Intensity Distribution

Fig. 17.12 shows the 2D normalised intensity \E\2/\Ein\2, where Ein is the incident electric field, for an evanescent exposure of a 140 nm pitch grating with Cr conductors (e = -13.24 + ¿14.62), 40nm thick suspended in free space (n = 1).

Fig.17.12. Normalised intensity distribution for a 140 nm pitch, 40 nm thick Cr grating in free space. The grating is illuminated from above by 436 nm TM polarised light (electric field E and magnetic field H directions are indicated). Contour plots of the normalised electric field intensity are shown |E|2/|Ein|2, where Ein is the incident electric field. The scale varies linearly from 0 (black) to 2.0 (white) in 10 linear steps

Fig.17.12. Normalised intensity distribution for a 140 nm pitch, 40 nm thick Cr grating in free space. The grating is illuminated from above by 436 nm TM polarised light (electric field E and magnetic field H directions are indicated). Contour plots of the normalised electric field intensity are shown |E|2/|Ein|2, where Ein is the incident electric field. The scale varies linearly from 0 (black) to 2.0 (white) in 10 linear steps

The grating is illuminated at normal incidence by TM polarised light with a wavelength X = 436 nm. Line-plots of the intensity are presented in Fig. 17.13 for the same exposure conditions as in Fig. 17.13 extracted at the exit aperture of the grating, and then 10, 20 and 50 nm below the grating. These figures illustrate two of the characteristics of an ENFOL exposure - the decaying amplitude of the intensity as we move further below the grating, and strong edge enhancements that are evident close to the exit aperture of the grating, such as can be seen in Fig. 17.12(a).

Fig. 17.13. Normalised intensity line plots for the simulation in Fig. 17.11. The line plots are taken at y = 0 (the exit plane of the grating), then at 10 nm, 20 nm, and 50 nm below the exit plane of the grating mask respectively

17.7.3 Depth of Field (DOF)

The depth of field (DOF) is a critical parameter for a lithography technique that relies on evanescent field components to expose photoresist. It defines the depth at which "sufficient" contrast is available for an exposure; but this is not a fixed value, it varies with different resist chemistries and different exposure conditions. We define the contrast k in the image at a distance y below the mask to be,

W here Imax and Imin are the maximum and minimum intensities in the x-z plane a distance y below the mask. We will define the depth of field, DOFk, as the depth below the grating at which the contrast k falls below a specified value.

Simulations of a conducting Cr grating suspended in free space have been performed and Fig. 17.14 plots DOFk versus the grating pitch for various k factors. These results show a linear relationship between grating pitch and depth of field, which is due to the near field nature of the exposure. In addition, the depth of field is greater for smaller k factors, as might be expected. This implies that the use of high contrast resists (which allow imaging at low k factors) will ease the ultra-thin-resist constraint imposed by the ENFOL technique. However, even for a contrast factor as low as k = 0.3, resist thicknesses below 100 nm are required to achieve resolution below 300 nm. The simulations also show that high contrast images are present in the near field regions of gratings with pitches as small as 20 nm, although in these cases the depth of field is less than 10 nm. This indicates the prospect for resolution of 20 nm pitch gratings in 3 nm of resist for k = 0.5. We believe that such resolution is experimentally achievable using new generation resist chemistries such as surface layer imaging resists (Herndon et al 1999) or self-assembled monolayer resists (Friebel et al 2000).

Fig. 17.14. Depth of Field (DOFk) versus pitch p for simulated gratings plotted for k values of 0.3, 0.5, 0.7, and 0.9

The linear nature of the relationship between DOFk and grating pitch can be qualitatively understood for an evanescent exposure by considering y m, the depth at which each diffracted component decays to 1/e of its initial intensity (Loewen and Popov 1997), y' =

41F-7

Where, m is the diffracted order. From Eq. 17.3 it is evident that the higher the diffracted order, the faster its intensity decays. This has an impact on the exposure at the depth defined by DOFk. For high values of k there exists a significant contribution from higher order (m > 1) evanescent components while at low k values there is generally only a significant contribution from the ±1 orders providing contrast. For gratings with deep sub-wavelength pitches p <<X/n, the m = ±1 components will dominate, and the linear relation y m «p/4n results from Eq. 17 3. Note that this is independent of X and n, so we expect the resolution of ENFOL to be independent of these parameters for deep sub-wavelength gratings. This opens the prospect of choosing an exposure wavelength for optimal resist performance, by-passing the usually difficult task of designing resist performance for an optimal exposure wavelength. The choice of resist thickness is crucial for a successful exposure, firstly to obtain sufficient contrast and secondly to ensure adequate process latitude. It is clear from Fig. 17.14 that the resist thickness should be chosen according to the smallest feature pitch to be patterned. To improve process latitude, operation at a high k is preferable which requires reducing the resist thickness further for a given resist system.

Operating at low k values also increases the likelihood of exposure variation. As we move further away from the grating where the higher order evanescent components have disappeared, the intensity is dominated by the zeroth diffracted order, with transmission coefficient T0 = |E0|2/|Ein|2 where E0 is the zeroth order electric field component. This is modulated by the contribution from the evanescent ±1 diffracted orders as shown in Fig. 17.12(d) for example. The exposure conditions are then heavily dependent on the magnitude of the T0 component, which can fluctuates with factors such as changes in the duty cycle of the grating mask (% of conductor width to the grating pitch), as well as being sensitive to grating resonances. Variations in T0 would make it difficult to expose gratings of different duty cycles in a single exposure. These effects are quantified in Fig. 17.15 for a 140 nm period grating suspended in air, in which DOF05 and the maximum intensity at this depth are plotted. Increasing the duty cycle improves the DOF at the expense of exposure intensity. The improvement with larger duty cycles is due to the decreasing magnitude of the zeroth diffracted order relative to the other diffracted orders, which provide the contrast for the exposure. However, while an improvement in contrast is obtained, a longer exposure is required to compensate for a reduction in the intensity.

Fig. 17.15. Depth of Field DOF05 for a 140 nm pitch grating (left axis) and the maximum intensity at this depth (right axis) versus duty cycle. The grating is suspended in free space and illuminated by 436 nm wavelength TM polarised light

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