chapter 6 model based characterization of optical...

SIMULATION OF SEMICONDUCTOR LITHOGRAPHY AND TOPOGRAPHY - ARN 157

CHAPTER 6 Model Based Characterization of Optical Projection Printing

Modeling and simulation plays a very important role in the development of new technolo-gies for manufacturing of integrated circuits. Optical projection printing is an excellent example of this activity which i9s described in this chapter. A brief introduction overviews the nature of characterization process and the role of modeling and simulation. The tradi-tional experimentally driven characterization techniques for various facets of optical pro-jection printing and their relation to simulation are then described. Basic resist and aerial image characterization are considered initially. Initially photoresist material characteriza-tion are considered. This is followed by the classical printed linewidth versus exposure-focus (SMILE plot) and allowed exposure-defocus for a given linewidth tolerance (E-D tree). Effects of mask errors and the the interplay of resist and aerial image properties are then considered. Techniques to extend the resolution through modified illumination, phase-shift masks and in-lens filtering are then discussed. Optical proximity effects and the ultimate limitations of projection printing conclude the chapter.

6.1 Introduction

To march to Moore’s law of ever decreasing device sizes, the process development and manufacturing engineers must push old technologies to the limit and invent new technol-ogy extensions. Optical projection printing is an excellent example of technology engi-neering because the source wavelengths have not scaled along with Moore’s law and a host of new technology extensions have been introduced to achieve the projected goals. These include more nonlinear resist behavior, antireflection coatings, modified illumina-tion with more off-axis rays, phase-shifting masks and in-lens filtering. These new exten-sions bring benefits to small feature sizes but they come at a price of side effects such as increased dependency on feature size and type. Also in modifying the materials, masks, exposure tools, and wafer topography to utilize thse new extensions the technologists

Connection between characterization and simulation

Flesh out characterization

Model Based Characterization of Optical Projection Printing

158 SIMULATION OF SEMICONDUCTOR LITHOGRAPHY AND TOPOGRAPHY - ARN 3/3/06

often encounter additional implementation dependent nonidealities which must be under-stood to achieve an adequate implementation.

Chatacteriszation of a unit process involves looking at all aspects which could possibly be involved. A divide and conquor aproach is used to first isolate and quantify each factor. Later their interplay together in manufacturing is considered. To do this cost effectively experiments which can easily be conducted on production equipment and analyzed with minimal effort are used. The results are usually compiled in the form of design graphs, sensitivity plots and process control charts.

Modeling and simulation are playing and increasingly important role in this characteriza-tion effort. Often the design chart is itself founded on a basic model and the measurements serve to quantify the parameters and hence severity of an effect. Knowledge from model-ing and simulation also gives an indication of where to focus experimantal characteriza-tion by identifying those effects which are apt to be dominant and the ranges of variables over which measurements are important. Simulation is particularly useful as a vehicle for integrating experimental observations be it diagnosing compounding effects or designing experiments which isolate effects. The ability to predict and assess outcomes in new situa-tions from existing measurements is one of the key strengths of simulation over experi-ment which can only proceed by further experiment. Of course to reap these benefits of simulation an investment in establishing models and calibrating the simulators must be made. In short the best overall approach is to grow the modeling and simulation capa-bility with the technology.

This chapter looks at traditional experimentally driven characterization techniques for materials, mask, exposure tools and wafer state in optical projection printing. In so doing we will relate these techniques to underlying physical models and simulation interpreta-tion of effects. The characterization techniques themselves are an ever changing method-ology which continues to evolve with the technology and availablity of automation. An extensive literature exists on these techniques. See for example {[rzz.auschnitts.lith-vlsi, rzz.lin.book chapter, rzz.thompson-wilson.acs.book, rzz.moreau.book, rzz.king.book.chapter, rzz.otoole.book.chapter, rzz.hershel-mack.book.chapter]}.

6.2 Basic Resist Characterization

The classical method of evaluating resist sensitivity and contrast is to plot thickness remaining versus the log10 of exposure dose as shown in Figure 6.1 for a negative tone electron-beam resist [rzz.thompson]. This technique which comes from photographic sci-ence can easily be applied by uniformly exposing large areas and developing to a fixed development time. development rate monitor curves are shown for several development times. A straight line is then fit to the data points in the intermediate thickness regions of a constant development time curve. The intercepts of this line with zero and the initial thick-ness are sensitivity parameters D0 and D1 respectively. For negative resists D0 is the sensi-tivity and the working dose for an 80% thickness remaining D0.8 is almost as high as D1. The contrast is defined as

Basic Resist Characterization

3/3/06 SIMULATION OF SEMICONDUCTOR LITHOGRAPHY AND TOPOGRAPHY - ARN 159

6.2 -1

where DMAX and DMIN are the maximum and minimum of D0 and D1 as determined by the polarity of the resist. An example of a similar curve for a positive tone photoresist as measured on the Perkin-Elmer development rate monitor (DRM) is shown in Figure 6.2 [rzz.zee.spie]. For a positive resist D0 is larger than D1 and the working dose to clear out the resist between features is larger than D0. Note that longer developer times give higher slope or contrast.

Unfortunately, this characterization technique does not distinguish between basic contrast due to the bulk resist chemistry and false contrast due to effects such as surface rate retardation or in the case of negative resists optical attenuation. To characterize resists with a strong surface rate retardation effect it is more appropriate to plot the thickness remaining as a function of development time as shown in Figure 6.3 [rzz.hofer.2400]. This plot requires many more measurements than a single thickness-versus dose curve and automatic in situ dissolution measurement equipment is generally used to obtain the data. In the thickness versus development time plot the surface rate retardation effects are clearly visible as the downward curvature of the curves. The slowness factor is propor-tional to the ratio of the final slope over the initial slope. The depth of the retardation effect is the thickness over which the slope differs from the final slope. If a remaining resist thickness of 80% is required in the unexposed areas a development time of 200 s could be used at a dose of around 20 mJ/cm2 at a wavelength of xxx nm. Note that the

FIGURE 6.1 Thickness remaining versus exposure dose for a negative tone electron-beam resist and the definition of standard doses and the contrast [rzz.thompson]

γ 1DMAXDMIN---------------------

⎝ ⎠⎜ ⎟⎛ ⎞

log

-----------------------------------=



downward curvature of the unexposed thickness versus time curve has allowed the devel-opment time to be a larger fraction of the time to completely remove the unexposed film. Optical attenuation in positive resists produces an upward curvature in plots of thickness

FIGURE 6.2 Thickness remaining versus exposure dose for a positive tone photoresist [rzz.zee.spie]

FIGURE 6.3 Thickness remaining versus development time for a positive tone photoresist which show surface rate retardation [rzz.hofer.2400].

Tests and Monitors for Basic Projection Printer Parameters


remaining versus development time while surface rate retardation produces a downward curvature.

These resist measurements on large uniformly exposed areas have important implications about the line-edge profiles of the photoresist in patterning wafers. The fact that the thick-ness remaining versus exposure is not vertical means that a threshold model for describing the remaining or removal of the resist is not adequate. It’s steep slope or large γ does, how-ever, magnify the slope in the aerial image and cause the resist thickness to sweep quickly from zero to full thickness. This steep slope allows the chemist to produce nearly square resist profiles from rather sinusoidal images. A steep slope or γ may also tend to make standing wave ripples visible on sidewalls due to exposure variations within the resist layer if special processing techniques such as post exposure bake are not used. A resist showing surface rate retardation of dissolution can also have more nearly square or even overhanging resist profiles. This dependence of the resist dissolution on depth as well as exposure also interplays with the aerial image and determines how its peak intensity, edge slope and minimum intensity influence the resulting resist profile.

Often other simple measurements are made on unpatterned resist on wafers to test produc-tive worthiness of the lithography process. The presence of particles on a wafer prior to resist coating can be monitored by using a bright columnated light to illuminate the wafer and observing the scattering of light in nonspecular directions. Once the resist is coated on the wafer its uniformity can be monitored by using a monochromatic light source such as a He lamp to inspect the wafer. Global variations in light intensity are an indication of thick-ness changes across the wafer. Local ‘comet’ shaped patterns are indications of the pres-ence of particles which have affected the flow during coating. Surface haze is an indication of problems in the solvent removal. Applying these inspections after open frame exposures at various doses and development is an excellent way to find nonunifor-mities due to both the resist and exposure tool. The adhesion to the substrate can be quickly tested by the ‘scotch tape test’ in which the tape is applied to the resist and then removed.

Measurement of the thickness remaining versus development time such as that in Figure 6.3 or thickness remaing versus exposure dose provides fundamental data for establishing the resist dissolution model used in line edge profile simulation. The ABC optical bleach-ing model for the resist as discussed in Chapter 5 must be determined first and techniques for doing this from a measurement of the transmission versus time will be described later in Chapter 9 on resists.

6.3 Tests and Monitors for Basic Projection Printer Parameters

Simple mask patterns can be used to characterize and observe some of the most funda-mental parameters of the exposure tool being used in projeciton printing. Test patterns of nonprintable features have, for example, been added to product wafers to monitor the exposure [rzz.widman.arden] . Inspection of arrays of contact holes can be used to deter-mine best focus [rzz.huynh.me]. Sets of special patterns on test masks can be utilized to characterize the illumination. The goal is to find patterns which are more sensitive to a particular critical parameter than the product wafers themselves. Just as coal miners used a



live canary to sense dangerous gases in the mines, the lithographer can use one of these test patterns as a quantitative canary for each of the critical parameters in lithography. It is of course desirable that the pattern used to monitor one parameter or physical effect have low sensitivity to others to reduce confounding. In building in extra sensitivity by design these patterns often place additional demands on mask making and mask character-ization. Thus their practical implementation and quantitaive interpretation requires both clare and cleverness. Developing effective test patterns is a challenging opportunity and it has been made especially interesting not that phase-shifting masks add another degree of flexibility. Combining these test patterns with automatic monitoring and the power statisti-cal metrology is an important frontier in CIM.

The use of non-printable features to reduce mask transmission was introduced by W. Arden and D. Widmann as a way to monitor exposue independent of focus [rzz.arden.wiedman]. These structures consist of an array of sub-imageable features which scatter light into angles outside the acceptance angle of the lens. A number of arrays with monitonically decreasing transmission are used in a set. An example of the printing of such a sized set of 17 of these individual arrays is shown in Figure 6.4 [rzz.huynh.me].

The printed wafer can then be quickly inspected with a low power microscope to deter-mine the first array which failed to clear or by observing the color of a particular array. As the exposure increases from 70, to 90 and 130 ms the number of individual arrays which cleared increases from 3, to 5, and 10.

The test patterns utilized may be either 1D or 2D, but 2D allows finer step sizes in trans-mission. Typical 2D patterns are shown in Figure 6.5 [rzz.huynh.me]. To diffract light rays outside of the capture cone of the lens the period in any direction must satisfy

FIGURE 6.4 Photographs of exposure monitor patterns printed with exposure dwell times of (a) 70, (b) 90 and (130) ms [rzz.huynh.me].



6.3 -1

For systems with modified illumination σ should be taken as large as largest off-axis rays incident on the mask. Typically periods are 0.6 λ/NA and smaller. Once only the specu-larly transmitted (0,0 direction) rays are collected by the lens their exposure relative to the clear field can be calculated. Their electric field strength is proportional to the fraction of the area which is open and the resulting intensity is the square of their electric field strength. For the case of open squares this gives

6.3 -2

And for the case of opaque squares it is

6.3 -3

The feature sizes SX and SY are typically 0.4 λ/NA or smaller which means that the mask making equipment is operating at half of the normal features sizes where no guarrantees are made on linewidths or their uniformity. In practice it is necessary not only to consider the average bias in mask making but also the actual variation in bias for a particular mask. This means that the actual transmission does not come out as designed. However, it can be

FIGURE 6.5 Eexposure monitor test patterns which are not sensitive to focus as introduced by Arden and Widmann [rzz.arden.widmann].

P 11 σ+------------- λ

NA---------=

I00 E00( )2 SX

PX---------

SYPY---------

⎝ ⎠⎜ ⎟⎛ ⎞ 2

= =

I00 E00( )2

1SXPX---------

SYPY---------–

⎝ ⎠⎜ ⎟⎛ ⎞ 2

= =



calibrated by measuring the mask transmission in the projection printer or a simple micro-scope set up.

Lithographers frequently check best focus by examining the quality with which contacts print. The contacts diffract light in all directions and thus make heavy use of the region of the lens near the maximum acceptance angle of the lens. The rays in this region are most strongly shifted in phase when defocus is present and hence the contacts are more sensi-tive than most patterns to focus. This contact test is quite similar to the Strehl ratio used to test lenses in which the brightness of the image of a point source is compared to its total energy. In this test the brightness decrease proportional to the rms average of the aberra-tions over the set of acceptance angles. By analogy the contact acts approximately as a pin hole and defocus is the aberration.

An array of contacts is thus a suitable canary for monitoring focus. Sized sets of individual arrays of contacts can be used to give a more graded scale as shown in Figure 6.6 [rzz.hynh.me]. The GCA 6200 10X stepper used in this study had a wavelength of 436 nm

a NA of 0.28 and σ of 0.7. The working resolution of 0.8 λ/NA is 1.25 μm and the Ray-leigh depth of focus is λ/(2NA2) or 2.78 μm. The focus unit on this tool is in 0.25 μm steps and the 12 steps used in the photos correspond to 3 μm steps or slightly more that one Rayleigh unit of defocus. Notice that the images of the contacts are far more sensitive to focus than the lines even though the lines are smaller (0.5 to 1.0 μm) than the width of the contacts (0.8 to 1.3 μm). Since the image quality degrades parabolically with focus and it is difficult to determine best focus from the data near focus (0 to 0.5 Rayleigh units). It is easier in practice to determine the rapid variation in the region of large defocus (0.5 to 1.0 Rayleigh units) above and below focus and interpolate.

FIGURE 6.6 Focus monitor test patterns of lines and contacts (a) layout, and printed pattern at (b) -3μm focus, (c) best focus and (d) + 3μm focus [rezz.huynh].



The illumination plays an important role in the overall optical system performance and there are several techniques of characterizing it. By design the ray angle bundle which makes up the illumination at the mask is brought to a focus at the entrance pupil to the lens. Some projection printers allow the illumination to be moved to the side so that the image in space at the location of the image pupil can be observed to check the illumination ray angle pattern shape. If the system has a variable NA it may be possible to measure the clear field intensity as a function of the NA and from the occluding of the illumination by the aperture stop determine its radial distribution. Arrays of lines of very fine pitches can also be used. When the pitch exceeds that given in Equation 6.3 -1 a modulated pattern should begin to be observed on the wafer. Note that σ’s of 0.7, 0.5 all modulation would dissapear at periods of 0.77, 0.67 and 0.59 λ/NA.

Partial coherence effects are directly observable in circuit patterns. When σ is low (around 0.3) the ends of lines begin to show ringing effects and look like match heads or tree frog toes. At high σ (around 0.7) line ends become very sloped and forshortened. The partial coherence controls the interaction between features and as s is reduced from 0.7 to 0.3 the contribution from an adjacent feature can change polarity from being additive to being subtractive as can be seen in Figure 6.7 [rzz.robertson]. Here the size of moderately small

(0.55l/NA) open feature changes as it goes from being isolated to being adjacent to large clear areas. Note that when σ is below 0.5 the proximity effect reduces the open line width and when σ is larger that 0.5 it tends to increase the open line width. Since this effect is produced by the pattern interacting with the sidelobes of the radially symmetric mutual coherence function test patterns which are circular should work even better for character-ization. Phase-shift masks offer the possibility of enhancing the effect further by matching the phase of of the sidelobes of the mutual coherence function.

FIGURE 6.7 Proximity effects on open lines and the effect of the partial coherence [rzz.robertson].



6.4 Aerial Image Characterization

6.4.1 Expected Ideal Lens Performance

We now turn to the basic behavior of aerial images in optical projection printing and in particular one of the most critical issues which is the lack of focus tolerance for small fea-tures. The basic effects of partial coherence, feature type, and defocus were briefly described in Chapter 5. The lens in a projection printer might be viewed as producing good images over a hockey puck shaped region. The diameter of the hockey puck is that of the field of the lens, while it’s height is the total focal range over which features are matained with adequate quality. To first order this height is rougly twice the Rayleigh focus distance. Developing a manufacturable process might be thought of as designing the height variations on the wafer and the positioning of the wafer to fit in the hockey puck under worst case scenarios. However, it is necessary to characterize the height of the hockey puck more carefully as it is a strong function of feature size, it is influenced by the partial coherence factor σ, and in practice it can even be warped and warped in different directions for radial and tangential features due to lens imperfections.

The anticipated effects for a diffraction limited lens as a function of features size for defo-cus at various partial coherence factors are shown in Figure 6.8 [rzz.oldham.shankar]. The

contrast is shown for equal line and equal space patterns for three values of σ. Here the focal error is in Rayleigh units and the spatial frequency is normalized according to the definitions introduced of cutoff for coherent illumination described in Chapter 3. Note that there is an abrupt decrease in contrast near a spatial frequency of 1. This decrease is partic-

FIGURE 6.8 Contrast in an equal line and space pattern as a function of feature size for partial coherence factors of 0.3, 0.5 and 0.7 [rzz.oldham.shankar].

Aerial Image Characterization


ularly steep for small σ. In all cases as defocus increases from 0.4, to 0.8 and 1.2 Rayleigh units the spatial frequency for which the contrast stays above even 0.6 is severly degraded from about 1.2 to 0.8. This means that while feature sizes of (0.5/0.8)λ/NA could be imaged at best focus a hockey puck of height 2(1.2)(λ/2NA2) could only be used with fea-tures (0.5/1.2)λ/NA.

These plots display the contrast for lenses which are essentially perfect, aside from defo-cus. Other aberrations depend upon the lens design and assembly. The defocus behavior also provides a clue to certain other lens imperfections. For example the residual astigma-tism can often be characterized as an equivalent focus error for radial (sagital) and tan-gential rays at various places in the field. This error typically increases with distance from the center of the lens and is known as field curvature. It is of course usually worse in the corners of the chip which are near the edge of the field. The fact that the error grows at dif-ferent rates means that a local pattern on the mask of a waggon wheel with tapered spokes (star pattern) should print with a football shaped blurr in the center which will rotate by 90 degrees as the wafer is moved through focus.

6.4.2 Nearly Direct and Direct Image Measurements

Measurements of image contrast can be utilized to characterize the performance of optical projection printers. A thin resist layer can be used as a threshold detector, and when com-bined with exposures of a periodic mask at many discrete dose steps the dose to first open and totally clear an area can be recognized [rzz.oldham.contrast.measure]. These doses are

FIGURE 6.9 Use of a thin resist layer exposed at a range of doses up to 100 time the normal exposure dose to determine the dose to just open the resist and dose to completely clear the resist and hence determine contrast [rzz.oldham.contrase.measure].



inversely proportional to IMAX and IMIN respectively and can be used to calculate the contrast. The experimental contrast determined in this manner is shown in Figure 6.9 superimposed upon the calculated contrast for a lens at wavelenght 436 nm, numerical aperture 0.28 and partial coherence factor 0.7. One set of curves is for the performance in the center of the field and the other set at some what lower contrast is for the performance at the corner of the 1 cm2 square field. The astigmatism is apparent in the difference in the contrast between horizontal and vertical patterns.

More direct measurements of the aerial image quality have been made using a floursence from fields of well defined small features as shown in Figure 6.10 [rzz.brunner.flour]. A

floursening detector is first fabricated by for example patterning resist on a wafer with a field of pairs of opaque lines well separated from one another. This wafer after develop-ment is reinserted in the wafer plane and the shutter held open with the origonal mask still in position. Multiple lines are used for invreased sensitivity. Where the exposure light strikes the resist it produces flouresnce of green light which can be monitored with a pho-todetector placed near the end of the lens. As the wafer is moved by the mechanical stage the detected light increases or decreases as more or less of the resist moves in or out of the areas of high intensity in the image. By deconvolving the shape of the resist profile the image intensity profile can be determined. This real-time image monitoring method revealed that vibration of the stepper due to motors moving a cassette of wafers greatly degraded performance.

An example of image intensity profiles measured using flouresence are shown in Figure 6.11 as a function of focus position for four locations in the field of a stepper (λ = 436nm, ΝΑ = 0.30, σ = 0.7) [rzz.brunner.flo.results]. These images were recorded after the source of vibrations had been removed. The theoretical values from the SAMPLE program are

FIGURE 6.10 Use of floursence of narrow features to measure the intensity in a projected image [rzz.brunner.zerox].

Resist Linewidth Characterization


also shown. While the theoretical image shows a symetrical behavior with rspsect to both horizontal position and defocus, the measured intensity is really not symmetrical with respect to either parameter. Considerable variation is also seen between various locations in the field and the best image does not occur at the best same focus at all positions in the field. This clearly indicates the importance of developing characterization techniques to fully examine the optical system performance over the entire focus*field volume.

Direct measurement of image quality with photodetectors made of arrays of lines [rzz.brunner.compahy] and contact holes [rzz.partlo, rzz.fields] is possible. An example of the image of a set of elbows is shown in Figure 6.12 [rzz.partlo]. This is for a DUV stepper at 248 nm at a NA of 0.5 and partial coherence factor of 0.5..

6.5 Resist Linewidth Characterization

6.5.1 SMILE Plot

More traditional characterization schemes have consisted of examining resist linewidth as a function of focus for various exposure doses. An example of this theoretically expected SMILE or Bossong plot is shown in Figure 6.13 [rzz.arnold.spie.smile]. The SMILE name is evident from the shape of the curves. In practice choosing the dose which producess the flattest curve produces the least sensitivity to focus. A simple threshold resist model and a sinusoidal intensity image can be used to explain the smile behavior [rzz.smile.king?]. As defocus is introduced the modulation in the image decreases. If the threshold level is at the average intensity level no change in linewidth is observed for moderate defocus. If the

FIGURE 6.11 Intensities measured by floursence at the center top, bottom, lkeft and right edges of the field for a range of focal positions and the expected diffraction limited image from simulation [rzz.brunner.images]



exposure dose is low the threshold falls on the peaks of the sinusoid and the linewidth decreases as positice or negative defocus is introduced. If the exposure dose is too high the

FIGURE 6.12 Directly measured image of elbows from using a photodiode [rzz.partlo].

FIGURE 6.13 SMILE or Bossong plot consisisting of linewidth verus focus for various exposure doses. The dose producing the flattest curve produces the least sensitivity to focal position [rzz.arnold.spie].

Resist Linewidth Characterization


threshold falls in the valley of the sinusoid and the linewidth increases as defocus reduces the modulation.

The basic SMILE plot can be modeled algebraically following the development by Michael King [rzz.smile.king]. The image intensity at high resolution is assumed to be a simple sinusoid given by

6.5 -1

Here ΔZ is the defocus distance and P is the period of the sinusoid. The contrast function C(ΔZ) is related to the MTF as

6.5 -2

Note that the contrast decreases with the square of defocus as

6.5 -3

The shift in the position of a line edge for a change in exposure ΔE or focus ΔZ for an intensity with a modulation which decreases as ΔZ

2 is

6.5 -4

Substituting the parabolic form of C(ΔZ) gives

6.5 -5

This formula for the line edge position variation ΔX or one half of the linewidth change ΔL was used to plot the theoretical SMILE behavior in Figure 6.13.

Experimental SMILE plots have been used by S. Lis [rzz.lis.smile.spie] to characterize stepper performance in terms of five parameters. The linewidth is modeled as

6.5 -6

Here Z0 is the best focus, E0 is the conjugate exposure, L0 is the linewidth obtained at the conjugate exposure, B is an exposure dependent resolution parameter, and A is a focus dependent resolution parameter. By extracting these five parameters under various condi-

I x( ) 1 2⁄( )I0 1 CΔZ 2πx( ) P⁄( )cos+( )=

C ΔZ( ) 4π---⎝ ⎠

⎛ ⎞ MTF ΔZ( ) 4π---⎝ ⎠

⎛ ⎞ 1 4π---⎝ ⎠

⎛ ⎞ λ2NAπ----------------⎝ ⎠

⎛ ⎞sin– 2 NA3

λP------------

⎝ ⎠⎜ ⎟⎛ ⎞

ΔZ2–

⎝ ⎠⎜ ⎟⎛ ⎞

= =

C ΔZ( ) C0 DΔZ2

–=

ΔXΔEE

--------⎝ ⎠⎜ ⎟⎛ ⎞ 1

E----

x∂∂E

⎝ ⎠⎛ ⎞

1– 12---⎝ ⎠

⎛ ⎞ 1E----

x∂∂E

⎝ ⎠⎛ ⎞

1– 1E----⎝ ⎠

⎛ ⎞

ΔZ2

2

d

d E

⎝ ⎠⎜ ⎟⎜ ⎟⎜ ⎟⎛ ⎞

ΔZ2

–=

ΔXP2π-------⎝ ⎠

⎛ ⎞ΔEE

--------1 C0 2πx( ) P⁄( )cos–( )

C0 2πx( ) P⁄( )sin------------------------------------------------------------ D

C DΔZ2

–------------------------ 2πx( ) P⁄( )ΔZ

2coth–

⎝ ⎠⎜ ⎟⎜ ⎟⎛ ⎞

=

L L0 BE E0–

E------------------

⎝ ⎠⎜ ⎟⎛ ⎞

– AE E0–

E------------------

⎝ ⎠⎜ ⎟⎛ ⎞

Z Z0–( )2

–=



tions issues such as stepper performance as a function of feature size and position in the field can be compared.

6.5.2 Exposure-Defocus Linewidth Tolerance Trees

The process lattitude is primarily determined by exposure and defocus. The region of acceptable focus and exposure values can be displayed through several techniques. Speci-fying for example that a 10% linewidth variation is acceptable the SMILE plot can be con-verted to a MOUTH plot as has been done by Arnold in Figure 6.14 [rzz.arnold.mouth].

This class of energy defocus or ED diagrams can be used to look at other performance metrics such as resist sidewall angle.

B.J. Lin has used ED diagrams in a form know as intensity-defocus ID trees to examine the lattitude limits in simultaneously printing features of different types and sizes [rzz.lin.ED.diagram]. The example in Figure 6.15 shows the difficulty in being able to simultaneously print lines, spaces and equal line space pairs of ??? sizes at a \(*l=???, NA=??? and $ sigma $=???. The criteria used to create these diagrams is that ??? [izz.lin.e-d. criteria?] which is consistent with intensity levels around 10 to 20% being the image quality dominate in forming features as dissed above. The situation is much improved when each of the features are individually biased as shown in Figure 3.4b.

Find more recent and typical example of Lin. Newmark study for ATT?

FIGURE 6.14 Exposure energy versus defocus (ED) diagram showing the boundary of acceptable values for two different feature sizes for a theoretical case [rzz.arnold.spie].

Resist Effects


{Popular technique for visualizing multiparameter effects and designing maks biases. Example 5 feature types, various rim biases, look at volume that remained, effectively summarized the aerial image behavior for 10,000 SPLAT runs}

6.6 Resist Effects

6.6.1 Thickness Effects and the Swing CurveThe thickness of the photoresist has strong effect on the coupling of energy into the resist from the aerial image and hence the linewidth produced by the subsequent development. As discussed in Chapter 5 the resist layer can act similar to a quarter wave optical coating (when it is an odd multiple of quarter wavelengths) or have little effect (when it is an even multiple of quarter wavelengths). This periodic dependence of linewidth on resist thick-ness is the so called swing curve used to characterize the sensitivity of linewidth to resist thickness. An example from a simulation for positive resist is shown in Figure 6.16. Both the local linewidth variation due to quarter wavelength changes in resist thickness and the global linewidth changes due thickness changes on the order of the step height can be see-nin the swing curve. The smallest linewidths occur for good coupling conditions. A change in resist thickness of λM/4 = 65 nm moves from the minimum to the maximum lin-ewidth. Resist thicknesses in spining can be controlled to +-5 nm and the nominanal thick-ness is centered about the minimum for good coupling for linewidth control.

FIGURE 6.15 Intensity-defocus tree like diagram which shows the acceptable window in printing features of different sizes and types at a +-2.5% linewidth control. Case (a) shows the failure of four different sized features to nest and in (b) a common window is found when the targeted linewidths have been adjusted [rzz.lin.idtree].



A dramatic illustration of the periodic dependence of energy coupling and hence linewidth on resist thickness can be seen in Figure 6.17 [rzz.neureuth.symp]. In this photo lines are

FIGURE 6.16 Linewidth as a function of resist thickness showing a local periodic dependence and a global increase with thickness increase [rzz.swing.mack?].

FIGURE 6.17 SEM of patterned positive photoresist showing linewidth variations in approaching and crossing a step. The standing wave effects produce resist plateaus which help visualize the linewidth variations.

Resist Effects


patterned perpendicular to a step. The step has produced a resist thickness variation in the spinning process. This in turn causes several changes through poor and good coupling as the lines approach the step in the high region (lower part of photo) or low region (upper part of photo). In the high region the resist is quite thin and when good coupling occurs a very small linewidth is produced. In the low region the resist is quite thick and very wide linewidths are produced when poor coupling occurs. Lateral reflection from tapered steps produce additional exposure and development of the resist known as reflective notching. High thin-film reflectivitiy enhances coupling and standing wave exposure variations in the resist which inturn require higher contrast aerial images for linewidth control.

The simulation used to generate Figure 6.16 has been used to systematically show the cross sections for various resist thickness in Figure 6.18 [rzz.neu.linewidth]. Both above

and below the step local variations in resist thickness cause the coupling of energy to go through a maximum and minimum which in turn causes the linewith to go through a mini-mum and a maximum. The worst situations are good coupling of energy above the step when the resist is thin (case a) and poor coupling below the step when the resist is thick (case d). These situation then produce the linewidth extremes as shown in the simulated resist profiles in Figure 6.16.

With regard to wafer topography, the resist must be about 2.3 times thicker than the step height to assure good step coverage. The thin-film stacks as viewed from within the resist should have a reflectivity less than that of silicon or else a higher contrast than the 0.8 to 0.9 commonly used for silicon. Reflectivity effects can be reduced through the use of anti-reflection coating (ARC) materials [rzz.brewer.kodak] and top antireflection (TAR)

FIGURE 6.18 Schematic diagram of the rest thickness changing through nodes of constructive and destructive interference corresponding to poor and good coupling of energy into the resist and simulated profiles for thicknesses a, b, c, and d in Figure 6.16.



[rzz.brunner.spie] coatings on top of the photoresist. Multi-layer resists can reduce effects of both resist thickness variations and substrate reflectivity. For single layer resists which must be exposed to the bottom a rule of thumb is that the product of the nonbleachable absorption times the thickness should be less than about 0.3 to allow adequate penetration of the light.

If the substrate were complete absorbing, the absorption of the resist could be used to maximize the exposure at the bottom of the resist in an analysis used in x-ray lithography [rzz.cox.az]. In this case the light decays as

6.6 -1

And the relative power delivered to the resist at a point z is

6.6 -2

Taking the dervative with respect to α gives

6.6 -3

Setting the derivative equal to zero shows the maximum energy absorption during expo-sure occurs when αz = 1.

6.6.2 Dissolution Effects

While earlier a simple threshold dissolution model explained the basic shape of the SMILE plot, a more detailed physical model of dissolution is needed to account for many of the properties of experimental SMILE plots. For example, the linewidth value at which a particular mask pattern becomes invariant to focus (isofocal resist linewidth) does not agree with the isofocal point seen in the aerial image (isofocal image linewidth). The aerial image in Figure 5.11 predicts an isofocal linewidth which is larger than the dark fea-ture on the mask and at an intensity of 30 to 40% of the clear field. In practice the isofocal resist linewidth is almost always observed to be at a linewidth smaller than the mask line-width and at an intensity value between 10 to 20 % of the clear field intensity. Thus some care should be used in using aerial images alone to assess lithography performance issues.

An example of an experimentally measured SMILE plot is shown in Figure 6.19 [rzz.yeung.spie]. {The conditons}. The thin resist case shows a nearly symmetrical SMILE shape and the isofocal linewidth is about 0.6 μm which is considerably smaller than the mask linewidth.

Both the dissolution properties of the resist and the inhomogeneous exposure due to stand-ing waves contribute to the difference between the experimental and image simulation iso-focal locations. Many studies have been carried out to try ot understand these effects. The basic problem is that the dissolution front which produces the resist profile travels along a curving and contracting and expanding path. It thus depends on properties at various

I z( ) I0e αz–=

P α z,( ) α I z( )( ) α I0e αz–⎝ ⎠⎛ ⎞= =

α∂∂ P α z,( )( ) I0e αz–

⎝ ⎠⎛ ⎞ 1 αz–( )=

Resist Effects


points in the image, the depth of the resist and the standing wave interference ridges. Basic simulation studies by O’Toole et al. [rzz.otoole.spie.Imin.role] using piecewise linear image models have shown that the intensity minimum must be in the range of 10 to 20% before image slope has any influence on the resist sidewall angle. The peak intensity, how-ever, also plays an important role in making the vertical penetration to the substrate possi-ble. It is especially important for example in opening contacts to size the contacts such that the peak intensity is approaching the clear field value.

For the thick resist in Figure 6.19 a new and very pronounced asymmetry is present and is attributed to additional phenomena which occur in exposing a resist whose thickness is not negligible compared to the Rayleigh depth of focus for the high NA lens. Here the resist is {thick compared to focus depth}. High NA effects are extremely important and in general both the dissolution and high NA imaging effects must be included in characterizing per-formance. While there is an additional tilt of the curves with focus the exposure linewidth with least curvature runs from about 0.45 to 0.6 μm and on average has a linewidth which is considerably smaller than the nominal linewidth.

6.6.3 Lumped Parameter ModelIn certain cases for single layer resists it is possible to make a reasonable estimate for the developed linewidth by assuming that the dissoluton first etches vertically down to the substrate and then etche laterally to open the resist profile. This simple two step apporoach has been used successfully by Watts [rzz.watts.3B.two.step.dev] in characterizing line-width variation versus development time. Today this aporoach is associated with the “lumped parameter model” of the linewidth variation of Hershel and Mack [rzz.her-shel.lith.vlsi]. The advantage ot their model is that it only requires information about resist

FIGURE 6.19 Experimental ED diagrams obtained by electrical measurements of etched silicode-polysilicon lines for thin and thick resist [rzz.yeung.spie].



development along a central vertical path and along the horizantal substrate interface to estimate the developed linewidth. The resist is modeled by means of a the striaight line thickness versus logarithm dose curve with slope γ. To make the algebraically tractable, standing wave effects and resist absorption are also neglected. [It also appears that in the time to develop vertically to the substrate is implicitly set to zero in the derivation.] The resulting equation is

6.6 -1

where ε(x) is the log energy to expose a space of width 2x and ε(0) is the energy to expose a CD of zero, that is to just clear the resist. The required image integration has been imple-meted in PROLITH to produce plots of the CD versus exposure dose such as that shown in Figure 6.20 which shows the effect of resist contrast. The user is able to get some impres-

sion for how resist and exposure tool parameters such as resist contrast, resist thickness, feature sizes, and defocus might affect linewidth.

6.6.4 High NA EffectsAt high numerical aperature several different imaging and resist exposure effects come into play. At high NA the image produced by the optical system in space is affected by the fact that the light has take-off anges which are not perpendicular to the mask (obliquity factor). In addition the extra path length with defocus must be modeled with the actual square root behavior (true defocus) instead of an approximated by a simple quadratic. A

FIGURE 6.20 Linewidth variation with exposure energy for different resist contrast as predicted by the lumped parameter model [rzz.hershel.mack].

ε x( ) ε 0( ) 1γ---⎝ ⎠

⎛ ⎞ ln 1 1tRESIST----------------------------+

⎝ ⎠⎜ ⎟⎛ ⎞

+=

Resist Effects


third concern is that polarization effects may occur such as that due to the electric fields from off-axis waves not being parallel and requiring vector addition.

Additional phenomena occur in exposing a resist whose thickness is of a thickness approaching that of the Rayleigh depth of focus. It is not possible to be fully in focus over the full resist thickness. An additional concern is amount by which the reflection from the substrate is out of focus. As a result the line edge profiles for thick resists typically show a considerable shape change over focus as shown in Figure 6.21 [rzz.bernard.kti].. Here xxx

and yyy.

Telltale signs of the resist profile effects can be seen in the SMILE or Bossung plot. This is apparent in Figure 6.19 where a very pronounced asymmetry is present. Here there is an additional tilt of the curves with focus the exposure linewidth as for example the dose with least curvature runs from about 0.45 to 0.6 μm. The resist is {thick compared to focus depth}.

Several authors have investigated polarization effects [rzz.flagello, rzz.yeung, rzz.sam-sung]. A reduction in intensity is expected to occur because the electric fields are not always parallel to each other. However, this effect is only a few percent at even at rela-tively high NA of 0.7 [rzz.yeung]. Flagello has used a clever method of testing for these effects shown in fig [rzz.flagell]. This SEM was produced by cross sectioning the wafer prior to development. A short development was then applied which etched the positive resist in the later direction and produce a relief image into the resist sidewall. Using a polarizing filter at the mask with orientations parallel and perpendicular to line edges and

FIGURE 6.21 Resist line edge profiles showing typical shape changes as a function of focus in thichk resists at high NA [rzz.bernard.kti].



examining SEMs of these sidewall relief images can be used to diagnose polarization effects.

Simulation methods for high NA image and thin-films effects are well established. Effects of obliquity and true defocus were pointed out by Cole et al [rzz.cole.na]. A clever exten-sion for including thin-film effects as lens aberrations has been suggested by Michael Yeung [rzz.yeung.lee.spie]. These effects will be discussed in detail in Chapter 9 on imag-ing.

6.7 Electrical Testing for Automating Statistical Metrology

The characterization of the statistical variations in manufacturing is becomming increas-ingly important as processsing becomes more complex and error budgets must be shared between additional contributing factors. This characterization has been termed statistical metrology [rzzBartlelink]. Electrical testing with automatic wafer probing offers a means of rapidly and efficiently collecting the large volume of data needed. For example in examining production capabilities it is useful to look at the lithography resolution at grid spacing of intervals of 1 to 2 mm across and entire 200 mm wafer. This data over several wafers can then be analysed to determine the dominant sources of the variation. The elec-trical measurement of each of the test sites can be taken from a patterned conducting film such as that shown in Figure 6.22 [rzzBrunner]. Here the sheet resistance (ressitivity/

thickness) is first determned with the VanDer Paul pattern by forcing a current through ter-minals AB and measuring the voltage on terminals CD.

pSHEET = pilnxx. 6.7 -1

FIGURE 6.22 Electrical test structure [rzz.brunner]

Electrical Testing for Automating Statistical Metrology


The linewidth is then determined from the long narrow structure by forcing a current from AtoB and measuring the voltage CtoD.

LWIDTH = Formula. 6.7 -2

The electrically determined linewidth is slightly different from the physical linewidth of the conducting layer seen in an SEM and also likely differs from that of the photoresist before the transfer process. However, it is the trend in the site to site linewith which gives feedback on the uniformity of the manufacturing process.

An example of mapping a full wafer and diagnosing contributing factors is shown in Fig-ure 6.23[rzz.crid]. Here on the left the linewidth from a 7x7 array on a mm square die is

plotted for each die on the wafer. The surface looks similar to the top of a rasbury gum-drop in that height changes for individual lumps on the rasbury can be seen. Not too suprising this local bumpy behavior is associated with the linewsidth variation within each field. Using statistical analysis this variationwith the field of the lens has been extracted and plotted on the left. Without the cost effective access to volumous data with electrical testing determining the contribution of the optics to the uniformity would have been very time consuming.

Electrical linewidth measurements across the stepper field can also give insight into the nature of the nonuniformity of the optical system. Curvature of the field is likely present and it is more rapid increase for tangential than radial (sagital) lines will likely also appear. To test the later the difference between linewidths for horizontal and vertical features from electrical test data is plotted in Figure 6.24 [rzzPrometrics]. The saddle shaped result is

FIGURE 6.23 Linewidth variation using an array of 7x7 electrical test sites on each die (a) variation across the wafer and (b) periodic compomnent showing linewidth variation across the field [rzz.crid].



consistent with the radial lines being the best resolved and smallest reguardless of if they are vertical lines at the top and bottom center of the die or horizontal lines in the middle of the die at the left and right edges. Note that the linewith difference is on the order of 20% of the feature size.

6.8 Mask Characterization

Mask making can contribute nonidealities and for this reason is granted part of the overall error budget for manufacturing. The mask maker must accurately pattern features across an entire plate which corresponds to a 1 to 10X view of the field of the lens. The kinds of problems which can occur are linewdith variations with position, butting errors where parts of features written in separate sub-fields do not match up, line edge roughness due to raster scanned beams, pixel sixe and shape effects in realizing 2D mask patterns.

The mask maker must convert the layout design data to properly placed, uniformly sized features over a large field. The move to lower demagnification factors in projection print-ing from 10, 5, 4, (possibly 2X) and 1X helps to reduce the mask size for large chips. However, the tolerances to which the mask must be made go inversely with this demagni-fication factor. The mask tolerances are only one factor in the overall budget of the many factors such as the uniformity of wafer coating, exposure, substrate reflectivity, develop-ment, and pattern transfer which affect linewidth variation. Unfortunately due to the phys-ics of imaging and resist dissolution the linewidth variation on the mask can be magnified in the litography process as shown in Figure 6.25 [rzz.langston.95]. Here, the magnifac-tion is as much as 1.5 for small lines and goes over 2 for small contacts. The magnification comes in part from the aerial image which due to the relatively large coherence over small

FIGURE 6.24 Difference in linewidth between horizontal and vertical lines with a saddle shape indiciative of radially increasing astigmatism between radial and sgital lines [rzz.Prometrics].

Image Enhancement Techniques


features tends toward being proportional to the square of the feature size. The resist disso-lution contributes in part in that a minimal peak intensity is necessary to produce develop-ment to the substrate and that standing waves and even diffusion in DUV resists may contribute additive linewidth bias effects.

The mask making tool may not be able to provide the sharpness of definition of features or the exact placement called for in the layout design. An example of a buting error and its images are shown in Figure 6.26 [rzz.arn.but]. Here a horizontal gap of xxx and a vertical offset of yyy has been specified. Image (a) is for a projection printer imaging the entire frame simultaneously. In this case the resulting image xxx. Case (b) corresponds to imag-ing first the left rectangle and then imaging the right rectangle as would occur in optical stitching. In this case xxx.

6.9 Image Enhancement Techniques

As pointed out in Chapter 5 one of the frontiers in optical projection printing is the design of the illumination source, mask and lens to emphasize the off-axis rays (high spatial fre-quencies) relative to the near-asix rays (low spatial frequencies) to improve the aerial image of small features. It was also pointed out that one of the drawbacks of any of these techniques is that they tend to enhance the dependency of image quality on feature size and type. As a result all three of the principal approaches require careful characterization. With the additional parameters associated with the enhancement technique and the host of specific patterns which must be examined this characterization is a great job for system-atic simulation. This characterization is currently an on-going process throughout the semiconductor industry. Several examples will be given here to illustrate the opportunities and issues in image enhancement.

FIGURE 6.25 Linewidth variation on the wafer as a function of linewidth varition on the mask [rzz.langston.95].



At high resolution where image enhancement is needed most only 2 or three of the dif-fracted orders from the mask are captured by the lens of the projection printing system. Thus we may simply look at the specular transmission and the plus and minus first dif-fracted orders to both establish an intuitive picture and simplify the discussion. Several examples are given in Figure 6.27 [rzz.]. Two themes common to the three principal tech-niques are shown. The first theme is to increase the fraction of the signal carried by the off-axis rays which have the highest spatial frequencies to turn the image on and off in across in moving horizontally across the wafer surface. The second theme is to place the energy in a set of rays which behave nearly similar with focus and thus reduce the sensitiv-ity to focus. For example if only rays at the edge of the lens are used, a change in their phase due to a focal error would affect all rays identically and the image would be com-plete immune. Note that both the resolution and immunity to focus errors can be improved simultaneously. The inherent limitation is that these improvements are only possible at a feature pitch which has a particular relationship to the illumination, mask type and filtering function. Thus they come at the expense of degredation at other feature sizes.

6.9.1 Modified IlluminationThe shape and uniformity of the filling of the lens with illumination rays has been a con-cern in improving the performance of projection printers for many years. In pushing the limits of optical lithography optical systems which allow the technologist to exploit non-uniform illumination have been introduced [rzz.canon.spie, rzz.nikon]. An example of the propagation vector (k-space) diagram for a quadrapole system is shown in Figure 6.28 [rzz.canon]. This system could be modeled as four systems with off-axis illumination. However, there is by design a particular relationship between the kx and ky placement of

FIGURE 6.26 Example of a butting error and its image as seen in (a) a projection printer and (b) an optical system with stitching [rzz.arn.but].



the four spots and the pattern pitch for which it works best. To achieve good focal behav-ior the first diffracted order must have the same radius in k-space as zero order. This means that for a pattern periodic in x with period Px

FIGURE 6.27 Resoultion enhancement can come about from (a) emphasizing off-axis rays with high spatial frequencies and (b) an associated reduction in sensitivity to focus [rxx.arn].

FIGURE 6.28 Quadrapole illumination k-space diagram [rzz.canon].



6.9 -1

and the period is given by

6.9 -2

Here sx is the relative loction of the center of one of the illumination spot in the entrance pupil of the lens. Since there is no illumination for small kx values the mask with this pitch creates no energy in the near-axis region. This same illumiation scheme looked at when rotated by 45o as it would be for non-Manhattan geometries is quite a differnent story. In this case two of the four spots or half of the energy is now nearly on axis. This means that non-Manhattan geometries will have a degraded rather than enhanced focal response. To have a similar response for non-Manhattan geometries an annular source with circular symmetry muste be used.

Examples of simulated images for a conventional ‘top hat’, quadrapole, rotated quadra-pole and annular sources are shown in Figure 6.29 [rzz.newmark]. Describe the images

when figure input.

FIGURE 6.29 Comparison of images for various illumination systems (a) conventional, (b) quadrapole, (c) rotated quadrapole, and (d) annular [rzz.newmark].

kox2πPx------- kox–=

Pxπ

kox--------- σx

λNA---------= =



6.9.2 Phase-Shifting MasksIn 1982 Levenson et al proposed shifting the phase of the light passing through adjacent opening to improve the image quality. With this technique very impressive results have been achieved in many applications and with several significant extensions. The potential of using phase-shifting masks is quite clead from that of the DRAM features shown in Figure xxx which are printed at a xxx. Edges where the phases makes a 180o transition have the interesting property that they produce narrowest known dark feature which is about 0.2 λ/NA. Such a mask has been used to print isolated narrow channel length devices [rzz.brunner rzz.mastshita] and narrow ring isolated contact landing pad [rzz.hita-chi.iedm]. By using multiple phase levels of 60o, 120o and 180o it has been shown possi-ble to make clear field phase transitions to accomodate the necessary changes in phase to resolve conflicting phase requirements [rzz.nistlor.spie]. While these strong forms of phase-shifting mask require require makor changes in mask and layout technology, two weak forms, rim and attenuated, may emerge as providing limited resolution enhancement with little technology change.

The four basic types of phase-shifting masks are shown in Figure 6.30 [rzz.arn]. Describe

stipple pattern, walk through what and how work. Weak form attenuated mask and suc-cess. How characterize performance. = or just point out simulation useful.

6.9.3 In-Lens FilterDUAL FOCUS EXAMPLE: {Fukuda case}Why SUPER FLEX IS better than flex.

RESULT: {Data and SPLAT case}

FIGURE 6.30 Four basic types of phase-shifting masks [rzz.arn].



Many simulators are available for assessing modified illumination, phase shifting masks and in-lens filtering. An example of the input deck and associated definitions for SPLAT is given in Figure [rzz.SPLAT]. More detailed examples of modified illumination, phase shift masks and in-lens filtering are available in the SPLAT User Guide which as well as the SPLAT source code is available from the ILP Softeare Office [rzz.ILP.address].

6.10 Optical Proximity Correction

Overview problem, nature of approaches and issues, success.

Basic example Newmark

More current approaches Nick Cobb.

6.11 Assessing the Impact of Defects

Overview - issues, tendencies.

Examplpe test mask an its printed image

Linewidth variation versus defect size figure and model.

Phase defects - issues and models - Print out of focus, 2x worse

Summary of rules of thumb.

6.12 Ultimate Limits of Optical Lithography

We now explore how image quality degrades as a function of feature size and attempt to determine the ultimate limits of optical projection printing beyond which no resist system could salvage the image. The extreme cases of isolated (resist) lines, isolated (open) spaces as well as equal line space arrays are shown in Figure olculimg The 0.35 $ lona $ feature size shown here is the smallest size for which the intensities still cross over each other. This is thus the resolution limit for any resist process based on pointwise response to the local intensity. Note that in the common threshold is around 30% of the clear field

Ultimate Limits of Optical Lithography


intensity. This is the same as was found for large features and means that both the large features would be print simultaneously.

A secondary issue of some practical interest is the optimum choince of the partial coher-ence parameter $ sigma $ for feature sizes less than 0.5 $ lona $. However when isolated feature types are also considered the intensities were found to have the best overall charac-teristics at $ sigma $ of 0.7. An important consequence of this observation that $ sigma $ on the order of 0.7 is optimum for features less than 0.5 $ lona $ is that from an imaging point of view illumination systems of existing projection printers will not have to be rede-signed to to push stepper performance with new resist systems such as contrast enhance-ment and top surface imaging materials.

The high recording quality possible with a threshold resist process can be illustrated by examining the bias and edge slope for a 30% threshold. Figure olculbia shows the bias for the three feature types as a function of feature size. The bias is positive is positive when the threshold is exceeded on the opaque region of the mask. The total range for the bias for

Figure olculimg



the 30% threshold is quite small and well centered. Down to feature sizes of 0.4 $ lona $ the use of windage to correct individual feature types or sizes is really unnecessary.

The process lattitude for variations in exposure due to illumination uniformity or energy coupling efficiency is proportional to line edge slope. The line edge slope for the three fea-ture types is shown as a function of feature type in Figure olculslo. Here the slope has been normalized by dividing by $ lona $ which for a given projection printer gives the relative absolute image slope. This absolute slope is surprisingly independent of both feature type and size down to almost 0.4 $ lona $. In fact the slope is better behaved than the traditional used contrast. This is a clear indication that a resist threshold process will give better per-formance for small feature sizes than a resist system which relies on the use of intensity extrema.

Figure olculbia

Figure olculslo

References


6.13 References

.nf 63:See for example [rzz.auschnitts.lith-vlsi, rzz.lin.book chapter, 64:rzz.thompson-wil-son.acs.book, rzz.moreau.book, rzz.king.book.chapter, 65:rzz.otoole.book.chapter, rzz.hershel-mack.book.chapter]. 81:Figure 1.1 for a positive resist [rzz.zee.spie]. 114:as shown in Figure 1.2 [rzz.thompson-wilson.book]. 190:can be recognized [rzz.oldham.con-trast.measure]. 205:features as shown in Figure 2.4 [rzz.brunner.flour]. 223:NA=0.30, \(*s=0.7) [rzz.brunner.flo.results]. 242:is shown in Figure 3.1 [rzz.arnold.spie.smile]. 255:The basic SMILE plot has been modeled theoretically by [rzz.smile.king?]. 347:Watts [rzz.watts.3B.two.step.dev] in characterizing linewidth 349:Basic simulation studies by O’Toole et al. [rzz.otoole.spie.Imin.role] 382:Experimental SMILE plots have been used by S. Lis [rzz.lis.smile.spie] 404:as has been done by Arnold [rzz.arnold.mouth]. 409:The ED diagram was first introduced by B.J. Lin [rzz.lin.ED.diagram] 426:been published by Hershel and Mack [rzz.hershel.lith.vlsi] 429:The approximation introduced by Watts [rzz.v-h.diss.3b] 468:which can be introduced in crossing steps [rzz.neu.linewidth]. 491:by Oldham et al [rzz.old.contrast.cor]. 518:Figure 4.2 due to Oldham [rzz.old-ham.contrast.resist.tech]. 542:[rzz.oldham.design.chart]. 580:on silicon like substrates [rzz.neu.rules]. .fi

6.14 Figures

chapter 6 model based characterization of optical...

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