Leakage Mechanisms Thin films, fully depleted Leakage controlled by combined thermionic / field emission across the Schottky barrier at the film-electrode interfaces. Film quality effects barrier height, and mobilities of carriers. Thicker films of interest for higher voltage applications Poorly understood 2000, S.K. Streiffer, Argonne National Laboratory, All Rights Reserved
Much effort has gone into studying the leakage of perovskitetype titanate thin films, including SrTiO 3, (Ba,Sr)TiO 3, and Pb(Zr,Ti)O 3 : J.F. Scott, et al., Proc. of the 1992 IEEE Int. Symp. Appl. Ferro., 356 (1992). T. Makita, et al., Mat. Res. Soc. Symp. Proc. 284, 529 (1993). T. Kuroiwa, et al., Ceramic Transactions 43, 219 (1994). C.S. Hwang, et al., Jpn. J. Appl. Phys. 34, 5178 (1995). M. Kiyotoshi and K. Eguchi, Appl. Phys. Lett. 67, 2468 (1995). R. Waser, in Science and Technology of Electroceramic Thin Films: NATO ASI Series Vol. 284, ed. O. Auciello and R. Waser (London: Kluwer Academic Publishers, 1995) pp. 223-248. G. Dietz, et al., J. Appl. Phys. 78, 1 (1995). S. Dey, et al., Jpn. J. Appl. Phys. 34, 3142 (1995). G. Dietz, et al., J. Appl. Phys. 82, 2359 (1997). G. Dietz and R. Waser, Thin Solid Films 299, 53 (1997) S. Zafar, et al., Appl. Phys. Lett. 73, 3533 (1998) 2000, S.K. Streiffer, Argonne National Laboratory, All Rights Reserved
Proposed conduction mechanisms for BST thin films: Fowler-Nordheim tunneling (interface, bulk) Poole-Frenkel effect (bulk) Thermionic emission across Schottky barriers (interface) The most favored mechanism: Schottky-barrier limited current flow 2000, S.K. Streiffer, Argonne National Laboratory, All Rights Reserved
ELECTRICAL C ONDUCTION MECHANISMS IN SOLIDS Hamann, Burghardt, and Frauenheim Bulk -Controlled vs. Interface -Controlled (Injection-Limited) Ionic (high T, long time) Schottky Emission Tunneling (through film) (High E) Bulk Doping (acceptors, donors, etc.) Photoexcitation (light effect) Trapping/Detrapping (Poole Frenkel) Field Emission Contact Photoexcitation Fowler-Nordheim Tunneling (can be bulk as well) Space-Charge-Limited (can be bulk as well) Hopping Conduction (Localization) Thin Films Thick(er) Films Failure Mode 2000, S.K. Streiffer, Argonne National Laboratory, All Rights Reserved
Lack of complete and careful analyses of leakage in BST thin films Experimental: Using a ramp or voltage step technique. danger of relaxation currents contribution in the analyses Field and temperature dependencies: Only field- or temperature-dependent data not sufficient for understanding the mechanism! Assumed values for the parameters in the model such as Richardson constant. Inhomogeneity of Schottky barrier, interfacial roughness, etc. 2000, S.K. Streiffer, Argonne National Laboratory, All Rights Reserved
metal W insulator x m ²W x W B E vac E c E F metal E v metal insulator
Leakage vs. A:B Site Ratio t = 30 nm; T = 125, 150, 175, & 200 C, 0 < V < 3.5V -5-10 51% Ti @200 C 51% Ti @125 C 53% Ti @200 C 53% Ti @125 C ln (J) -15-20 400 500 600 700 800 900 1000 1100 E 1/2 (V/cm) 1/2 2000, S.K. Streiffer, Argonne National Laboratory, All Rights Reserved
Leakage vs. A:B Site Ratio -16-18 51% Ti -16-18 53% Ti Predicted ln(j/t 2 ) -20-22 -24-26 -28 Predicted ln(j/t 2 ) -20-22 -24-26 -28-30 -30-32 -32-30 -28-26 -24-22 -20-18 -16 ln(j/t 2 ) -32-32 -30-28 -26-24 -22-20 -18-16 ln(j/t 2 ) ln J T 2 = ln A + αe 1/ 2 W b k B T
Leakage vs. A:B Site Ratio J = A T 2 exp αe1/2 W b k B T Ti Content W b (ev) α A (A/cm 2 K 2 ) 51% 1.05 0.00085 4.0e-6 51.5 1.28 0.00066 4.2e-3 52 1.44 0.00080 1.2e-2 53 1.17 0.00069 9.1e-5 53.5 0.92 0.00084 3.3e-9
Depletion Widths Issue: What are the depletion lengths? 5 10 nm > film thickness (i.e. > 100 nm) Why is this an issue? Explanation of C-V behavior Affects development directions and ultimate performance predictions Case for fully depleted film Field dependence in a thickness series: J(E,T) is almost independent of thickness!field dropping across entire film thickness Frequency dependence of permittivity Depletion layer! step frequency dependence 2000, S.K. Streiffer, Argonne National Laboratory, All Rights Reserved
Electrode Depletion Layer Film Bulk Depletion Layer Electrode Consider 2 cases for a 200 nm film d i = 10 nm τ = C i R Case 1: Case 2: τ < 10-4 Hz! R b ~ 10 11 Ω! n ~ 10 11 m -3 Not high enough carrier density to cause band bending τ > 10 9 Hz d 2d i σ b = ~ 30 (Ωm) -1 AR b This is strongly semiconducting. 2000, S.K. Streiffer, Argonne National Laboratory, All Rights Reserved
BST Depletion Widths M. Copel et al., Appl. Phys. Lett. 70, 3227 (1997): W = 70nm for CVD films 2000, S.K. Streiffer, Argonne National Laboratory, All Rights Reserved
Failure Modes: Resistance Degradation Change in resistivity of a sample caused by migration of charged point defects, leading to increased leakage and eventually breakdown Bulk and single crystals: R. Waser, T. Baiatu, and K.-H. Härdtl, J. Am. Cer. Soc. 73, 1645 (1990); 73, 1654 (1990); J. Am. Cer. Soc. 73, 1663 (1990). Current Density (A/cm 2 ) 10-1 10-2 10-3 10-4 10-5 53.3 at%ti Thickness: 40 nm Field: 875 kv/cm T = 225 C (-) (+) Resistance degradation in a polycrystalline (Ba,Sr)TiO 3 film, after C. Basceri et al., Ferroelectric Thin Films VI, MRS Symp.Proc. 493 (1998) 10-1 10 0 10 1 10 2 10 3 10 4 Time (s) 2000, S.K. Streiffer, Argonne National Laboratory, All Rights Reserved
Resistance Degradation and Lifetime: Thickness Dependence Observed thickness dependence manifests itself as a decrease in the activation energy with respect to temperature. Current Density (A/cm 2 ) 10 1 10 0 10-1 10-2 10-3 10-4 10-5 53.3 at%ti Field: 750 kv/cm T = 225 C 160 nm 80 nm 40 nm 24 nm 10-1 10 0 10 1 10 2 10 3 10 4 10 5 Time (s) d (s) Measured Lifetime, t 10 6 10 5 10 4 10 3 10 2 n=1.85 n=1.48 n=1.47 @200 C @225 C @250 C 10 1 0 20 40 60 80 100 Thickness (nm) Waser: bulk SrTiO 3, n ~ 2.5 @ 2 kv/cm, 270 C J. Am. Ceram. Soc. 73, 1645-1663 (1990).
Resistance Degradation and Lifetime: Composition Effect d (s) Measured Lifetime, t 10 6 10 5 10 4 10 3 10 2 51.0 at%ti (n=10.7) 52.0 at%ti (n=9.5) 53.0 at%ti (n=8.3) 53.5 at%ti (n=8.1) 10 1 T = 225 C Thickness: 30 nm 10 0 400 600 800 1000 1200 1400 Field (kv/cm) The measured resistance degradation lifetime at this temperature and in this field increases as the Ti content is increased to 52.0 at%ti, and then decreases with higher at%ti.
Resistance Degradation and Lifetime: Temperature Dependence Temperature dependence clearly follows an Arrhenius-type behavior: t d = t 0 exp Q T (V) kt Measured Lifetime, t d (s) 10 6 10 5 10 4 10 3 10 2 10 1 53.3 at%ti Thickness: 40 nm Field: 875 kv/cm 1.8 1.9 2 2.1 2.2 2.3 1000/T (1/K)
Resistance Degradation and Lifetime: Voltage/Field Dependence It is difficult to distinguish the different functional forms of voltage/field dependence, given the electric field range investigated: t d = t 0 exp qv most conservative Q (T) t d = t 0 n V v Q v(t) t d = t 0 exp qv least conservative
Resistance Degradation and Lifetime: Estimation of Lifetimes 51.0 at%ti BST Films d (s) Extrapolated Lifetime, t 10 14 10 12 10 10 10 8 10 6 10 4 (Previously extrapolated to 1.6 V) 10 years 85 C 51.0 at%ti 30 nm BST 70 nm BST 150 nm BST 10 2 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 1000/T (1/K) d (s) Extrapolated Lifetime, t 10 14 10 12 10 10 10 8 10 6 10 4 (Previously extrapolated to 85 C) 1.6 V 51.0 at%ti 30 nm BST 70 nm BST 150 nm BST 10 years 10 2 0 2 4 6 8 10 12 14 Voltage (V)
Resistance Degradation and Lifetime: Modification Of Leakage Behavior Oxygen vacancies are mobile defects under the given experimental conditions: electromigration toward cathode. Modification of Schotky barrier heights/band structure (different than bulk resistance degradation mechanism) Also: Spatial modification of carrier concentrations due to the spatial variation in the oxygen vacancy concentration between the two electrode: change in conductivity of the bulk film. The accumulation of oxygen vacancies in front of the cathode creates an internal built-in potential at the interface. This space charge modifies the band structure and thus interfacial energy barriers: The difference in barrier heights then appears as an internal bias in the film. 2000, S.K. Streiffer, Argonne National Laboratory, All Rights Reserved
Resistance Degradation and Lifetime: Modification Of Leakage Behavior The differences in barrier heights: 4xt s : 0.13 ev 5xt s : 0.21 ev 7xt s : 0.22 ev -4-4 -8 53.0 at%ti Thickness: 40 nm T = 25 C Fresh -8 53.0 at%ti Thickness: 40 nm T = 25 C 7xt s (+ deg.) lnj (A/cm 2 ) -12-16 (-) Polarity 4xt (- deg.) s 5xt (- deg.) s lnj (A/cm 2 ) -12-16 (+) Polarity Fresh -20-20 700 800 900 1000 1100 1200 E 1/2 (V/cm) 1/2 700 800 900 1000 1100 1200 E 1/2 (V/cm) 1/2 2000, S.K. Streiffer, Argonne National Laboratory, All Rights Reserved
Resistance Degradation and Lifetime: Modification Of Leakage Behavior The peak shift in C-V: 0.12 V 55 0.0100 C/A (ff/µm 2 ) 50 45 40 35 30 25 20 53.0 at%ti t: 40 nm T = 25 C Fresh 4xt s (-deg.) Peak Shift: 0.12 V tanδ 0.0080 0.0060 0.0040 0.0020 15-5 -4-3 -2-1 0 1 2 3 4 5 Bias (V) 0.0000-5 -4-3 -2-1 0 1 2 3 4 5 Bias (V)
Resistance Degradation and Lifetime: Modification Of Leakage Behavior The peak shift in C-V: 0.20 V 55 0.0100 C/A (ff/µm 2 ) 50 45 40 35 30 25 20 53.0 at%ti t: 40 nm T = 25 C Fresh 5xt s (-deg.) Peak Shift: 0.20 V tanδ 0.0080 0.0060 0.0040 0.0020 15-5 -4-3 -2-1 0 1 2 3 4 5 Bias (V) 0.0000-5 -4-3 -2-1 0 1 2 3 4 5 Bias (V)
Resistance Degradation and Lifetime: Modification Of Leakage Behavior The peak shift in C-V: 0.20 V 55 0.0100 C/A (ff/µm 2 ) 50 45 40 35 30 25 20 53.0 at%ti t: 40 nm T = 25 C Fresh 7xt s (+ deg.) Peak Shift: 0.20 V tanδ 0.0080 0.0060 0.0040 0.0020 15-5 -4-3 -2-1 0 1 2 3 4 5 Bias (V) 0.0000-5 -4-3 -2-1 0 1 2 3 4 5 Bias (V)
Resistance Degradation and Lifetime: Modification Of Leakage Behavior Recovery anneal studies: Negative polarity currents were completely recovered. Positive polarity currents decreased further? Current Density (A/cm 2 ) 10-1 10-2 10-3 10-4 10-5 10-6 10-7 10-8 10-9 10-10 53.3 at%ti Thickness: 40 nm T = 25 C Fresh Contact (+) After 11 cycles (+) 550 C, 40 min, Air (+) Fresh Contact (-) After 11 Cycles (-) 550 C, 40 min, Air (-) 0 0.5 1 1.5 2 2.5 V 1/2
Resistance Degradation and Lifetime: Modification Of Leakage Behavior C-V behavior indicates that resistance degradation is recoverable. C/A (ff/µm 2 ) 55 50 45 40 35 30 25 20 53.3 at%ti t: 40 nm T = 25 C Fresh Contact After 11 Cycles After Air Anneal (550 C, 40 min) tanδ 0.0100 0.0080 0.0060 0.0040 0.0020 15-4 -2 0 2 4 Bias (V) 0.0000-4 -2 0 2 4 Bias (V)