High‐Uniformity Threshold Switching HfO2‐Based Selectors with Patterned Ag Nanodots

Abstract High‐performance selector devices are essential for emerging nonvolatile memories to implement high‐density memory storage and large‐scale neuromorphic computing. Device uniformity is one of the key challenges which limit the practical applications of threshold switching selectors. Here, high‐uniformity threshold switching HfO2‐based selectors are fabricated by using e‐beam lithography to pattern controllable Ag nanodots (NDs) with high order and uniform size in the cross‐point region. The selectors exhibit excellent bidirectional threshold switching performance, including low leakage current (<1 pA), high on/off ratio (>108), high endurance (>108 cycles), and fast switching speed (≈75 ns). The patterned Ag NDs in the selector help control the number of Ag atoms diffusing into HfO2 and confine the positions to form reproducible filaments. According to the statistical analysis, the Ag NDs selectors show much smaller cycle‐to‐cycle and device‐to‐device variations (C V < 10%) compared to control samples with nonpatterned Ag thin film. Furthermore, when integrating the Ag NDs selector with resistive switching memory in one‐selector‐one‐resistor (1S1R) structure, the reduced selector variation helps significantly reduce the bit error rate in 1S1R crossbar array. The high‐uniformity Ag NDs selectors offer great potential in the fabrication of large‐scale 1S1R crossbar arrays for future memory and neuromorphic computing applications.

This could lead to a large variation in the selector performance.   The distributions of V th and V hold of the negative loops are also plotted in Supporting Information Figure S5a~b. The C V for -V th and -V hold are 5% and 13%, respectively.

S1. Analysis of the variation in the threshold and hold voltages
In the Ag NDs-based selector device, the formation of conductive filaments is a result of field-induced drift of Ag ions, which can be described by a field-driven, temperature activated migration model. During the rupture process of the conductive filaments, the Ag atoms spontaneously diffuse from the filament region to the electrodes, driven by the tendency of surface energy minimization. The switching process of the device is affected by the two processes above, as described by the following equation [1,2] : where A is a pre-exponential constant, E bulk is the energy barrier for field-driven drift, q is the elementary charge, V is the applied voltage, a is the barrier lowering coefficient, D s is the surface diffusion coefficient, γ is the surface tension, δ is the inter-atomic distance, k is the Boltzmann's constant, ϕ is the conductive filament diameter, E surf is the energy barrier for surface diffusion and T is the ambient temperature.
During the selector turn-on process, the voltage-controlled filament growth is dominant.
Ag filaments tend to form under the same voltage thanks to the highly ordered Ag NDs. So the variation of V th is small. During the selector turn-off process, the spontaneous diffusion of Ag atoms is dominant. The spontaneous diffusion process is not only related to the morphology of conductive filaments, but also affected by environmental conditions surrounding the filaments, as given by Equation 1. Therefore, the coefficient of variation for V hold is slightly larger than that of V th . Figure S9. a) BER for the entire 1S1R array in different array sizes. b) I-V curves for 1S1R

S2. BER simulation of 1S1R array
device of different cycles of DC voltage sweep.
In this work, we model the 1S1R crossbar array using experimentally derived device data for the selectors and RRAMs. The schematic diagram of 1S1R crossbar array structure is shown in Figure 6a in the main text. All of the node states in the 1S1R array can be calculated based on the Kirchhoff's Law. In order to study the effect of interconnect resistance (r i ) on the array, all the RRAM devices are set to the low-resistance state (LRS) at the beginning. During the bit error rate (BER) testing, every 1S1R cell in the array is read under a voltage of 0.75 V applied on one end of the word line. If the read current is small (< 0.01 μA), suggesting the selector is not correctly turned on, it is counted as one error bit. To obtain the BER statistically, the read operation is repeated for more than 10 9 times while taking the V th variation of the selectors and the interconnect resistance into consideration. To highlight the influence of device uniformity on the 1S1R array performance, Figure 6e in the main text shows the BER for the 1S1R cell located at the farthest corner from the word-and bit-lines (the worst case scenario). [3] In addition, we have also calculated the BER for the entire 1S1R array as shown in Figure S9a. Both results confirm that the 1S1R array with Ag NDs-based selectors shows a much lower BER compared to that with Ag thin film ones, especially for larger array size (e.g., >64×64) and higher interconnect resistance (e.g., r i > 1 ). Furthermore, Figure S9b (re-drawn from Figure 6d in the main text) confirms that the 1S1R cell can still maintain good uniformity after several cycles of SET/RESET operations.
As the Ag NDs-based selector has shown a high endurance over 10 8 cycles, it can be expected that the 1S1R array can maintain a low BER after multiple cycles of read and SET/RESET operations.