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Flat Gauss illumination for the step-and-scan lithographic system
Optics Communications 372 (2016) 201–209
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Flat Gauss illumination for the step-and-scan lithographic system Ming Chen a,b, Ying Wang a, Aijun Zeng a,b,n, Jing Zhu a,b, Baoxi Yang a,b, Huijie Huang a,b a b
Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China University of the Chinese Academy of Sciences, Beijing 100049, China
art ic l e i nf o
a b s t r a c t
Article history: Received 27 January 2016 Received in revised form 19 March 2016 Accepted 13 April 2016 Available online 19 April 2016
To meet the uniform dose exposure in optical lithography, it is desirable to get uniform illumination in the scanning direction on wafer for the step-and-scan lithographic system. We present a flat Gauss illumination for the step-and-scan lithographic system in this paper. Through flat Gauss illumination in scanning direction, pulse quantization effect could be reduced effectively. Correspondingly, the uniformity of the reticle and wafer is improved. Compared with the trapezoid illumination, flat Gauss illumination could keep the slit edge fixed, and pulse quantization effect will not be enhanced. Moreover flat Gauss illumination could be obtained directly without defocusing and blocking, which results in high energy efficiency and high throughput of the lithography. A design strategy for flat Gauss illumination is also proposed which offers high uniformity illumination, fixed slope and integral energy of flat Gauss illumination in different coherence factors. The strategy describes a light uniform device which contains first microlens array, second microlens array, one-dimensional Gauss diffuser and a Fourier lens. The device produces flat Gauss illumination directly at the scanning slit. The design and simulation results show that the uniformity of flat Gauss illumination in two directions satisfy the requirements of lithographic illumination system and the slope. In addition, slit edge of flat Gauss illumination does not change. & 2016 Published by Elsevier B.V.
Keywords: Photolithography Illumination design Flat Gauss Pulse quantization effect
1. Introduction Optical lithography is one of the key technologies for the semiconductor industry. It has been used to manufacture integrated circuits (ICs) by etching various patterns onto a silicon wafer with an exposure system and a lithographic projection system [1,2]. Dose uniformities at both the reticle and wafer are required, as the variance of the intensity on the wafer introduces hard control of the patterns line width [3,4] in the step-and-scan lithographic system. The earlier rectangle illumination is widely used in lithographic illumination system. When the step-and-scan lithographic system appears, the rectangle illumination is replaced by the trapezoid illumination for the pulse quantization effect which seriously affects the dose uniformity. Later we will illustrate the definition of the pulse quantization effect. The pulse quantization effect is impacted by the slope of trapezoid illumination. Therefor the pulse quantization effect will be enhanced, when trapezoid illumination approaches rectangle illumination in small coherence factor [5]. In addition, trapezoid illumination can be obtained by defocusing the uniform illumination in the direction
of optical axis and blocking the collapse edge of the illumination in non-scan direction by using the scanning slit. We find that the collapse energy of the illumination in the non-scan direction is lost [5]. So we present a flat Gauss illumination to solve the problem mentioned above in this paper. Compared with the trapezoid illumination, flat Gauss illumination could be obtained directly without defocusing and blocking, and energy will be used more efficiently and the throughput of the lithography is also improved. Flat Gauss illumination also could keep the slit edge fixed, and pulse quantization effect will not increase. Therefore, a uniform flat Gauss illumination is required. The slope and integral energy of flat Gauss illumination should be fixed in different coherence factors (Traditional, Annular, Dipole and Quadrupole) for the stepand-scan lithographic system. We describe a generation of light uniform device which produces flat Gauss illumination directly at scanning slit. Then, we design and simulate the lithographic illumination system to verify the generation method of flat Gauss illumination. The simulation results could satisfy the requirement of the step-and-scan lithographic system.
2. Definition of flat Gauss model n
Corresponding author at: Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China. E-mail addresses: [email protected], [email protected] (A. Zeng). http://dx.doi.org/10.1016/j.optcom.2016.04.033 0030-4018/& 2016 Published by Elsevier B.V.
Lithography illumination system should offer high uniformity illumination in different coherence factors. In this paper, we will
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Fig. 1. A-rectangle illumination.
illumination,
B-trapezoid
illumination,
C-flat
Gauss
introduce a flat Gauss illumination as shown in Fig. 1. Before describing generation of flat Gauss illumination, it is necessary to define a flat Gauss model. Flat Gauss model could be represented as many forms. According to Fourier optics and requirements of lithographic illumination system, flat Gauss equation can be obtained by a Gauss equation convolution with a rectangular equation. This model ensures that the slope of flat Gauss illumination could be adjusted according to the requirement of lithography. The slope and slit edge of flat Gauss illumination should be fixed at different coherence factors in order to ensure integral energy of flat Gauss illumination stable. So a flat Gauss equation could be expressed as
G (x) ⊗ R (x) =
x+ L
∫x − L 2 e
2
−τ p 2 dτ
2
⎡ ⎛ ⎛ L⎞ L ⎞⎤ R (x) = ⎢ g ⎜ x + ⎟ − g ⎜ x − ⎟ ⎥ ⎝ ⎣ ⎝ 2⎠ 2 ⎠⎦
(1)
(2)
2
G (x) = e
−x p2
(3)
where, R(x) is rectangle equation, G(x) is the Gauss equation. It assumes that the amplitude of Gaussian equation and rectangular equation are normalized. L is the width of the rectangular equation. The p is characteristic parameter of Gauss equation. The flat Gauss equation expressed by this model could ensure that the slit edge of flat Gauss equation is fixed and equal to L. The slope of flat Gauss could be adjusted by changing the value of p. For example, it assumes L¼ 13 and p ¼0.5, 1, 1.5, 2 and the convolution result of Gauss equation and rectangular equation is flat Gauss equation as shown in Fig. 2. According to the Fig. 2, the slope of flat Gauss is different when the value p of Gauss equation is changed. The value of slope for the flat Gauss is decided by the value of p. The width of slit edge for the flat Gauss equation is not going to change and is equal to the width L of rectangle equation. So the profile of flat Gauss equation is decided by the value L and p.
3. Pulse quantization effect We already know how to get the flat Gauss equation above, and next, we will introduce the pulse quantization effect in the
Fig. 2. Convolution result of Gauss equation and rectangular equation.
following with reference to Fig. 3. In general, excimer laser is used in the step-and-scan lithographic system and its pulse repetition rate achieves 4 KHz. Fig. 3(a) shows a rectangular illumination which is exposed in reticle as moving along the scan direction. The time window during which one point on the reticle is exposed by whole rectangular illumination with a length L. Light pulses emitted by the excimer laser are represented by elongated rectangles P1, P2 … P9. Here it is assumed that the first point is exposed to three consecutive pulses P4, P5, and P6 during the movement of rectangular illumination at the scan direction. Fig. 3 (b) shows a similar graph, but for a second point on the reticle is exposed later and time has passed Δt. The time window of length L has now a different time relationship to the sequence of pulses P1–P9. As a result, not only three pulses, but also four pulses P4, P5, P6 and P7 contribute to the irradiance on the second point during the time interval of length T. This means that the first point receives only three quarters of the light energy that is received by the second point. Thus different points on the reticle are not uniformly irradiated although each light pulse P1–P9 is assumed to have the same intensity. This error mentioned above is called pulse quantization effect. Fig. 3(c) and (e) show the same situation for the trapezoid illumination and flat Gauss illumination distribution in scan direction. Due to the smooth slopes of trapezoid illumination and flat Gauss illumination, the light pulses P1–P9 do not contribute equally to the irradiance on a specific point on the reticle. Instead, the light pulses P4 and P6 contribute with nearly half of energy to the irradiance on the first point in Fig. 3(c) and (e). The first point receives nearly two pulse energy. In the Fig. 3 (d) and (f), the light pulses P4 and P7 contribute with less energy to the irradiance on the second point. The second point also receives nearly two pulse energy. It has been found out that shifting the trapezoid illumination and flat Gauss illumination along the time axis does not alert the sum of the areas. The pulse quantization effect of trapezoid illumination and flat Gauss illumination is far less than the rectangular illumination. Next, we use formula to explain the difference of pulse quantization effect caused by the rectangular illumination, trapezoid illumination and flat Gauss illumination in detail. Light pulse period emitted by the excimer laser are represented by elongated rectangles, and it can be viewed as a periodic rectangular equation. It assumes that amplitude of each excimer laser pulse is equal to 1. The periodic rectangular equation could be expanded into Fourier series shown below.
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illumination moves along the scan direction, the light exposure of reticle in different time could expressed as t+ L
f (t ) ⊗ R (t ) =
∫t − L 2 f (τ ) dτ 2
⎛ = L × ⎜⎜ a 0 + ⎝
∞
⎛
⎞
⎞⎞
⎛
∑ an Sa ⎜⎝ nπL ⎟⎠ cos ⎜⎝ 2πnt ⎟⎠ ⎟⎟
n= 1
T
T
⎠
(8)
nπL
⎛ nπL ⎞ sin T ⎟ = nπL Sa ⎜ ⎝ T ⎠
(9)
T
⎡ ⎛ ⎛ L⎞ L ⎞⎤ R (t ) = ⎢ u ⎜ t + ⎟ − u ⎜ t − ⎟ ⎥ ⎠ ⎝ ⎣ ⎝ 2 2 ⎠⎦
(10)
It assumes that amplitude of rectangle equation is 1. Where, R (t) is rectangle equation about time. L is the time length of rectangle illumination for scanning one point of reticle once. In the same situation, as shown in Fig. 3(c) and (d), when the trapezoid illumination moves along the scan direction, the light exposure of reticle in different time could be expressed as
T (t ) ⊗ f (t )
(11)
⎧0 ⎪ ⎪ ⎪b T (t ) = ⎨ ⎪1 ⎪ ⎪ ⎩a
(12)
(t > b, t < − b) 1 (t + b) ( − b < t < − a) −a ( − a < t < a) 1 (t − b) (a < t < b) −b
where, T(t) is the trapezoid equation about time, a is top base width of trapezoid, b is bottom base width of trapezoid, L is the midline width of trapezoid and (a þb)/2¼L. We know that a flat Gauss equation can be obtained by a Gaussian equation convolution with a rectangular equation according to the Eq. (1). It could be expressed as
G (t ) ⊗ R (t )
Fig. 3. (a) (b) pulse quantization effect of rectangle illumination; (c)(d) pulse quantization effect of trapezoid illumination; (e)(f)pulse quantization effect of flat Gauss illumination.
n =∞
f (t ) = a 0 +
∑
[an cos (nwt ) + bn sin (nwt )]
n= 1
T 2 −T 2
a0 =
1 T
∫
an =
2 T
∫− T2 R (t ) cos (nwt ) dt = 2nEπ sin ⎝ nTπu ⎠
bn = 0
T
R (t ) dt =
Eu T
(5)
⎛ ⎜
2
(4)
⎞ ⎟
(6)
(7)
where, f(t) is the periodic rectangular equation of excimer laser pulse about time, ω ¼2π/T, 1/T is the pulse repetition rate of excimer laser, E¼ 1 is the pulse amplitude of excimer laser, u is the width of an excimer laser pulse. When the rectangular
(13)
where, R(t) is rectangle equation about time, G(t) is the Gauss equation about time. In the same situation, as shown in Fig. 3(e) and (f), when the flat Gauss illumination moves along the scan direction, the light exposure of reticle in different time could be expressed as
⎛ G (t ) ⊗ R (t ) ⊗ f (t ) = ⎜⎜ ⎝
t+ L
∫t − L 2 e 2
2
⎞
−τ p 2 dτ ⎟
⎟ ⊗ f (t ) ⎠
(14)
where, G(t) is the Gauss equation about time, G(t)⊗R(t) is the flat Gauss illumination. In order to find the specific differences for different illumination modes more directly, we give an example of pulse quantization effect for the rectangle illumination and flat Gauss illumination. We choose a numerical aperture NA0.75 ArF step-and-scan lithographic illumination system as an example, the frequency of excimer laser is 1/T ¼4 KHz, a pulse width of excimer laser is u ¼70 ns, the speed of scanning slit is 350 mm/s, the width of rectangle illumination is L ¼13 mm. Top base width of trapezoid is a¼ 4 mm, bottom base width of trapezoid is b¼ 22 mm, L¼ 13 is the midline width of trapezoid. In order to comparison, the width of top base and bottom base of flat Gauss illumination is 4 mm and 22 mm respectively and L¼ 13 mm. It can be calculated the value p of flat Gauss illumination is 1.65 according to Eq. (14). It has about 150 pulses in a period of scanning for the exposure. In this
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Fig. 4. Comparison of pulse quantization effect for (a) rectangle illumination (b) trapezoid illumination and (c) flat Gauss illumination in case of NA0.75 lithographic illumination system.
condition, we calculate the pulse quantization effect of the rectangle illumination, trapezoid illumination and flat Gauss illumination. Fig. 4 shows the different values of pulse quantization effect in the rectangle illumination, trapezoid illumination and flat Gauss illumination. Fig. 4(a) is the pulse quantization effect of the rectangle illumination for three periods. We find that the difference between maximum and minimum pulse quantization effect of the rectangle illumination is exposure amount of a pulse. Because it assumes the amplitude of a pulse is 1, so pulse quantization effect of the rectangle illumination is about 70 10 9 1 (equal to a pulse energy). We also find that the pulse quantization effect of the rectangle illumination decrease with the frequency of excimer laser increasing. So the pulse quantization effect of the rectangle illumination is obviously in the conditions of low frequency. Fig. 4(b) is the pulse quantization effect of trapezoid illumination for three periods and its value is about 5 10 12. Fig. 4 (c) is the pulse quantization effect of flat Gauss illumination for three periods and its value is about 2 10 12. We find that the pulse quantization effect of trapezoid illumination and flat Gauss illumination are basically the same value and much smaller than the pulse quantization effect of rectangle illumination. So the trapezoid illumination and flat Gauss illumination could improve the result of pulse quantization effect than the rectangle illumination due to the smooth slopes. According to the above description, trapezoid illumination is also good for reducing the pulse quantization effect due to the smooth slopes. However the slope of trapezoid illumination will become precipitous and trapezoid illumination will approach rectangle illumination when the coherence factor becomes small [5]. The pulse quantization effect will increase when the trapezoid approaches rectangle according to the Fig. 4. The flat Gauss illumination proposed in this paper is different from the trapezoid illumination and could keep the slope fixed in different coherence factors. It will be explained in the next section.
4. Generation of flat gauss illumination The previous section discusses the general description of flat Gauss equation. In this section, we will introduce a design method of light uniform device which could produce flat Gauss illumination directly. For achieving illumination with good irradiance uniformity, most illumination systems containing optical elements that homogenize the light, which is usually called light uniform device [6]. In order to illustrate the method conveniently, we define the non-scan direction as x direction, the scan direction as y direction and z axis as the direction of optical axis in the lithographic. In the last section, the flat Gauss equation can be obtained according to the (Eqs. (1)–3). This principle could be applied in the step-and-scan lithographic illumination system according to
Fourier optics. The flat Gauss illumination applied in lithography illumination has the rectangle distribution in non-scan direction and flat Gauss distribution in scan direction. So we will design the illumination distribution of two directions respectively. We know that the light uniform device which contains rectangle microlens array could produce rectangle illumination [7] as shown in Fig. 5. The light uniform device contains first microlens array, second microlens array, one-dimensional Gauss diffuser [8] and Fourier lens. The position of second microlens array is after the first microlens array and is close to the back focal plane of the first microlens array. The position of one-dimensional Gauss diffuser is at back focal plane of the first microlens array and is also at front focal plane of the Fourier lens. The microlens array L1 plays the role of an optical integrator in the light uniform device, and we choose the microlens array with cross-oriented cylindrical lenses on both sides, contributing to the lowering cost and easier production compared with the traditional ones. The second microlens array has the same number of unit with the first microlens array and plays the role of the field lens in two directions (scan and nonscan directions). One-dimensional Gauss diffuser is designed to scatter incident beam just in scan direction and it is just an optical flat in non-scan direction. So the incident beam with diverging angle θ passes the first microlens array, second microlens array, one-dimensional Gauss diffuser and Fourier lens could overlap at the same area and a rectangle illumination could be obtained at back focal plane of the Fourier lens in x direction as shown in Fig. 5 (a). We define the width of the rectangle illumination as W which is expressed as
W = 2 × f f × NA x.
(15)
where, NAx is the numerical aperture of microlens array unit in x direction, ff is the focal length of Fourier lens. As show in Fig. 5(b), because the one-dimensional Gauss diffuser has the effect of Gauss scatting in scan direction, so when the incident beam passes the one-dimensional Gauss diffuser, the each incident ray (solid line in Fig. 5(b)) with different angles could be scatted into Gauss distribution (dotted line in Fig. 5(b)). When the incident beam passes the first microlens array, second microlens array, one-dimensional Gauss diffuser and Fourier lens, the convolution of the rectangle and Gauss distribution is formed at scanning slit in y direction. According to the Fig. 2 and Eq. (1), the result of convolution is a flat Gauss illumination at scanning slit. It could be expressed as
F − G (x) =
x+ L
∫x − L 2 e
2
−τ p 2 dτ
2
(16)
L = 2 × f f × NAy
(17)
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Fig. 5. Schematic diagram of flat Gauss illumination illumination in non-scan direction(x-z) and scan direction(y-z); L1 is first microlens array; L2 is second microlens array; L3 is one-dimensional Gauss diffuser.
where, NAy is the numerical aperture of first microlens array unit in y direction, ff is the focal length of Fourier lens, L is the width of rectangle distribution at scanning slit and it also is the slit edge width of the flat Gauss illumination. It can be calculated the top width and bottom width of flat Gauss illumination according to Eq. (16). The slope of flat Gauss illumination can be calculated from the value of top width and bottom base. The characteristic parameter p of Gauss equation will affect the slope of flat Gauss illumination. It is known that the slope of flat Gauss illumination is just decided by the parameter p of one-dimensional Gauss diffuser. Parameter p represents scattering angle of one-dimensional Gauss diffuser. Scattering angle is a fixed parameter of diffuser. So the value of p has no relationship with coherence factors. The flat Gauss illumination could keep the slope fixed in different coherence factors There is no strict requirement for the choice of value of parameter p. It is known that the big value of parameter p means smooth slope of flat Gauss illumination which could reduce pulse quantization effect effectively. But the bigger value of parameter p will increase difficulty of manufacture and lose more energy for the diffuser. So a suitable value of parameter p is needed.
5. Optical design and simulation The previous section discusses the general description of the design method of flat Gauss illumination. In this section, some of the optical design issues are presented. We choose a numerical aperture NA0.75 ArF step-and-scan lithographic illumination system as design examples to certify the feasibility of design method mentioned in previous section. Fig. 6 is the simplified illumination system of NA0.75 step-andscan lithographic system. The illumination system is a typical Kohler illumination. An Excimer laser beam passes through the
Fig. 6. Simplified illumination of step-and-scan lithographic system. 1. Excimer laser; 2. Expander; 3. Diffractive optical elements (DOEs); 4. Zoom lens; 5. Axicon; 6. Light uniform device; 7. Scanning slit; 8. Relay lens; 9. Reticle.
expander and enters the diffractive optical elements (DOEs) [9]. The DOEs are placed at the front focal plane of the zoom lens. DOEs are adopted in pupil shaping unit of most of the step-andscan lithography machines to achieve off-axis illumination (OAI) [10,11] because of their design flexibility, high-quality freeform illumination mode generation and stable output against the fluctuation of the input laser beam. DOEs could modulate the phase distribution of incident beam, the required diffractive patter can be obtained at back focal plane of the zoom lens. Several classical algorithms such as iterative Fourier transformation algorithm (IFTA) [12], simulated annealing algorithm [13] and genetic algorithm [14] have been used to design DOE. We design three kinds of DOEs (Traditional, Quasar and Dipole) by using the iterative Fourier transformation algorithm (IFTA). By changing the focal length of the zoom lens, the desired size of the diffractive pattern can be obtained. Following the zoom lens is the axicon. By moving one of the axicon elements, the coherence factor sout/in is adjusted accordingly. After the axicon, the beam passes through the dashed frame of Fig. 6 which is the light uniform device mentioned in previous section and the surface of the light uniform device is also the back focal plane of the zoom lens. The light uniform device could produce a flat Gauss illumination directly at scanning slit, and the flat Gauss illumination could be imaged at the reticle plane by the relay lens.
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Fig. 7. The coherence factor sout and sin in different coherence factor, (a) Traditional; (b) Annular; (c) Quasar; (d) Dipole. Table 1 Requirements of the NA0.75 lithographic illumination system. Items Design wavelength Coherence factor Flat Gauss illumination at reticle (X Y)
Non-uniformity
Requirements ArF excimer laser Traditional/Annular/Dipole/Quasar Size of rectangular illumination in X direction Midline size of the flat Gauss illumination in Y direction Top base size of the flat Gauss illumination in Y direction Bottom base size of the flat n Gauss illumination in Y direction In non-scan (X) direction In scan (Y) direction
For the NA0.75 lithographic illumination system, we can obtain the different coherence factor in according to Eq. (18)
Φ MLA × (σout − σ in ) = 2 × tan θ DOE × fzoom .
(18)
Where, the ΦMLA is the clear aperture of the microlens array when the NA of lithographic system at wafer is 0.75, sout and sin is the coherence factor to change the diameter of the effective beam that passes through in the microlens array [15],the θDOE is the
193.368 nm 0.26 r sout r 0.88, sout-sin Z 0.24 104 mm 13 mm 4 mm 22 mm o 1.2% o 1.7%
diffraction angle of DOEs. We can adjust the sout and sin by changing the focal length of zoom lens and moving one of the axicon elements. According to Eq. (18), by changing the focal length of the zoom lens, the (sout-sin) can be adjusted, and the range of the fzoom can be also confirmed on the basis of the requirement of (sout-sin). By moving one of the axicon elements, we can adjust the sin and obtain the off-axis illumination. In general, the off-axis illumination method utilizes a special coherence factor, including annular, dipole, quasar or other patterns [16,17], as
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Table 2 Design results of the NA0.75 lithographic illumination system. Items DOEs Zoom lens First microlens array
Second microlens array
Fig. 8. Non-uniformity varies with the number of microlens array unit increasing.
show in Fig. 7. In conclusion, by changing the focal length of the zoom lens, we can change the value of (sout-sin). By moving one of the axicon elements, we can change the value of sin. We can design specific parameters according to the Table 1 that gives the requirements of the NA0.75 lithographic illumination system. It assumes that the reduction ration of projection lens and relay lens of NA0.75 lithographic illumination system is 4:1 and 1:3 respectively, and the focal length of the Fourier lens ff is 120 mm. We can calculate the image numerical aperture of the Fourier lens is NAf ¼0.75 (3/4) ¼0.5625, the clear aperture of Fourier lens is Φf ¼NAf ff 2 ¼135 mm, and the clear aperture of microlens array ΦMLA ¼ Φf ¼135 mm. According to (Eqs. (15) and 17), we calculate the NA of microlens array unit is NAx ¼0.1444(34.667 mm/ 2/ff) (NAy ¼0.018). For the microlens array, we chose the microlens array with cross-oriented cylindrical lenses on both sides. The cylindrical
One-dimensional Gauss diffuser Fourier lens
Results Effective size Diffraction angle Range of focal length Size NAx dMLA-X NAy dMLA-Y Unit number of the Microlens array Size NAx dMLA-X NAy dMLA-Y Unit number of the Microlens array Size Parameter p Focal length Clear aperture
25mm 25 mm 1.433° 600–2500 mm 135 mm 135 mm 0.1444 1.433 mm 0.018 0.178 mm 94 758 135 mm 135 mm 0.1444 1.433 mm 0.018 0.178 mm 94 758 135 mm 135 mm 1.65 120 mm Φ135 mm
microlens array had been widely used by Nikon [18], Canon [19] and LIMO [20].The NA of first microlens array unit also satisfies the equation NAx ¼dMLA-X/fMLA-X, NAy ¼dMLA-y/fMLA-y. Where dMLA-X and dMLA-Y are the size of microlens array unit in x and y direction respectively,and the fMLA-X and fMLA-Y are the focal length of first microlens array unit in x and y direction respectively. The second microlens array plays the role of the field lens and has the same number unit as the first microlens array. As show in Fig. 8, when the number of microlens array unit increases, the non-uniformity gradually decreases and becomes a steady value. In order to obtain better uniformity, the number of microlens array unit should be more than 100. According to the requirement of Table 1, the top base and
Fig. 9. (a) Flat Gauss illumination distribution, (b) Non-uniformity of horizon cut in non-scan direction, (c) Non-uniformity of vertical cut in scan direction.
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Fig. 10. NA0.75 lithographic illumination system for simulation.
Table 3 Simulation results of the flat Gauss illumination in the Traditional pattern at reticle. sout/in
sout ¼0.26
sout ¼0.6
sout ¼ 0.88
Non-uniformity(y-direction) Non-uniformity(x-direction) Midline size(mm)
0.67% 1.10% 13.004
0.66% 0.86% 13.006
0.52% 1.04% 13.007
Table 4 Simulation results of the flat Gauss illumination in the Annular pattern at reticle. sout/in
sout ¼0.44 sin ¼0.20
sout ¼0.6 sin ¼ 0.36
sout ¼0.88 sin ¼0.64
Non-uniformity(y-direction) Non-uniformity(x-direction) Midline size(mm)
0.85% 1.21% 13.003
0.73% 1.16% 13.001
0.84% 1.40% 13.013
Table 5 Simulation results of the flat Gauss illumination in the Quasar pattern at reticle. sout/in
sout ¼ 0.44
sout ¼ 0.6
sout ¼ 0.88
Non-uniformity(y-direction) Non-uniformity(x-direction) Midline size(mm)
0.97% 0.99% 13.031
0.91% 1.02% 13.006
0.88% 0.90% 12.999
Table 6 Simulation results of the flat Gauss illumination in the Dipole pattern at reticle. sout/in
sout ¼ 0.44
sout ¼ 0.6
sout ¼ 0.88
Non-uniformity(y-direction) Non-uniformity(x-direction) Midline size(mm)
1.00% 1.22% 13.009
0.92% 1.15% 13.006
1.01% 1.37% 13.007
midline of flat Gauss illumination is 4 mm and 13 mm respectively. According to (Eqs. (16) and 17), we can calculate the parameter p of Gauss equation is 1.65. Dose uniformity on both the reticle and the wafer is required, as the variance of the intensity on the wafer that makes it hard to control the line width of the patterns. The non-uniformity is expressed as
Non−uniformity =
Imax − Imin . Imax + Imin
(19)
These non-uniformities influence the final exposure dose coherence of the wafer. Therefore, they should be strictly controlled [21]. Usually, the non-uniformity of the non-scan and scan direction reached 1.2% and 1.7% respectively under all coherence factors [22]. As show in Fig. 9, the non-uniformity of flat Gauss illumination is defined in both directions. Any cross-sectional line for the non-uniformity of the flat Gauss illumination in scan and non-scan direction needs to satisfy the requirements of the lithographic system. In scan direction (y), the non-uniformity(y-direction) is just calculated at the top base zone of the flat Gauss illumination, and in non-scan direction (x), the non-uniformity(x-direction) is calculated at the all the zone of the rectangle. From Table 2, we can obtain the design results of the DOEs, zoom lens, first microlens array, second microlens array, one-dimensional Gauss diffuser and Fourier lens. After finishing the designed model as described above, we can perform the optical simulation to verify its performance: 1) Nonuniformity of the flat Gauss illumination, 2) The fixed midline size of flat Gauss illumination in different coherence factors. The software called Light Toolss is utilized to execute the task, as show in the Fig. 10. For the purpose of the comparison, the simulation contains four coherence factors: 1) Traditional, 2) Annular, 3) Dipole and 4) Quadrupole and every coherence factor are set three kinds of coherence factor sout and sin. The simulation results of the flat Gauss illumination in different patterns at reticle are shown in Tables 3– 6.
M. Chen et al. / Optics Communications 372 (2016) 201–209
From Tables 3–6, they show that the non-uniformity satisfies the requirement 1.2% and 1.7% respectively in x and y direction. We also find that the slope and midline of flat Gauss illumination is fixed in different coherence factors according to (Eqs. (16) and 17).
6. Conclusions This work proposed the designs of a light uniform device that can offer both high uniform illumination and the fixed slope and integral energy of flat Gauss illumination in different coherence factors (Traditional, Annular, Dipole and Quadrupole). The detailed procedures are presented and explained in this paper. The simulation results show that the non-uniformity satisfies the requirements of lithographic illumination system and the slope and midline of flat Gauss illumination does not change. This method is simply based on first microlens array and second microlens array lens, one-dimensional Gauss diffuser and a Fourier lens. Its principle is that a flat Gauss equation can be obtained by a Gaussian equation convolution with a rectangular equation. By this way, we can control the parameter p of Gauss equation to obtain the required slope of flat Gauss illumination and keep the slope of flat Gauss illumination is fixed in different pattern. We also discuss the advantage of flat Gauss illumination. Compared with the rectangle illumination, flat Gauss illumination in scanning direction could reduce pulse quantization effect effectively and improves the uniformity of the reticle and wafer. Compared with the trapezoid illumination, flat Gauss illumination also could keep the slit edge fixed, and pulse quantization effect will not increase. Flat Gauss illumination could be obtained directly without defocusing and blocking, which results in high energy efficiency and high throughput of the lithography is improved. The flat Gauss illumination is believed to be helpful for step-and-scan lithographic illumination technology.
Acknowledgment This work was supported by International Science & Technology Cooperation Programs of China (2011DFR10010, 2012DFG51590); Science and Technology Commission of Shanghai Municipality (14YF1406300); National Science and Technology Major Project of China (2011ZX02402).
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
Flat Gauss illumination for the step-and-scan lithographic system Ming Chen a,b, Ying Wang a, Aijun Zeng a,b,n, Jing Zhu a,b, Baoxi Yang a,b, Huijie Huang a,b a b
Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China University of the Chinese Academy of Sciences, Beijing 100049, China
art ic l e i nf o
a b s t r a c t
Article history: Received 27 January 2016 Received in revised form 19 March 2016 Accepted 13 April 2016 Available online 19 April 2016
To meet the uniform dose exposure in optical lithography, it is desirable to get uniform illumination in the scanning direction on wafer for the step-and-scan lithographic system. We present a flat Gauss illumination for the step-and-scan lithographic system in this paper. Through flat Gauss illumination in scanning direction, pulse quantization effect could be reduced effectively. Correspondingly, the uniformity of the reticle and wafer is improved. Compared with the trapezoid illumination, flat Gauss illumination could keep the slit edge fixed, and pulse quantization effect will not be enhanced. Moreover flat Gauss illumination could be obtained directly without defocusing and blocking, which results in high energy efficiency and high throughput of the lithography. A design strategy for flat Gauss illumination is also proposed which offers high uniformity illumination, fixed slope and integral energy of flat Gauss illumination in different coherence factors. The strategy describes a light uniform device which contains first microlens array, second microlens array, one-dimensional Gauss diffuser and a Fourier lens. The device produces flat Gauss illumination directly at the scanning slit. The design and simulation results show that the uniformity of flat Gauss illumination in two directions satisfy the requirements of lithographic illumination system and the slope. In addition, slit edge of flat Gauss illumination does not change. & 2016 Published by Elsevier B.V.
Keywords: Photolithography Illumination design Flat Gauss Pulse quantization effect
1. Introduction Optical lithography is one of the key technologies for the semiconductor industry. It has been used to manufacture integrated circuits (ICs) by etching various patterns onto a silicon wafer with an exposure system and a lithographic projection system [1,2]. Dose uniformities at both the reticle and wafer are required, as the variance of the intensity on the wafer introduces hard control of the patterns line width [3,4] in the step-and-scan lithographic system. The earlier rectangle illumination is widely used in lithographic illumination system. When the step-and-scan lithographic system appears, the rectangle illumination is replaced by the trapezoid illumination for the pulse quantization effect which seriously affects the dose uniformity. Later we will illustrate the definition of the pulse quantization effect. The pulse quantization effect is impacted by the slope of trapezoid illumination. Therefor the pulse quantization effect will be enhanced, when trapezoid illumination approaches rectangle illumination in small coherence factor [5]. In addition, trapezoid illumination can be obtained by defocusing the uniform illumination in the direction
of optical axis and blocking the collapse edge of the illumination in non-scan direction by using the scanning slit. We find that the collapse energy of the illumination in the non-scan direction is lost [5]. So we present a flat Gauss illumination to solve the problem mentioned above in this paper. Compared with the trapezoid illumination, flat Gauss illumination could be obtained directly without defocusing and blocking, and energy will be used more efficiently and the throughput of the lithography is also improved. Flat Gauss illumination also could keep the slit edge fixed, and pulse quantization effect will not increase. Therefore, a uniform flat Gauss illumination is required. The slope and integral energy of flat Gauss illumination should be fixed in different coherence factors (Traditional, Annular, Dipole and Quadrupole) for the stepand-scan lithographic system. We describe a generation of light uniform device which produces flat Gauss illumination directly at scanning slit. Then, we design and simulate the lithographic illumination system to verify the generation method of flat Gauss illumination. The simulation results could satisfy the requirement of the step-and-scan lithographic system.
2. Definition of flat Gauss model n
Corresponding author at: Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China. E-mail addresses: [email protected], [email protected] (A. Zeng). http://dx.doi.org/10.1016/j.optcom.2016.04.033 0030-4018/& 2016 Published by Elsevier B.V.
Lithography illumination system should offer high uniformity illumination in different coherence factors. In this paper, we will
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Fig. 1. A-rectangle illumination.
illumination,
B-trapezoid
illumination,
C-flat
Gauss
introduce a flat Gauss illumination as shown in Fig. 1. Before describing generation of flat Gauss illumination, it is necessary to define a flat Gauss model. Flat Gauss model could be represented as many forms. According to Fourier optics and requirements of lithographic illumination system, flat Gauss equation can be obtained by a Gauss equation convolution with a rectangular equation. This model ensures that the slope of flat Gauss illumination could be adjusted according to the requirement of lithography. The slope and slit edge of flat Gauss illumination should be fixed at different coherence factors in order to ensure integral energy of flat Gauss illumination stable. So a flat Gauss equation could be expressed as
G (x) ⊗ R (x) =
x+ L
∫x − L 2 e
2
−τ p 2 dτ
2
⎡ ⎛ ⎛ L⎞ L ⎞⎤ R (x) = ⎢ g ⎜ x + ⎟ − g ⎜ x − ⎟ ⎥ ⎝ ⎣ ⎝ 2⎠ 2 ⎠⎦
(1)
(2)
2
G (x) = e
−x p2
(3)
where, R(x) is rectangle equation, G(x) is the Gauss equation. It assumes that the amplitude of Gaussian equation and rectangular equation are normalized. L is the width of the rectangular equation. The p is characteristic parameter of Gauss equation. The flat Gauss equation expressed by this model could ensure that the slit edge of flat Gauss equation is fixed and equal to L. The slope of flat Gauss could be adjusted by changing the value of p. For example, it assumes L¼ 13 and p ¼0.5, 1, 1.5, 2 and the convolution result of Gauss equation and rectangular equation is flat Gauss equation as shown in Fig. 2. According to the Fig. 2, the slope of flat Gauss is different when the value p of Gauss equation is changed. The value of slope for the flat Gauss is decided by the value of p. The width of slit edge for the flat Gauss equation is not going to change and is equal to the width L of rectangle equation. So the profile of flat Gauss equation is decided by the value L and p.
3. Pulse quantization effect We already know how to get the flat Gauss equation above, and next, we will introduce the pulse quantization effect in the
Fig. 2. Convolution result of Gauss equation and rectangular equation.
following with reference to Fig. 3. In general, excimer laser is used in the step-and-scan lithographic system and its pulse repetition rate achieves 4 KHz. Fig. 3(a) shows a rectangular illumination which is exposed in reticle as moving along the scan direction. The time window during which one point on the reticle is exposed by whole rectangular illumination with a length L. Light pulses emitted by the excimer laser are represented by elongated rectangles P1, P2 … P9. Here it is assumed that the first point is exposed to three consecutive pulses P4, P5, and P6 during the movement of rectangular illumination at the scan direction. Fig. 3 (b) shows a similar graph, but for a second point on the reticle is exposed later and time has passed Δt. The time window of length L has now a different time relationship to the sequence of pulses P1–P9. As a result, not only three pulses, but also four pulses P4, P5, P6 and P7 contribute to the irradiance on the second point during the time interval of length T. This means that the first point receives only three quarters of the light energy that is received by the second point. Thus different points on the reticle are not uniformly irradiated although each light pulse P1–P9 is assumed to have the same intensity. This error mentioned above is called pulse quantization effect. Fig. 3(c) and (e) show the same situation for the trapezoid illumination and flat Gauss illumination distribution in scan direction. Due to the smooth slopes of trapezoid illumination and flat Gauss illumination, the light pulses P1–P9 do not contribute equally to the irradiance on a specific point on the reticle. Instead, the light pulses P4 and P6 contribute with nearly half of energy to the irradiance on the first point in Fig. 3(c) and (e). The first point receives nearly two pulse energy. In the Fig. 3 (d) and (f), the light pulses P4 and P7 contribute with less energy to the irradiance on the second point. The second point also receives nearly two pulse energy. It has been found out that shifting the trapezoid illumination and flat Gauss illumination along the time axis does not alert the sum of the areas. The pulse quantization effect of trapezoid illumination and flat Gauss illumination is far less than the rectangular illumination. Next, we use formula to explain the difference of pulse quantization effect caused by the rectangular illumination, trapezoid illumination and flat Gauss illumination in detail. Light pulse period emitted by the excimer laser are represented by elongated rectangles, and it can be viewed as a periodic rectangular equation. It assumes that amplitude of each excimer laser pulse is equal to 1. The periodic rectangular equation could be expanded into Fourier series shown below.
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illumination moves along the scan direction, the light exposure of reticle in different time could expressed as t+ L
f (t ) ⊗ R (t ) =
∫t − L 2 f (τ ) dτ 2
⎛ = L × ⎜⎜ a 0 + ⎝
∞
⎛
⎞
⎞⎞
⎛
∑ an Sa ⎜⎝ nπL ⎟⎠ cos ⎜⎝ 2πnt ⎟⎠ ⎟⎟
n= 1
T
T
⎠
(8)
nπL
⎛ nπL ⎞ sin T ⎟ = nπL Sa ⎜ ⎝ T ⎠
(9)
T
⎡ ⎛ ⎛ L⎞ L ⎞⎤ R (t ) = ⎢ u ⎜ t + ⎟ − u ⎜ t − ⎟ ⎥ ⎠ ⎝ ⎣ ⎝ 2 2 ⎠⎦
(10)
It assumes that amplitude of rectangle equation is 1. Where, R (t) is rectangle equation about time. L is the time length of rectangle illumination for scanning one point of reticle once. In the same situation, as shown in Fig. 3(c) and (d), when the trapezoid illumination moves along the scan direction, the light exposure of reticle in different time could be expressed as
T (t ) ⊗ f (t )
(11)
⎧0 ⎪ ⎪ ⎪b T (t ) = ⎨ ⎪1 ⎪ ⎪ ⎩a
(12)
(t > b, t < − b) 1 (t + b) ( − b < t < − a) −a ( − a < t < a) 1 (t − b) (a < t < b) −b
where, T(t) is the trapezoid equation about time, a is top base width of trapezoid, b is bottom base width of trapezoid, L is the midline width of trapezoid and (a þb)/2¼L. We know that a flat Gauss equation can be obtained by a Gaussian equation convolution with a rectangular equation according to the Eq. (1). It could be expressed as
G (t ) ⊗ R (t )
Fig. 3. (a) (b) pulse quantization effect of rectangle illumination; (c)(d) pulse quantization effect of trapezoid illumination; (e)(f)pulse quantization effect of flat Gauss illumination.
n =∞
f (t ) = a 0 +
∑
[an cos (nwt ) + bn sin (nwt )]
n= 1
T 2 −T 2
a0 =
1 T
∫
an =
2 T
∫− T2 R (t ) cos (nwt ) dt = 2nEπ sin ⎝ nTπu ⎠
bn = 0
T
R (t ) dt =
Eu T
(5)
⎛ ⎜
2
(4)
⎞ ⎟
(6)
(7)
where, f(t) is the periodic rectangular equation of excimer laser pulse about time, ω ¼2π/T, 1/T is the pulse repetition rate of excimer laser, E¼ 1 is the pulse amplitude of excimer laser, u is the width of an excimer laser pulse. When the rectangular
(13)
where, R(t) is rectangle equation about time, G(t) is the Gauss equation about time. In the same situation, as shown in Fig. 3(e) and (f), when the flat Gauss illumination moves along the scan direction, the light exposure of reticle in different time could be expressed as
⎛ G (t ) ⊗ R (t ) ⊗ f (t ) = ⎜⎜ ⎝
t+ L
∫t − L 2 e 2
2
⎞
−τ p 2 dτ ⎟
⎟ ⊗ f (t ) ⎠
(14)
where, G(t) is the Gauss equation about time, G(t)⊗R(t) is the flat Gauss illumination. In order to find the specific differences for different illumination modes more directly, we give an example of pulse quantization effect for the rectangle illumination and flat Gauss illumination. We choose a numerical aperture NA0.75 ArF step-and-scan lithographic illumination system as an example, the frequency of excimer laser is 1/T ¼4 KHz, a pulse width of excimer laser is u ¼70 ns, the speed of scanning slit is 350 mm/s, the width of rectangle illumination is L ¼13 mm. Top base width of trapezoid is a¼ 4 mm, bottom base width of trapezoid is b¼ 22 mm, L¼ 13 is the midline width of trapezoid. In order to comparison, the width of top base and bottom base of flat Gauss illumination is 4 mm and 22 mm respectively and L¼ 13 mm. It can be calculated the value p of flat Gauss illumination is 1.65 according to Eq. (14). It has about 150 pulses in a period of scanning for the exposure. In this
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Fig. 4. Comparison of pulse quantization effect for (a) rectangle illumination (b) trapezoid illumination and (c) flat Gauss illumination in case of NA0.75 lithographic illumination system.
condition, we calculate the pulse quantization effect of the rectangle illumination, trapezoid illumination and flat Gauss illumination. Fig. 4 shows the different values of pulse quantization effect in the rectangle illumination, trapezoid illumination and flat Gauss illumination. Fig. 4(a) is the pulse quantization effect of the rectangle illumination for three periods. We find that the difference between maximum and minimum pulse quantization effect of the rectangle illumination is exposure amount of a pulse. Because it assumes the amplitude of a pulse is 1, so pulse quantization effect of the rectangle illumination is about 70 10 9 1 (equal to a pulse energy). We also find that the pulse quantization effect of the rectangle illumination decrease with the frequency of excimer laser increasing. So the pulse quantization effect of the rectangle illumination is obviously in the conditions of low frequency. Fig. 4(b) is the pulse quantization effect of trapezoid illumination for three periods and its value is about 5 10 12. Fig. 4 (c) is the pulse quantization effect of flat Gauss illumination for three periods and its value is about 2 10 12. We find that the pulse quantization effect of trapezoid illumination and flat Gauss illumination are basically the same value and much smaller than the pulse quantization effect of rectangle illumination. So the trapezoid illumination and flat Gauss illumination could improve the result of pulse quantization effect than the rectangle illumination due to the smooth slopes. According to the above description, trapezoid illumination is also good for reducing the pulse quantization effect due to the smooth slopes. However the slope of trapezoid illumination will become precipitous and trapezoid illumination will approach rectangle illumination when the coherence factor becomes small [5]. The pulse quantization effect will increase when the trapezoid approaches rectangle according to the Fig. 4. The flat Gauss illumination proposed in this paper is different from the trapezoid illumination and could keep the slope fixed in different coherence factors. It will be explained in the next section.
4. Generation of flat gauss illumination The previous section discusses the general description of flat Gauss equation. In this section, we will introduce a design method of light uniform device which could produce flat Gauss illumination directly. For achieving illumination with good irradiance uniformity, most illumination systems containing optical elements that homogenize the light, which is usually called light uniform device [6]. In order to illustrate the method conveniently, we define the non-scan direction as x direction, the scan direction as y direction and z axis as the direction of optical axis in the lithographic. In the last section, the flat Gauss equation can be obtained according to the (Eqs. (1)–3). This principle could be applied in the step-and-scan lithographic illumination system according to
Fourier optics. The flat Gauss illumination applied in lithography illumination has the rectangle distribution in non-scan direction and flat Gauss distribution in scan direction. So we will design the illumination distribution of two directions respectively. We know that the light uniform device which contains rectangle microlens array could produce rectangle illumination [7] as shown in Fig. 5. The light uniform device contains first microlens array, second microlens array, one-dimensional Gauss diffuser [8] and Fourier lens. The position of second microlens array is after the first microlens array and is close to the back focal plane of the first microlens array. The position of one-dimensional Gauss diffuser is at back focal plane of the first microlens array and is also at front focal plane of the Fourier lens. The microlens array L1 plays the role of an optical integrator in the light uniform device, and we choose the microlens array with cross-oriented cylindrical lenses on both sides, contributing to the lowering cost and easier production compared with the traditional ones. The second microlens array has the same number of unit with the first microlens array and plays the role of the field lens in two directions (scan and nonscan directions). One-dimensional Gauss diffuser is designed to scatter incident beam just in scan direction and it is just an optical flat in non-scan direction. So the incident beam with diverging angle θ passes the first microlens array, second microlens array, one-dimensional Gauss diffuser and Fourier lens could overlap at the same area and a rectangle illumination could be obtained at back focal plane of the Fourier lens in x direction as shown in Fig. 5 (a). We define the width of the rectangle illumination as W which is expressed as
W = 2 × f f × NA x.
(15)
where, NAx is the numerical aperture of microlens array unit in x direction, ff is the focal length of Fourier lens. As show in Fig. 5(b), because the one-dimensional Gauss diffuser has the effect of Gauss scatting in scan direction, so when the incident beam passes the one-dimensional Gauss diffuser, the each incident ray (solid line in Fig. 5(b)) with different angles could be scatted into Gauss distribution (dotted line in Fig. 5(b)). When the incident beam passes the first microlens array, second microlens array, one-dimensional Gauss diffuser and Fourier lens, the convolution of the rectangle and Gauss distribution is formed at scanning slit in y direction. According to the Fig. 2 and Eq. (1), the result of convolution is a flat Gauss illumination at scanning slit. It could be expressed as
F − G (x) =
x+ L
∫x − L 2 e
2
−τ p 2 dτ
2
(16)
L = 2 × f f × NAy
(17)
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Fig. 5. Schematic diagram of flat Gauss illumination illumination in non-scan direction(x-z) and scan direction(y-z); L1 is first microlens array; L2 is second microlens array; L3 is one-dimensional Gauss diffuser.
where, NAy is the numerical aperture of first microlens array unit in y direction, ff is the focal length of Fourier lens, L is the width of rectangle distribution at scanning slit and it also is the slit edge width of the flat Gauss illumination. It can be calculated the top width and bottom width of flat Gauss illumination according to Eq. (16). The slope of flat Gauss illumination can be calculated from the value of top width and bottom base. The characteristic parameter p of Gauss equation will affect the slope of flat Gauss illumination. It is known that the slope of flat Gauss illumination is just decided by the parameter p of one-dimensional Gauss diffuser. Parameter p represents scattering angle of one-dimensional Gauss diffuser. Scattering angle is a fixed parameter of diffuser. So the value of p has no relationship with coherence factors. The flat Gauss illumination could keep the slope fixed in different coherence factors There is no strict requirement for the choice of value of parameter p. It is known that the big value of parameter p means smooth slope of flat Gauss illumination which could reduce pulse quantization effect effectively. But the bigger value of parameter p will increase difficulty of manufacture and lose more energy for the diffuser. So a suitable value of parameter p is needed.
5. Optical design and simulation The previous section discusses the general description of the design method of flat Gauss illumination. In this section, some of the optical design issues are presented. We choose a numerical aperture NA0.75 ArF step-and-scan lithographic illumination system as design examples to certify the feasibility of design method mentioned in previous section. Fig. 6 is the simplified illumination system of NA0.75 step-andscan lithographic system. The illumination system is a typical Kohler illumination. An Excimer laser beam passes through the
Fig. 6. Simplified illumination of step-and-scan lithographic system. 1. Excimer laser; 2. Expander; 3. Diffractive optical elements (DOEs); 4. Zoom lens; 5. Axicon; 6. Light uniform device; 7. Scanning slit; 8. Relay lens; 9. Reticle.
expander and enters the diffractive optical elements (DOEs) [9]. The DOEs are placed at the front focal plane of the zoom lens. DOEs are adopted in pupil shaping unit of most of the step-andscan lithography machines to achieve off-axis illumination (OAI) [10,11] because of their design flexibility, high-quality freeform illumination mode generation and stable output against the fluctuation of the input laser beam. DOEs could modulate the phase distribution of incident beam, the required diffractive patter can be obtained at back focal plane of the zoom lens. Several classical algorithms such as iterative Fourier transformation algorithm (IFTA) [12], simulated annealing algorithm [13] and genetic algorithm [14] have been used to design DOE. We design three kinds of DOEs (Traditional, Quasar and Dipole) by using the iterative Fourier transformation algorithm (IFTA). By changing the focal length of the zoom lens, the desired size of the diffractive pattern can be obtained. Following the zoom lens is the axicon. By moving one of the axicon elements, the coherence factor sout/in is adjusted accordingly. After the axicon, the beam passes through the dashed frame of Fig. 6 which is the light uniform device mentioned in previous section and the surface of the light uniform device is also the back focal plane of the zoom lens. The light uniform device could produce a flat Gauss illumination directly at scanning slit, and the flat Gauss illumination could be imaged at the reticle plane by the relay lens.
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Fig. 7. The coherence factor sout and sin in different coherence factor, (a) Traditional; (b) Annular; (c) Quasar; (d) Dipole. Table 1 Requirements of the NA0.75 lithographic illumination system. Items Design wavelength Coherence factor Flat Gauss illumination at reticle (X Y)
Non-uniformity
Requirements ArF excimer laser Traditional/Annular/Dipole/Quasar Size of rectangular illumination in X direction Midline size of the flat Gauss illumination in Y direction Top base size of the flat Gauss illumination in Y direction Bottom base size of the flat n Gauss illumination in Y direction In non-scan (X) direction In scan (Y) direction
For the NA0.75 lithographic illumination system, we can obtain the different coherence factor in according to Eq. (18)
Φ MLA × (σout − σ in ) = 2 × tan θ DOE × fzoom .
(18)
Where, the ΦMLA is the clear aperture of the microlens array when the NA of lithographic system at wafer is 0.75, sout and sin is the coherence factor to change the diameter of the effective beam that passes through in the microlens array [15],the θDOE is the
193.368 nm 0.26 r sout r 0.88, sout-sin Z 0.24 104 mm 13 mm 4 mm 22 mm o 1.2% o 1.7%
diffraction angle of DOEs. We can adjust the sout and sin by changing the focal length of zoom lens and moving one of the axicon elements. According to Eq. (18), by changing the focal length of the zoom lens, the (sout-sin) can be adjusted, and the range of the fzoom can be also confirmed on the basis of the requirement of (sout-sin). By moving one of the axicon elements, we can adjust the sin and obtain the off-axis illumination. In general, the off-axis illumination method utilizes a special coherence factor, including annular, dipole, quasar or other patterns [16,17], as
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Table 2 Design results of the NA0.75 lithographic illumination system. Items DOEs Zoom lens First microlens array
Second microlens array
Fig. 8. Non-uniformity varies with the number of microlens array unit increasing.
show in Fig. 7. In conclusion, by changing the focal length of the zoom lens, we can change the value of (sout-sin). By moving one of the axicon elements, we can change the value of sin. We can design specific parameters according to the Table 1 that gives the requirements of the NA0.75 lithographic illumination system. It assumes that the reduction ration of projection lens and relay lens of NA0.75 lithographic illumination system is 4:1 and 1:3 respectively, and the focal length of the Fourier lens ff is 120 mm. We can calculate the image numerical aperture of the Fourier lens is NAf ¼0.75 (3/4) ¼0.5625, the clear aperture of Fourier lens is Φf ¼NAf ff 2 ¼135 mm, and the clear aperture of microlens array ΦMLA ¼ Φf ¼135 mm. According to (Eqs. (15) and 17), we calculate the NA of microlens array unit is NAx ¼0.1444(34.667 mm/ 2/ff) (NAy ¼0.018). For the microlens array, we chose the microlens array with cross-oriented cylindrical lenses on both sides. The cylindrical
One-dimensional Gauss diffuser Fourier lens
Results Effective size Diffraction angle Range of focal length Size NAx dMLA-X NAy dMLA-Y Unit number of the Microlens array Size NAx dMLA-X NAy dMLA-Y Unit number of the Microlens array Size Parameter p Focal length Clear aperture
25mm 25 mm 1.433° 600–2500 mm 135 mm 135 mm 0.1444 1.433 mm 0.018 0.178 mm 94 758 135 mm 135 mm 0.1444 1.433 mm 0.018 0.178 mm 94 758 135 mm 135 mm 1.65 120 mm Φ135 mm
microlens array had been widely used by Nikon [18], Canon [19] and LIMO [20].The NA of first microlens array unit also satisfies the equation NAx ¼dMLA-X/fMLA-X, NAy ¼dMLA-y/fMLA-y. Where dMLA-X and dMLA-Y are the size of microlens array unit in x and y direction respectively,and the fMLA-X and fMLA-Y are the focal length of first microlens array unit in x and y direction respectively. The second microlens array plays the role of the field lens and has the same number unit as the first microlens array. As show in Fig. 8, when the number of microlens array unit increases, the non-uniformity gradually decreases and becomes a steady value. In order to obtain better uniformity, the number of microlens array unit should be more than 100. According to the requirement of Table 1, the top base and
Fig. 9. (a) Flat Gauss illumination distribution, (b) Non-uniformity of horizon cut in non-scan direction, (c) Non-uniformity of vertical cut in scan direction.
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Fig. 10. NA0.75 lithographic illumination system for simulation.
Table 3 Simulation results of the flat Gauss illumination in the Traditional pattern at reticle. sout/in
sout ¼0.26
sout ¼0.6
sout ¼ 0.88
Non-uniformity(y-direction) Non-uniformity(x-direction) Midline size(mm)
0.67% 1.10% 13.004
0.66% 0.86% 13.006
0.52% 1.04% 13.007
Table 4 Simulation results of the flat Gauss illumination in the Annular pattern at reticle. sout/in
sout ¼0.44 sin ¼0.20
sout ¼0.6 sin ¼ 0.36
sout ¼0.88 sin ¼0.64
Non-uniformity(y-direction) Non-uniformity(x-direction) Midline size(mm)
0.85% 1.21% 13.003
0.73% 1.16% 13.001
0.84% 1.40% 13.013
Table 5 Simulation results of the flat Gauss illumination in the Quasar pattern at reticle. sout/in
sout ¼ 0.44
sout ¼ 0.6
sout ¼ 0.88
Non-uniformity(y-direction) Non-uniformity(x-direction) Midline size(mm)
0.97% 0.99% 13.031
0.91% 1.02% 13.006
0.88% 0.90% 12.999
Table 6 Simulation results of the flat Gauss illumination in the Dipole pattern at reticle. sout/in
sout ¼ 0.44
sout ¼ 0.6
sout ¼ 0.88
Non-uniformity(y-direction) Non-uniformity(x-direction) Midline size(mm)
1.00% 1.22% 13.009
0.92% 1.15% 13.006
1.01% 1.37% 13.007
midline of flat Gauss illumination is 4 mm and 13 mm respectively. According to (Eqs. (16) and 17), we can calculate the parameter p of Gauss equation is 1.65. Dose uniformity on both the reticle and the wafer is required, as the variance of the intensity on the wafer that makes it hard to control the line width of the patterns. The non-uniformity is expressed as
Non−uniformity =
Imax − Imin . Imax + Imin
(19)
These non-uniformities influence the final exposure dose coherence of the wafer. Therefore, they should be strictly controlled [21]. Usually, the non-uniformity of the non-scan and scan direction reached 1.2% and 1.7% respectively under all coherence factors [22]. As show in Fig. 9, the non-uniformity of flat Gauss illumination is defined in both directions. Any cross-sectional line for the non-uniformity of the flat Gauss illumination in scan and non-scan direction needs to satisfy the requirements of the lithographic system. In scan direction (y), the non-uniformity(y-direction) is just calculated at the top base zone of the flat Gauss illumination, and in non-scan direction (x), the non-uniformity(x-direction) is calculated at the all the zone of the rectangle. From Table 2, we can obtain the design results of the DOEs, zoom lens, first microlens array, second microlens array, one-dimensional Gauss diffuser and Fourier lens. After finishing the designed model as described above, we can perform the optical simulation to verify its performance: 1) Nonuniformity of the flat Gauss illumination, 2) The fixed midline size of flat Gauss illumination in different coherence factors. The software called Light Toolss is utilized to execute the task, as show in the Fig. 10. For the purpose of the comparison, the simulation contains four coherence factors: 1) Traditional, 2) Annular, 3) Dipole and 4) Quadrupole and every coherence factor are set three kinds of coherence factor sout and sin. The simulation results of the flat Gauss illumination in different patterns at reticle are shown in Tables 3– 6.
M. Chen et al. / Optics Communications 372 (2016) 201–209
From Tables 3–6, they show that the non-uniformity satisfies the requirement 1.2% and 1.7% respectively in x and y direction. We also find that the slope and midline of flat Gauss illumination is fixed in different coherence factors according to (Eqs. (16) and 17).
6. Conclusions This work proposed the designs of a light uniform device that can offer both high uniform illumination and the fixed slope and integral energy of flat Gauss illumination in different coherence factors (Traditional, Annular, Dipole and Quadrupole). The detailed procedures are presented and explained in this paper. The simulation results show that the non-uniformity satisfies the requirements of lithographic illumination system and the slope and midline of flat Gauss illumination does not change. This method is simply based on first microlens array and second microlens array lens, one-dimensional Gauss diffuser and a Fourier lens. Its principle is that a flat Gauss equation can be obtained by a Gaussian equation convolution with a rectangular equation. By this way, we can control the parameter p of Gauss equation to obtain the required slope of flat Gauss illumination and keep the slope of flat Gauss illumination is fixed in different pattern. We also discuss the advantage of flat Gauss illumination. Compared with the rectangle illumination, flat Gauss illumination in scanning direction could reduce pulse quantization effect effectively and improves the uniformity of the reticle and wafer. Compared with the trapezoid illumination, flat Gauss illumination also could keep the slit edge fixed, and pulse quantization effect will not increase. Flat Gauss illumination could be obtained directly without defocusing and blocking, which results in high energy efficiency and high throughput of the lithography is improved. The flat Gauss illumination is believed to be helpful for step-and-scan lithographic illumination technology.
Acknowledgment This work was supported by International Science & Technology Cooperation Programs of China (2011DFR10010, 2012DFG51590); Science and Technology Commission of Shanghai Municipality (14YF1406300); National Science and Technology Major Project of China (2011ZX02402).
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