Tilt-modulated spatial phase imaging method forwafer-mask leveling in proximity lithography
Shaolin Zhou,1,2,* Yong Yang,1 Lixin Zhao,1 and Song Hu1
1State Key Laboratory of Optical Technologies for Microfabrication, Institute of Optics & Electronics,Chinese Academy of Sciences, Chengdu 610209, China
2Graduate University of Chinese Academy of Sciences, Beijing 100039, China*Corresponding author: [email protected]
Received June 3, 2010; revised August 26, 2010; accepted August 26, 2010;posted August 30, 2010 (Doc. ID 129469); published September 15, 2010
Wafer-mask leveling, an adjustment of the gap inconsis-tency between the wafer and mask in the process of gapcontrol in proximity lithography, has always been an es-sential process and the key factor to determine featuresize [1]. Traditionally, the leveling process is achievedby performing a gap measurement at three or more spots[2,3]. Most techniques directly determine the vertical po-sition of the wafer at each spot by inspecting the image ofthe bar or slot like geometric marks on a detector [4,5].These geometric marks are imaged through a reflectionat the wafer surface. The accuracy of these geometricimaging methods is limited compared with other homo-dyne [6,7] or heterodyne methods [8], which measure thevertical position of the wafer by detecting the intensity orphase of interfered beams that diffract from the waferand mask. None of these techniques can remedy tilts be-tween the wafer and mask by carrying out gap measure-ment at only one spot.In this Letter, we propose a method that can achieve
local wafer-mask leveling at just one spot with the accu-racy preserved. The principle of this method can be ex-plained by referring to Fig. 1. Two gratings G1 and G2with close periods P1 and P2 ðP2 < P1Þ are placed adja-cently on the mask, which is assumed to be parallel withthe wafer. The zox plane, determined by the incidentbeam and normal, is defined as the cross section, andthe zoy plane perpendicular to it is defined as the long-itudinal section. At the normal incidence of a monochro-matic planar wave with wavelength λ, diffractions takeplace at the surfaces of the two gratings. At a certaingap, the reflected first-order B1 from G1 spatially over-laps the first-order B2 from G2 at the mask, creatingan interference field, the intensity of which can bederived as
I ¼ I1 þ I2 þ 2ffiffiffiffiffiffiffiffiffiI1I2
pcos
�2πλ ðsin θ1 − sin θ2Þxþ φ0
�:
ð1Þ
Here, grooves of the two gratings are etched along the xaxis; I1, I2 and θ1, θ2 are the intensity and diffractionangles of beams B1 and B2; and φ0 is their original phasedifference. Introducing the diffraction equations of G1and G2, the intensity field can be readily simplified as
I ¼ I1 þ I2 þ 2ffiffiffiffiffiffiffiffiffiI1I2
pcosð2πf 0xþ φ0Þ; ð2Þ
where f 0 ¼ ðsin θ1 − sin θ2Þ=λ ¼ 1=P1 − 1=P2 denotes theoriginal value of the spatial frequency of the interfer-ence field.
When the wafer is tilted in the longitudinal section andcross section by certain small angles δφ and δθ, the re-flected beam B1 from the wafer is deflected in two sec-tions by 2δφ and 2δθ accordingly, causing changes tointerference ofB1 andB2: the interference plane is rotatedand the interference angle is varied. In such a way, phasedistribution of the intensity field is relocated and modu-lated. According to the vector geometrics, the modulatedfield can be readily derived as
Fig. 1. Interference of two beams B1 and B2 diffracted fromG1and G2.
− sin θ2;tan 2δφffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
csc2ðθ1 þ 2δθÞ þ tan2 2δφp
�
indicates the fringe distribution: the value and angle of thespatial frequency and X ¼ ðx; yÞ denotes coordinates inthe xoy plane. According to Eq. (3), rotation of the inter-ference plane is caused by a tilt in the longitudinal section,and a tilt in the cross section induces distinct frequencyvalue variation. Usually the tilted angles in both sectionsare tiny, so variation of the frequency value can be mainlyattributed to tilt in the cross section, and the frequencyvector can be simplified as
F ¼ f expðjθf Þ;
f ¼ jF j ≈ sinðθ1 þ 2δθÞ − sin θ2λ ≈ f 0 þ
2δθλ · cos θ1;
θf ≈ a tan
�cosðθ1 þ 2δθÞ tan 2δφsinðθ1 þ 2δθÞ − sin θ2
�:
Here, f denotes the frequency value of the modulated in-terference field and θf denotes the angle of the wave vec-tor and the rotated angle of the interference field in thexoy plane. A positive or negative value of δθ and δφ de-notes a clockwise or counterclockwise incline of thewafer in both sections, respectively.
To double the sensitivity, we adopt two sets of gratingsbeside each other with a reverse arrangement to generatetwo sets of interference fringes, as shown in Fig. 2. Anytilts in the two sections induce reverse variations in thefrequency values and angles of the two sets of fringes;thus they can be measured and adjusted according tothe discrepancies.
To confirm the feasibility and high sensitivity of thismethod, simulations and experiment are performed.Two gratings with P1 ¼ 2 μm and P2 ¼ 2:2 μm are etchedon the quartz substrate, and a 633 mn laser beam is used.The interference fringes are captured by aWAT902HCCDwith pixel width of about 8 μm and a lens with the magni-fication of 8. Simulation results in Fig. 3 and interceptedexperimental images in Fig. 4 show the process of thewafer being gradually adjusted to be parallel with themask. Figures 3(a) and 4(a) are obtained when the tilts intwo sections are set to be about δθ ¼ 2 × 10−3 rad andδφ ¼ 1 × 10−3 rad. Figures 3(b) and 3(c) indicate that tiltin the longitudinal section and cross section is separatelyremedied. Figures 4(b) and 4(c) are experimentally re-cordedwhen thewafer is separately tilted in two sections.
Fig. 2. Two sets of gratings etched beside each other on a mask.
Fig. 3. Distribution of two sets of fringes when the wafer is tilted in (a) both sections, (b) only the cross section, (c) only thelongitudinal section, and (d) leveled.
Figure 3(d) indicates that tilts in two sections are ideallyremedied, and Fig. 4(d) is recorded under such a condi-tion. In addition, Fig. 5 quantitatively plots the normalizedfrequency deviation and angle deviation of the two sets offringes with regard to tilts in both sections. Two wave-lengths and four sets of gratings with different periodmis-matches are used, shown in the box at the left-hand side ofFig. 5. Tilts in the two sections show good linearity withrespect to the frequency and angle deviation within a cer-tain small angular scope. These curves indicate that theangular sensitivities in the two sections are enhancedwitha smaller grating period mismatch or smaller wavelengthfor the same gratings. And the efficient linear scope isshrunk with the enhanced sensitivity. Computation andexperiment also confirm that angular resolutions in twosections lie nearly at the same magnitude, with the resol-vable tilt in the longitudinal section a little finer than that incross section.
In summary, we present a tilt-modulated phase ima-ging method that can achieve wafer-mask leveling at onlyone spot with preserved accuracy of better than 10−3 rad.Tilts in different directions can be directly remedied ac-cording to the phase distribution of the interference field.Furthermore, finer tilts are expected to be resolved bythis method with robust image-processing algorithms.
We thank Changqing Xie for the mask design andelectron-beam lithography and Wenbo Jiang for maskfabrication. We also acknowledge financial supportfrom the National Natural Science Foundation ofChina (NSFC) through grants 60976077, 60906049, and60776029.
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Fig. 5. Normalized frequency and angular deviation of twosets of fringes with respect to tilt in the (a) cross sectionand (b) longitudinal section.
Fig. 4. Experimental results that correspond to the wafertilted (a) in both sections, (b) only in the cross section, (c) onlyin the longitudinal section, and (d) leveled.
