Unraveling the Correlation between Raman and Photoluminescence in Monolayer MoS2 through Machine Learning Models

Unraveling the Correlation between Raman and Photoluminescence in Monolayer MoS2 through Machine Learning Models

Item Type Article

Authors Lu, Ang-Yu;Martins, Luiz Gustavo Pimenta;Shen, Pin-Chun;Chen, Zhantao;Park, Ji-Hoon;Xue, Mantian;Han, Jinchi;Mao,

Nannan;Chiu, Ming-Hui;Palacios, Tomás;Tung, Vincent;Kong, Jing Citation Lu, A., Martins, L. G. P., Shen, P., Chen, Z., Park, J., Xue, M.,

Han, J., Mao, N., Chiu, M., Palacios, T., Tung, V., & Kong, J. (2022). Unraveling the Correlation between Raman and Photoluminescence in Monolayer MoS 2 through Machine

Learning Models. Advanced Materials, 2202911. Portico. https://

doi.org/10.1002/adma.202202911 Eprint version Post-print

DOI

10.1002/adma.202202911

Publisher Wiley

Journal Advanced Materials

Rights Archived with thanks to Advanced Materials Download date 2024-01-25 20:26:02

Link to Item

http://hdl.handle.net/10754/679769

Unraveling the correlation between Raman and photoluminescence in monolayer MoS

2

through machine learning models

Ang-Yu Lu¹, Luiz Gustavo Pimenta Martins², Pin-Chun Shen¹, Zhantao Chen³, Ji-Hoon Park¹, Mantian Xue¹, Jinchi Han¹, Nannan Mao¹, Ming-Hui Chiu^1,4, Tomás Palacios¹, Vincent Tung^4,5, Jing Kong^1*

1 Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA

2 Physics Department, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

3 Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

4 Physical Science and Engineering Division, King Abdullah University of Science & Technology (KAUST), Thuwal, Saudi Arabia

5 Department of Chemical System and Engineering, University of Tokyo, Tokyo 113-8654, Japan

*Corresponding author: Prof. Jing Kong, jingkong@mit.edu

Supplementary Information

1. Methods

1.1 CVD-grown MoS2 1.2 Exfoliation of MoS2

1.3 Raman and PL characterization 1.4 Data Preprocessing

1.5 Programming Environment and Setup 1.6 Curve Fitting

1.7 Statistical Analysis

1.8 Densely Connected Convolutional Network (DenseNet)

1.9 Extreme gradient boosted (XGBoost) machine with SHapley Additive exPlanations (SHAP) 1.10 Support Vector Machine (SVM)

1.11 Gaussian Mixture Model (GMM) 2. Discussion

2.1 The correlation between exciton and trion in MoS2 monolayers 2.2 Effects of defective structures in MoS2 monolayers

2.3 The Regional feature in XGBoost model and SHAP explainer Supplementary Tables

Supplementary Figures Reference

Supplementary Information 1. Methods

1.1 CVD-grown MoS

2

CVD-grown MoS2 flakes are deposited on 300 nm SiO2/Si substrates using molybdenum trioxide (MoO3) with 20 mg and sulfur (S) with 20 mg powders as the precursors. Perylene-3,4,9,10-tetracarboxylic acid tetrapotassium (PTAS) solutions were spin-coated onto clean SiO2/Si substrates, serving as the seed promoters. Before the growth, the CVD system was purged using an Argon (Ar) flow of 1000 sccm for 5 mins for removing oxygen (O2) and water residual gas. During the growth, the furnace was heated up to the temperature of 625 °C with a ramping rate of 30 °C min^-1. The sulfur powders are kept at 180 °C in the upstream tube. The MoS2 monolayers are grown at 625 °C for 3 mins at atmospheric pressure with an Ar flow of 20 sccm and an O2 flow of 0-1 sccm as the carrier gas and reactant gas, respectively. After the growth procedure, the furnace was naturally cooled down to room temperature with an Ar flow of 1000 sccm, preventing further unintentional reactions.

1.2 Exfoliation of MoS

2

The MoS2 crystals were obtained from SPI Supplies and 2D semiconductors, and mechanically exfoliated and deposited onto a 300 nm SiO2/Si substrate. The SPI crystals were naturally grown, while the 2D semiconductor crystals were synthetic. The exfoliated flakes were termed natural and synthetic, accordingly.

1.3 Raman and PL characterization

Raman and PL characterizations were carried out by Horiba HR800 with a fixed laser wavelength of 532 nm (2.33 eV). The laser power was ~1 mW with an acquisition time of 0.5 sec due to the measuring time constraint for each spectral map. The measuring time is about ~30 mins for taking a spectral map with 1600 pixels (40*40 spatial dimensions) in our measurement setup. Therefore, it spent >1.5 hours measuring a MoS2 crystal including the system calibrations. Figure S4 shows that lower laser power energy requires longer accumulation time. For example, if we require the SNR of 105 (the black dash line), the accumulation times are 0.5 s, ~7 s, ~80 s for the laser power of 1 mW, 100 μW, and 10 μW, respectively. The formula of signal-to-noise ratio is defined below.

𝑆 𝑁=

𝑆𝐴1′−𝑆_{𝑏𝑎𝑐𝑘𝑔𝑟𝑜𝑢𝑛𝑑}

√𝑆𝑏𝑎𝑐𝑘𝑔𝑟𝑜𝑢𝑛𝑑 (S1) Meanwhile, we compared the spectral profiles with the different laser power of 1 mW and 10 μW for Raman and PL spectra in Fig. S16. As can be seen, the spectral profiles show no difference in Raman and PL spectra for the two laser powers. Therefore, we used the laser power of 1 mW for the measurements with the acceptable SNR and the measuring time. Furthermore, we compared the PL fitting results with and without B exciton in Fig. S17, showing that the B exciton is neglectable in the PL fitting process. Therefore, we focus on the trion/exciton peaks in PL spectra. The 100X objective lens provides a spot of 1um diameter.

The Raman spectra were normalized by the intensity of Si peak and calibrated by the Si Raman frequency at 520.6 cm^-1. The spectral gratings of 1800 and 300 gr/mm are used for Raman spectra and PL measurements, respectively. For Raman spectral and PL maps, the spatial size depends on the domain size

1.4 Data Preprocessing

The Raman and PL spectral maps were first sent to the curve fitting procedure, described in the curve fitting section. Each characteristic feature is fitted by a Voigt profile, obtaining three parameters: frequencies, FWHM, and intensity. All the characteristic features are normalized by the Raman intensity at 520.6 cm^-1 from the Si substrates. According to the normalized 𝐼_𝐴

1′ of MoS2 monolayers are smaller than 0.5, we applied a hard thresholding to the regions of multilayer MoS2. (Fig. S2) The outliers in the maps are shown in Fig.

S1c as single points which are not connected to MoS2 domains. Therefore, we used a binary opening matrix, as shown below, to remove the outliers.

1.5 Programming Environment and Setup

All machine learning models were implemented using Python in Google Colaboratory. The datasets were divided into proportions of 0.8 and 0.2 for training and validation datasets by the scikit-learn library (sklearn)^[40]. All the results were visualized using Matplotlib, a Python data visualization library, and Matlab.

1.6 Curve Fitting

The curve fitting procedure is implemented in Python. The spectral backgrounds were subtracted using the BaselineRemoval package with the ZhangFit method^[41]. The Voigt profile function was imported from the Scipy library, including four parameters: Raman feature frequency, 𝜎 (the standard deviation of Normal distribution part), 𝛾 (the half-width at half-maximum of the Cauchy distribution part), and Raman feature intensity. The optimized algorithm used the least-squares function from the Scipy library. The FWHM is calculated through the Eq. S2-S4 below.

𝑓_𝐺=2𝜎√2𝑙𝑛2 (S2)

𝑓_𝐿=2𝛾 (S3)

𝛤 ≈0.5346𝑓_𝐿+ √0.2166𝑓_𝐿²+ 𝑓_𝐺² (S4)

1.7 Statistical Analysis

Pre-processing of data: All the spectra are applied to the curve fitting with Voigt profiles. The outliers are evaluated by the intensity ratio of 𝐴₁^′ mode and the Si peak from the substrates.

Sample size: The total number of 7023 points is used for the XGBoost and the SVM models. For the DenseNet model, we included all the pixels with and without Raman/PL signals and applied a 90-degree rotation as the dataset; the total number of patched maps in the dataset is 35596.

Softwares: We used matlab and Python with the packages of Pytorch, Scipy, and Numpy for the statistical analysis.

1.8 Densely Connected Convolutional Network (DenseNet)

The architecture of the DenseNet was modified with two dense blocks based on the original design^[16]. Before entering the first dense block, a convolution with 12 output channels was applied to the

input image. Each dense block consists of batch normalizations, relu layers, convolutional layers with 1x1 and 3x3 kernels, and a dropout of 0.1. In between two dense blocks, the transition layer consists of a batch normalization, a relu layer, a convolutional layer with 1x1 kernel size, followed by an average pooling layer. After the end of the last dense block, an adaptive average pooling is performed with three output channels, and then a linear layer is attached with three final outputs. The DenseNet was deployed using PyTorch. The relative absolute error (RAE) used for evaluating DenseNet is described in Eq. S5, where 𝑦_𝑖^′ is the predictions from DenseNet, and 𝑦_𝑖 is experimental value from the PL measurement.

𝑅𝐴𝐸 = ^[∑

𝑛𝑖=1 (𝑦_𝑖^′−𝑦_𝑖)²]

1 2

[∑^𝑛_𝑖=1 𝑦_𝑖²]

1 2

(S5)

1.9 Extreme gradient boosted (XGBoost) machine with SHapley Additive exPlanations (SHAP)

Extreme gradient boosting (XGBoost) is an ensemble model constructed from decision trees^[20] for supervised learning problems, which has been extensively used in many machine learning tasks. The hyperparameters of the XGBoost regressor were automatically optimized by Bayesian Optimization^[42] with a number of gradient boosted trees of 700, a learning rate of 0.05, and a maximum depth of a tree of 15.

Root mean square log error (RMSLE) was used as the evaluation metric for reducing errors generated by outliers. SHapley Additive exPlanations (SHAP)^[21] was implemented as the tree explainer to reveal the correlations between Raman spectra and PL in the trained XGBoost model and visualize the results.

1.10 Support Vector Machine (SVM)

Support vector machines (SVM) possess many advantages. For example, SVM generalizes well on a sparse dataset and performs robust against overfitting^[43]. The Support vector regressor, a type of SVM for regression problems, was deployed using the Scikit-learn (sklearn) library^[44]. Before sending the input data into the SVM, all the features were standardized by removing their means and scaling to unit variance. The hyperparameters of the support vector regressor were automatically optimized by Bayesian Optimization^[42]

with a regularization parameter (C) of 0.1, an epsilon of 0.05, a gamma of 0.2, and the tolerance of 1e-4.

Radial basis function (RBF) was used as the kernel function due to its similarity to the Gaussian distribution, which can be expressed as Eq. S6

𝐾(𝑥, 𝑥′) = 𝑒𝑥𝑝 (−^{||𝑥−𝑥′||}_2𝜎2 ²) (S6) where 𝜎 is a free parameter.

1.11 Gaussian Mixture Model (GMM)

Gaussian mixture model (GMM) is a probabilistic model which can be used to evaluate the density estimation for each sample. GMM contains multiple distribution functions to describe the probability density distribution characteristics, which is more accurate than a single probability distribution. The GMM was deployed using the sklearn library with three components and the full covariance metrics. The trained GMM outputs the negative log probability for sampling points in Fig. S12d.

2. Discussion

2.1 The correlation between exciton and trion in MoS2 monolayers

Although our PL data are dominated by trions, the predictions from the ML models can be modified for the exciton-dominated PL signals. The energy difference between the exciton and trion for MoS2 monolayers is the binding energy for the additional charge, which can be described by the relation of E_exciton = E_trion + binding energy. Therefore, we analyze the effects of strain, doping, and substrate screening on the binding energy of the MoS2 monolayer. (1) Strain effects: D. Lloyd et al.^[25] demonstrated that the energy difference between exciton and trion is fixed within the range of the strain level of 2.5%. (2) Doping effects: K. F. Mak et al.^[45] showed that the binding energy is a linear relation to the fermi level of MoS2

monolayers, showing a slope of 1.2 and an intercept of 18 meV. (3) Substrate screening: M. Drüppel et al.^[46] demonstrated that the exciton transition energy of MoS2 is reduced by increasing the dielectric constant of target substrates. The exciton transition energies of MoS2 are 2.13, 2.12, 2.11, and 2.08 on dielectric constant substrates of vacuum (𝜀_𝑟=1), SiO2 (𝜀_𝑟=3.9), hexagonal boron nitride (𝜀_𝑟=4.10), and Au (𝜀_𝑟=∞), respectively. Meanwhile, the trion transition energies of MoS2 are 2.08, 2.08, 2.07, and 2.05 in a vacuum and on SiO2, h-BN, and Au substrates. The results reveal that exciton and trion energies redshift 50 and 30 meV from vacuum to Au substrate, respectively, indicating that exciton is affected more by substrate screening than trion. Notably, the redshifts of exciton/trion energies are only 20/10 meV on insulating substrates (vacuum to hBN) compared to metal substrates (vacuum to Au). Therefore, our models with the modified values can still predict the exciton-dominated PL.

2.2 Effects of defective structures in MoS2 monolayers

Other defects, such as edges, grain boundaries, and substitutional dopants, introduce strain by reconstructing lattice structures and adding electrostatic charges by unbalanced binding configurations.

Figure 1a depicts a mechanism diagram for MoS2 monolayer with external perturbations. First, for pure strain perturbations, the lattice of MoS2 is stretched or compressed, which alters phonon vibrations and energy band structures. The changes in phonon vibrations can be probed by Raman spectroscopy, and the bandgap transition can be observed by photoluminescence. Furthermore, for pure electrical doping via additional charges, the lattice structure and the band structure of MoS2 largely remain unchanged, but its Fermi level shifts with the number of additional free carriers. Other defects, such as edges, grain boundaries, and substitutional dopants, introduce strain and add charges by reconstructing lattice structures with unbalanced binding configuration. For example, sulfur vacancies (Vs) in MoS2 monolayers introduce lattice compression and electrostatic doping. S. Wang et al.^[47] revealed that Vs along the zigzag direction results in lattice compression and bandgap reduction. Furthermore, J. Wang et al.^[48] calculated that the lower concentration of the Vs yields p-doping characteristics, whereas the higher concentration of Vs yields n- doping characteristics. Similarly, dislocations can be considered as a line of vacancies, and oxygen substitutional dopants can be considered as oxygen atoms in vacancy positions. These factors reconstruct the MoS2 lattice and provide extra charges on MoS2 monolayers, leading to strain and doping effects, respectively. Also, we added various defect-based vectors on MoS2 Raman frequencies from the literature in Fig. S13, including Mn⁺ ion-bombardment^[49] (blue line), hydrogen-plasma^[50] (cyan line), argon- plasma^[51] (green line), and electron-radiation^[52] (purple line) treated MoS2.

2.3 The Regional feature in XGBoost model and SHAP explainer

The DenseNet model used patched Raman maps containing the regional information from neighboring pixels, showing higher accuracy on PL predictions than the XGBoost model without the regional information. Hence, we added a regional feature to the XGBoost model and interpreted it by SHAP values based on the following approach. First, we converted the 𝐼_𝐴

1′ maps with 5-by-5 pixels into binary matrices (0 and 1). Afterward, we element-wise multiply the binary matrices with a Gaussian blur matrix (5-by-5) and then sum them up into vectors as the regional feature. For an example in Eq. S7,

(S7)

The regional feature slightly improves the coefficient of determination (R²) of the XGBoost model, as shown in Fig. S15b. The SHAP values of XGBoost with the additional regional feature are shown in Fig.

S14. The local explanations of SHAP values display that the higher regional feature leads to higher PL energy, narrower PL FWHM, and stronger PL intensity. This result indicates that the edges of MoS2

monolayers typically exhibit lower crystallinities than the interior regions. The global importance of the regional feature is lower than 𝐴₁^′ and 𝐸^′ features but higher than the 2LA feature. To explain this result, we projected the regional features on the Raman frequencies plot in Fig. S15a. Although the regional feature provides the edges/interior information, the quality of MoS2 monolayers is dominated by their crystallinity and defect types.

Supplementary Tables

Strain

Strain Type Sample Preparation

E' Intrinsic

A1' Intrinsic

E' shift rate (cm^-1/%)

A' shift rate (cm-1/%)

A exciton (meV/%strain)

PL Energy/

Laser Energy uniaxial

tensile^[53]

CVD

MoS2/suspended 386 405.5 -2.1 -0.75 -38 1.89 eV

514.5nm, 20µW uniaxial

tensile^[22] Exfoliated 385.3(Exp) 376.1(DFPT)

402.4(Exp) 397.83(DFPT)

-2.1(Exp) -2.22(DFPT)

-0.4(Exp)

-0.55(DFPT) 514.5 nm, <1 mW

uniaxial

tensile^[26] Exfoliated 384 403 -4.5 0 -45 (Exp)

-59 (GW0-BSE)

1.82 eV 532 nm, ~100 uW uniaxial

tensile^[54] Exfoliated 384 403 -2.5 0 532 nm

uniaxial

tensile^[55] Exfoliated -70 ~1.9 eV

532 nm, <50 uW uniaxial

tensile^[56] Exfoliated -48 476 nm

uniaxial

strain^[57] DFT -50.86

biaxial tensile^[34]

CVD MoS2 /

SiO2 nanocone 385.6 404.9 -4.48 -1.02 -110 (direct)

-240 (indirect)

1.83 eV 532 nm, <1 mW biaxial

tensile^[25]

CVD MoS2 /

suspende pressure 385 405 -5.2 -1.7 -99 1.86, 1.89 eV

532 nm, <10 uW biaxial

tensile^[58]

Exfoliated / temperatured

substrate

-105 532 nm, 10uW

biaxial tensile^[59]

Exfoliated / temperatured

substrate

-51 (Exp)

-110 (Theory) ~1.9 eV

Table 1. Summary of Raman frequencies and PL of monolayer MoS2 with strain effects.

Doping

Strain Type Sample Preparation

E^’ Intrinsic

A1’

Intrinsic

nE (cm^-1/10¹³ cm^-2)

nA (cm^-1/10¹³ cm^-2)

A exciton (meV/10¹³ cm^-2)

PL Energy/

Laser Energy

p-n doping^[24] Exfoliated 386 405 -0.27

-0.15 (-0.5V)

-2.5 -1.9 (-0.5V)

-105 (n doping) -24 (p doping)

~1.9 eV 514 nm, 0.5mW

p-n doping^[23] Exfoliated -0.03 -0.6 514.5 nm

n doping^[60] Exfoliated -0.33 (estimated) -2.22 (estimated)

p doping^[61] Exfoliated 385 404 0 1.85 eV

466 nm, <20 uW

p doping^[3] Exfoliated 0 0 0

Table 2. Summary of Raman frequencies and PL of monolayer MoS2 with doping effects.

Supplementary Figures

Figure S1. optical microscopy images of CVD-grown MoS2 flakes with triangle, random, and hexagonal shapes.

Figure S2. Data preprocessing on a synthetic MoS2 flake. a, the optical microscopic image of the synthetic MoS2 showing multilayer and monolayer regions. b, the intensity of 𝐴^′₁ map normalized by the Si intensity (~520.6 cm^-1) from the substrate. c, the signals of multilayer MoS2 were screened by the normalized intensity above 0.5 and the outliers were removed by a binary opening matrix.

Figure S3. The Voigt profiles with a fixed area of 1 for various FWHM of 1.15 (red curve), 1.64 (Greeb), and 2.13 (Blue).

Figure S4. Scattered plots of CVD-grown and exfoliated MoS2 monolayers on Raman features. a, the plot of 𝜔_𝐴

1′ versus 𝜔_𝐸′ for various types of MoS2. b, the plot of 𝛤_𝐴

1′ versus 𝛤_𝐸′ shows a linear correlation with a slope of 0.72 and an intercept of 2.7. c, 𝐼_𝐴

1′ versus 𝐼_𝐸^′ shows a linear correlation with a slope of 1.4 and an intercept of 0.

Figure S5. The correlation between FWHM and intensity in a Voigt function for a fixed area of 0.1 without (blue, Eq. 1) and with (red, Eq. 2) the background.

Figure S6. Signal-to-noise ratios (SNR) as the function of acquisition time with different laser power:

Figure S7. The data preparation for a hexagonal-shape MoS2 for the DenseNet model, including an optical microscopic image, 8 Raman feature maps, and 3 PL feature maps.

Figure S8. The schematic illustration for the DenseNet dataset. The cropped Raman spectral images with 8 channels are used as input data and the PL signal of the central pixel is used as the output.

Figure S9. PL mapping predictions of e energy, f FWHM, g intensity for CVD-grown MoS2 with random shape. Left: the measured PL maps as the ground truth for the DenseNet model. Middle: the predicted results by the trained DenseNet with 5-by-5 patch inputs. Right: the relative error between measured and predicted PL maps.

Figure S10. The relative errors and the coefficient of determination of a PL energy, b PL FWHM, and c PL intensity for validation dataset predicted by the DenseNet model.

Figure S11. The scatter plot of various MoS2 monolayers on Raman frequencies of 𝜔_𝐴

1′ versus 𝜔_𝐸′.

Figure S12. Scattered plots of CVD-grown and exfoliated MoS2 monolayers on Raman features of 𝜔_𝐴

1′

versus 𝜔_𝐸′. The coded colors indicate a, PL energy, b, PL FWHM, and c, PL intensity. d, the density probability estimated by a GMM model.

Figure S13. Schematic representation of external-perturbation and defect-structure vectors for (𝜔_𝐴

1′ , 𝜔_𝐸^′) coordinates. The orange circle is denoted as the intrinsic point, defined as the charge-neutral and unstrained state. The red and black solid lines correspond to strain and doping, respectively. The blue, cyan, green, and purple solid lines correspond to Mn⁺ bombardment^[49], hydrogen plasma^[50], argon plasma^[51], and electron radiation^[52] treated MoS2, respectively.

Figure S14. Correlation analysis for Raman and PL by XGBoost/SHAP values with an additional regional feature. a PL energy, b PL FWHM, and c PL intensity results are interpreted by the trained XGBoost model by Shapley additive explanations (SHAP). The regional feature is discussed in SI 2.3.

Figure S15. Raman features of MoS2 monolayers with an additional Regional feature. a A scatter plot of MoS2 monolayers on Raman features of 𝜔_𝐴

1′ versus 𝜔_𝐸′ with the coded color of the values of the regional feature. b A bar chart of coefficient of determination (R²) for ML models on PL features.

Figure S16. a, Raman and b, PL spectra with the laser power of 10 𝜇W and 1 mW.

Figure S17. Fitting results for a PL spectrum of triangle MoS2 a, without and b, with B exciton fitting. I, E, and W correspond to the intensity, energy, and FWHM of PL.

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