Machine learning investigation of high-k metal gate processes for dynamic random access memory peripheral transistor

The demand for high-speed data communication has experienced an explosive increase in recent years, necessitating a corresponding increase in the bandwidth of the dynamic random access memory (DRAM). To operate at a higher speed and with a minimized leakage current, it is essential for peripheral transistors in DRAM to reduce the off-current (I_off). However, conventional polysilicon oxynitride (pSiON) transistors have encountered limitations in controlling the drain-induced barrier lowering (DIBL) as the chip sizes shrink because of the short-channel effect. This issue leads to increased power consumption, posing a significant challenge in the DRAM technology. In response to these challenges, researchers have explored the use of high-k/metal gate (HKMG) transistors for DRAM peripheral transistors.^1–3 In comparison with the pSiON technology, HKMG offers several advantages, including improved speed and better control of the leakage current. Furthermore, HKMG presents potential solutions to the increased power consumption problem caused by DIBL in pSiON transistors, thus enhancing the power efficiency and performance of DRAM. We compare the structures [Fig. 1(a)] and the performances [Figs. 1(b)–1(d)] of the 10 nm third generation DRAM products of Samsung Electronics that utilize the HKMG transistors and the conventional pSiON transistors. The HKMG transistors were found to exhibit a 38% reduction in I_off [Fig. 1(b)], a 60% increase in the on-current [I_on, Fig. 1(c)], and a 26% decrease in the propagation delay time (tPD) as compared to pSiON transistors. These results suggest that HKMG transistors maintain a lower I_off while achieving a higher I_on, indicating their potential to reduce power consumption in high-speed DRAM applications.

Implementation of HKMG technology in DRAM comes with its own set of challenges. Reliability concerns, such as the negative bias thermal instability (NBTI), interface trap problems related to hafnium oxide (HfO), and V_th variations due to Fermi level pinning, significantly impact the performances of the DRAM devices, hindering the achievement of optimal power efficiency.⁴ Although previous studies reported the effects of nitrogen (N) concentration and channel silicon germanium (c-SiGe) layer on the performances of the HKMG transistors,^5–7 a deeper understanding of the relationships among the process parameters and the electrical properties is required to further optimize the performances. We propose an implementation of machine learning (ML) analysis to investigate the multi-dimensional and complex correlations among the process parameters and the electrical properties.^8–11 By constructing ML regression models and utilizing the explainable artificial intelligence (XAI) algorithms, the degree of impact of the process parameters on the electrical properties is quantified and the main parameters affecting the performance of the HKMG transistor are identified.¹² We also discuss the use of the imputation ML algorithms to fill in the missing data, a very common issue in the semiconductor industry to conserve time and resources.^13,14

The HKMG transistors in this study were prepared using a gate-first process to avoid the Fermi-level pinning caused by the high heat of DRAM fabrication procedures [Fig. 1(a)].^3,4,15 First, a c-SiGe layer was epitaxially grown on the silicon substrate to enhance the hole mobility.² This process reduces both threshold voltage (V_th) and off-current (I_off), which improves the performance of p-type metal oxide semiconductor (PMOS) devices and makes them suitable for low-power DRAM applications. The formation of the interlayer (IL), which includes silicon oxynitride (SiON), was achieved by using oxidation and radio frequency nitridation (RFN). IL prevents reaction between the Hf-based high-k (HK) layer and the Si substrate. By adjusting the N concentration within IL, Si–N bonds are controlled, reducing the interface traps that easily capture the hole carriers.^5–7 This indicates that RFN instigated radical-induced re-oxidation, leading to an increase in capacitance-equivalent thickness (CET).^2,3,15,16 Subsequently, a layer of hafnium silicate (HfSiON) was deposited on top of IL as a HK gate dielectric. HfSiON is known to be stable compared to HfO₂ in a high thermal budget.^2,17 Next, a de-coupled nitridation (DPN) process was used to form the HK dielectric layer. Since N atoms play a role in filling the oxygen vacancies of HK dielectric layers as well as in controlling the dielectric constant, fine-tuning the DPN process is essential to obtain suitable gate dielectrics.^18,19 Aluminum (Al)–titanium nitride (TiN) stacks were then subsequently deposited on top of the HfSiON layer to control the work function. The application of a metal gate with high-k becomes crucial to avoid the V_th control challenges and interface disparities present when using conventional polysilicon.²⁰ Upon completing the fabrication of the HKMG stacks, the devices underwent the standard DRAM fabrication processes.

For machine learning analysis in this study, we consider the five critical process parameters as input features, which are the nitrogen concentration of the interlayer (IL N%), thickness of the interlayer (IL Thk), nitrogen concentration of the HfSiON layer (HK N%), channel length (L_ch), and the gate spacer offset width (L_offset). The seven electrical properties of the HKMG module considered for machine learning analysis are the propagation delay time (tPD), threshold voltage (V_th), on-current (I_on), off-current (I_off), overlap capacitance (Cov), gate oxide thickness (Tox), and threshold voltage shift by negative-bias temperature instability (NBTI). The processing parameters of ion implantation conditions (channel, source, and drain doping), annealing, and device profile were kept consistent.

Typically, not all the process parameters and electrical properties are monitored and measured for every wafer to conserve time and resources in the semiconductor industry. Consequently, missing data in the measurement dataset is inevitable. Of the available 17 241 wafers, the measurements of both process parameters and electrical properties were carried out only for 353 wafers. Additionally, the data of the seven electrical properties showed an average missing rate of 4%, while the five process parameters exhibited a high average missing rate of 59%(Table I), each of which is missing completely at random (MCAR). The MCAR characteristic of the missing values in DRAM can be attributed to random variations in the manufacturing processes and measurement conditions. The imputation methods using machine learning have been utilized to fill in the missing data.

Machine learning analysis has been carried out as schematically shown in Fig. 2. First, the five process parameters and the seven electrical properties of the wafers containing HKMG were collected and tabulated. The missing data rate for each parameter was identified (Table I). Second, the imputation machine learning algorithms were employed to fill in the missing data. Since the process parameters are expected to have local correlations with each other, we applied imputation algorithms by incorporating all the features of electrical properties and process parameters. Prior to the imputation process, we randomly removed 1%, 5%, 10%, and 30% of the known values for each feature item from the original data. Then, nine different imputation algorithms of the expectation–maximization (EM),²¹ mean imputation (Mean), median imputation (Median), iterative imputation with automatic model selection (Hyperimpute),²² nonparametric random forest (Missforest),²³ imputation by chained equations (Ice),²⁴ multiple imputation by chained equations (Mice),²⁵ low-rank matrix approximation (Softimpute),²⁶ and the generative adversarial imputation nets (GAIN)²⁷ were constructed to fill in the missing data with different rates. Following the imputation (data-filling) process, the data for each feature were normalized (min-max scaler) to handle the varying distribution ranges among individual features. The RMSE values were then calculated between the original dataset and the imputed dataset for each removal rate and each imputation algorithm. The imputation algorithm with the lowest RMSE value was then selected and used to fill in the missing data. In the third step (Fig. 2), machine learning based regression models were constructed to predict the electrical properties with the input features of the process parameters. All the models were created using the data that had been imputed using the selected imputation algorithm. The regression models of random forest (RF),²⁸ extremely randomized trees (Extratrees),²⁹ extreme gradient boosting (XGBoost),³⁰ gradient boosting (GBoost),³¹ categorical boosting (CatBoost),³² and the support vector regression (SVR)³³ were built. The hyper-parameters of each model were selected based on the grid search³⁴ (Table S1). For the dataset from the 353 wafers, an 80% (training)–20% (test) split was used with a fivefold cross-validation.³⁵ A regression model with the smallest RMSE value was selected. SHAP (Shapley additive explanations) analysis was then conducted for the selected regression model³⁶ to quantify the influence of individual variables on the model’s predictions.

Figure 3 and Table S2 present the imputation errors in RMSE determined from the nine imputation ML models for the datasets with data removal rates of 1%, 5%, 10%, and 30%. Notably, algorithms such as Mice, Ice, GAIN, and Softimpute consistently showed relatively high errors, with RMSE values exceeding 0.15. The iterative imputation algorithms, such as Ice and Mice, are more appropriate for the MAR dataset and thus less suited for our MCAR dataset.³⁷ In contrast, Missforest, Hyperimpute, and EM exhibited robust performances, maintaining RMSE values below 0.16 even when dealing with the dataset with a 30% removal rate. The MCAR characteristic of the data in this work would allow EM to effectively offer statistically robust and practical imputation and result in a low RMSE value (Fig. 3 ).^38–40 In addition, tree-based Missforest and Hyperimpute algorithms seem to address the complex relation between the missing data and other parameters well, leading to low RMSE values.

Simultaneously, tree-based Missforest and Hyperimpute algorithms show compatibility with the complex interaction patterns observed in our missing data. However, when using the Missforest or Hyperimpute techniques for imputation, the filled-in data can significantly influence the model training process, especially for tree-based regression models, potentially leading to overfitting.⁴¹ In contrast, the EM algorithm takes an iterative approach with two key steps: the expectation step (E-step) and the maximization step (M-step).^21,42 These steps work within the parametric models to iteratively estimate model parameters, enabling the algorithm to maximize the likelihood estimates for imputation. Therefore, as a statistical and generative model, EM operates independently of various regression algorithms. Therefore, we selected EM as the imputation algorithm and all the missing data were filled using EM, as shown in Fig. 4. The interpolated datasets are found to closely resemble the distribution of the original data.

Within the hyper-parameter ranges presented in Table S1, various regression models, including RF, Extratrees, XGBoost, GBoost, CatBoost, and SVR, were optimized using the grid search method. The optimized models were then validated through the fivefold cross-validation, and the average R² scores and RMSE were determined as presented in Table S3. It is evident from the table that the overall R² performance is not exceptionally high. Considering the inherent complexity of semiconductor manufacturing processes involving numerous steps, the construction of highly reliable regression models may be a considerable challenge. Despite this challenge, we observe promising results, with the highest R² scores of 0.765 for V_th [Extratrees, Fig. 5(a)], 0.923 for I_off [CatBoost, Fig. 5(b)], and 0.790 for Tox [CatBoost, Fig. 5(c)]. The R² scores for Cov, I_on, NBTI, and tPD are lower than 0.6 (Table II and Fig. S1), indicating that these variables inadequately account for variance in the data,⁴³ making them unsuitable for SHAP analysis. The lower R² scores of these properties, including Cov, I_on, and tPD, can be attributed to their weaker correlation with the HKMG process parameters. These properties may exhibit a substantial sensitivity to other descriptors that are not used in this paper. We, therefore, focus our SHAP analysis exclusively on V_th, I_off, and Tox.

Figure 6(a) shows the SHAP mean absolute values for all the features of the prediction model for V_th, and Fig. 6(b) shows the SHAP individual value summary plot. It can be seen from the figures that HK N% exhibits the most dominant influence on V_th. In addition, both HK N% and IL N% exhibit a positive correlation with V_th. Injection of nitrogen into both the HK layer and the IL is essential for reducing pre-existing oxygen vacancies and regulating the dielectric constant. However, an excessive nitrogen content can lead to the generation of the interface states and positive fixed charges, increasing the number of interface traps (Nits), which subsequently leads to an increase in V_th.²⁰ The HK layer has a higher permittivity compared to the IL [permittivity: HfSiOx (HK): 15, SiON (IL): 4–8], hence, HK N% exerts a more significant influence on the formation of Nits compared to IL N%. Increasing L_ch reduces the V_th roll-off phenomenon, thus contributing to an increase in V_th. The positive relation between IL thk and V_th is a well-known behavior, as can be confirmed by the result in Fig. 6(b). L_offset is observed to have a positive impact on the effective channel length, which can be attributed to the occurrence of the lightly doped drain (LDD) overlap, thus, confirming the positive influence on V_th. Nevertheless, it is evident from the results shown in Fig. 6 that L_ch, IL Thk, and L_offset have a relatively minor impact on V_th.

Figure 7 shows the SHAP double-feature dependence plots for V_th. As shown in Fig. 7(a), for the normalized IL N% range of 0–0.7, the feature does not significantly contribute to the increase in V_th. However, beyond 0.7, an increase in IL N% has a noticeable contribution to the increase in V_th by closely interacting with HK N%. Similarly, it is shown in Fig. 7(b) that the SHAP values of L_ch on V_th vary depending on the L_ch range, and they appear to have a combined effect with L_offset to have a positive impact on V_th. Double-feature dependencies are less pronounced in other feature pairs, as shown in Fig. S2.

From the SHAP analysis on the regression model for I_off, we notice that the influence of HK N% is dominant, followed by that of L_offset, IL N%, IL Thk, and L_ch [Fig. 8(a)]. HK N%, L_offset, and IL N% are found to exhibit negative correlations with I_off [Fig. 8(b)]. As previously discussed, the increase in IL N% and HK N% leads to an increase in Nits, subsequently leading to an increase in V_th and a decrease in I_off. In addition, the influence of HK N% on V_th and I_off is more pronounced than that of IL N% because of higher permittivity of the HK layer in comparison with the IL. Figure. 8 shows that I_off exhibits a substantially negative correlation with L_offset, and a minor correlation with L_ch. An increase in IL Thk would theoretically lead to an increase in Tox, which, in turn, might contribute to a reduction in I_off.⁴⁴ Due to the presence of numerous factors influencing I_off beyond Tox, however, the contributions of IL Thk on I_off were found to be minor. Double-feature dependency is not pronounced for the regression model of I_off (Fig. S3).

The result of the SHAP analysis for Tox shown in Fig. 9(a) identifies the two most significant contributors of IL N% and IL Thk. As shown in Fig. 9(b), IL N% exhibits a negative correlation with Tox, while IL Thk appears to have a positive correlation with Tox. The directional influence of these factors is consistent with our prior observation: increase in IL N% results in an increase in Nits and a decrease in IL Thk, ultimately resulting in a reduction in Tox. It is expected that HK N% has a more significant impact on Tox compared to IL N%, considering that the HK layer is designed to be thicker than the IL. However, the analysis revealed that IL N% has a greater mean absolute SHAP value than HK N%. The double-feature dependency is not pronounced for the regression model of Tox (Fig. S4).

The results shown in Figs. 6–9 highlight the ability of SHAP analysis to provide individual factor influences, which have been challenging to characterize through traditional linear graph-based analyses or by black-box machine learning models.⁴⁵ The consistency between the SHAP results and domain knowledge underscores the effectiveness of EM imputation to fill in the missing data and the capability of XAI to analyze the complex relation between the process parameters and the electrical properties.⁴⁶ The achievement of desired electrical properties through process parameter control can be effectively fulfilled when considering the correlations among factors with multiple interdependencies, rather than relying solely on the limited number of primary causes.

In this paper, we utilized machine learning to explore the intricate relationships among the process parameters and electrical properties in the HKMG DRAM technology. Various imputation ML algorithms were tested, and the EM imputation adeptly addressed the challenge associated with missing data. The application of machine learning regression models unveiled non-linear and intricate relationships. The prediction models for V_th, I_off, and Tox consistently achieved high R² scores, allowing reliable SHAP analysis. The results of the XAI model found that the most significant process parameters for V_th, I_off, and Tox are all related to the concentration of nitrogen. The directional relations and double-feature dependencies have been analyzed for the features and the outputs in conjunction with the domain knowledge of the semiconductor industry. We believe that a similar strategy that combines the imputation and XAI algorithms can be used to unveil other complex relations among the process parameters and product characteristics, which may provide an opportunity for the rapid development of new DRAM products.

The supplementary material provides the hyper-parameters and additional results of the machine learning analysis used in this work.

This research was supported by Samsung Electronics Co., Ltd. (Grant No. IO201211-08077-01), the Korea Institute for Advancement of Technology (KIAT) (Grant No. P0008458), and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (Grant No. 2021R1A4A1029780).

The authors have no conflicts to disclose.

Namyong Kwon and JoonHo Bang contributed equally to this work.

Namyong Kwon: Investigation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). JoonHo Bang: Investigation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). Won Ju Sung: Data curation (equal). Jung Hoon Han: Data curation (equal). Dongin Lee: Writing – review & editing (equal). Ilwoo Jung: Writing – review & editing (equal). Se Guen Park: Writing – review & editing (equal). Hyodong Ban: Writing – review & editing (equal). Sangjoon Hwang: Writing – review & editing (equal). Won Yong Shin: Supervision (equal); Validation (equal). Jinhye Bae: Writing – review & editing (equal). Dongwoo Lee: Project administration (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.