Resistive random access memory (RRAM) has attracted increasing attention as potential next-generation nonvolatile memory.^[1–6] To achieve the increasing requirements for enormous data densities and nonvolatile storage, some new technologies of memory are of growing interest due to their significant potential for the replacing or complementing existing memory technology.^[7–9] High density 3-dimensional (3D) integrated technology in RRAM, such as 3D 1D1R crossbar array (1D1R: one diode one RRAM), is a very promising candidate for future non-volatile memory integration applications, and also is one of the most effective methods to meet the requirement of ultra-high density and ultra-large data storage.^[10–12] To compete with the ultra-high density 3D NAND FLASH, a technical modeling of the underlying physical mechanism during operation is very essential. The 1D1R cell usually displays unipolar switching (Set and Reset operation at the same voltage polarity), and the Reset process is controlled by Joule heat.^[3,13–15] The physical understanding of the programming and reliability mechanisms in unipolar 1D1R array requires a detailed characterization of the electrical and thermal conduction properties of the memory cell.

It is well known that the Joule heat can result in the temperature increase of the device inside, which can induce the uneven distribution of thermal stress due to the different thermal expansion coefficients for different materials inside the device. Therefore, the Joule heating effect would seriously affect the stability, reliability, and life of semiconductor devices.^[16–18] With the increase of the integration level in the 3D integrated RRAM device, which will sharply increase the storage unit number and chip area, the thermal effect caused by Joule heat will become more serious. Especially, with the improving of the storage cell density and hence the distance between the adjacent unit being reduced, the thermal crosstalk of neighboring units will seriously hinder the development and application of 3D integrated RRAM. Therefore, establishing a thermal effect model of 3D integrated RRAM will contribute to further promoting the development of 3D integrated RRAM devices.

In our previous work,^[19] the degradation of retention performance under the thermal crosstalk effect and scaling potential of the 3D RRAM array have been systematically investigated. In the present work, we will consider another case, that is, the unit cell adds the electrode component between the RRAM and diode. For this case, with continuously scaling down the feature size, the electrode component will be reduced with the unit cell and finally become filamentous. Due to the filamentous nature of the electrode when the feature size is comparatively small, the thermal reliability of the electrodes should be seriously considered, which could strongly relate to the endurance performance of the integrated array. Otherwise, based on the simulation result, the endurance performance of the 3D crossbar array under the thermal effect is analyzed in detail. Possible methods to alleviate these thermal effects are also provided.

To clearly describe the present work, we firstly establish the structure of the 3D integrated RRAM, as shown in Fig. 1. Figure 1(a) shows the schematics of the 1D1R crossbar array structure. Figure 1(b) reveals the unit cell components which are only composed of an RRAM cell (colored in blue) and a diode (colored in red) connected in series, as well as our previous work. In order to introduce the electrode effect, we add the electrode component based on the unit cell component in Fig. 1(b). Figure 1(c) shows the modified 1D1R structure within this work by introducing the electrode component (colored in brown) which connects the RRAM and diode components. Figure 1(d) shows the schematic diagram of typical DC I–V characteristic including set and reset operations for the 1D1R cell. Both set and reset occur at the same voltage polarity. Otherwise, voltage is applied to the electrode connected with the RRAM cell, while keeping the opposite electrode ground for the set/reset operations.

Fig. 1.

Figure Option ViewDownloadNew Window

Fig. 1. (a) Schematic of the 1D1R crossbar array structure; (b) the unit cell composed of a RRAMdevice and a diode connected in series; (c) the unit cell added the electrode component based on the unit cell component in panel (b); and (d) schematic diagram of typical DC I–V characteristic of a 1D1R cell. In the present work, voltage is applied to the electrode (WL/BL: word lines (WL), bit lines (BL)) that is connected with RRAM cell while keeping the opposite electrode ground for the reset operation.

In our previous work,^[19] the electrode connecting the RRAM and diode components is neglected (see Figs. 1(a) and 1(b)). Generally, the electrode area of the diode cell is usually larger compared to the conductive filament of the RRAM component, and the potential drop on the electrode, and hence the Joule heating process of the electrode could be ignored for the sake of simplicity. However, with the feature size scaling down (such as, < 100 nm), the electrode component will reduce and finally become filamentous. The reduced electrode may be comparable with the conductive filament in the RRAM cell, and could not be neglected as a result under the thermal effect, as schematically shown in Fig. 2.

Fig. 2.

	Figure Option ViewDownloadNew Window
	Fig. 2. Schematics of the 1D1R cell with continuously scaling down the feature size. Electrode component (colored in brown) between the RRAM and diode cells will become filamentous.

Due to the filamentous nature of the electrode when the feature size is comparatively small, the thermal reliability of the electrode should be seriously considered, as well as the RRAM and diode. In order to clearly exhibit the change of the electrode in a smaller size, we describe the degradation mechanisms of electrode structure, as shown in Fig. 3. The electrode component could be destroyed by Joule heat during the reset transition. However, differing from the conductive filament in the RRAM cell, the destroyed electrode component could not be rehabilitated by “set operation”, since the electrode is a kind of metal, such as Pt, Ag, etc. Therefore, the destroyed electrode would deteriorate the operation life time (i.e., endurance performance) of the cross-point array.

Fig. 3.

	Figure Option ViewDownloadNew Window
	Fig. 3. Schematics of the 1D1R unit and the degradation mechanisms of electrode structure.

To estimate the operation life time of the cross-point array, the Arrhenius law is usually used as^[20,21]

Fig. 4.

	Figure Option ViewDownloadNew Window
	Fig. 4. Arrhenius plot of the life time of the electrode component for different activation energy. Here, the life time with Ea = 1.5 eV under T = 400 K is assumed to be 10 years.

Then, the temperature evolution maps of the cross-sections are simulated in the array structure with the electrode connecting the RRAM and diode components, based on 3D Fourier heat flow equation, expressed as

The array structure with various sizes from 3×3×1 to 3×3×3 block array, respectively, is shown in Figs. 5(a)–5(c), at which the Pt electrode component (thickness is 30 nm, and radius is 12 nm) connects the RRAM and diode. Figure 5(d)–5(f) illustrates the temperature evolution maps of the cross-sections (blue planes) in Figs. 5(a)–5(d). Here the critical feature size used for analysis is 30 nm. The other input parameters are the same as those in Ref. [19]. The programmed cells are connected with the diodes in green color (on state). Otherwise, the electrode can be treated as a metallic conductive filament, being similar to our previous work based on the Arrhenius plot used to evaluate the endurance performance under the thermal effect.^[19] By connecting the temperature at t = 50 ns in the electrode of the programmed bit and the characteristic reset time t_reset, endurance cycles n_endurance can be described as

Fig. 5.

	Figure Option ViewDownloadNew Window
	Fig. 5. (a)–(c) Schematics of the array structure including the Pt electrode component with various sizes from 3×3×1 to 3×3×3 block array, respectively. (d)–(f) Temperature maps of the cross-sections (blue planes) in (a)–(c). The programmed RRAMs are connected with diodes in green color.

By connecting Eqs. (1) and (5), the endurance performance of the programmed cellcan be calculated. Figure 6 shows the estimation of the endurance performance of the programmed cell for different array blocks in Fig. 5. The same evaluation method in terms of the Arrhenius plot in Fig. 4 is adopted. As can be seen from Fig. 6 that, with E_a = 1.5 eV, the electrode cell would be destroyed after 1×10⁸ consecutive program/erase cycles due to the thermal effect (maximum endurance is 1×10⁸ cycles).

Fig. 6.

	Figure Option ViewDownloadNew Window
	Fig. 6. Calculated endurance dependence on Ea of different array blocks with 3×3×1, 3×3×2, and 3×3×3 array size, respectively.

Degradation of the electrode is mainly attributed to the metal atom dissipation to the surrounding isolation material. The adoption of the isolation material around the electrode region with higheractivation energy E_a of metal atom migration, which could suppress the dissipation of the electrode material under the Joule heating effect, is a possible method to increase the array endurance performance. As shown in Fig. 6, with the activation energy E_a increasing from 1.5 eV to 3 eV, the endurance performance can be increased by orders of magnitude (e.g., 10 orders of magnitude from 1×10⁷ cycles to 1×10¹⁷ cycles for the 3×3×3 array block).

The endurance performance under the thermal effect of the 3D RRAM array was analyzed in detail based on the numerical simulation, which originates from the thermal reliability degradation of the electrode component at relative small feature size. Based on the proposed theoretical methods, with array size increasing, the thermal effect on the endurance performance gets more severe. Using isolating material with higher activation energy of metal atom migration around the electrode material region could increase the endurance characteristics of the array and hence further promote the scaling potential. The simulated results reveal that with the activation energy E_a increasing from 1.5 eV to 3 eV, the endurance performance can be increased by 10 orders of magnitude.