2.1.

Basic Concept

In 1988, a team of Massachusetts Institute of Technology (MIT) proposed to improve the imaging of x-ray lithography by using an absorber that produces a $\pi$-phase shift in addition to about 10 dB attenuation.¹⁹ The higher local image contrast of attPSM relies on the destructive interference of light that passes through the clear openings of a mask with $\pi$-phase shifted light, which is transmitted through the semi-transparent absorber covered areas of this mask. Following Terasawa et al.,²⁰ Fig. 1 explains the concept of an attPSM by a comparison with a binary mask. The binary mask consists of a transparent substrate and the chromium absorber that completely blocks the light in the nominally dark areas. In the Kirchhoff approach (thin-mask model), the amplitude of the transmitted light directly below the mask exhibits a sharp jump from zero (chromium covered area) to a finite positive value in the open area of the mask. The diffraction limited projection lens generates a blurred intensity distribution at the wafer. The absorber of the attPSM on the right of Fig. 1 consists of a thinned (halftone) chromium layer, which transmits a part of the light, and a transparent layer, which shifts the phase of the transmitted light. The thicknesses of the chromium and shifter are chosen to produce a phase shift of $\pi$, which causes a flip of the sign of the amplitude of the transmitted light. The amplitude of the transmitted light directly below the mask jumps between a small negative value in the absorber-covered area and a larger positive value in the open area. The resulting image of the attPSM is impacted by the diffraction as well. However, the destructive interference of light from the absorber and open area, respectively, causes a minimum intensity between these areas and increases the slope of the bright spot below the open area. In lithographic terms, it increases local contrast, NILS, and exposure latitude. Similar explanations can be found in other early publications on attPSM by Lin,²¹ and Buck and Rieger²² as well.

Fig. 1

Conceptual explanation of attPSM (right) in comparison to a binary mask (left). Adapted from Terasawa et al.²⁰

Figure 2 presents simulated images of an isolated 180-nm-wide slit for varying intensity transmission $T$ of the absorber. To visualize the impact of $T$ on the shape of the central intensity peak, the image cross-sections on the left of the figure are normalized to their maximum value. These cross-section plots demonstrate that an increased transmission $T$ of the $\pi$-phase shifted absorber sharpens the intensity peak at the center of the slit. As shown on the right of the figure, the sidelobes on both sides of the main feature mitigate the image blur versus defocus and increase the depth of focus (DoF) as well. Depending on the transmission $T$ and photoresist threshold, sidelobes with higher intensity peaks will start to print as (non-intended) individual features. The risk of printing sidelobes might even become worse for certain wave aberrations of the projection lens. Printability of sidelobes is one of the limiters of the usable transmission of attPSM. It is strongly influenced by feature size, pitch, coherency of exposing radiation, and resist sensitivity.²³ The risk of printing sidelobes can be mitigated by appropriate biasing of main features and by placing additional dark opaque features at sidelobe locations.^24,25

Fig. 2

Simulated image aerial images of an attPSM with an isolated 180-nm-wide slit for varying transmission $T$ of the absorber. Imaging settings: wavelength $\lambda =193\mathrm{nm}$, $\mathrm{NA}=0.5$, and circular illumination with $\sigma =0.3$. Left: image cross-section at nominal image plane (defocus = 0); right: image intensity versus defocus and $x$.

Although originally proposed for the improved printing of isolated features, attPSM can be also combined with off-axis illumination to improve the printing of dense features. This can be demonstrated by the imaging of dense L/S patterns with a spacewidth $w$, and period $p$. For a thin-mask model, the complex valued diffraction amplitude $a_m$ of the $m$’th diffraction order is given by analytic expressions²⁶

Figure 3 presents plots of the real valued diffraction efficiencies ${\eta }_m=a_m{a}_m^{*}$ of the zeroth and first diffraction order for a phase shift $\mathrm{\Phi }=\pi$ and several values of $T$. The $\pi$-phase shifted background transmission of the mask increases the diffraction efficiency of the first order at the expense of the zeroth order. This suggests that the value of $T$ and the phase shift can be used to balance the intensities of the two diffraction orders. The contrast values on the right are derived from a two beam interference between zeroth and first diffraction order, as obtained in a typical off-axis illumination scenario close to the resolution limit. High contrast images of binary masks can be only achieved by smaller spaces. The corresponding negative biasing of bright features implies larger values of the required exposure dose. AttPSM with $T>0$ provides high contrast values for larger spacewidths. In other words, attPSM requires less negative biasing of bright features and supports the printing with lower exposure dose. In two-beam interference, the optimum transmission of 4.9% for $w=p/2$ is close to the 6% transmission value of standard MoSi-type masks for DUV lithography.

Fig. 3

Zeroth (left) and first (center) order diffraction efficiency ${\eta }_{\mathrm{0,1}}$ versus spacewidth-to-pitch ratio $w/p$ for different values of background intensity transmission $T$. Right: interference contrast $c$ of the orders versus $w/p$.

The practical realization of a phase shift $\pi$ requires an optical path difference $\lambda /2$ between light passing the absorber with a refractive index $n$ and thickness $d$ and light traveling the same distance in the absorber free areas with a refractive index of 1. The transmission $T$ and phase shift $\mathrm{\Phi }$ of light after a single pass of a homogeneous absorber layer with a thickness $d$ are obtained by

The first attPSM for $i$-line and KrF lithography combined a thinned chromium layer with a spin-on-glass to adjust the phase of the transmitted light.^28,29 These bilayer absorbers were replaced by MoSi-based single layers.^30,31 The refractive index $n$ and extinction coefficient $k$ of these MoSiO or MoSiON layers can be adjusted by deposition conditions and enables the fabrication of $\pi$ shifters with transmission values between 5% and 20%.³² MoSi-based attPSM, sometimes also referred as embedded PSM, were later adapted for ArF lithography.^33,34

The successful introduction of MoSi-based absorber layers made the fabrication of attPSM very similar to chromium on glass mask making. AttPSM can be used for any arbitrary mask pattern. In general, attPSM offer a larger exposure latitude and DoF at a lower exposure dose than binary masks. OPC software is used to identify the optimum tradeoff between large process margins and the risk to print sidelobes. Attenuated PSMs are well established in manufacturing for DUV lithography.

Although there is no universal solution, high transmission attPSM can offer the largest benefits for imaging certain layouts close to the resolution limit.³⁵ Investigations on new materials and processes for high transmission attPSM for DUV are still ongoing.^36,37

2.2.

Selected Learnings

The practical implementation and use of attPSM for DUV lithography involved extensive investigations on mask design, materials, patterning techniques, metrology, inspection, and other components of the mask infrastructure.³⁸ Here, we will focus on aspects that are important to understand the imaging characteristics of attPSM. Certain aspects of this imaging characteristics are not accessible by simplified thin-mask, i.e., Kirchhoff-type models that describe the mask as an infinitely thin object with a given transmission and phase. The detailed understanding of light diffraction and imaging using state-of-the-art DUV (and EUV) masks requires the consideration of the full 3D geometry and of the optical properties (refractive index $n$ and extinction coefficient $k$) of the involved materials. Effects that cannot be described by a thin-mask model and depend on the 3D geometry, and optical material properties are referred as mask topography or mask 3D effects.²

2.2.1.

Impact of phase errors

Before going into details about mask 3D effects for DUV, we will discuss the impact of phase errors on the imaging of attPSM. The impact of phase and transmission errors of attPSM has been investigated by several authors, see for example Refs. 3940.–41. The following simulation examples use dedicated parameter settings to demonstrate several effects that are important for the understanding of mask 3D effects for DUV and EUV lithography.

The simulation results in Fig. 4 demonstrate the impact of the (background) phase $\mathrm{\Phi }$ of attPSM on the through-focus imaging behavior. The left column of the figure indicates a shift of the best focus (BF) position of an isolated space versus $\mathrm{\Phi }$. For the nominal value of $\mathrm{\Phi }=\pi$, the image is symmetric around the BF at zero. Deviations from the nominal phase value move the image along the defocus axis and make it asymmetric with respect to the BF position with the highest contrast.

Fig. 4

Simulated image intensity versus defocus and $x$ for attPSM ($T=6\%$) with different values of the phase shift $\mathrm{\Phi }$. Imaging settings: wavelength $\lambda =193\mathrm{nm}$, $\mathrm{NA}=0.5$; left column: isolated 180-nm-wide space, and circular illumination with $\sigma =0.3$, other columns: 110 nm dense L/S, illumination left/right single poles and dipole at $\sigma =0.8$.

The images in the other three columns are obtained for dense L/S and single point sources (poles) or a dipole illumination, respectively. For single pole illumination, the interference of the two contributing diffraction orders within the NA (zeroth and first or zeroth and −first) creates an array of stripes that is tilted with respect to the defocus axis, i.e., it exhibits a pronounced nontelecentricity (nTC) or variation of feature position versus defocus. Superposition of the two single pole intensity distributions using the dipole illumination recovers the symmetry and removes the image tilt along the defocus axis (nTC).

Modification of the phase $\mathrm{\Phi }$ moves the interference pattern (single-pole images) along the $x$-axis. For $\mathrm{\Phi }=\pi$, the image at zero defocus is symmetric with respect to $x$. Deviations from the nominal phase shift of $\pi$ and the resulting opposite shifts of the single-pole images blur the resulting dipole image at the nominal zero defocus position. The BF with highest contrast of the dipole images moves away from the nominal zero defocus position.

In general, illumination systems for DUV imaging are symmetric to avoid non-telecentricities. Due to the off-axis illumination of the mask, these non-telecentricities and related effects cannot be completely removed in reflective EUV imaging systems. The specific settings in Fig. 4 are chosen to demonstrate that a phase error of the attPSM, i.e., a deviation from the nominal phase $\mathrm{\Phi }=\pi$ results in shifts of the BF position. Phase errors of attPSM can also result in lateral image shifts and blur of images that are generated by different parts of the source. The specific impact of the phase error depends on the sources shape. We will come back to this second observation in Sec. 4.2.

2.2.2.

Mask 3D effects

The first investigation on mask 3D effects for attPSM were performed by Wong and his colleagues at Berkeley and IBM.^42–44 He employed the rigorous finite-difference time-domain simulator TEMPEST to compute the light diffraction and imaging for selected geometries and materials. The simulation results and comparison to experimental data from an aerial image measurement system demonstrated the impact of light scattering at the absorber edges on phase errors, pitch- and feature size-dependent shifts of the BF position, and image asymmetries around the BF position. He observed that these effects are less pronounced for bright field masks (isolated lines and pillars) than for dark field masks (spaces or holes). The simulation results indicated that light tends to propagate into higher index material. This well-known phenomenon is important for the understanding of mask 3D effects in EUV as well.

Diffraction analysis of the mask, i.e., computation of the diffraction efficiency and phase of the diffracted light for propagating orders in the far-field of the mask provided additional insights into the impact of mask 3D effects on the performance of attPSM.^45,46 Figure 5 presents simulated diffraction efficiency and phase values in the far-field of a MoSi-type attPSM with dense L/S (duty ratio 1:1) versus the wafer-scale linewidth. Results of the thin-mask model (Kirchhoff) and of rigorous simulations with $x$ [transverse magnetic (TM)]- and $y$ [transverse electric (TE)]-polarized light are shown. For large linewidths, all simulation results indicate an almost perfect balancing of the zeroth and first diffraction order. The differences between the results of the used model assumptions increase for linewidths below 100 nm. The thin-mask model cannot predict significant variations of the diffraction efficiency and phase of the diffracted light for sub-100-nm linewidths. Interestingly, the variation of diffraction efficiency is more pronounced for $y$-polarized light. The negative values of fraction of polarization (FoP) indicate that the mask starts to act as an $x$- or TM-polarizer with negative impact on the image contrast. Additional observations on the unfavorable polarization performance of standard MoSi-type attPSM for DUV were described by several authors.^47–49 The increased variation of the phase for small linewidths indicates mask 3D effects that are very similar to wave aberrations of the projection lens.^50–52 The significant impact of mask 3D effects on the phase and polarization characteristics of attPSM was confirmed by quantitative phase imaging. Shanker et al.⁵³ analyzed thick-mask edge-diffraction effects in attPSM by extracting the optical phase at the wafer plane from a series of through-focus aerial images with 193 nm light.

Fig. 5

Diffraction analysis for a standard MoSi-type attPSM with dense L/S for vertical incidence and a wavelength of 193 nm. Left/upper: diffraction efficiency of the zeroth order. Left/lower: diffraction efficiency of the first order. Right/upper: FOP for zeroth and first first order. Right lower: phase difference between zeroth and first, result of Kirchhoff (thin-mask) model and rigorous simulation using $x$ (TM)- and $y$ (TE)-polarized light, respectively. This figure has been reprinted from our JM3-paper on this topic.⁴⁶ More detailed explanations on the setting, used simulation parameters, and the definition of the FoP is given there.

The findings on mask induced polarization and aberration-like mask 3D effects triggered investigations on alternative absorbers for attPSM in DUV lithography. Bubke et al.⁵⁴ compared the polarization characteristics of standard chromium, standard MoSi-type, and a $\mathrm{Ta}/{\mathrm{SiO}}_2$ bilayer aborber for ArF. Both rigorous calculations and direct measurements of diffraction efficiency demonstrated a significant impact of material, pitch, and incidence angle of the light on the polarization characteristics. Similar investigations were also reported by other authors.^55–57 We employed multiobjective optimization techniques in combination with rigorous diffraction and imaging simulations to identify bilayer attPSM stacks with a favorable imaging performance.⁵⁸ Despite of certain advantages of $\mathrm{Ta}/{\mathrm{SiO}}_2$ and several other bilayer stacks, none of them has been used in high volume manufacturing. Instead, a new opaque MoSi on glass mask blank (OMOG) has been introduced into manufacturing due to its reduced mask 3D effects.^59,60 Because of its low transmission, OMOG cannot be considered as an attPSM.

3.1.

Basic Geometry and Properties

EUV lithography employs reflective masks, which consist of an absorber on top of a multilayer. Figure 6 presents a simplified schematic of an EUV mask. More details on additional components of the mask, their fabrication and metrology for EUV masks are described by Ahn and Jeon.⁶² The Bragg-type multilayer reflects the incident light, whereas the absorber defines the pattern on the mask by blocking or modifying the reflected light from the absorber-covered areas. It is important to note that (most of) the incident EUV light is not reflected from the top of the multilayer, but from layer interfaces inside the multilayer. For typical Mo/Si multilayers and directions of the incident light, the reflections from the individual interfaces add up to about 65% to 70% reflected light from a virtual reflection plane about 50 nm below the top surface of the multilayer. The distance between the absorber and the virtual reflection plane, sometimes referred as $Z_{\mathrm{eff}}$, contributes significantly to the 3D aspects of light diffraction from EUV masks. Alternative RuSi multilayers with a smaller $Z_{\mathrm{eff}}$ can help to mitigate mask 3D effects.^63–65

Fig. 6

Schematic of an EUV mask. (a) Geometrical representation by an absorber on the top of a reflective multilayer. (b) “Double diffraction” scheme: first diffraction of the incident light (green bold arrow) by the absorber pattern, backreflection from the multilayer, and second diffraction from the absorber.⁶¹

The “double diffraction” scheme on the right of Fig. 6 indicates that the EUV light is diffracted by the absorber twice. First, the incident light from the illumination system is diffracted toward the multilayer. Second, the backreflected (upward propagating) light from the multilayer is diffracted toward the projector in the far-field of the mask. The mixing of different diffraction orders by the double diffraction has important consequences on the resulting images.^17,61,66 Specific consequences of the double diffraction for attPSM are discussed in Sec. 4.2.

The ranges of accessible refractive index $n$ and extinction coefficient $k$ at a wavelength of 13.5 nm are much smaller than corresponding ranges for DUV lithography, see also data in Fig. 8. This limits the optical material contrast of possible material combinations for EUV masks. The absorber interacts both with the incident light from the source and with the backreflected light from the multilayer. It has to be thick compared to wavelength to enable a sufficient modulation of the intensity and phase of the reflected light. Another consequence of the lower optical material contrast is the lower sensitivity of light diffraction from EUV masks to the polarization of the incident light. Absorber gratings with very small pitches or incidence angles close to the Brewster angle are required to provoke significant polarization effects by interaction with EUV masks or multilayers.^68,69

To separate the reflected from the incident light, the illumination of the mask has to be tilted with respect to the surface normal of the mask. The oblique illumination with a propagation vector in the $xz$-plane introduces a dependency of the imaging from the orientation of the features on the mask.⁷⁰ In general, the asymmetric illumination of horizontal ($y$-parallel) features makes them more sensitive to mask 3D effects. The situation changes with the transition to anamorphic systems in high NA systems. The orientation-dependent mask scale ($8\times$ in tilt direction along the $y$ axis and $4\times$ along the $x$ axis) mitigates certain mask 3D effects for horizontal features in high NA systems.^71,72 However, the smaller vertical ($x$-parallel) features on the mask become more sensitive to mask 3D effects.

3.2.

Mask 3D Effects in EUV Systems

The described peculiarities of reflective EUV masks involve several characteristic mask 3D effects.^73–75 Selected observations for $\mathrm{NA}\le 0.33$ systems are highlighted in Fig. 7. The asymmetric illumination of the mask introduces an asymmetric shadowing and a variation of the position of the printed feature versus the focus position (nTC). The amount of nTC depends on the absorber thickness, feature orientation, position in the exposure slit, and illumination geometry.

Fig. 7

Typical mask 3D effects in EUV systems. See Ref. 75 for a more detailed discussion of the shown phenomena and the relevant settings.

Different feature positions and nontelecentricities of images, which are generated by individual parts of the illumination source, cause a blur of the image, which is generated by the complete source. Such image blur and the resulting contrast fading have been observed both for DUV and for EUV^76,77 systems. Over certain thickness ranges, the contrast fading tends to increase with the absorber thickness. The amount of blur and its behavior versus absorber thickness depends on the refractive index and extinction of the absorber material. The importance of such blur effects for the imaging characteristics of attPSM for EUV will be discussed in Sec. 4.2.

The plot of the phase on the lower left of Fig. 7 indicates the wavefront deformation that occurs when EUV light propagates through an absorber. Further details, methods for the quantitative analysis of the involved effects and their impact on imaging are discussed in Refs. 78–79. Most importantly, the mask-induced deformation of the wavefront results in a feature size and pitch dependent shift of the BF position, where the images with the highest contrast can be obtained. Because the wavefront deformation tends to increase for low-$n$ absorber materials, the understanding of the involved effects is of key importance for the optimization of attPSM for EUV.

Several strategies including new absorber materials,^80,81 alternative mask stacks,⁸² assist features,^11,83 and source optimization^84,85 have been proposed to mitigate mask 3D effects in EUV systems with a NA of 0.33, see our 2017 review article⁷⁵ and references therein for further details. Over the past 5 years, a considerable effort has been spent for the exploration of new absorber materials for EUV. The next section provides a brief overview on material options for EUV mask absorbers. The perspectives of attPSM and low-$n$ absorbers to mitigate mask 3D effects and to push EUV imaging to a smaller technology factor $k_1$ is discussed in Sec. 4.

3.3.

Material Options

Figure 8 presents a plot of the accessible refractive index $n$ and extinction coefficient $k$ of materials at a wavelength of 13.5 nm. The optical material data ($n$ and $k$) have been taken from the CXRO database.⁶⁷ Several specific materials with the lowest refractive index and/or largest extinction coefficient are highlighted in the plot. Certain combinations of materials can be also deposited as alloys and provide access to the area of the $nk$-space between these materials.^86–89 The specific $n$ and $k$ values of absorber layers depend on the deposition conditions. More accurate experimental $n$ and $k$ values, which consider these deposition conditions, are determined by analyzing EUV reflectivity data.^90,91 The practical choice of material for EUV mask is governed by additional criteria such as durability for mask cleaning, mask lifetime, and scanner compatibility.^88,92,93

The data in Fig. 8 indicate three groups of materials. 30 to 40-nm-thick absorbers with high extinction coefficient $k$ exhibit reflectivities below 1% and can provide high contrast binary masks for EUV. Table 1 presents an overview on several proposed/investigated alternative materials/stacks for binary EUV mask. The cited investigations, including first wafer prints,⁹⁹ have demonstrated the potential of high-$k$ absorbers to improve the imaging of L/S patterns. However, due to the involved intensity loss and high dose requirements, high-$k$ absorbers cannot provide favorable solutions for several other patterns such as arrays of contact holes.

Fig. 8

Plot of materials from the CXRO database⁶⁷ (small blue dots) versus refractive index $n$ and extinction coefficient $k$ ($nk$-space). TaBN represents a state-of-the-art absorber material.¹⁶

Table 1

Proposed/investigated alternative materials/stack for binary EUV mask.

Materials with a refractive index close to 1 minimize the deformation of the phase, BF shifts and nTC. However, most of these $n\approx 1$ materials, including aluminum, have only a small extinction and do not provide sufficient contrast at a small thickness. Thin absorber materials from the lower left region of the $nk$-space generate an increasing amount of reflected light from the nominally dark regions of the mask. Appropriate combinations of materials and thickness values can establish attPSM absorbers for EUV and will be discussed in the next section.

In addition to the investigation of specific material systems, several studies have been performed to characterize the impact of $n$ and $k$ independent from specific material combinations^81,100 or for flexible material compositions that provide access to large regions of the $nk$-space.¹⁶ Timmermans et al.¹⁰¹ proposed a mask decision tree that exhibits the achievable imaging gain and indicates remaining potential challenges for different use cases. Tanabe¹⁰² employed the ratio $k/(1-n)$ to classify EUV masks into four categories. More details on low-$n$ materials and attPSM for EUV are discussed in the next section.

4.1.

Search for a $\pi$ Shifter

The first proposal to use attPSM in EUV lithography was made in 1993 by Nguyen et al.¹⁰³ They observed sidelobes in simulated images of a 60-nm-thick carbon absorber “similar to that for attenuated phase shifted mask” and proposed to employ this effect to sharpen line edges. Shortly afterward, Wood et al.¹⁰⁴ reported on the first experimental realization of attPSM for EUV using a transmission mask with a bilayer absorber that consisted of a 262-nm-thick bottom layer of polymethylmethacrylate (PMMA) and a 27-nm-thick top layer of Ge. Similar concepts for transmissive attenuated phase mask are still used today in the application of transmissive phase shift masks for (achromatic) EUV Talbot lithography.¹⁰⁵ It is also interesting to note that the reflectivity of currently used approximately 60 nm-thick TaBN absorbers on top of Mo/Si multilayers is approximately 3% of the reflectivity of the absorber-free multilayer blank and involves a phase shift of $0.9\pi$. In other words, the currently used TaBN absorber can be also considered as a poorly optimized attPSM. Selected aspects of the non-zero reflectivity of TaBN absorbers with varying thickness were discussed by Kamo et al.¹⁰⁶ and Tanabe et al.¹⁰⁷

In general, the transmission $T$ and phase shift $\mathrm{\Phi }$ of attPSM for EUV can be implemented by single or multiple layer absorbers on top of standard multilayer blanks or by combinations of etched/deposited multilayers. Figure 9 exhibits a selection of proposed geometries. Although several of the etched multilayer configurations in the center and right column of Fig. 9 can offer additional options to mitigate mask 3D effects for EUV and few masks with such geometries have even been fabricated and experimentally characterized, they cannot offer manufacturable solutions in near future. The discussions in the remaining part of Sec. 4 will focus on attPSM configurations that involve single or bilayer absorbers on standard multilayers.

Fig. 9

Proposals on geometries of attPSM for EUV lithography. The figures are reprinted from the original publications of the authors.^108–112 Similar configurations were proposed in Refs. 113 and 114.

Similar to attPSM for DUV, the practical implementation of absorbers with a given $T$ and $\mathrm{\Phi }$ requires a special combination of refractive index $n$, extinction coefficient $k$, and thickness $d$. Considering that light passes through the absorber in both downward and in upward direction, a factor of 2 has to be added to the thickness in the classical thin film Eq. (2). The incidence angle $\theta$ is given by the chief ray angle of incidence of 6 deg in EUV systems with a NA of 0.33 and 5.4 deg in the next generation high NA systems ($\mathrm{NA}=0.55$). The bilayer and trilayer absorber configurations in the left column of Fig. 9 combine a shifter layer with small extinction and low refractive index with a high-$k$ attenuator. Jeong et al. proposed an extra ${\mathrm{Al}}_2{\mathrm{O}}_3$ layer in the stack as an additional knob to tune the reflectivity and enable better inspection of the absorber.^108,115

Table 2 provides an overview on proposed/investigated material options for the shifter and attenuator layers. These material options include both bilayer systems and alloys. The majority of the proposed bilayer systems combine a low-$n$ shifter layer with a thin higher $k$ attenuation layer to adjust the desired reflectivity of the absorber. The phase shift and reflectivity of alloy-based absorbers can be tuned by the relative amount of materials and the thickness of the absorber.⁸⁹ Material combinations and alloys that provide the desired phase shift and reflectivity have to fulfill many additional requirements resulting from the processing of the materials during mask fabrication, mask repair, and use of the mask in the scanner.^87,92 The references cited in Table 2 discuss some of these aspects for specific material combinations. Studies of specific material systems were complemented by investigations of the impact of $n$ and $k$ on the imaging characteristics largely independent of specific material combinations.^16,81,100

Table 2

Proposed/investigated materials for shifter and absorber layers in bilayer attPSM for EUV. In addition to this nonexhaustive list, commercial providers of mask blanks have reported on the status of their developments.116,117

Fig. 10

First experimental demonstration of improved through-focus imaging performance of EUV attPSM (bottom row) in comparison to a binary mask (top row) using the Berkeley National Lab’s EUV actinic inspection tool for 18 nm dense L/S, $\mathrm{NA}=0.25$, off-axis illumination (monopole with radius $\sigma =0.5$). Reprinted from Ref. 119.

Simulations of Yu et al.¹²⁵ demonstrated that 30-nm-thick absorbers with $n=0.88$ and $k=0.04$ have the potential to reduce mask 3D (shadowing) effects in EUV systems with larger NA. In a follow up publication, they reported on problems of off-axis illumination in combination with attPSM for EUV caused by “… additional phase shift between the two diffraction orders. This leads to a positional shift of the resultant aerial image … we may conclude that single-patterning EUVL will probably end at a technology node with the minimum pitch of 22 nm, unless we can come up with other innovative ways for performing EUVL imaging …”⁷⁷

4.2.

Toward the Optimum Low-Refractive-Index Absorber

Extensive simulation studies were performed to characterize and understand the observed BF and lateral pattern shifts in the imaging of EUV masks.^74,78,126 It was demonstrated that the effects depend on mask properties such as absorber material, thickness, and, tonality but also on the illumination of the mask. This section discusses selected recent findings that provide a better understanding of the involved imaging mechanisms and enable a more efficient design and use of attPSM for EUV. The classical approach to design an absorber is exclusively based on the intensity and phase of the reflected light from a homogeneous thin film stack cannot provide the ultimate best solution. Double diffraction of light by the absorber and the guidance of light through open areas of a low-$n$ absorber introduce additional criteria for the identification of good attPSM absorbers. The introduction of a low-$n$ material does not only shift the phase of the transmitted/reflected light, it impacts the intensity and phase distribution in the vicinity of absorber patterns as well. This has consequences for the exposure dose, BF position, biasing, and selection of tonality. Several routes to unlock the full potential of attPSM for EUV are briefly discussed at the end of this section.

Burkhardt¹⁰⁰ introduced a phasor diagram to analyze the impact of the phase shifts between zeroth and first diffraction order on the imaging of dense L/S patterns. Figure 11 exhibits such phasor diagram and the corresponding monopole and dipole images. Any imaginary component of the phasor (and the corresponding phase shift between the zeroth and first diffraction order) creates spatially shifted images of the individual monopoles and causes a drop of the contrast for the dipole image. Note that the image cross sections on the right of Fig. 11 exhibit a similar behavior as simulated images of attPSM with phase errors in Fig. 4 at fixed focus positions. Burkhardt applied this methodology both to high-$k$ and low-$n$ absorber candidates for EUV and concluded “… that the image split (between the poles) can be reduced or even eliminated by either moving to an index matched to vacuum ($n=1$) at the cost of reduced intrinsic contrast, or by moving to a more dielectric phase shifting material at a thickness that gives approximately a phase shift of $\pi$…”¹⁸ Note that the phase shift in his argument does not refer to the phase shift of a homogeneous absorber but to the observed standing wave pattern in the near-field of a patterned EUV mask.

Fig. 11

Dipole illumination on the left for a 28-nm pitch L/S grating, phasor diagram, and resulting aerial images for monopoles and dipole. In the case of horizontal patterning in EUV, we have different images for the small angle pole (magenta) and the large angle pole (green). Reprinted from an article of Burkhardt.¹⁰⁰

In recent simulations for a very special imaging scenario, we observed a strong impact of the absorber refractive index $n$ on image cross-sections of single-pole and dipole images, and on the NILS of dipole images, see Fig. 12. The simulations investigated the imaging of L/S with a pitch of 32 nm with a high NA system. The position of the used leaf-shaped poles is optimized for a pitch of 16 nm. For the chosen combination of illumination and pitch, a significant part of light in the first diffraction order is blocked by the center obscuration of the system. This special configuration makes the described test case very sensitive to mask 3D effects. The partial blocking of the first diffraction order increases the impact of the second diffraction order and related amplitude and phase effects on the image. This enhances the sensitivity of the imaging results to the refractive index and extinction coefficient of the absorber material.

Fig. 12

Simulated impact of refractive index $n$ of absorber on image cross-sections of single-pole and dipole images and on NILS of dipole images. See Ref. 61 for further details.

The simulation results in Fig. 12 demonstrate a significant impact of the absorber $n$ both on the contrast of the single-pole images and on the shift between the single-pole images. A low-refractive-index of the absorber improves the contrast of images, which are obtained with single pole illumination. On the other hand, low-$n$ materials introduce an image shift between images of different poles. Although this result was obtained for a very specific imaging scenario and poorly optimized attPSM (see remark in first paragraph of Sec. 4.1), it emphasizes the specific importance of the absorber $n$ for high NA EUV imaging.

Figure 13 from a presentation of van Lare et al.¹²² provides rigorously simulated NILS values of contact holes imaged with different absorber candidates versus thickness. The vertical dashed lines in the plots indicate the absorber thickness, which provides a phase shift $\mathrm{\Phi }$ of $\pi$ according to classical thin film considerations [similar to Eq. (2)], and the absorber thickness, which provides the highest NILS. Although this simulation result was obtained for a specific illumination and mask bias, it predicts the same tendencies as the results of our multiobjective optimizations of attPSM stacks for similar use cases, which included variation of the mask bias and source shape.¹⁶ AttPSM absorbers with a combination of refractive index and absorber thickness, which correspond to phase shifts $\mathrm{\Phi }>\pi$, can provide better imaging performance than “classical” $\pi$-shifters. Van Lare et al.¹²² suggested a rule of thump ${\mathrm{\Phi }}_{\mathrm{opt}}=1.2\pi$. We observed similar values in our simulations but also demonstrated that combinations of $n$, $k$, and absorber thickness, which provide attPSM absorbers with the same transmission $T$ and phase $\mathrm{\Phi }$, may exhibit a different imaging behavior versus pitch.¹²⁷

Fig. 13

NILS versus pitch and mask absorber thickness for contact holes with $\mathrm{CD}=16.8\mathrm{nm}$, NA 0.55, and small-annular illumination, showing the optimum mask thickness per pitch for Ru (a), Pd (b), and Mo (c). (d) The mask properties of the optima chosen for the different materials. Reprint of Fig. 7 from van Lare et al.¹²²

The reason for these specific characteristics of attPSM for EUV was originally attributed to nonspecific mask 3D effects or to an effective phase term that is picked up by the light traveling adjacent to the absorber with the real part of the index of refraction different from vacuum.^102,126 Recent simulations by a semi-analytical double diffraction model¹⁷ and hybrid mask models of the Fraunhofer IISB lithography simulator Dr. LiTHO^127–129 provided deeper insights. This is demonstrated in Fig. 14, which presents simulated phase shifts between zeroth and first diffraction order versus the absorber phase $\mathrm{\Phi }$. Both, the fully analytical model and the semi-analytical model of van Lare et al.¹⁷ computed the complex diffraction amplitudes $r_n$ in the far-field of the reflective EUV mask by a weighted superposition of diffraction orders and the equation is given as

Fig. 14

Simulation of phase shift between zeroth and first diffraction order ($\mathrm{\Delta }$ phase) in a reflective EUV mask by a fully analytical model (left and center) and by a semi-analytical model¹⁷ (right) versus the phase $\mathrm{\Phi }$ of the attPSM for dense L/S with a half-pitch of 8 nm. The results of the analytical model are plotted for absorbers with different transmission and multilayer with different BWs. The complex diffraction amplitudes of the semi-analytical model are obtained for a 35-nm-thick Ru absorber with $n=0.88$ and $k=0.02$. The phase $\mathrm{\Phi }$ of the semi-analytical model is obtained from thin film calculations.

The analytical model calculates the complex diffraction amplitudes according to Eq. (1) from Sec. 2.1. It is important to consider that the light passes through the absorber twice, i.e., the total phase $\mathrm{\Phi }$ and transmission $T$ has to be split to $\mathrm{\Phi }/2$ and $\sqrt{T}$ in downward and upward direction, respectively. The multilayer reflectivity $R$ is specified by a parametric model, which describes the multilayer by a region with a constant high reflectivity within a distinct angular range or bandwidth (BW) and by the position of the effective reflection plane inside the real multilayer ($Z_{\mathrm{eff}}$).⁶⁴ The semi-analytical model computes the diffraction amplitudes by fitting to rigorous diffraction calculations, see Ref. 122 for details.

Despite the different modeling approaches, both models exhibit a similar tendency versus the phase $\mathrm{\Phi }$ of the attPSM. The optimum value of $\mathrm{\Phi }$ is obtained for a $\mathrm{\Delta }$ phase of zero, which minimizes the pattern shift. The asymmetric behavior of the analytical model for $T>0$ results from the split of the absorber phase $\mathrm{\Phi }$ into two identical parts (double pass of the absorber) and different illuminations of the thin absorber in forward and backward direction. Notably, the optimum phase value of the mask for a multilayer with a limited angular range of high reflectivity ($\mathrm{BW}=11\mathrm{deg}$) is larger than that of a fictive multilayer that reflects light from all incidence directions ($\mathrm{BW}=90\mathrm{deg}$). The results of the analytical model suggest that the deviation of the optimum phase of the mask from $\pi$ can be explained with a thin absorber model, which includes the double diffraction phenomenon for EUV masks. Of course, the thick absorber contributes to the specific value of $\mathrm{\Phi }$ as well.

This is confirmed by Fig. 15, which presents simulated diffraction efficiencies and $\mathrm{\Delta }$ phase between zeroth and first diffraction order versus incident angle and half-pitch (hp). Results of two different modeling approaches are shown. The hybrid model in the top row combines a Kirchhoff-type thin-mask with (total) transmission $T=4.9\%$ and phase $\mathrm{\Phi }=225\mathrm{deg}$ with a real Mo/Si multilayer. The results in the bottom row are obtained by fully rigorous simulations for a 50.3-nm-thick absorber with $n=0.92$ and $k=0.032$ on the top of the same Mo/Si multilayer. The models predict similar trends of $\mathrm{\Delta }$ phase versus incident angle and hp, and characteristic drops of diffraction efficiencies for larger incidence angles and smaller half-pitches. The position of these drops is determined by the finite angular support (limited angular range with high reflectivity) of the multilayer.

Fig. 15

Simulations of diffraction efficiencies and $\mathrm{\Delta }$ phase between zeroth and first diffraction order versus incident angle and half-pitch (hp) for a hybrid mask model (top row) and for fully rigorous diffraction simulation (bottom row). Details about the modeling assumptions and results for other versions of the hybrid and fully rigorous mask model are presented in Mesilhy et al.¹²⁷

The difference between the models increases for half-pitches below 11 nm, where waveguide effects become more prominent. Waveguide modes in the spaces of low-$n$ absorbers couple light between neighbored diffraction orders, see discussion of this effect by Mesilhy et al.³⁰

The guidance of light through the openings of low-$n$ absorbers and related waveguide effects introduce another important aspect for the use of attPM in EUV lithography. The simulation example in Fig. 16 demonstrates that the light propagation through small spaces in low-$n$ EUV absorbers is governed by waveguide modes. The analytical result on the left of the figure is obtained by a linear superposition of analytically computed waveguide modes. The difference with respect to the rigorously simulated near-field (RCWA result in the center of figure) is caused by light scattering from top corners of the absorber into non-propagating modes, see Ref. 130 for further discussion of the differences between the analytical model and rigorous RCWA results. The excitation of waveguide modes depends strongly on the illumination direction.

Fig. 16

Downward propagating near-field inside the absorber and the difference between analytically computed modes and the near-field inside the absorber from the RCWA simulation. Slit opening of 8 nm × 4 (in mask scale), TaBN absorber ($n=0.95$, $k=0.031$), and incidence angle of 5 deg. Reprint of Fig. 7 from Mesilhy et al.¹³⁰

Another important consequence of the guidance of EUV light by low-$n$ absorbers is highlighted in Fig. 17. It exhibits the intensity and phase of reflected near-fields of 11 nm square contacts with a pitch of 22 nm in $x$ and $y$ (wafer scale) for a low-$k$ absorber with two different $n$. In each case four near-fields are plotted for the illumination directions of an optimized quadrupole illumination. The elongated shapes of near-field plots are a consequence of the used scaling of the mask in an anamorphic system ($4\times$ in $x$ and $8\times$ in $y$).

Fig. 17

Intensity and phase of reflected near-fields of 11 nm square contacts with a pitch of 22 nm in $x$ and $y$ (wafer scale) for a low extinction $k=0.02$ 40-nm-thick absorber with two different $n$. The near-fields are plotted on mask scale of an anamorphic system for four illumination directions of a quasar illuminator.

Although both absorbers have the same extinction $k$, the low-$n$ mask transmits much more light through the opening than its high-$n$ counterpart. The low-$n$ mask shows a much better (near-field) contrast. The advantage of the low-$n$ absorber becomes obvious without consideration of the phase. Of course, the near-field phase of both absorbers looks very different as well. The high-$n$ absorber exhibits only a weak deformation of the phase. The phase inside the openings of the low-$n$ absorber exhibits strong variations versus illumination direction and location on the mask. This variation impacts both the BF and lateral shift of images of individual poles.

The guidance of light through the openings of low-$n$ absorbers can help to make more efficient use of the incident light and to reduce the required exposure dose. This effect is also important for high-$k$ absorbers with a low $n$. In other words, the refractive index of the absorber material is important for binary EUV masks as well. The more efficient use of light in low-$n$ absorbers adds to the advantages of attPSM in printing bright features with less negative bias compared to binary mask, see discussion in Sec. 2.1. On the other hand, the occurrence of discrete modes and the sensitivity of these modes to feature sizes and directions of the incident light increase the interaction between source shape and mask geometries.

The investigations of observed BF and lateral pattern shifts of low-$n$ absorbers have demonstrated that optical properties and thickness of absorber impact both contrast for individual illumination directions (monopoles) and image shift between different illumination directions. The nTC of monopole images is strongly pitch dependent. The superposition of shifted images with different nTC has a significant impact on BF for various pitches and impact the usable DoF.¹²² This better understanding of physical effects and their dependency on the absorber material will help to improve materials and SMO methods for low-$n$ absorbers. First comparisons of SMO using different absorbers have already demonstrated the advantages of low-$n$ materials for representative layout designs.^131–133 Future SMO solutions can be complemented by adaptation of data-efficient artificial intelligence (AI) solutions for alternative absorber materials.¹³⁴

Figure 18 exhibits the first experimental comparison of the imaging performance of a low-$n$ mask with a Ta-based reference mask. These results demonstrate that the EUV low-$n$ mask improves both local critical dimension (CD) uniformity and dose for dense features.¹³³

Fig. 18

First experimental comparison of the imaging performance of a low-$n$ mask with a Ta-based reference mask. Reprint from the article of van Lare.¹³³

Further improvements are required to unlock the full potential of attPSM for EUV. Several options have been discussed by van Lare et al.¹³³ Optimization of target and mask bias is very effective for mitigation of focus shifts. Assist features can help to mitigate shifts of the BF position, see Refs. 7, 75, and 126 for further details. The tonality of a mask has an important impact on mask-induced BF shifts as well. In general, bright field masks exhibit less BF shifts than dark field masks.^78,135,136 The use of monopole illumination could provide even more drastic improvements.^100,135 Alternative absorbers can also offer advantages in combination with EUV dark field lithography.¹³⁷