Relaxation Currents. 2000, S.K. Streiffer, Argonne National Laboratory, All Rights Reserved

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1 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!

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

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

4 Current-Time Regimes in BST Transitory Relaxation Steady-state Leakage Resistance Degradation 10-2 Pt/BST/Pt 1.0 V 167 kv/cm 10-4 J (A/cm 2 ) 10-6 Charging log (t) Breakdown 10-8 Discharging Time (s)

5 10-4 ) at%ti 60 nm 25 C +833 kv/cm Charge kv/cm Discharge kv/cm Discharge +267 kv/cm Charge Time (s)

6 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).

7 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).

8 Dielectric Relaxation The phenomenology of the dielectric response is welldescribed in terms of Curie-von Schweidler behavior. J p 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 (ω n-1 ).

9 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)

10 Dielectric Relaxation Can be modeled semi-analytically (for now ignore leakage) Time-domain polarization currents described as : Frequency domain response is just the Fourier tranform of the time domain response: J χ(ω) = F p = ( Ωt n +χ 0 δ(t) ) e iωt dt ε 0 E 0 =ΩΓ(1 n) sin nπ 2 = Aω n 1 +χ 0 ( ) J P =ε 0 E 0 Ωt n +χ 0 δ(t) 0 i cos nπ 2 ω n 1 +χ 0

11 Dielectric Relaxation Dielectric loss in the frequency domain is then given by: tanδ = ε ΩΓ(1 n)cos nπ 2 ω n 1 = ε χ 0 +ΩΓ(1 n)sin nπ 2 ω n 1 cot nπ 2, ω 0 Have also assumed that dielectric is (sufficiently) linear and nonhysteretic

12 Conversion between time and frequency domain data J p ~ t V, 167 kv/cm ε ~ ω (0.925) (a) Time (Seconds) 100 (b) Frequency (Hz)

13 ε ~ ω (0.999) Frequency (Hz) Figure 3.5 Permittivity and loss tangent for a well-behaved sample. The dotted lines are a fit to the permittivity, and the loss tangent calculated via Equation (3.5) from that fit, respectively. Pt/BST/Pt/SiO 2 /Si

14 J.D. Baniecki et al., Appl. Phys. Lett. 72, 498 (1998)

15 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)

16 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 add to 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!

17 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) =ε 0 E(t) f(t) =ε 0 E(t) ( Ωt n +χ 0 δ(t) ) P(t,E = 1 H(t)) = A(t) =ε 0 t 0 f(τ)dτ = ε 0 Ωt1 n 1 n +ε 0 χ 0

18 After charging for time, a certain amunt of polarization has been created: P(, E 0 ) = E 0 A( ) = ε 0 E 0 Ω 1 n 1 n +ε 0 E 0 χ 0 In the absence of leakage, this polarization will remain constant, but the electric field will change because of the time dependence of the susceptibility.

19 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(, E 0 ) A( t ) = E 0 1 n +χ 0 +χ 0 Ω 1 n Ω + ( t ) 1 n 1 n

20 Voltage Retention Simulations n = tanδ = 0.15% n = tanδ = 12% V/V V/V Write length = 10 ns Write length = 1 µs 0.2 Write length = 10 ns Write length = 1 µs Time (s) Time (s)

21 Voltage Retention as a Function of Loss ns Write Pulse 10ns Write Pulse 100ns Write Pulse E/E Tanδ

22 Worst Case