Optimal Energetic-Trap Distribution of Nano-Scaled Charge Trap Nitride for Wider V_th Window in 3D NAND Flash Using a Machine-Learning Method

Abstract

A machine-learning (ML) technique was used to optimize the energetic-trap distributions of nano-scaled charge trap nitride (CTN) in 3D NAND Flash to widen the threshold voltage (V_th) window, which is crucial for NAND operation. The energetic-trap distribution is a critical material property of the CTN that affects the V_th window between the erase and program V_th. An artificial neural network (ANN) was used to model the relationship between the energetic-trap distributions as an input parameter and the V_th window as an output parameter. A well-trained ANN was used with the gradient-descent method to determine the specific inputs that maximize the outputs. The trap densities (N_TD and N_TA) and their standard deviations (σ_TD and σ_TA) were found to most strongly impact the V_th window. As they increased, the V_th window increased because of the availability of a larger number of trap sites. Finally, when the ML-optimized energetic-trap distributions were simulated, the V_th window increased by 49% compared with the experimental value under the same bias condition. Therefore, the developed ML technique can be applied to optimize cell transistor processes by determining the material properties of the CTN in 3D NAND Flash.

1. Introduction

In recent years, solid-state drives (SSDs) have been developed to satisfy the requirements for rapidly storing and using large amounts of data. NAND Flash is a key and widely used component in SSDs because of its suitability for mass production and reasonable bit cost [1]. NAND Flash has been developed with innovation in three-dimensional (3D) architecture and charge trap nitride (CTN) as a storage node [2,3,4,5]. Further, the bit cost of NAND Flash has been reduced using multi-level cell (MLC) technology, which stores multiple bits in each single cell [6].

An MLC creates more threshold-voltage (V_th) states in one cell by subdividing the amount of charge injected into the storage node. As more V_th states are created, the number of bits stored per cell increases, and therefore, the bit cost considerably reduces [7,8]. Unfortunately, the number of sections with overlaps between subdivided V_th states also increases, making it difficult to distinguish the actual V_th states and thereby degrading the device reliability [9,10,11].

Multiple V_th states are created within a limited V_th window between the erase (ERS) and the program (PGM) V_th [12,13]. Then, if the V_th window is widened, the errors in distinguishing V_th states can be reduced by obtaining the margin of each V_th state. In the previous works, wide V_th windows were achieved by adopting new materials and bias conditions [14,15]. However, qualitative analyses for improving the V_th window have not sufficiently focused on the material properties of the storage node.

The energetic-trap distribution is an important material property of the CTN, a nano-scaled thin film in 3D NAND Flash. Previously, it was discussed based on the analytical model for charges [16]. The energetic-trap distribution can be extracted using retention models [17] and trap spectroscopy by charge injection and sensing (TSCIS) [18]. Furthermore, the energetic-trap distributions are determined by the gas flow ratio deposited on the CTN [19,20]. These studies indicated that energetic-trap distributions are controllable and that their profiles determine the ERS V_th (V_th,ers) and PGM V_th (V_th,pgm) [17,21]. We tried to maximize the V_th window, that is, the sum of the absolute value of V_th,ers (|V_th,ers|) and V_th,pgm, by optimizing the energetic-trap distributions.

We also used a novel machine-learning (ML) method to improve the V_th window. Recently, ML has been used for predicting and optimizing nanoscale transistors [22,23,24]. Moreover, it can help quantitatively determine the complex material properties of the CTN with high speed and accuracy. Therefore, an artificial neural network (ANN) [25] was trained by modeling eight inputs that determine the energetic-trap distributions and the two outputs |V_th,ers| and V_th,pgm. Next, the energetic-trap distributions were investigated to realize a large V_th window by the gradient-descent method, a widely used optimization algorithm.

In this study, the ML method helps determine the optimized energetic-trap distributions and thereby control the material properties of the CTN in 3D NAND Flash. We quantitatively found the energetic-trap distributions that resulted in the largest V_th window. The remainder of this paper is organized as follows. In Section 2, the simulation data and ML method used to train the ANN are introduced. In Section 3, we discuss the results of training and optimization of ML-based analysis. Finally, the conclusions are drawn in Section 4.

2. Simulation and Machine-Learning Method

We obtained data from TCAD simulations for training the ANN [26]. Shockley–Read–Hall recombination, drift-diffusion transport, mobility (high-field, doping and interface dependent) and Hurkx band-to-band tunneling models were adopted for the poly-Si channel. Furthermore, the nonlocal tunneling model was used to describe charge transport in ERS/PGM operations.

Figure 1 shows the schematic diagrams of 3D NAND Flash used in the simulation. Figure 1a shows a part of the 3D NAND Flash string. It has a cylindrical structure, and both ends are connected by a bit line (BL) and a source line (SL). V_th is extracted from the BL current (I_BL) of 1 μA vs. selected word line (WL_Sel) voltage in the middle of the string. Figure 1b shows the half cross-sectional view of the cylindrical structure and a gate stack. Furthermore, ERS (PGM) state is the condition when holes (electrons) are filled in the CTN. The simulation structure was derived from the manufactured device [27].

Figure 2 shows two energetic-trap distributions following the Gaussian distribution of the bandgap in the CTN. Donor- and acceptor-like traps capture holes and electrons, respectively. Each distribution consisted of the trap densities (N_TD and N_TA), peak energy levels (E_TD and E_TA), capture cross sections (CCS_D and CCS_A), and standard deviations (σ_D and σ_A). These eight inputs determine the profile of the distributions, and V_th,ers and V_th,pgm change accordingly.

Figure 3 shows V_th with the ERS/PGM operating time. Each operation was performed by applying a single pulse; the PGM operation started from the ERS state, whereas the ERS operation started from the PGM state. Under the same bias condition (V_PGM = 15 V, V_ERS = 20 V), the simulation data (solid lines) were calibrated with the experimental data (symbols) by adjusting the energetic-trap distributions of the CTN. The calibrated simulation data were then used as training data for the ML-based analysis. In this study, the V_th window is the sum of |V_th,ers| and V_th,pgm at time = 10⁻² s. The corresponding V_th window contains the difference between the ERS and the highest PGM V_th states of an MLC.

Figure 4 shows a schematic of the ANN. First, datasets are produced from TCAD simulation for 3D NAND Flash cell. These extracted datasets are used to design the ANN. A multilayer perceptron (MLP), in which several layers of perceptrons are sequentially attached, was used for training [28]. MLP is suitable for solving nonlinear functions that cannot be solved using a single-layer perceptron, so it is useful for the training complex model. In this study, this feedforward network contains one hidden layer with 15 nodes and tanh as an activation function. In addition, it was trained using MATLAB to model the inputs and outputs [29]. The Levenberg–Marquardt method was used for the backpropagation of training, and the cost function was calculated by the mean squared error (MSE). The MSE indicates the accuracy of ML training. The smaller it is, the better is the training of the ANN. After training, the gradient-descent method was used in the backward direction to determine the optimal inputs that resulted in a large V_th window. This method is widely used for finding the minimum value of the cost function in ML. Finally, we set the cost function in the direction of making large outputs. In summary, we trained the ANN using well-calibrated simulation data and then used the well-trained ANN to determine the optimal inputs that resulted in the largest outputs.

Table 1. Input parameters of energetic-trap distributions of the CTN.

Trap Parameter	Min	Max	Calibrated
Density of donor-like traps, NTD (cm−3·eV−1)	5.00 × 1018	5.00 × 1019	1.00 × 1019
Peak energy level of donor-like traps, ETD (eV)	2.00	3.00	2.50
Capture cross section of donor-like traps, CCSD (cm2)	1.00 × 10−15	1.00 × 10−11	1.00 × 10−13
Standard deviation of donor-like traps, σD (eV)	0.10	0.50	0.35
Density of acceptor-like traps, NTA (cm−3·eV−1)	8.00 × 1018	8.00 × 1019	2.00 × 1019
Peak energy level of acceptor-like traps, ETA (eV)	0.80	1.50	1.00
Capture cross section of acceptor-like traps, CCSA (cm2)	1.00 × 10−15	1.00 × 10−11	1.00 × 10−13
Standard deviation of acceptor-like traps, σA (eV)	0.10	0.50	0.30

summarizes the calibrated values and ranges of the eight inputs for training and optimizing of the ANN. These inputs were randomized within each range uniformly, and different |V_th,ers| and V_th,pgm values were derived, accordingly. N_TD, N_TA, CCS_D, and CCS_A were logged, and then all parameters were standardized to improve the prediction accuracy of the ANN. In addition, there is no correlation between inputs. The calibrated values are generally the median of each range, and the entire range is reasonable [27,30]. Other material properties of the CTN were fixed only to verify the effect of energetic-trap distributions.

3. Results and Discussion

Figure 5 shows the example of MSEs in the training and validation sets with epochs. Here, epoch refers to the number of times the entire data have passed through the neural network. A total data of 1980 samples were used for ML training. First, they were used for training and test sets with a weight of 80/20. Then, the training sets were divided five-fold. Each fold became a validation set once, and the mean value of the five evaluations was used to determine the performance of the corresponding model. We also repeated this entire process five times by splitting the nodes of the hidden layer to increase the reliability of the model. As a result, the 15 nodes of the hidden layer have the lowest MSE, and the results of applying the model to test sets are shown in Figure 6. Furthermore, the model was well-generalized with no overfitting and underfitting because of the five-fold cross validation.

Figure 6a compares the simulated and the estimated values of |V_th,ers| and V_th,pgm in the test sets. For one input set, two outputs appear simultaneously, and the estimation is expected to be good as the two symbols overlap. Figure 6b shows the errors in the individual values. Each error is extremely small and is within the acceptable range of ±5%. Furthermore, each MSE is 0.7368 × 10⁻³ and 0.8472 × 10⁻³; therefore, the prediction accuracy is very high. These results confirmed that the ANN was trained well. Furthermore, the ANN model was superior in learning speed and accuracy in our datasets compared with other regression models, the random forest, etc.

Figure 7 shows the raw simulated and optimized values of the V_th window; the latter are all larger than the former. We set the cost function in the direction of maximizing the V_th window. The gradient-descent method was used to determine the slope of the cost function. After setting the random inputs within the range listed in Table 1, the estimated V_th window was derived using the well-trained ANN. Then, the random inputs were set again until the slope reached the extreme value. Finally, the inputs that resulted in a large V_th window were found.

Table 2. Optimized input parameters of energetic-trap distributions of the CTN.

Trap Parameter	Value
NTD (cm−3·eV−1)	5.00 × 1019
ETD (eV)	2.00
CCSD (cm2)	1.00 × 10−15
σD (eV)	0.50
NTA (cm−3·eV−1)	8.00 × 1019
ETA (eV)	1.45
CCSA (cm2)	1.00 × 10−15
σA (eV)	0.50

lists the optimized inputs that resulted in the largest V_th window after 2000 iterations.

Figure 8 compares the calibrated and the optimized energetic-trap distributions. The ML results indicated that N_TD, N_TA, σ_TD, and σ_TA strongly influenced the V_th window. When they increased, both |V_th,ers| and V_th,pgm increased significantly. This is because many available trap sites could capture more holes or electrons. When E_TD decreased and E_TA increased, both |V_th,ers| and V_th,pgm increased slightly. This is because the deeper energy of each distribution reduced the attempt-to-escape factor [31]. However, E_TD and E_TA mainly determined the retention characteristics; therefore, the correlation with the V_th window was weak. Similarly, CCS_D and CCS_A had small effects on the V_th window. In summary, large N_TD, N_TA, σ_TD, and σ_TA resulted in a large V_th window owing to the availability of a larger number of trap sites. However, E_TD, E_TA, CCS_D, and CCS_A had a small correlation with the V_th window because we did not consider the retention characteristics.

Figure 9 shows the experimental and simulated |V_th| values optimized by ML. Here, the simulated V_th window was calculated from the best inputs in Table 2. In this case, the |V_th| error between the simulation and the ANN was within 4.34%. Therefore, the simulated V_th windows were reliable. The V_th window increased by 49%. In other words, the V_th window can be sharply increased by optimizing the energetic-trap distributions. Therefore, we can provide a guideline for maximizing the V_th window, although the precise process remains difficult.

4. Conclusions

ML-based analysis was used to obtain optimized energetic-trap distributions for the CTN in 3D NAND Flash to improve the V_th window. The ANN enables modeling the relationship between eight inputs that determine the energetic-trap distributions and the two outputs, |V_th,ers| and V_th,pgm. The ANN was trained using well-calibrated simulation data with experiments, and the MSEs were found to be small. Then, we used the gradient-descent method to determine the best inputs that resulted in the largest V_th window. N_TD, N_TA, σ_TD, and σ_TA significantly influenced the V_th window. As they increased, the V_th window grew because of the large number of trap sites. In particular, when the best inputs obtained using ML were employed, the V_th window increased by 49% compared with the experimental value. This study should enable the determination of the V_th window from the material properties of the CTN in 3D NAND Flash. More generally, this work implies that ML can help to solve the complex problem of nanomaterials accurately and optimize it rapidly.