Stand-alone diamond binary phase transmission gratings for the EUV band

doi:10.1364/OE.19.014008

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Stand-alone diamond binary phase transmission gratings for the EUV band

C. Braig, T. Käsebier, E.-B. Kley, and A. Tünnermann »View Author Affiliations

Optics Express, Vol. 19, Issue 15, pp. 14008-14017 (2011)
http://dx.doi.org/10.1364/OE.19.014008

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Abstract

We report on the development of true free-standing phase transmission gratings for the extreme ultraviolet band. An ultra-nanocrystalline, 300 nm thin diamond film on a backside etched silicon wafer is structured by electron-beam lithography to periods of 1 μm. In this way, flat and stable gratings of 400 μm in diameter are fabricated. First-order net efficiencies up to 28% are obtained from measurements at a synchrotron beamline within a wavelength range from 5.0 nm to 8.3 nm, whereas the 0^th order is suppressed to 1% near 6.8 nm. Higher diffraction orders up to the 3^rd one contribute less than 7% in sum to the far-field pattern.

1. Introduction

EUV and soft X-ray gratings represent important tools not only for high-resolution plasma spectroscopy in the laboratory [1

M. L. Schattenburg, E. H. Anderson, and H. I. Smith, “X-ray/VUV Transmission Gratings for Astrophysical and Laboratory Applications,” Phys. Scripta 41, 13–20 (1990). [CrossRef]

, 2

C. Peth, F. Barkusky, and K. Mann, “Near-edge x-ray absorption fine structure measurements using a laboratory-scale XUV source,” J. Phys. D: Appl. Phys. 41, 105202 (2008). [CrossRef]

] and on space-borne astronomical instruments [1

M. L. Schattenburg, E. H. Anderson, and H. I. Smith, “X-ray/VUV Transmission Gratings for Astrophysical and Laboratory Applications,” Phys. Scripta 41, 13–20 (1990). [CrossRef]

, 3

R. K. Heilmann, M. Ahn, A. Bruccoleri, C.-H. Chang, E. M. Gullikson, P. Mukherjee, and M. L. Schattenburg, “Diffraction efficiency of 200-nm-period critical-angle transmission gratings in the soft x-ray and extreme ultraviolet wavelength bands,” Appl. Opt. 50, 1364–1373 (2011). [CrossRef] [PubMed]

], but also for the development of precise and efficient masks in the emerging field of short-wavelength interference lithography [4

H. H. Solak, “Nanolithography with coherent extreme ultraviolet light,” J. Phys. D 39, R171–R188 (2006). [CrossRef]

]. In the past, blazed reflective optics have been built and tested as monochromators at a synchrotron beamline [5

M. Itou, T. Harada, and T. Kita, “Soft X-ray monochromator with a varied-space plane grating for synchrotron radiation: design and evaluation,” Appl. Opt. 28, 146–153 (1989). [CrossRef] [PubMed]

]. Despite well-designed focusing properties by means of continuous variations of the grating period, the modest diffraction efficiencies obtained probably prohibit their implementation in low-signal applications, i.e. astronomy. Current techniques make still use of blazed devices for reflection [6

H. Lin, L. Zhang, L. Li, C. Jin, H. Zhou, and T. Huo, “High-efficiency multilayer-coated ion-beam-etched blazed grating in the extreme-ultraviolet wavelength region,” Appl. Opt. 49, 4450–4459 (2010).

] and “classical” amplitude transmission gratings [7

D. R. McMullin, D. L. Judge, C. Tarrio, R. E. Vest, and F. Hanser, “Extreme-ultraviolet efficiency measurements of freestanding transmission gratings,” Appl. Opt. 43, 3797–3801 (2004). [CrossRef] [PubMed]

], which may suffer from low misalignment tolerances [8

K. Flanagan, M. Ahn, J. Davis, R. Heilmann, D. Huenemoerder, A. Levine, H. Marshall, G. Prigozhin, A. Rasmussen, G. Ricker, M. Schattenburg, N. Schulz, and Y. Zhao, “Spectrometer concept and design for X-ray astronomy using a blazed transmission grating,” in Optics for EUV, X-Ray, and Gamma-Ray Astronomy III , Stephen L. O’Dell and Giovanni Pareschi, eds., Proc. SPIE 6688, 66880Y (2007).

], surface imperfections [9

F. Salmassi, P. P. Naulleau, E. M. Gullikson, D. L. Olynick, and J. A. Liddle, “EUV Binary Phase Gratings: Fabrication and Application to Diffractive Optics,” http://escholarship.org/uc/item/6d42k5t7 (2005).

] or naturally limited diffraction efficiencies, regardless their precise fabrication [10

P. Predehl, H. W. Braeuninger, A. C. Brinkman, D. Dewey, J. J. Drake, K. A. Flanagan, T. Gunsing, G. D. Hartner, J. Z. Juda, M. Juda, J. S. Kaastra, H. L. Marshall, and D. A. Swartz, “X-ray calibration of the AXAF Low Energy Transmission Grating Spectrometer: effective area,” in Grazing Incidence and Multilayer X-Ray Optical Systems , R. B. Hoover and A. B. C. Walker II, eds., Proc. SPIE 3113, 172–180 (1997).

]. Recent developments also turned to transmissive phase-shifting molybdenum (Mo) versions [11

P. P. Naulleau, C. H. Cho, E. M. Gullikson, and J. Bokor, “Transmission phase gratings for EUV interferometry,” J. Synchrotron Rad. 7, 405–410 (2000). [CrossRef]

, 12

M. Saidani and H. H. Solak, “High diffraction-efficiency molybdenum gratings for EUV lithography,” Microel. Eng. 86, 483–485 (2009). [CrossRef]

]. However, their performance is severely limited by solid substrates made of silicon nitride (Si₃N₄). In particular, an additional absorption of ≈ 58% caused by this membrane has to be accepted.

In this paper, we present true free-standing binary EUV phase transmission gratings for the spectral band beyond the carbon K-edge, fabricated from ultra-nanocrystalline (UNC) diamond films. We review general basics of diffractive EUV transmission optics in Sect. 2 and develop in Sect. 3 the specific design and thereon the technological manufacturing procedure as well. In Sect. 4, the experimental scheme for the measurements is described and the results are analyzed in detail. After a brief discussion of prospective applications in Sect. 5, we conclude with an outlook to further steps in Sect. 6.

2. Principles of phase transmission gratings with absorption

We consider a structure made of N ≫ 1 rectangular bars (B) and slits (S), whose periodicity is denoted by d. Its duty cycle or fill factor (FF) is defined as f ≡ b/d, where the quantity b < d represents the width of the bars. A schematic cross-section is shown in Fig. 1. The material properties in the EUV and X-ray range are well described by the complex refractive index n = 1 – δ – iβ, which accounts for both the weak refractive power – the typical case, near absorption edges or towards long wavelengths, deviations from this rule arise – by 0 < δ ≪ 1 and significant absorption. Within this work however, we use an equivalent two-dimensional set of parameters to characterize the spectral behavior of a given optical design. In particular,

N_{0} \equiv \frac{δ}{2 π β} and H_{λ} \equiv 2 \frac{δ}{λ} Δ t \to H_{λ} = \frac{δ}{δ_{c}} \frac{λ_{c}}{λ} with δ_{c} \equiv δ (λ_{c}) .

(1)

As defined by Yang [13

B. X. Yang, “Fresnel and refractive lenses for X-rays,” Nucl. instr. in Phys. Res. A 328, 578–587 (1993). [CrossRef]

], the “critical zone number” N ₀ quantifies the number of π phase shifts within one absorption length. H_λ accounts for the normalized phase shift within the bars B_n via the π -thickness Δt _π = λ_c /2δ_c . The symbol δ_c abbreviates the refractive index increment at a certain “design wavelength” λ_c . Using the definitions from Eq. (1) and based on scalar diffraction [14

C. Braig, P. Predehl, and E.-B. Kley, “Efficient extreme ultraviolet transmission gratings for plasma diagnostics,” Opt. Eng. 50(6), 066501 (2011). [CrossRef]

], the wavelength-dependent efficiency in an order m ≠ 0 is found as

P_{m} (λ) = C_{m}^{2} (1 - 2 cos (π H_{λ}) e^{- \frac{1}{2 N_{0}} H_{λ}} + e^{- \frac{1}{N_{0}} H_{λ}}) with C_{m} \equiv {| π m |}^{- 1} | sin (π f m) | .

(2)

As it follows from Eq. (2), which applies to all “thin” transmission gratings in the scalar approximation, P_m (λ) smoothly peaks for a fill factor f = 0.5 around λ_c , regardless of m ≠ 0. Moreover, an ambiguity with respect to complementary values, i.e. f and 1 – f, is incorporated in the factor C_m . Whereas higher orders with |m| ≥ 2 are strongly suppressed at least ∝ (πm)⁻², phase gratings may concentrate the dominant fraction of the flux into the (±1)^st orders for N ₀ ≳ 1. In case of maximal and negligible absorption, i.e. 0 < N ₀ < ∞, the (±1)^st order efficiency is found as

lim_{N_{0} \to 0} P_{\pm 1} (λ_{c}) = 1 / π^{2}

and

lim_{N_{0} \to \infty} P_{\pm 1} (λ_{c}) = 4 / π^{2}

, respectively. In the EUV, the best materials provide typical efficiencies P _±1 up to ≈ 32%. In contrast, the 0^th order contribution to the diffraction pattern turns out to be quite sensitive to variations of the fill factor. We find

P_{0} (λ) = F_{S}^{2} + 2 cos (π H_{λ}) e^{- \frac{1}{2 N_{0}} H_{λ}} F_{S} F_{B} + e^{- \frac{1}{N_{0}} H_{λ}} F_{B}^{2} with F_{S} \equiv 1 - f and F_{B} \equiv f .

(3)

The asymmetric functional dependence of P ₀(λ) on f for N ₀ < ∞ leads to an optimized fill factor for best 0^th order suppression. From the condition ∂_f P ₀ = 0 we find (1/f)_opt = 1 + exp(−1/2N ₀) at λ_c . As a function of the critical zone number, this fill factor increases with absorption from f ≳ 0.5 for N ₀ ≫ 1 to f ≲ 1.0 in the limit N ₀ → 0. Fig. 2 illustrates the (±1)^st and the 0^th order for realistic values of H_λ and N ₀ in the EUV and soft X-ray band, specified for the fill factor of the sample in use (Sect. 3). As it is shown on the left of Fig. 2, the 0^th order minimum with P ₀(λ) ≤ 0.1% is strongly confined to H_λ ≈ 1.0 and 1.6 ≲ N ₀ ≲ 2.3, an accessible region for λ ≲ 8 nm using high-purity diamond samples (see also Fig. 8 in Sect. 4). If matched for H_λ = 1 at λ_c , the power ratio between the (±1)^st and the 0^th order is found as

P_{\pm 1} / P_{0} = C_{1}^{2} {(1 + G_{N_{0}})}^{2} / {(F_{S} - F_{B} G_{N_{0}})}^{2} with G_{N_{0}} \equiv e^{- 1 / 2 N_{0}} .

(4)

As it follows from Eq. (4), an infinite contrast would be reached for an exactly adapted fill factor f _opt from above – however, inevitable fabrication errors will set limits to this singularity.

Fig. 1 Geometry of plane binary phase gratings, consisting of N slits S_n and bars B_n with 1 ≤ n ≤ N. Their thickness Δt and the fill factor f are drawn to scale with the sample in use. The TE-polarized incident (k⃗ _inc) – and diffracted (k⃗ _out) – light to an angle θ_m is indicated by red arrows, whose relative lengths represent the (Gaussian) intensity distribution.

Fig. 2 General description of binary transmission gratings using the parameters H_λ and N ₀. For the sample in use with f = 0.564, efficiencies of the 0^th and (±1)^st order are shown. The hatched regions indicate an efficiency ≤ 0.1% (left) and ≥ 30% (right), respectively.

Fig. 8 The real and imaginary increment of the refractive index n = 1 − δ − iβ for diamond (left) and the critical zone number N ₀ = δ/(2πβ) (right). In each case, ideal values of pure carbon (black), based on [15

B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92,” Atomic Data and Nuclear Data Tables 54(2), 181–342 (1993). [CrossRef]

], and experimental data (red) of the sample in use are shown.

3. Design constraints and fabrication

Just beyond the K-edge near 4.36 nm, pure carbon excels in terms of its transparency with an absorption length up to 1.0 μm [15

]. Due to its density ≤ 3.52 g cm⁻³, diamond permits the lowest π-thickness Δt_π among all carbon phases, an advantage for an accurate application of the scalar theory – the question of its validity is addressed in the appendix – from Sect. 2 within that “proof-of-concept” work. In Fig. 3, the predicted performance based on Eq. (2) and Eq. (3) is shown in dependence on the fill factor and the thickness Δt, using the data from [15

]. Since the upper extremal regions with Δt > 0.6 μm refer to multiples of the π-thickness, we select the lowest one to obtain the highest (±1)^st order efficiency. In this way, the recommended design is given by f _opt = 0.556 and λ_c = 5.89 nm for Δt = 0.31 μm. This thickness is indeed the fixed parameter of the diamond film in use: We use polished, ∼ 500 μm thick 4” Si wafers in 〈100〉 orientation, coated with a (0.3 ± 0.06) μm thin UNCD film whose density is specified to 3.30 g cm⁻³ [16

Diane P. Hickey, Advanced Diamond Technologies Inc., 429 B Weber Road, #286, Romeoville, IL 60446, United States, http://www.thinDiamond.com (personal communication, 2010).

]. By means of scanning wide-band reflectometry in the ultraviolet and visible regime for a 6% decrease [16

Diane P. Hickey, Advanced Diamond Technologies Inc., 429 B Weber Road, #286, Romeoville, IL 60446, United States, http://www.thinDiamond.com (personal communication, 2010).

] with respect to the nominal refractive index in this wavelength band [17

M. Bass, C. DeCusatis, G. Li, V. N. Mahajan, and E. van Stryland, Handbook of Optics: Optical properties of materials, nonlinear optics, quantum optics (McGraw Hill Professional, New York, 2009).

], the thickness Δt of the unstructured Diamond-on-Silicon (DoSi) layer at the position of the future grating sample is initially determined with an accuracy of ±2%.

Fig. 3 Optimization of binary diamond gratings as a function of the fill factor and thickness Δt. All plots are based on the scalar theory for λ_c = 5.89 nm. Hatched regions indicate an efficiency ≤ 1% (left) or ≥ 30% (middle) and an intensity ratio ≥ 30 (right), respectively.

The grating fabrication is divided into front- and backside-structuring. As shown in Fig. 4, we start with the etching process of the diamond layer. A metal hard mask, 50 nm chromium in this case, is coated by magnetron sputtering. On top, 300 nm of the chemically amplified electron beam resist FEP 171 is spin coated. Therefore, a low electron dose of 9.5 μC cm⁻² is sufficient. With a variable shaped beam electron beam writer (Vistec SB 350 OS), a large area with sub-micron structures can be exposed rapidly. The dry etching of the chromium mask is done with reactive ion etching (RIE) in a conventional parallel-plate reactor SI-591 (Sentech Instruments, Berlin) by means of a chlorine-oxygen plasma. The diamond etching itself is done in the same plasma reactor (SI-591) and stops perfectly on the Si substrate.

Fig. 4 Fabrication of stand-alone binary gratings from DoSi wafers. The Si wafer is colored in light blue, the diamond film in red, and chromium in blue. Resist layers are drawn in gray.

At this point, the front side structuring is finished. The chromium on top of the gratings remains tentatively for protecting the diamond gratings in the following steps of backside structuring. Now the Silicon is etched from the backside through the wafer to the diamond layer on the front side towards self-supporting diamond membranes. To form circular, mm-sized windows in the Si wafer, approximately 14 μm of the DNQ-Novolak based standard photoresist AZ 4562 (Clariant) is spin coated on the backside of the wafer. After soft baking on a hot plate, the resist is exposed with a photo mask in an EVG mask aligner AL 6-2. Due to the large structures in the mm range, there is no need for high resolution. The 14 μm AZ resist layer is fully sufficient to etch more than 700 μm in silicon. The residual chromium on top of the diamond gratings is now removed by RIE. Afterwards, the trough-wafer etching (VIAS) is done by ICP-RIE etching based on the BOSCH® process in a SI-500 C etching tool (Sentech Instruments) at 300 K. Since the Si etching process stops quite well on the diamond, no separate etch stop layer is required for this final step.

A series of free-standing, about 1.4 mm wide membranes and inscribed gratings with a period of 1.0 μm and fill factors 0.55 ≲ f ≲ 0.63 is obtained. To avoid stress-induced irregularities in the grating topography and an associated optical derogation, we choose a circular shape with perpendicular stabilizers (50 μm period), located in the central low stress area of the membrane. SEM pictures are shown in Fig. 5. From the incorporated fill factor variation with an increment of ≈ 10 nm, the best match to the value for f _opt from above is found as f _emp = 0.564 ± 0.006; this sample is selected for the measurements described in Sect. 4.

Fig. 5 SEM pictures of the grating with a period of 1 μm. (a) Backside-etched Si window, spanned by the UNCD membrane (b) Perpendicular support bar (5 μm in width) with adjacent grating structure (c) Determination of the fill factor (d) Crystalline grains of the UNCD film (e) FIB cut of three grating bars (f) Tilted view on the grating-support transition.

4. Measurement technique and results

In normal incidence transmission, all measurements are based on the angular-dependent far-field diffraction pattern recorded in a distance of 980 mm from the sample by a photo diode whose entrance slit width is specified to 1 mm. Filtered by a monochromator to a relative bandwidth of ≲ 10⁻³ and collimated to few 10² μm, efficiencies are determined from the normalized transmission of the TE-polarized synchrotron beam with a nearly symmetric two-dimensional Gaussian intensity profile g(r⃗). In particular, its full widths at half maximum (FWHM) are found from edge scans as (206 ± 2)μm and (196 ± 5)μm. Centered to the grating sample with an accuracy of ±10μm using the local 0^th order transmission minimum, the weighted coverage of the unstructured diamond membrane by the Gaussian beam amounts to 15.7%, including both the stabilizing grid and the surrounding area. In order to deduce the contribution of this non-diffracted light to the 0^th order, the wavelength-dependent transmission through an unstructured stand-alone membrane is measured elsewhere on the DoSi wafer. From its thickness ratio to the sample film – evaluated via reflectometry again – valid results can be extrapolated to T ₀(λ) for the grating sample in use, as listed in Tab. 1. An estimation of the artificial 0^th order contribution P̃ ₀(λ) from non-grating regions covered by the beam is straightforward now,

{\tilde{P}}_{0} (λ) = \int_{ℝ^{2}} g (\vec{r}) Θ_{pur} (\vec{r}) T_{0} (λ) d^{2} r, where \int_{ℝ^{2}} g (\vec{r}) d^{2} r = 1

(5)

denotes the normalization for the Gaussian beam shape from above. The “Heaviside” function Θpur(r⃗) ɛ {0, 1} restricts the integration to non-grating regions. P̃ ₀(λ) decreases almost linearly from ≈ 12% at λ = 5 nm to ≈ 7% at λ = 8 nm and should be subtracted from the raw 0^th order data and fractionally added to all observed orders |m| ≥ 1 according to Eq. (2) to receive the net grating performance. Table 2 gives an overview on both data sets for the diffracted efficiency P _±m with 1 ≤ |m| ≤ 3 within the scanned wavelength region from 5 nm to 7.5 nm. As justified by the measurements, almost equal results from the negative and positive orders are averaged in each case,

P_{\pm m}^{(\circ)} = (P_{- m}^{(\circ)} + P_{+ m}^{(\circ)}) / 2

. The (±1)^st order clearly dominates with corrected efficiencies beyond 20%. In contrast, the (±2)^nd order drops to almost negligible values < 1%, whereas the (±3)^rd order yields ∼ 2%, in good agreement with Eq. (2). Due to its particular importance, the 0^th order is measured within an extended band from 5 nm to 8.3 nm. The results are presented in Fig. 6. We detect an almost perfect collapse of the corrected data at 6.77 nm to P ₀ = 1.0%, an indicator for the good optical quality of our gratings. The error bars shown in Fig. 6 refer to the uncertainty in the artificial 0^th order contribution P̃ ₀(λ) which originates from the standard deviation of the FWHM beam diameters from above. On the right of Fig. 6, the power ratio between the (±1)^st and the 0^th order is shown, with the same error estimation as before. Since this contrast is mainly driven by the 0^th order, the peak is found for the same wavelength, which may be identified with the empirical result for λ_c . Near this central wavelength, the raw data for

P_{0}^{\circ} (λ)

reach their – original – minimum at 6.85 nm. Fig. 7 shows the far field pattern recorded at this wavelength for both the raw and corrected data set again. The efficiencies detected in this scan agree quite well with the results from Tab. 2. However, the 0^th order intensity differs by 0.4% – an aberration which might be attributed to slight alignment tolerances between those independent measurements. Compared to Fig. 3, λ_c is shifted towards longer wavelengths by about 1 nm. This effect may be explained by deviations of the intrinsic optical properties of the diamond sample, namely δ(λ), from its tabulated values. We apply semi-analytical best-fit procedures which adjust Eq. (2) and Eq. (3) to the corrected data using appropriate parameters for H_λ and N ₀. In conjunction with the measured thickness Δt from above, the complex refractive index parameters of the diamond sample can be derived, as shown on the left in Fig. 8. In this case, the statistical uncertainty is negligible and error bars have been omitted, although systematic discrepancies might arise, based on the non-ideal shape of P ₀(λ) around its minimum. From its definition, the critical zone number N ₀ is now directly obtained from those estimations for δ and β, as illustrated on the right of Fig. 8. The error bars in this plot rely on the proximate 2% tolerance in the measured thickness Δt.

Fig. 6 Diffraction efficiency of the 0^th order (left) and the (±1)^st/0^th order power ratio (right) of the measured sample. The center-of-mass symbol indicates the extremal values 1.0% and 29 of the corrected data set. For clarity, only each 2^nd error bar is drawn.

Fig. 7 Far-field diffraction pattern of the sample grating with a period of 1.0μm, measured at λ = 6.85 nm (TE polarization). The plateau-like shape of the peaks originates from the limited width of the detector entrance slit. Only a few error bars in the 0^th order are drawn.

Table 1 Transmission of an unstructured, solid membrane having the same thickness as the structured grating sample, extrapolated from a neighbored region. See text for explanation.

λ[nm]	5.0	5.3	5.6	5.9	6.2	6.5	6.8	7.1	7.4	7.7	8.0
T ₀ [%]	76.4	72.3	68.2	63.8	59.9	56.8	54.0	51.4	48.7	46.0	43.9

Table 2 Measured diffraction efficiencies for |m| ≤ 3 in [%]. Raw data

P_{\pm m}^{\circ}

from the Physikalisch-Technische Bundesanstalt (PTB) are typed in gray, corrected ones in black.

λ [nm]	5.00	5.25	5.50	5.75	6.00	6.25	6.50	6.75	7.00	7.25	7.50
$P_{\pm 1}^{\circ} [%]$	16.0	19.6	22.1	23.6	24.4	24.9	24.9	24.6	24.0	23.2	22.1
P _±1[%]	20.7	24.2	26.5	27.7	28.3	28.6	28.4	28.0	27.3	26.3	25.1
$P_{\pm 2}^{\circ} [%]$	0.37	0.42	0.46	0.47	0.49	0.49	0.48	0.48	0.47	0.45	0.41
P _±2[%]	0.56	0.60	0.63	0.64	0.64	0.64	0.62	0.62	0.60	0.58	0.52
$P_{\pm 3}^{\circ} [%]$	1.46	1.81	2.05	2.19	2.28	2.33	2.35	2.34	2.30	2.20	2.09
P _±3[%]	1.84	2.16	2.39	2.52	2.59	2.62	2.63	2.61	2.55	2.45	2.32

That moderate drop-down of N ₀ by ∼ 15% is typical for “real” high-purity materials whose underlying refractive index data are close to the ideal ones. An investigation of its origin would be nonetheless worthwhile. The manufacturer of the DoSi sample claims negligible metallic contaminations like ₁₃Al, ₂₆Fe and ₇₄W on the ppb level or below [16

Diane P. Hickey, Advanced Diamond Technologies Inc., 429 B Weber Road, #286, Romeoville, IL 60446, United States, http://www.thinDiamond.com (personal communication, 2010).

]. Potential sources of refraction and transmission losses might be rather found in low-Z elements like nitrogen (₇N) and oxygen (₈O), due to their nearby absorption edges near 3.0 nm and 2.3 nm, respectively.

5. Towards applications

The results from above should be regarded as a proof-of-principle in the subject of stand-alone EUV phase transmission gratings. Compared to reflective optics, such components are usually favored with respect to their weight and alignment tolerances – advantages which are of particular interest in astrophysics. Significant progress in plasma spectroscopy requires a resolving power λ/Δλ of at least 10⁴ [18

K. S. Wood, M. P. Kowalski, R. G. Cruddace, and M. A. Barstow, “EUV spectroscopy in astrophysics: The role of compact objects,” Adv. Space Res. 38, 1501–1508 (2006). [CrossRef]

], associated with grating periods in the order of ∼ 100 nm for typical beam diameters around 10⁻³ m and aspect ratios up to ∼ 10. If properly designed, a good (±1)^st order performance would be still maintained for “thick” structures, as it is shown in Tab. 3. Serious but not insuperable technical challenges come along with decreasing grating periods; amongst others, an improved etching procedure has to be developed. The 0^th order is usually not in the scope of interest for spectroscopy. However, 0^th and higher (|m| ≥ 2) order contributions degrade the contrast in interference lithography [4

H. H. Solak, “Nanolithography with coherent extreme ultraviolet light,” J. Phys. D 39, R171–R188 (2006). [CrossRef]

]. Their suppression is thus considered as one of the main tasks in the design of useable EUV phase masks. For the sample from Tab. 3, the 0^th order decreases to ≤ 0.01% near 6.6 nm whereas all orders with |m| ≥ 2 sum up to 7.4%. Advanced gratings are currently investigated in our research group which are capable to diminish this amount of light and provide a resolution down to few 10 nm by frequency doubling [4

H. H. Solak, “Nanolithography with coherent extreme ultraviolet light,” J. Phys. D 39, R171–R188 (2006). [CrossRef]

]. For instance, variations of the binary profile with a period of ∼ 60 nm reduce the summed contribution for |m| ≠ 1 to 2% – with a (±1)^st order efficiency up to 34%.

Table 3 Efficiencies from a rigorous coupled wave analysis (RCWA) of a grating made from UNC diamond with d = 0.1 μm, Δt = 0.32 μm and f = 75% in TE polarization.

λ [nm]	4.6	5.0	5.4	5.8	6.2	6.6	7.0	7.4	7.8	8.2	8.6
$P_{\pm 0}^{*} [%]$	59.6	29.3	14.2	5.56	1.22	0.01	1.02	3.63	7.30	11.5	15.8
$P_{\pm 1}^{*} [%]$	10.1	21.4	27.2	30.5	31.9	31.6	30.5	28.4	25.7	22.4	19.0

6. Conclusion

In summary, we fabricate and test free-standing binary phase transmission gratings made of commercially available diamond films for the EUV band with a (±1)^st order efficiency up to ≈ 28%. An absorbing support layer is avoided, making optics of that type suitable for high-efficient spectroscopy on board of future space-borne missions or for plasma diagnostics in the laboratory. The suppression of the 0^th order to 1% further suggests an application to near-field interference lithography. Next research steps should optimize the optical performance and reduce the grating period to 0.1 μm or less to receive an ultra-high spectral and spatial resolution. Moreover, their astronomical usage requires large-scale segmented assemblies for which robust low-stress ultra-thin membranes should be combined with an appropriate support grid.

Appendices

Within this work, we use the scalar theory which permits an elegant access to the analysis of absorbing phase gratings. Deviations to an exact RCWA calculation arise for “thick” gratings and small feature sizes, compared to the wavelength [19

D. A. Pommet, M. G. Moharam, and E. B. Grann, “Limits of scalar diffraction theory for diffractive phase elements,” J. Opt. Soc. Am. A 11, 1827–1834 (1994). [CrossRef]

]. In the following, we investigate how the period affects the efficiencies P_m (λ) for the design from Sect. 3. Since the error

P_{m}^{★} (λ) - P_{m}^{•} (λ)

between the RCWA model (

P_{m}^{★}

) and the scalar approach (

P_{m}^{•}

) strongly varies with λ we define a universal quantity σ _{P_m} to characterize the wavelength-independent discrepancy via

σ_{P_{m}}^{2} \equiv \frac{1}{λ_{max} - λ_{min}} \int_{λ_{min}}^{λ_{max}} {[P_{m}^{★} (λ) - P_{m}^{•} (λ)]}^{2} d λ for 5.0 nm \leq λ \leq 7.5 nm,

(6)

in analogy to the well-known root-mean-square (RMS) from statistics. Results are shown in Fig. 9. As expected, the mean error significantly increases towards small periods. For d = 1.0 μm, we obtain σ _{P_m} ≲1% for all orders, an acceptable level for sufficiently accurate results. Table 4 gives an explicit overview for this chosen feature size. Aside from the relatively small efficiency errors, the positions of the 0^th order minimum – a sensitive mismatch indicator –differ by 0.036 nm, which is within the uncertainty of 0.050 nm for the acquired data sample.

Fig. 9 RMS difference σ _{P_m} between RCWA calculations and the scalar theory within the spectral range 5.0nm ≤ λ ≤ 7.5nm for |m| ≤ 3. The lines are drawn as a guide to the eye.

Table 4 Comparison of diffraction efficiencies as obtained from an RCWA simulation (

P_{\pm m}^{★}

) and the scalar theory (

P_{\pm m}^{•}

) for the design from Sect. 3 and a period of 1.0 μm.

λ [nm]	5.00	5.25	5.50	5.75	6.00	6.25	6.50	6.75	7.00	7.25	7.50
$P_{\pm 0}^{★} [%]$	18.2	8.65	3.17	0.53	0.05	1.22	3.63	6.88	10.8	15.1	19.7
$P_{\pm 0}^{•} [%]$	17.6	8.16	2.82	0.39	0.15	1.60	4.29	7.85	12.1	16.7	21.6
$P_{\pm 1}^{★} [%]$	27.2	30.4	31.8	32.1	31.5	30.1	28.3	26.1	23.8	21.3	18.7
$P_{\pm 1}^{•} [%]$	27.0	30.1	31.5	31.8	31.1	29.8	28.0	25.8	23.5	21.0	18.5
$P_{\pm 2}^{★} [%]$	0.93	1.00	1.03	1.01	0.96	0.90	0.83	0.76	0.68	0.61	0.54
$P_{\pm 2}^{•} [%]$	1.08	1.20	1.26	1.27	1.24	1.19	1.12	1.03	0.94	0.84	0.74
$P_{\pm 3}^{★} [%]$	2.27	2.57	2.72	2.78	2.75	2.67	2.53	2.37	2.18	1.98	1.77
$P_{\pm 3}^{•} [%]$	2.12	2.36	2.47	2.49	2.44	2.34	2.19	2.03	1.85	1.65	1.45

Acknowledgments

This work was part of the project “Zentrum für Innovationskompetenz ultra optics”, funded by the German Federal Ministry of Education and Research (BMBF) with the fund number 03Z1HN32. All EUV measurements have been performed by F. Scholze, C. Laubis, C. Buchholz and coworkers from the PTB at the synchrotron radiation facility BESSY II in Berlin.

References and links

1.	M. L. Schattenburg, E. H. Anderson, and H. I. Smith, “X-ray/VUV Transmission Gratings for Astrophysical and Laboratory Applications,” Phys. Scripta 41, 13–20 (1990). [CrossRef]
2.	C. Peth, F. Barkusky, and K. Mann, “Near-edge x-ray absorption fine structure measurements using a laboratory-scale XUV source,” J. Phys. D: Appl. Phys. 41, 105202 (2008). [CrossRef]
3.	R. K. Heilmann, M. Ahn, A. Bruccoleri, C.-H. Chang, E. M. Gullikson, P. Mukherjee, and M. L. Schattenburg, “Diffraction efficiency of 200-nm-period critical-angle transmission gratings in the soft x-ray and extreme ultraviolet wavelength bands,” Appl. Opt. 50, 1364–1373 (2011). [CrossRef] [PubMed]
4.	H. H. Solak, “Nanolithography with coherent extreme ultraviolet light,” J. Phys. D 39, R171–R188 (2006). [CrossRef]
5.	M. Itou, T. Harada, and T. Kita, “Soft X-ray monochromator with a varied-space plane grating for synchrotron radiation: design and evaluation,” Appl. Opt. 28, 146–153 (1989). [CrossRef] [PubMed]
6.	H. Lin, L. Zhang, L. Li, C. Jin, H. Zhou, and T. Huo, “High-efficiency multilayer-coated ion-beam-etched blazed grating in the extreme-ultraviolet wavelength region,” Appl. Opt. 49, 4450–4459 (2010).
7.	D. R. McMullin, D. L. Judge, C. Tarrio, R. E. Vest, and F. Hanser, “Extreme-ultraviolet efficiency measurements of freestanding transmission gratings,” Appl. Opt. 43, 3797–3801 (2004). [CrossRef] [PubMed]
8.	K. Flanagan, M. Ahn, J. Davis, R. Heilmann, D. Huenemoerder, A. Levine, H. Marshall, G. Prigozhin, A. Rasmussen, G. Ricker, M. Schattenburg, N. Schulz, and Y. Zhao, “Spectrometer concept and design for X-ray astronomy using a blazed transmission grating,” in Optics for EUV, X-Ray, and Gamma-Ray Astronomy III , Stephen L. O’Dell and Giovanni Pareschi, eds., Proc. SPIE 6688, 66880Y (2007).
9.	F. Salmassi, P. P. Naulleau, E. M. Gullikson, D. L. Olynick, and J. A. Liddle, “EUV Binary Phase Gratings: Fabrication and Application to Diffractive Optics,” http://escholarship.org/uc/item/6d42k5t7 (2005).
10.	P. Predehl, H. W. Braeuninger, A. C. Brinkman, D. Dewey, J. J. Drake, K. A. Flanagan, T. Gunsing, G. D. Hartner, J. Z. Juda, M. Juda, J. S. Kaastra, H. L. Marshall, and D. A. Swartz, “X-ray calibration of the AXAF Low Energy Transmission Grating Spectrometer: effective area,” in Grazing Incidence and Multilayer X-Ray Optical Systems , R. B. Hoover and A. B. C. Walker II, eds., Proc. SPIE 3113, 172–180 (1997).
11.	P. P. Naulleau, C. H. Cho, E. M. Gullikson, and J. Bokor, “Transmission phase gratings for EUV interferometry,” J. Synchrotron Rad. 7, 405–410 (2000). [CrossRef]
12.	M. Saidani and H. H. Solak, “High diffraction-efficiency molybdenum gratings for EUV lithography,” Microel. Eng. 86, 483–485 (2009). [CrossRef]
13.	B. X. Yang, “Fresnel and refractive lenses for X-rays,” Nucl. instr. in Phys. Res. A 328, 578–587 (1993). [CrossRef]
14.	C. Braig, P. Predehl, and E.-B. Kley, “Efficient extreme ultraviolet transmission gratings for plasma diagnostics,” Opt. Eng. 50(6), 066501 (2011). [CrossRef]
15.	B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92,” Atomic Data and Nuclear Data Tables 54(2), 181–342 (1993). [CrossRef]
16.	Diane P. Hickey, Advanced Diamond Technologies Inc., 429 B Weber Road, #286, Romeoville, IL 60446, United States, http://www.thinDiamond.com (personal communication, 2010).
17.	M. Bass, C. DeCusatis, G. Li, V. N. Mahajan, and E. van Stryland, Handbook of Optics: Optical properties of materials, nonlinear optics, quantum optics (McGraw Hill Professional, New York, 2009).
18.	K. S. Wood, M. P. Kowalski, R. G. Cruddace, and M. A. Barstow, “EUV spectroscopy in astrophysics: The role of compact objects,” Adv. Space Res. 38, 1501–1508 (2006). [CrossRef]
19.	D. A. Pommet, M. G. Moharam, and E. B. Grann, “Limits of scalar diffraction theory for diffractive phase elements,” J. Opt. Soc. Am. A 11, 1827–1834 (1994). [CrossRef]

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(340.7480) X-ray optics : X-rays, soft x-rays, extreme ultraviolet (EUV)

ToC Category:
X-ray Optics

History
Original Manuscript: May 9, 2011
Revised Manuscript: June 9, 2011
Manuscript Accepted: June 19, 2011
Published: July 7, 2011

Citation
C. Braig, T. Käsebier, E.-B. Kley, and A. Tünnermann, "Stand-alone diamond binary phase transmission gratings for the EUV band," Opt. Express 19, 14008-14017 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-15-14008

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References

M. L. Schattenburg, E. H. Anderson, and H. I. Smith, “X-ray/VUV Transmission Gratings for Astrophysical and Laboratory Applications,” Phys. Scripta 41, 13–20 (1990). [CrossRef]
C. Peth, F. Barkusky, and K. Mann, “Near-edge x-ray absorption fine structure measurements using a laboratory-scale XUV source,” J. Phys. D: Appl. Phys. 41, 105202 (2008). [CrossRef]
R. K. Heilmann, M. Ahn, A. Bruccoleri, C.-H. Chang, E. M. Gullikson, P. Mukherjee, and M. L. Schattenburg, “Diffraction efficiency of 200-nm-period critical-angle transmission gratings in the soft x-ray and extreme ultraviolet wavelength bands,” Appl. Opt. 50, 1364–1373 (2011). [CrossRef] [PubMed]
H. H. Solak, “Nanolithography with coherent extreme ultraviolet light,” J. Phys. D 39, R171–R188 (2006). [CrossRef]
M. Itou, T. Harada, and T. Kita, “Soft X-ray monochromator with a varied-space plane grating for synchrotron radiation: design and evaluation,” Appl. Opt. 28, 146–153 (1989). [CrossRef] [PubMed]
H. Lin, L. Zhang, L. Li, C. Jin, H. Zhou, and T. Huo, “High-efficiency multilayer-coated ion-beam-etched blazed grating in the extreme-ultraviolet wavelength region,” Appl. Opt. 49, 4450–4459 (2010).
D. R. McMullin, D. L. Judge, C. Tarrio, R. E. Vest, and F. Hanser, “Extreme-ultraviolet efficiency measurements of freestanding transmission gratings,” Appl. Opt. 43, 3797–3801 (2004). [CrossRef] [PubMed]
K. Flanagan, M. Ahn, J. Davis, R. Heilmann, D. Huenemoerder, A. Levine, H. Marshall, G. Prigozhin, A. Rasmussen, G. Ricker, M. Schattenburg, N. Schulz, and Y. Zhao, “Spectrometer concept and design for X-ray astronomy using a blazed transmission grating,” in Optics for EUV, X-Ray, and Gamma-Ray Astronomy III , Stephen L. O’Dell and Giovanni Pareschi, eds., Proc. SPIE6688, 66880Y (2007).
F. Salmassi, P. P. Naulleau, E. M. Gullikson, D. L. Olynick, and J. A. Liddle, “EUV Binary Phase Gratings: Fabrication and Application to Diffractive Optics,” http://escholarship.org/uc/item/6d42k5t7 (2005).
P. Predehl, H. W. Braeuninger, A. C. Brinkman, D. Dewey, J. J. Drake, K. A. Flanagan, T. Gunsing, G. D. Hartner, J. Z. Juda, M. Juda, J. S. Kaastra, H. L. Marshall, and D. A. Swartz, “X-ray calibration of the AXAF Low Energy Transmission Grating Spectrometer: effective area,” in Grazing Incidence and Multilayer X-Ray Optical Systems , R. B. Hoover and A. B. C. Walker, eds., Proc. SPIE3113, 172–180 (1997).
P. P. Naulleau, C. H. Cho, E. M. Gullikson, and J. Bokor, “Transmission phase gratings for EUV interferometry,” J. Synchrotron Rad. 7, 405–410 (2000). [CrossRef]
M. Saidani and H. H. Solak, “High diffraction-efficiency molybdenum gratings for EUV lithography,” Microel. Eng. 86, 483–485 (2009). [CrossRef]
B. X. Yang, “Fresnel and refractive lenses for X-rays,” Nucl. instr. in Phys. Res. A 328, 578–587 (1993). [CrossRef]
C. Braig, P. Predehl, and E.-B. Kley, “Efficient extreme ultraviolet transmission gratings for plasma diagnostics,” Opt. Eng. 50(6), 066501 (2011). [CrossRef]
B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92,” Atomic Data and Nuclear Data Tables 54(2), 181–342 (1993). [CrossRef]
Diane P. Hickey, Advanced Diamond Technologies Inc., 429 B Weber Road, #286, Romeoville, IL 60446, United States, http://www.thinDiamond.com (personal communication, 2010).
M. Bass, C. DeCusatis, G. Li, V. N. Mahajan, and E. van Stryland, Handbook of Optics: Optical properties of materials, nonlinear optics, quantum optics (McGraw Hill Professional, New York, 2009).
K. S. Wood, M. P. Kowalski, R. G. Cruddace, and M. A. Barstow, “EUV spectroscopy in astrophysics: The role of compact objects,” Adv. Space Res. 38, 1501–1508 (2006). [CrossRef]
D. A. Pommet, M. G. Moharam, and E. B. Grann, “Limits of scalar diffraction theory for diffractive phase elements,” J. Opt. Soc. Am. A 11, 1827–1834 (1994). [CrossRef]

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