Direct band gap hierarchy in doped MoS2 thin films

M. Gaither-Ganim, H. Samassekou, D. Mazumdar Department of Physics, University of Southern Illinois, Carbondale, Illinois 62901, USA ���

(August 1, 2015)

Molybdenum disulphide (MoS2) is a unique semiconductor due to its transition from an indirect to a direct band gap system when its dimensionality is reduced from three to two.1 Although the 1.2 eV indirect transition defines the fundamental band-gap in a 3D structure, the 1.8 eV direct gap is also predicted from theoretical calculations.2 Using various optical spectroscopy techniques we report here the various band gaps of 3D MoS2and Nb-doped MoS2. We find that the 1.8 eV direct gap is preserved irrespective of the film thickness implying that this transition is largely insensitive to disorder. We also find spectroscopic evidence of a higher 2.3 eV band gap which from theory can be assigned to a Gamma point transition.2 This direct band gap hierarchy is also verified by modeling the optical constants of MoS2. The values are slightly lower in Nb-doped MoS2, which is also consistent with theoretical predictions.9,10,13

   

Introduction Research in two-dimensional materials has

taken huge leaps ever since the discovery of graphene in 2004 by Geim and Novasolov.3 This discovery won them the 2010 Nobel Prize in Physics. Apart from intellectual advancement, intense activity in the field is fueled by the fact that these materials show exceptional room temperature properties such as high electrical conduction and mechanical functions.4 Graphene, however, suffers from the drawback that it is a zero band-gap semiconductor, making it an inefficient material for micro-electronic devices.4 Thankfully, a number of other 2D materials have been discovered since graphene with a band-gap higher than 1 eV. MoS2 is one such candidate.

Even though bulk 3D MoS2 is a popular dry lubricant, it was only recently shown that 2D MoS2 can be realized experimentally, and has quite distinct properties compared to 3D MoS2.1 The most notable is the fact the band-gap character of MoS2 changes from indirect to direct as a perfect 2D layer is achieved. Direct band-gap systems are preferred over indirect ones, as they will make efficient optoelectronic devices.

In this work we experimentally investigate the direct band-gaps of 3D MoS2 fabricated in the form of thin films. Even though the lowest gap in 3D MoS2 is of indirect nature (1.2 eV indirect versus 1.8 eV direct), theoretical calculations show that the 1.8 eV direct-gap is preserved irrespective of the number of MoS2 layers.2 This feature makes it easier to investigate such direct-gaps. Combining absorprtion spectroscopy and ellipsometry we show that the 1.8 eV direct-gap is insensitive to disorder and also provide

evidence for a 2.3 eV higher direct gap. Comparing with theoretical report, we assign the 2.3 eV gap to a Gamma point transition. This gap hierarchy is not unusual and has been reported on other complex thin film materials.5 Methods

I. Physical Vapor Deposition – Sputtering MoS2 and Niobium-doped MoS2 thin films were sputtered under high vacuum conditions (~2x10-6 Torr) utilizing both DC magnetron sputtering (on Niobium target) and RF magnetron sputtering (on MoS2 target) simultaneously. Argon is used as the process gas and is introduced into the chamber at 5mTorr during sputtering sessions. All samples were prepared on glass substrates at 310° to 340° Celsius and with 50 Watts of RF bias on the MoS2 target. Different doping concentrations were produced by varying DC bias on the Niobium target while film thickness was varied by sputtering for different lengths of time. The samples presented in this analysis include a ~20 nm MoS2 film (sputtered for 10 minutes), a ~120 nm MoS2 film (sputtered during five 10-minute sessions), and a ~120 nm Nb-doped MoS2 film (same as above) sputtered with 30 Watts DC bias on the Niobium target.

II. Absorption Spectroscopy

Optical absorption measurements were performed on each sample using a Hach DR/4000U spectrophotometer and scanning over wavelengths in the ultraviolet and visible range. This form of spectroscopy measures the complex portion of the refractive index, k, by the relation:

𝛼 = !!"!

(1) where λ is the wavelength in centimeters of the incident light, α is the absorption coefficient, and k is the extinction coefficient. Direct band-gap values were extracted from the resulting absorption data by plotting (𝛼𝐸)! vs. 𝐸 where 𝐸 = ℎ𝜈 is the incident photon energy.

III. Spectroscopic Ellipsometry

Samples were then characterized with variable angle spectroscopic ellipsometry. Measurements were taken with a J. A. Woollam Co. M-2000V ellipsometer and corresponding WVASE32 software6 also designed by the company. Experimental data was primarily collected in the form of the optical constants forming the complex refractive index:

   𝑛 =  𝑛!  +  𝑖𝑘 (2) where 𝑛! is the real part such that 𝑣   =  𝑐/𝑛! with c being the speed of light in a vacuum and k being the afore mentioned extinction coefficient.12

Data was collected at 65°, 70°, and 75° angles of incidence for each sample, and a spectroscopic scan over the visible range was performed at each angle. Optical constants were modeled for some samples using Cauchy, Lorentz, and Tauc-Lorentz oscillators. Mean Squared Error (MSE) was minimized to gauge the quality of fit for each model.7 Once again, (𝛼𝐸)!

vs. 𝐸 direct gap analysis was conducted and compared against values obtained from absorption spectroscopy as well as theoretical literature values for bulk MoS2.2 The nature of our direct gap analysis carries a margin of error of ± 0.1 eV for all gap values. Results

Direct gap analysis of absorption spectroscopy data is presented in Figure 1. The 1.7 eV energy gap for 20 nm un-doped yields MoS2 the well-known direct gap value for bulk MoS2.1,2 The 120 nm un-doped sample, however, displays a larger direct gap at 2.4 eV and no smaller gap at 1.8 eV. We expect that the nature of the absorption edge in this analysis obscures the features of the 1.8 eV gap in the 120 nm un-doped sample. The dotted green tangent line in Figure 1 suggests the possibility of this obscured feature. The 120 nm doped sample shows a slightly lower energy gap when compared to the un-doped sample of the same thickness. This is consistent with what we would expect to see from a sample with a low p-type dopant concentration.9,10,13

When comparing these features against the

gap analysis of the experimental ellipsometry data we find general agreement in gap values. Not only do we reconfirm the known gap of 1.7 eV, but we also reconfirm the existence of a higher direct gap transition at 2.2 eV (see Figure 2a). It should be noted that the 120 nm doped sample also exhibits both gaps but at slightly lower values (although within ± 0.1 eV of the un-doped gap values) indicating the tunable nature of these gaps though chemical doping. A model of the 120 nm un-doped experimental data using two Tauc-Lorentz oscillators further substantiates this evidence, yielding gap values of 1.4 eV (likely indirect) and 2.2 eV (see Table 1).

Figure 1. (𝛼.𝐸)! vs. 𝐸 direct gap analysis of absorption spectroscopy data for 120nm doped, 120nm un-doped, and 20nm un-doped MoS2 thin films. X-intercepts of green tangent lines indicate gap values and dotted tangent line indicates supposed obscured feature.

Figure 2. (𝛼.𝐸)! vs. 𝐸 direct gap analysis of experimental ellipsometry data at 75° angle of incidence for (a) 120 nm un-doped and (b) 120 nm doped MoS2 thin films. X-intercepts of green tangent lines indicate gap values. Note slightly lower gap values for doped than un-doped sample.

Discussion An examination of the theoretical band

structure of bulk MoS2 – calculated by Kuk et al2 using first principal Density Functional Theory (DFT) calculations in the scheme of PBE (Perdew-Burke-Ernzerhof) functionals – reveals a strong candidate for a 2.3 eV direct-gap transition at the Gamma point of the Brillouin Zone (see Figure 3). Should this direct-gap transition be experimentally confirmed, a band-gap hierarchy, much like what has been found for other semiconducting materials,5 also exists for MoS2. Such a hierarchy would augment the already tunable nature of the MoS2 band structure, and could have implications for the use of MoS2 in optoelectronic devices.

Additionally, reproduction of the 1.7 eV direct gap for both 20 nm and 120 nm samples indicates the insusceptibility of this transition to disorder in the crystal, given that our 120 nm samples exhibit greater crystallinity than that of the 20 nm sample. The robustness of this gap is promising and can be relied upon without the necessity of highly ordered MoS2.

Further experimentation on a broader range of MoS2 films is required to confirm a Gamma point 2.3

eV direct gap transition. Since our optical analysis necessitated glass substrates, we were unable to anneal our samples at high temperatures, leaving them somewhat amorphous. This limited our analysis to direct gap only, since indirect gap transitions depend on phonon transitions within the lattice and are therefore dependent on lattice periodicity. Hence, future analysis should seek to reproduce results and perform indirect analyses with more crystalline films.

Our optical analysis could be improved through an examination of additional optical data garnered from spectroscopic ellipsometry and a more exhaustive modeling of optical constants. Absorption spectroscopy data could also be performed on a machine that measures reflectance (a quantity generally negligible for transparent materials), yielding a more accurate calculation for the absorbance coefficient (see Appendix). This experimental limitation may be a cause for slight discrepancies between direct gap values garnered from absorption spectroscopy those gathered from ellipsometry. It also prevented us from examining a broader range of Nb-doping concentration.

Should this direct band gap hierarchy be confirmed in MoS2, the ability to tune the Gamma point transition is the next direction of research. The behavior of this transition with respect to chemical doping, mechanical strain, or layer thickness could have important implications for the use of MoS2 in optoelectronic devices due to preferentially high symmetry at the Gamma point as compared to the K point. Summary

Optical analysis utilizing absorption spectroscopy and spectroscopic ellipsometry techniques suggests a band gap hierarchy in bulk MoS2, confirming the known experimental direct band gap of 1.8 eV and suggesting a new 2.3 eV direct gap transition at the Gamma point. Such a transition awaits further experimental validation yet holds promising implications for the already tunable band

Table 1. Direct gap values (in units of eV) for 20 nm and 120 nm un-doped MoS2 films. Values produced from theoretical DFT/PBE models2, a T-L model of experimental optical constants, and experimental values from UV-VIS absorption spectroscopy and spectroscopic ellipsometry.

Sample Direct-Gap DFT/PBE T-L Model Experimental Gaps 20 nm un-doped (KK) 1.8 -- 1.7 [from (αE)2 vs. E) plot] UV-VIS

120 nm un-doped (KK) 1.8 -- 1.7 [from (αE)2 vs. E) plot] UV-VIS 1.7 [from (αE)2 vs. E) plot] Ellip

(ΓΓ) 2.3 2.20 2.2 [from (αE)2 vs. E) plot] Ellip 2.4 [from (αE)2 vs. E) plot] U-VIS

Figure 3. Band structure of bulk MoS2 following the path ΓΜΚΓ and calculated at the DFT/PBE level. Dotted red line represents Fermi level, and arrows represent gap transitions. Image taken from Kuc et al.2 Arrow and value in red have been added to original diagram.  

structure of MoS2, which may have applications in the development of new optoelectronic devices. Acknowledgements I would like to thank the NSF for funding this REU program (DMR -1461255), and Southern Illinois University Carbondale for extending the opportunity and for hosting me. I would additionally like to thank my advisor Dipanjan Mazumdar for his mentorship and guidance through the research process, and program directors Boyd Goodson and Saikat Talapatra for making the REU program possible at SIUC.

Appendix Using an approximation of Beer’s law for highly transparent materials, the equation:

𝐼 = !!(!!!)!!!!"

!!!!!!!!" (3)

becomes 𝐼 = 𝐼!𝑒!!" (4)

when the reflectance, 𝑅, is negligible and with 𝐼, 𝐼!, 𝛼, and 𝑡 being transmitted-light intensity, incident-light intensity, the absorption coefficient, and layer thickness respectively.12

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