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Haze Aberration Detection using Weir PW. Haze aberration has been shown to result in side-lobe formation next to the immediate edge.

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haze aberration detection using weir pw

Haze Aberration Detection using Weir PW

Haze aberration has been shown to result in side-lobe formation next to the immediate edge.

Side-lobe formation results not from the mathematical Gibbs Phenomenon description but rather from the physical introduction of Spherical Aberration and other perturbations into the optical train

The reticle is an intimate part of the optical system of the scanner.

Haze introduces scatter and aberrations that:

Result in image perturbations that reach way beyond the immediate deposition

Influence adjacent features

Result in perturbations even when they do not touch the feature.

First degrade the Bossung Response of the reticle image and eventually the dose required to create an on-size image.


Reticle Haze

Haze formation on feature edges does directly influence the edge, however the effects are more far-reaching.

Critical Reticle Haze

Directly influences this features definition through side-lobe ringing artifacts (Gibbs Phenomenon) that distort the square wave of the chrome or PSM edge



Feature Edge Effects

  • Three graphic instances of reticle-face haze formation are shown in this illustration.
  • Feature Edge formations
    • Most likely to form since they represent they form on high-energy initiation seed sites where edge scatter and depositions will first adhere to the mask. Previous presentation illustrated the influence based on the Gibbs effect that results in square-wave degradation by image “ringing” resulting in edge-intensity over/under shoot and in side-lobe generation
  • Clear area Haze
    • Not addressed as a factor
  • On-Feature Haze formation
    • Not addressed as a factor

On Obscuration Feature Haze Formation

Influence on Feature profile?

Critical Reticle Haze

Directly influences this features definition through side-lobe ringing artifacts (Gibbs Phenomenon) that distort the square wave of the chrome or PSM edge


Influence on Feature Response?

seed sites for haze
Seed sites for Haze
  • Haze deposition first forms on high-energy areas known as seed-sites
  • Seed sites are not singularities forming at one or two isolated points
  • Haze initiation will form across an extended area of the mask surface
    • Formation is a function of the interaction of the feature loading
    • localized optical wavefront characteristics (lens edge verses center)
    • Wavelength of illumination
    • Local surface contaminants on the mask
      • From manufacture
      • Cleaning
      • Also tend to located on high-energy feature edges
    • Areas where edges are undercut or chrome is thinned from etch.
    • Areas of unequal etch or PSM feature thickness that result in non-optimum wave extinction during phase shifting.
knife edge optical effects
Knife-edge optical effects

To see the effects of haze formation at a feature edge consider the opticians knife-edge.

The thin chrome obscuration acts as a knife edge discontinuity. Knife edge analyses have been used for years in optics development because they allow the aberrations of the lens to be accurately measured.

The Profile at the edge of the knife edge is NOT a pure Dirac step function as assumed in the Gibbs Phenomenon. It is a complex Intensity gradient that incorporates the basic “Gibbs Phenomenon” artifact plus a stronger variance caused by optics- limited distortions, scatter and localized changes in the effective Numeric Aperture caused by the finite edge. This results in an intensity profile that behaves like a Gibb’s function but is actually stronger in intensity than described in the original presentation.

The Chrome is not a true knife edge in that it’s thickness is actually many wavelengths across. The thickness therefore directly compounds profile changes by polarization and coherence perturbations.

Intensity Profile


scatter effects



Scatter effects

The chrome feature image is further complicated in that it is supported by a quartz substrate. The wavefront at the feature edge therefore encounters a change in the index of refraction (Quartz-to-Air) at the same time that it encounters the chrome feature obscuration.

The index change at the edge results in scatter and this in turn reduces the edge resolution. The effect also interacts with the image wavefront to induce localized aberrations.

AT&T, in 1982, was issued a series of patents for glass photomask coverplates to protect the chrome photomask elements. The coverplate interface to the mask incorporated an index matching fluid to prevent this scatter and reflection interference. This patent also noted the improvement in image resolution and depth-of-focus that resulted because the chrome was now encapsulated in a continuous index of refraction and scatter was eliminated.


Intensity Profile



open area haze formation



Open-area haze formation
  • Haze does not form randomly. It needs a high-energy seed-site.
  • Seed-sites therefore start areas containing:
    • localized damaged from repair
    • Undercut
    • Impurities or localized stress in the quartz substrate
  • The resulting wavefront will be a convolution of the intensity profile across the hazed area PLUS the chrome edge profiles from nearby features as far as 2 microns away PLUS the scatter added by the chrome edge, haze edge and internal haze phase boundaries from acrylic crystalline transitions.
  • The translucent haze area also behaves as a micro-lens and introduced refractive aberrations that further interfere with the wavefront.
  • Summary: Isolated haze introduces wavefront distortions and aberrations that influence nearby features.

Haze profile

Chrome edge profile

chrome obscured haze
Chrome-obscured haze

Chrome is not a complete blocker of the wavefront. It’s complex index of refraction results in a portion of the electromagnetic wave that penetrates and thin film and interacts with the overall image formation. In short, chrome is translucent even at deep-UV illumination.

The wavefront intensity and phase immediately above the chrome surface is not zero. A haze element will react with the chrome causing thinning, cracking and other localized physical reactions.

Scatter from other parts of the imaging layer will interact with this wavefront and also be gathered by the lenticular behavior of the translucent haze. This results in localized aberrations of near edge images not directly involved with the haze seed.

Summary: On chrome haze has a smaller but still finite perturbing influence on the wavefront that introduces aberrations and scatter.

effects of haze seed formation summary
Effects of Haze Seed Formation: Summary
  • Haze does not form on isolated singularities
    • Haze formation is a high-energy area effect.
  • Haze does not have to be intimately associated with a feature edge to influence image formation
    • Early-formation isolated segments act as micro-lens elements
    • On-feature surface haze influences overall scatter and dark-image formation.
  • The image of the photomask is converted to a frequency spectrum at the entrance pupil of the lens. Scatter and aberrations from haze change this spectrum and also change the influence of the inherent lens aberrations on the image that results in large-area image degradation
    • All lenses retain finite coma and spherical aberration as balanced aberrations tuned to the ideal photomask image.
consider thirty years of process windows
Consider: Thirty years of process windows

Collapsed line


  • J. Bossung, SPIE 1977 vol. 100
  • This is a well established technique

Next few slides are from TEA Systems Class: “Lithograph Control and Characterization”

review bossung curve analysis


Feature Size






One curve for each dose


Review: Bossung curve analysis
  • A = Isofocal Dose
    • Dose at which feature size is independent of Focus
  • B = Locus of Best Focus
    • “Best Focus” is located at the maxima or minima of each dose curve
    • The greater the curvature, the greater will be the aberrations of the system
    • Upper and Lower Control Limits for the process
  • EL
    • Exposure Latitude or the dose range over which the feature size lies between the UCL and LCL
  • DoF
    • Depth of Focus or the focus range over which the feature size lies between the UCL and LCL

Zernike Analyses are a quantitative method of lens aberration analysis.

Bossung curve characteristics can show the presence and effect of aberrations.

More strongly than dose reduction, HAZE CAUSES ABERRATIONS

typical bossung focus analysis for center site
Typical Bossung Focus analysis for center-site

Field Layout with measured-site shown in red.

J. W. Bossung,

SPIE (1977) Vol. 100

sites from field center 4 corners
Sites from field center & 4 corners

Plotted sites in red

  • An aberration free lens would result in exactly duplicated feature response.
  • The scatter and aberrations caused by localized haze result in this phenomenon.
  • More haze = more scatter + Image perturbations
ideal focus aberration response of features
Ideal focus/aberration response of features

Feature Size

  • Aberration free features result in
    • Linear feature size response to dose (blue line)
    • An unchanging Best Focus response (flat) of the features for changes in dose as shown here for the near-zero change in focus with dose
aberration influence on feature response
Aberration influence on Feature response

Cd vs size curves

Feature Size

Dense Best Focus

Isolated Best Focus

  • In this example of Contact response and proximity we see:
    • Un-influenced (flat) Best Focus response for widely separated contacts (blue & black lines)
    • Aberrated Best Focus response (red line) for small, dense vias
  • The onset of Haze introduces aberrations that can be seen much sooner than simple dose change from neutral density obscuration effects.

Side Lobe

Cause: Aberration and scatter NOT dose-change

  • In experimental SEMs, side lobes are seen inside a line (left) and outside a trench (right )
  • Figure shows experimental SEMs of side lobes for a line and trench for 8% attPSM. Because the Gibb's phenomenon takes place on either side of the discontinuity, the side lobes can be seen inside the line and outside the trench.

Side Lobe

Notice the perturbation of CD and feature profiles as a result of the side-lobes resulting from induced aberrations

influence of spherical aberration
Influence of Spherical Aberration

i-line rim PSM 0.35 um contact

hole SEM (overexposed)

10% attenuation PSM, 0.35 um hole

NA=0.5, DUV, s=0.3

Calculated with 3rd & 5th Orders

From TEA Systems Class: “Lithograph Control and Characterization”

side lobe formation
Side Lobe Formation
  • The intensity of a side lobe increases with higher transmission.
  • However the stronger effect is the aberration of the wavefront emanating from the local hazed area
    • Wavefront will influence both the immediate feature AND other nearby features through the introduction of spherical aberrations into the image.
conclusions 1
Conclusions #1
  • Previously Shown:
    • Resist erosion is inevitable, however, when using att PSM with higher transmissions.
    • The constructive interference among the secondary maxima of nearest neighbors increases the intensity of side lobes.
    • The worst situation is when the secondary maxima of four neighboring contact holes interact at their diagonal interaction and produce maximum intensity regions.
  • Now Recognize
    • The overexposures shown previously do not illustrate the effect of the haze on overall profile and process response.
    • Process aberrations will extend well beyond the hazed area
conclusions 2
Conclusions #2
  • Weir PW:
    • Aberrations are quickly discovered through the Weir PW analysis of perturbation and feature response uniformity across the full-wavefront process window.
    • The influence of the haze-induced aberration directly upon the process-robustness of the reticle feature can be directly measured using our techniques.
    • This technique will discover the onset of haze formation very much earlier than reflectance or transmission intensity monitors
    • The following slides illustrate the Weir PW tools for detection, identification and location of the influence of Haze Formation.
process window derived feature and dof
Process-Window Derived Feature and DoF

Focus Uniformity

Focus Response Analysis

Depth of Focus Uniformity

The Feature Derived Best Focus is next calculated for every site on the field. This focus-contour is not the exact focus-wavefront of the lens but it is the response surface experienced by the measured feature and rapidly degrades with the onset of Haze. Similarly the features Depth-of-Focus (DoF) can be visualized for every point on the exposure.

isofocal analysis
Isofocal Analysis

Isofocal deviant curves

Aberration level at each dose

Dose Response Analysis

  • Isofocal Analysis: All-sites on field, BCD features Vertical (black) and Horizontal (red)
  • Calculate IsoFocal dose for each feature and site
    • Classic: IsoFocal point is found when the 2nd derivative of the process window = 0
    • Bossung: IsoFocal deviant = the magnitude of the 3rd Bossung curve coefficient
    • Isofocal point is at the minimum for the curve
  • 2) Lower curves: Level of aberrations for the dose plotted as magnitude of 2nd Bossung curve coefficient
  • 3) IsoFocal performance is highly sensitive to both lens and feature design and so responds to Haze
exposure latitude @ best focus
Exposure Latitude @ Best Focus

Exposure Latitude % at Best Focus


Dose Analysis Derivatives


Contour Plot

Vector Format Plot

The Exposure Latitude Percentage uniformity can now be plotted for the field at Best Focus providing an improved characterization for resist setup.

Any point modeled in the field will see the influence of nearby haze incidence and EL% will degrade as haze increases

dose uniformity @ bf for 80 nm
Dose Uniformity @ BF for 80 nm

BCD Horizontal

Dose Analysis Derivatives

BCD Vertical

Focus errors removed and having calculated the “Feature v Dose” response for each site, we can now calculate the optimum dose needed to obtain the feature target value at each site. These contours still contain reticle non-uniformity, lens aberration and scan-perturbations. Haze onset will quickly degrade this reticle and scanner specific signature

at best focus dose for 80 nm
At Best Focus/dose for 80 nm


Focus Error at 22 mj/cm2


conclusions 3
Conclusions #3
  • Weir PW:
    • The Weir PW techniques directly measure the process degradation of the reticle to feature profiles, loss of Exposure Latitude and Depth-of-Focus reduction through modeling of the response across the entire image wavefront.
    • Weir PW answers the need for rapid haze detection and the avoidance of process yield loss long before the effects are noticed through the demands of the haze for increase exposure-dose.
      • When first detected, the user can monitor the gradual degradation in full-field process window and conveniently schedule reticle cleaning or process correction