Image formation in optical projection litography Flashcards
Condenser lens and objective lens: tasks
The condenser lens has the task to illuminate the reticle in an uniform way, both in terms of light intensity and range of incident light angles.
At the reticle plane, the light is diffracted in a series of diffraction orders, indicating the principal directions in which the light is traveling further with respect to the optical axis, defined by the Bragg law:
sin(alfa_n)=n*lambda/P
where:
n=diffraction order;
lambda= exposure wavelength;
alfa_n=corresponding diffraction angle;
P=period or pitch betweent he reticle apertures.
The objective lens is then going to capture the lower diffraction orders that fall within the capture range of the lens and the image will be reconstructed on the wafer level as an approximation of the original mask object, since only the lower order information can be taken into account and the high order information is lost and does not contribute to image reconstruction.
Rayleigh equation for resolution
Considering the extreme case when first order diffracted light is incident at the outer edge of the projection lens the Rayleigh equation for resolution:
P=nlambda/sin(alfa_n)=lambda/sin(alfa_n)
In the case of a regualar/equal line/space pattern:
P=2CD=lambda/sin(alfa_n)
so the resolution R=CD=lambda/2sin(alfa_n)=lambda/2NA
This is the diffracted limited resolution because we are assuming that the projection lens is free from aberrations and thus the resolution depends only on the collection of diffraction order.
A more general form of expression for risolution:
R=CD=k1*lambda/NA
How to improve resolution
R=CD=k1*lambda/NA
1 smaller exposure wavelength lambda: need for development of new exposure sources so strong challenges to reduce the wavelenghts (UV to DUV, to EUV and eventually x_ray)
2 larger NA in the projection lens: larger lenses could be too expensive and unpractical, and large NA reduces DOF and causes fabrication difficulties;
3 smaller k1(litographic factor): phase shifts masks, off-axis illumination, etc…
Effect on NA on imaging
- resolve better the line image (higher image contrast);
- gives brighter image (higher image intensity).
Effect of NA on lens fabrication
To increase the NA of the projection lens, projection lenses have been steadily growing to accomodate the increased angle of light incidence as well as the increasing exposure field size.
The projection lens has become a considerable portion of the total price of an exposure tool. This is related to the number and size of the optical lens elements forming the projection lens.
An exponential trend is observed in the amount of optical material needed to meet the NA of the next generation projection lenses which woul lead to an exponential trend in the lens price. Clever lens
design tricks have allowed the reduction of the amount of fused silica needed in the next generation lens, and, as such, also the lens price.
Besides the amount of fused silica, also the polishing
requirements are becoming increasingly severe, in
order to control the aberration levels in the lens.
Effect of pitch on imaging
High angle diffraction orders are not collected by the lens with a realistic NA hence the re-combined diffraction image is missing the original high frequency.
Under the same lambda, when feature pitch gets smaller (higher spatial frequency), the diffration angle becomes larger.
Light as a carrier of information on the mask
At least the first order is needed to rebuild some light modulation since 0th diffraction order only contains the average of the photomask pattern.
Large lenses capture more diffracted light, and those higher order diffracted light carries high frequency (detail of fine features on mask) information.
Fundamentally light is a carrier of information on the mask. When more light is collected, more information is collected, leading to higher resolution.
Depht of focus
It is the range in which the image is in focus and clearly resolved (good resolution of the projected image).
DOF=k2lamda/2(NA^2)
Rayleigh criteria dor DOF
1 “If the length of two optical paths, one on-axis, one from lens edge or limiting aperture, not differ by more than lambda/4, two objects are focused.”
On axis the optical path is increased by OC-OB=§
From edge, increased by AC-AB=DC(for small teta)=§cos(teta)
DOF=§=lambda/2NA^2
2 DOF=§=pm k2 (lambda/2NA^2)
Consequence of the second criteria: larger NA gives smaller DOF! which is against the resolution where larger NA improves it. A compromise is needed between R and DOF.
Combining the two Raylerigh criteria:
DOF=(k2R^2)/(k1^2lambda)
Optimal focal plane
Light should be focused on the middle point of the resist layer thickness.
Variations in surface heights of a processed wafer must be less than the optical DOF. Thus, for high resolution litography the surface mus t be planar (flat).
Modulation transfer function
It is also known as image contrast and is needed to quantify the quality of the aerial image, which dictates the amount of information provided to the resist and subsequently the quality and controllability of the final resist profile.
MTF=Imax-Imin/Imax+Imin
where Imax is the maximum light intensity (in the center of the image of the space) and Imin is the minimum light intensity (in the center of the line).
Ideally Imin should be «_space;Imax, giving a contrast approaching 1 for high quality (high contrast) image.
Problem with the MFT
It samples the aerial image at the wrong place. The center of the space and the center of the line are not the most important regions of the image to worry about. What is important is the shape of the image near the nominal edge. The edge between bright and dark determines the position of the resulting photoresist edge.
The steeper the intensity transition, the better the edge definition of the image, and as a result the better the edge definition of the resist pattern.
If the lithographic property of concern is the control of the photoresist linewidth (i.e., the position of the resist edges), then the image metric that affects this lithographicresult is the slope of the aerial image intensity near the desired photoresist edge
Normalized image log-slope (NILS)
The slope of the image intensity as of function of position (dI/dx) measures the steepness of the image in the transition from bright to dark.
However, to be useful it must be properly normalized with respect to the source intensity and features width. Dividing the slope by the intensity will normalize out effect of the dose (source intensity). The resulting metric is called the image log-slope:
d ln(I)/dx
where this log slope is measured at the nominal desired line edge.
Since variations in the photoresist edge positions (linewidths) are typically expressed as a percentage of the nominal linewidth, the position coordinate x can also be normalized by multiplying the log-slope by the nominal linewidth w, to give the normalized image log-slope (NILS):
NILS=w dln(I)/dx
The NILS is the best single metric to judge the lithographic usefulness of an aerial image. Values between 6 –8 are good.
