Crystalline Phase-Dependent Emissivity of MoSi₂ Nanomembranes for Extreme Ultraviolet Pellicle Applications

Abstract

Extreme ultraviolet (EUV) pellicles must withstand intense thermal stress during exposure due to their limited heat dissipation, which results from their ultrathin geometry and the vacuum environment within EUV scanners. To address this challenge, we investigated the crystalline phase-dependent emissivity of nanometer-thick molybdenum disilicide (MoSi₂) membranes. Membranes exhibiting amorphous, hexagonal, and tetragonal phases were independently prepared via controlled annealing, and their thermal radiation properties were evaluated using heat-load testing under emulated EUV scanner conditions. The Hall effect measurements revealed distinct variations in carrier density and mobility across phases, which were theoretically correlated with emissivity using the Lorentz–Drude model. The results demonstrate that emissivity increases in the hexagonal phase due to increased carrier density and reduced scattering, offering improved thermal radiation performance. These findings establish the phase engineering of conductive silicides as a viable strategy for enhancing radiative cooling in EUV pellicles and offer a theoretical framework applicable to other high-temperature nanomaterials.

1. Introduction

The scaling limitations of 193 nm ArF lithography led to the development of next-generation lithography technologies employing a 13.5 nm wavelength light source, referred to as extreme ultraviolet (EUV) lithography. With the implementation of EUV lithography in high-volume semiconductor manufacturing at technology nodes of 5 nm or smaller, effective contamination control within EUV scanners becomes crucial to ensuring high yield [1,2]. One key strategy for achieving such contamination control is EUV pellicle implementation. An EUV pellicle is a cover membrane that protects the EUV mask from contamination during exposure. It must be ultrathin—only tens of nanometers thick—to minimize throughput losses while maintaining stability under extreme conditions, posing significant technical challenges [3,4]. Additionally, during exposure, EUV radiation absorption increases the temperature of the pellicle membrane, resulting in thermal stress that can cause structural damage and wrinkling, leading to potential image distortion and membrane failure [5]. This phenomenon indicates the need to effectively cool the pellicle during lithography processes.

Heat dissipation in materials is primarily mediated via conduction, convection, and radiation [6]. However, the nanoscale thickness of the pellicle limits conductive heat transfer, and the high-vacuum environment within the EUV scanner considerably suppresses convective cooling, leaving radiative heat transfer as the dominant thermal dissipation pathway [7]. To improve radiation efficiency, previous studies have explored high-emissivity materials, including Ru, metal silicides, and metal carbides [8,9,10]. In particular, molybdenum disilicide (MoSi₂) has been identified as a promising EUV pellicle material due to its high EUV transmittance, low reflectance, and excellent mechanical strength [11]. As the thermal properties of MoSi₂ can be influenced by its crystalline phase, evaluating the efficiency of radiative cooling across different phases, including the amorphous, hexagonal, and tetragonal phases, is crucial for its effective implementation in EUV pellicle applications [12,13].

In this study, the influence of the crystalline phase of MoSi₂ on its thermal radiation efficiency was systematically investigated. Phase-dependent and phase-induced variations in charge carrier density were quantitatively analyzed to evaluate their impacts on emissivity. The observed relationship was then theoretically validated using the Lorentz–Drude model, confirming the underlying mechanism driving changes in emissivity. Based on the results, the optimal crystalline phase for maximizing the thermal emissivity of MoSi₂-based EUV pellicles is proposed.

2. Materials and Methods

2.1. Sample Fabrication and Analysis

The MoSi₂/SiN_x pellicle composite fabrication process is illustrated in Figure 1. First, a 60 nm silicon nitride layer was deposited on a silicon wafer via low-pressure chemical vapor deposition at 820 °C using dichlorosilane (SiH₂Cl₂) and ammonia gas. Photolithography and reactive-ion etching were then employed to form a backside window. Subsequently, wet etching was carried out in a 30% potassium hydroxide solution at 60 °C, followed by a cleaning process, resulting in a 10 mm × 10 mm free-standing SiN_x membrane. The 20 nm MoSi₂ layer was deposited onto the membrane using the co-sputtering method, with substrate heating performed at 400 °C to enhance the film density. The MoSi₂/SiN_x composite pellicle was crystallized using the rapid thermal annealing (RTA) system at 600 and 900 °C.

In this study, transmission electron microscopy (TEM) was used to measure the thicknesses of MoSi₂ films subjected to different annealing temperatures. The crystalline phase transitions of the thin MoSi₂ films were characterized using X-ray diffraction (XRD). Based on the measured film thickness results, Hall effect measurements were employed to determine the resistivity, carrier density, and mobility of the films. For Hall effect measurements, five independent thin-film samples were prepared and measured for each annealing condition. Unless otherwise specified, the reported values represent the average across these five films, and the error bars indicate root-mean-square (RMS) deviations.

2.2. Heat-Load Test

A heat-load tester, as illustrated in Figure 2, was used to evaluate the emissivity of the crystallized MoSi₂/SiN_x pellicle composite. The equipment included a vacuum chamber that maintains a pressure below 4 × 10⁻⁴ Pa to replicate the EUV scanner environment. A rotating slit mechanism was incorporated to simulate a 1:9 scanning duty cycle.

Reference [7] reported on the temperature increase caused by absorption during EUV exposure, where the pellicle was uniformly irradiated using a 13.5 nm wavelength beam shaped into a curved rectangular slit pattern. To replicate this condition, a 7 mm × 7 mm square-shaped 808 nm laser was used to irradiate the pellicle, and the emissivity was calculated based on the absorbed heat energy. The absorption at 808 nm was measured using an ultraviolet–visible spectrometer, and the pellicle temperature was monitored using a two-channel pyrometer, which operated within a range of 400–1500 °C with a ±2% accuracy. For the heat-load experiments, five independent free-standing MoSi₂/SiN_x membranes were measured under each annealing condition. The reported temperature and emissivity values represent the average of these five membranes, and the error bars correspond to RMS deviations.

3. Results and Discussion

3.1. MoSi₂ Thin-Film Characteristics According to Annealing Temperature

Figure 3 presents cross-sectional TEM images of the MoSi₂/SiN_x films in the as-deposited state and after annealing at 600 and 900 °C. The film thickness remained constant at 20 nm under all annealing conditions, indicating that crystallization did not affect film thickness. Importantly, supplementary optical simulations confirm that a 20 nm MoSi₂ membrane achieves >90% transmittance at 13.5 nm, verifying that the selected thickness is representative of application-level EUV pellicle requirements (Supplementary Figure S1). In the as-deposited state, the MoSi₂ layer exhibited an amorphous structure. Upon annealing at 600 °C, nanometer-scale crystallites began to form, while annealing at 900 °C resulted in the growth of comparatively larger crystalline grains. To further quantify this observation, AFM measurements were conducted on three independent samples under each condition. The averaged root-mean-square roughness increased slightly from 0.576 nm (as-deposited) to 0.777 nm (600 °C) and 0.939 nm (900 °C), as summarized in Supplementary Figure S2. Although this increase reflects grain coarsening at increased temperature, the absolute roughness remains well below the EUV wavelength (13.5 nm), indicating a negligible contribution to additional scattering [14]. To identify the corresponding crystalline phases, XRD analysis was conducted. As shown in Figure 4, no distinct crystalline phase was observed in the as-deposited MoSi₂ film. After annealing at 600 °C, the MoSi₂ film exhibited a hexagonal phase, while annealing at 900 °C resulted in the formation of a tetragonal phase. In addition to XRD analysis, compositional characterization was conducted using XPS depth profiling. The results confirmed a uniform Mo:Si ratio close to 1:2 across the film depth, consistent with the expected stoichiometry of MoSi₂ (Supplementary Figure S3)_.

3.2. Dependence of the MoSi₂ Crystalline Phase on the Electrical Characteristics of Materials

The crystalline phase of a material intrinsically determines its band structure by defining the lattice symmetry and atomic arrangement. Phase transitions induce band structural reconstruction, which modifies the density of states and the bandgap. These electronic changes directly affect carrier density and activation, which subsequently influence the scattering mechanisms within the material. As emissivity is governed by both electron–electron and electron–phonon interactions, it is also sensitive to variations in carrier behavior [15,16].

To investigate this relationship, Hall effect measurements were performed on the MoSi₂ thin films subjected to different annealing temperatures. As shown in Figure 5a, the resistivity progressively decreased from 2186 (as-deposited) to 1625 (600 °C) and 1552 μΩ·cm (900 °C), indicating enhanced electrical conductivity at increasing annealing temperatures.

The origin of this trend was further investigated through carrier density and mobility measurements, as illustrated in Figure 5b. In the as-deposited amorphous state, electrons were identified as the majority carriers, with a carrier density of 3.75 × 10²² cm⁻³ and a mobility of 0.075 cm²/V·s. Although MoSi₂ typically exhibits p-type behavior in its crystalline form, the presence of delocalized states and nanocrystallites in the amorphous phase could support electron-dominated conduction through various mechanisms such as hopping or multiband transport [17,18].

After annealing at 600 °C, a hexagonal phase was formed, and holes became the majority carrier type. The carrier density increased to 7.26 × 10²² cm⁻³, while mobility decreased slightly to 0.06 cm²/V·s. This behavior indicates enhanced carrier activation accompanied by increased carrier scattering.

Upon subsequent annealing at 900 °C, the tetragonal phase emerged. At this stage, the hole carrier density decreased dramatically to 2.85 × 10²¹ cm⁻³, while mobility increased considerably to 1.49 cm²/V·s. This behavior indicates a reduction in scattering due to the lower carrier concentration, allowing for more efficient charge transport, thus resulting in reduced resistivity.

3.3. Effects of Carrier Density on the Emissivity of Crystallized MoSi₂

Figure 6a shows the results of a heat-load test conducted on the MoSi₂/SiN_x composite pellicle at an applied thermal power density of 1.5 W/cm². The measured average peak temperatures for the as-deposited film and the films annealed at 600 and 900 °C were 643.1, 607.7, and 728.8 °C, respectively. These temperature values were subsequently used to calculate the emissivity based on the Stefan–Boltzmann law as follows [19]:

$$\alpha ·P=ϵ·\sigma ·S·\left(T^4-T_s^4\right),$$

(1)

where α is the material’s absorption coefficient, P is the incident light power, ϵ is the emissivity, σ is the Stefan–Boltzmann constant (5.67 × 10⁻⁸ W/m²K), S is the radiating area, T is the peak temperature, and T_s is the surrounding temperature.

Figure 6b shows the correlation between emissivity, derived using Equation (1), and the square root of the carrier density. The calculated emissivity values for the as-deposited film and the films annealed at 600 and 900 °C were 0.375, 0.439, and 0.277, respectively. A comparison with the square root of the measured carrier densities revealed a consistent trend, indicating a direct correlation between the square root of the carrier density and emissivity. To validate the theoretical basis of this relationship, additional analyses were conducted on the physical parameters that govern thermal emissivity.

At several hundred degrees Celsius, thermal radiation mainly occurs in the infrared region, as described by Planck’s law. Under steady-state conditions, Kirchhoff’s law states that the emissivity of a material is equal to its absorbance at a given wavelength. Absorbance is determined by the material’s optical transmittance and reflectance, both of which depend on the refractive index (n) and the extinction coefficient (k) [20,21].

These optical constants are associated with the material’s dielectric response, which varies with frequency, described by the complex permittivity. The Lorentz–Drude model provides a framework for expressing this frequency-dependent response as follows [22]:

$$\epsilon \left(\omega \right)=1+{\epsilon }_{Drude}+{\sum }_n{\epsilon }_{Lorentz},$$

(2)

In Equation (2), the optical responses in the ultraviolet and visible spectral regions are predominantly governed via interband transitions, which are described using the Lorentz oscillator terms. In contrast, the response in the infrared region is dominated by the intraband transitions of free carriers and is characterized using the Drude term. Given that MoSi₂ is a conductive material with a relatively high carrier density, its optical response in the infrared region can be approximated using only the Drude term as follows:

$${\epsilon }_{Drude}\left(\omega \right)={\epsilon }_{\infty }-{\displaystyle \frac{{\omega }_p^2}{-{\omega }^2-i\frac{\omega }{\tau }}},$$

(3)

where the plasma frequency ${\omega }_p$ is defined as

$${\omega }_p=\sqrt{{\displaystyle \frac{n{e}^2}{{\epsilon }_0{m}_e^{\ast }}}},$$

(4)

where n is the carrier density, $\mathrm{e}$ is the elementary charge, ${\epsilon }_0$ is the vacuum permittivity, and $m_e^{\ast }$ is the carrier effective mass.

The extinction coefficient $\mathrm{k}$, which characterizes the imaginary component of the complex refractive index in the infrared region, can be approximated from the complex permittivity (${\mathsf{\epsilon }}_1+\mathrm{i}{\mathsf{\epsilon }}_2$) as follows [23]:

$$k\approx {\displaystyle \frac{1}{2}}\left|{\displaystyle \frac{{\epsilon }_2}{{\epsilon }_1}}\right|\sqrt{\left|{\epsilon }_1\right|}, ({\epsilon }_1>0),$$

(5)

$$k\approx \sqrt{\left|{\epsilon }_1\right|}\hspace{1em}\hspace{1em}({\epsilon }_1<0),$$

(6)

According to these relations, $\mathrm{k}$ is proportional to the square root of ${\omega }_p$, which, in turn, is proportional to the square root of the carrier density. As the emissivity is governed by $\mathrm{k}$, it is directly affected by the carrier density.

The crystallization of MoSi₂ modifies its band structure, thereby altering the carrier density and inducing a shift in the plasma frequency, as described in Equation (4). These shifts lead to variations in emissivity. It should be noted that the applicability of the Lorentz–Drude model to explain phase-dependent emissivity is particularly relevant for metal silicides and related intermetallic compounds, where phase transitions can substantially alter carrier density and electronic structure. In contrast, for pure metals with intrinsically high and relatively invariant carrier densities, phase transitions are expected to have only a minor impact on the free-carrier contribution; thus, the model’s explanatory power is limited. Nevertheless, uncertainties may arise from factors such as grain boundary scattering, effective mass assumptions, and the coexistence of multiple phases that should be considered when interpreting the quantitative accuracy of the model [9].

Consequently, the emissivity of MoSi₂ thin films is phase-dependent and exhibits a strong correlation with the square root of the carrier density. These findings confirm that emissivity modulation originates from the structural phase transition and establish that the carrier density is a crucial design parameter for materials intended for use in high-temperature radiative environments.

4. Conclusions

In this study, the relationship between the carrier density and emissivity in MoSi₂ nanomembranes was experimentally investigated as a function of the crystalline phase. The results were theoretically validated based on the Lorentz–Drude model. Phase transitions of the membrane film were induced through controlled annealing processes, and corresponding changes in their resistivity were observed. These resistivity variations were attributed to changes in carrier density and mobility within the MoSi₂ thin films.

To experimentally verify the influence of carrier density on emissivity, heat-load tests were conducted under conditions designed to emulate the EUV scanner environment. Emissivity trends, analyzed within the Lorentz–Drude framework, confirmed the correlation between the electrical and radiative properties. Although the experiments were performed on coupon-sized membranes (10 mm × 10 mm) due to fabrication constraints, the observed trends represent an important step towards the development of full-size EUV pellicle. When scaled to full-size pellicles, however, additional factors such as stress distribution across the membrane, interfacial mismatch with supporting border, and fabrication-induced defects may influence emissivity. These aspects highlight the need for further investigation to establish scalability and reproducibility under practical manufacturing conditions.

These findings demonstrate that the hexagonal phase in MoSi₂ enhances emissivity, thereby improving the thermal radiation efficiency and ensuring greater thermal stability in EUV pellicle applications. Furthermore, the theoretical framework established in this study can be extended to other metal silicide materials, highlighting its broader applicability.

Compared with conventional pellicle materials such as SiN_x, Ru, and metal carbides, phase-engineered MoSi₂ membranes provide enhanced radiative cooling efficiency while maintaining high EUV transmittance. Nevertheless, challenges remain with regard to oxidation resistance, hydrogen radical durability, and scalability for full-size pellicle fabrication, warranting further study.