Mid-Range Flare Control in ArF Exposure Tools

Most advanced semiconductor manufacturers are at the 90 nm node with their mass production, and they are accelerating 65 nm development. To meet the lithography requirements to move to the next generation every two to three years, shorter wavelengths and higher numerical apertures (NAs) have been applied to lithography tools, with process engineering challenges being overcome to work with the small k₁ factor.
 
In today's leading-edge device production, the wavelength is 193 nm ArF, NA is 0.85, and the k₁ factor is falling into the range of 0.35-0.30. To manage this low k₁, the tools are required to strictly suppress aberration. By analysis methods called wavefront engineering,¹ in which wavefront aberration is broken into Zernike polynomials, extremely small aberration of <10 mλ RMS has been realized.

Researchers have pointed out, however, that the aberration evaluation is not sufficient just by looking at 36 terms of Zernike polynomials, so the study of the higher-order component of aberration started to get some attention.² The higher-order component acts as flare, and degrades image contrast and CD uniformity. The effect, being in reverse proportion to the square of the wavelength, is apparently important with shorter-wavelength tools. A 193 nm light source can suffer from 1.65× greater flare than does 248 nm (KrF), and a 157 nm (F₂) light source has 2.5× greater flare.³ Flare, also called scattered light or stray light, refers to all unnecessary light that comes through unprescribed routes of the optical system. The source of flare varies, and common categorization is made by its area of influence — mid-range flare (MRF) and long-range flare (LRF). MRF scatters from a few millimeters to 100 mm from the pattern in concern. The density of the transparent area in a device pattern will change the amount of scattered light at a certain position of the field. This can lead to degradation of CD uniformity, or a redesign of optical proximity correction (OPC).

LRF, on the other hand, strays from a few hundred millimeters to a full field area, and is caused, for example, by surface irregularity of the glass element or multiple reflection of the light among the optical contributors, mask, wafer or glass surfaces. The amount of LRF is almost proportional to the transparency of the reticle as a whole. It is less dependent on local density of the pattern, and the distribution throughout the field is not large. LRF causes shrinkage of exposure dose window by degraded contrast. For today's low-k₁ lithography, which pursues perfect CD control, MRF presents the more crucial challenge.

MRF reaches in the periphery of the pattern, and is caused by light scattered at relatively small angles to the nominal ray at the lens surface. The generator in the optical system is the scatter at the surface and volume scattering within the glass element. The intensity of scattered light at the surface is proportional to (σ_R/λ)², where σ_R is the RMS of surface roughness, and σ is wavelength. The angle of scattering by the shape of surface is proportional to the space frequency of surface shape error. The angle Θ satisfies the equation sinΘ=λ/Λ, where Λ is the spatial wavelength determined by sinusoidal surface of the shape. The higher the frequency is, the wider the flare spreads.⁴ Thus, flare amount and the distribution from the surface, whose roughness can be expressed as the integral of random frequencies, can conveniently be evaluated by using power spectrum density (PSD), which is obtained by Fourier transfer of the surface roughness.

Figure 1 shows an example of lens surface measurement. The graph shows the measured PSD for space frequency by two different frequency tools, one for frequency lower than 1 cycle/mm, one higher. These measurements help to estimate the scatter at the lens surface. Since the surface PSD is approximately proportional to the square of space frequency, the flare intensity decays in accordance with the square of the scatter angle.

1. Indicating different tools used for different spatial frequency areas, this chart shows power spectrum density for surface error. The black line shows approximation proportional to X-2.

Another cause of mid-range flare in the optics system is volume scattering of optical material. The scattering is caused by the three-dimensional distribution of the reflective index. While roughness-induced flare occurs only at the surface, the volume scattering is determined along the thickness direction of the material. Strictly speaking, the effect is only determined by an unrealistic measurement of 3-D distribution of the index. Realistically, homogeneity measurements are used for the purpose, assuming that the index stays the same along the ray. The requirement for the optical element, which is derived from the optics system necessity, was specified by surface shape expressed by Peak-Valley or by Zernike polynomials. If we take flare into consideration, the PSD, Fourier transfer of homogeneity distribution, becomes a useful tool because the high-frequency optical index component is considered in addition to the conventional interest in surface shape.

Here we estimate the relationship between the mid-range flare amount and wavefront aberration from the scatter intensity change by the effect of surface roughness. Total integrated scattering (TIS) from the reflection surface with its roughness σ_R can be expressed by the following equation⁴:

(1)

Assumptions were made that the roughness is far smaller than wavelength (σ_R <<λ), and that the scattering angle of MRF is small enough (cosθi≈1).

If the ideal incident wavefront comes across this surface, the RMS of the wavefront reflected at the surface σW is expressed by σ _W=2σ _R/λ. The MRF amount in turn is MRF=(2πσ_W)² from Equation 1 , meaning that the amount is in proportion to the square of the wavefront aberration. In real scanner tools, the scatter is generated not by surface reflection, but by going through the glass. Therefore, the equation is modified a little:

σ _W=(N-1)σ _R / λ

σ _W=Ndσ_H/λ

where σ_W is the RMS of wavefront aberration, σ_R is surface roughness, N is the reflective index of the optical element, d is the thickness of the element, and σ_H is the RMS of high-order homogeneity.

The higher-order component of the total lens system can be represented by the root of the sum of each surface squared, since the roughness or homogeneity can be understood to be random and a synthesis of various space frequencies. Mid-range flare of a lens system can be estimated by the following equation from the data of each surface or homogeneity measurement:

(2)

where σ_W is the RMS of wavefront aberration of the total lens system, and i is the lens number.

2. This schematic diagram of a lens and flare spread position shows that the wavefront aberration of the lens consists of only one pupil spatial frequency component (F); “y” indicates the flare position.

Our next concern here is the frequency component of wavefront aberration, and the flare distribution area (Fig. 2 ). We already know that the sine of scatter angle sinθ is proportional to the wavelength λ, and reverse to spatial wavelength L. Wavefront aberration is assumed to be expressed by a sole frequency f. Phase deviation at the pupil is defined as δφ(x,z)=a*sin(2πfx) at (x,z). Spatial frequency of one cycle is regarded as one cycle over the diameter of the pupil. Numerical aperture (NA) is defined as NA=D/2F, where the pupil of the lens is D, and focal length is F. When the light with wavelength λ goes in, image is formed and flare appears by the f_x frequency of wavefront aberration. The scatter angle θ is very small to allow us to assume tanθ ≈ sinθ, and the flare image is formed at y by the lens. From Figure 2 , we understand geometrically:

y = F sinθ = Fλf / D = λ / 2NA (3)

which means that the distance between the location of the flare and the image is proportional to the frequency of wavefront aberration.

By applying Fourier transfer to the wavefront aberration, the relationship between the aberration and the range and amount of the scatter can be directly calculated.² To estimate the scattering range from surface roughness or glass homogeneity, it is necessary to convert the spatial frequency into the frequency at the pupil. Spatial frequency at the pupil fp can be expressed using the i-th surface's sub clear aperture diameter as fp(Cycle)=Di(mm)*fx(Cycle/mm). (Sub clear aperture means the diameter of light from one point at the lens surface.)

This way, the contribution to the amount and the range of the flare of one single surface can be estimated by computing the PSD of the glass surface error or homogeneity. Conventional aberration, usually expressed by Zernike low-order terms, is not a simple sum of every surface profile error's contribution. By clocking or spacing of elements, aberration cancellation or adjustment is still possible. On the other hand, flare is a total sum of each lens component as shown in Equation 2 . The control of flare, therefore, is done through the control of element accuracy. Surface roughness allowance of each surface is determined by setting the flare tolerance of the optical system. The design starts by setting the tolerance of the system, which in turn is deployed to the roughness or homogeneity criteria of the elements.

Several flare evaluation methods, in which the system exposes the photoresist, are widely known. Examples include determination of dose to clear using a certain resist, defining flare amount as the ratio of dose increment amount in order to make predefined remaining resist pattern shrinkage to the dose to clear in the transparent area,^5-6 and definition by modulation transfer function (MTF) to the spatial frequency of contrasts obtained from relatively large lines and spaces of several dimensions.⁷ These methods use relatively large doses. Another proposed method to determine flare and its effect on CD uniformity is through CD change measurement after the second duplicated exposure.⁸

3. The box pattern for the evaluation of mid-range flare. Box sizes are 2, 4 and 8 µm, and window sizes are 3-200 µm.

Using a variation of Kirk's method, we have been able to measure MRF in various ranges⁹ by arranging oblique box patterns of several sizes surrounded by different sizes of transparent windows (Fig. 3 ). The center of the box pattern receives flare from the surrounding transparent area and finally disappears by over exposure. The ratio of the disappearing dose to clear is defined as the amount of MRF in the transparent area between the box and window. The amount is the same as the MRF that scatters from one point and spreads between the box and the window.

There are restrictions to the size of the box for better accuracy because, if the box is too small, negative effects of lateral development, influence of diffraction, low-order aberration or defocus can turn into noise. The box should be larger than 4-5× l/NA or 8-10 cycles at the pupil.¹⁰ Flare, aberration and wavefront can be understood differently — while flare can be expressed as Fourier transfer of wavefront, the low-frequency region is better represented by Zernike aberration than Fourier to describe the optical characteristics.

Figure 4 shows a result of evaluation using the test pattern sets. The binary mask was to test a 0.85 NA ArF lens with a box size of 2, 4 and 8 µm, and a window size of 3-200 µm. The illuminator was 2/3 annular and pattern disappearing dose was measured for each combination of the box-window to determine MRF. Resist used was 270 nm PAR-811.

4. Experimental MRF results, with a 2/3 annular illumination mode, and NA=0.85. The blue square dots indicate simulation results for each window size with a 2 µm box pattern.

As the figure shows, the MRF was 1.7% with box=2 µm/window=200 µm. The quantity is reasonably small, and the MRF with this condition means that the scatter spreads out to the mid range, 1-100 µm from one point. A 9 µm window gives 1.1% flare for a 2 µm box, meaning 0.6% for a 9-200 µm window. Similar results are obtained if we look at an 8 µm box, 0.6% for a 200 µm window. Out of all the flare for 1-100 µm, one-third stays within a radius of ≤2 µm, one-third at 2-4 µm, and another third at ≥4 µm. The accuracy of the experiment is determined by the dose step and 0.1% for this test.

MRF of this test can also be calculated by applying Fourier transfer to the aberration gauged by a phase measurement interferometer (PMI), as explained in the relationship between flare and wavefront aberration. The pink square plots in Figure 4 indicate the calculation result for a 2 µm box vs. a changing window size. The calculation is made by the PSD that corresponds to the spatial frequency of the range between the box and the window. The calculation accords with experiments very well, and MRF estimation from a PMI wavefront is practical.

This section describes simulation methods of the flare effect to the optical performance. Flare distribution is known to be expressed by Gaussian point spread function (PSF) as Equation 4:⁵

(4)

where R is the radius at which the intensity becomes 1/e. Properly tuning I and R in the equation enables good accordance with the MRF 2 µm box exposure result.⁹ Furthermore, expression by the sum of two Gaussian terms is proposed.¹¹

The methods, in addition to the conventional partially coherent aerial image calculation result, overlay MRF as incoherent point spread function expressed by Equation 4 , taking the pattern density at the surrounding points into account. Accuracy of the simulation is determined by the pitch of the sampling in the surrounding area and the exactitude of diffraction efficiency estimation.

Another method of including MRF in simulation is to include higher-frequency component wavefront aberration in the aerial image calculation. Results of the experiment in Figure 4 show that a large part of flare spreads within the 30 µm window area. This corresponds to 132 cycles at the pupil for 0.85 NA ArF. By considering the wavefront aberration up to this order, 90% of MRF is taken into consideration. The pupil plane is divided into two-dimensional mesh in the actual calculation of aerial image, and the calculation partition pitch is 2× as dense as the spatial frequency of the calculation area.

Furthermore, the effect from the outside of the partially coherent calculation is to be included by modeling and adding the flare as incoherent light intensity. PSF in this area, unlike Equation 4 , is expressed as Q(r)=I*r^-γ (γ approximately -3), and the effect is to be computed as the product of PSF Q(r) and pattern density P(r). Q(r) is obtained by fitting the experimental result beyond 30 µm (Fig. 4 ). This way, highly accurate simulation results, considering that all the MRF within 200 µm is obtained by first computing imaging characteristics using the high-frequency component of wavefront aberration and secondly superimposing the flare from the exterior of the area as incoherent light.

We have clarified the relation between the key contributors of MRF, lens surface roughness and glass homogeneity, and flare, showing evaluation and target setting methods. The relationship between wavefront aberration and MRF is drawn as well from the scatter at the surface. As a way to evaluate MRF by exposure, we've introduced an overdose experiment with results from the latest ArF tool. The experimentally determined MRF and the calculation from the wavefront aberration are in good accordance. Based on the experiment, we have presented the concept of simulating optical performance with MRF.