Estimation of steady state leakage current in polycrystalline PZT thin films Estimation of steady state leakage current in polycrystalline PZT thin films Yury Podgorny, Konstantin Vorotilov, and Alexa[.]
Estimation of steady-state leakage current in polycrystalline PZT thin films Yury Podgorny, Konstantin Vorotilov, and Alexander Sigov Citation: AIP Advances 6, 095025 (2016); doi: 10.1063/1.4964147 View online: http://dx.doi.org/10.1063/1.4964147 View Table of Contents: http://aip.scitation.org/toc/adv/6/9 Published by the American Institute of Physics AIP ADVANCES 6, 095025 (2016) Estimation of steady-state leakage current in polycrystalline PZT thin films Yury Podgorny, Konstantin Vorotilov, and Alexander Sigov Moscow Technological University (MIREA), Vernadsky pr 78, 119454 Moscow, Russia (Received 29 June 2016; accepted 21 September 2016; published online 28 September 2016) Estimation of the steady state (or “true”) leakage current J s in polycrystalline ferroelectric PZT films with the use of the voltage-step technique is discussed Curie-von Schweidler (CvS) and sum of exponents (Σexp) models are studied for current-time J (t) data fitting Σexp model (sum of three or two exponents) gives better fitting characteristics and provides good accuracy of J s estimation at reduced measurement time thus making possible to avoid film degradation, whereas CvS model is very sensitive to both start and finish time points and give in many cases incorrect results The results give rise to suggest an existence of lowfrequency relaxation processes in PZT films with characteristic duration of tens and hundreds of seconds © 2016 Author(s) All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/) [http://dx.doi.org/10.1063/1.4964147] Ferroelectric thin films having unique physical properties are explored for application in different electronic devices, e.g., ferroelectric random access memory (FRAM), piezoelectric microelectromechanical systems (MEMS), high permittivity capacitors, etc.1,2 Leakage currents is an important point that should be taken into account in construction and operation of ferroelectric devices In addition, leakage current is a sensitive diagnostic tool for monitoring material properties, such as defects, interfaces, etc The voltage-ramp and the voltage-step are commonly used techniques for current-voltage J (V) measurements of ferroelectric capacitors.3,4 For the first case, the measurements are restricted by the voltage sweep rate dependence as a result of transient currents arising at voltage increase.5–7 In addition, despite the fact of the film pre-polarization, a polarization recovery current due to partial depolarization of ferroelectric film may occur that gives an ambiguous interpretation and leads in some cases to observation of negative differential conductivity.8 So the voltage-ramp method makes it possible to obtain rapidly an overall picture of leakage currents at different electric field strengths, but it is hard to obtain a steady-state or “true” leakage current in ferroelectric films by this technique In the voltage-step method the current-time J (t) dependences are measured at different fixed voltages V Just after a voltage step application a relaxation current caused by linear polarization and polarization recovery dominates, and after some time J (t) should reach a plateau with the steady-state leakage current J s Depending on film quality, voltage, temperature, etc., J s estimation takes longterm measurements (typically tens of minutes) and may be interrupted as a result of film degradation, e.g time-dependent dielectric breakdown (TDDB).3,4,9 The minimum current value is usually taken as the steady-state current,3,4 although this value is higher than the steady-state one due to not only incomplete relaxation, but due to the film degradation already taking place Therefore, to reduce the observation time a correct fitting model of J (t) dependence is needed to obtain a true steady-state J s value When the voltage step is applied to a ferroelectric capacitor, then after about one second the current response may be approximated by the Curie–von Schweidler (CvS) empirical law J = J0 × t −γ + Js , (1) where J s is the steady-state current density, J o is a constant, and γ is usually less than unity (0.6-0.8).3,4,6,10 2158-3226/2016/6(9)/095025/5 6, 095025-1 © Author(s) 2016 095025-2 Podgorny, Vorotilov, and Sigov AIP Advances 6, 095025 (2016) Different mechanisms for CvS behavior are known: relaxation times distribution, space charge trapping, and a many-body interaction model.9–12 CvS power model is commonly used for J (t) fitting in ferroelectric films, but there is no information concerning minimum observation time for the steady-state current estimation Another J (t) fitting model is the sum of exponents model (Σexp) with the relaxation times distribution: Xn J (t) = Jmi × exp (−t/τi ) + Js , (2) i=1 where J mi is the initial current value, τi is the relaxation time, and J s is the steady-state current Some authors believe that this model is suitable for polycrystalline ferroelectrics with internal grain boundaries (e.g BST), and it is not adequate for columnar grain ferroelectrics (e.g PZT).9,11 On the other hand, Podgorny et al.13 have successfully used Σexp model for simulation of short-circuit relaxation current in sol-gel PZT thin films Two relaxation processes with different relaxation times have been found, e.g τ1 ∼ 60 s, τ2 ∼ 330 s for the PZT film annealed at 650o C In the present paper we use Σexp model for relaxation charging current description, taking into account that relaxation processes in the course of ferroelectric capacitor discharging and charging are identical.4,14,15 We compare CvS and Σexp models for current-time J (t) dependences fitting and the steady-state current estimation in PZT films PbZr0.48 Ti0.52 O3 films with the thickness from 213 to 1165 nm were prepared on Si - SiO2 (300 nm) - TiO2 (10 nm) - Pt (150 nm) substrates by chemical solution deposition by the procedure described earlier.16,17 Crystallization heat treatment was performed at 650 ◦ C during 20 The films have typical columnar grain perovskite structure with mixed (111) and (100) texture.17 Mercury probe (MDC Corp.) with 760 µm contact diameter was used to provide electrical measurements Polarization hysteresis P(E) was measured at the frequency of 100 Hz (aix ACCT Systems GmbH, TF 2000 E), while J(t) dependences were measured by the Hewlett Packard 4140B pico-ampermeter (voltage-step technique, observation during 18 min) The films have remanent polarization Pr = 19.8 − 24.3 µC/cm2 and coercive field E c = 54-63 kV/cm (thinner film has lower polarization and highest coercive field values due to a “dead” layer effect).18 Figure shows typical experimental J (t) dependences for 1165 nm thick film measured at different values of voltage steps (negative voltage on the upper electrode is presented as example) and fitting curves obtained according to CvS (Eq (1)) and Σexp (Eq (2) at n = 3) with the use of nonlinear regression In general, Σexp model gives somewhat better fitting than CvS one, e.g for the FIG Experimental current density-time J (t) dependences of PZT film (d=1165 nm) measured at different values of the voltage step and fitting curves obtained with CvS (dashed line) and Σexp (solid line) models 095025-3 Podgorny, Vorotilov, and Sigov AIP Advances 6, 095025 (2016) voltage of 15 V the correlation coefficient R = 0.999 for Σexp model, and R = 0.997 for CvS one Similar results are obtained for the films with another thicknesses Figure shows the steady-state leakage current J s obtained by CvS and Σexp models as a function of the electric field strength E for the film with the thickness of 1165 nm Obtained by CvS model, the value of J s increases with E up to a certain maximum, after that it decreases, that is erroneous Moreover, negative values of J s may be observed under certain conditions (see insertion for the film with d=552 nm) Σexp model shows a steady increase of J s with E Linear approximation of J s in the range of E = 40 - 155 kV/cm (see dashed line in Figure 2, R > 0.994) permits to obtain the value of equivalent ohmic conductivity of PZT film σ ∼ 0.012 pS/cm Ohmic contact behavior between Pt and PZT is associated with the positive work function difference between metal and PZT.19,20 It should be noted that this value is obtained for the film with the thickness of 1152 nm, whereas in the case of thinner films the linear region cannot be clearly distinguished due to space-charge-limited current (leakage current at higher than coercive fields has strong thickness dependence).21 Calculations of the steady-state leakage current J s and the relaxation charge Q at different values of the start time t st and finish time t fin are performed to study an effect of the observation time range on the fitting results Relaxation charges are obtained by the following equations: X3 QΣ = Jmi × τi , (3) i=1 tfin QCvS = J0 × t −γ dt = (1−γ) (1−γ) J0 · −tfin + tst , γ−1 (4) tst where t st ≥ s (typical minimum value of the start time, see e.g X Chen et al.11 ) and the maximum value of t fin = 18 (maximum value of the observation time used in this work) are chosen regardless of the actual fitting ranges Figure shows the dependences of J s and Q as functions of the observation time t fin varied from to 18 minutes for the film with the thickness of 1165 nm Calculations are performed by approximation of J(t) dependence measured at the voltage step 15 V by Σexp and CvS models at different values of t st (6.1, 11.6 and 17.2 s) CvS model is very sensitive to both t st and t fin , while Σexp fitting gives results that are practically independent of these parameters if t fin ≥ CvS model gives lower values of J s and higher values of relaxation charges Q (up to ∼ times) in comparison with Σexp model Table I shows the low-frequency relaxation times values for the films with different thickness The simulation is performed by the sum of two or three exponential functions with appropriate choice of t st Low-frequency relaxation in PZT films with different thickness is characterized by FIG The steady-state leakage current J s obtained by CvS and Σexp models as a function of electric field strength for the film with the thickness of 1165 nm (for d=552 nm in insertion) Dashed line is the linear approximation for the ohmic conductivity estimation 095025-4 Podgorny, Vorotilov, and Sigov AIP Advances 6, 095025 (2016) FIG The steady-state leakage current J s (solid line) and the relaxation charge Q (dotted line) obtained by Σexp and CvS models as functions of finish time t fin at different values of the start time t st for the film with d=1165 nm (E = 130 kV/cm) three specific relaxation times τi (average τi values for different t st are shown in Table I), they are closely related to each other and to relaxation times obtained earlier for the short-circuit discharging current.13 Figure shows the low-frequency components of relaxation charge as functions of the electric field for the film with d = 1165 nm and d=552 nm (insertion in Fig 4) It can be seen that the longer-term relaxation process with τ1 gives a higher contribution to the relaxation charge comparing to the faster one with τ2 Qτ2 (E) dependence tends to saturation at E > 150-170 kV/cm for the films with different thickness A possible reason may be complete traps filling/depletion in the PZT bandgap.9,11,22 On the other hand, Qτ1 (E) has no saturation that possibly suggests oxygen vacancies moving.22 It should be mentioned that the relaxation charge in thinner film (d = 552 nm) is higher not only due to higher defect density, but as a result of higher capacity due to lower thickness Anyway, there exist low-frequency relaxation processes in PZT films whose relaxation times are sufficiently different (tens and hundreds seconds) The nature of these processes calls for further investigations (oxygen vacancies moving, traps filling, electric charge hopping, interfacial polarization, etc.).6,11,12,15,23–27 TABLE I Low-frequency relaxation times for PZT films with different thickness d,nm t st , s 213 552 552 1067 1067 1165 1165 10-22 25-35 10-22 25-35 10-22 25-35 10-22 Average, s MRS, % 160 ∼ 40 τ1, s Charge 360 368 442 365 405 246 386 367 17 Discharge13 330 τ2, s τ3, s 52 59 65 55 66 54 59 59 10 11 12 10.5 11 60 095025-5 Podgorny, Vorotilov, and Sigov AIP Advances 6, 095025 (2016) FIG The relaxation charge Q as a function of electric field strength for the film with the thickness of 1165 nm and 552 nm (insertion) Qτ1 and Qτ2 are charge values for relaxation times τ1 and τ2 respectively In conclusion, we consider estimation of the steady-state (“true”) leakage current in polycrystalline PZT thin films using the voltage-step technique by CvS and Σexp models The Σexp model provides good accuracy of the steady-state leakage current J s determination at reduced measurement time that is important to avoid film degradation Estimation of the steady-state leakage current J s permits to perform correct analysis of leakage current mechanisms and to obtain trustworthy values of film ohmic conductivity, that is important in applied fields The obtained values of relaxation times are close to those obtained earlier 13 at simulation of short-circuit relaxation current that suggests at least two basic low-frequency relaxation processes with characteristic relaxation times of tens and hundreds seconds The second one has higher contribution to relaxation charge, whereas the faster process gives saturation of relaxation charge at E > 150-170 kV/cm probably due to complete traps filling/depletion This work is supported by the program of Ministry of Education and Science (N 11.28.2014K) and Russian Foundation for Basic Research (RFBR, 16-02-00845) N Setter, D Damjanovic, L Eng, G Fox, S Gevorgian, S Hong, A Kingon, H Kohlstedt, N Y Park, G B Stephenson, I Stolitchnov, A K Taganstev, D V Taylor, T Yamada, and S Streiffer, J Appl Phys 100, 051606 (2006) J F Scott, Science 315, 954 (2007) P Zubko, D J Jung, and J F Scott, J Appl Phys 100, 114113 (2006) G W Dietz, M Schumacher, R Waser, S K Streiffer, C Basceri, and A I Kingon, J Appl Phys 82, 2359 (1997) A Sigov, Yu Podgorny, K Vorotilov, and A Vishnevskiy, Phase Trans 86, 1141 (2013) I Stolichnov and A Tagantsev, J Appl Phys 84, 3216 (1998) Y V Podgorny, K A Vorotilov, and A S Sigov, Phys Solid State 54, 911 (2012) Y Podgorny, K Vorotilov, and A Sigov, Appl Phys Lett 105, 182904 (2014) R Waser and M Klee, Integr Ferroelectr 2, 257 (1992) 10 A K Jonscher, Dielectric Relaxation in Solids (Chelsea Dielectrics Press Ltd., London, 1983) 11 X Chen, A I Kingon, L Mantese, O Auciello, and K Y Hsieh, Integr Ferroelectr 3, 355 (1993) 12 D Dimos, W L Warren, M B Sinclair, B A Turtle, and R W Schwartz, J Appl Phys 76(7), 4305 (1994) 13 Y V Podgorny, D S Seregin, A S Sigov, and K A Vorotilov, Ferroelectr 439, 56 (2012) 14 R Waser, NATO ASI Series, edited by O Auciello and R Waser (Kluwer, Dordrecht, 1995), 284, p 223 15 S.-G Yoon, A I Kingon, and S.-H Kim, J Appl Phys 88, 6690 (2000) 16 K Vorotilov, A Sigov, D Seregin, Yu Podgorny, O Zhigalina, and D Khmelenin, Phase Transitions 86, 1152 (2013) 17 N M Kotova, K A Vorotilov, D S Seregin, and A S Sigov, Inorganic Materials 50, 612 (2014) 18 A K Tagantsev and G Gerra, J Appl Phys 100, 051607 (2006) 19 J F Scott, Integr Ferroelectr 9, (1995) 20 A Van der Ziel, Solid State Physical Electronics, 2nd Ed (Prentice-Hall, New York, 1968), pp 266–274 21 P Zubko, D J Jung, and J F Scott, J Appl Phys 100, 114112 (2006) 22 S B Desu, and I.K Yoo, Integr Ferroelectr 3, 365 (1993) 23 M Al-Hadidi, J P Goss, P R Briddon, R Al-Hamadany, M Ahmed, and M J Rayson, Ferroelectr 498, 12 (2016) 24 M Schumacher, G W Dietz, and R Waser, Integr Ferroelectr 10, 231 (1995) 25 M Schumacher and R Waser, Integr Ferroelectr 22, 109 (1998) 26 A R Von Hippel, Dielectrics and Waves (J Wiley & Sons, New York, 1954) 27 T Rojac, S Drnovsek, A Bencan, B Malic, and D Damjanovic, Phys Rev B 93, 014102 (2016) ... consider estimation of the steady- state (“true”) leakage current in polycrystalline PZT thin films using the voltage-step technique by CvS and Σexp models The Σexp model provides good accuracy of the...AIP ADVANCES 6, 095025 (2016) Estimation of steady- state leakage current in polycrystalline PZT thin films Yury Podgorny, Konstantin Vorotilov, and Alexander Sigov Moscow Technological... September 2016; published online 28 September 2016) Estimation of the steady state (or “true”) leakage current J s in polycrystalline ferroelectric PZT films with the use of the voltage-step technique