Nanoscale-Barrier Formation Induced by Low-Dose Electron-Beam ...
SUPPORTING INFORMATION
Nanoscale-Barrier Formation Induced by Low-Dose Electron-Beam Exposure in Ultrathin MoS2 Transistors
M. Matsunaga, A. Higuchi, G. He, T. Yamada, P. Krüger, Y. Ochiai, Y. Gong, R. Vajtai, P. M. Ajayan, J. P. Bird, and N. Aoki
Section 1: Drain bias dependence of the SGM response In Figure 1 of the main manuscript, the pinned SGM response arising from electron-beam induced strain is demonstrated for a single, fixed drain bias (Vd = 0.2 V). In Figure S2, however, we present SGM results obtained by varying both the magnitude and direction of this bias. As the magnitude of Vd is increased for either polarity, it is clear that the SGM response becomes increasingly pronounced in intensity. The detailed structure in the SGM moreover clearly matches that shown in Figure 1 of the main manuscript, and once again remains pinned near the right electrode when the polarity of the drain bias is reversed. Most notably, these results indicate that the presence of the barrier formed within the channel remains a significant factor for transport, even as the drain bias in increased. An additional aspect revealed in the images of Figure S1 is the presence of fine structure in the SGM response that is pinned at the left electrode (as indicated by the arrows in the figure). This structure is only observed for the largest drain bias values (Vd = 1.0- & 1.5-V), and so was consequently not apparent in the data of Figure 1 of the main manuscript. We suggest that the additional features near the left electrode in Figure S1 may also be related to induced strain, in this case corresponding to that introduced during electron-beam lithography of the electrode.
− S1 −
b Vd = 1.0 V
SGM response
a
GND
c
GND
Vd = 0.5 V
d
GND
Vd =1.0 V
GND
Vd = 1.5 V
Figure S1. (a) SGM image obtained with biasing drain voltage (indicated) at the left electrode. (b) - (d) SGM images obtained by reversing the polarity of the drain bias relative to panel (a). The arrows in panels (c) and (d) indicate the position of the additional SGM response that emerges near the edge of the injection (grounded) electrode under the stronger-biasing conditions. All of these images were obtained for a fixed tip potential (Vtip) of 8 V and the scale bar in panel (a) denotes a distance of 3 μm. The color bar in the image denotes the variation of Id (ISGM) induced by the scanning tip.
Section 2: SGM response in the channel region, with and without a domain boundary present In the discussion presented here, we have focused on examples where the SGM response of the MoS2 channel is dominated by the presence of a strain-induced barrier in the channel interior. Such a barrier is not always present within the channel, in which case one may instead observe the barrier formed between the metal electrodes and the MoS2. The difference between the Cr workfunction and the MoS2 electron affinity implies the presence of an injection barrier at this contact, which can be understood as corresponding to the “off state” of a Schottky contact [S1, S2] (since our measurements are made in air at zero gate voltage, where oxygen absorption causes modest p-type doping). Consequently, when the channel is subject to source-drain biasing, it is possible to observe a clear SGM response associated with this barrier. Such a response is illustrated in the right inset of Figure S2(a), which was obtained in an FET that showed no evi− S2 −
dence of any barrier within the channel interior. In this figure it is clear that the SGM response is maximal along the electrode edge, while the main panel reveals that its amplitude decays steadily on moving into the channel. This is clearly very different in nature to the behavior discussed in the main paper, as we highlight also in the left inset, and in the main panel, of Figure S2; the SGM response is clearly peaked away from the electrode, consistent with the presence of the strain-induced barrier. An important point that can be made here is that, for the cases discussed in the main text, the same ohmic barrier should be present at the interface between the Cr electrodes and the MoS2. Nonetheless, since the voltage drop at these injection barriers is much smaller than that arising at the strain-induced barrier (recall the SGM results of Figure 2 of the main manuscript), the presence of the former barrier is not detected in SGM. In Figure S2(b), we account for these different SGM responses in terms of the distinct band-bending conditions in the strained and unstrained channels.
a
b
SGM active
SGM response (pA)
120 GND +Vd
110
Cr/Au
MoS2
SGM active
Cr/Au
GND
100 +Vd
90 8
6
4
2
0
-2
MoS2
-4 Cr/Au
Cr/Au
Distance (m) Figure S2. (a) Comparison of the SGM response exhibited by FETs with (pink solid line) and without (blue solid line) a strain-induced internal barrier. Distance in this figure is measured relative to the edge of the metal electrode, and the left and right insets to the main panel show the SGM response exhibited by the strained and unstrained devices, respectively. The line plots in the main panel correspond to the results of line scans taken along the dashed lines in the respective SGM images (b) Schematics indicating the form of the band bending in biased FETs with (top) and without (bottom) an internal barrier present.
− S3 −
Section 3: Calculation of the strain-induced bandgap variation Strain-dependent bandstructure calculations were performed using the local density approximation (LDA) to density functional theory (DFT), as well as the Perdew-Burke-Enzerhof (PBE) gradient approximation. The projector-augmented-wave method, as implemented in the VASP code24, was used with an energy cut-off of 400 eV and a Gamma-centered 12 × 12 × 1 grid for the Brillouin zone sampling. Repeated MoS2 monolayers were separated by over 10 Å of vacuum. The isotropic (biaxial) strain is denoted as ε = (a − a0)/a0, where a0 is the equilibrium lattice constant. The linear variation of the gap is then expressed as Eg = Eg(a0) + γε. The results obtained for these parameters from our calculations are summarized in the table immediately below: Table S1 Summary of the differences between calculated and experimental values.
Model
a0 (Å)
Eg(a0) (eV)
γ (eV)
Range of direct-gap
LDA
3.123
1.86
-12.3
-0.5% < ε < 1.0%
PBE
3.183
1.68
-11.6
-1.5% < ε < 0.1%
Experiment
3.16*
1.9
−
− *
Bulk in-plane lattice constant
Inspection of this table reveals that the lattice constants obtained by both LDA and PBE are within 1 % of the experimental value. As it is common for DFT, the insulating gap is somewhat underestimated, namely by 2 % (12 %) in LDA (PBE). From these results we conclude that the MoS2 monolayer has a direct gap at equilibrium, and for compressive strain (ε < 0) of up to 0.5 % at the least. The values for γ moreover indicate that the gap increases by 0.12 eV per 1 % of strain.
− S4 −
Section 4: Basic transport characteristics In Figure S3, we show the transfer (Id-Vg) and transistor (Id-Vd) characteristics of the single barrier (panels (a) & (b)), the double barrier (panels (c) & (d)) and the normal device (panels (e) & (f)). All of these curves were measured at room temperature under ambient conditions. The values of the threshold voltage, the estimated mobility, and the ON/OFF ratio of each device are summarized in Table S2. While it cannot be said that there is any systematic variation in the characteristics exhibited by these different devices, as was noted in the main text, the presence of the barriers implies that the effective channel geometry is not simply defined by the source-drain contact separation. The table moreover indicates that the threshold voltage is lowest in the device without any barrier present, and that it increases as the number of barriers increases, a characteristic that may point to the role of additional depletion introduced by the barriers. Similarly, the ON current value is lowest in the double-barrier device. The overall current level is highest in the single-barrier device, however, which clearly indicates that statistics collected from larger numbers of devices are required.
Table S2 Summary of the transistor characteristics.
Sample
Threshold voltage (V)
Mobility (cm2/Vs)
ON/OFF ratio
Single barrier
21 ±1
0.2
1.2 × 104
Double barrier
25 ±1
0.1
1.3 × 103
No barrier
17 ±1
0.1
7.0 × 103
− S5 −
60 40 20
Vg = 5 V Vg = 0 V
0
10-9
10-11 10-12
20
-1x10
-4
30
-4 -2
Back gate voltage (V)
30
d
2.0x10-9
20
10
0
2
4
10
20
Vg = 0 V
0.0
-4 -2
Back gate voltage (V)
Vg = 0 V
10-10 10-11 10-12 -4
40 20 0 0
10
20
30
2
4
6
8
10
2.0x10-9 Vg = 15 V Vg = 10 V Vg = 5 V Vg = 0 V
0.0
-9
-2.0x10
Back gate voltage (V)
Drain current (A)
f
Vd = 1 V
60
0
-2 0 2 4 Drain voltage (V)
Drain voltage (V)
Drain current (A)
Drain current (nA)
e
10
Vg = 5 V
-2.0x10
30
8
Vg = 15 V
-9
0
6
Vg = 10 V
Drain current (A)
Vd = 1 V
0
-2 0 2 4 Drain voltage (V)
Drain voltage (V)
Drain current (A)
10
Vg = 0 V
10-10
-7
0
Drain current (nA)
Vg = 10 V
Drain current (A)
80
Vg = 15 V
Drain current (A)
Vd = 1 V
0
c
1x10-7
b
100
Drain current (nA)
a
-4
-2
0
2
-10
Vg = 0 V
10
-11
10
-12
10
-13
10
-4
4
-2 0 2 4 Drain voltage (V)
6
8
10
Drain voltage (V)
Figure S3. (a) Id-Vg and (b) Id-Vd properties of the single-barrier MoS2 FET, shown in Figure 1 of the main paper. (c), (d) Properties of the double-barrier MoS2 FET, shown in Figure 6 of the main paper. (e), (f) Properties of the barrierfree MoS2 FET, shown in Figure S3 of this Supporting Information. The insets show the Id-Vd curve at Vg = 0 V, with the current plotted on a logarithmic scale.
− S6 −
REFERENCES S1.
Kang, J.; Liu, W.; Sarkar, D.; Jena, D.; Banerjee, K. Computational Study of Metal Contacts to Monolayer Transition-Metal Dichalcogenide Semiconductors. Phys. Rev. X 2014, 4, 031005.
S2.
Allain, A.; Kang, J.; Banerjee, K.; Kis, A. Electrical Contacts to Two-Dimensional Semiconductors. Nat. Mater. 2015, 14, 1195–1205.
− S7 −
Nanoscale-Barrier Formation Induced by Low-Dose Electron-Beam Exposure in Ultrathin MoS2 Transistors
M. Matsunaga, A. Higuchi, G. He, T. Yamada, P. Krüger, Y. Ochiai, Y. Gong, R. Vajtai, P. M. Ajayan, J. P. Bird, and N. Aoki
Section 1: Drain bias dependence of the SGM response In Figure 1 of the main manuscript, the pinned SGM response arising from electron-beam induced strain is demonstrated for a single, fixed drain bias (Vd = 0.2 V). In Figure S2, however, we present SGM results obtained by varying both the magnitude and direction of this bias. As the magnitude of Vd is increased for either polarity, it is clear that the SGM response becomes increasingly pronounced in intensity. The detailed structure in the SGM moreover clearly matches that shown in Figure 1 of the main manuscript, and once again remains pinned near the right electrode when the polarity of the drain bias is reversed. Most notably, these results indicate that the presence of the barrier formed within the channel remains a significant factor for transport, even as the drain bias in increased. An additional aspect revealed in the images of Figure S1 is the presence of fine structure in the SGM response that is pinned at the left electrode (as indicated by the arrows in the figure). This structure is only observed for the largest drain bias values (Vd = 1.0- & 1.5-V), and so was consequently not apparent in the data of Figure 1 of the main manuscript. We suggest that the additional features near the left electrode in Figure S1 may also be related to induced strain, in this case corresponding to that introduced during electron-beam lithography of the electrode.
− S1 −
b Vd = 1.0 V
SGM response
a
GND
c
GND
Vd = 0.5 V
d
GND
Vd =1.0 V
GND
Vd = 1.5 V
Figure S1. (a) SGM image obtained with biasing drain voltage (indicated) at the left electrode. (b) - (d) SGM images obtained by reversing the polarity of the drain bias relative to panel (a). The arrows in panels (c) and (d) indicate the position of the additional SGM response that emerges near the edge of the injection (grounded) electrode under the stronger-biasing conditions. All of these images were obtained for a fixed tip potential (Vtip) of 8 V and the scale bar in panel (a) denotes a distance of 3 μm. The color bar in the image denotes the variation of Id (ISGM) induced by the scanning tip.
Section 2: SGM response in the channel region, with and without a domain boundary present In the discussion presented here, we have focused on examples where the SGM response of the MoS2 channel is dominated by the presence of a strain-induced barrier in the channel interior. Such a barrier is not always present within the channel, in which case one may instead observe the barrier formed between the metal electrodes and the MoS2. The difference between the Cr workfunction and the MoS2 electron affinity implies the presence of an injection barrier at this contact, which can be understood as corresponding to the “off state” of a Schottky contact [S1, S2] (since our measurements are made in air at zero gate voltage, where oxygen absorption causes modest p-type doping). Consequently, when the channel is subject to source-drain biasing, it is possible to observe a clear SGM response associated with this barrier. Such a response is illustrated in the right inset of Figure S2(a), which was obtained in an FET that showed no evi− S2 −
dence of any barrier within the channel interior. In this figure it is clear that the SGM response is maximal along the electrode edge, while the main panel reveals that its amplitude decays steadily on moving into the channel. This is clearly very different in nature to the behavior discussed in the main paper, as we highlight also in the left inset, and in the main panel, of Figure S2; the SGM response is clearly peaked away from the electrode, consistent with the presence of the strain-induced barrier. An important point that can be made here is that, for the cases discussed in the main text, the same ohmic barrier should be present at the interface between the Cr electrodes and the MoS2. Nonetheless, since the voltage drop at these injection barriers is much smaller than that arising at the strain-induced barrier (recall the SGM results of Figure 2 of the main manuscript), the presence of the former barrier is not detected in SGM. In Figure S2(b), we account for these different SGM responses in terms of the distinct band-bending conditions in the strained and unstrained channels.
a
b
SGM active
SGM response (pA)
120 GND +Vd
110
Cr/Au
MoS2
SGM active
Cr/Au
GND
100 +Vd
90 8
6
4
2
0
-2
MoS2
-4 Cr/Au
Cr/Au
Distance (m) Figure S2. (a) Comparison of the SGM response exhibited by FETs with (pink solid line) and without (blue solid line) a strain-induced internal barrier. Distance in this figure is measured relative to the edge of the metal electrode, and the left and right insets to the main panel show the SGM response exhibited by the strained and unstrained devices, respectively. The line plots in the main panel correspond to the results of line scans taken along the dashed lines in the respective SGM images (b) Schematics indicating the form of the band bending in biased FETs with (top) and without (bottom) an internal barrier present.
− S3 −
Section 3: Calculation of the strain-induced bandgap variation Strain-dependent bandstructure calculations were performed using the local density approximation (LDA) to density functional theory (DFT), as well as the Perdew-Burke-Enzerhof (PBE) gradient approximation. The projector-augmented-wave method, as implemented in the VASP code24, was used with an energy cut-off of 400 eV and a Gamma-centered 12 × 12 × 1 grid for the Brillouin zone sampling. Repeated MoS2 monolayers were separated by over 10 Å of vacuum. The isotropic (biaxial) strain is denoted as ε = (a − a0)/a0, where a0 is the equilibrium lattice constant. The linear variation of the gap is then expressed as Eg = Eg(a0) + γε. The results obtained for these parameters from our calculations are summarized in the table immediately below: Table S1 Summary of the differences between calculated and experimental values.
Model
a0 (Å)
Eg(a0) (eV)
γ (eV)
Range of direct-gap
LDA
3.123
1.86
-12.3
-0.5% < ε < 1.0%
PBE
3.183
1.68
-11.6
-1.5% < ε < 0.1%
Experiment
3.16*
1.9
−
− *
Bulk in-plane lattice constant
Inspection of this table reveals that the lattice constants obtained by both LDA and PBE are within 1 % of the experimental value. As it is common for DFT, the insulating gap is somewhat underestimated, namely by 2 % (12 %) in LDA (PBE). From these results we conclude that the MoS2 monolayer has a direct gap at equilibrium, and for compressive strain (ε < 0) of up to 0.5 % at the least. The values for γ moreover indicate that the gap increases by 0.12 eV per 1 % of strain.
− S4 −
Section 4: Basic transport characteristics In Figure S3, we show the transfer (Id-Vg) and transistor (Id-Vd) characteristics of the single barrier (panels (a) & (b)), the double barrier (panels (c) & (d)) and the normal device (panels (e) & (f)). All of these curves were measured at room temperature under ambient conditions. The values of the threshold voltage, the estimated mobility, and the ON/OFF ratio of each device are summarized in Table S2. While it cannot be said that there is any systematic variation in the characteristics exhibited by these different devices, as was noted in the main text, the presence of the barriers implies that the effective channel geometry is not simply defined by the source-drain contact separation. The table moreover indicates that the threshold voltage is lowest in the device without any barrier present, and that it increases as the number of barriers increases, a characteristic that may point to the role of additional depletion introduced by the barriers. Similarly, the ON current value is lowest in the double-barrier device. The overall current level is highest in the single-barrier device, however, which clearly indicates that statistics collected from larger numbers of devices are required.
Table S2 Summary of the transistor characteristics.
Sample
Threshold voltage (V)
Mobility (cm2/Vs)
ON/OFF ratio
Single barrier
21 ±1
0.2
1.2 × 104
Double barrier
25 ±1
0.1
1.3 × 103
No barrier
17 ±1
0.1
7.0 × 103
− S5 −
60 40 20
Vg = 5 V Vg = 0 V
0
10-9
10-11 10-12
20
-1x10
-4
30
-4 -2
Back gate voltage (V)
30
d
2.0x10-9
20
10
0
2
4
10
20
Vg = 0 V
0.0
-4 -2
Back gate voltage (V)
Vg = 0 V
10-10 10-11 10-12 -4
40 20 0 0
10
20
30
2
4
6
8
10
2.0x10-9 Vg = 15 V Vg = 10 V Vg = 5 V Vg = 0 V
0.0
-9
-2.0x10
Back gate voltage (V)
Drain current (A)
f
Vd = 1 V
60
0
-2 0 2 4 Drain voltage (V)
Drain voltage (V)
Drain current (A)
Drain current (nA)
e
10
Vg = 5 V
-2.0x10
30
8
Vg = 15 V
-9
0
6
Vg = 10 V
Drain current (A)
Vd = 1 V
0
-2 0 2 4 Drain voltage (V)
Drain voltage (V)
Drain current (A)
10
Vg = 0 V
10-10
-7
0
Drain current (nA)
Vg = 10 V
Drain current (A)
80
Vg = 15 V
Drain current (A)
Vd = 1 V
0
c
1x10-7
b
100
Drain current (nA)
a
-4
-2
0
2
-10
Vg = 0 V
10
-11
10
-12
10
-13
10
-4
4
-2 0 2 4 Drain voltage (V)
6
8
10
Drain voltage (V)
Figure S3. (a) Id-Vg and (b) Id-Vd properties of the single-barrier MoS2 FET, shown in Figure 1 of the main paper. (c), (d) Properties of the double-barrier MoS2 FET, shown in Figure 6 of the main paper. (e), (f) Properties of the barrierfree MoS2 FET, shown in Figure S3 of this Supporting Information. The insets show the Id-Vd curve at Vg = 0 V, with the current plotted on a logarithmic scale.
− S6 −
REFERENCES S1.
Kang, J.; Liu, W.; Sarkar, D.; Jena, D.; Banerjee, K. Computational Study of Metal Contacts to Monolayer Transition-Metal Dichalcogenide Semiconductors. Phys. Rev. X 2014, 4, 031005.
S2.
Allain, A.; Kang, J.; Banerjee, K.; Kis, A. Electrical Contacts to Two-Dimensional Semiconductors. Nat. Mater. 2015, 14, 1195–1205.
− S7 −
