Rapid, non-destructive evaluation of ultrathin WSe₂ using spectroscopic ellipsometry

Transition metal dichalcogenides (TMDs) with a formula of MX₂, where M is the transition metal and X is the dichalcogenide (i.e., MoS₂, WS₂, and WSe₂) are of particular interest for electronic^1–5 and optoelectronic^6,7 devices. This is because TMDs have a variety of properties applicable to such devices, including the transition from an indirect to direct gap as the material is thinned to a single atomic layer.^8–10 Recently, the TMD tungsten diselenide (WSe₂) has attracted increasing attention due to its high current on/off ratios¹¹ and bandgap (1.66 eV) at the monolayer limit.^3,11 Therefore, the development of techniques that rapidly, and non-destructively evaluate the properties of these films are vital to the advancement of WSe₂ in optoelectronic applications.

The importance of finding non-destructive methods to accurately measure TMD film properties (thickness, refractive index, extinction coefficient, and bandgap) is critical when considering these materials for device layers. However, the optical properties including the refractive index (n) and extinction coefficient (k) have not been reported for WSe₂ films less than 30 nm thick.¹² Utilization of spectroscopic ellipsometry (SE)¹³ enables non-destructive measurements of film thickness, optical constants, and band structure by monitoring the change in polarized light upon light reflection on a sample as a function of wavelength. Recently, SE has been used to determine the optical properties of graphene,^14,15 SnS,¹⁶ and MoS₂,¹⁷ but SE characterization of the optical properties for ultra-thin WSe₂ has not been reported. Here, we report the optical properties of ultra-thin WSe₂ films (2–35 nm) grown via metal-organic chemical vapor deposition.

Tungsten diselenide was synthesized via chemical vapor deposition (CVD) using tungsten hexacarbonyl (W(CO)₆) and dimethylselenide (DMSe) as the tungsten (W) and selenium (Se) precursors, respectively. Sapphire substrates were prepared by sonication for 5 min in acetone, and iso-propanol followed by a DI rinse and soak in Nanostrip®, a stabilized mixture of sulfuric and hydrogen peroxide, for 20 min at 80 °C. A final DI rinse and nitrogen blow-dry was carried out prior to loading the samples into a vertical, water cooled, cold wall CVD system. Samples were grown in a hydrogen ambient at a pressure of 100 Torr and total flow of 100 sccm using a Se:W ratio of 27. Substrates were synthesized at temperatures of 500–700 °C heated at 80 °C per min for growth times of 5–30 min to obtain various film thicknesses. The variation in growth temperature and time allowed for growth of different film thicknesses. Films were characterized via Raman spectroscopy, SE, field emission scanning electron microscopy (FESEM), and atomic force microscopy (AFM). Raman characterization of the WSe₂ films were accomplished using a WiTEC confocal Raman system with a 633 nm excitation wavelength. AFM measurements were carried out on a Dimension DI 3100 using tapping mode to obtain morphology and film thickness (Figure 1). Spectroscopic ellipsometry of the WSe₂ thin films were measured using a M2000 SE instrument by J.A. Woollam Co. with a wavelength range of 200–1000 nm, using an angle of incidence of 75° and a rotating compensator. Spectroscopic ellipsometry measurements were fit using CompleteEASE 5.0 by J.A. Woollam Co., taking into account surface roughness of the WSe₂ films.¹³ 

In a multiple layered structure, such as the work presented here, it is important to define the optical response of the underlying sapphire substrate in order to minimize optical correlation effects between layers and to more accurately estimate values for the optical constants and thickness of the WSe₂. Therefore, SE spectra of bare sapphire (Al₂O₃) substrates were first measured and found to fit previously reported index of refraction as function of wavelength for sapphire.¹⁸ The optical properties of the WSe₂ were subsequently extracted from SE measurement of the amplitude ratio [psi (Ψ)] and difference in phase [delta (Δ)] of the p and s polarized components of the reflected light. The ratio rho (ρ) is measured by SE and defined as¹³ 

where r_p and r_s are the amplitude and reflection coefficients for the p-polarized and s-polarized light, respectively.¹³ 

To extract the optical properties of the WSe₂ layer, a two layer model structure was created with the unknown WSe₂ thin film on a known sapphire substrate. The surface roughness of the WSe₂ film was accounted for in the model by mixing the optical constants of the WSe₂ layer with the optical constants of a “void” where n = 1 and k = 0. The Bruggeman Effective Medium Approximation (EMA Model)¹³ is used to calculate the effective optical constants of this mixed layer. The n and k for WSe₂ is fit to the Gen-Osc model consisting of Psemi-MO and Psemi-Tri functions, which are a subset of the more general Herzinger-Johs Parameterized Semiconductor Oscillator function.¹³ More information on the Psemi fit parameters are presented in the supplementary material.¹⁹ The fitting parameters of the WSe₂ oscillators were refined until the best fit between the experimental and simulated spectra was achieved, where the mean squared error (MSE) provides guidance on the goodness of fit of the model to the experimental data.¹³ The Levenberg-Marquardt nonlinear regression algorithm minimizes the MSE during the fitting process.¹³ Film thickness and roughness values were then extracted along with the optical constants n and k. Finally, the optical bandgap values for various thickness films were then calculated based on the extracted k values.

Films grown using MOCVD in this work result in nanocrystalline WSe₂. While the films are nanocrystalline, such films are favored for applications requiring ultra-low thermal conductivity.²⁰ Atomic force microscopy of a thin 2.8 nm WSe₂ film (Fig. 1(a)) and 23 nm WSe₂ (Fig. 1(b)) reveal nanometer-scale islands rising approximately 13 nm above the film surface. The root mean squared (rms) roughness of the sample for a 2 × 2 μm area varied from 0.65 nm for a 2.8 nm film to 8.5 nm for the 23 nm film. Figure 1(d) shows the Raman spectra as a function of sample thickness. As can be seen, the in-plane (E_2g) and out-of-plane (A_1g) vibrational modes are difficult to separate for films 2.8–23 nm with a heavily convoluted peak ranging from 256–260 cm⁻¹, respectively; and only slight separation of the E_2g (254 cm⁻¹) and A_1g (259 cm⁻¹) peak for a WSe₂ film measuring 1.3 nm. While the trending in peak fits do appear to evolve with thickness, nanoscale variations (i.e., defects, strain) in film properties lead to non-uniform results when attempting to correlate Raman with thickness of these nanocrystalline films. As a result, the process of determining layer thickness via Raman, such as that reported for MoS₂ and WS₂,²¹ is not favorable in the current WSe₂ films. Therefore, we must utilize other techniques to non-destructively evaluate film thickness.

Utilization of spectroscopic ellipsometry provides a direct route to non-destructive evaluation of WSe₂ ultra-thin films. The experimental and simulated spectra of Ψ and Δ for a 2.8 nm (Fig. 2(a)) and 23 nm (Fig. 2(b)) WSe₂ sample yield a MSE of 10 and 18, respectively. While a MSE of 1 is considered ideal, the MSE of 10 and 18 are considered good for complex samples such as those in this work. There is a discontinuity of Δ as the phase passes 270° and continues to be plotted from −90°. More spectral data for other samples (1.3, 4.3, and 8.6 nm samples) are presented in Figure S1 of the supplementary material.¹⁹ The data extracted from SE measurements can then be utilized to further understand the film characteristics of WSe₂. The measured refractive index (Fig. 2(c)) and extinction coefficient (Fig. 2(d)) of MOCVD WSe₂ films indicate that the optical constants for ultra-thin films does not vary significantly with thickness down to an equivalent thickness of two monolayers, but are heavily dependent on wavelength. This phenomenon is similar to MoS₂,¹⁷ and the small variation between samples results from the changes in Ψ. The variation in Ψ from 2.8 nm (Fig. 2(a)) and 23.9 nm (Fig. 2(b)) with incident wavelength shows distinct changes in the behavior of Ψ, and thus n.¹³ This is likely related to an evolution of strain in the film with thickness, which can lead to strong modifications in the polarization of light, and thus the Ψ parameter.⁷ The refractive index as a function of wavelength is typical for semiconducting materials, and is a result of the dispersion in the material.¹³ The extinction coefficient for WSe₂ (Fig. 2(d)) shows peaks at 755 nm, 562 nm, 437, and 376, respectively which correspond to the A, A^′/B, B^′ band transitions due to splitting of the ground and excited states in the WSe₂ electronic structure.^12,22 Higher energy peaks are also observed at 388 nm and 251 nm, labeled as C and E, which arise from the optical transitions between the density of states peaks in both conduction and valence bands.^12,22 The extracted thickness values from modelling the n and k of WSe₂ are: 1.3 nm, 2.8 nm, 4.3 nm, 8.6 nm, and 23.9 nm for each film; which is in excellent agreement (<9% error) with AFM measurements (Fig. 1(c)).

Finally, the optical bandgap can be experimentally extracted from the optical absorption coefficient (α) using the known wavelength (λ) and measured extinction coefficient k:¹³ 

The absorption coefficient (α) is also related to the photon energy by¹³ 

where K is a constant, hυ is the incident photon energy, E_g is the optical bandgap, and m is a number characterizing the transition process.¹³ The bandgap transition type (direct or indirect) dictates the value of m, where m equals 1/2 for a direct transition or 2 for an indirect transition. In this case, the WSe₂ films grown are multilayer WSe₂, which is predicted to be indirect bandgap semiconductor,¹³ resulting in m = 1/2. Rearranging Eq. (3), and plotting (αhυ)^1/2 versus hυ, provides a facile means to extract E_g. A fit is applied to the linear part of the plot (Fig. 3(a)), and extended to (αhυ)^1/2 = 0, where hυ = E_g; E_g is then extracted and correlated to sample thickness (Fig. 3(b)). Additional spectra are presented for remaining samples in (Fig S1) of the supplementary material.¹⁹ Clearly evident, is the strong correlation of film thickness with E_g, where E_g continually increases from 1.2 eV for bulk WSe₂ to 1.55 eV as the films reduce in thickness to an equivalent thickness of two atomic layers.²³ This data trends closely to that expected by theory,⁵ and recent data published for mechanically exfoliated WSe₂ (Fig. 3(b), inset).²⁴ The difference in indirect bandgap 1 and indirect bandgap 2 on the plot arises from a shift in the conduction band minimum points so that recombination occurs at either the K or the Λ point in momentum space.²⁴ 

In summary, spectroscopic ellipsometry was used to non-destructively characterize ultra-thin WSe₂ films grown via chemical vapor deposition. The excellent agreement between AFM and SE measurements demonstrates that SE is a universal method to not only evaluate optical properties of 2D materials, but to also non-destructively extract layer thickness. SE is capable of directly correlating the optical properties with thickness, and provides a means to understand the optoelectronic evolution of 2D layered materials from bilayer to bulk without modification of film properties.

This work was supported in part by the Center for Low Energy Systems Technology (LEAST), one of six centers of STARnet, a Semiconductor Research Corporation program sponsored by MARCO and DARPA.