in contrast to MTJs with Al2O3 barriers. These results are explained by screening dueto charge and spin accumulation at the interfaces. © 2007 American Institute of Physics.#DOI: 10.1063/1.2719032$

Magnetic tunnel junctions1 !MTJs" are promising candi-dates for a wide range of spintronic applications, such asmagnetic random access memory. One of the major recentdevelopments in this field has been the theoreticalprediction2 and experimental verification3–6 of extremelyhigh tunneling magnetoresistance !TMR" in MTJs with MgObarriers. Recent work reports room temperature TMR valuesover 470% and above 800% at low temperatures.6 The trans-port in MTJs depends sensitively on the details of the elec-tronic, magnetic, and geometric structures of the interfacesbetween the ferromagnets !FMs" and the barrier. In this let-ter, we attempt to address how this sensitivity plays a role infrequency-dependent magnetotransport, which is naturallyrelevant for high-speed storage applications. Impedancespectroscopy is a straightforward way to investigatefrequency-dependent transport phenomena. More simply,however, even the value of the junction capacitance in MTJs,aside from its possible spin dependence, is still under inves-tigation. Significant variations from the geometrical capaci-tance have been observed for a variety of insulating barriers,such as Ta2O5, AlOx, ZnS, and Ba0.5Sr0.5TiO3, which hasbeen attributed to interface effects.7–10 Consequently, tunnel-ing junctions have been intensively investigated by ac im-pedance techniques.8,11–13

In this letter, we report the interface-related impedance!Z" properties of MgO-based MTJs. The Z of the MTJs iswell fit to an equivalence circuit of a parallel resistor !R" andeffective capacitor !C" network. We observe a significant“tunneling magnetocapacitance” effect !TMC", which issmaller than the TMR. The equivalent circuit of the junctionindicates a negative effective interfacial capacitance !Ci", re-sulting from a combination of charge and spin accumulation,and attractive interactions between the ions at the interfaces.

MTJs fabricated with the structure !5 nm" Ta/ !20 nm"CuN/ !3 nm" Ta/ !15 nm" PtMn/ !2.5 nm"

Co70Fe30/ !0.85 nm" Ru/ !3 nm" Co60Fe20B20/ !tMgO"MgO/ !3 nm" Co60Fe20B20/ !10 nm" Ta/ !4 nm" Ru withtMgO=2.5, 3, and 3.5 nm were grown on thermally oxidizedSi wafers using a magnetron sputtering system !CanonAnelva C7100". The details of the deposition conditions andprocessing have been presented previously.5,14 PatternedMTJs of differing junction areas were characterized by bothdc and ac electrical transport using a four probe technique.The ac impedance measurements were performed using anHP4294A impedance analyzer.

The MTJs with 2.5, 3, and 3.5 nm thick MgO layersexhibit TMR values of 247%, 221%, and 160%, respectively,at room temperature with 10 mV dc bias voltage. Approxi-mately the same values of TMR are found using 10 mVrms acvoltage at low frequency !!1 kHz; discussed later in thetext". The TMR was calculated by extracting the resistanceof the junction from the Z and " !phase angle". We haveinitially modeled the junction as a parallel network of R andC, as shown in the inset of Fig. 1. These two components arerelated to the measured total Z and " of the parallel RCnetwork by the expressions R2=Z2!1+tan2 "" and C2

= !Z#"!2!1+ !1/ tan2 """!1, where # is the frequency in rad/s.The R and C of the MTJ with 3 nm thick MgO !junction

a"Electronic mail: [email protected]"Author to whom correspondence should be addressed; electronic mail:

[email protected]

FIG. 1. !Color online" Magnetic-field-dependent resistance !a" and capaci-tance !b" of the magnetic tunnel junction !MTJ" with 3 nm thick MgObarrier layer at various temperatures. Inset shows the circuit equivalent ofthe MTJ.

APPLIED PHYSICS LETTERS 90, 142105 !2007"

0003-6951/2007/90"14!/142105/3/$23.00 © 2007 American Institute of Physics90, 142105-1Downloaded 04 Apr 2007 to 130.160.201.32. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp

.../CoFeB/MgO/CoFeB ...via Anelva


Bi2NiMnO6–La2NiMnO6 superlattices

• magnetodielectric materials

• strongly T-dependent capacitance

• ‘lossy’ near FM Curie temp

• coupling of FM and dielectric order!

J. Phys.: Condens. Matter 21 (2009) 306004 P Padhan et al

or the formation of antiferromagnetically ordered regions [21]at the interfaces of LNMO and BNMO. From figures 3 and 4it appears that the alternate stacking of LNMO and BNMOdoes not significantly influence the temperature- and field-dependent magnetization of the constituents, as is the casefor other FM–FM multilayers [22]. Note that in the presentmultilayer series both FM components are insulating. It is thusexpected that the magnetic properties are the result of 180!

superexchange interactions between transition metal cations(Goodenough–Kanamori rules) [23], rather than through thedouble exchange interaction [24] present, for example, in theall-metallic La0.7Sr0.3MnO3–SrRuO3 multilayer system [22].

In order to model the dielectric responses of thesemultilayers, we first considered the entire multilayer as aparallel network of a resistor (R) and a ‘leaky’ capacitor (C)with a complex dielectric function, !(") = !1(") + i!2("),as explained in our previous reports on LNMO [16] andBNMO [15] thin films. In this way, from measurements ofimpedance and phase angle we can determine the effectivecapacitance Ceff and dissipation factor (tan # " !2/!1) of themultilayer as a whole. In figure 5 we show the temperature-dependent effective capacitance and dissipation factor ofseveral multilayers measured with a 100 mV RMS ac voltageat a frequency of f = 100 kHz in zero applied magnetic field.Both Ceff and tan # show a rapid variation with temperature.In all cases, the dissipation factor of the multilayers increasesbelow room temperature, reaching a maximum at T # 148 K,and subsequently decreases to a negligible value for lowertemperatures down to T = 4 K. The effective capacitancedecreases monotonically with decreasing temperature fromroom temperature to T $ 100 K, with a rapid transitionat T $ 150 K, below which it remains constant down toT = 4 K. We note that the peak in tan # and the rapiddecrease of Ceff near T $ 150 K shift to slightly highertemperatures as the measurement frequency is increased from10 to 100 kHz, similar to our earlier observations on singleLNMO films [16]. Most notably, for all multilayer samplesthere is a large variation in capacitance with temperature in arange well below, but in the vicinity of, the onset of magneticordering (see figure 3) [15].

Although there is a slight shift of dissipation peakand a corresponding variation in Ceff for the multilayerstLNMO = 2 u.c., the effective capacitance and dissipationfactor show no significant variation in either magnitude ortemperature dependence for larger thicknesses. Exceptingthe multilayers with tLNMO = 2 u.c., where slight thicknessvariations of the extremely thin LNMO spacer may playa more significant role, the lack of a significant thicknessdependence argues for a dominant interfacial contributionto the effective capacitance. Since the conductivity of theLNMO–BNMO multilayers decreases rapidly for T ! 120 K,as indicated by the temperature dependence of tan #, forsufficiently low temperatures the influence of carrier effectson the dielectric properties is expected to be negligible. Athigher frequencies, the low-temperature capacitance shouldtherefore provide a measure of the intrinsic permittivities ofthe constituent layers [25]. If for the moment we assume nointerfacial effects, the effective capacitance in that limit would

Figure 5. Temperature-dependent (a) dissipation factor tan # and(b) effective capacitance Ceff of the multilayers withtLNMO = 2, 4, 6, 8, 10 u.c. grown on a (100)-oriented 0.5 wt%Nb-doped STO substrate measured at f = 100 kHz. The verticaldashed lines indicate the peak in loss tangent measured for individualBNMO and LNMO films.

simply be a series combination of capacitors representing theindividual LNMO and BNMO layers: C%1

eff = nBNMOC%1BNMO +

nLNMOC%1LNMO, where nBNMO = 10 and nLMNO = 11 are the

numbers of BNMO and LNMO layers, respectively. If wefurther assume that the capacitance of each individual layerscales inversely with its thickness, then the dependence ofC%1

eff on the LNMO layer thickness tLNMO should show a linearrelationship, whose slope and interface give the capacitancesfor individual LNMO and BNMO layers, respectively. Weobserve no significant dependence of Ceff on tLNMO, whichsuggests that either the interface capacitance or that of theBNMO layers dominates the overall effective capacitance.Based on the effective capacitance measured for relativelythick ($80 u.c.) individual LNMO and BNMO films, wecalculate the effective capacitance of a single 10 u.c. BNMOlayer as $40, and $55 nF for a single 10 u.c. LNMO layer.Using these values, we calculate an effective capacitance fora multilayer with tLNMO = 10 u.c. of $2 nF, roughly two tofive times lower than the observed value. In the absence ofinterfacial effects, this alone would suggest an enhancementof the individual LNMO and BNMO dielectric constants by afactor of $2–5; combined with the lack of a dependence of Ceff

on tLNMO, an interfacial explanation seems in order.In an attempt to more accurately model the capacitive

dielectric response of these multilayers including interfacialeffects, we considered each component of the multilayer as aparallel combination of a resistor (R) and a ‘leaky’ capacitor(C) with a complex dielectric function [15, 16]. We further

4


• near transition temperature, strong variation of dielectric constant with magnetic field

• fluctuations in electric & magnetic dipole ordering

• interface-induced stress

• changes in dielectric constant correlate with magnetization


included a parallel RC contribution for each BNMO–LNMOinterface to account for, e.g., interface polarization. Assumingthe same value of capacitance for each individual layer andeach interface, the effective capacitance of the multilayer canbe expressed as C!1

eff = nBNMOC!1BNMO + nLNMOC!1

LNMO +nintC!1

i , where nint = 20 is the number of LNMO–BNMOinterfaces6. Given that the measured effective capacitanceis significantly larger than expected, however, the seriescapacitor model only enhances the discrepancy: any interfacialseries capacitance will only serve to lower the calculatedeffective capacitance. This suggests either a much largerenhancement of the individual LNMO and BNMO dielectricconstants if interfacial effects are to be included in this manner,or an interface polarization opposite to that of the LNMO andBNMO layers—effectively, a negative interface capacitance.

We also note that the Ceff determined from ourmeasurements at room temperature show a significantdiscrepancy with the values calculated within a simple RCnetwork model above. In our view, this can attributedto the significant leakage of LNMO and BNMO at highertemperatures. As the temperature is increased from T =10 K, a rapid change of effective capacitance is observed,and the ferroelectric/dielectric behaviour of the multilayerbecomes dominated by the strong leakage current. The leakybehaviour is also clearly reflected in a strong reduction ofimpedance as temperature increases. This is corroborated byan increase in the dissipation factor for higher measurementfrequencies. Previously, we observed similar behaviour inindividual LNMO films [16].

The qualitative behaviour of the temperature-dependentCeff of these multilayers with an applied in-plane magneticfield is similar to the zero field variation shown in figure 5.In the presence of magnetic field, the change in theeffective capacitance can be quantified by an effectivemagnetodielectric constant (MDC), defined by MDC =[C(!, H ) ! C(!, 0)]/C(!, 0). The MDCs measured atf = 100 kHz for various temperatures in an applied in-planemagnetic field of µ0 Hext = 7 T are shown in figure 6. AtT = 10 K the MDC of the multilayer with tLNMO = 2 u.c. is0.6%, increasing very slowly with increasing temperature andreaching a maximum at T " 144 K, thereafter decreasingrapidly to #0.1% at T = 200 K. Above T = 200 K, thevariation of the MDC is negligible. Multilayers with largertLNMO exhibit larger MDC. Again excepting the multilayerswith tLNMO = 2 u.c. there is no significant change in the peakposition with LNMO thickness.

The qualitative behaviour of the f = 100 kHz, µ0 Hext =7 T MDC of these multilayers is similar to that of itsLNMO [16] and BNMO [15] constituents, which has beenexplained by a coupling between electric and magnetic dipoleordering and fluctuations [16, 15]. The LNMO layer thicknessdoes play a significant role in determining the maximum MDCobserved, however. As shown in figure 6(a), with increasingtLNMO, the peak in MDC(T ) shifts towards lower temperatures,

6 The LNMO capping layer has a constant thickness of 10 u.c., whereas theother 10 LNMO layers within the repeated LNMO–BNMO bilayer have avariable thickness of tLNMO. We have taken this detail into account in theequivalent circuit modelling.

Figure 6. (a) Temperature-dependent magnetodielectric constantMDC of multilayers with tLNMO = 2, 4, 6, 8, 10 u.c. grown on a(100)-oriented 0.5 wt% Nb-doped STO substrate measured atf = 100 kHz in the presence of 7 T in-plane magnetic field.(b) Maximum MDC of multilayers • and the expected MDC basedon a weighted average of the individual LNMO and BNMOcontributions $ versus LNMO thickness tLNMO.

while the maximum MDC itself increases as tLNMO increasesfrom 2 to 6 u.c., approaching saturation for higher thicknesses,as shown in figure 6(b). The dotted lines in figure 6(b) indicatethe observed maximum MDC for thin films of BNMO andLNMO alone [16, 15].

The magnitude of the MDC is significantly larger thanexpected based on the MDC of the individual constituentlayers, presuming no interfacial magnetodielectric coupling.The open circles in figure 6(b) are the expected MDCvalues calculated using a thickness-weighted average of theMDC observed for individual 80 u.c. LNMO and BNMOfilms [16, 15]. As expected, the measured and calculated MDCincreases and shows a tendency toward saturation for largertLNMO, reflecting the relatively larger MDC for individualLNMO layers. The value of the MDC observed for themultilayers, however, is significantly above that expectedeven for pure LNMO films, again suggesting a significantinterfacial magnetodielectric coupling between BNMO andLNMO. Further, the MDC of the multilayers with tLNMO >

6 u.c. is essentially independent of the LNMO layer thickness,which also indicates that there is a significant interfacemagnetoelectric effect independent of the thickness of theLNMO layer. As these multilayers have nominally identicalinterfaces, the interfacial contribution to the magnetoelectriceffect should be same for all multilayers. The thicknessvariation of MDC below tLNMO = 6 u.c. also indicates that theobserved magnetoelectric effect is an intrinsic property of thismultilayer system. The variation of MDC with LNMO spacerlayer thickness is also reminiscent of the thickness dependenceof the stress along the c axis of the multilayer. The LNMOspacer layer thickness dependent MDC is tentatively attributedto fluctuations in electric dipole ordering and magnetic dipoleordering due to the substrate induced stress and the stressat interfaces. The relatively higher value of MDC of themultilayers with tLNMO > 6 u.c. could be a result of the canting

5


Figure 7. MDC and M4 versus in-plane magnetic field H for amultilayer with tLNMO = 10 u.c. measured at T = 120 K withf = 100 kHz.

of spin at the interfaces of LNMO and BNMO [25]. Such non-collinear alignments are very difficult to resolve in magneticmeasurements, as despite the number of interfaces the volumefraction is relatively small.

The magnetoelectric effect can be described within theGinzburg–Landau theory of phase transitions [26, 27, 5], whichgives rise to a magnetoelectronic coupling of the form ! P2 M2,where P and M are the polarization and magnetizationrespectively, and the coupling constant ! is typically a functionof temperature [26, 27]. This coupling leads to a deviation ofthe electric susceptibility, and thus dielectric constant, belowthe magnetic ordering temperature (TC) as we observe here.If one neglects the temperature dependence of the couplingconstant, the resulting variation of the dielectric constant belowTC should be proportional to the square of the magnetic orderparameter, or in our notation, MDC ! M2. Indeed, wehave previously observed this behaviour for single BNMOlayers [15], though it is not obeyed in our single LNMOlayers [16]. In the present case, we do not convincingly observean M2 dependence, but rather the dielectric constant and MDCappear to follow an M4 dependence, as shown in figure 7,where both M4 and MDC are plotted as a function of in-planemagnetic field for a multilayer with tLNMO = 10 u.c., measuredat T = 120 K with f = 100 kHz. Although the possiblereasons for this higher-order correlation are unclear, it has beensuggested that nonlinear magnetoelectric effects arising fromhigher-order magnetoelectric coupling terms may be realizedin systems with reduced dimensionality [5], in line with ourobservation of a significant interface magnetodielectric effect.Non-collinear spins at BNMO–LNMO interfaces may alsoplay a role in the present case [28].

4. Conclusions

In conclusion we have fabricated multilayers consistingof multiferroic Bi2NiMnO6 and ferromagnetic La2NiMnO6

double perovskites on pure and Nb-doped SrTiO3 substrates

using the pulsed laser deposition technique. The c-axis latticeparameter of a series of multilayers with fixed thickness ofBNMO strongly depends on the thickness of the LNMOlayers. The field-dependent magnetization of these multilayersat T = 10 K is independent of LNMO layer thickness, whilethe Curie temperature increases with increasing LNMO layerthickness. The multilayers grown on conducting Nb-dopedSrTiO3 exhibit an enhanced effective capacitance, which isfurther increased in the presence of magnetic field for a limitedtemperature range below the magnetic ordering temperature.The maximum magnetocapacitance is strongly dependentupon the LNMO layer thickness, which is attributed to thefluctuations in electric dipole ordering and magnetic dipoleordering due to the substrate induced and interfacial stress.The enhanced magnetodielectric effect of the multilayer withLNMO thicknesses larger than 6 u.c. is potentially explainedby the canting of spin at the interfaces of LNMO and BNMOand possibly the effects of reduced dimensionality. Finally, wefind that the magnetodielectric effect scales as the fourth powerof the magnetization of the multilayers.

Acknowledgments

This work was supported by ONR grant No N000140610226(C E Wood) and NSF NIRT grant No CMS-0609377. Thework performed at Oregon State University is supported byNSF grant (DMR 0804167).

References

[1] Shimuta T, Nakagawara O, Makino T, Arai S, Tabata H andKawai T 1996 J. Appl. Phys. 91 2290

[2] Erbil A, Kim Y and Gerhardt R 1996 Phys. Rev. Lett. 77 1628[3] Wang C, Fang Q, Zhu Z, Jiang A, Wang S, Cheng B and

Chen Z 2003 Appl. Phys. Lett. 82 2880–2[4] Harigai T and Tsurumi T 2007 Ferroelectrics 346 56[5] Eerenstein W, Mathur N D and Scott J F 2006 Nature

442 759–65[6] Murugavel P, Saurel D, Prellier W, Simon C and

Raveau B 2004 Appl. Phys. Lett. 85 4424–6[7] Kida N, Yamada H, Sato H, Arima T, Kawasaki M,

Akoh H and Tokura Y 2007 Phys. Rev. Lett. 99 197404[8] Scott J 2007 J. Mater. Res. 22 2053[9] Greenwald S and Smart J 1950 Nature 166 523

[10] Qu D, Zong W and Prince R 1997 Phys. Rev. B 55 11218[11] Shen J and Ma Y 2000 Phys. Rev. B 61 14279[12] Rogado N, Li J, Sleight A and Subramanian M A 2005 Adv.

Mater. 17 2225[13] Azuma M, Takata K, Saito T, Ishiwata S, Shimakawa Y and

Takano M 2005 J. Am. Chem. Soc. 127 8889[14] Guo H, Burgess J, Street S, Gupta A, Calvarese T G and

Subramanian M A 2006 Appl. Phys. Lett. 89 022509[15] Padhan P, LeClair P, Gupta A and Srinivasan G 2008 J. Phys.:

Condens. Matter 20 355003[16] Padhan P, Guo H, LeClair P and Gupta A 2008 Appl. Phys.

Lett. 92 022909[17] Padhan P and Prellier W 2007 Phys. Rev. B 76 024427[18] Padhan P, Prellier W and Mercey B 2004 Phys. Rev. B

70 184419[19] See http://ccp14.sims.nrc.ca/ccp/ccp14/ftp-mirror/diffax/pub/

treacy/DIFFaXIv1807/

6


VO2 metal-insulator transition

• still poorly-explained metal-insulator transition

• percolation of metallic regions?

• impedance spectra should help ...


capacitance vanishes at M-I transitionresistance drops‘leaky’ capacitor model

-120k-100k-80k-60k-40k-20k0

100 1k 10k 100k 1M10

100

1k

10k

100k

!’’

(")

360 K

250 K

!’ ("

)

f (Hz)

360 K

250 K

100

101

102

103

104

250 300 350 4000.0

0.5

1.0

1.5 (b)

εr

τ

1/ρdc

σ

σ (Ω

-1cm

-1)

(a)

ε r (a.u

.)

T (K)

10-8

10-7

10-6

10-5

τ (s

)

percolation of metallic regions?

‘dielectric’ changes little below transition

The University of Alabama Center for Materials for Information Technology P. LeClair Toshali Sands, Puri, 8 Jan 2009

How to measure a derivative?

• drive system with Vdc + δVacsin ωt• measure response at ω or 2ω

frequency / phase sensitive technique

… lock-in amplifiers … a lot of electronics

€

I(Vdc + δVac cosωt) = I(Vdc ) +dIdV

δVac cosωt( ) +d2IdV 2

δIac2

4cos 2ωt( )

⎛

⎝ ⎜

⎞

⎠ ⎟ +…

The University of Alabama Center for Materials for Information Technology P. LeClair Toshali Sands, Puri, 8 Jan 2009

DU

T

DC

LIAdI

dV

DC

LIA

A

÷

÷

x

Vdc

Vac

20, 40, 400, 4000

1, 10, 102, 103, 104

unity gain1:1 add

101-104

lo & hi passEG&G 113

current preamp103-106 V/AKeithley 428

I

V

101-104

EG&G 113+ notch filter

home-made summing ampKeithley 263

Stanford 830 Stanford 830

Stanford 830

HP 3458A

HP 3478A

x+

How to measure a derivative?

transport facilities - technology accessibilitypleclair.ua.edu/capabilities.pdf · 2011-09-08 ·...

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