1. Introduction

In the field of optics, probably the most stringent conditions for surface accuracy and smoothness are made on optical components for deep ultraviolet (DUV) and extreme ultraviolet (EUV) lithography, where the specifications for surface figure accuracy and surface smoothness need to achieve sub-nanometer magnitude simultaneously [1–3]. Surface figure error and surface roughness within different frequency ranges would affect the optical system performances. The surface figure error is defined as low-spatial frequency error (LSFE) with wavelength greater than 1mm, which plays an important role in guaranteeing aberration control. The other surface errors with shorter wavelength are divided to mid-spatial frequency roughness (MSFR: spatial wavelength of 1mm-1μm) and high-spatial frequency roughness (HSFR: spatial wavelength of 1μm-1nm). The MSFR is related to the near-angle scattering of light at the surface where it affects the contrast of the imaging optics, while the HSFR causes high-angle scattering and is regarded as a loss mechanism in EUV light. The manufacture of such high degree accuracy and quality optical surfaces urgently requires advanced optical fabrication technologies. Ion beam figuring (IBF) possesses the advantage of nanometer precision with material removed by physical sputtering effect [4, 5]. The IBF process is highly deterministic, highly stable, and noncontact, which makes it advantageous over conventional figuring technology [4]. M. Weiner from Carl Zeiss in Germany points out that IBF is the most suitable method for the final figuring of lithography optics after his researches [1], and this application sufficiently embodies the machining capability of IBF.

Since figures are sensitive to optical substrate thermal expansion, to preserve figure accuracy of the optics, low thermal expansion materials are usually used as substrates for EUVL optics. Zerodur, with its ability to match zero thermal expansion very closely, has been used as one of the prime material candidates [6, 7]. Zerodur belongs to glass ceramic material and contains both non-crystalline (amorphous SiO₂) and crystalline (crystalline quartz) composite [6]. The thermal expansion coefficient of the non-crystalline phase is positive, while the crystalline phase has a negative thermal expansion coefficient, and the mixture is adjusted so that the resultant expansion coefficient is near zero [8]. However, the sputtering characteristics vary according to the dual phase material, and thus finished surfaces of the substrate become rougher during surface figure error correction by IBF. It is quite difficult to achieve the specification for HSFR at a surface roughness less than 0.15 nm RMS.

The purposes of the work presented in this paper are to investigate the microscopic morphology evolution and realize the ultra-smooth machining of Zerodur surfaces. Through theoretical analysis and experimental researches, we show that granular nanopatterns are easily formed in morphology and lowest achievable smooth surface may be limited due to dual phase of the material. Subsequently, to overcome roughening of the Zerodur substrate during ion sputtering, we propose a new method for IBF of Zerodur optics assisted by deterministic IBA technology. Through final experimental investigation, Zerodur optics with surface roughness down to 0.15nm RMS level are obtained.

2.Microscopic morphology evolution

2.1 Experiment details

All figuring experiments are performed in our self-developed IBF systems (2.5 × 10⁻³ Pa work pressure) under the bombardment of Ar⁺ ions at normal incidence. Within the experiments the ion energy E_ion≤1000eV, the applied beam current J_ion ranges from 10mA to 30mA and work temperature T≈60°C. To observe the surface morphology evolution, the Bruke Dimension Icon atomic force microscopy (AFM) is used to investigate the microscopic morphologies on Zerodur surfaces after IBF removing material of different depths. AFM measurements are performed at fixed scan size 1μm × 1μm with a resolution of 512 × 512 pixels. In addition, comparative experiments are made on the fused silica (amorphous SiO₂) sample and quartz (crystalline quartz) sample to investigate the morphology evolution of the primary compositions of Zerodur material. The three samples are prepared by using a pitch lap to give a similar surface quality, where the averaged surface roughness is about 0.18 nm RMS.

2.2 Experimental results

Figure 1 shows the experimental results of the material removal depth-dependent morphology evolution on Zerodur surfaces under our frequently-used conditions (ion energy E_ion = 800eV, beam current J_ion = 30mA), where the surface roughness value of original morphology is 0.18nm RMS [Fig. 1(a)] and the removal depth is increased from 30nm to 90nm. In Fig. 1(b), we can observe embryonic granular patterns formation on the surface after only removing material of 30nm depth, resulting in a slight increase of surface roughness value. When the removal depth is increased further, the distribution of the granular patterns becomes dense, contributing to the surface roughness going up to 0.46 nm after 90nm depth material being removed. Obviously, granular pattern can be clearly observed on Zerodur surface after ion beam sputtering from the AFM image in Fig. 1(d). All those features also can be appreciated from the corresponding line profiles as displayed in Fig. 2, where the granular nanostructures are developed throughout the surface and the final height is about 1.0 nm.

 

Fig. 1 AFM images of Zerodur surface at different removal depth: (a) original morphology; (b)-(d) surface morphologies after the removal depth increasing from 30nm, 60nm to 90nm.

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Fig. 2 The corresponding line profiles of AFM images in Fig. 1.

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In contrast, experimental results in Fig. 3 show the surface quality of both amorphous SiO₂ and quartz is effectively improved after removing 90nm depth material by IBF. The original morphology [Figs. 3(a) and 3(c)] shows that obvious microscopic scratches and protuberances, produced from the pre-finishing process, exist on the two sample surfaces. However, the microscopic defects are effectively removed after IBF, where their surfaces are smoothed until the surface becomes ultra-smooth with surface roughness value less than 0.1nm RMS [Figs. 3(b) and 3(d)]. Consequently, ion sputtering can directly smooth amorphous SiO₂ and quartz surfaces and obtain ultra-smooth surfaces.

 

Fig. 3 AFM images of amorphous SiO₂ and quartz surfaces before and after IBF: (a) original surface of amorphous SiO₂; (b) surface morphology of amorphous SiO₂ after IBF; (c) original surface of quartz; (b) surface morphology of quartz after IBF.

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For completeness, figuring experiments are repeated on these three samples under different processing conditions. Before very figuring experiment, the samples are prepared to give a similar original surface quality described in section 2.1. Figures 4(a) and 4(b) summarize the experimental results quantitatively where the RMS surface roughness is plotted as a function of removal depth under different processing parameters. In Fig. 4, Zerodur surfaces are all roughened rapidly under different processing conditions and all their final roughness values reach more than 0.4nm RMS, which indicates that it is unavoidable to generate nanostructures after direct ion sputtering. However, IBS is very effective for both amorphous SiO₂ and quartz surfaces in all experiments, where the surface roughness values are down to 0.10nm RMS.

 

Fig. 4 Surface roughness variation with removal depth under different processing parameters: (a) surface roughness variation under different ion beam currents and (b) surface roughness variation under different ion energies.

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2.3 Experimental result analysis

For further investigation of the morphology evolution of the three samples, we take the PSD functions of the data from AFM images (Figs. 1 and 3) for comparison. In Fig. 5, the PSD curves illustrate that the morphology evolution process of amorphous SiO₂ and quartz surface is similar. It is evident that surface errors within the measured frequency range are effectively removed by the ion-induced smoothing. However, for Zerodur surface, the PSD curve climbs rapidly within [0.002 nm⁻¹ 0.06 nm⁻¹] and maintains invariability when the spatial frequency f >0.06 nm⁻¹after IBF. In addition, the presence of the peak in the PSD curve at f = 0.018nm⁻¹ reveals that nanoscale patterns with characteristic periodicity of about 55 nm have been formed on Zerodur surfaces, and the corresponding granular patterns can be observed in Figs. 1(b)–1(d).

 

Fig. 5 PSD functions of the three samples during IBF process

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Meanwhile, Fig. 4 shows that the experimental results are very similar under various processing conditions, which indicates that the morphology evolution with removal depth of Zerodur surface is independent of ion energy and ion beam current. In our experiments, we find the sputtering rates of quartz (Y_q) and fused silica (Y_a) to be strongly dependent on processing parameters, but their sputtering rate ratio R_Y = Y_q/Y_a is a constant. Tables 1 and 2 identically display the sputtering rate ratio R_Y≈0.83. Interestingly the sputtering rates of these two forms of SiO₂ are inversely proportional to the bulk density ρ, where the density of quartz and fused silica are 2.65 × 10³kg/m³ and 2.2 × 10³kg/m³, respectively. Furthermore, it shows the preferential sputtering (fused silica is sputtered faster than quartz) is directly determined by material properties and the fixed sputtering rate ratio is responsible for the similar experimental results under various processing conditions.

Table 1. Sputtering rates (nm/min) change with ion beam current under ion energy E_ion = 800 eV

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Table 2. Sputtering rates (nm/min) change with ion energy under ion beam current J_ion = 20 mA

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Summarized from the above experimental results and PSD analysis, ion sputtering of Zerodur material often results in the formation of granular nanopatterns on the surfaces, which seriously degrades optical surface quality. However, amorphous SiO₂ and quartz are smoothed until the surfaces achieve ultra-smooth level. Consequently, it indicates that different smoothing and roughening behaviors occur on these material surfaces during IBF, and especially the difference of sputtering rates of the dual phase materials play an important part in microscopic morphology evolution on Zerodur surface.

3. Theoretical analysis and discussion

It is well known that ion sputtering of an amorphous or crystalline material also produces periodic nanoscale patterns under some processing conditions [9–11]. The first successful explanation of periodic patterns formation was developed by Bradley and Harper based on Sigmund’s sputtering theory [9]. Later, the linear BH theory was extended to include nonlinear and noise terms [12], which can explain more experimental features, such as amplitude saturation and wavelength coarsening. An essential premise of all above models is that the bombarded material is amorphous or can be amorphized, which are not adapted to explain ion patterning on Zerodur surfaces because of its dual phase composites. Recently, Shenoy et al. [13] proposed a model to describe ion sputtering of alloy surface, which includes the surface morphology evolution and composition modulation process. Based on this model, we can develop a continuum model to reveal the formation of granular nanopattern on Zerodur surface during ion sputtering.

Figure 6 shows an ion beam sputtering of Zerodur surface with an ion flux F. The surface atoms will sputter from the surface when they obtain enough energy from impinging Ar ions. Due to the difference of sputtering characteristics for the two elemental materials, a compositionally modulated surface layer with a constant thickness of ∆ will be generated during sputtering process [13]. In the following, we consider the time evolution of surface morphology h(x,y,t) and composition perturbations ζ(x,y,t), which are applied to characterize this surface profile. For the perturbed surface, the change in the flux of the sputtered particles for amorphous SiO₂ and crystalline quartz, to first order in h and ζ, can be written as δF_a = FY_a(ζ_a-v_hc_a) and δF_q = FY_q(ζ_q-v_hc_q) [13], where ζ_q = -ζ_a = ζ; c_a, c_q = 1-c_a respectively denote the fraction of lattice sites at the surface occupied by amorphous SiO₂ and quartz; $v_h=G{\nabla }^{2}h$ represents curvature-dependent of the sputter rate. Based on the ion-induced patterning mechanisms [9, 14–16] and above composition modulation process, we can obtain simultaneous equations for the time evolution of surface morphology and composition, given as follows:

 

Fig. 6 Schematic of ion beam sputtering of Zerodur surface

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Where Ω, r and μ denote particle volume, the surface energy and the viscosity;

From Eq. (1), ion nanopatterning on Zerodur surfaces result from the interplay between morphology evolution and composition modulation, and this model is an extension of the former linear theory. Equation (1) also indicates that the formation of the altered composition layer is strongly affected by the sputtering yield ratios R_Y, which is determined by the distribution of the deposited energy and surface material properties. For a given ion sputtering parameter, the sputtering rate only depends on the atomic masses, binding energies and the density [10]. Since the primary composition of amorphous SiO₂ and quartz is SiO₂, it appears quite unlikely that the binding energies of these two forms of SiO₂ differ significantly enough to explain for the different sputtering rates [10]. The primary parameter remaining is composition density. The experimental results in Tables 1 and 2 show the sputtering rate agrees with the expected Y$\propto$ρ⁻¹. Therefore, the surface is enriched in the quartz composition and the granular crystalline quartz protrude from the Zerodur surface [shown in Figs. 1(b)–1(d)], which could be attributed to composition modulation [Eq. (1)] caused by preferential sputtering during ion beam bombardment.

From the experimental results and theoretical analysis, we can conclude that preferential sputtering together with curvature-dependent erosion overcomes ion-induced smoothing effects leading to the granular nanopattern formation on surfaces, which makes it quite difficult to obtain ultra-smooth Zerodur surface by direct IBS. Consequently, lowest achievable smooth surface on Zerodur substrate may be limited for its application for EUV optics.

4. Strategy to IBS of Zerodur optics

4.1 Theoretical analysis

From Eq. (1), we can also find that, in absence of the preferential sputtering, this model can be reduced from simultaneous equations to a single equation:

Where the first term results from curvature-dependent sputtering [9]; Y, a, and Γ denote the sputtering yield, the mean depth of energy deposition, and the effective surface tension coefficients, respectively. The second term denotes ballistic smoothing; E is the mean number of recoils and d is the mean distance of recoil displacement [15]. The last term is ion-enhanced viscous flow [16].

Equation (2) indicates the surface morphology evolution can be attributed to the interplay between ion-induced smoothing and roughening process. In addition, Makeev et al. [14] point out that that the local sputter noise η would also influence the evolution of the surface morphology at long time scales and needs to be taken into account. Based on the solution for Eq. (2), the PSD function is obtained with [17]

Where C(q) = C₂q⁻²-C₄q⁻⁴, C₂ = FΩ(YaГ-Ed), C₄ = r△³/2μ and q = f/2π (f is the spatial frequency). The noise η is characterized by a zero mean value and$〈\eta (r,t)\eta (r\text{'},t\text{'})〉=$ $2A\delta (r-r\text{'})\delta (t-t\text{'})$.

From Eq. (3), it is evident that the surface with frequency q would be smoothed if C(q)<0. When surface smoothing dominates for all wave number q, namely parameter C(q) is constant less than zero for the entire spectrum, the asymptotic solution of Eq. (3) is

Equation (4) indicates the PSD of the surface morphology is strongly related to the power n of polynomial qⁿ in parameter C(q), and each polynomial represents different evolution mechanism above mentioned. Here the PSD function is approximately proportional to q⁻² at low frequencies and q⁻⁴ at high frequencies [in Fig. 5]. In the logarithmic coordinate, the PSD curve will approach the corresponding asymptotes with slope −2 and −4, which correspond to the ballistic smoothing and ion-enhanced viscous flow, respectively. Therefore, we can identify the evolution mechanism based on the experimental conditions and the PSD analysis.

Our previous researches have demonstrated that ultra-smooth amorphous SiO₂ surfaces can be obtained with surface roughness value R_q<0.15 nm at near-normal ion incidence, where the surface smoothing dominates for all wave number q [17]. From Figs. 3 and 5, we also can find the smoothing effect dominates the surface morphology evolution within the measured spatial frequency range, which indicates that the coefficient C₂ is negative and coefficient C₄ is positive. Consequently, the parameter C(q) is negative for all q leading to the smoothing of the surface. It is worthwhile to mention that the PSD function of the final smooth surface is proportional to q⁻² within the frequency range [0.002 mm⁻¹ 0.03 mm⁻¹], and also the transition from ~q⁻² to ~q⁻⁴ phenomenon at a spatial frequency 0.03 mm⁻¹ is indicated. The results display that the morphology evolution process includes both q⁻² and q⁻⁴-dependent smoothing mechanisms, which are in agreement with the above theoretical analysis.

Summarized from the above analysis, ion sputtering of SiO₂ material can smooth microscopic surface morphology, where ballistic smoothing together with ion-enhanced viscous flow suppresses curvature-dependent sputtering. Besides, previous researches indicate that direct IBS is also feasible for the ultra-smoothing of Si material and the smoothing mechanism is similar to SiO₂ material [18, 19]. Therefore, the ultra-smooth finishes can be obtained on SiO₂ and Si material surfaces.

Fortunately, since the current designs for EUV system require several projection optical components to reflect light at the wavelength about 13nm, the Mo/Si multilayer (comprising 50 bilayers) is usually deposited on the substrate to improve reflectivity [6,7]. Consequently, first we can utilize surface modification method to deposit a suitable material layer on Zerodur surface, and then an IBS step is used to smooth this surface. Moreover, a thin added material layer remaining on the Zerodur substrate should have no influence on the further processing of the optical component.

4.2 Implementation with deterministic IBA technology

In our proposed method the pre-finished Zerodur surface is deposited by a suitable material layer through deterministic IBA technology, where this method can maintain and even improve original surface figure accuracy during material adding process. Subsequently, for achieving the specification for HSFR of 0.15nm RMS, an IBS step is used to smooth this surface. Since direct IBS can obtain ultra-smooth surface on SiO₂ and Si surface, these two materials are the candidates for this added layer.

IBA purpose is not to deterministically remove material from optical surface to control the surface error, but to deterministically add material to the local low areas of optical surface to correct its surface error. The IBA process utilizes a Kaufman ion beam source with an ion diaphragm to bombard the target material, and a stable particle beam is generated to deterministically add material to the local low areas on optical surface. Based on the computer-controlled optical surfacing (CCOS) principle, the IBA method described here assumes a constant particles adding, so that the process can be represented by a convolution equation and the dwell time solution is a deconvolution operation. In IBA process, the local low areas on optical surface are corrected through rastering the stable particles beam across the workpiece at varying velocities according to the dwell time. The details for IBA technology can be found in Ref [20,21].

Compared with IBF, the IBA method has the stronger ability to smooth the mid-to-high spatial frequency errors and can provide uniform convergence of surface errors [20,21]. Furthermore, IBA is a highly deterministic and highly stable surface correction method that can improve surface figure accuracy during material adding process, which makes it advantageous over conventional coating technology. Consequently, IBA is a feasible method for deterministically adding a suitable material layer on the extremely precise zerodur surface.

5. Ultra-smoothing experiment and discussion

For investigation of IBS of Zerodur optics assisted by IBA, two patterned Zerodur samples are prepared by ion beam sputtering of 90nm depth material under the same processing conditions described in section 2.1. Figures 7(a) and 7(d) show that granular crystalline quartz protrudes from the surfaces, resulting in the surface roughness going up to more than 0.4nm RMS. In the first step, two samples are respectively added with Si and SiO₂ material by IBA, and the added thickness is about 150nm. Due to the IBA process, the surface roughness of the both samples is already reduced to 0.26 nm RMS. The results in Figs. 7(b) and 7(e) also indicate that the granular nanostructures are covered with the added surface layer.

 

Fig. 7 Experimental results of IBS of Zerodur optics assisted by IBS. Top row: morphology evolution process of sample added with Si; Bottom row: morphology evolution process of sample added with SiO₂.

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Subsequently, the added surface layers are smoothed further by IBS runs. Several researches validates that ion sputtering of Si surface at normal incidence would produce dot patterns leading to the coarsening of the surfaces, and the optimized conditions are ion energy E_ion< 700eV and the oblique incidence angles within (30°-60°) [18, 19]. In our experiment, the added Si layer is bombarded by Ar⁺ ions with ion energy E_ion = 600eV at 40° incidence angle. After removing about 100nm depth material, the final surface roughness value of the sample added with Si decreases to 0.11nm RMS [in Fig. 7(c)]. Besides, the surface roughness of the sample added with SiO₂ is also improved to 0.12 nm RMS after removing about 120nm depth material, where the processing conditions are identical with the experiments in section 2.1. The experimental results show the surface quality of Zerodur optics is effectively improved, which demonstrates the feasibility of this method.

Compared with experimental results, both samples achieve ultra-smooth level, but the machining process and final performance for Zerodur optics would be different. On one hand, for the added Si layer, after the smoothing process the remaining thin Si layer should be no hindrance to the final performance of the optics, because the following thin Si buffer layer is usually deposited on the optical substrate [6, 7]. Therefore, the IBS assisted by Si layer may be superior to SiO₂ layer, but it needs further investigation. On the other hand, the optimized incidence angle for IBS of Si surface is about 45°, meaning that the ion beam must obliquely bombard the Zerodur aspherical surface at every incidence point, which brings great difficulty to preserve the surface figure accuracy during the whole IBS process. However, the IBS process of SiO₂ layer is done at normal incidence, which is identical with the IBF of the Zerodur substrate, so the SiO₂ layer is an expected candidate for assisting IBS of Zerodur optics.

6. Conclusion

Ion sputtering of Zerodur substrate often results in the formation of nanoscale patterns on the surfaces, which seriously degrades optical surface quality. Through experimental researches and theoretical analysis, we find that the preferential sputtering together with curvature-dependent erosion overcomes ion-induced smoothing effects leading to granular nanopattern formation on surfaces and the coarsening of the Zerodur surface. In this work, we propose a method for IBS of Zerodur optics assisted by deterministic IBA technology. Final smoothing experiments indicate that this method can realize the ultra-smooth machining of Zerodur optics with surface roughness down to 0.15nm RMS level, which effectively improve the smoothness of the optical surfaces.