- Email: [email protected]
Modified Rayleigh criterion for 90 nm lithography technologies and below
Microelectronic Engineering 71 (2004) 139–149 www.elsevier.com/locate/mee
Modified Rayleigh criterion for 90 nm lithography technologies and below Gek Soon Chua a
a,*
, Cho Jui Tay a, Chenggen Quan a, Qunying Lin
b
Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore b Advanced Module Technology Development, Mask Technology, Chartered Semiconductor Manufacturing Ltd., 60 Woodlands Industrial Park D, Street 2, Singapore 738406, Singapore Received 14 August 2003; received in revised form 14 August 2003; accepted 21 October 2003
Abstract In this paper, we have systematically investigated the dependencies of k1 on illumination conditions such as coherence setting and opening angle in off-axis illumination scheme. As result, conventional Rayleigh’s equations are not sufficient to address the effect of NA and coherence on DOF. Therefore, a new metric called coherency factor (rc ) is proposed as a complementary new metric of the low k1 lithography. Coherency factor (rc ) is defined as the ratio of areas of captured first-order and zero-order light. The theory is based on simple geometrical analysis of the diffraction orders in the pupil plane. Areas of different diffraction orders captured by the pupil are evaluated as a function of wavelength, numerical aperture and pitch. As corresponding to experimental results, higher rc value concurs to larger depth of focus. Extracting from Fraunhofer diffraction equation for a single slit and incorporating coherency factor rc , we have modified and extend the use of Rayleigh’s equations for 90 nm processes and below. Results show that the extension of Rayleigh’s equations is capable to optimize the depth of focus and map out the forbidden pitch locations for any design rules and illumination conditions. More importantly, it can complement the concept of objective lens pupil filling to provide the theoretical ground for illumination design in order to suppress the forbidden pitch phenomenon. Ó 2003 Elsevier B.V. All rights reserved. Keywords: Rayleigh’s equations; Off-axis illumination; Dipole illumination; Diffraction orders; Forbidden pitch; Fraunhofer diffraction; Low k1 imaging; Depth of focus
1. Introduction The resolution limit in conventional projection optical lithography is determined by the well-
*
Corresponding author. Tel.: +65-63605272; fax: +6563622945. E-mail address: [email protected] (G.S. Chua).
known Rayleigh’s equations [1,2]. The lithographic factor k1 has long been the standard or the conventional metric for estimating the difficulty of lithographic processes in semiconductor manufacturing. Although k1 is a function of k, NA and resolution (minimum resolvable feature) R, lithographic conditions may vary a lot depending on even a slight change in illumination conditions such as coherence setting, opening
0167-9317/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2003.10.003
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angle and NA in off-axis illumination scheme. Moreover, there is no one-to-one correspondence between illumination scheme (and coherence setting) and k1 . In other words, the ÔsimilarÕ process difficulty can give various k1 values because of variety in coherence setting. Fig. 1 shows the dependencies of k1 on illumination conditions such as coherence setting and opening angle in off-axis illumination scheme. The drive towards 90 nm processes and below makes addressing k1 more immediate as off-axis illumination systems have been used more extensively to improve overall contrast on existing 248 and 193 nm exposure tools. Henceforth, conventional Rayleigh’s equations are not sufficient to address the effect of NA and coherence on DOF. We need to revisit the metric that we have been using to describe the lithographic conditions.
In this paper, a new metric called coherency factor (rc ) is proposed as a complementary new metric of the low k1 lithography. The theory is based on simple geometrical analysis of the diffraction orders in the pupil plane. Optimal depth of focus is obtained when the beams captured by the pupil are symmetrical to the optical axis. This agrees with the theory of 2-beam imaging. Fig. 2 shows the conceptual view of 3-beam and 2-beam imaging. The center image-forming ray does not shift with focus for an on-axis point source; but it moves with focus for an off-axis source point. This concurs to the trend of illumination source shape used in circuit printing to develop into symmetrical shape (from conventional to annular, quadrupole and dipole). The analytical derivation for the modified Rayleigh’s equations is presented in this paper.
Fig. 1. Dependencies of k1 on different illumination conditions.
Fig. 2. Conceptual view of 3-beam and 2-beam imaging.
G.S. Chua et al. / Microelectronic Engineering 71 (2004) 139–149
Based on our modified Rayleigh’s equations, the forbidden pitch locations for any design rules and illumination conditions can be mapped out. It can complement the concept of objective lens pupil filling to provide the theoretical ground for illumination design to suppress the forbidden pitches.
141
center of the pupil, but at an angle to the optical axis. The first-order rays emerge at angles of d with respect to the zeroth-order ray. At the resolution limit, one of the first-order rays passes through the side of the lens pupil opposite to that of the zeroth-order ray, whereas the other complement first-order ray is blocked and falls completely outside of the lens pupil.
2. Theoretical analysis 2.2. Diffraction through a mask
2.1. Forbidden pitch phenomena Several papers have shown [3,4] that off-axis illuminations can improve specific regions; nevertheless there are some pitches (‘‘forbidden pitch’’) that are not enhanced but are degraded by the use of a particular OAI [5,6]. These illuminations bring light to the mask at an oblique angle. Diffraction of light from the patterns on the mask occurs at angles that depend on the pitch of the patterns. Off-axis illumination is optimized at one single pitch such that the angle of illumination striking the mask matches the angle of diffraction for a given pitch to give optimum performance (spread of the diffraction orders evenly about the center of the stepper lens). When the off-axis illumination is optimized for the smallest pitch on the mask, there will be some pitches where the angle of the illumination interferes destructively with the angle of diffraction to produce a very bad distribution of diffraction orders in the lens. This results in poor depth of focus for that pitch. This can be explained in Fig. 3 where one diffraction order is in the center of the lens and the others at the outer edges of the lens. Zeroth-order light no longer passes through the
Light rays traveling through the transparent features of the reticle will be diffracted, and will interfere constructively or destructively with each other. Only the rays diffracted at certain angles will interfere constructively and form peaks. In this way a diffraction pattern is formed. This diffraction pattern is partially caught by the objective lens, which will use it to reconstruct the image. The angles of constructive interference are: sinðdÞ ¼
nk ; P
ð1Þ
where d is the diffraction angle; n equals 0; 1; 2; . . . (order of light); k is the wavelength; P is the period between the lines. In off-axis illumination, the incident coherent light rays do not travel perpendicular to the reticle plane but at an angle / (/ is the angle of incidence) as shown in Fig. 4. The diffraction pattern does not change but is shifted over a distance sinð/Þ=k. A partially coherent light source can be treated as a finite number of coherent light sources, all generating coherent light rays, striking the reticle at different angles /, and creating a diffraction pattern (as shown in Fig. 5) on the objective lens.
Fig. 3. Distribution of diffraction orders in the lens.
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It was determined that the larger the partial coherence factor, the higher the resolvable spatial frequency. The larger the angular separation between the two rays, the tighter will be the spatial period. Fig. 6 shows the schematic diagram of light rays striking on the mask gratings to form diffraction pattern. In optical lithography, the imageforming light rays propagate with angles h1 , h2 , such that jsinðh2 h1 Þj 6 sin a:
ð2Þ
The highest spatial frequency is thus produced from interference of the most oblique rays having an angle d between them. Extracting from Fraunhofer diffraction for a single slit: constructive interference occurs when the path difference is a multiple of the wavelength [7]: p sin d ¼ nk Fig. 4. Schematic diagram of diffraction through a binary mask.
ðn ¼ 1; 2; 3; . . .Þ;
ð3Þ
where d is the angle between the zeroth- and firstorder light and p is the pitch. A diffracted image cannot be truly reconstructed unless at least first-order or higher order light is collected. These two diffraction orders are sufficient for imaging. Hence therefore for a particular pitch, at an illumination setting (light traveling in shaded sector), feature is patterned if sinðdÞ is less than sinðaÞ as shown in Fig. 6. Henceforth for a range of incidence angle d between h1 and h2 , related to illumination coherency at a particular pitch size would image the pattern. For different off-axis illumination schemes
Fig. 5. Diffraction pattern for off-axis illumination (annular or dipole) scheme.
2.3. Fraunhofer diffraction theory In lithography, diffraction can be described by Fraunhofer diffraction because we are working in the far field region. For repeating patterns (such as a line/space array), the diffraction pattern becomes discrete diffracted orders. Diffraction orders correspond to condition of constructive interference. Information about the pitch is contained in the positions of the diffracted orders, and the amplitude of the orders determines the duty cycle.
Fig. 6. Schematic diagram for explanation for Fraunhofer diffraction.
G.S. Chua et al. / Microelectronic Engineering 71 (2004) 139–149
and different pitch sizes, we can better understand the relationship between coherence setting (h1 and h2 ), diffraction orders and pitch sizes through use of Fraunhofer diffraction in Fig. 6. Knowing this, we can map out the pitch size where the incidence angle will not be captured fully or partially. 2.4. Extension of Rayleigh criterion From the concept of objective lens pupil filling, we know that ri , ro and pitch p would affect DOF. Decreasing the pitch will shift the firstorder diffraction order closer to zeroth-order light, and for some pitches up to forbidden pitch will lie inside the lens aperture. This will relax the coherency factor rc where we define it as the contrast gain, i.e., overlap of zeroth- and firstorder light. Therefore coherency factor rc / k=ðpðNAÞÞ:
ð4Þ
We introduced the coherency factor rc as a complementary new metric of the low k1 lithography, Coherency factor rc area of captured first-order light : ¼ area of zero-order light
ð5Þ
The coherency factor rc is defined as in Eq. (5), which means the ratio of the captured first-order light to the total zero order light. Different illumination conditions can be degenerated into each coherency factor rc . For higher order light contributing to imaging (although zero and first diffraction orders are sufficient for imaging), we can compute the overall coherency factor (OCF) taking into consideration of higher order light that contribute to imaging as shown in Fig. 7.
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From Rayleigh equation, increasing NA would reduce DOF. In a way as we can see from Fraunhofer diffraction equation, increasing NA, functional smallest pitch will reduce, therefore up to this smallest functional pitch, increasing pitch would reduce DOF. Beyond this pitch, scattering bars and optical proximity corrections are required. Therefore; incorporating coherency factor rc ; DOF ¼ ðk3 =pÞ ½k=ðNA2 Þ;
ð6Þ
where k3 is a measure of illumination coherency k3 ¼ ðDOFÞ ½p ðNA2 Þ=k: Therefore;
k3 / 1=r2c :
ð7Þ ð8Þ
Hence, we have the extension of Rayleigh Criterion that is now capable of relating DOF with pitch, taking consideration of the coherency factor rc of illumination. It can now be used to compare DOF equation for various different illumination and partial coherence. It can be used to map out the forbidden pitch locations for any feature size and illumination conditions. More importantly, it can complement the concept of objective lens pupil filling to provide the theoretical ground for illumination design in order to suppress the forbidden pitch phenomenon. One should use the maximum partial coherence factor available if resolution is the primary concern. Nevertheless, overfilling the pupil does not further decrease the resolution limit. The magnitude of depth of focus is scaled by the factor k3 ð/ 1=r2c Þ representing light loss due to overfilling of the pupil by the illumination. Therefore incorporating coherency factor rc , as pitch decreases, k3 decreases at an even faster rate. Hence depth of
Fig. 7. Computation of overall coherency factor (OCF) for higher order light that contribute to imaging.
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focus will not go unreasonably large as pitch reduces.
3. Experimental conditions All experiments are carried out on an ArF Step & Scan system, where projection lens equipped with a variable NA up to 0.75. Dipole illumination is performed using 35° opening angle with 0° orientation. All the wafer experiments are exposed using binary mask for different illumination settings to investigate the effects of NA, ri and ro . Table 1 illustrates the design of experiment. All wafer measurements were done using top-down CD-SEM. Low voltage beam was optimized to minimize the resist slimming effects. The evaluated patterns were 140–120 nm line and space (L&S) short patterns without mask bias, and their pitch was 1:1.
4. Results and discussions 4.1. Coherency factor (rc ) and k3 We have derived an analytical expression for coherency factor rc . Coherency factor rc is eval-
uated as the ratio of areas of diffracted orders captured by the pupil plane. All interaction surfaces can be computed easily as a superposition of portions of circles. When the pitch becomes larger, we can have different situations, for example, interaction between higher diffracted orders and zeroth-order. We see that increasing ro would lead to loss in exposure latitude, as the contrast is reduced. Increasing NA nevertheless will help to increase the exposure latitude across pitch, because increasing NA can be deemed as reducing the pitch size and pushing the first-order light closer to zeroth-order light. Fig. 8 shows the relation between k3 =R and depth of focus for different illumination scheme (annular, dipole and conventional). Result shows a linear relation between k3 =R and depth of focus, independence of illumination scheme. Furthermore, higher k3 represents a clear indication of larger depth of focus. From Fig. 8, dipole illumination (for varying coherency setting; NA, ri and ro ) are capable of obtaining largest depth of focus as compared to annular and conventional illumination. This shows that k3 =R (normalized for each technology node R) can vary for different illumination conditions but same k3 =R value still yields the same depth of focus (regardless of illumination
Table 1 Design of experiment (Illumination settings) Cassette slot
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Illumination settings
Feature target
NA
Sigma out
Sigma in
90
0.65 0.75 0.7 0.7 0.7 0.75 0.65 0.75 0.7 0.7 0.7 0.75 0.65 0.75 0.7 0.7 0.75
0.8 0.8 0.7 0.8 0.7 0.7 0.8 0.8 0.7 0.8 0.7 0.7
0.5 0.3 0.5 0.5 0.4 0.5 0.5 0.3 0.5 0.5 0.4 0.5
90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90
PC ¼ 0.8 PC ¼ 0.8 PC ¼ 0.7 PC ¼ 0.8 PC ¼ 0.7
Illumination condition # Annular Annular Annular Annular Annular Annular Dipole 35° angle Dipole 35° angle Dipole 35° angle Dipole 35° angle Dipole 35° angle Dipole 35° angle Conventional Conventional Conventional Conventional Conventional
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1
1.8 1.6
k3/R
1.4
Annular Dipole Conventional
1.2 1 0.8 0.6 0.4
0.8 0.7 2
R = 0.9229
0.6
Annular Dipole Conventional
0.5 0.4 0.3 0.2 0.1
0.2
0
0 0
100
200
300
400
Fig. 8. Relation between k3 =R and depth of focus for different illumination scheme.
scheme). The analytical derivation for the modified Rayleigh’s equations: k3 ¼ ðDOFÞ ½p ðNA2 Þ=k (where k3 is a measure of illumination coherency) has been proven using experimental result. Fig. 9 shows the relation between coherency factor rc and depth of focus for different illumination scheme (annular, dipole and conventional). We see that for each illumination scheme, there is a linear relation between its coherency factor rc and depth of focus. Clearly, higher coherency factor rc will yield larger depth of focus for each illumination scheme (regardless of its illumination setting; NA, ri and ro and opening angle). Furthermore, we see that there is intersection between
0.9 0.8 0.7
Annular Dipole Conventional
0.6 0.5 0.4 0.3 0.2 0.1 0 0
100
200
300
0
100
200
300
400
Depth of focus (nm)
Depth of focus (nm)
coherency factor, sigma
coherency factor, sigma
0.9
400
Depth of focus (nm) Fig. 9. Relation between coherency factor rc and depth of focus for different illumination scheme.
Fig. 10. Linear relation between coherency factor rc and depth of focus for different illumination scheme.
annular and conventional illumination, indicating that for the same coherency factor rc , regardless of its illumination conditions, we will still yield the same depth of focus. Considering that there is a clear indication that there is a linear relation between its coherency factor rc and depth of focus, Fig. 10 examines the possible linear relation for coherency factor rc and depth of focus for different illumination scheme. High R2 value indicates a strong linear relation. We can better understand the relation between the coherency setting on depth of focus. These coherency settings which includes pitch sizes and illumination conditions have been shown to follow a strong linear relation to depth of focus. Using Fig. 10 as our lookup graph, for coherency factor rc value lower than 0.4 is considered weak for imaging and should be avoided and classified as the forbidden pitch locations for that particular design rules and illumination conditions. It can be used to complement the concept of objective lens pupil filling to provide the theoretical ground for illumination design to suppress the forbidden pitches. Fig. 11 shows the linear relation between k3 =R and coherency factor rc for different illumination scheme. Result shows that coherency factor rc (describing the optical conditions of wavelength and NA, illumination settings and including the effect of typical resolution enhancement techniques such as scattering bars) is related to depth of focus through k3 =R as derived in the modified Rayleigh’s equations: k3 ¼ ðDOFÞ ½p ðNA2 Þ=k
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G.S. Chua et al. / Microelectronic Engineering 71 (2004) 139–149
1.8 1.6
k3/R
1.4
Annular Dipole Conventional
1.2 2
R = 0.9036
1 0.8 0.6 0.4 0.2 0 0
0.5
1
coherency factor, sigma Fig. 11. Relation between k3 =R and coherency factor rc for different illumination scheme.
(where k3 is a measure of illumination coherency). Moreover, coherency factor rc for other resolution enhancement techniques such as alternating or attenuated phase shift mask can also be derived for further studies. 4.2. Illumination optimization Table 2 shows the frequency distribution of the first diffraction orders in the objective lens for Table 2 Diffraction patterns for different coherence setting
90 nm equal lines and spaces for different dipole and annular illuminations, varying NAs and sigmas. Top-down SEM images for 90 nm equal lines and spaces through defocus using ArF, for different annular illumination, varying NAs and sigmas are shown in Fig. 12. We see that using annular illumination, contrast is lower as there is now more amount of light that contributes to background. Table 3 shows the experimental data for depth of focus for different illumination settings. EL-DOF windows are determined by a rectangle EL-DOF fit in the process window. DOF is defined as DOF at 10% EL. For comparison, annular illumination on an identical setting was measured to have a maximum EL of 6%. The coherency factor rc is measured by the amount of first-order light divided by the amount of zeroth-order light. We will be able to determine whether there is more zeroth-order light that contributes to background light and reduces contrast (i.e., in turn reducing exposure latitude) from this coherency factor rc . This coherency factor rc is therefore useful for application to all off-axis illumination that includes Quasar and Quadrupole, as it can take into consideration of each
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Fig. 12. Top-down SEM images for 90 nm equal lines and spaces through defocus using ArF, for different annular illumination, varying NAs and sigmas.
Table 3 Experimental results: DOF-EL for different off-axis illumination settings, (varying NAs and sigmas)
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Fig. 13. Top-down SEM images for 90 nm equal lines and spaces through defocus using ArF, for different dipole illumination, varying NAs and sigmas.
illumination scheme that have opening angles and orientations. Top-down SEM images for 90 nm equal lines and spaces through defocus using ArF, for different dipole illumination, varying NAs and sigmas are shown in Fig. 13. The concept of objective lens pupil filling can be used to maximize DOF and EL. It can also be used as criteria for selecting illumination aperture. Largest DOF can be obtained with the largest overlap between the zeroth- and first-orders light. Aerial image contrast (EL) can be maximized and it depends on the amount of first-order diffracted light captured by the projection lens. These are illustrated in Table 3. The pitch defines the location of the first diffraction orders. The zero order is displayed in white, the first orders in dark gray. The overlap region is displayed as a mix of the two colors (lighter gray). The depth of focus can be optimized using this method. For a given wavelength, pitch, NA and for every illumination shape, the partial coherence can be optimized by matching
the highest coherency factor rc . We notice that the usual rc value is between 0.4 and 0.8 today.
5. Conclusion In this paper, we have systematically investigated the methodology of using concept of objective lens pupil filling to print 90 nm equal lines and spaces. The methodology for the process optimization used is based on simple geometrical analysis of the diffraction orders in the pupil plane. A new metric called coherency factor (rc ) is proposed as a complementary new metric of the low k1 lithography. As corresponding to experimental results, higher rc value concurs to larger depth of focus. Extracting from Fraunhofer diffraction equation for a single slit and incorporating coherency factor rc , we have modified and extend the use of Rayleigh’s equations for 90 nm processes and below.
G.S. Chua et al. / Microelectronic Engineering 71 (2004) 139–149
We propose a modified Rayleigh’s equation that considers the influence of coherencies on lithographic resolution, and confirm that lithographic performance can be predicted more accurately by the modified equation than by the conventional equation. Results show that the extension of Rayleigh’s equations is capable to optimize the depth of focus and map out the forbidden pitch locations for any design rules and illumination conditions.
Acknowledgements The authors would like to thank Tan Sia Kim and Andrew Khoh from Chartered Semiconductor Mfg. Ltd. for their technical advice. The authors would also like to thank Donis and Anita from ASML for their help in printing the dipole demo wafers.
149
References [1] Max Born, Emil Wolf, Principles of Optics, seventh ed., Cambridge University Press, 2002, Chapter VII, pp. 371. [2] Max Born, Emil Wolf, Principles of Optics, seventh ed., Cambridge University Press, 2002, Chapter VIII, pp. 461–465. [3] J. Fung, Chen, Tom Laidig, Kurt E. Wampler, Roger Caldwell, Kent H. Nakagawa, Armin Liebchen, A practical technology path to sub-0.10 micron process generations via enhanced optical lithography, SPIE 3873 (1999) 995– 1016. [4] Gek Soon Chua, Qunying Lin, Cho Jui Tay, Chenggen Quan, Sub-0.10 lm lithography technology with resolution enhancement technique, SPIE 4691 (2002) 1563–1574. [5] Robert Socha, Mircea Dusa, Luigi Capodieci, Jo Finders, Fung Chen, Donis Flagella, Kevin Cummings, Forbidden Pitches for130 nm lithography and below, SPIE 4000 (2000) 1140–1155. [6] Xuelong Shi, Stephen Hsu, Fung Chen, Michael Hsu, Robert J. Socha, Micea Dusa, Understanding the forbidden pitch phenomenon and assist feature placement, SPIE 4689 (2002) 985–996. [7] Max Born, Emil Wolf, Principles of Optics, seventh ed., Cambridge University Press, 2002, Chapter VIII, pp. 446–453.
Modified Rayleigh criterion for 90 nm lithography technologies and below Gek Soon Chua a
a,*
, Cho Jui Tay a, Chenggen Quan a, Qunying Lin
b
Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore b Advanced Module Technology Development, Mask Technology, Chartered Semiconductor Manufacturing Ltd., 60 Woodlands Industrial Park D, Street 2, Singapore 738406, Singapore Received 14 August 2003; received in revised form 14 August 2003; accepted 21 October 2003
Abstract In this paper, we have systematically investigated the dependencies of k1 on illumination conditions such as coherence setting and opening angle in off-axis illumination scheme. As result, conventional Rayleigh’s equations are not sufficient to address the effect of NA and coherence on DOF. Therefore, a new metric called coherency factor (rc ) is proposed as a complementary new metric of the low k1 lithography. Coherency factor (rc ) is defined as the ratio of areas of captured first-order and zero-order light. The theory is based on simple geometrical analysis of the diffraction orders in the pupil plane. Areas of different diffraction orders captured by the pupil are evaluated as a function of wavelength, numerical aperture and pitch. As corresponding to experimental results, higher rc value concurs to larger depth of focus. Extracting from Fraunhofer diffraction equation for a single slit and incorporating coherency factor rc , we have modified and extend the use of Rayleigh’s equations for 90 nm processes and below. Results show that the extension of Rayleigh’s equations is capable to optimize the depth of focus and map out the forbidden pitch locations for any design rules and illumination conditions. More importantly, it can complement the concept of objective lens pupil filling to provide the theoretical ground for illumination design in order to suppress the forbidden pitch phenomenon. Ó 2003 Elsevier B.V. All rights reserved. Keywords: Rayleigh’s equations; Off-axis illumination; Dipole illumination; Diffraction orders; Forbidden pitch; Fraunhofer diffraction; Low k1 imaging; Depth of focus
1. Introduction The resolution limit in conventional projection optical lithography is determined by the well-
*
Corresponding author. Tel.: +65-63605272; fax: +6563622945. E-mail address: [email protected] (G.S. Chua).
known Rayleigh’s equations [1,2]. The lithographic factor k1 has long been the standard or the conventional metric for estimating the difficulty of lithographic processes in semiconductor manufacturing. Although k1 is a function of k, NA and resolution (minimum resolvable feature) R, lithographic conditions may vary a lot depending on even a slight change in illumination conditions such as coherence setting, opening
0167-9317/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.mee.2003.10.003
140
G.S. Chua et al. / Microelectronic Engineering 71 (2004) 139–149
angle and NA in off-axis illumination scheme. Moreover, there is no one-to-one correspondence between illumination scheme (and coherence setting) and k1 . In other words, the ÔsimilarÕ process difficulty can give various k1 values because of variety in coherence setting. Fig. 1 shows the dependencies of k1 on illumination conditions such as coherence setting and opening angle in off-axis illumination scheme. The drive towards 90 nm processes and below makes addressing k1 more immediate as off-axis illumination systems have been used more extensively to improve overall contrast on existing 248 and 193 nm exposure tools. Henceforth, conventional Rayleigh’s equations are not sufficient to address the effect of NA and coherence on DOF. We need to revisit the metric that we have been using to describe the lithographic conditions.
In this paper, a new metric called coherency factor (rc ) is proposed as a complementary new metric of the low k1 lithography. The theory is based on simple geometrical analysis of the diffraction orders in the pupil plane. Optimal depth of focus is obtained when the beams captured by the pupil are symmetrical to the optical axis. This agrees with the theory of 2-beam imaging. Fig. 2 shows the conceptual view of 3-beam and 2-beam imaging. The center image-forming ray does not shift with focus for an on-axis point source; but it moves with focus for an off-axis source point. This concurs to the trend of illumination source shape used in circuit printing to develop into symmetrical shape (from conventional to annular, quadrupole and dipole). The analytical derivation for the modified Rayleigh’s equations is presented in this paper.
Fig. 1. Dependencies of k1 on different illumination conditions.
Fig. 2. Conceptual view of 3-beam and 2-beam imaging.
G.S. Chua et al. / Microelectronic Engineering 71 (2004) 139–149
Based on our modified Rayleigh’s equations, the forbidden pitch locations for any design rules and illumination conditions can be mapped out. It can complement the concept of objective lens pupil filling to provide the theoretical ground for illumination design to suppress the forbidden pitches.
141
center of the pupil, but at an angle to the optical axis. The first-order rays emerge at angles of d with respect to the zeroth-order ray. At the resolution limit, one of the first-order rays passes through the side of the lens pupil opposite to that of the zeroth-order ray, whereas the other complement first-order ray is blocked and falls completely outside of the lens pupil.
2. Theoretical analysis 2.2. Diffraction through a mask
2.1. Forbidden pitch phenomena Several papers have shown [3,4] that off-axis illuminations can improve specific regions; nevertheless there are some pitches (‘‘forbidden pitch’’) that are not enhanced but are degraded by the use of a particular OAI [5,6]. These illuminations bring light to the mask at an oblique angle. Diffraction of light from the patterns on the mask occurs at angles that depend on the pitch of the patterns. Off-axis illumination is optimized at one single pitch such that the angle of illumination striking the mask matches the angle of diffraction for a given pitch to give optimum performance (spread of the diffraction orders evenly about the center of the stepper lens). When the off-axis illumination is optimized for the smallest pitch on the mask, there will be some pitches where the angle of the illumination interferes destructively with the angle of diffraction to produce a very bad distribution of diffraction orders in the lens. This results in poor depth of focus for that pitch. This can be explained in Fig. 3 where one diffraction order is in the center of the lens and the others at the outer edges of the lens. Zeroth-order light no longer passes through the
Light rays traveling through the transparent features of the reticle will be diffracted, and will interfere constructively or destructively with each other. Only the rays diffracted at certain angles will interfere constructively and form peaks. In this way a diffraction pattern is formed. This diffraction pattern is partially caught by the objective lens, which will use it to reconstruct the image. The angles of constructive interference are: sinðdÞ ¼
nk ; P
ð1Þ
where d is the diffraction angle; n equals 0; 1; 2; . . . (order of light); k is the wavelength; P is the period between the lines. In off-axis illumination, the incident coherent light rays do not travel perpendicular to the reticle plane but at an angle / (/ is the angle of incidence) as shown in Fig. 4. The diffraction pattern does not change but is shifted over a distance sinð/Þ=k. A partially coherent light source can be treated as a finite number of coherent light sources, all generating coherent light rays, striking the reticle at different angles /, and creating a diffraction pattern (as shown in Fig. 5) on the objective lens.
Fig. 3. Distribution of diffraction orders in the lens.
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It was determined that the larger the partial coherence factor, the higher the resolvable spatial frequency. The larger the angular separation between the two rays, the tighter will be the spatial period. Fig. 6 shows the schematic diagram of light rays striking on the mask gratings to form diffraction pattern. In optical lithography, the imageforming light rays propagate with angles h1 , h2 , such that jsinðh2 h1 Þj 6 sin a:
ð2Þ
The highest spatial frequency is thus produced from interference of the most oblique rays having an angle d between them. Extracting from Fraunhofer diffraction for a single slit: constructive interference occurs when the path difference is a multiple of the wavelength [7]: p sin d ¼ nk Fig. 4. Schematic diagram of diffraction through a binary mask.
ðn ¼ 1; 2; 3; . . .Þ;
ð3Þ
where d is the angle between the zeroth- and firstorder light and p is the pitch. A diffracted image cannot be truly reconstructed unless at least first-order or higher order light is collected. These two diffraction orders are sufficient for imaging. Hence therefore for a particular pitch, at an illumination setting (light traveling in shaded sector), feature is patterned if sinðdÞ is less than sinðaÞ as shown in Fig. 6. Henceforth for a range of incidence angle d between h1 and h2 , related to illumination coherency at a particular pitch size would image the pattern. For different off-axis illumination schemes
Fig. 5. Diffraction pattern for off-axis illumination (annular or dipole) scheme.
2.3. Fraunhofer diffraction theory In lithography, diffraction can be described by Fraunhofer diffraction because we are working in the far field region. For repeating patterns (such as a line/space array), the diffraction pattern becomes discrete diffracted orders. Diffraction orders correspond to condition of constructive interference. Information about the pitch is contained in the positions of the diffracted orders, and the amplitude of the orders determines the duty cycle.
Fig. 6. Schematic diagram for explanation for Fraunhofer diffraction.
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and different pitch sizes, we can better understand the relationship between coherence setting (h1 and h2 ), diffraction orders and pitch sizes through use of Fraunhofer diffraction in Fig. 6. Knowing this, we can map out the pitch size where the incidence angle will not be captured fully or partially. 2.4. Extension of Rayleigh criterion From the concept of objective lens pupil filling, we know that ri , ro and pitch p would affect DOF. Decreasing the pitch will shift the firstorder diffraction order closer to zeroth-order light, and for some pitches up to forbidden pitch will lie inside the lens aperture. This will relax the coherency factor rc where we define it as the contrast gain, i.e., overlap of zeroth- and firstorder light. Therefore coherency factor rc / k=ðpðNAÞÞ:
ð4Þ
We introduced the coherency factor rc as a complementary new metric of the low k1 lithography, Coherency factor rc area of captured first-order light : ¼ area of zero-order light
ð5Þ
The coherency factor rc is defined as in Eq. (5), which means the ratio of the captured first-order light to the total zero order light. Different illumination conditions can be degenerated into each coherency factor rc . For higher order light contributing to imaging (although zero and first diffraction orders are sufficient for imaging), we can compute the overall coherency factor (OCF) taking into consideration of higher order light that contribute to imaging as shown in Fig. 7.
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From Rayleigh equation, increasing NA would reduce DOF. In a way as we can see from Fraunhofer diffraction equation, increasing NA, functional smallest pitch will reduce, therefore up to this smallest functional pitch, increasing pitch would reduce DOF. Beyond this pitch, scattering bars and optical proximity corrections are required. Therefore; incorporating coherency factor rc ; DOF ¼ ðk3 =pÞ ½k=ðNA2 Þ;
ð6Þ
where k3 is a measure of illumination coherency k3 ¼ ðDOFÞ ½p ðNA2 Þ=k: Therefore;
k3 / 1=r2c :
ð7Þ ð8Þ
Hence, we have the extension of Rayleigh Criterion that is now capable of relating DOF with pitch, taking consideration of the coherency factor rc of illumination. It can now be used to compare DOF equation for various different illumination and partial coherence. It can be used to map out the forbidden pitch locations for any feature size and illumination conditions. More importantly, it can complement the concept of objective lens pupil filling to provide the theoretical ground for illumination design in order to suppress the forbidden pitch phenomenon. One should use the maximum partial coherence factor available if resolution is the primary concern. Nevertheless, overfilling the pupil does not further decrease the resolution limit. The magnitude of depth of focus is scaled by the factor k3 ð/ 1=r2c Þ representing light loss due to overfilling of the pupil by the illumination. Therefore incorporating coherency factor rc , as pitch decreases, k3 decreases at an even faster rate. Hence depth of
Fig. 7. Computation of overall coherency factor (OCF) for higher order light that contribute to imaging.
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focus will not go unreasonably large as pitch reduces.
3. Experimental conditions All experiments are carried out on an ArF Step & Scan system, where projection lens equipped with a variable NA up to 0.75. Dipole illumination is performed using 35° opening angle with 0° orientation. All the wafer experiments are exposed using binary mask for different illumination settings to investigate the effects of NA, ri and ro . Table 1 illustrates the design of experiment. All wafer measurements were done using top-down CD-SEM. Low voltage beam was optimized to minimize the resist slimming effects. The evaluated patterns were 140–120 nm line and space (L&S) short patterns without mask bias, and their pitch was 1:1.
4. Results and discussions 4.1. Coherency factor (rc ) and k3 We have derived an analytical expression for coherency factor rc . Coherency factor rc is eval-
uated as the ratio of areas of diffracted orders captured by the pupil plane. All interaction surfaces can be computed easily as a superposition of portions of circles. When the pitch becomes larger, we can have different situations, for example, interaction between higher diffracted orders and zeroth-order. We see that increasing ro would lead to loss in exposure latitude, as the contrast is reduced. Increasing NA nevertheless will help to increase the exposure latitude across pitch, because increasing NA can be deemed as reducing the pitch size and pushing the first-order light closer to zeroth-order light. Fig. 8 shows the relation between k3 =R and depth of focus for different illumination scheme (annular, dipole and conventional). Result shows a linear relation between k3 =R and depth of focus, independence of illumination scheme. Furthermore, higher k3 represents a clear indication of larger depth of focus. From Fig. 8, dipole illumination (for varying coherency setting; NA, ri and ro ) are capable of obtaining largest depth of focus as compared to annular and conventional illumination. This shows that k3 =R (normalized for each technology node R) can vary for different illumination conditions but same k3 =R value still yields the same depth of focus (regardless of illumination
Table 1 Design of experiment (Illumination settings) Cassette slot
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Illumination settings
Feature target
NA
Sigma out
Sigma in
90
0.65 0.75 0.7 0.7 0.7 0.75 0.65 0.75 0.7 0.7 0.7 0.75 0.65 0.75 0.7 0.7 0.75
0.8 0.8 0.7 0.8 0.7 0.7 0.8 0.8 0.7 0.8 0.7 0.7
0.5 0.3 0.5 0.5 0.4 0.5 0.5 0.3 0.5 0.5 0.4 0.5
90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90 90
PC ¼ 0.8 PC ¼ 0.8 PC ¼ 0.7 PC ¼ 0.8 PC ¼ 0.7
Illumination condition # Annular Annular Annular Annular Annular Annular Dipole 35° angle Dipole 35° angle Dipole 35° angle Dipole 35° angle Dipole 35° angle Dipole 35° angle Conventional Conventional Conventional Conventional Conventional
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1
1.8 1.6
k3/R
1.4
Annular Dipole Conventional
1.2 1 0.8 0.6 0.4
0.8 0.7 2
R = 0.9229
0.6
Annular Dipole Conventional
0.5 0.4 0.3 0.2 0.1
0.2
0
0 0
100
200
300
400
Fig. 8. Relation between k3 =R and depth of focus for different illumination scheme.
scheme). The analytical derivation for the modified Rayleigh’s equations: k3 ¼ ðDOFÞ ½p ðNA2 Þ=k (where k3 is a measure of illumination coherency) has been proven using experimental result. Fig. 9 shows the relation between coherency factor rc and depth of focus for different illumination scheme (annular, dipole and conventional). We see that for each illumination scheme, there is a linear relation between its coherency factor rc and depth of focus. Clearly, higher coherency factor rc will yield larger depth of focus for each illumination scheme (regardless of its illumination setting; NA, ri and ro and opening angle). Furthermore, we see that there is intersection between
0.9 0.8 0.7
Annular Dipole Conventional
0.6 0.5 0.4 0.3 0.2 0.1 0 0
100
200
300
0
100
200
300
400
Depth of focus (nm)
Depth of focus (nm)
coherency factor, sigma
coherency factor, sigma
0.9
400
Depth of focus (nm) Fig. 9. Relation between coherency factor rc and depth of focus for different illumination scheme.
Fig. 10. Linear relation between coherency factor rc and depth of focus for different illumination scheme.
annular and conventional illumination, indicating that for the same coherency factor rc , regardless of its illumination conditions, we will still yield the same depth of focus. Considering that there is a clear indication that there is a linear relation between its coherency factor rc and depth of focus, Fig. 10 examines the possible linear relation for coherency factor rc and depth of focus for different illumination scheme. High R2 value indicates a strong linear relation. We can better understand the relation between the coherency setting on depth of focus. These coherency settings which includes pitch sizes and illumination conditions have been shown to follow a strong linear relation to depth of focus. Using Fig. 10 as our lookup graph, for coherency factor rc value lower than 0.4 is considered weak for imaging and should be avoided and classified as the forbidden pitch locations for that particular design rules and illumination conditions. It can be used to complement the concept of objective lens pupil filling to provide the theoretical ground for illumination design to suppress the forbidden pitches. Fig. 11 shows the linear relation between k3 =R and coherency factor rc for different illumination scheme. Result shows that coherency factor rc (describing the optical conditions of wavelength and NA, illumination settings and including the effect of typical resolution enhancement techniques such as scattering bars) is related to depth of focus through k3 =R as derived in the modified Rayleigh’s equations: k3 ¼ ðDOFÞ ½p ðNA2 Þ=k
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1.8 1.6
k3/R
1.4
Annular Dipole Conventional
1.2 2
R = 0.9036
1 0.8 0.6 0.4 0.2 0 0
0.5
1
coherency factor, sigma Fig. 11. Relation between k3 =R and coherency factor rc for different illumination scheme.
(where k3 is a measure of illumination coherency). Moreover, coherency factor rc for other resolution enhancement techniques such as alternating or attenuated phase shift mask can also be derived for further studies. 4.2. Illumination optimization Table 2 shows the frequency distribution of the first diffraction orders in the objective lens for Table 2 Diffraction patterns for different coherence setting
90 nm equal lines and spaces for different dipole and annular illuminations, varying NAs and sigmas. Top-down SEM images for 90 nm equal lines and spaces through defocus using ArF, for different annular illumination, varying NAs and sigmas are shown in Fig. 12. We see that using annular illumination, contrast is lower as there is now more amount of light that contributes to background. Table 3 shows the experimental data for depth of focus for different illumination settings. EL-DOF windows are determined by a rectangle EL-DOF fit in the process window. DOF is defined as DOF at 10% EL. For comparison, annular illumination on an identical setting was measured to have a maximum EL of 6%. The coherency factor rc is measured by the amount of first-order light divided by the amount of zeroth-order light. We will be able to determine whether there is more zeroth-order light that contributes to background light and reduces contrast (i.e., in turn reducing exposure latitude) from this coherency factor rc . This coherency factor rc is therefore useful for application to all off-axis illumination that includes Quasar and Quadrupole, as it can take into consideration of each
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Fig. 12. Top-down SEM images for 90 nm equal lines and spaces through defocus using ArF, for different annular illumination, varying NAs and sigmas.
Table 3 Experimental results: DOF-EL for different off-axis illumination settings, (varying NAs and sigmas)
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Fig. 13. Top-down SEM images for 90 nm equal lines and spaces through defocus using ArF, for different dipole illumination, varying NAs and sigmas.
illumination scheme that have opening angles and orientations. Top-down SEM images for 90 nm equal lines and spaces through defocus using ArF, for different dipole illumination, varying NAs and sigmas are shown in Fig. 13. The concept of objective lens pupil filling can be used to maximize DOF and EL. It can also be used as criteria for selecting illumination aperture. Largest DOF can be obtained with the largest overlap between the zeroth- and first-orders light. Aerial image contrast (EL) can be maximized and it depends on the amount of first-order diffracted light captured by the projection lens. These are illustrated in Table 3. The pitch defines the location of the first diffraction orders. The zero order is displayed in white, the first orders in dark gray. The overlap region is displayed as a mix of the two colors (lighter gray). The depth of focus can be optimized using this method. For a given wavelength, pitch, NA and for every illumination shape, the partial coherence can be optimized by matching
the highest coherency factor rc . We notice that the usual rc value is between 0.4 and 0.8 today.
5. Conclusion In this paper, we have systematically investigated the methodology of using concept of objective lens pupil filling to print 90 nm equal lines and spaces. The methodology for the process optimization used is based on simple geometrical analysis of the diffraction orders in the pupil plane. A new metric called coherency factor (rc ) is proposed as a complementary new metric of the low k1 lithography. As corresponding to experimental results, higher rc value concurs to larger depth of focus. Extracting from Fraunhofer diffraction equation for a single slit and incorporating coherency factor rc , we have modified and extend the use of Rayleigh’s equations for 90 nm processes and below.
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We propose a modified Rayleigh’s equation that considers the influence of coherencies on lithographic resolution, and confirm that lithographic performance can be predicted more accurately by the modified equation than by the conventional equation. Results show that the extension of Rayleigh’s equations is capable to optimize the depth of focus and map out the forbidden pitch locations for any design rules and illumination conditions.
Acknowledgements The authors would like to thank Tan Sia Kim and Andrew Khoh from Chartered Semiconductor Mfg. Ltd. for their technical advice. The authors would also like to thank Donis and Anita from ASML for their help in printing the dipole demo wafers.
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