© 2000, S.K. Streiffer, Argonne National Laboratory, All Rights ReservedNC State

Relaxation Currents

Dielectric relaxation is the result of time depedence of the polarization mechanisms active in a material.

Relaxation currents occur in all dielectrics that exhibit finite loss (tanδ).

In high-permittivity materials, the flow of polarization charge caused by application of a step voltage is large enough that it is easily measured as time-dependent current flow, even at long times!

© 2000, S.K. Streiffer, Argonne National Laboratory, All Rights ReservedNC State

Adapted from Kingery, Bowen, and Uhlmann, Introduction to Ceramics

© 2000, S.K. Streiffer, Argonne National Laboratory, All Rights ReservedNC State

Adapted from Kingery, Bowen, and Uhlmann, Introduction to Ceramics

© 2000, S.K. Streiffer, Argonne National Laboratory, All Rights ReservedNC State

Current-Time Regimes in BST

log (t)

Transitory Relaxation

Steady-state Leakage

Resistance Degradation

Breakdown10-8

10-6

10-4

10-2

10-6 10-4 10-2 100 102 104

J (A

/cm

2 )

Time (s)

Pt/BST/Pt1.0 V

167 kV/cm

Charging

Discharging

© 2000, S.K. Streiffer, Argonne National Laboratory, All Rights ReservedNC State

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-1 100 101 102 103 104

2 )

Time (s)

+833 kV/cmDischarge

+267 kV/cmDischarge

+267 kV/cmCharge

+833 kV/cmCharge

52.0 at%Ti60 nm25°C

© 2000, S.K. Streiffer, Argonne National Laboratory, All Rights ReservedNC State

Polarization currents follow a power-law time dependence of approximately t-n where n < 1.

Curie - von Schweidler behavior

J. Curie, Ann. Chim. Phys. 18, 203 (1889) E. von Schweidler, Ann. Phys. 24, 711 (1907) A.K. Jonscher, Dielectric Relaxation in Solids (London: Chelsea

Dielectrics Press, 1983).

BST thin films fall into this class of materials.

S.K. Streiffer, C Basceri, A.I. Kingon, S. Lipa, S. Bilodeau, R. Carl, and P.C. van Buskirk, Mater. Res. Soc. Symp. Proc. 415, 219 (1996).

T. Horikawa, T. Makita, T. Kuroiwa, and N. Mikami, Jpn. J. Appl.Phys. 34, 5478 (1995).

© 2000, S.K. Streiffer, Argonne National Laboratory, All Rights ReservedNC State

Dielectric Relaxation and Capacitor Discharge References

T. Horikawa, T. Makita, T. Kuriowa, N. Mikami, Jpn. J. Appl. Phys. 34, 5478 (1995).

M. Schumacher, G.W. Dietz, and R. Waser, Integr. Ferro. 9, 317 (1995).

G.W. Dietz, M. Schumacher, and R. Waser, Science and Technology of Electroceramic Thin Films. Proceedings of the NATO Advanced Research Workshop, 269. Ed. O. Auciello and R. Waser (Kluwer, 1995).

S.K. Streiffer, C. Basceri, A.I. Kingon, S. Lipa, S. Bilodeau, R. Carl, and P.C. van Buskirk, MRS Symp.Proc. 415, 219 (1996).

R. Waser, Integr. Ferro. 15, 39 (1997) J.D. Baniecki, et al., Appl. Phys. Lett. 72, 498 (1998).

© 2000, S.K. Streiffer, Argonne National Laboratory, All Rights ReservedNC State

Dielectric Relaxation

The phenomenology of the dielectric response is well-described in terms of Curie-von Schweidler behavior.

Jp ≈ βt-n

The microscopic origin has not been presently agreed upon.

The time-dependent polarization behavior manifests itself as the dispersion in permittivity with respect to frequency (ωn-1).

© 2000, S.K. Streiffer, Argonne National Laboratory, All Rights ReservedNC State

Dielectric Relaxation Can be modeled via equivalent circuit methods

(series of RC elements that match distribution)

Adpated from N. Mikami, in Thin Film Ferroelectric Materials and Devices, ed. R, Ramesh (Kluwer Academic Publishers, Norwell, MA, 1997)

© 2000, S.K. Streiffer, Argonne National Laboratory, All Rights ReservedNC State

Dielectric Relaxation Can be modeled semi-analytically (for now ignore leakage) Time-domain polarization currents described as :

χ(ω) = FJ p

ε0 E0

= Ωt −n + χ0δ(t)( )

0

∞

∫ e−iωtdt

= ΩΓ(1− n) sinnπ2

− i cos

nπ2

ωn−1 + χ0

= Aωn−1 + χ0

JP = ε0 E0 Ωt−n + χ0δ(t)( ) Frequency domain response is just the Fourier tranform of

the time domain response:

© 2000, S.K. Streiffer, Argonne National Laboratory, All Rights ReservedNC State

Dielectric Relaxation

Dielectric loss in the frequency domain is then given by:

tanδ = ′ ′ ε ′ ε

=ΩΓ (1− n)cos

nπ2

ω

n−1

χ0 + ΩΓ(1− n)sinnπ2

ω

n−1

≈ cotnπ2

, ω →0

Have also assumed that dielectric is (sufficiently) linear and nonhysteretic

© 2000, S.K. Streiffer, Argonne National Laboratory, All Rights ReservedNC State

Conversion between time and frequency domain data

10-7

10-6

10-5

10-4

10-3

10-2

10-1

10-5 10-4 10-3 10-2 10-1 100

Time (Seconds)

Jp ~ t0.925

1V , 167 kV/cm

(a)

500

400

300

200

100

0102 103 104 105 106

Frequency (Hz)

ε ~ ω(0.925)-1

(b)

© 2000, S.K. Streiffer, Argonne National Laboratory, All Rights ReservedNC State

260

250

240

230

220

210102 103 104 105 106 107

Frequency (Hz)

0.010

0.008

0.006

0.004

0.002

0.000

εεεε ~ ωωωω (0.999)-1

Figure 3.5 Permittivity and loss tangent for a well-behaved sample. The dottedlines are a fit to the permittivity, and the loss tangent calculatedvia Equation (3.5) from that fit, respectively.

Pt/BST/Pt/SiO2/Si

© 2000, S.K. Streiffer, Argonne National Laboratory, All Rights ReservedNC StateJ.D. Baniecki et al., Appl. Phys. Lett. 72, 498 (1998)

© 2000, S.K. Streiffer, Argonne National Laboratory, All Rights ReservedNC State

Mechanisms for Curie-von Schweidler Behavior

Distribution of relaxation times R. Waser and M. Klee, Integr. Ferro. 2, 257 (1992)

Distribution of hopping probabilities H. Scher and E.W. Montroll, Phys. Rev. B 12, 2455 (1975)

Space charge trapping S.R. Wolters and J.J. Van Der Schoot, J. Appl. Phys. 58, 831

(1985) Maxwell-Wagner relaxation

H. Neumann and G. Arlt, Ferroelectrics 69, 179 (1986) Energetically inequivalent, self-similar multi-well potential for

ionic configurations Dissado & Hill, Nature 279, 685 (1979)

© 2000, S.K. Streiffer, Argonne National Laboratory, All Rights ReservedNC State

Dielectric Relaxation: Problem DRAM write or refresh pulse is of the order of 10 ns in

duration: Polarization processes operating on time scales longer

than 10 ns, do not contribute usable stored charge to the device.

Curie-von Schweidler relaxation currents do not addto the material performance.

Even worse: the dielectric will relax after it has been polarized, into states that cannot be depolarized quickly.

Stored charge can’t be read out!

© 2000, S.K. Streiffer, Argonne National Laboratory, All Rights ReservedNC State

This effect can be quantified by measuring the voltage drop of a polarized dielectric under open-circuit conditions

Calculate polarization under a unit step voltage:

P(t) = ε0 E(t) ∗ f (t) = ε0 E(t) ∗ Ω t−n + χ0δ(t )( )

P(t,E = 1× H(t)) = A(t) = ε0 f (τ )dτ0

t∫

=ε0Ωt1−n

1− n+ ε0χ0

© 2000, S.K. Streiffer, Argonne National Laboratory, All Rights ReservedNC State

After charging for time ∆, a certain amunt of polarization has been created:

P(∆, E0 ) = E0 A(∆)

=ε0 E0Ω∆1−n

1− n+ ε0 E0χ0

In the absence of leakage, this polarization will remain constant, but the electric field will change because of the time dependence of the susceptibility.

© 2000, S.K. Streiffer, Argonne National Laboratory, All Rights ReservedNC State

The thoery of Laplace transforms and transfer functions can then be used to show that this voltage drop after a time t is:

E( ′ t ) = P(∆, E0 )A( ′ t )

= E0 ⋅

Ω∆1−n

1− n+ χ0

Ω ∆ + ′ t ( )1−n

1− n+ χ0

© 2000, S.K. Streiffer, Argonne National Laboratory, All Rights ReservedNC State

Voltage Retention Simulations

0

0.2

0.4

0.6

0.8

1

10-9 10-7 10-5 10-3 10-1 101

Write length = 10 nsWrite length = 1 µµµµs

V/V

0

Time (s)

n = 0.999tanδδδδ = 0.15%

0

0.2

0.4

0.6

0.8

1

10-9 10-7 10-5 10-3 10-1 101

Write length = 10 nsWrite length = 1 µµµµs

V/V

0Time (s)

n = 0.925tanδδδδ = 12%

© 2000, S.K. Streiffer, Argonne National Laboratory, All Rights ReservedNC State

Voltage Retention as a Function of Loss

0.75

0.80

0.85

0.90

0.95

1.0

0.000 0.005 0.010 0.015 0.020

1ns Write Pulse 10ns Write Pulse100ns Write Pulse

E/E

0

Tanδδδδ

© 2000, S.K. Streiffer, Argonne National Laboratory, All Rights ReservedNC State

Worst Case