Characteristics towards Bio-Realistic Synaptic. Emulation

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1 MoS 2 Memristors Exhibiting Variable Switching Characteristics towards Bio-Realistic Synaptic Emulation Da Li 1, Bin Wu 1, Xiaojian Zhu 2, Juntong Wang 1, Byunghoon Ryu 1, Wei D. Lu 2, Wei Lu 1 and Xiaogan Liang *,1 1 Department of Mechanical Engineering, 2 Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI *Contact xiaoganl@umich.edu Supporting Information 1

2 Figure S1. DC-programmed switching characteristics of ten MoS 2 memristors with channel length of 1 µm, which were fabricated under the same condition. All of these memristors exhibit 2

3 a rectification-mediated switching characteristic, and the corresponding hysteretic I-V curves are smooth without exhibiting any abrupt change of conductance. Figure S2. Discrete pulse-programmed switching characteristics measured from the few-layer MoS 2 memristor shown in Fig. 7. (set process: 20-12V, 250ns pulses; reset process: V, 250 ns pulses). 3

4 Figure S3. Pulse-programmed switching characteristic curve (I n curve) measured from an Ar plasma-treated memristor. Measurement cycle condition: a train of 15 +8V, 300ns set pulses for increasing the device conductance followed by a train of 15-8V, 300ns reset pulses for decreasing the conductance. Calculation of Atomic Percentages of Mo and S Atoms Based on AES Spectra Atomic percentages of Mo and S atoms within various sampling areas are calculated using a MultiPak TM software package. The basic calculation is based on the following equation: / / 4

5 In this equation, is the atomic concentration (or atomic percent) of Element i to be quantified in an AES sampling area; and are peak-to-valley heights of the derivative Auger spectrum features associated with Elements i and j, respectively; and are the relative sensitivity factors of Elements i and j, respectively. Typically, S LVV and Mo MVV transitions are employed to quantify the concentrations of S and Mo atoms, respectively. 1 In our calculation, the relative sensitivity factors used for S LVV transitions (~153 ev) and Mo MVV transitions (~186 ev) are and 0.268, respectively, which are calibrated by the AES spectrum of a pristine MoS 2 ingot. Table S1 lists the kinetic energy positions of the AES transition features associated with S and Mo atoms, which were measured from different sampling areas. Table S2 lists the peak and valley readings of the first order derivative AES features associated with S LVV and Mo MVV transitions. Based on these data extracted from AES spectra, atomic percentages of S and Mo atoms in different AES sampling areas have been determined and also listed in Table S2. In addition, these atomic percentage data are also plotted in Figs. 10 (e) and (f). Figure S4. Auger spectra with a full energy range ( ev) captured from the sampling areas in (a) control and (b) electrically-treated memristors, respectively. 5

6 Table S1. Kinetic Energy Positions of the AES Transition Features Associated with Sulfur (S) and Molybdenum (Mo) in Each Sampling Area Kinetic Energies of AES Transitions (ev) Sampling Areas S Mo Mo (calibrated) a Electrically-Treated Area Electrically-Treated Area Electrically-Treated Area Control (Intact) Area Control (Intact) Area a The Mo (calibrated) column is used to show the calibrated energy positions of the Mo MVV transitions measured from different sampling areas in case that all corresponding S features are shifted to a constant position (153eV). Table S2. Peak and Valley Readings of The First Order Derivative AES Features Associated with S LVV and Mo MVV Transitions as well as Calculated Atomic Percentages of S and Mo Atoms S LVV Transitions Features Mo MVV Transitions Features Sampling Areas Peak (a.u.) Valley (a.u.) S (at%) Peak (a.u.) Valley (a.u.) Mo (at%) Electrically-Treated Area Electrically-Treated Area Electrically-Treated Area Control (Intact) Area Control (Intact) Area

7 Kinetic Monte Carlo Simulation of Motion and Aggregation of Defects To explore the mesoscopic mechanisms responsible for the observed memristiveswitching characteristics as well as the transition between different switching modes, we set up a quasi-quantitative model based on Monte Carlo calculations to simulate the kinetic behaviors of S vacancies in a MoS 2 memristor channel. The detailed information about this model is described below. The most abundant defects in mechanically exfoliated monolayers of MoS 2 are sulfur defects. The distance between two neighboring sulfur defects is about 0.25 nm. 2 In the simulation we consider a 2D MoS 2 sample with the length and width of 0.25 µm, which is sufficiently large to capture key behaviors. This corresponds to a simulation domain of grids with a grid spacing of 0.25 nm. The density of sulfur defects is about 0.12 nm This means that about 0.75% of the grid points are occupied by defects. Therefore, we start a simulation by randomly select 0.75% of the grid points as occupied by defects, while the other grid points are possible locations for the defects to jump to. After a defect jumps to a neighboring grid point, the original grid point that the defect has occupied becomes available for other defects to jump to and for this defect to jump back to. A defect can jump left, right, up and down with certain rates. When an electric field is applied, say to the right, the right jump rate is increased while the left jump rate is decreased. Based on the transition state theory, the up jump rate Г 2, and down jump rate Г 4 are given by Г Г Г, where v is the escapeattempt frequency, is the mobility energy barrier of defects, is the Boltzmann constant, 7

8 and T is temperature. 3 The value of Г can be related to the diffusion coefficient, which provides a time scale for the simulation. The physical time of our simulation is proportional to 1/Г. The right jump rate Г, is accelerated by the electric field, giving Г / exp Г Г, where q = 2e is the charge of the defect, / is the strength of the applied electric field in the device and a = 0.25 nm is the hopping distance. These values give S=1.156 at T = 300 K. The left jump rate Г, is de-accelerated by the electric field, giving Г / exp Г Г. After each hopping event we detect and combine defects and/or clusters next to each other into a cluster. A cluster consisting of m defects moves as one with a reduced diffusion rate, so that Г reduces to Г.4 At the same time, the cluster carries more charges so that S increases to. We assume that the combination of defects is irreversible, i.e. a defect can join a cluster but will not detach from a cluster. The following is the algorithm of our kinetic Monte Carlo simulation, which we have implemented in MATLAB. (a) Initialize the domain with 0.75% of the grid points occupied by defects. Detect those defects next to each other in the left, right, up or down direction using the Hoshen- Kopelman algorithm, and lump them together as a defect cluster. 5 (b) Calculate the jumping rates of each defect and defect cluster Г,, where the integer n (n=1, 2,, N) is the identifier of each defect or defect cluster in the domain and i (i=1, 2, 3, 4) represents the jump direction. The possibility of defect or defect cluster n jumping along 8

9 direction i is, Г, / Г,. Order the array in the form of A = (,,,,,,,,,,,,,,,,,,,, ) which has a total of 4N possible jumping events. Define. (c) Generate a random number (0,1) and match the range (, ) such that < (k=2,3, 4N-1) or < or. The selected jumping event is or or, respectively. (d) Execute the event (i.e., move the selected defect or defect cluster along the selected direction). (e) Check whether this move causes the selected defect or defect cluster to jump outside the domain. If so, quit this jump and go to step (c). (f) Generate another random number (0,1) to determine the evolution time of the. system as ln (1 )/ Г, (g) Check whether any two defects and/or defect clusters become next to each other using the Hoshen-Kopelman algorithm. 5 If they do, combine them into a larger cluster. Note that the total number N, decrease after defects and/or defect clusters join to form larger clusters. (h) Go back to step (b) with the updated identifiers of defect and defect clusters. Figure S5 shows kinetic Monte Carlo simulation of motion and aggregation of Sulfur defects. Specifically, Figure S5 (a) shows the initial stage of the simulation, where S vacancies are uniformly distributed over the whole MoS 2 channel (areal density: cm -2 ). 2, 6 In case of zero external electric field, the in-plane diffusion of each vacancy is isotropic, 7-9 and therefore the areal density of S vacancies remains uniform. When an electric field ( V/cm) is applied over the MoS 2 channel, the diffusion of each vacancy exhibits a preferential direction 9

10 along the electric field, and more and more S vacancies accumulate in the proximity region of the MoS 2 /Ti interface, to which the electric field points (i.e., the right-side region in Fig. S5 (b)). During this accumulation process, the accumulated S vacancies result in a gradually enhanced doping effect to the right-side region and are expected to gradually increase the Schottky barrier at the right MoS 2 /Ti interface, as implied by our experimental results discussed above. Such simulated kinetic motion of S vacancies can qualitatively explain the analogue switching characteristics observed from our MoS 2 memristors. Here, we further speculate that if the memristor experiences a relatively mild electrical stress during a switching course (i.e., relatively low programming voltage magnitude, small number of applied voltage pulses with the same polarity, and short duration time for continuously applying a DC bias), not a significant number of S vacancies are expected to aggregate (or to be trapped) at the MoS 2 /Ti interface before the reset operation. In this case, the memristor is expected to remain at the analogue switching mode. However, if a high electric stress (e.g., a sequential train of V, 2ms pulses or 20V DC bias for more than 20 sec, which are implied in our experiments) is applied to the memristor during a switching course, a significant number of S vacancies aggregate at the MoS 2 /Ti interface. Figure S5 (c) displays the Monte Carlo simulation result for this case. The simulation indicates that once many S vacancies aggregate at the MoS 2 /Ti interface, these accumulated S vacancies undergo an energetically preferred agglomeration process and merge into larger vacancies, as shown in Fig. S5 (c). The simulation also implies that in comparison with single atomic vacancies, such large vacancies (or vacancy clusters) have higher diffusion barriers and are therefore highly localized around the MoS 2 /Ti interface. Their effect on the MoS 2 /Ti Schottky barrier is expected to sensitively depend on their atomic scale distances away from the MoS 2 /Ti interface. Although an applied electric field can hardly drive the large vacancy clusters 10

11 to move over the entire MoS 2 channel, it is still expected to induce atomic scale shifts of the clusters around the MoS 2 /Ti interface, and such small shifts are expected to result in abrupt changes in the MoS 2 /Ti Schottky barrier and the channel conductance. Based on this quasiquantitative simulation analysis, we tentatively attribute the observed analog-to-discrete switching mode transition to the vacancy agglomeration induced by high electrical stresses. The aggregated defects play an important role in tuning the Schottky barrier of the MoS 2 -Ti interface. By matching to experimental time, we can estimate Г ~ 10 /, which in turn implies the migration energy barriers for S vacancies or other defects is around 0.6 ev. Figure S5. Time-dependent snapshots from a Monte Carlo simulation of the kinetic behaviors of S vacancies in a MoS 2 memristor channel that is biased with a DC voltage of 30 V. 11

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