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© 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