Focus calibration method based on the illumination beam scanning angle modulation in a grating alignment system

Tao Zhang; Tao Zhang; Yarui Ma; Jiean Li; Tao Sun; Xingyu Zhao; Jiwen Cui

doi:10.1364/OE.420761

1. Introduction

Process nodes of integrated circuits have been developed to 10 nm and smaller [1,2]. The demand for integrated circuit manufacturing is a huge driving force to promote lithography technology [3]. Due to the adoption of complex patterns, especially in the case of multiple patterning technology and advanced materials, the requirements for overlays are become more and more challenging. This has created a dire need for ultra-high-precision lithography alignment [4–6].

A key subsystem of lithography equipment is the lithography alignment measurement system, which ensures the position accuracy of each layer in multi-layer lithography by measuring the accurate position of alignment marks. Its measurement performance will directly determine the characteristic lithography process nodes [7–9]. With the gradual development of a lithography equipment technology node with a feature line width less than 10 nm, alignment measurement accuracy is required to reach the subnanometer level. Additionally, more stringent requirements are put forward in many other measurement performance indicators [10–12].

Grating alignment systems have proven to be very suitable for lithography exposure alignment because they enable high accuracy and a very large dynamic range [13]. Alignment measurement methods are also different, depending on the different characteristics of the measured objects, and the operating principle has been explained in many studies [13–16]. Alignment accuracy is affected by various factors, such as optical system errors and intrinsic noise of optoelectronic devices [17]. An important factor that affects the alignment accuracy is defocus-induced alignment error [17,18]. A characteristic feature of the alignment sensor is its small depth of focus. Because variations in wafer thickness and local alignment mark height can be considerably larger, the measurement performance of the alignment may be affected. But up to now, there is no relevant literature report on directly solving this problem.

In the actual lithography equipment, the grating mark is located on the wafer, and the wafer must be accurately located within the depth of focal (DOF) of the high numerical aperture projection objective to ensure high-precision exposure. With today’s wavelengths and NA, the DOF is roughly of the order of 50 nm [19]. In lithography, a so-called level sensor should be used to measure the wafer and resist height variation across the wafer before exposed. Capacitive height sensors [20] are non-contact, have sufficient theoretical accuracy and performance, which have been used in the earlier lithography equipment. However, the stack of thin films on the wafer would affect the properties of the measurement. At present, the level sensor in mainstream lithography production company are almost adopted the principle of optical triangulation and double telocentric projection system [21,22]. According to the optical transmission mode of level sensor, it can be divided into transmission mode [22,23] and reflection mode [24]. These level sensors are mainly based on geometric imaging [25–27] and interference schemes which can effectively express the surface variation and local reflectivity variation of wafer. Usually, the measurement based on interference schemes with a highly complex structure [22,28] should be easy to obtain the high accuracy, compared to the image processing technology based on a CCD or other position sensitive detectors. According to their own characteristics, these technologies have been applied in related fields of lithography.

In the lithography equipment, the focus calibration accuracy obtained by the level sensor is generally higher than the focus calibration requirement of the alignment measurement device. As a result, after high-precision height/tilt adjustment of the wafer, it generally meets the focus calibration requirements of the alignment measurement of the grating mark. In most cases, it is not necessary to calibrate the focus property of the alignment measurement system independently.

However, before using the above level sensor measurement device in lithography equipment, the relative relationship with other mechanisms should be considered to ensure that it can cooperate with other modules well. The result of multi mechanism interaction will inevitably increase the redundancy and complexity of the mechanism. More importantly, the alignment measurement system lacks the function and theoretical method of using its own measurement performance to achieve focus calibration. Although it can ensure that the alignment measurement system will not seriously affect by the defocus-induced error with the help of the special level sensor in lithography. However, this is not a fundamental solution to the defocus-induced error in the alignment measurement system. If the alignment measurement device is used alone, or similar optical measurement structure is used in other fields, the effect of defocus error still needs to be considered.

In this study, we present a novel method for the calibration of the focus of the alignment system. We use the ASML (ASML Holding, Netherlands) alignment measurement optical system [15] as an example and first analyze the focus dependence of the measurement system in Section 2. On this basis, we propose a focus calibration method based on illumination beam scanning angle modulation in the grating alignment system in Section 3. We also introduce a theoretical model that describes the amplitude of the focus calibration signal, which is measured behind the reference grating using phase sensitive detection, as a function of the z-position of the alignment grating mark.

Further, we present the experimental setup and results in Sections 4 and 5, respectively, which demonstrate the validity of the proposed method. The defocus-induced error of the grating alignment system was evaluated to determine the potential use of the alignment measurement system and lithography equipment. We also present a discussion in Section 6 where the achieved method and results are positioned, and the conclusions are presented Section 7.

2. Focus dependency effects of the alignment system

The phase grating alignment system can be considered as a double lens 4f system [15,17], which means that the object plane is projected for a distance of four times the focus distance into the image plane. This indicates that the two lenses are positive and have the same focus distance. The reference grating is positioned directly behind the image plane, as shown in Fig. 1.

Fig. 1. Schematic diagram of the focus/tilt dependency effect of the alignment system. (a) Basic principle of grating alignment optical system. (b) Grating alignment optical system for a tilted mark out of focus.

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Figure 1(a) illustrates the effect of defocus. While a light beam illuminates the grating alignment mark, it produces reflected + n and –n orders, which produce an interference pattern in the object plane. The interference pattern is projected on the image plane, which results in a sinusoidal variation of the transmitted intensity. The phase of this sinusoidal variation is linearly related to the position of the grating alignment mark.

Follow-up analysis is based on the fact that the position x₀ of the alignment grating with period P_g is linearly proportional to the phase difference between 2 diffraction orders n and -n:

(1)$${x_0} = {P_g}\frac{{({{\varphi_n} - {\varphi_{ - n}}} )}}{{4n\pi }}$$

However, if an alignment grating mark is scanned with a particular tilt or focus offset underneath the measurement system, a shifted alignment position may be obtained. An alignment grating mark in the focus of a single lens produces an image at infinity, and the wavefront in the pupil plane is flat. In Fig. 1(b), as the alignment grating mark obtains a defocus Δf, the image will approach the lens at a distance ƒ²/Δƒ. Thus, the wavefront becomes spherical with a radius of curvature f²/Δf.

For a mark out of focus, this will not lead to a shift in position because the change in phase for each order n is the same for negative and positive orders.

(2)$$\varphi = \frac{{2\pi }}{\lambda } \cdot \Delta f = \frac{{2\pi }}{\lambda } \cdot \frac{{{\xi _{}}^2}}{{2({{{{f^2}} / {\Delta f}}} )}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} where{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\xi _{}} = \frac{{\lambda f}}{{{P_g}}},$$

where ξ is the coordinate in the pupil plane that is related to the spatial frequency k using the following relation:

(3)$$\xi = \frac{{{k_{}}}}{{2\pi }}\lambda \cdot \Delta f.$$

Then, the phase shift in Eq. (2) can be expressed as:

(4)$${\varphi _{}} = \frac{{k_{}^2}}{{4\pi }}\lambda \cdot \Delta f.$$

Because the mark is tilted by an angle θ, the shift over a spatial frequency Δk can be expressed as $\Delta k = 4\pi \cdot {\theta / \lambda }$.

A defocus-induced phase shift will occur when the mark is tilted according to:

(5)$$\Delta \varphi = \frac{{\textrm{d}\varphi }}{{\textrm{d}k}}\Delta k = 2k \cdot \Delta f \cdot \theta .$$

The phase shift that the + n and –n orders now obtain is asymmetric. The antisymmetric component leads to a position shift of

(6)$$\Delta x = {P_g}\frac{{({\Delta {\varphi_{ + n}} - \Delta {\varphi_{ - n}}} )}}{{4n\pi }} = 2\Delta f \cdot \theta .$$

Hence, the alignment error is proportional to the defocus (Δf) and tilt angle (θ), which results in an alignment position offset in the system.

3. Principle and method

3.1 Focus calibration method

A schematic diagram of the proposed system is shown in Fig. 2. A focus calibration method based on illumination beam scanning angle modulation is employed to suppress the effects of the grating mark tilt and defocus on the aligned position in the grating alignment system.

Fig. 2. Schematic diagram of the focus calibration system. (a) Grating alignment optical system with an illumination scanning module. (b) Angular modulation of the aerial image in the x-z plane. (c) Beam scanning module.

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The alignment measurement system can be considered as a 4f optical system. After the diffracted beam passes through the aperture of the pupil plane, the ± n diffraction order beam marked by the grating enters the subsequent optical path and forms an interference image on the imaging plane. Based on the alignment measurement system, a light beam scanning module is inserted into the illumination beam between the illumination source and the in-couple prism, as shown in Fig. 2(a). It is slightly tilted with respect to the optical axis, causing parallel displacement of the illumination beam.

Before lens 1, the illumination beam is a spherical wave. After lens 1, the parallel displacement is converted into an angular cone-like movement of the collimated beam, which pivots around the focus of lens 1 and the alignment grating mark surface. The diffraction orders from the grating mark will undergo the same angular movement. For an x-alignment grating mark, this results in a purely angular modulation in the x-z plane of the interference image at the reference grating [see Fig. 2(b)].

It should be noted that, for the convenience of analysis, we assumed that the focal lengths of lens 1 and lens 2 in the 4f optical alignment measurement system are the same. Therefore, the defocus of the grating mark in the object side of the system and the interference image in the image side are equal. Similarly, the tilt angle of the alignment grating mark in the object side is equal to that of the interference image in the image side; the beam angle introduced by the beam scanning is the same on the object and image sides. If the focal length of lens 1 and lens 2 are not the same, the above parameters only need to be multiplied by a fixed scale factor related to the focal lengths of lenses 1 and 2.

In Fig. 2(b), the angular movement of the interference image pivots around the reference grating in the measurement system. In the ideal case, the interference image coincides with the focus of lens 2 [position R_ideal in Fig. 2(b)], which coincides with the position of the reference grating; therefore, the transmitted intensity is not affected by the angular modulation. However, if the interference image does not lie exactly in the focal plane (e.g. position R_actual), the angular movement will induce periodic modulation of the x-position of the aerial image at the reference grating surface. The size of the aerial interference image is d_r and the focus size L is given by d_r/tan(α_s). For a small magnitude of defocus in the object side (i.e. Δf<< P_g/α_s, with P_g as the grating period and α_s as the amplitude of the angular modulation), the amplitude of the position modulation is equal to α_sΔf, and there is also some defocus Δ in the image side. Therefore, the alignment signal collected directly behind the reference grating has both a direct current (DC) component, corresponding to the regular alignment signal, and an alternating current (AC) component, owing to the angular modulation of the diffracted beams.

Figure 2(c) presents a schematic diagram of the beam scanning module, which primarily includes the scanning galvanometer and scanning lens. Thus, rotation of the scanning galvanometer around the optical axis leads to a circular parallel movement of the beam. As shown in Fig. 2(c), the distance between the scanning galvanometer and scanning lens is f_s, where f_s is the focal length of the scanning lens. The scanning beam is focus on the rear focal plane of the scanning lens, and reflected by the reflector into the alignment measurement optical system as shown in Fig. 2(a). At the same time, it is necessary to ensure that the front focal plane of lens 1 [in Fig. 2 (a)] coincides with the rear focal plane of scanning lens [in Fig. 2(c)]. The swing angle of the scanning galvanometer has a linear relationship with its control voltage. When the deflection angle of the galvanometer is half the angle of θ, the incident beam deflects by θ. After passing the F-theta lens, the beam converges on its focal plane. The lateral offset of the parallel beam at the rear focal plane of the scanning lens is approximately f_s·θ.

The light beam enters the optical measurement system, shown in Fig. 2(a), after being reflected by the mirror. The front focal plane of lens 1 and the back focal plane of the F-theta lens are located at the same position. Therefore, the light beam exits in parallel at an angle of α_s after passing through lens 1 and illuminates the measured alignment grating mark. The value of α_s can be described as:

(7)$${\alpha _s} = \arctan \left( {\frac{{{f_s} \cdot \theta }}{f}} \right)$$

The scanning galvanometer is deflected at a uniform angular velocity, which is dependent on the input signal. Thus, the outgoing beam is also scanned and incident to the F-Theta lens at a uniform angular velocity; however, its scanning angular velocity is twice the deflection angular velocity of the galvanometer. To scan the spot at a constant speed on the focal plane, the linear scanning speed of the spot should be linearly related to the beam deflection angular velocity:

(8)$${v_s} = {f_s} \cdot {w_s},$$

where v_s is the scanning velocity of the spot on the focal plane of the F-theta lens and w_s is the angular velocity of the beam scanning.

3.2 Model

This section presents a model to explain the data analysis for the focus calibration. The focus calibration theoretical model proposed in this study is based on the minimal scanning angle modulation of the mark image in focus for varying illumination beam tilts. The combination a scanning galvanometer and an F-theta lens module in the illumination beam results in a circular motion imposed on the beam. After propagation through lens 1 in Fig. 2(a), this circular motion is transformed to an angular motion; the illumination beam forms a cone with its point aimed at the phase grating mark on the object plane. At the reference grating position, the interference image also makes a conical motion (scanning angle modulation) around the optical axis, as shown in Fig. 2(b). This is a sinusoidal motion in the direction perpendicular to the optical axis. The position of the interference image is:

(9)$$x(t) = {x_0} + {\alpha _s}({z - {z_0}} )\cos ({\omega t} ),$$

where x₀ is the position offset of the alignment grating mark (object plane) relative to the reference grating mark (image plane), α_s is the modulation angle of the beam scanning module, ω is the rotation frequency of the scanning galvanometer, z₀ is the ideal focus position of the alignment grating mark, and z is the actual position of the alignment grating mark in the z-direction.

The illumination beam irradiates the grating mark to form positive and negative n-th order diffracted beams. Generally, the field distribution of the n-th order diffracted beam can be written as:

(10)$${E_{ {\pm} n}}(x,t) = {A_{ {\pm} n}}(x,t)\exp [{i{\varphi_{ {\pm} n}}({x,t} )} ]{e^{ {\pm} ik[{x - x(t )} ]}},$$

where A_n is the n-th order diffraction efficiency of the grating mark. Each diffracted beam has a time- and position-dependent amplitude and phase additional to the phase factor from the mark position x(t). Assuming that only the ± n-th order and diffraction beams pass through the pupil plane diaphragm of the 4f optical system, the intensity distribution of the interference field formed by the two beams in the image plane can be expressed as:

(11)$$\begin{array}{l} {I_{im}}(x,t) = A_{ - n}^2(x,t) + A_{ + n}^2(x,t)\\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} + 2{A_{ - n}}(x,t){A_{ + n}}(x,t)\cos \{{[{2kx - 2kx(t )} ]+ [{{\varphi_{ + n}}(x,t) - {\varphi_{ - n}}(x,t)} ]} \}. \end{array}$$

Owing to the scanning of the illumination beam, the position of the interference image (image plane) will be modulated at the beam scanning rotation frequency relative to the position x₀ with an amplitude equal to α_s(z-z₀), as shown in Fig. 2(b). The measured signal is the integrated intensity as measured through the reference mark slits. Note that the integrated intensity is defined relative to the average signal; thus, the scaling factor can be determined independently. The time-dependent intensity transmitted by the reference grating can be expressed as:

(12)$$\begin{array}{l} S(t )= A_{ - n}^2(x,t) + A_{ + n}^2(x,t)\\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} + 2{A_{ - n}}(x,t){A_{ + n}}(x,t)\frac{2}{\pi }\cos \left\{ {\frac{{4\pi }}{{{P_g}}}[{{x_0} + {\alpha_s}({z - {z_0}} )\cos ({\omega t} )} ]- \Delta \varphi (t)} \right\}. \end{array}$$

For a general symmetrical grating mark, Δφ(t) = 0. Similarly, the symmetry of the grating mark also infers that A_-n=A_+n. Thus, the above formula can be expressed as follows:

(13)$$S(t )= 2{A^2}(t) + 2{A^2}(t)\frac{2}{\pi }\cos \left\{ {\frac{{4\pi }}{{{P_g}}}[{{x_0} + {\alpha_s}({z - {z_0}} )\cos ({\omega t} )} ]} \right\}.$$

A lock-in amplifier is used to demodulate the time-dependent signal S(t). For a lock-in detection, the signal is multiplied with a reference signal, the frequency component of which has exactly the same frequency ω, and the phase is a sharply defined cosine reference signal. The signal component at the modulation frequency can be expressed as follows:

(14)$${F_f} = \frac{\omega }{\pi }\int\limits_0^{\frac{{2\pi }}{\omega }} {S(t )\cdot \cos ({\omega t} )dt} .$$

Substituting Eq. (13) into Eq. (14), the focus calibration function of the demodulated signal as a function of z-position can now be calculated:

(15)$${F_f}(z )={-} \frac{4}{\pi }\sin \left( {\frac{{4\pi }}{{{P_g}}}{x_0}} \right){J_1}\left[ {\frac{{4\pi }}{{{P_g}}}{\alpha_s}({z - {z_0}} )} \right],$$

where J₁(u) is the first-order Bessel function.

This is a periodic function with a frequency of ω and a z-dependent amplitude, and it provides a signal variation owing to the scanning angle modulation of a homogeneous beam. The first-order Bessel function can be approximated and simplified while (z-z0)<< P_g/α_s. Therefore, the amplitude of the focus calibration function is proportional to α_s(z-z0)/P_g, which can be easily derived from Fig. 2(b).

Optimizing the beam scanning parameters may change the focus calibration function curve and effectively improve the accuracy of the focus calibration for a scanning angle of α_s=20 mrad, P_g=16 μm, z₀=0. Figure 3 shows the simulated position errors generated by the focus calibration function with mark alignment offset x₀ at 0, 1, 1.5, and 2 μm.

Fig. 3. Focus calibration function with scanning angle α_s=20 mrad and P_g=16 μm for different values of x_0.

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As shown in the figure, regardless of the value of x₀, the focal position z₀ corresponds to the point where the value of the focus calibration function (F_f) is equal to 0. We primarily use the zero-value position of the focus calibration function to determine the focus position z₀; thus, we need to obtain the z-dependent curve of the focus calibration function.

This function curve is obtained from grating alignment measurements at different z-positions, and the discrete values of the focus calibration function at different z-positions are obtained using the calculation of Eqs. (13)–(15). The curve of the focus calibration function is then obtained by fitting.

It should be noted that with the change of z-positions, the value of the function exhibits oscillating changes; thus, there will be multiple zero-value positions. Therefore, when using the focus calibration method in this study, an appropriate z-direction measurement range should be selected to minimize the disturbance caused by multiple zero-value positions on the focus calibration. While x₀ is equal to 0, the corresponding focus calibration function is constant and equal to 0; when x₀ increases, the slope of the focus calibration function near the focus increases significantly. Clearly, when the slope of the focus calibration function curve near the focus is larger, the sensitivity of the focus acquisition will increase. Therefore, by appropriately adjusting the grating mark alignment offset x₀, the focus acquisition accuracy may be improved.

Similarly, the scanning amplitude α_s will also affect the focus acquisition accuracy in this study. For the mark alignment offset x₀=2 μm, P_g=16 μm, z₀=0, Fig. 4 shows the simulated position errors generated by the focus calibration function with mark alignment offset α_s at 5, 10, 15, and 20 mrad.

Fig. 4. Focus calibration function with scanning angle x₀=2 μm and P_g=16 μm for different values of α_s.

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It can be observed from the results in Fig. 4 that while α_s increases, the slope of the focus calibration function near the focus increases significantly, and the sensitivity of the focus acquisition will also increase, which is similar to the effect of adjusting x₀ in the previous analysis.

For a small amount of defocus Δf, the amplitude of the AC signal relative to the DC signal is typically 2α_sΔf/P_g. The criterion for the choice of α_s is that the change of the AC amplitude over the grating mark z-direction adjustment range can be measured with sufficient accuracy. Based on the hardware used in the experimental device, the scanning angle amplitude is chosen to be α_s=20 mrad in the subsequent experiments and analysis.

As mentioned above, the alignment grating mark should be scanned through z during a focus measurement. However, in the actual measurement, this z-axis may not be the same as the optical axis, owing to gluing tolerances of the optical elements. For a more accurate analysis of the focus data, a possible directional difference is included in the focus model through the error angle α_r. Misalignment of the optical axis and the mechanical z-axis by an angle of α_r is easily addresses by replacing x₀ in Eq. (15) by x₀+α_r(z-z₀). Thus, the focus calibration function becomes:

(16)$${F_f}(z )={-} \frac{4}{\pi }\sin \left\{ {\frac{{4\pi }}{{{P_g}}}[{{x_0} + {\alpha_r}({z - {z_0}} )} ]} \right\}{J_1}\left[ {\frac{{4\pi }}{{{P_g}}}{\alpha_s}({z - {z_0}} )} \right].$$

For the scanning angle α_s=20 mrad, α_r = 8 mrad, P_g=16 μm, z₀=0, the focus calibration function in Eq. (16) is plotted for several values of the mark alignment offset x₀ in Fig. 5.

Fig. 5. Focus calibration function with scanning angle α_s=20 mrad, α_r=8 mrad, and P_g=16 μm for different values of x₀.

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Fig. 6. Change in the focus calibration function per unit change in mark position for different values of x_0.

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Note that the envelopes of the function present more severe oscillations and a further increased number of zero-crossings, which may affect the judgment of the focus position. Moreover, the more complex envelopes of the focus calibration function may reduce the accuracy of the determination of z₀ from a fit when there is a particular measurement error.

In addition, the error α_r may also exhibit deviations in lateral position, owing to the residual roughness of the specially-machined sliding surfaces or noise in the z-position controller. Lateral deviations are equivalent to deviations of the mark position x₀ [see Eq. (16)]. We are only interested in variations in the focus signal, owing to lateral position deviations.

(17)$$\Delta {F_f}(z) = \frac{{\partial {F_f}}}{{\partial {x_0}}} \cdot \Delta {x_0} = \cos \left\{ {\frac{{4\pi }}{{{P_g}}}[{x_0} + {\alpha_r}(z - {z_0})]} \right\}{J_1}\left[ {\frac{{4\pi }}{{{P_g}}}{\alpha_s}(z - {z_0})]} \right].\Delta {x_0}$$

Thus, the alignment offset error Δx₀ introduced by the α_r parameter can be expressed as:

(18)$$\Delta {x_0} = {{\Delta {F_f}(z )} / {\frac{{\partial {F_f}}}{{\partial {x_0}}}}}.$$

For the scanning angle α_s=20 mrad, α_r=8 mrad, P_g=16 μm, and z₀=0, the expression ∂F/∂x₀ as a function in Eq. (18) is plotted for several values of the mark alignment offset x₀ in Fig. 6.

For the case of x₀=0 in Fig. 6, the function curve of ∂F/∂x₀ behaves linearly around the focus point. For the range z=-50 μm to +50μm, ∂F/∂x₀≈0.6. Assuming ΔF_f(z) is 0.005, according to Eq. (18), the corresponding Δx₀ is approximately 8.3 nm. This error may also affect the measurement performance of the alignment system, and it should be corrected in the alignment measurement process.

To find the focus, the measured data was directly fitted to Eq. (15) or Eq. (16). The challenge of a non-linear fit procedure is that all fit parameters have to be given an initial value, particularly for the case of the α_r parameter in Eq. (16). By iteration, the values for the fit parameters that minimize the least-squares sum are then identified. Obtaining good initial values for the fit parameters constitutes most of the work in a non-linear fit. Starting with values that significantly differ from the actual value can result in large errors. The non-linear fit may be replaced by a linearization of the focus signal around the focus and a fit of the measured data can be performed.

Even if there is the influence of parameter α_r in the system, it can still be approximately linear near the focus position, and the focus position can be obtained by using the linear fitting of the focus calibration function in this paper. But in this case, the linear region of the focus calibration function is smaller. If the parameter “α_r” is not corrected, the measurement accuracy of the focus calibration might slightly decrease while the corresponding x₀ is smaller.

4. Experimental setup

In our implementation, and referring again to Fig. 2, a 21 mW He-Ne laser (HNL210LB, 632.8 nm, Thorlabs, USA) was used to implement the illumination and interferometry. The alignment grating mark on the object plane is a rectangular phase grating with a period of 16 μm, and the reference grating mark on the image plane is an amplitude grating with a period of 8 μm. The focal length of lens 1 and lens 2 in Fig. 1(a) is 160 mm. The beam scanning module combined with the galvanometer (GVS211/M, Thorlabs, USA) and the F-theta lens (FTH160-1064, Thorlabs, USA) with a 160 mm focal length realizes single-axis beam scanning and yields a displacement that is linear with respect to the rotation angle. In particular, the focal length of the F-theta lens of the scanning module in this study is the same as that of the lens in the 4f imaging system. The optical elements with such parameters are selected for more convenient system construction and scanning angle calculation. By setting apertures in the pupil plane, the ±1st diffraction order beams can be selected to form the interference image. Finally, the intensity signal through the reference grating can be measured. An amplified photodetector sensor (PDA36A - Si switchable gain detector, 350–1100 nm, 10 MHz, Thorlabs, USA) was employed to measure the intensity signal. An analog-to-digital conversion card (PCI-6143, National Instruments, USA) was applied to sample the measured intensity signals.

It should be noted that, to demonstrate the ability and performance of the proposed system, the alignment grating mark is fixed on a multi-degree-of-freedom positioning stage, as shown in the Fig. 7. The displacement of the alignment grating mark is obtained using the capacitance sensor in the positioning stage. Meanwhile, a reflector mirror was fixed with the grating mark, which is used to measure the tilt angle of the alignment grating mark using an auto-collimation angle measurement optical module, shown in Fig. 7.

Fig. 7. Multi-degree-of-freedom positioning stage with an auto-collimation angle measurement setup_.

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The above mentioned multi-degree-of-freedom positioning stage was composed of several parts: a two-dimensional piezoelectric ceramic was primarily used for alignment grating scanning in the x-direction (alignment offset measurement requires a scanning alignment grating mark) and z-direction alignment grating mark step positioning (corresponding to the focus calibration method in this study, the z-dependence focus calibration function was obtained to perform a grating mark measurement at different z-positions). To adjust and correct the error described in Eq. (16), the two-dimensional piezoelectric ceramic was fixed on a direct drive rotation stage (DDR100/M, Thorlabs, USA), which is used to adjust the posture of the two-dimensional displacement table in R_y to ensure that the scan z-direction of the piezoelectric ceramic is the same as the optical axis of the optical system. The alignment grating mark was installed on the two-dimensional piezoelectric ceramic using a rotating tooling, which is primarily used for the adjustment and correction of the tilt of the grating mark in R_y. The rotating tooling is manually adjusted and the adjustment angle is monitored using the auto-collimation setup. All of the devices were set on an active self-leveling isolation system (PTR52514 and PTS602, Thorlabs, USA) to reduce the effects of vibration on the measurement as much as possible.

5. Results

This section details the results of a series of experiments performed to verify the effectiveness of the method proposed above. According to the analysis in a previous study, the focus calibration function curve can be obtained by changing the z-position for different values of x₀. Utilizing the two-dimensional piezoelectric, as shown in Fig. 7, the alignment grating mark was driven to move along the z-direction with an interval of 15 μm and to move 20 times, resulting in a total distance of 300 μm. For x₀=0, 1, 1.5, and 2 μm, we scanned the alignment grating mark and performed alignment measurements for the grating mark at each z-position. Then, the light intensity signal behind the reference grating was obtained, according to Eqs. (13)–(16), and the corresponding value of the focus calibration function was calculated. In Fig. 8, the points represent the values of the focus calibration function versus different positions in z. These results were obtained by performing 25 measurements at each position in z. Figures 8(a)–8(d) represent the focus calibration function values obtained by taking different values of x₀.

Fig. 8. Initial measurement results of the focus calibration function for different values of x₀. (a) x₀=0 μm, (b) x₀=1 μm, (c) x₀=1.5 μm, (d) x₀=2 μm.

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The focus adjustment procedure consists of fitting the theory to the measured z-dependence of the signal. The measurement results at different z-positions are averaged and fitted, and the data fitting curves are compared and analyzed at different values of x₀, as shown in Fig. 9. The fit yields a value for the misalignment angle α_r=5.7 mrad, which can be determined independently of the fitting procedure, thereby confirming the consistency of the results. As an additional consistency check, the procedure may be repeated for different positions of x₀.

Fig. 9. Fit curves of the measurement results of focus calibration function for different x_0.

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The rotation stage (DDR100/M, Thorlabs, USA) is used to adjust the misalignment angle α_r of the optical axis and the mechanical z-axis, and the focus calibration function curves are calculated again. Therefore, the misalignment angle α_r is corrected, and the approximate focus position is determined from the results of the above experiments. A more accurate focus calibration can be conducted in a smaller range near the focus, and the alignment grating mark is driven to move along the z-direction with an interval of 5 μm for 20 times, resulting in a total distance of 100 μm. The measurements and data processing are performed similarly to the experiments above, the results of which are shown in Fig. 10.

Fig. 10. Misalignment angle corrected measurement results of the focus calibration function for different values of x₀. (a) x₀=0 μm, (b) x₀=1 μm, (c) x₀=1.5 μm, (d) x₀=2 μm.

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A measurement error in the datapoints will also lead to an error in the determination of the focus. In the experiments, several datapoints are considered for each z-position. These datapoints are averaged, and the standard deviation is calculated. The focus calibration function near the focus can be approximately fitted with a linear function, which is expressed as:

(19)$${F_{fit}}(z )={-} \frac{1}{2}{\alpha _s}\sin \left( {\frac{{4\pi }}{{{P_g}}}{x_0}} \right)({z - {z_0}} )= {L_{fit}} \cdot ({z - {z_0}} ).$$

Note that these standard deviations are dimensionless because they have been calculated for the dimensionless focus signal in Eq. (15).

Using the last expression in Eq. (19) as a fit function, the focus can be obtained from any set of data. The standard deviation on the focus can also be obtained from the error on each datapoint F_i:

(20)$$\sigma ({{z_0}} )= \frac{1}{{|{{L_{fit}}} |\sqrt N }}\sigma ({{F_i}} ),$$

where N is the number of datapoints.

For most cases, except x₀=0, the focus signal behaves approximately linear around the focus, and Eq. (13) can be used to calculate the error on the focus as a function of the error on the datapoints. To include the case for x₀≈0, the least-squares optimization has been calculated using Eq. (15) with the first-order approximation for the J₁-function. Optimization of the least-squares sum with a focus of z₀ as the only fit parameter results in z₀ as the root of a polynomial. We can now calculate the error of the focus by entering the focus data.

Performing repeated measurements at each position in z provides the focus error as a function of the standard deviation of the errors, σ(F_i), and the mark position x₀, where the parameter σ(F_i) is the relative noise on the focus calibration signal. Considering the measurement results of Fig. 10(d) (x₀= 2 μm) as an example, the variation range of σ(F_i) of the focus calibration function values measured at different z-positions is 0.0035–0.0061. In the case where the focus signal behaves linearly around the focus, a focus error is obtained from a noise standard deviation (0.0035–70 nm, 0.0061–122 nm).

To further verify the effectiveness of the focus calibration method in this study, we measured the alignment offset of the grating mark in different states (defocus and tilt) on the basis of the above focus calibration results. According to Eq. (6) in a previous study, no additional alignment measurement error will be generated, regardless of the grating tilt, while the grating mark is in the focus position. However, while the grating mark is in the defocus position, the grating will introduce different alignment measurement errors for different tilts.

Firstly, the focus position of the grating is determined according to the focus calibration results in the previous section (Fig. 10 results), and a grating rotation is manually applied randomly using the grating rotating tool. The angle shift was accurately detected using the auto-collimation angle measurement optical path in Fig. 7.

It should be noted that the tilt error of a general grating is of the order of tens to hundreds of μrad. However, the alignment errors caused by the tilt with such a magnitude are indistinguishable from the actual measurement results. To analyze the characteristics of the measurement error caused by the focus/tilt, the tilt error of the grating mark introduced by the grating rotation tool is generally larger.

When the grating mark is on the focus position, the alignment position offset of the grating mark is measured under different tilt angles, and the results corresponding to grating mark tilt angles of 0, 15.32 mrad, 27.56 mrad, and 38.33 mrad are shown in Fig. 11.

Fig. 11. Alignment offset measurement results of the grating mark at the focus position for different tilt angles. (a) θ=0, (b) θ=15.32 mrad, (c) θ=27.56 mrad, (d) θ=38.33 mrad.

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For the repeated measurement of a single attitude grating alignment mark, the standard deviation of the measurement results is within 4.5 nm, which is caused by noise and other non-ideal factors in the measurement system. When comparing the alignment measurement results under different tilt angles, it can be observed that the measurement results for three different tilt angles are approximately consistent.

The mean values of the results for three different tilt angles ranged between −0.54 and 0.83 nm, which is in agreement with the previous analysis, and it proved that the grating mark was in the focus position in the z-direction.

In addition, the grating alignment mark was driven by the two-dimensional piezoelectric moving a distance of 500 nm along the z-direction. The alignment offset of the alignment grating mark for four different tilt angles (0, 15.36 mrad, 32.56 mrad, 45.72 mrad) was measured. The measurements and data processing were the same as for the previous experiments. The measurement results are shown in Fig. 12.

Fig. 12. Alignment offset measurement results of the grating mark with a 0.5 μm defocus for different tilt angles. (a) θ=0, (b) θ=15.36 mrad, (c) θ=32.56 mrad, (d) θ=45.43 mrad.

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It can be observed from the results in Fig. 12 that there are clear deviations in the measurement results for the four different tilt angles. The average values of the measurement results are -1.35 nm, 12.64 nm, 29.75 nm, and 42.16 nm, respectively.

The alignment measurement results for different focus and tilt conditions were compared and analyzed according to the focus/tilt characteristics of the grating alignment measurement system. The focus position could be deduced according to Eq. (6) (for Δf=500 nm), and it yields a deviation d_f from the focus position obtained by the calibration method:

(21)$${d_f} = 500\textrm{nm} - \frac{1}{3}\left( {\frac{{13.99\textrm{nm}}}{{2 \times 15.36\textrm{mrad}}} + \frac{{31.10\textrm{nm}}}{{2 \times 32.56\textrm{mrad}}} + \frac{{43.51\textrm{nm}}}{{2 \times 45.43\textrm{mrad}}}} \right)\textrm{ = 29}\textrm{.38nm}$$

These results are consistent with our expectations; thus, the analysis and comparison experiments verify the correctness of the theory proposed in this study.

6. Discussion

The analysis and experimental results above illustrate the ability of the proposed approach and system to perform a focus calibration. The significance of this study is that on the basis of the existing alignment measurement mechanism, the focus calibration of the alignment measurement system can be realized only through its own measurement performance without the help of other measurement devices. Compared with the traditional method, it has obvious advantages of convenience and economy. This study serves as a supplement to previous alignment measurement research that will improve the performance and application potential of grating alignment measurement system in lithography and other ultrahigh precision equipment.

The focus calibration proposed in this study would not be more accurate but more efficient than using a complex level sensor to perform the focus calibration of the alignment measurement system. The performance of proposed method could be improved by improving the experimental conditions and device performance. Combined with the Eq. (6) and the focus calibration accuracy obtained in this study can get the defocus-induced error, which can meet the requirement of alignment measurement. According to Eqs. (19) and (20), it can be seen that the accuracy of the focus calibration method proposed in this paper depends on the following three parameters, L_fit, N and σ(F_i), in which the first term L_fit is proportional to the scanning parameter α_s. The experimental results were obtained on the basis of α_s = 20 mrad. According to the pervious analysis, it can be seen that the focus calibration accuracy could increase with the parameter α_s increases. In this paper, no larger scanning parameter is selected because 20 mrad can achieve better focus calibration accuracy to meet the requirement of the alignment measurement system. However, it should be noted that when α_s is larger than 180 mrad, the beam intensity would be unstable due to the larger scanning angle. The accuracy of focus calibration is also related to the number of samples in the measurement data group. Because this is related to the root of N, the effect of increasing the measurement samples on improving the focus calibration accuracy is not obvious. At the same time, selecting too many measurement samples will reduce the measurement efficiency of the focus calibration process. Moreover, the parameter σ(F_i) is the relative noise on the focus calibration signal which is proportional to the noise signal of a specific frequency component in the alignment measurement signal. The source of this noise is difficult to analyze, it can be optical or electronical, such as the imperfections in the optics used in the measurement system or intrinsic noise of optoelectronic devices and AD conversion error.

The focus calibration method proposed in this paper needs to be combined with a multi-degree-of-freedom positioning stage to realize the focus calibration method. The multi-degree-of-freedom positioning stage used in this paper (Fig. 7) has two translational degrees of freedom and two rotational degrees of freedom. There is no doubt that such a stage is complicated. The increase of degrees of freedom will reduce the stability of the mechanism and increase the cost. In the experiment, the multi-degree-of-freedom positioning stage should have at least two degrees of freedom x and z. In the previous analysis, we can see that if the parameter “α_r” is not corrected, the focus position can also be obtained by Eq. (16), but this may increase the complexity of parameter fitting and reduce the accuracy of focus calibration. Therefore, the direct drive rotation stage (used to adjust the posture of the two-dimensional displacement table in R_y to correct the parameter “α_r”) in Fig. 7 could be omitted. Meanwhile, the function of the rotating tooling in the multi-degree-of-freedom positioning stage is only to better illustrate the correctness of the proposed method and verify the focus calibration performance of the proposed method, which is not needed in the actual focus calibration measurement. Fortunately, in the actual lithography equipment, the grating mark(on the wafer) is on the wafer stage, which is a six degree of freedom high-precision positioning stage used to carry the wafer, and can adjust the position of multiple degrees of freedom. The scanning displacement in x and z directions, and rotation in R_y could be realized by the wafer stage and the processing of the focus calibration method proposed in this paper could be directly applied in lithography equipment.

7. Conclusion

We presented a focus calibration method based on illumination beam scanning angle modulation in a grating alignment system to suppress effects of the grating mark tilt and defocus on the aligned position.

In the proposed method, a galvanometer and F-theta lens are employed to perform a regular scanning of the illumination beam. The scanning illumination beam is diffracted by the grating mark to form the interference light field with scanning angle modulation on the image plane on the reference grating. The measurement signal is obtained with respect to the scanning angle modulation.

A theoretical model is developed, and it describes the amplitude of the focus calibration signal, measured behind the reference grating using phase sensitive detection, as a function of the z-position of the alignment grating mark. The focus adjustment procedure consists of fitting the theory to the measured z-dependence of the signal. The measurement results at different z-positions are averaged and fitted, and the data fitting curves are used for the focus calibration of alignment system. At the focus position, the alignment offset is independent of the incident beam tilt. The influence of illumination scanning parameters of the system on the focus extraction accuracy is analyzed.

The system integration of the proposed method is realized in this study, and the elements are described in detail. The measurement system with the illumination scanning module and proposed method is used to evaluate the focus calibration performance of the grating alignment system. As a result of the analysis and data processing, the focus calibration accuracy of the proposed method is estimated to be 70 nm to 122 nm (standard uncertainty) for 0.35% to 0.61% relative noise on the focus calibration signal.

According to the focus/tilt characteristics of the grating alignment measurement system, the alignment measurement results for different values of focus and tilt were compared and analyzed. The focus position was deduced according to Eq. (6) (for Δf=500 nm), and it yields a 29.38 nm deviation from the focus position obtained using the calibration method. Thus, the results are consistent with expectations.

Based on this reported performance, it can be concluded that the theoretical models and methods proposed in this study will facilitate a more accurate determination and calibration of the focus position in grating alignment systems and suppress the defocus-induced error on the alignment offset measurement. Thus, the techniques may improve alignment measurement to the accuracy necessary for lithography systems and ultrahigh precision machine applications.

Funding

National Natural Science Foundation of China (51805118); China Postdoctoral Science Foundation (2018M641821); Heilongjiang Provincial Postdoctoral Science Foundation (LBH-Z18080).

Disclosures

The authors declare no conflicts of interest.

References

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Focus calibration method based on the illumination beam scanning angle modulation in a grating alignment system

Abstract

1. Introduction

2. Focus dependency effects of the alignment system

3. Principle and method

3.1 Focus calibration method

3.2 Model

4. Experimental setup

5. Results

6. Discussion

7. Conclusion

Funding

Disclosures

References

Cited By

Figures (12)

Equations (21)

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