Two-Dimensional Thickness-Dependent Avalanche Breakdown Phenomena in MoS 2 Field Effect Transistors under High Electric Fields

Transcription

1 Supporting Information Two-Dimensional Thickness-Dependent Avalanche Breakdown Phenomena in MoS 2 Field Effect Transistors under High Electric Fields Jinsu Pak,,# Yeonsik Jang,,# Junghwan Byun, Kyungjune Cho, Tae-Young Kim, Jae-Keun Kim, Barbara Yuri Choi, Jiwon Shin, Yongtaek Hong, Seungjun Chung,*, and Takhee Lee*, Department of Physics and Astronomy, and Institute of Applied Physics, Seoul National University, Seoul 08826, Korea Department of Electrical and Computer Engineering, Inter-university Semiconductor Research Center (ISRC), Seoul National University, Seoul 08826, Korea Photo-electronic Hybrids Research Center, Korea Institute of Science and Technology (KIST), Seoul 02792, Korea KEYWORDS: MoS 2, avalanche multiplication, 2D materials, field-effect transistors, electrical breakdown # These authors contributed equally to this work. Corresponding authors (T. L) tlee@snu.ac.kr; (S. C) seungjun@kist.re.kr 1

2 1. Device fabrication Figure S1 illustrates the MoS 2 field effect transistors (FETs) fabrication processes. To prepare MoS 2 channel layers, MoS 2 flakes were transferred from a bulk MoS 2 crystal on a 270 nm-thick SiO 2 /Si substrate using a micromechanical exfoliation method. Onto the transferred MoS 2 channels, we spin-coated the double electron resistor layers with methyl methacrylate (MMA) (9% concentration in ethyl lactate) and polymethyl methacrylate (PMMA) 950K (5% concentration in anisole) at 4000 rpm, sequentially. Each layer was baked at 180 C for 90 s on a hot plate. After the source and drain electrodes patterns were defined using electron beam lithography (JSM-6510, JEOL), Ti (5 nm) and Au (30 nm) were deposited using an electron beam evaporator (KVE-2004L, Korea Vacuum Tech.) sequentially for the source and drain electrodes formation. The fabricated MoS 2 FETs were annealed at 200 C in Ar atmosphere for 2 h to achieve better electrical performances by eliminating residues on the surface of the MoS 2 channels. Figure S1. Schematics of the process flow for the MoS 2 FET fabrication. 2

3 2. Photoluminescence data Figure S2 shows the photoluminescence spectra (PL) of monolayer to multilayer MoS 2. The decreased PL intensity with increasing thickness of MoS 2 indicates its inherent band structure transition from direct bandgap to indirect bandgap. The peak A and B correspond the direct band-to-band transition from the conduction band to two different valence bands which are split by spin-orbit coupling effect. Intensity (a. u.) A B 1L 2L 3L 4L Photon energy (ev) 2.2 Figure S2. Photoluminescence spectra of monolayer to multilayer MoS 2. 3

4 3. Transconductance of a monolayer MoS 2 FET Figure S3 shows the transconductance value versus gate voltage (V GS ) with different drain-source voltages (V DS ). The transconductance was derived from the output curve (I DS V GS ) by a formula: =. The peak transconductance value was 0.17 µs at V DS = 3 V V DS (V) G m (S) V GS (V) Figure S3. The transconductance of a monolayer MoS 2 FET with different V DS. 4

5 4. Electrical breakdown of MoS 2 FETs with ohmic-contact and non-ohmic contact. Figures S4a and S4d show the I DS V DS characteristics at various gate bias ranging from 0 V to 40 V with a step of 10 V. Optical images are also included in inset. Log-log plots shown in Figures S4b and S4e present the relationship I DS V β DS with the average β (linearity parameter) values of ~1.01 and 1.72, respectively. This value closed to 1 indicates the ohmic-contact formation between the MoS 2 channel and Au/Ti electrodes. This comparison supports that the MoS 2 FET shown in Figure S4a has an ohmic-contact formation (Figure S4b) and the other shown in Figure S4d has non-ohmic-contact with Schottky barrier (Figure S4e). Despite of the different contact property, the similar E CR values of 2.32 MV/cm and 2.11 MV/cm were observed as shown in Figures S4c and S4f, respectively. Therefore, the electrical breakdown exhibiting abruptly increased currents was dominantly affected by lateral E-fields, not Schottky barrier. It is one of the evidences that this electrical breakdown is related to avalanche multiplication. Figure S4. Electrical breakdown of the multilayer MoS 2 FETs with (top) ohmic-contact and (bottom) non-ohmic contact with Schottky barriers. 5

6 5. The effect of contact resistance on the avalanche multiplication The total resistance in FET consists of the channel resistance and the parasitic contact resistances, = 2 as shown in Figure S5. Figure S5. A simple equivalent circuit diagram of MoS 2 FET. R ch is modulated by gate bias. The contact resistances were obtained by the Y-function method, which has been generally used for evaluating the contact resistance for various materials such as carbon nanotube, organic materials, and MoS 2 FETs. S1-S3 I DS in a linear regime with the consideration of contact resistance can be expressed as = 1 = 1, where,,, W, L, R C, V th, and donate the intrinsic mobility in linear regime, the mobility attenuation factor from channel, the capacitance between the MoS 2 channel and the gate per unit area, the channel width, the channel length, the contact resistance, the threshold voltage and the mobility attenuation factor from both the channel and contact regions. The Y- function is given by 6

7 = = =, where = is transconductance. The attenuation factor can be expressed by = =, where is the mobility attenuation factor from the contact regions. Consequentially, the contact resistance can be obtained by the following equation, =, where S 1 and S 2 are derivative values of Y and by V GS. For the further investigation on the effects of contact resistance, we did our best to minimize the effect of contact resistance by fabricating additional three more MoS 2 FETs having much lower contact resistance values, and then E CR values were extracted. The fabricated multilayer MoS 2 FETs had a contact resistance values of 4.89 kω, 14.8 kω and 15.0 kω extracted from Y-function method as shown in Figure S6, and then the channel resistances of 2.27 MΩ, 4.11 MΩ, and 7.09 MΩ were calculated from the I D V GS characteristics, respectively by the equation of R tot = R ch + 2R c (Figure S5). Note that the contact resistance values were much lower (> one-order) than that of the MoS 2 FET (160 kω) in the main manuscript. Even, in the MoS 2 FETs minimized the effect of contact resistance with our best, most of the voltage drops occurred across the MoS 2 channel layer (> 99 %), and the extracted E CR values were 1.55 MV/cm, 1.45 MV/cm, and 1.23 MV/cm, respectively. Those were also included in a range of E CR of multilayer MoS 2 FETs having relatively large contact resistance values presented in Figure S7. The E CR values are summarized in Table S1. These results indicate the effects of contact resistance did not significantly affect the 7

8 avalanche multiplication. Figure S6. I DS V GS curves, Y-function, and 1 for three MoS 2 FETs which minimized the effect of contact resistance. The scale bar in inset images is 10 µm. 8

9 Figure S7. (a-c) E CR values for three MoS 2 FETs which minimized the effect of contact resistance. All of the calculated E CR are consistent with those of multilayer MoS 2 FETs with relative high contact resistances shown in (d). The scale bar in inset images is 10 µm. Table S1. The summarized resistance values and E CR value for three MoS 2 FETs which minimized the effect of contact resistance compared to the MoS 2 FETs presented in the main manuscript. 9

10 6. The reversible output characteristics during multiple V DS sweeps Figures S8a and S8b show the output curve (I DS V DS ) and the transfer curve (I DS V GS ) of a multilayer MoS 2 FET measured in air. As shown in Figure S8c, the reversible output curves including the electrical breakdown were measured under the multiple V DS sweeps. This result supports that the MoS 2 channel was not damaged after the reversible electrical breakdown by thermal stress originated by Joule heating. Figure S8. (a) I DS V DS and (b) I DS V GS characteristics of a MoS 2 FET. (c) The reversible I DS - V DS curves were measured during the multiple V DS sweeps. 10

11 7. The maximum current density per a layer of MoS 2 FETs Figure S9 shows the maximum current density per a layer at the electrical breakdown. As the number of layer of MoS 2 channel increased, the maximum current density per a layer decreased because of the interactions by van der Waals force between neighboring layers without the direct chemical bounding. Therefore, lower values of maximum current density per a layer in multilayer MoS 2 were observed in comparison with that of monolayer MoS 2 FETs. The further details are under investigations. Breakdown current density per a layer (μa/cm 2 ) Number of layers Figure S9. The maximum current density per a layer at electrical breakdown as a function of the number of MoS 2 layers. 11

12 8. The output curve exhibiting permanent electrical breakdown in MoS 2 FETs Figure S10 indicates the I DS -V DS characteristics of multilayer MoS 2 FETs. The channel current abruptly increased in the high V DS regimes (reversible current multiplication) where the E CR were 0.92 MV/cm and 1.96 MV/cm for device 1 and device 2 with multilayer MoS 2, respectively. And then the current dropped sharply, which indicates a permanent breakdown. These are consistent with the results shown in Figure S10. The difference of the E CR between device 1 and 2 is attributed to the different bandgap energy, i.e., difference of MoS 2 thicknesses. (a) Device 1 V GS = 0 V Length = 2.5 μm Number of layers = 72 E CR =0.92 MV/cm 50 I DS (μa)100 I DS (μa) (b) Device V GS = 0 V Length = 6.6 μm Number of layers = 15 E CR =1.96 MV/cm V DS (V) V DS (V) Figure S10. The output curve exhibiting permanent electrical breakdown in high V DS. 12

13 9. Optical and SEM images before and after permanent device failures by Joule heating Figure S11 shows the optical and SEM images after permanent device failures by Joule heating. All the failures occurred at the interfaces between MoS 2 channel and electrodes (i.e., contact regions), not in the MoS 2 channel. Figure S11. Optical and SEM images of before and after permanent device failures by Joule heating. 13

14 10. The electrical breakdown of MoS 2 FET in air and vacuum Figure S12 shows the representative output curves (I DS V DS ) measured in air and in vacuum. In vacuum, the saturated current increased by removing moisture and oxygen molecules on MoS 2, and avalanche breakdown was observed at the higher E-field. The adsorbed air molecules damp down the vibration of the out of plane phonons, which leads to reduced energy loss by electron-phonon scattering. Therefore, avalanche breakdown can occur at lower V DS, i.e., lower E CR in GS = 0 V I DS (µa) vacuum air V DS (V) Figure S12. The output curve indicating electrical breakdown in air and vacuum. 14

15 11. The resistivity and E CR values of MoS 2 FETs Figure S13 shows the resistivity and E CR values of bilayer MoS 2 FETs (4 devices). Although they exhibited the variation over two orders of the channel resistivity, similar E CR values were observed with an averaged value of 2.62 MV/cm and the small standard deviation value of 0.44 MV/cm. Optical images for each FETs are included in inset (scale bar = 3 µm). This result supports that the reversible electrical breakdown was not dominantly affected by the presence of defects and adsorbates on MoS 2. Figure S13. The resistivity and E CR values for 4 different MoS 2 FETs. 15

16 12. The electrical and thermal parameters for the thermal simulation Table S2. The electrical and thermal parameters for the thermal simulations. 16

17 13. Calculated peak temperature at MoS 2 channel and contact region Figure S14 shows the calculated temperatures at the channel region and the contact region with increasing I DS. The thermal simulations were conducted on two different multilayer MoS 2 FETs, one is the device presented in Figure 2b (labeled 1) and the other is MoS 2 FET #1 indicated in Table S1 having a contact resistance value of 160 kω and 4.89 kω, respectively. The peak temperatures at the channel and contact regions drastically increased as I DS increases over 10 µa and 100 µa for the MoS 2 FETs having high- and low-contact resistances, respectively. If I DS increases over 1 ma as with the result of previously reported results, S8 the temperature could be also drastically increased (Figures S14a and 14b) in our model regardless of the contact resistance, and it obviously will cause the permanant device failure. In our experiments, we fixed V GS (V GS = 0 V and V GS = 10 V for our MoS 2 FETs with high- and low-contact resistance, respectively) to limit the channel current for preventing the permanent device failure. So, the actual I DS values were 1.80 µa and 25.2 µa when the avalanche multiplication observed for each FET, which are marked as dashed lines in Figures S14a and S14b. At I DS of 1.80 µa and 25.2 µa, small increases in the temperature at the MoS 2 channel below 3 K and 7 K for each FET were calculated. The 2D simulation results for these two FETs show the heat distribution generated by Joule heating (I DS of 1.80 µa and 25.2 µa) in the MoS 2 FET structures reflecting real geometrical parameters. Please note that the generated heat was mainly localized on the MoS 2 channel rather than the contact regions due to the higher resistance and poor heat dissipation ability in MoS 2 channel. 17

18 Figure S14. Calculated peak temperature at the MoS 2 channel and contact region versus the channel current at fixed R contact, and 2D simulation result in the two different devices. Figures S15a and S15b show the thermal simulation results indicating the temperature variation at the contact region with changing the contact resistance from from 0.1 kω to 1 MΩ (The extracted contact resistances of 160 kω and 4.89 kω are marked as dashed lines). Even though the contact resistance increased up to 1 MΩ in the thermal simulation, the temperature at the contact regions was below 295 K that means the temperature increment at the contact region was below 2 K due to the much higher channel resistance (43.6 MΩ and 2.27 MΩ) regardless of I DS in our FETs (1.80 µa and 25.2 µa). Therefore, the contact resistance in our study cannot affect the significant temperature increments due to the high channel resistance. 18

19 Figure S15. Calculated peak temperature at contact region versus the contact resistance at fixed I DS. 19

20 14. The heat distribution of MoS 2 FET simulated by COMSOL Multiphyscis 20

21 Figure S16a indicates the calculated peak temperatures of MoS 2 FET in air and in vacuum. Due to the inefficient heat dissipation in vacuum, the peak temperature at both contact and channel regions in vacuum was slightly higher than those calculated in air. The heat generated by Joule heating also increased the peak temperature of contact regions, but it could not be efficiently dissipated in vacuum resulting the higher temperature at the contact regions compared to that calculated in air. Therefore, the temperature difference between the contact region and the channel region was relatively smaller in vacuum compared to the case in air (Figure S16a). For the further clear understanding, we performed the simulation with the fixed temperature boundary condition at the contact region ( K), as shown in Figure S16b. The result (Figure S16b) indicates that the temperature increment at the channel region was slightly higher in vacuum. This is because the thermal energy can be dissipated through the interactions with neighboring atoms and molecules in air while that should be dissipated via thermal radiation in the form of electromagnetic radiation in vacuum, leading to the relatively poor heat dissipation ability in vacuum. 21

22 Figure S16. The heat distribution of MoS 2 FET (a) in steady state and (b) with the fixed temperature condition at the contact regions. 22

23 15. AFM images of before and after avalanche breakdown Figure S17 shows AFM images before and after the reversible avalanche breakdown. The surface roughness values of the MoS 2 channel area marked with a red box before and after avalanche breakdown were 1.59 nm and 1.25 nm in peak-to-valley, 0.17 nm and 0.19 nm in RMS, respectively (in a scan size of 2 µm 2 µm). This small difference of the average roughness value indicates that the electrical breakdown induced by avalanche multiplication do not affect morphological characteristics of MoS 2. Figure S17. AFM images of before and after avalanche breakdown. 23

24 16. The V EB and E CR values versus V GS V EB (V) E CR (MV/cm) V GS (V) 1 Figure S18. The V EB where the electrical breakdown occurred and corresponding E CR values as a function of the gate voltages. 24

25 17. Gate bias effect on avalanche multiplication Figure S19 shows the gate bias dependence of carrier concentration n (black symbols) and I DS / V DS (blue symbols). The carrier concentration was calculated by using the formula = =, where C Gate is the capacitance of the SiO 2 dielectric layer and e is the elementary charge. n (x10 12 cm 2 ) V GS (V) ΔIDS /ΔV DS (μa/v) Figure S19. The carrier concentration n and the amount of variation of channel current by unit drain voltage change ( I DS / V DS ) as a function of gate bias. 25

26 18. Representative avalanche multiplication in the output curves of MoS 2 FETs having a different thickness (a) 3 GS = 0 V I DS (μa) Electric field (MV/cm) (c) Trilayer GS = 0 V 5 I DS (na) (b) (d) 40 GS = 0 V Electric field (MV/cm) GS = 0 V 2.4 I DS (na) Electric field (MV/cm) I DS (μa) Electric field (MV/cm) Figure S20. Avalanche multiplication for (a) monolayer, (b) bilayer, (c) trilayer, and (d) multilayer (11 nm) MoS 2 FETs. 26

27 19. Comparison of E CR values in our work with those of other studies Figure S21. Comparison of E CR values in our work with those of other studies. 27

28 20. Derivation of impact ionization rate (α) The additional current generated by avalanche multiplication can be written as =, (S1) where is the current density in a two-dimensional (2D) semiconductor, is the electron (hole) concentration, and is the drift velocity of electron (hole). Assuming that additional electron-hole pairs are generated by only electron, ( ) S12, = =. (S2) After substituting eq. (S2) in eq. (S1), integrating over the channel length (L) to calculate the total additional current, and using the current in a 2D semiconductor equation we obtain = =, (S3). (S4) For a uniform electric field ( = ), and, eq. (S4) can be simplified to =, (S5) where was calculated = (I sat is the saturated drain-source current and W is the channel width). Therefore, the α values for MoS 2 FETs can be extracted by investigating the relationship between the current density and time. 28

29 21. Electrical characteristics of MoS 2 FET under various temperatures Figure S22 show the transfer curve of a multilayer MoS 2 FET in the temperature range from 80 K to 400 K (measured at V DS = 0.1 V). Inset shows the output curve at V GS = 0 V measured in the temperature range from 80 K to 400 K. I DS (μa) V DS = 0.1 V I DS (μa) 12 V GS = 0 V 400 K 300 K 250 K K 0 80 K V DS (V) V GS (V) Figure S22. Electrical characteristics of a multilayer MoS 2 FET in the temperature range from 80 K to 400 K. 29

30 22. Impact ionization rate (α) under various temperatures Figure S23 shows the α values versus 1/E under various temperatures ranging from 80 K to 400 K. The α values decreased significantly as temperature increased, which is attributed to increased electron-phonon scattering leading to the energy loss for avalanche multiplication E (10 5 V/cm) K 150 K 200 K 250 K 300 K 400 K α(cm 1 ) /E(10 6 cm/v) Figure S23. The α value versus 1/E characterized in the temperature range from 80 K to 400 K. 30

31 References S1. Ghibaudo, G. New Method for the Extraction of MOSFET Parameters. Electron. Lett. 1988, 24, 543. S2. Choi, S. J.; Bennett, P.; Takei, K.; Wang, C.; Lo, C. C.; Javey, A.; Boker, J. Short-Channel Transistors Constructed with Solution-Processed Carbon Nanotubes. ACS Nano 2013, 3, 798. S3. Chang, H.-Y.; Zhu, W.; Akinwade, D. On the Mobility and Contact Resistance Evaluation for Transistors Based on MoS 2 or Two-Dimensional Semiconducting Atomic Crystals. Appl. Phys. Lett. 2014, 104, S4. Gu, X.; Li, B.; Yang, R. Layer Thickness-Dependent Phonon Properties and Thermal Conductivity of MoS 2. J. Appl. Phys. 2016, 119, S5. Cheiwchanchamnangij, T.; Lambrecht, W. R. L. Quasiparticle Band Structure Calculation of Monolayer, Bilayer, and Bulk MoS 2. Phys. Rev. B 2012, 85, S6. Peng, B.; Zhang, H.; Shao, H.; Xu, Y.; Zhang, X.; Zhu, H. Thermal Conductivity of Monolayer MoS 2, MoSe 2, and WS 2 : Interplay of Mass Effect, Interatomic Bonding and Anharmonicity. RSC Adv. 2016, 6, S7. Haynes, W. M. CRC Handbook of Chemistry and Physics 97th edu; CRC Press S8. Yalon, E.; McClellan, C. J.; Smithe, K. K. H.; Rojo, M. M.; Xu, R. L.; Suryavanshi, S. V.; Gabourie, A. J.; Neumann, C. M.; Xiong, F.; Farimani, A. B.; Pop, E. Energy Dissipation in Monolayer MoS 2 Electronics. Nano Lett. 2017, 17, S9. Liu, H.; Neal, A. T.; Ye, P. D. Channel Length Scaling of MoS 2 MOSFETs. ACS Nano 2012, 6, S10. Yoon, Y.; Ganapathi, K.; Salahuddin, S. How Good can Monolayer MoS 2 Transistors be?. Nano Lett. 2011, 11,

32 S11. Zhang, F.; Appenzeller, J. Tunability of Short-Channel Effects in MoS 2 Field-Effect Devices. Nano Lett. 2015, 15, S12. Lee, C. A.; Logan, R. A.; Batdorf, R. L.; Kleimack, J. J.; Wiegmann, W. Ionization Rates of Holes and Electrons in Silicon. Phys. Rev. 1964, 134, A