Dielectric Screening of Excitons and Trions in Single-Layer MoS2
Supporting Information
Dielectric Screening of Excitons and Trions in Single-Layer MoS2 Yuxuan Lin†, Xi Ling†, Lili Yu†, Shengxi Huang†, Allen L. Hsu†, Yi-Hsien Lee¶, Jing Kong†, Mildred S. Dresselhaus*,†,§, Tomás Palacios*,† †
Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA ¶
Material Sciences and Engineering, National Tsing-Hua University, Hsinchu, 30013, Taiwan §
Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
This file includes: 1. Methods 2. PL in air before and after each solvent-encapsulated measurement 3. PL spectra fitting 4. Basic properties of the organic solvents 5. More results of the solvent-dependent Photoluminescence and Raman spectroscopy results 6. Photoluminescence and Raman spectroscopy results of single-layer MoS2 in air vs. in vacuum 7. Modeling 8. Valence band splitting as a function of the effective dielectric constant 9. Raman and PL as a function of the high-frequency dielectric constant
1. Methods A MoS2 monolayer was synthesized using the seeding promoter assisted CVD method[S1]. Briefly, molybdenum trioxide (MoO3) and sulfur (S) were used as precursors and were loaded in two separated crucibles. Under the growth temperature (650 ℃), MoO3 and S react and form MoS2. A 300 nm SiO2/Si substrate, where the
seeding promoter perylene-3,4,9,10-tetracarboxylic acid tetrapotassium salt (PTAS) was loaded, was placed face-down on the crucible together with MoO3. The MoS2 thus formed was nucleated with the assistance of PTAS, and monolayer MoS2 films were thus obtained on the substrate. To characterize the samples, AFM (Dimension 3100, Veeco Instruments Inc.) and optical microscope (Axio Imager, Carl Zeiss) were used to characterize the morphology of the MoS2 samples. A confocal Raman spectroscopy system (Horiba Jobin-Yvon HR800) was used to carry out the solvent-encapsulated Raman and PL measurements. The wavelength of the excitation laser is 532.8 nm. The laser power on the sample was about 1 mW. A 100X objective with the numerical aperture (NA) of 0.6 and the working distance (WD) of 7.6 mm was used to focus the laser beam. For each spectroscopy measurement, the MoS2/SiO2/Si sample was loaded into a quartz cell filled with one of the organic solvents. Multiple spectroscopy measurements were taken as the laser was focused on different locations throughout the continuous CVD MoS2 film for each solvent environment. In between two solvent-encapsulated spectroscopy runs, the sample and the quartz cell were rinsed with acetone and isopropyl alcohol to prevent residues from the previous solvents. Several microscopy measurements were taken with the sample exposed in air after the rinsing process to make sure the solvents do not change
the PL. The PL spectra were fitted with three Lorentzian functions (details are shown later). Because of the reflection and absorption differences induced by the solvents and the quartz cell, the intensities of the PL cannot be compared with each other directly. Therefore, we normalized the PL spectra by the A1g intensities that were taken in the same spectroscopy run and the same sample.
2. PL in air before and after each solvent-encapsulated measurement
Figure S1 Time-sequence PL peak energies. The black, red and green dots are the peak positions of the A- trion, and the A and B excitons, respectively. The gray regions are PL measurements of single-layer MoS2 in air, and the white regions are PL measurements in specific solvents. The dotted lines indicate the average peak positions in air. The peak energies in the grey regions do not change much, which means the sample is not contaminated by previous solvents.
3. PL spectra fitting
Figure S2 PL spectra of single-layer MoS2 in 10 different solvents fitted with 3 Lorentzian peaks.
Figure S2 (cont.) PL spectra of single-layer MoS2 in 10 different solvents fitted with 3 Lorentzian peaks. The PL spectra of single-layer MoS2 in different solvents are fitted with three Lorentzian functions, which are shown in Figure S2. In order to justify the reliability of the fitting, we compared the fitting with 2, 3 and 4 Lorentzian functions. Figure S3 and Figure S4 show two typical spectra when MoS2 is immersed in Anisole and in Methonal, respectively. The 2-peak fitting cannot resemble the asymmetry features of the major PL peaks, whereas 3-peak fitting seems to be much better. The 4-peak fitting, however, turns out to be rather random: the fitting results do not converge very well, and may lead to
different fitting values depending on different starting points of the parameters. Figure S5 shows the relative errors of the fitted peak intensities, and the mean squared errors (MSEs) of the fitting results, from which we can obviously see the advantage of 3-peak fitting.
Figure S3 PL spectra (grey dots) of MoS2 measured in anisole and fitted with (a) 2 Lorentzian functions, (b) 3 Lorentzian functions, and (c) 4 Lorentzian functions. The green curves are individual Lorentzian functions, and the red curve is the summation of all the Lorentzian functions.
Figure S4 PL spectra (grey dots) of MoS2 measured in methanol and fitted with (a) 2 Lorentzian functions, (b) 3 Lorentzian functions, and (c) 4 Lorentzian functions. The green curves are individual Lorentzian functions, and the red curve is the summation of all the Lorentzian functions.
Figure S5 (a) Relative errors of the peak intensities from the fittings with two (red), three (blue) and four (yellow) Lorentzian functions. (b) Mean squared errors (MSEs) of the fittings with two (red), three (blue) and four (yellow) Lorentzian functions.
4. Basic properties of the organic solvents [S2] Table S1 Basic Physical Properties of the Organic Solvents Used in the Experiment
Air/Vacuum --
Static Dielectric Constant 1
Refractive Index (Visible range) 1
High-freq. Relative Density Boiling Point Melting Point Dielectric (°C) Polarity (g/mL) (°C) Constant 1 -----
Hexanes
1.89
1.375
1.89
0.009
0.655
69
-95
Benzene
2.28
1.501
2.25
0.111
0.879
80.1
5.5
Toluene
2.38
1.497
2.24
0.099
0.867
110.6
-93
Anisole
4.33
1.516
2.30
0.198
0.996
153.7
-37.5
13
1.54
2.37
0.608
1.042
205.4
-15.3
18.3
1.378
1.90
0.546
0.785
82.4
-88.5
2-Butanone
18.5
1.379
1.90
0.506
0.808
99.5
-114.7
Acetone
20.7
1.359
1.85
0.355
0.786
56.2
-94.3
Ethanol Methanol
24.6 32.6
1.361 1.328
1.85 1.76
0.654 0.762
0.789 0.791
78.5 64.6
-114.1 -98
Solvent Name
Benzyl Alcohol Isopropyl Alcohol
Chemical Formula
Figure S6 Raman spectra of the organic solvents listed in Table S1.
5. More results of the solvent-dependent PL and Raman spectroscopy
Figure S7 Full width at half maximum (FWHM) of PL peaks as a function of the solvent dielectric constant. The dots are the mean value for all the solvents used, weighted according to their errors here. The same approach was used for the average values given for other parameters in the SI.
Figure S8 FWHM of the (a) E2g1 and (b) A1g Raman peaks of single-layer MoS2 as a function of the static dielectric constant of the solvents.
Figure S9 (a) Peak difference and (b) intensity ratio of the two Raman modes of singlelayer MoS2 as a function of the static dielectric constant of the solvents.
6. Photoluminescence and Raman spectroscopy results of single-layer MoS2 in air vs. in vacuum
Figure S10 PL and (inset) Raman spectra of single-layer MoS2 in air (black) and in vacuum (red).
7. Modeling A. Coulomb potential distribution Consider the dielectric-sandwiched structure with the relative dielectric constants of the top, bottom and the middle layer denoted by κ1, κ2 and κs, respectively, as shown in Figure S11. The thickness of the middle layer is denoted by D. The origin of the x-z coordinate in Figure S8 (a) is located in the center of the middle layer. Assuming there is one positive charge (+q) and one negative charge (-q) fixed at (L/2,0) and (-L/2,0), respectively, infinite arrays of image charges will be generated by the mirror surfaces of the interfaces between different materials, as shown in Figure S8 (b).
Figure S11 (a) Schematic the coordinates and related parameters of the Coulomb potential problem. (b) Schematic of the generation of the image charges.
If the image charges and positions are denoted by {qX,n} and {(xX,n, zX,n)}, where X replaced by T+ (images charges in the top dielectrics originated from the positive charge), T- (images charges in the top dielectrics originated from the negative charge), B+ (image charges in the bottom dielectrics originated from the positive charge) or B- (image charges in the bottom dielectrics originated from the negative charge), and n=1,2,3,..., The net Coulomb potential originated from the two charges +q, -q at a certain point (x, z) is given by V ( x, z ) =
1 + q0 − q0 + + 2 2 πε 4πε 0κ s ( x − L / 2) 2 + z 2 4 ( x + L / 2) + z 0κ s 1
∑ X ,n
qX ,n ( x − x X ,n )2 + ( z − z X ,n )2
where ε0 is the vacuum permittivity, κs is the relative dielectric constant of the middle layer, and ±q0 are the effective charges located at (±L/2,0). The image charges and positions are summarized below. i) When |z|
Dielectric Screening of Excitons and Trions in Single-Layer MoS2 Yuxuan Lin†, Xi Ling†, Lili Yu†, Shengxi Huang†, Allen L. Hsu†, Yi-Hsien Lee¶, Jing Kong†, Mildred S. Dresselhaus*,†,§, Tomás Palacios*,† †
Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA ¶
Material Sciences and Engineering, National Tsing-Hua University, Hsinchu, 30013, Taiwan §
Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
This file includes: 1. Methods 2. PL in air before and after each solvent-encapsulated measurement 3. PL spectra fitting 4. Basic properties of the organic solvents 5. More results of the solvent-dependent Photoluminescence and Raman spectroscopy results 6. Photoluminescence and Raman spectroscopy results of single-layer MoS2 in air vs. in vacuum 7. Modeling 8. Valence band splitting as a function of the effective dielectric constant 9. Raman and PL as a function of the high-frequency dielectric constant
1. Methods A MoS2 monolayer was synthesized using the seeding promoter assisted CVD method[S1]. Briefly, molybdenum trioxide (MoO3) and sulfur (S) were used as precursors and were loaded in two separated crucibles. Under the growth temperature (650 ℃), MoO3 and S react and form MoS2. A 300 nm SiO2/Si substrate, where the
seeding promoter perylene-3,4,9,10-tetracarboxylic acid tetrapotassium salt (PTAS) was loaded, was placed face-down on the crucible together with MoO3. The MoS2 thus formed was nucleated with the assistance of PTAS, and monolayer MoS2 films were thus obtained on the substrate. To characterize the samples, AFM (Dimension 3100, Veeco Instruments Inc.) and optical microscope (Axio Imager, Carl Zeiss) were used to characterize the morphology of the MoS2 samples. A confocal Raman spectroscopy system (Horiba Jobin-Yvon HR800) was used to carry out the solvent-encapsulated Raman and PL measurements. The wavelength of the excitation laser is 532.8 nm. The laser power on the sample was about 1 mW. A 100X objective with the numerical aperture (NA) of 0.6 and the working distance (WD) of 7.6 mm was used to focus the laser beam. For each spectroscopy measurement, the MoS2/SiO2/Si sample was loaded into a quartz cell filled with one of the organic solvents. Multiple spectroscopy measurements were taken as the laser was focused on different locations throughout the continuous CVD MoS2 film for each solvent environment. In between two solvent-encapsulated spectroscopy runs, the sample and the quartz cell were rinsed with acetone and isopropyl alcohol to prevent residues from the previous solvents. Several microscopy measurements were taken with the sample exposed in air after the rinsing process to make sure the solvents do not change
the PL. The PL spectra were fitted with three Lorentzian functions (details are shown later). Because of the reflection and absorption differences induced by the solvents and the quartz cell, the intensities of the PL cannot be compared with each other directly. Therefore, we normalized the PL spectra by the A1g intensities that were taken in the same spectroscopy run and the same sample.
2. PL in air before and after each solvent-encapsulated measurement
Figure S1 Time-sequence PL peak energies. The black, red and green dots are the peak positions of the A- trion, and the A and B excitons, respectively. The gray regions are PL measurements of single-layer MoS2 in air, and the white regions are PL measurements in specific solvents. The dotted lines indicate the average peak positions in air. The peak energies in the grey regions do not change much, which means the sample is not contaminated by previous solvents.
3. PL spectra fitting
Figure S2 PL spectra of single-layer MoS2 in 10 different solvents fitted with 3 Lorentzian peaks.
Figure S2 (cont.) PL spectra of single-layer MoS2 in 10 different solvents fitted with 3 Lorentzian peaks. The PL spectra of single-layer MoS2 in different solvents are fitted with three Lorentzian functions, which are shown in Figure S2. In order to justify the reliability of the fitting, we compared the fitting with 2, 3 and 4 Lorentzian functions. Figure S3 and Figure S4 show two typical spectra when MoS2 is immersed in Anisole and in Methonal, respectively. The 2-peak fitting cannot resemble the asymmetry features of the major PL peaks, whereas 3-peak fitting seems to be much better. The 4-peak fitting, however, turns out to be rather random: the fitting results do not converge very well, and may lead to
different fitting values depending on different starting points of the parameters. Figure S5 shows the relative errors of the fitted peak intensities, and the mean squared errors (MSEs) of the fitting results, from which we can obviously see the advantage of 3-peak fitting.
Figure S3 PL spectra (grey dots) of MoS2 measured in anisole and fitted with (a) 2 Lorentzian functions, (b) 3 Lorentzian functions, and (c) 4 Lorentzian functions. The green curves are individual Lorentzian functions, and the red curve is the summation of all the Lorentzian functions.
Figure S4 PL spectra (grey dots) of MoS2 measured in methanol and fitted with (a) 2 Lorentzian functions, (b) 3 Lorentzian functions, and (c) 4 Lorentzian functions. The green curves are individual Lorentzian functions, and the red curve is the summation of all the Lorentzian functions.
Figure S5 (a) Relative errors of the peak intensities from the fittings with two (red), three (blue) and four (yellow) Lorentzian functions. (b) Mean squared errors (MSEs) of the fittings with two (red), three (blue) and four (yellow) Lorentzian functions.
4. Basic properties of the organic solvents [S2] Table S1 Basic Physical Properties of the Organic Solvents Used in the Experiment
Air/Vacuum --
Static Dielectric Constant 1
Refractive Index (Visible range) 1
High-freq. Relative Density Boiling Point Melting Point Dielectric (°C) Polarity (g/mL) (°C) Constant 1 -----
Hexanes
1.89
1.375
1.89
0.009
0.655
69
-95
Benzene
2.28
1.501
2.25
0.111
0.879
80.1
5.5
Toluene
2.38
1.497
2.24
0.099
0.867
110.6
-93
Anisole
4.33
1.516
2.30
0.198
0.996
153.7
-37.5
13
1.54
2.37
0.608
1.042
205.4
-15.3
18.3
1.378
1.90
0.546
0.785
82.4
-88.5
2-Butanone
18.5
1.379
1.90
0.506
0.808
99.5
-114.7
Acetone
20.7
1.359
1.85
0.355
0.786
56.2
-94.3
Ethanol Methanol
24.6 32.6
1.361 1.328
1.85 1.76
0.654 0.762
0.789 0.791
78.5 64.6
-114.1 -98
Solvent Name
Benzyl Alcohol Isopropyl Alcohol
Chemical Formula
Figure S6 Raman spectra of the organic solvents listed in Table S1.
5. More results of the solvent-dependent PL and Raman spectroscopy
Figure S7 Full width at half maximum (FWHM) of PL peaks as a function of the solvent dielectric constant. The dots are the mean value for all the solvents used, weighted according to their errors here. The same approach was used for the average values given for other parameters in the SI.
Figure S8 FWHM of the (a) E2g1 and (b) A1g Raman peaks of single-layer MoS2 as a function of the static dielectric constant of the solvents.
Figure S9 (a) Peak difference and (b) intensity ratio of the two Raman modes of singlelayer MoS2 as a function of the static dielectric constant of the solvents.
6. Photoluminescence and Raman spectroscopy results of single-layer MoS2 in air vs. in vacuum
Figure S10 PL and (inset) Raman spectra of single-layer MoS2 in air (black) and in vacuum (red).
7. Modeling A. Coulomb potential distribution Consider the dielectric-sandwiched structure with the relative dielectric constants of the top, bottom and the middle layer denoted by κ1, κ2 and κs, respectively, as shown in Figure S11. The thickness of the middle layer is denoted by D. The origin of the x-z coordinate in Figure S8 (a) is located in the center of the middle layer. Assuming there is one positive charge (+q) and one negative charge (-q) fixed at (L/2,0) and (-L/2,0), respectively, infinite arrays of image charges will be generated by the mirror surfaces of the interfaces between different materials, as shown in Figure S8 (b).
Figure S11 (a) Schematic the coordinates and related parameters of the Coulomb potential problem. (b) Schematic of the generation of the image charges.
If the image charges and positions are denoted by {qX,n} and {(xX,n, zX,n)}, where X replaced by T+ (images charges in the top dielectrics originated from the positive charge), T- (images charges in the top dielectrics originated from the negative charge), B+ (image charges in the bottom dielectrics originated from the positive charge) or B- (image charges in the bottom dielectrics originated from the negative charge), and n=1,2,3,..., The net Coulomb potential originated from the two charges +q, -q at a certain point (x, z) is given by V ( x, z ) =
1 + q0 − q0 + + 2 2 πε 4πε 0κ s ( x − L / 2) 2 + z 2 4 ( x + L / 2) + z 0κ s 1
∑ X ,n
qX ,n ( x − x X ,n )2 + ( z − z X ,n )2
where ε0 is the vacuum permittivity, κs is the relative dielectric constant of the middle layer, and ±q0 are the effective charges located at (±L/2,0). The image charges and positions are summarized below. i) When |z|
