The origin of massive nonlinearity in Mixed-Ionic-Electronic-Conduction (MIEC)–based Access Devices, as revealed by numerical device simulation A. Padilla, G. W. Burr, R. S. Shenoy, K. V. Raman§ , D. Bethune, R. M. Shelby, C. T. Rettner, J. Mohammad, K. Virwani, P. Narayanan, A. K. Deb§ , R. K. Pandey† , M. Bajaj† , K. V. R. M. Murali† , B. N. Kurdi and K. Gopalakrishnan‡ IBM Research – Almaden, 650 Harry Road, San Jose, CA 95120 (‡ IBM T. J. Watson Research Center, Yorktown Heights, NY 10598) (§ IBM India Research Labs, Bangalore KA, India 560045) († IBM SRDC India, Bangalore KA, India 560045) Tel: (408) 927–1512, Fax: (408) 927–2100, E-mail: [email protected] Abstract Numerical modeling is used to explain the origin of the large ON/OFF ratios, ultra-low leakage, and high ON current densities exhibited by BEOL-friendly Access Devices (AD) based on Cucontaining MIEC materials [1-5]. Motion of large populations of copper ions and vacancies leads to exponential increases in hole current, with a turn-ON voltage that depends on material bandgap. Device simulations match experimental observations as a function of temperature, electrode aspect-ratio, thickness, and device CD. Keywords: Access device, MIEC, NVM, PCM, RRAM, MRAM Introduction Mixed-Ionic-Electronic-Conduction (MIEC)-based ADs [1–5] exhibit ideal characteristics for 3D-stacking of large crosspoint arrays of any resistive nonvolatile memory (NVM) in the BEOL, including bipolar diode-like characteristics (Fig.1), large ON/OFF ratios, high voltage margin Vm (for which leakage stays below 10 nA), ultra-low leakage (< 10 pA), and high ON current densities. Although dependent on total electrode area [1,2,4], the Vm of any given MIEC device structure is mostly independent of the size of the gap between the two electrodes, dgap (Fig. 2). In addition, transient response is markedly faster for points higher up the I–V curve (Fig. 3), with turn-on times varying from >1µsec (for I 1µA) to 15nsec for I >100µA[4]. The operation of MIEC devices has been qualitatively attributed to the modulation of electronic current by the motion of Cuions [1,5]. In this work, we quantify this theory using Sentaurus TCAD. Adapting features for tracking mobile H+ ions [6], we perform 2–D numerical device simulations of Cu-based MIEC semiconductors containing large concentrations of mobile positive + Cu+ ions and negative V− Cu vacancies. Cu ions are allowed to invacancies do not interact teract with conduction electrons, yet V− Cu with holes. The simulator self-consistently solves the continuity and Poisson equations, along with ionization-recombination kinetics (Fig. 4) and a ‘Unified Contact’ Schottky model [7] at each ion-blocking metal electrode. While 1–D models have been developed (Fig.5), none have incorporated Schottky interfaces, minority carriers, and electron-ion recombination simultaneously. Modeling MIEC ADs In the absence of ions, a metal-semiconductor-metal (MSM) structure is simply two Schottky diodes connected back-to-back. As bias increases, current originally limited by the reverse-biased diode increases due to minority-carrier diffusion. However, unlike MIEC ADs, turn-on voltages Vm are large and depend strongly on dgap (Fig.6). In such a p-type MSM structure, a metal work-function very close to the valence band should imply large current flow even at low bias voltages. The large number of mobile positive ions in Cucontaining MIEC materials (Fig. 7) interact with conduction-band electrons and change this behavior markedly (Fig. 8). At zero bias (Fig.9(a)), mobile ions settle into a U-shaped distribution with large electric fields at each interface, maintaining a dynamic equilibrium between electrostatic ion drift towards, and ion diffusion away from, each interface [8]. This ion accumulation results in narrow depletion widths and residual electron tunneling at each interface, yet strong suppression of holes and hole current. At low bias, holes are injected from the positively-biased electrode (Fig. 9(b)), eventually resulting in significant hole diffusion current (with a characteristic SS of ∼85 mV/dec) as the device transitions out of the OFF-state dominated by electron current. Copper ions move away from (and vacancies move towards) the positive electrode, where current is limited at high bias by hole tunneling. Hall-effect measurements performed on MIEC-based materials (Fig. 8, inset) confirm hole-dominated currents at large carrier densities. This behavior is consistent with a suppressed interaction between V− Cu vacancies and holes (large energy barrier), unlike the interaction between Cu+ ions and electrons. Role of Electrode Gap Within a device with a large electrode-gap dgap , a distinct − ‘quasi-neutral’ region where [Cu+ ] ∼ [VCu ] separates the regions of extreme ion aggregation at each interface. This allows the device characteristics to be independent of dgap until these interfacial regions begin to interfere with each other, leading to a decrease in the voltage margin Vm (at 10nA) (Fig. 10). Filaments are not modeled here, but may also form across a narrow dgap . While simulated trends of Vm do show an increase as devices are scaled in CD (Fig.10), the trend is not as strong as that seen experimentally[2]. Device Asymmetry and Transient Response Simulated IV characteristics become asymmetric for devices with highly asymmetric electrode areas, such as conductive-AFM measurements of blanket films (Fig. 11), and show an increase in leakage current as temperature increases. Transient simulations of the MIEC AD response (Fig. 12) show rapid response at high bias and high current, with a slower response at low bias and low current, similar to experiments (Fig. 3). However, the modeled interplay — between fast ion migration that turns on the device, and the slower interaction between ions and electrons that allows hole current to dominate (Fig. 13) — does not exhibit the same vast dynamic range in response speeds (from ∼25ns to ∼100ms) observed experimentally, suggesting that further model refinement, possibly involving interfacial Cu+ reduction, will be necessary. Finally, by carefully tuning simulation mesh against TEM images, precise matching of IV characteristics can be obtained (Fig.14). Conclusions A commercial device simulator was adapted to explain the large ON/OFF ratios, ultra-low leakage, and high ON current densities offered by BEOL-friendly Access Devices (AD) based on Cu-containing Mixed-Ionic-Electronic-Conduction (MIEC) materials [1-5]. Ultra-low leakage at low bias is due to residual electron tunneling, with hole current suppressed by a central ‘quasineutral’ region. Device turn-on occurs as hole injection from the positively-biased electrode increases sharply, driven by motion of large populations of copper ions and vacancies. Simulated trends in turn-on voltage Vm vs. dgap and CD, transient response, temperature dependence, and highly asymmetric device geometries all match experimental observations. References [1] K. Gopalakrishnan et. al., VLSI Tech. Symp., 19.4 (2010). [2] R. S. Shenoy et. al., VLSI Tech. Symp., 5B.1 (2011). [3] G. W. Burr et. al., VLSI Tech. Symp., T5.4 (2012). [4] K. Virwani et. al., IEDM Tech. Digest, 2.7 (2012). [5] G. W. Burr et. al., VLSI Tech. Symp., T6.4 (2013). [6] Sentaurus TCAD, www.synopsys.com (2012). [7] M. Ieong et. al., IEDM Tech. Digest, 733 (1998). [8] J. Maier, in Prog. Solid St. Chem. 23 171 (1995). 100uA Normalized (300ns) 1uA 100nA 10nA Vm~1.53V 1nA 100pA DC IV 10pA 1pA -1.5 -1.0 -0.5 0 0.5 1.0 Blanket 80% Bridges tip MIEC Diode-in-via BEC oxide Si wafer C-AFM 40% tip TEC SiN 1.5 MIEC BEC 100 oxide Si wafer 1000 VBL MIEC 100nm Isat ~ 50uA VWL 3uA 1uA Fig. 4 Sentaurus TCAD[6] is used to model drift, diffusion, 100nA and two rate-equation inter10ns 100ns 1us 10us 100us 1ms Time actions between mobile copFig. 3 Larger applied voltages with higher per ions (Cu+ ), atoms (Cu0 ), saturation currents lead to faster turn-on of mobile vacancies (V − ), and Cu MIEC access devices. electrons. dgap [nm] 300nA Fig. 2 Measured turn-on voltages depend strongly on device CD[2] (not shown), but are insensitive to the gap between electrodes (dgap ) down to very small thicknesses. Fig. 1 Access Devices (ADs) based on Cu-containing Mixed-Ionic-ElectronicConduction (MIEC) materials exhibit bipolar diode-like characteristics with ultra-low leakage and large ON/OFF ratios[1-5]. VBL 10uA C-AFM 60% 10 Voltage [V] 30uA C rent Curr Voltage Margin Current [uA] Higher 100% pulsed IV 10uA 1e21 Ignores… Results: 1D Model predicts linear dc IV curves Gil et al. Solid State Ionics 179 (2008) • MSM structure • mobile acceptors & holes OR • mobile donors & electrons • minority carriers 1D Model • Schottky/ohmic predicts nature of contacts various dc IV curves Strukov et al. small 5, No. 9 (2009) • MSM structure • mobile ions, electrons, holes • fixed acceptors • bulk-limited transport, with ohmic contacts t t for f electrons l t • electron-ion recombination kinetics • Schottky nature of contacts 13 Table: 1nA 100 150 1fA 100nm Voltage 1e-21 -8 -6 -4 -2 2f , 2r = 1.86e-9 1 86e-9 e -0.1955/kBT , 1e3 cm-3 s-1 [V] 0 2 4 6 (b) 1 V+ 30um measurements I20um Van der Pauw 1e17 1 A 1uA Hall-effect Van der Pauw MIEC V- 1e16 dgap= 300nm 1e15 10nA dgap= 40nm cylinder simulation 1e14 100pA cylinder simulation Current 1nA 10nA 100nA 1uA 10uA dggapp= 40nm CD = 40nm 1nA 100pA Electron current Fig. 7 Important parameters in our nu10pA 2D BoR merical model for MIEC ADs include Voltage [V] 1pA -1.5 -1 -0.5 0 0.5 1 1.5 bandgap Eg , the large number of copper atoms (Cu0 ) contributing mobile Fig. 8 Simulated IV curve for a cylindrical MIEC − ions (Cu+ ) and vacancies (VCu ), and AD. As bias increases, electron-dominated current the associated interaction rates (Fig.4). gives way to holes, matching Hall–effect measurements (inset). (e) (d) 8 Fig. 6 While a simulated MSM structure without ions has an MIEClike IV, currents are too low and ONtransition voltages are large and depend strongly on dgap . 1D (Metal-MIEC-Metal) Models have been proposed previously. 1e18 100nA 1f , 1r = 3e-9 , 6e2 cm-3 s-1 dgap = TEC=BEC = 50nm I+ 1e19 10uA [Cu0] = 1e21 cm-3 = 4.05 4 05 eV V 200 Hole carrier density [cm-3] 1e20 100uA cylinder simulation “Body-of-rotation” simulation (c) 1 Electron quasi-Fermi level 0.5 0.5 0 0 -0.5 Valence band -1 -0.5 Hole quasi-Fermi level -1 -1.5 15 Electrons V=0V V 0V -20 -15 Cu+ V=0.4V ((10pA) p ) Holes V=0.8V (5nA) Y position [nm] -10 -5 0 5 10 15 20 -20 -15 -10 -5 0 5 1e22 1e20 1e18 1e16 1e14 1e12 1e10 1e8 1e6 1e4 100 10 TEC: 0.000V 0 000V 15 20 -20 BEC: 0.400V -15 -10 -5 0 5 10 TEC: 0.000V 0 000V 15 V=1.5V (160uA) V=1.2V (17uA) 20 -20 BEC: 0.800V -15 -10 -5 0 5 10 TEC 0.000V TEC: 0 000V 20 -20 BEC: 1.200V -15 15 -10 -5 0 5 10 15 Occ cupancie es [cm-3] VCu- 1e22 1e20 1e18 1e16 1e14 1e12 1e10 1e8 1e6 1e4 100 -1.5 15 Cu0 Electron E Energy [eeV] Ele ectron En nergy [eV V] dgap [nm] 5 1e-18 Fig. 5 1D Metal-MIEC-Metal models proposed previously — none combine Schottky interfaces, minority carriers, and electron-ion recombination. (a) Conduction band Occupa ancies [cm-3] 10 0 DCu+ = DVCu- = 8e-4 cm2/s M = 5.375 eV 15 1pA 1D Model predicts memristor IV curves Eg = 1.4 eV 30 Flatband 25 Voltage [V] 20 C rrentt Cur Models… Currren nt Reference: Arribart et al. • p p-type yp semiconductor • minorityy carriers ElectroChimica • mobile Cu+ & holes • Schottky/ohmic Acta 24 (1978) • Fixed acceptors nature of contacts • Cu+ reduction at cathode 20 TEC: 0.000V BEC: 1.500V TEC: 0.000V BEC: 0.000V 200 1.8 dgap [nm] 1.6 1.4 1.2 1 0.8 0.6 2D BoR 0.4 CD [nm] “Body-of-rotation” simulation 0.2 0 0 50 dgap= 80nm CD = 80nm 100 150 200 2.0V 250 300 Fig. 10 Variation in simulated voltage margin as thickness (dgap ) and diameter (CD) vary around the CD = 40nm, dgap = 40nm cylinder shown in Fig.8. Fig. 3 limits 100uA Simula ated curre ent 10uA 150oC 1 2V 1.2V 10uA 1.0V 1uA 10nA 0 8V 0.8V 1nA 10ns 100ns 1us 10us Time 100us 1e22 1e20 1e18 1e16 1e14 1e12 1 10 1e10 1e8 1e6 1e4 100 Occ cupancies [cm m-3] 100nA 1 0.5 0 -0.5 -1 -1.5 1ms Fig. 12 Transient simulations of MIEC AD response show that the ion migration needed to turn on an MIEC AD occurs slowly at low bias and current, yet rapidly at high bias and current, although not with the same wide dynamic range observed in experiments (Fig. 3). Transient data at higher temperature is likely to be faster, accommodated by adjusting the rate constants in Figs.4 & 7 with the appropriate energy barriers. ((a)) Silver paint MIEC TiN Oxide 120oC 60oC 100nA 30oC MIEC 1uA 180oC 10nA 120oC 90oC 60oC 30oC 150oC 1nA 100pA 20 mm / 40 nm 10nA Asymmetry: 500,000x -0.6 06 10uA 100nA 1uA 1 A 90oC -0.4 04 -0.2 02 0 10pA 1pA 4 um / 25 nm Asymmetry: 160x -0.8 0 8 -0.6 0 6 -0.4 0 4 -0.2 02 02 0.2 AFM tip voltage [V] 0 0 2 0.4 0.2 0 4 0.6 06 Voltage (Small electrode) [V] Fig. 11 (a) Conductive-AFM measurements of blanket films show highly asymmetric IV characteristics because of the large asymmetry in electrode areas, and noise floor increases with temperature. These features can be (b) qualitatively matched in simulation. ((c)) Conduction band Current Electron quasi-Fermi quasi Fermi level Cu0 Holes 10uA V l Valence band b d Cu+ (pulses) 100uA Hole quasi-Fermi level 1e22 1 20 1e20 1e18 1e16 1e14 1e12 1e10 1e8 1 6 1e6 1e4 100 Y position [nm] -40 -30 -20 Simullated cu urrent 150 curre ent 2 100 AFM 50 Energy [eV] 0 Occupa ancies [cm-3] Volta age Margin (at 100nA) [V V] Fig. 9 At zero bias (a), the large number of mobile positive ions settle into a U-shaped distribution with large electric fields at each interface, maintaining dynamic equilibrium between electrostatic ion drift towards, and ion diffusion away from, each interface. This ion accumulation results in narrow depletion widths and residual electron tunneling at each interface, yet strong suppression of holes and hole current. As bias increases (b,c,d), holes are injected from the positively-biased electrode (TEC, at left), the hole barrier presented by the valence band shrinks, and hole current increases exponentially. Copper ions move away from (and vacancies move towards) the TEC, where current is limited at high bias by hole tunneling. At high bias (e), Cu0 , the lattice copper sites that can contribute ions, are depleted at the TEC side and over-saturated at the BEC side, possibly initiating damage of the material. C AFM TIP C-AFM 180oC Simulated 1uA VCu- 20ns 1ns Electrons Total Current 100nA 10nA Experiment p 1nA (b) 100pA (d) 10ns 1us Y position [nm] -10 0 10 20 30 40 -40 -30 -20 -10 0 Simulated (DC) MIEC Electron current 10pA 10 20 30 40 Fig. 13 After a voltage ramp to 1.0V (a, 1ns), hole occupancy remains suppressed by the large Cu+ population diffusing slowly away from the positive (left) interface (b, 10ns). After 20ns (c), this ion population has departed, flattening the bands and allowing some hole injection. By 1us (d), the slow interaction between Cu+ and electrons has suppressed electron current, allowing hole current to dominate. Voltage 1pA -1 5 -1.5 -1 -0 5 -0.5 0 05 0.5 1 15 1.5 Fig. 14 By carefully tuning the simulation mesh against TEM images for dimensions and the slight recess into the bottom electrode, precise matching of IV characteristics can be obtained, including ultra-low leakage currents, voltage turn-ON values, and >7 orders of magnitude in ON–OFF ratio.