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Effect of Noncircular Channel on Variation of Threshold Voltage in 3D NAND Flash Memory

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02 August 2023

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03 August 2023

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Abstract
Variations in threshold voltage (VTH) and charge distributions in noncircular cells of three-dimensional (3D) NAND flash memory are investigated. The electric field difference in the circular and spike regions causes nonuniform trapped electron density in the charge trap layer (CTL) and influences the VTH variation. Such less-trapped electron (LT) regions in CTL between the circular and spike regions exhibit a lower electric field during the program, resulting in a higher current flow through that region. For the two-spike cells, the charge distribution and VTH variation are analyzed at different heights (HSpike) and angles between spikes. These irregular cells decrease VTH as the HSpike increases.
Keywords: 
Subject: Engineering  -   Electrical and Electronic Engineering

1. Introduction

Three-dimensional (3D) vertically stackable structures are the mainstream in NAND flash memory. An increase in the word-line (WL) stack in 3D NAND is required to achieve high capacity and reduce bit costs [1,2,3,4]. The high-aspect-ratio (HAR) gate-all-around (GAA) polysilicon channel is effective in enhancing gate controllability and suppressing electrical fluctuations [5,6,7,8]. With GAA structures, triple-level and quadruple-level cells have been successfully commercialized in 3D NAND flash memory [9,10,11,12]. However, these multilevel operations are susceptible to threshold voltage (VTH) variation because of the narrower margins in the programmed VTH distribution compared with those of single-level cells [13]. In addition, the HAR structure significantly increases process complexity, affecting electrical performance and reliability [14,15,16,17]. A tapered structure is typically observed in etched HAR holes, from top to bottom [18,19,20,21,22,23]. The tapered shape may primarily affect the program/erase (P/E) window of each cell along the WL string [24,25]. Simultaneously, a microtrench structure frequently forms close to the bottom region of the tapered etch hole. The cross-section of the microtrench generates a noncircular channel with spike-wise deformation, which can further degrade the uniformity of the electrical characteristics [26,27]. Although the electrical behavior of noncircular channel shape has been reported in some studies [28], it is not clear how the spike affects electrical properties of the cell and how VTH is determined by the spike. In this study, the distributions of trapped electrons and inversion electron density were investigated for noncircular cells with single or two spikes using Synopsys Sentaurus technology computer-aided design (TCAD). The channel current density and VTH variations were correlated with the spike height and angle between spikes.

2. Simulation Structure and Methods

Figure 1a shows a schematic of the 3D NAND flash memory with three WL cells. The radial structure of a cell is composed of a metal gate, blocking oxide (BOX), charge trap layer (CTL), band-engineered tunneling layer (BE-TOX) consisting of O1/N1/O2, polysilicon (poly-Si) channel, and macaroni oxide. Figure 1b,c,d show the cross-sectional schematics of the circular cell (C-cell), single-spike cell (SSC), and two-spike cell (TWSC), respectively. Parameter θ was introduced to analyze the effect of the distance between spikes in the TWSC cells, as shown in Figure 1d. The height (HSpike) and angle (θ) between the two spikes varied from 5 to 15 nm and 20° to 135°, respectively.
Figure 2 depicts a spike used in the simulation. The spike region was generated by overlapping a conventional circle and an ellipse, as shown in Figure 2a. The center of the ellipse is away from the center of the circle by the HSpike, inducing a spike shape in each layer, as shown in Figure 2b. The thickness of each layer in spike region was set to be thicker than in circular region.
The Hurkx band-to-band tunneling model for gate-induced drain leakage, high-field-saturation mobility model in the channel were adopted. The quantum confinement effect was also incorporated to accurately analyze the channel current. The oxide layers in the BE-TOX and BOX layers were assumed to have no defects. Transient simulations with a nonlocal tunneling model were performed to simulate the P/E operation. Carriers in the CTL were transported according to the drift-diffusion model, and Shockley–Read–Hall (SRH) model was applied to the capture or emission of carriers into traps. The material properties of the CTL used in this study are listed in Table 1. Silicon nitride has gaussian energy distribution for both electron and hole trap. The spatial distribution of the traps was set constant as we focused on the change in electrical properties due to the noncircular channel shape.
The program (PGM), erase (ERS), and read conditions were VPGM = 16 V / tPGM = 100 μs, VERS = −16 V / tERS = 1 ms, VPASS = 5 V / VBL = 0.05 V, respectively. Figure 3 shows the bit-line current (IBL) vs. gate voltage (VG) curves of the C-cell and noncircular cells at the initial, ERS, and PGM states using 3D TCAD simulation. VTH was extracted using an IBL of 2 μA. The VTH values of the C-cell were −0.5, −2, and 3.67 V in the initial, ERS, and PGM states, respectively. For the SSC and TWSC cells, the VTH in the initial and ERS states were the same as or less different from VTH in the C-cell as shown in Figure 3a. However, in the PGM state, a negative shift of VTH was clearly observed for noncircular cells, owing to structural deformation as shown in Figure 3b. The SSC and TWSC cells were simulated with various HSpike and θ values to further reveal their electrical behaviors.

3. Results and Discussions

3.1. SSC Characteristics

Figure 4a shows the distribution of the trapped electron density (e-density) in the CTL in the PGM state of the SSC. A gradual decrease in the e-density was observed in the region between the spike and circular regions. The less-trapped electron (LT) region is newly defined as where the e-density decreases by 10% of the circular region. Figure 4b shows the maximum electric field (Emax) on the O1 layer of BE-TOX at VPGM = 16 V in the SSC. The peak in the spike region showed the highest electric field compared with the LT and circular regions. The concave shape in the LT region could reduce Emax and induce smaller trapped charges in the LT region.
Figure 5a shows the distribution of the average trapped e-density in the PGM state along the A-A` perimeter with different HSpike values. The average e-density was obtained by radially integrating the overall charge at each position in the CTL. For the C-cell, a uniform trapped e-density of 1.6 × 1019 cm−3 was obtained. For the SSC cell, a fully trapped electron of 5 × 1019 cm−3 was obtained in the spike region. As HSpike increased, the minimum trapped e-density decreased, and the LT region expanded from 5.6 to 10 nm. The distribution of the trapped e-density depended on the HSpike values, influencing the current flow in the channel and the corresponding VTH values. A lower VTH is associated with a reduction in the trapped e-density in the CTL of the circular structure. An increase in HSpike lowered VTH, although it increased the trapped e-density in the SSC, as shown in Figure 5b.
Figure 6a shows the cross-sectional distribution of channel electrons in the SSC with HSpike = 10 nm at Vread = VTH. Because the trapped e-density was high in the spike region, the inversion electron in that region was locally smaller than in other channel regions. However, the LT region had a smaller trapped e-density; thus, more channel electrons and a higher current density were induced. Figure 6b shows the average channel e-density along the A-A` perimeter with different HSpike values. The calculated channel e-density of the C-cell was as high as 4.6 × 1016 cm−3. The e-density peak coincided with the minimum trapped e-density in CTL (Figure 5a). As HSpike increased, the peak value increased from 1.6 × 1017 to 2.1 × 1017 cm−3. Figure 6c shows the ratio of the currents flowing in the three regions to the total channel current (at Vread = VTH) in the SSC in the PGM state. At HSpike = 15 nm, the calculated normalized perimeter was as high as 70% for the circular region, 18% for the spike region, and 12% for the two LT regions, respectively. The intensity of current in the LT region became dominant with increasing HSpike. For the SSC with HSpike = 15 nm, 57% of the total current flowed through the two LT regions. During a PGM operation, a reduced electric field in the LT region induced a lower trapped e-density, which again increased the channel e-density.

3.2. TWSC Characteritsics

Figure 7 shows the distributions in the trapped e-density in CTL and channel e-density at Vread = VTH along the B-B` perimeter between two spikes in the PGM state. The angle between the spikes varied from 20° to 135° with HSpike = 10 nm. The cross-sectional distribution of the trapped electrons in the CTL is shown in the insets. At θ = 135°, two LT regions were observed in the B-B' region where the minimum trapped e-density of 2.1 × 1016 cm−3 and the peak channel e-density of 1.3 × 1017 cm−3 (Figure 7d). At θ = 90°, two LT regions were close and the minimum trapped e-density is unchanged, but peak channel e-density increased to 5 × 1017 cm−3 (Figure 7c). As the angle decreased, the LT regions overlapped, and at θ = 45°, the LT region with the minimum trapped e-density of 2.5 × 1012 cm−3 and the peak channel e-density of 3 × 1013 cm−3 was formed (Figure 7b). Both θ = 45° and θ = 20°, the B-B' region between two spikes showed a negligible electron density compared with the circular region, suggesting that the channel current mostly flowed through the circular region and the two LT regions outside B-B’ (Figure 7a).
Figure 8a shows the current ratio flowing in the LT regions as functions of HSpike and θ for the TWSCs. The channel current primarily flowed in the LT and circular regions and was lower than 1% in the spike regions. The current ratio was maximum at θ = 90°; it significantly increased with a high HSpike value, increasing from 40% for HSpike = 5 nm to 80% for HSpike = 15 nm. Figure 8b shows the VTH variation for TWSCs with different HSpike and θ values. The dashed line represents the VTH value of the C-cell. All the SSCs and TWSCs showed a lower VTH than the C-cell, and a higher spike induced a more significant decrease in VTH. For the TWSC cells at approximately θ = 90°, VTH reduction was observed because of the increased channel e-density at that angle (Figure 7c).

4. Conclusions

We investigated the impact of a noncircular channel with spikes on the VTH characteristics using 3D TCAD simulations in vertical NAND flash memory. The region with lower trapped charges in the CTL between the spike and circular regions expanded as the spike height increased. SSCs and TWSCs showed lower VTH than the C-cell. In particular, for the TWSCs, the VTH variation became severe at θ = 90° as the spike height increased.

Author Contributions

Conceptualization, D.G., and J.W.K.; methodology, J.P., D.K., and G.S.Y.; writing-original draft preparation, D.G., J.K., and J.-S.L.; writing-review & editing, D.G., J.K., and J.-S.L.; supervision, J.-S.L.

Funding

This work was supported by National R&D Program through the National Research Foundation of Korea (NRF) funded by Ministry of Science and ICT (2020M3H2A1078045) and by Samsung POSTECH Research Center (SPRC) funded by Samsung Electronic.

Acknowledgments

The EDA tool was supported by the IC Design Education Center.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. (a) Schematic of 3D NAND flash memory with three WL. Cross-sectional (C1 plane) of (b) circular cell (C-cell) and noncircular cells with (c) single spike and (d) two spikes at an angle θ in between.
Figure 1. (a) Schematic of 3D NAND flash memory with three WL. Cross-sectional (C1 plane) of (b) circular cell (C-cell) and noncircular cells with (c) single spike and (d) two spikes at an angle θ in between.
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Figure 2. Description of noncircular cell: (a) Overlapped circle and ellipse for creating noncircular cell and (b) detailed values for the thickness of each layer in circular and spike region.
Figure 2. Description of noncircular cell: (a) Overlapped circle and ellipse for creating noncircular cell and (b) detailed values for the thickness of each layer in circular and spike region.
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Figure 3. Bit-line current vs. gate voltage (IBL–VG) curves plotted on the log and linear scales: (a) Initial, ERS and (b) PGM states for C-cell, SSC (HSpike = 10 nm), and TWSC (HSpike = 10 nm, θ = 90°).
Figure 3. Bit-line current vs. gate voltage (IBL–VG) curves plotted on the log and linear scales: (a) Initial, ERS and (b) PGM states for C-cell, SSC (HSpike = 10 nm), and TWSC (HSpike = 10 nm, θ = 90°).
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Figure 4. (a) Cross-sectional distribution of trapped electrons in CTL in PGM state and (b) maximum vertical electric field extracted in O1 layer of BE-TOX during the PGM operation.
Figure 4. (a) Cross-sectional distribution of trapped electrons in CTL in PGM state and (b) maximum vertical electric field extracted in O1 layer of BE-TOX during the PGM operation.
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Figure 5. SSC: (a) Concentration of trapped electrons in CTL with different HSpike values along A-A` perimeter. (b) VTH of C-cell (HSpike = 0) and SSC in PGM state with different HSpike values. Inset: Total trapped electron density vs. HSpike value.
Figure 5. SSC: (a) Concentration of trapped electrons in CTL with different HSpike values along A-A` perimeter. (b) VTH of C-cell (HSpike = 0) and SSC in PGM state with different HSpike values. Inset: Total trapped electron density vs. HSpike value.
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Figure 6. SSC: (a) Cross-sectional distribution of channel electrons with HSpike = 10 nm at Vread = VTH and (b) concentration of channel electrons with different HSpike along A-A` perimeter. (c) Ratio of current flowing through circular, LT, and spike regions to total channel current (IBL = 2 μA) with different HSpike values.
Figure 6. SSC: (a) Cross-sectional distribution of channel electrons with HSpike = 10 nm at Vread = VTH and (b) concentration of channel electrons with different HSpike along A-A` perimeter. (c) Ratio of current flowing through circular, LT, and spike regions to total channel current (IBL = 2 μA) with different HSpike values.
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Figure 7. TWSC with HSpike = 10 nm and θ for (a) 20°, (b) 45°, (c) 90°, and (d) 135° in PGM state. The concentration of trapped electrons in CTL and channel electrons with different θ values along B-B` perimeter are shown. Inset: Corresponding cross-sectional distribution of trapped electrons in CTL.
Figure 7. TWSC with HSpike = 10 nm and θ for (a) 20°, (b) 45°, (c) 90°, and (d) 135° in PGM state. The concentration of trapped electrons in CTL and channel electrons with different θ values along B-B` perimeter are shown. Inset: Corresponding cross-sectional distribution of trapped electrons in CTL.
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Figure 8. (a) Ratio of current flowing through LT region to total channel current (IBL = 2 μA) with HSpike and θ of TWSCs and (b) VTH in PGM state of TWSCs depending on HSpike and θ of spike.
Figure 8. (a) Ratio of current flowing through LT region to total channel current (IBL = 2 μA) with HSpike and θ of TWSCs and (b) VTH in PGM state of TWSCs depending on HSpike and θ of spike.
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Table 1. Material properties of silicon nitride used in CTL.
Table 1. Material properties of silicon nitride used in CTL.
Parameter Value
Bandgap 5.0 eV
Peak Energy Level of Electron Trap 1.0 eV
Standard Deviation of Electron Trap 0.1 eV
Total Density of Electron Trap (NT) 5 × 1019 cm−3
Peak Energy Level of Hole Trap 2.5 eV
Standard Deviation of Hole Trap 0.1 eV
Total Density of Hole Trap 5 × 1018 cm−3
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Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.
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