Resolution Enhancement Techneques

Recall that the resolution limit previously stated at the beginning

R= k₁ λ

NA (15)

has a different form to the one obtained in the previous section

R= λ

NA. (16)

The two differs by a factor k₁. This parameter k₁ is the Process Parameter, known as such because it is quite literally a parameter that depends on the process. The value of k₁usually has a lower limit of 1, but over the years researchers have developed tricks to further lower k₁ to as far as 0.5, effectively doubling the resolution to what is normally possible. These tricks are referred to as RET (Resolution Enhancement Techniques).

As of currently, there are three main types of RET in industrial use. Off-axis illumi-nation (OAI), optical proximity correction (OPC), and phase shifting mask (PSM). Each of them is able to enhance the resolution of the aerial image through different physical mechanisms.

Figure 27: Off-axis illumination. The imaging resolution of an optical system can be doubled simply by tilting the angle of the illumination optics.

Off-Axis Illumination

Recall that previously when defining the resolution limit, the criterion is set such that at least the ±1^st order diffraction are received by the optical system, since the 0^th order contains only background energy but no information. Here, by the same logic, one could argue that only one of the ±1^st order are necessary for the reconstruction of the image since the two diffraction orders are symmetric. Therefore, one way to improve resolution is to simply tilt the illumination to one side [26], hence the name off-axis illumination, as shown in Figure27. The resulting diffraction patterns will undergo a shift in one direction.

This way, by sacrificing one diffraction order, the available angular space is now twice as large, effectively doubling the resolution.

This method is not without faults, however. Since information of the mask pattern is contained in the ±1^storder and the 0^thorder contains only background energy, eliminating one of the ±1^st order diffraction results in a significant decrease in the contrast of the intensity of the aerial image. Also, since the enhancement of resolution is achieved by tilting the illumination to one side, the enhancement is therefore in one direction only.

These demerits must be taken into consideration if OAI is to be utilized.

Figure 28: Using a phase shifted mask effectively doubles the periodicity of the mask pattern.

Phase Shifting Mask

Another method to improve the resolution is to use a specialized mask. By covering the mask pattern with small blocks of material in an alternating fashion as portrayed in Figure28, a phase shift of half the wavelength can be introduced. Doing so doubles the effective periodicity of the mask pattern, and therefore the resolution can be increased to twice as that of an unshifted mask. [27]

One other advantage of using a PSM is that in this configuration, the 0^thorder diffrac-tion is minimized. Looking at the comparison of the transmittance in Figure28reveals that the average of the amplitude function of the transmittance of the unshifted mask is 0.5, which means a significant portion of the total energy is directed to the DC offset (0^th order). In the case of the PSM however, the average of the amplitude function of the transmittance is zero, therefore no energy is wasted to the 0^th order diffraction. This means that in comparison to a unshifted mask, using the PSM is advantageous in that it doubles the resolution, and at the same time improves the aerial image intensity contrast.

However, one obvious setback of the PSM is that it can be applied to transmission masks only, and that it is difficult to apply to irregular and non-repeating features.

Figure 29: Optical proximity correction makes minor adjustments to the mask such that the imaged pattern stays the same to the pattern intended as much as possible.

Optical Proximity Correction

Since realistic optical systems are finite in size, the higher frequency information outside of the lens aperture are lost in the imaging process. The most pronounced consequence of the loss of high frequency information is that the blurring of the edge sharpness in the intensity of the imaged pattern, causing an inevitable distortion. OPC attempts to make minor alterations to the mask, in order that the final reconstructed image stay as close to the intended pattern as possible. [28] An example of this is shown in Figure29.

OPC differs from OAI and PSM in the sense that it does not alter the pitch resolution at all, however it still comes under the RET catagory because it helps to maintain the correctness of the image.

RET Enhanced Resolution

Taking RET into account and partial coherence into account, a more complete description of the resolution are given below [6]

• Coherent Illumination

R= k₁ λ

NA (17)

• Partially Coherent Illumination

R= k₁ λ

NA(1 + σ ) (18)

• Off-Axis Partially Choerent Iluumination

R= k₁ λ

NA+ NAσ + sin θ (19)

Depth of Field and Depth of Focus

The depth of field (DOF) and depth of focus (also DOF) refers to a range of depth in which the mask and wafer can be placed while still maintaining the image quality above a given threshold, and is related to the NA of the optical system, given by

DOF = k₂ λ

NA² (20)

similar to the pitch resolution.

Both the depth of focus and depth of field are abbreviated as DOF, with depth of field on the mask (object) side and depth of focus on the wafer (image) side. Both are related to one another by a factor proportional to the square of the magnification of the optical system, given by

DOF_Focus= M²· DOF_Field (21)

Figure 30: the location of the ±1^st order diffraction shifts according to the local pitch of the mask pattern illuminated.

Forbidden Pitch

For a lithography tool optimized with OAI, there is a pitch resolution where the projec-tion tool performs excepprojec-tionally poor, and is therefore referred to as the forbidden pitch.

In designing the mask pattern, lithographers must inform the designer to avoid placing features at the forbidden pitch to ensure optimum result.

When employing OAI optimized for one feature CD, one inevitable consequence is that at larger feature pitch, the location of the 1^th order diffraction shifts closer to the 0^th order diffraction as depicted in the right part of Figure30. This induces an optical path difference between the two orders when they recombine at the wafer.

The worst case scenario occurs at the point where the diffraction order shifts to the midpoint between where the two orders were, as shown in Figure 31. As the feature pitch increases to the point where the 1^th order diffraction is at the center of the lens NA, maximum OPD is reached. At this point, the resultant image quality at the wafer is at its poorest. This pitch is referred to as the Forbidden Pitch, and should be avoided in the mask design where possible.

Figure 31: The forbidden pitch, where the 1^st order diffraction is at the center of the pupil, with maximum OPD.

Figure 32: Comparison between off-axis illumination and phase shift mask.

As a side note, although the PSM have similar enhancement effects to OAI, the two rely on different physical mechanisms, as shown in Figure32. The OAI technique sac-rifices one of the ±1^st order for the gain in resolution, while the PSM introduces a half wavelength phase shift to every second feature in the pattern. As such, the PSM does not suffer from the effect of the forbidden pitch as OAI does.

Objec ve

Wafer

Figure 33: If the imaging target is immersed, the effective NA in air is enhancd by a factor almost equal to the refractive index of the the immersion medium/fluid.