Supporting Information: Band alignment in MoS2 /WS2 transition metal ...
Supporting Information: Band alignment in MoS2/WS2 transition metal dichalcogenide heterostructures probed by scanning tunneling microscopy and spectroscopy Heather M. Hill†%‡, Albert F. Rigosi†%‡, Kwang Taeg Rim§, George W. Flynn§, and Tony F. †%*
Heinz †
Departments of Physics and Electrical Engineering, Columbia University, New York, NY 10027, United States §
Department of Chemistrty, Columbia University, New York, NY 10027, United States
%
Department of Applied Physics, Stanford University, Stanford, CA 94305, United States
and SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, United States
Corresponding Author: [email protected] Fax: 212-854-1909
S1
1.
Sample Preparation and Characterization Sample Preparation To prepare samples for the STM measurements, a chemical-free gold coating method (shadow
mask) was implemented to avoid the use of any polymers or chemical processing. This process enables the preparer to keep surface residue to a minimum. We cut a grid, which was originally intended for transmission electron microscopy (TEM), in half with a sharp razor, and then pick it up with a piece of PDMS, a flexible polymer with multiple purposes in device fabrication, to allow us to nudge the position of the grid over the sample. A cut portion of one of the grid bars, typically measuring about 10-15μm in width, acts as a shadow mask for most of the sample and leaves some of the sample exposed for the eventual metal deposition. Once the TEM grid is successfully placed by hand on the sample, the gold evaporation and deposition is performed with an Edwards Auto 306 Thermal Evaporator, and 20 nm of Au is deposited. Once complete, the PDMS, which still sticks to the TEM grid, gets peeled off, and this motion also removes the grid. The unexposed area is then a viable region to be scanned by the STM, since it allows a current to flow in and out of the sample. An illustration is shown in Figure S1.
S2
Figure S1. Here is an illustration of using the TEM grid as a shadow mask for gold deposition onto a surface without the use of chemicals typical in e-beam lithography.
S3
Sample characterization: photoluminescence and Raman spectra For further characterization of the individual layers and heterostructures, photoluminescence and Raman measurements of the TMDCHs were carried out. The measurements were performed using continuous-wave laser excitation at 532 nm in a commercial (Renishaw InVia) Raman microscope. As shown in Figure S2 the MoS2/WS2 system, we obtain PL spectra (left) for both the separated monolayers and the overlapping heterostructure. In the PL, individual layers exhibit a strong peak corresponding to emission from the A exciton. The Raman spectra of the heterostructure region in Figure S2 (right) roughly match the combined spectra of the individual layers.
Figure S2. PL and Raman spectra for the TMDCH system, with results shown for the separated layers, as well as for the overlapping region. The PL intensity is plotted on a log scale, and the main peaks are labeled for the individual layers and the corresponding heterostructures.1,2
S4
Sample characterization: atomic force microscopy The TMDCH systems are characterized using atomic force microscopy measurements and comparing the relevant thicknesses of the individual layers to that of the heterostructure. A representative AFM image of the heterostructure is shown in Figure S3.
5 μm
Figure S3. The dashed lines show the boundaries between different regions of the structure, with the pale green zone inside both the blue and red boundaries corresponding to the heterostructure of the two labeled monolayers.
S5
2.
Current Simulation and Modeling Mathematical Details To generate a suitable model for the STS data, we begin with the following equation presented
in the main text: =
ସగ ħ
ିஶ ஶ
ଵ
ഄషೇ ଵା ೖ
−
ଵ
ഄ
ଵା ೖ
ௌ ி − + ் ி + , (1)
If the bracketed term is labeled ‘f’, then the derivative can be written out in a more compact form (tip local density of states, or LDOS, is constant). Focusing on the conduction band for sake of example, we have: ஶ ೖ ~ ିஶ ௌ ഄషೇ మ ௗ ቆଵା ೖ ቇ ഄషೇ
ௗூ
ஶ ~ ିஶ ௗ ௗூ
ഄషೇ
ೖ
ഄషೇ మ ቆଵା ೖ ቇ
+
ௌ + ௌ
డఘೄ డ
డ்
డ
+ ௌ డ (2) డ்
+ |ாೞ (3)
This is the formula used for the STS data modeling, where Eonset is the value of the band edge at the conduction band minimum that is optimized by least squares regression. To fit data which is most likely to be uninfluenced by noise or high-voltage currents where the model becomes less valid due to current from multiple bands, the following steps are taken: (1) The logarithm of the data is taken first. (2) The instrument’s average background plus three sigma of its standard deviation is subtracted from the data. (3) The lower bound is a factor of 5 above the average background to reduce the impact from defects. The upper bound is an additional 500 meV away from the low voltage bound, or 1 eV in the case that the lower bound is a bottom-layer Q or Γ onset. See the main text for the additional parameters used in this formulation.
S6
Figure S4. The dashed lines show an example of how the data for χ2 minimization is selected. The dashed red line shows the average background. The data cutoff (purple arrows) is found by multiplying the background by a factor of five (dark blue dashed line). This cut-off is meant to drastically reduce any defect state influence on the modeling of the band gap. The region of minimization (from the cutoff to the dashed green line) is meant to include a region which, while not influenced by low-bias effects, also avoids the inherent model inaccuracies that occur at higher bias-voltages. In the case of the heterostructure, the data from the bottom layer spanning 1 V from the Q or Γ onset is included.
S7
Effects of Thermal Broadening Following the arguments by Chen,3 for a simple band gap conduction band that can be described by a step function, the second derivative of current would become a Delta function. When the integral for the current is evaluated, assuming all terms are constant except for the Fermi function and the sample LDOS (presumed to be a step function for the case of the conduction band), the following integral arises: ~ ିஶ ஶ
ଵ
ഄషೇ ଵା ೖ
−
~ ௫ ௗ మ
ഄ
ଵା ೖ
Differentiating this expression twice yields ( = ௗమ ூ
ଵ
ఌି ்
௦
(1)
):
ሺ௫ିଶሻ ೣ ା௫ାଶ
(2)
( ೣ ିଵ)య
Instead of a Delta function, a peak of width 5.4kT, or 135 meV at room temperature, when integrated, can be used to describe the onset of a band edge. 3.
Tip-Induced Band Bending (TIBB) Model Acknowledgments The value of the TIBB in all samples was calculated using SEMITIP Version 6, introduced by
R. Feenstra in 2011. The Film2 package was also utilized.4 5 6 The relevant parameters are as follows: Table S1. Parameters for TIBB calculation shown here. Value –{MoS2, WS2}
Parameter Definition
10
Tip Radius (nm)
0.6
Thickness of Total Film (nm)
0.5
Contact Potential (eV)7,8
1
Number of Different Semiconductor Regions
S8
{2.16, 2.38}
Band Gap (eV)
{0.35, 0.3}
Conduction Band Effective Mass
0.44
Light Hole Effective Mass
{0.14, 0.4}
Spin-Orbit Splitting (eV)
1
Degeneracy Indicator (1 = Degenerate)
0
Inversion Indicator (0 = Include Possible Inversion)
4
Dielectric Constant in Film 9
3.8
Dielectric Constant in Substrate
300
Temperature (K)
1
Number of Different Types of Surfaces
2.00E+12
Density of Charge Carriers (cm^-2)
For the case of measuring TIBB on the heterostructure, the bottom layer was treated as the substrate, with values of the relative dielectric constant reported as 4-6.10 The tip was an additional 0.6 nm away, and in both stacking orientations, the TIBB was less than 5 meV.
S9
REFERENCES
(1) Lee,
C.; Yan, H.; Brus, L. E.; Heinz, T. F.; Hone, J.; Ryu, S. Anomalous Lattice Vibrations of
Single- and Few-Layer MoS2. ACS Nano 2010, 4, 2695– 2700. (2)
Berkdemir, A.; Gutierrez, H. R.; Botello-Mendez, A. R.; Perea-Lopez, N.; Elias, A. L.; Chia,
C.-I.; Wang, B.; Crespi, V. H.; Lopez-Urias, F.; Charlier, J.-C.et al. Identification of Individual and Few Layers of WS2 Using Raman Spectroscopy. Sci. Rep. 2013, 3. (3) Chen, C. J. Introduction to Scanning Tunneling Microscopy; Oxford University Press: New York, 1993. (4) Feenstra, R. M. Electrostatic Potential for a Hyperbolic Probe Tip near a Semiconductor. J. Vac. Sci. Technol., B 2003, 21, 2080. (5) Feenstra, R. M.; Meyer, G.; Rieder, K.-H. Transport limitations in tunneling spectroscopy of Ge(111)c(2×8) surfaces. Phys. Rev. B 2004, 69, 081309. (6) Feenstra, R. M.; Gaan, S.; Meyer, G.; Rieder, K.-H. Low-temperature tunneling spectroscopy of Ge(111)c(2x8) surfaces. Phys. Rev. B 2005, 71, 125316. (7) Feenstra, R. M.; Dong, Y.; Semtsiv, M. P.; Masselink, W. T. Influence of Tip-Induced Band Bending on Tunneling Spectra of Semiconductor Surfaces. Nanotech. 2007, 18 ( 4) 044015. (8) Liu, W.; Cao, W.; Kang, J.; Banerjee, K. High-Performance Field-Effect-Transistors on Monolayer WSe2. ECS Trans. 2013, 58, 281. (9) Santos, E. J. G.; Kaxiras, E. Electrically Driven Tuning of the Dielectric Constant in MoS2 Layers. ACS Nano 2013, 7, 10741.
S10
(10) Chang, J. W.; Register, L. F.; Banerjee, S. K. Ballistic Performance Comparison of Monolayer Transition Metal Dichalcogenide MX2 (M = Mo, W; X = S, Se, Te) Metal-OxideSemiconductor Field Effect Transistors. J. Appl. Phys. 2014, 115, 084506.
S11
Heinz †
Departments of Physics and Electrical Engineering, Columbia University, New York, NY 10027, United States §
Department of Chemistrty, Columbia University, New York, NY 10027, United States
%
Department of Applied Physics, Stanford University, Stanford, CA 94305, United States
and SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, United States
Corresponding Author: [email protected] Fax: 212-854-1909
S1
1.
Sample Preparation and Characterization Sample Preparation To prepare samples for the STM measurements, a chemical-free gold coating method (shadow
mask) was implemented to avoid the use of any polymers or chemical processing. This process enables the preparer to keep surface residue to a minimum. We cut a grid, which was originally intended for transmission electron microscopy (TEM), in half with a sharp razor, and then pick it up with a piece of PDMS, a flexible polymer with multiple purposes in device fabrication, to allow us to nudge the position of the grid over the sample. A cut portion of one of the grid bars, typically measuring about 10-15μm in width, acts as a shadow mask for most of the sample and leaves some of the sample exposed for the eventual metal deposition. Once the TEM grid is successfully placed by hand on the sample, the gold evaporation and deposition is performed with an Edwards Auto 306 Thermal Evaporator, and 20 nm of Au is deposited. Once complete, the PDMS, which still sticks to the TEM grid, gets peeled off, and this motion also removes the grid. The unexposed area is then a viable region to be scanned by the STM, since it allows a current to flow in and out of the sample. An illustration is shown in Figure S1.
S2
Figure S1. Here is an illustration of using the TEM grid as a shadow mask for gold deposition onto a surface without the use of chemicals typical in e-beam lithography.
S3
Sample characterization: photoluminescence and Raman spectra For further characterization of the individual layers and heterostructures, photoluminescence and Raman measurements of the TMDCHs were carried out. The measurements were performed using continuous-wave laser excitation at 532 nm in a commercial (Renishaw InVia) Raman microscope. As shown in Figure S2 the MoS2/WS2 system, we obtain PL spectra (left) for both the separated monolayers and the overlapping heterostructure. In the PL, individual layers exhibit a strong peak corresponding to emission from the A exciton. The Raman spectra of the heterostructure region in Figure S2 (right) roughly match the combined spectra of the individual layers.
Figure S2. PL and Raman spectra for the TMDCH system, with results shown for the separated layers, as well as for the overlapping region. The PL intensity is plotted on a log scale, and the main peaks are labeled for the individual layers and the corresponding heterostructures.1,2
S4
Sample characterization: atomic force microscopy The TMDCH systems are characterized using atomic force microscopy measurements and comparing the relevant thicknesses of the individual layers to that of the heterostructure. A representative AFM image of the heterostructure is shown in Figure S3.
5 μm
Figure S3. The dashed lines show the boundaries between different regions of the structure, with the pale green zone inside both the blue and red boundaries corresponding to the heterostructure of the two labeled monolayers.
S5
2.
Current Simulation and Modeling Mathematical Details To generate a suitable model for the STS data, we begin with the following equation presented
in the main text: =
ସగ ħ
ିஶ ஶ
ଵ
ഄషೇ ଵା ೖ
−
ଵ
ഄ
ଵା ೖ
ௌ ி − + ் ி + , (1)
If the bracketed term is labeled ‘f’, then the derivative can be written out in a more compact form (tip local density of states, or LDOS, is constant). Focusing on the conduction band for sake of example, we have: ஶ ೖ ~ ିஶ ௌ ഄషೇ మ ௗ ቆଵା ೖ ቇ ഄషೇ
ௗூ
ஶ ~ ିஶ ௗ ௗூ
ഄషೇ
ೖ
ഄషೇ మ ቆଵା ೖ ቇ
+
ௌ + ௌ
డఘೄ డ
డ்
డ
+ ௌ డ (2) డ்
+ |ாೞ (3)
This is the formula used for the STS data modeling, where Eonset is the value of the band edge at the conduction band minimum that is optimized by least squares regression. To fit data which is most likely to be uninfluenced by noise or high-voltage currents where the model becomes less valid due to current from multiple bands, the following steps are taken: (1) The logarithm of the data is taken first. (2) The instrument’s average background plus three sigma of its standard deviation is subtracted from the data. (3) The lower bound is a factor of 5 above the average background to reduce the impact from defects. The upper bound is an additional 500 meV away from the low voltage bound, or 1 eV in the case that the lower bound is a bottom-layer Q or Γ onset. See the main text for the additional parameters used in this formulation.
S6
Figure S4. The dashed lines show an example of how the data for χ2 minimization is selected. The dashed red line shows the average background. The data cutoff (purple arrows) is found by multiplying the background by a factor of five (dark blue dashed line). This cut-off is meant to drastically reduce any defect state influence on the modeling of the band gap. The region of minimization (from the cutoff to the dashed green line) is meant to include a region which, while not influenced by low-bias effects, also avoids the inherent model inaccuracies that occur at higher bias-voltages. In the case of the heterostructure, the data from the bottom layer spanning 1 V from the Q or Γ onset is included.
S7
Effects of Thermal Broadening Following the arguments by Chen,3 for a simple band gap conduction band that can be described by a step function, the second derivative of current would become a Delta function. When the integral for the current is evaluated, assuming all terms are constant except for the Fermi function and the sample LDOS (presumed to be a step function for the case of the conduction band), the following integral arises: ~ ିஶ ஶ
ଵ
ഄషೇ ଵା ೖ
−
~ ௫ ௗ మ
ഄ
ଵା ೖ
Differentiating this expression twice yields ( = ௗమ ூ
ଵ
ఌି ்
௦
(1)
):
ሺ௫ିଶሻ ೣ ା௫ାଶ
(2)
( ೣ ିଵ)య
Instead of a Delta function, a peak of width 5.4kT, or 135 meV at room temperature, when integrated, can be used to describe the onset of a band edge. 3.
Tip-Induced Band Bending (TIBB) Model Acknowledgments The value of the TIBB in all samples was calculated using SEMITIP Version 6, introduced by
R. Feenstra in 2011. The Film2 package was also utilized.4 5 6 The relevant parameters are as follows: Table S1. Parameters for TIBB calculation shown here. Value –{MoS2, WS2}
Parameter Definition
10
Tip Radius (nm)
0.6
Thickness of Total Film (nm)
0.5
Contact Potential (eV)7,8
1
Number of Different Semiconductor Regions
S8
{2.16, 2.38}
Band Gap (eV)
{0.35, 0.3}
Conduction Band Effective Mass
0.44
Light Hole Effective Mass
{0.14, 0.4}
Spin-Orbit Splitting (eV)
1
Degeneracy Indicator (1 = Degenerate)
0
Inversion Indicator (0 = Include Possible Inversion)
4
Dielectric Constant in Film 9
3.8
Dielectric Constant in Substrate
300
Temperature (K)
1
Number of Different Types of Surfaces
2.00E+12
Density of Charge Carriers (cm^-2)
For the case of measuring TIBB on the heterostructure, the bottom layer was treated as the substrate, with values of the relative dielectric constant reported as 4-6.10 The tip was an additional 0.6 nm away, and in both stacking orientations, the TIBB was less than 5 meV.
S9
REFERENCES
(1) Lee,
C.; Yan, H.; Brus, L. E.; Heinz, T. F.; Hone, J.; Ryu, S. Anomalous Lattice Vibrations of
Single- and Few-Layer MoS2. ACS Nano 2010, 4, 2695– 2700. (2)
Berkdemir, A.; Gutierrez, H. R.; Botello-Mendez, A. R.; Perea-Lopez, N.; Elias, A. L.; Chia,
C.-I.; Wang, B.; Crespi, V. H.; Lopez-Urias, F.; Charlier, J.-C.et al. Identification of Individual and Few Layers of WS2 Using Raman Spectroscopy. Sci. Rep. 2013, 3. (3) Chen, C. J. Introduction to Scanning Tunneling Microscopy; Oxford University Press: New York, 1993. (4) Feenstra, R. M. Electrostatic Potential for a Hyperbolic Probe Tip near a Semiconductor. J. Vac. Sci. Technol., B 2003, 21, 2080. (5) Feenstra, R. M.; Meyer, G.; Rieder, K.-H. Transport limitations in tunneling spectroscopy of Ge(111)c(2×8) surfaces. Phys. Rev. B 2004, 69, 081309. (6) Feenstra, R. M.; Gaan, S.; Meyer, G.; Rieder, K.-H. Low-temperature tunneling spectroscopy of Ge(111)c(2x8) surfaces. Phys. Rev. B 2005, 71, 125316. (7) Feenstra, R. M.; Dong, Y.; Semtsiv, M. P.; Masselink, W. T. Influence of Tip-Induced Band Bending on Tunneling Spectra of Semiconductor Surfaces. Nanotech. 2007, 18 ( 4) 044015. (8) Liu, W.; Cao, W.; Kang, J.; Banerjee, K. High-Performance Field-Effect-Transistors on Monolayer WSe2. ECS Trans. 2013, 58, 281. (9) Santos, E. J. G.; Kaxiras, E. Electrically Driven Tuning of the Dielectric Constant in MoS2 Layers. ACS Nano 2013, 7, 10741.
S10
(10) Chang, J. W.; Register, L. F.; Banerjee, S. K. Ballistic Performance Comparison of Monolayer Transition Metal Dichalcogenide MX2 (M = Mo, W; X = S, Se, Te) Metal-OxideSemiconductor Field Effect Transistors. J. Appl. Phys. 2014, 115, 084506.
S11
