Supplementary Materials for

Transcription

1 Supplementary Materials for Extremely Low Operating Current Resistive Memory Based on Exfoliated 2D Perovskite Single Crystals for Neuromorphic Computing He Tian,, Lianfeng Zhao,, Xuefeng Wang, Yao-Wen Yeh, Nan Yao, Barry P. Rand *,,, Tian-Ling Ren *, Institute of Microelectronics and Tsinghua National Laboratory for Information Science and Technology (TNList), Tsinghua University, Beijing 184, China Department of Electrical Engineering, Princeton University, Princeton, New Jersey 8544, United States Princeton Institute for Science and Technology of Materials, Princeton University, Princeton, New Jersey 8544, United States Andlinger Center for Energy and the Environment, Princeton University, Princeton, New Jersey 8544, United States * Corresponding author. brand@princeton.edu (B.P.R.); RenTL@tsinghua.edu.cn (T.- L.R.) These authors contributed equally to this work. This PDF file includes: Supplementary Figures S1 to S9 Monte Carlo Simulation Procedure 1

2 Supplementary Figures Figure S1. Optical image, SEM, XRD and absorption spectrum of CH 3 NH 3 PbBr 3 single crystals. (a) A photograph, and (b) an SEM image of the single crystal. (c) Experimental XRD patterns of the single crystal. (d) Absorption spectrum of the single crystal. 2

3 Figure S2. The resistive switching behaviors using graphene (Gr) as top electrode. (a) The optical image of a Gr/2D perovskite/au device. (b) The AFM image showing the morphology of Gr/2D perovskite/au. (c) The forming curve showing 1 7 on/off ratio. (d) The multi-level operations by setting the compliance current at different level. The unipolar operation for (e) 1 st and (f) 2 nd cycles. 3

4 Figure S3. STEM image and EDS mapping of perovskite/au vertical structure. (a) STEM images of the graphene/2d perovskite/au vertical structure with an additional Au protection layer on top and the corresponding elemental mapping results of (b) Au, (c) C, (d) Br, and (e) Pb. 4

5 Figure S4. A particular comparison of Br and Pb distribution with and without voltage stress. A cross-sectional STEM image of the device (a) without voltage stress and (b) with a pulsed voltage stress and the corresponding EDX line profile. 5

6 Figure S5. STEM image and EDS mapping of perovskite/au vertical structure with filament. (a) STEM images of the filament region of the graphene/2d perovskite/au vertical structure, with an additional Au protection layer on top and the corresponding elemental mapping results of (b) Au, (c) C, (d) Br, and (e) Pb. 6

7 a Current (A) 1-1 HRS LRS b Voltage (V) set reset D Perovskite Thickness (nm) D Perovskite Thickness (nm) Figure S6. The thickness dependence of (a) set/reset voltage and (b) on/off resistance. Simulation Method Figure S7. The flow of Monte Carlo simulations used in this work. There are four major components to our Monte Carlo simulations: (1) Current calculation, (2) Electric field distribution calculation, (3) Temperature update and (4) Vacancies generation and recombination probability calculation. Next we will interpret them one-by-one in detail. 7

8 1. Current calculation: As mentioned, the TAT model is used to calculate the current. For the total current, three major parts determine it: electron tunneling between two V o, between V o and anode, between V o and cathode. The electron occupation probability of all V o traps can be written as equation (1): df n dt = (1 f ) r f f r (1 f ) + R (1 f ) R f n m nm m n m nm m cn n na n (1) f Where is electron occupation probability at trap m. is the electron hopping rate between m two traps (Equation (2)). [S1] r nm Rcn and Rna are the electron tunneling rates of trap-cathode and trap-anode respectively, which can be calculated by Equation (3). r exp( 2 / / ) hopping = ν d ξ+ q V kt (2) L * tunneling = ν fermi dirac ( ) exp( 2 / h 2 ( c ( ) ) E f R F E m E E qv x dx de (3) ν is approximately 1 13 Hz for equation (2) and 1 14 Hz for equation (3), ξ is the electron wavefunction localization length, d is the traps distances, q is the unit charge. V is the trap L * voltage difference. is the trap-electrode distance. m is the 2D perovskite effective mass. In order to model the 2D perovskite material, the layered structure is taken into account. When the electrons located at nts, n= 1,2,3..., where ts is thickness of single layer, extra barrier Ebe will be added in equations (2) and (3). That is q V > q V+ ie be in equation (2) and V( x) > V( x, ie be ) in equation (3), where i is the number of interlayer barrier between two traps. Because the interlayer barrier exists, the current both in LRS and HRS can be effectively reduced compared to bulk resistive switching materials such as HfO x and AlO x. 8

9 We assume that during each iteration step, the electron occupation probability is fixed. Therefore, the df n dt is equal to and every trap electron occupation probability can be obtained by solving equations group made of equation (1) and the total current can be calculated by equation (4). I= q ( R (1 f ) R f ) n cn n na n (4) 2. Electric field distribution calculation: The Poisson equation of electrical potential (equation 5) is used to get the potential distribution φ φ φ ε x 2 φ = y= y y= ρ( x, y) ε = V = φ ε x x= x= x = = (5) Where is electrical potential, is dielectric constant of 2D perovskite, is applied voltage. φ ε V ρ ( x, y) is local charge density, if there is no V o in (x, y), ρ ( x, y) =. When potential is known, the electrical field can be calculated by equation (6) E = φ (6) 3. Temperature update: The temperature change during the resistive switching process can be updated by Equation (7) [S2], Where is the CF equivalent thermal resistance and is room temperature (3 K). Rth T T= T+ V I R th (7) 4. Vacancy generation and recombination probability calculation: The Equation (8) and (9) are the equations for V o generation and recombination probability respectively. 9

10 P = t / t exp( ( E qae )/ kt) g a (8) P= C P r g (9) t t E Where and the lattice vibration time (~1-13 s) are simulation time step respectively, is the magnitude of electrical field, C is the Br - ion concentration, a and a are the lattice constant and forming energy of V o respectively. E We have compared the Monte Carlo simulation and experimental results of HRS and LRS at 3 K, 32 K and 34 K, which are shown as Figure S8. From the simulation and experimental results we can find that high temperature cause the decrease of the resistance in HRS, which indicates the validation of the TAT model. Figure S8. Simulated and experimental resistance change of HRS and LRS under 3 K, 32 K, 34 K. 1

11 Synaptic applications 3 Peak 2 Measure the first time Measure the second time PSC (pa) 2 1 Peak 1 Peak 1 Peak Time (s) Figure S9. Two times sweep of paired pulse facilitation (PPF). The device was swept twice by two pulses (7 V, 1 ms). As shown in Figure S9, for both sweeps, peak 2 is higher than peak 1. Moreover, the overall current level for the second sweep is higher than that of the first sweep. These two observations all prove that the ions can be accumulated after each pulse, which can mimic the synaptic behaviors of short-term potentiation. It looks like no current retention after the pulse measurement. In fact, this is because the RRAM is still in off-state with large resistance, which result in read current below noise current level. References [S1] Mott, N.; Davis, E. In Electronic Process in Non-Crystalline Materials; 2nd Clarendon Press; Oxford, 1979; pp [S2] Guan, X.; Yu, S.; Wong, H.-S. P., On the Switching Parameter Variation of Metal-Oxide RRAM - Part I: Physical Modeling and Simulation Methodology, IEEE Trans. Electron Devices 212, 59,