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88-571: SADP may refer to : Science and Technology Self-Aligned Double-Patterning , a Multiple patterning technique used in semiconductor manufacturing Selected Area Diffraction Pattern , the pattern of spots in Selected area diffraction sADP, "slow after depolarizing current", an experimental response of Neurons Other El Palomar Airport , Argentina - ICAO code SADP The School of Architecture, Design, and Planning (SADP), former name of

176-403: A Fourier transform (FT) relation. In addition, a uniform function over a circular area (in one FT domain) corresponds to J 1 ( x )/ x in the other FT domain, where J 1 ( x ) is the first-order Bessel function of the first kind. That is, a uniformly-illuminated circular aperture that passes a converging uniform spherical wave yields an Airy disk image at the focal plane. A graph of

264-501: A 10 nm thermal SiO 2 masking layer. A fundamental aspect of this approach is the correlation between damage width and damage pitch; both widen at the same time for fixed ion mask height and ion beam angle. The method of complementary exposures is another way of reducing mask exposures for multiple patterning. Instead of multiple mask exposures for individual vias, cuts or blocks, two exposures of opposing or complementary polarity are used, so that one exposure removes interior portions of

352-421: A blurred point in the image plane. For a single lens , an on-axis point source in the object plane produces an Airy disc PSF in the image plane. It can be shown (see Fourier optics , Huygens–Fresnel principle , Fraunhofer diffraction ) that the field radiated by a planar object (or, by reciprocity, the field converging onto a planar image) is related to its corresponding source (or image) plane distribution via

440-474: A conducting feature, then ultimately it must be cut at no less than two locations to separate the feature into two or more conducting lines as typically expected. On the other hand, if the spacer corresponds to a dielectric feature, cutting would not be necessary. The prediction of how many cuts would be needed for advanced logic patterns has been a large technical challenge. Many approaches for spacer patterning have been published (some listed below), all targeting

528-428: A cut mask) is therefore necessary to break the line pattern more robustly. The earliest implementation of multiple patterning involved line cutting. This first occurred for Intel's 45nm node, for 160 nm gate pitch. The use of a second mask to cut lines defined by a first mask does not help increase feature density directly. Instead it allows definition of features, e.g., brick patterns, which are based on lines spaced at

616-431: A feature pattern inherently contains more than one pitch, and furthermore, these pitches are incompatible to the extent that no illumination can simultaneously image both pitches satisfactorily. A common example, again from DRAM, is the brick pattern defining the active regions of the array. In addition to the narrow pitch of the active regions, there is also the pitch between the active region separations or breaks, which

704-460: A finite area in the image plane. (In some branches of mathematics and physics, these might be referred to as Green's functions or impulse response functions. PSFs are considered impulse response functions for imaging systems. When the object is divided into discrete point objects of varying intensity, the image is computed as a sum of the PSF of each point. As the PSF is typically determined entirely by

792-493: A given process formulation. Typical applications have been regular lines and spaces as well as arrays of closely packed holes or cylinders. However, random, aperiodic patterns may also be generated using carefully defined guiding patterns. The line edge roughness in block copolymer patterns is strongly dependent on the interface tension between the two phases, which in turn, depends on the Flory "chi" (χ) parameter. A higher value of χ

880-611: A honeycomb structure, making its patterning simpler. SADP may be applied twice in a row to achieve an effective pitch quartering. This is also known as self-aligned quadruple patterning (SAQP). With SAQP, the primary feature critical dimension (CD), as well as the spacing between such features, are each defined by either the first or second spacer. It is preferred to have the second spacer define non-conducting features for more flexible cutting or trimming options. SAQP has advantages in two-dimensional 28 nm pitch routing (followed by two selective etch cut/trim steps), compared to EUV, due to

968-584: A minimum pitch, in particular, when the lines are near the resolution limit and are generated by the two-beam interference mentioned above. The two-beam interference still dominates the diffraction pattern. In fact, in the absence of a separate cut exposure, the gap between the ends of the minimum pitch lines will be prohibitively large. This is due to rounding resulting from reduced spatial frequencies. The line cut shapes themselves are subject to rounding; this rounding can be minimized with optimized illumination, but cannot be eliminated completely. When applying

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1056-424: A number of situations which lead to multiple patterning being required. The most obvious case requiring multiple patterning is when the feature pitch is below the resolution limit of the optical projection system. For a system with numerical aperture NA and wavelength λ, any pitch below 0.5 λ/NA would not be resolvable in a single wafer exposure. The resolution limit may also originate from stochastic effects, as in

1144-413: A perfect spherical wave in all directions of space is not needed. This is because the lens has only a finite (angular) bandwidth, or finite intercept angle. Therefore, any angular bandwidth contained in the source, which extends past the edge angle of the lens (i.e., lies outside the bandwidth of the system), is essentially wasted source bandwidth because the lens can't intercept it in order to process it. As

1232-478: A pre-patterned feature. A spacer is formed by deposition or reaction of the film on the previous pattern, followed by etching to remove all the film material on the horizontal surfaces, leaving only the material on the sidewalls. By removing the original patterned feature, only the spacer is left. However, since there are two spacers for every line, the line density has now doubled. This is commonly referred to as self-aligned double patterning (SADP). The spacer technique

1320-485: A pre-patterned hardmask layer. This technique is used in DRAM cells and is also used for advanced logic to avoid multiple exposures of pitch-splitting contacts and vias. Since 32 nm node, Intel has applied the above-mentioned self-aligned via approach, which allows two vias separated by a small enough pitch (112.5 nm for Intel 32 nm metal) to be patterned with one resist opening instead of two separate ones. If

1408-412: A result, a perfect point source is not required in order to measure a perfect point spread function. All we need is a light source which has at least as much angular bandwidth as the lens being tested (and of course, is uniform over that angular sector). In other words, we only require a point source which is produced by a convergent (uniform) spherical wave whose half angle is greater than the edge angle of

1496-471: A sample Airy disk is shown in the adjoining figure. Therefore, the converging ( partial ) spherical wave shown in the figure above produces an Airy disc in the image plane. The argument of the function J 1 ( x )/ x is important, because this determines the scaling of the Airy disc (in other words, how big the disc is in the image plane). If Θ max is the maximum angle that the converging waves make with

1584-502: A second cut exposure is necessary. When patterns include feature sizes near the resolution limit, it is common that different arrangements of such features will require specific illuminations for them to be printed. The most basic example is horizontal dense lines vs. vertical lines (half-pitch < 0.35 λ/NA), where the former requires a North-South dipole illumination while the latter requires an East-West dipole illumination. If both types are used (also known as cross-quadrupole C-Quad),

1672-411: A sequence of (at least) two separate exposures and etchings of independent patterns into the same layer. For each exposure, a different photoresist coating is required. When the sequence is completed, the pattern is a composite of the previously etched subpatterns. By interleaving the subpatterns, the pattern density can theoretically be increased indefinitely, the half-pitch being inversely proportional to

1760-474: A set of regularly spaced lines. Breaks in such lines, e.g., brick patterns, are deviations from the interference pattern. Such breaks generally do not dominate the pattern, and are thus small deviations. These deviations are insufficient to completely offset the constructive or destructive interference of the underlying regular line pattern; sidelobes often result. Line end gaps are easily bridged under dipole illumination. Another mask exposure (usually referred as

1848-526: A subsequent process. The process requires the use of angled ion beams which penetrate to just the right depth, so as not to damage already processed layers underneath. Also, the ion masking layer must behave ideally, i.e., blocking all ions from passing through, while also not reflecting off the sidewall. The latter phenomenon would be detrimental and defeat the purpose of the ion masking approach. Trenches as small as 9 nm have been achieved with this approach, using 15 keV Ar+ ion implantation at 15-degree angles into

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1936-425: A tradeoff between shrinking the line width (i.e., the width of the line tip) and shrinking the gap between opposite facing tips. As the line width shrinks, the tip radius shrinks. When the line tip is already less than the point spread function (k 1 ~0.6–0.7), the line tip naturally pulls back, increasing the gap between opposite facing tips. The point spread function likewise limits the resolvable distance between

2024-410: A uniform spectrum of propagating plane waves, but a uniform spectrum of exponentially decaying ( evanescent ) waves as well, and it is these which are responsible for resolution finer than one wavelength (see Fourier optics ). This follows from the following Fourier transform expression for a 2D impulse function, The quadratic lens intercepts a portion of this spherical wave, and refocuses it onto

2112-421: A weighted sum of 2D impulse functions, and then expressing the image plane field as a weighted sum of the images of these impulse functions. This is known as the superposition principle , valid for linear systems . The images of the individual object-plane impulse functions are called point spread functions (PSF), reflecting the fact that a mathematical point of light in the object plane is spread out to form

2200-538: Is a useful concept in Fourier optics , astronomical imaging , medical imaging , electron microscopy and other imaging techniques such as 3D microscopy (like in confocal laser scanning microscopy ) and fluorescence microscopy . The degree of spreading (blurring) in the image of a point object for an imaging system is a measure of the quality of the imaging system. In non-coherent imaging systems, such as fluorescent microscopes , telescopes or optical microscopes,

2288-488: Is also named more directly as "LELE" (Litho-Etch-Litho-Etch). This approach has been used for the 20 nm and 14 nm nodes. The additional cost of extra exposures was tolerated since only a few critical layers would need them. A more serious concern was the effect of feature-to-feature positioning errors (overlay). Consequently, the self-aligned sidewall imaging approach (described below) has succeeded this approach. A "brute force" approach for patterning trenches involves

2376-433: Is applicable for defining narrow gates at half the original lithographic pitch, for example. As pitch splitting has become more difficult due to possible differences in feature positions between different exposed parts, sidewall image transfer (SIT) has become more recognized as the necessary approach. The SIT approach typically requires a spacer layer to be formed on an etched feature's sidewall. If this spacer corresponds to

2464-504: Is different from Wikidata All article disambiguation pages All disambiguation pages Multiple patterning Even with single exposure having sufficient resolution, extra masks have been implemented for better patterning quality such as by Intel for line-cutting at its 45nm node or TSMC at its 28nm node. Even for electron-beam lithography , single exposure appears insufficient at ~10 nm half-pitch, hence requiring double patterning. Double patterning lithography

2552-448: Is different from that of the narrow pitch in the same direction. When the narrow pitch is < λ/NA (but still > 0.5 λ/NA), it cannot be imaged simultaneously with the double pitch due to the focus limitations of the latter. Selective etching, along with SADP or SAQP (to be described below), is the current best approach to achieve the simultaneous patterning of both pitches. A two-beam interference pattern (half-pitch <0.5 λ/NA) forms

2640-423: Is larger than the minimum pitch (~0.7 λ/NA). This also contributes to hot spots for feature sizes of ~0.4 λ/NA or smaller. For this reason, it is advantageous to first define line patterns, then cut segments from such lines accordingly. This of course, requires additional exposures. The cut shapes themselves may also be round, which requires tight placement accuracy. The rounding of line tips naturally leads to

2728-471: Is limited to >32 nm pitch. Recent studies of optimizing the EUV mask features and the illumination shape simultaneously have indicated that different patterns in the same metal layer could require different illuminations. On the other hand, a single exposure only offers a single illumination. For example, in a cross-pitch source-mask optimization for 7nm node, for 40-48 nm pitch and 32 nm pitch,

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2816-401: Is made up of photoresist features edged between mask features, which can be transferred into the final layer underneath. This allows a doubling of feature density. Sometimes, it is necessary to "stitch" two separately printed features into a single feature. A variation on this approach which eliminates the first hardmask etch is resist freezing , which allows a second resist coating over

2904-493: Is more expensive than three 193i exposures (i.e., LELELE), considering the throughput. Moreover, EUV is more liable to print smaller mask defects not resolvable by 193i. Some aspects of other considered multi-patterning techniques are discussed below. Self-aligned triple patterning has been considered as a promising successor to SADP, due to its introduction of a second spacer offering additional 2D patterning flexibility and higher density. A total of two masks (mandrel and trim)

2992-403: Is often found to vary with position in the image (an effect called anisoplanatism). In ground-based adaptive optics systems, the PSF is a combination of the aperture of the system with residual uncorrected atmospheric terms. The PSF is also a fundamental limit to the conventional focused imaging of a hole, with the minimum printed size being in the range of 0.6-0.7 wavelength/NA, with NA being

3080-447: Is preferred for reduced roughness; the interfacial width between domains is equal to 2a(6χ) , where a is the statistical polymer chain length. Moreover, χN > 10.5 is required for sufficient phase segregation, where N is the degree of polymerization (number of monomer repeats in the chain). On the other hand, the half-pitch is equal to 2(3/π ) aN χ . The fluctuations of the pattern widths are actually only weakly (square root) dependent on

3168-478: Is small, the Airy disc is large (which is just another statement of Heisenberg's uncertainty principle for Fourier Transform pairs, namely that small extent in one domain corresponds to wide extent in the other domain, and the two are related via the space-bandwidth product ). By virtue of this, high magnification systems, which typically have small values of Θ max (by the Abbe sine condition ), can have more blur in

3256-408: Is sufficient for this approach. The only added cost relative to SADP is that of depositing and etching the second spacer. The main disadvantage of SATP succeeding SADP is that it would only be usable for one node. For this reason, self-aligned quadruple patterning (SAQP) is more often considered. On the other hand, the conventional SID SADP flow may be extended quite naturally to triple patterning, with

3344-433: Is the cut/block locations in the core/mandrel features are already patterned in the first mask. There are secondary features which emerge from the gaps between spacers after further patterning. The edge between a secondary feature and the spacer is self-aligned with the neighboring core feature. The use of SID may be applied to 2D arrays, by iteratively adding features equidistant from the previously present features, doubling

3432-495: Is the image of the impulse function δ ( x o − u , y o − v ) {\displaystyle \delta (x_{o}-u,y_{o}-v)} . The 2D impulse function may be regarded as the limit (as side dimension w tends to zero) of the "square post" function, shown in the figure below. We imagine the object plane as being decomposed into square areas such as this, with each having its own associated square post function. If

3520-704: The University of Kansas School of Architecture, Design, and Planning The Socialist Alliance Democracy Platform , a left wing electoral alliance in England (1992-2005) Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title SADP . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=SADP&oldid=922992098 " Category : Disambiguation pages Hidden categories: Short description

3608-421: The numerical aperture of the imaging system. For example, in the case of an EUV system with wavelength of 13.5 nm and NA=0.33, the minimum individual hole size that can be imaged is in the range of 25-29 nm. A phase-shift mask has 180-degree phase edges which allow finer resolution. Point spread functions have recently become a useful diagnostic tool in clinical ophthalmology . Patients are measured with

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3696-447: The PSF can be mathematically modeled using the concepts of Gaussian beams . For instance, deconvolution of the mathematically modeled PSF and the image, improves visibility of features and removes imaging noise. The point spread function may be independent of position in the object plane, in which case it is called shift invariant . In addition, if there is no distortion in the system, the image plane coordinates are linearly related to

3784-448: The PSF is the impulse response or impulse response function (IRF) of a focused optical imaging system. The PSF in many contexts can be thought of as the shapeless blob in an image that should represent a single point object. We can consider this as a spatial impulse response function . In functional terms, it is the spatial domain version (i.e., the inverse Fourier transform) of the optical transfer function (OTF) of an imaging system . It

3872-418: The PSF is the same everywhere in the imaging space, the image of a complex object is then the convolution of that object and the PSF. The PSF can be derived from diffraction integrals. By virtue of the linearity property of optical non-coherent imaging systems, i.e., the image of an object in a microscope or telescope as a non-coherent imaging system can be computed by expressing the object-plane field as

3960-461: The aberrations of any optical system with rotational symmetry. Recent analytic results have made it possible to extend Nijboer and Zernike's approach for point spread function evaluation to a large volume around the optimum focal point. This extended Nijboer-Zernike (ENZ) theory allows studying the imperfect imaging of three-dimensional objects in confocal microscopy or astronomy under non-ideal imaging conditions. The ENZ-theory has also been applied to

4048-407: The ample supply of point sources ( stars or quasars ). The form and source of the PSF may vary widely depending on the instrument and the context in which it is used. For radio telescopes and diffraction-limited space telescopes , the dominant terms in the PSF may be inferred from the configuration of the aperture in the Fourier domain . In practice, there may be multiple terms contributed by

4136-419: The case of EUV . Consequently, 20 nm linewidth still requires EUV double patterning, due to larger defectivity at larger pitches. It is well-established that dense two-dimensional patterns, which are formed from the interference of two or three beams along one direction, as in quadrupole or QUASAR illumination, are subject to significant rounding, particularly at bends and corners. The corner rounding radius

4224-472: The centers of the line tips (modeled as circles). This leads in turn to a tradeoff between reducing cell width and reducing cell height. The tradeoff is avoided by adding a cut/trim mask (see discussion below). Hence, for the EUV-targeted 7nm node, with an 18 nm metal linewidth (k 1 =0.44 for λ=13.5 nm, NA=0.33), the line tip gap of less than 25 nm (k 1 =0.61) entails EUV single patterning is not sufficient;

4312-410: The characterization of optical instruments with respect to their aberration by measuring the through-focus intensity distribution and solving an appropriate inverse problem . In microscopy, experimental determination of PSF requires sub-resolution (point-like) radiating sources. Quantum dots and fluorescent beads are usually considered for this purpose. Theoretical models as described above, on

4400-493: The cut has to extend over more than one line. Self-aligned line cutting (to be discussed below) may be a preferred option. The earliest form of multiple patterning involved simply dividing a pattern into two or three parts, each of which may be processed conventionally, with the entire pattern combined at the end in the final layer. This is sometimes called pitch splitting , since two features separated by one pitch cannot be imaged, so only skipped features can be imaged at once. It

4488-422: The density with each iteration. Cuts not requiring tight positioning may be made on this spacer-generated grid. Samsung recently demonstrated DRAM patterning using a honeycomb structure (HCS) suitable for 20 nm and beyond. Each iteration of spacer patterning triples the density, effectively reducing 2D pitch by a factor of sqrt(3). This is particularly useful for DRAM since the capacitor layer can be fit to

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4576-408: The fact that a point source in the 2D object plane can only radiate a perfect uniform-amplitude, spherical wave — a wave having perfectly spherical, outward travelling phase fronts with uniform intensity everywhere on the spheres (see Huygens–Fresnel principle ). Such a source of uniform spherical waves is shown in the figure below. We also note that a perfect point source radiator will not only radiate

4664-423: The final layer. This is best described by considering a process example. A first exposure of photoresist is transferred to an underlying hardmask layer. After the photoresist is removed following the hardmask pattern transfer, a second layer of photoresist is coated onto the sample and this layer undergoes a second exposure, imaging features in between the features patterned in the hardmask layer. The surface pattern

4752-399: The first developed resist layer. JSR has demonstrated 32 nm lines and spaces using this method, where the freezing is accomplished by surface hardening of the first resist layer. In recent years, the scope of the term 'pitch splitting' has gradually been expanded to include techniques involving sidewall spacers. In spacer patterning , a spacer is a film layer formed on the sidewall of

4840-419: The foreseen need to first print a series of lines and then cut them; a single EUV exposure pattern has difficulty with line end-to-end spacing control. In addition, the line end placement is significantly impacted by photon shot noise. The existing 0.33 NA EUV tools are challenged below 16 nm half-pitch resolution. Tip-to-tip gaps are problematic for 16 nm dimensions. Consequently, EUV 2D patterning

4928-472: The height, h , of the post is maintained at 1/w , then as the side dimension w tends to zero, the height, h , tends to infinity in such a way that the volume (integral) remains constant at 1. This gives the 2D impulse the shifting property (which is implied in the equation above), which says that when the 2D impulse function, δ( x  −  u , y  −  v ), is integrated against any other continuous function, f ( u , v ) , it "sifts out"

5016-452: The illumination limitations of the latter. The number of masks used for sidewall spacer patterning may be reduced with the use of directed self-assembly (DSA) due to the provision of gridded cuts all at once within a printed area, which can then be selected with a final exposure. Alternatively, the cut pattern itself may be generated as a DSA step. Likewise, a split via layout may be recombined in pairs. Much progress had been reported on

5104-464: The image formation process is linear in the image intensity and described by a linear system theory. This means that when two objects A and B are imaged simultaneously by a non-coherent imaging system, the resulting image is equal to the sum of the independently imaged objects. In other words: the imaging of A is unaffected by the imaging of B and vice versa , owing to the non-interacting property of photons. In space-invariant systems, i.e. those in which

5192-439: The image plane using the same weighting function as in the object plane, i.e., O ( x o , y o ) {\displaystyle O(x_{o},y_{o})} . Mathematically, the image is expressed as: in which PSF ( x i / M − u , y i / M − v ) {\textstyle {\mbox{PSF}}(x_{i}/M-u,y_{i}/M-v)}

5280-414: The image, owing to the broader PSF. The size of the PSF is proportional to the magnification , so that the blur is no worse in a relative sense, but it is definitely worse in an absolute sense. The figure above illustrates the truncation of the incident spherical wave by the lens. In order to measure the point spread function — or impulse response function — of the lens, a perfect point source that radiates

5368-404: The imaging system (that is, microscope or telescope), the entire image can be described by knowing the optical properties of the system. This imaging process is usually formulated by a convolution equation. In microscope image processing and astronomy , knowing the PSF of the measuring device is very important for restoring the (original) object with deconvolution . For the case of laser beams,

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5456-411: The improved management (and reduction) of the cuts. As spacer materials are commonly hardmask materials, their post-etch pattern quality tends to be superior compared to photoresist profiles after etch, which are generally plagued by line edge roughness. The main issues with the spacer approach are whether the spacers can stay in place after the material to which they are attached is removed, whether

5544-427: The inappropriate dipole degrades the image of the respective line orientation. Larger pitches up to λ/NA can have both horizontal and vertical lines accommodated by quadrupole or QUASAR illumination, but diagonally spaced features and elbow features are degraded. In DRAM , the array and periphery are exposed at different illumination conditions. For example, the array could be exposed with dipole illumination while

5632-420: The irradiance, NA is numerical aperture, c is the speed of light, f is the photon frequency of the imaging beam, I r is the intensity of reference beam, a is an adjustment factor and ρ {\displaystyle \rho } is the radial position from the center of the beam on the corresponding z-plane . The diffraction theory of point spread functions was first studied by Airy in

5720-443: The lens axis, r is radial distance in the image plane, and wavenumber k  = 2π/λ where λ = wavelength, then the argument of the function is: kr tan(Θ max ) . If Θ max is small (only a small portion of the converging spherical wave is available to form the image), then radial distance, r, has to be very large before the total argument of the function moves away from the central spot. In other words, if Θ max

5808-405: The lens. Due to intrinsic limited resolution of the imaging systems, measured PSFs are not free of uncertainty. In imaging, it is desired to suppress the side-lobes of the imaging beam by apodization techniques. In the case of transmission imaging systems with Gaussian beam distribution, the PSF is modeled by the following equation: where k-factor depends on the truncation ratio and level of

5896-404: The logarithm of the half-pitch, so they become more significant relative to smaller half-pitches. DSA has not yet been implemented in manufacturing, due to defect concerns, where a feature does not appear as expected by the guided self-assembly. There have been numerous concerns that multiple patterning diminishes or even reverses the node-to-node cost reduction expected with Moore's Law . EUV

5984-414: The minimum pitch with defocus. The inclusion of both isolated and dense features is a well-known instance of multi-pitch patterning. Subresolution assist features (SRAFs) have been designed to enable the patterning of isolated features when using illumination tailored for the dense features. However, not all pitch ranges can be covered. In particular, semi-dense features may not be easy to include. For

6072-431: The nineteenth century. He developed an expression for the point spread function amplitude and intensity of a perfect instrument, free of aberrations (the so-called Airy disc ). The theory of aberrated point spread functions close to the optimum focal plane was studied by Zernike and Nijboer in the 1930–40s. A central role in their analysis is played by Zernike's circle polynomials that allow an efficient representation of

6160-430: The number of subpatterns used. For example, a 25 nm half-pitch pattern can be generated from interleaving two 50 nm half-pitch patterns, three 75 nm half-pitch patterns, or four 100 nm half-pitch patterns. The feature size reduction will most likely require the assistance of techniques such as chemical shrinks, thermal reflow, or shrink assist films. This composite pattern can then be transferred down into

6248-426: The object plane coordinates via the magnification M as: If the imaging system produces an inverted image, we may simply regard the image plane coordinate axes as being reversed from the object plane axes. With these two assumptions, i.e., that the PSF is shift-invariant and that there is no distortion, calculating the image plane convolution integral is a straightforward process. Mathematically, we may represent

6336-441: The object plane field as: i.e., as a sum over weighted impulse functions, although this is also really just stating the shifting property of 2D delta functions (discussed further below). Rewriting the object transmittance function in the form above allows us to calculate the image plane field as the superposition of the images of each of the individual impulse functions, i.e., as a superposition over weighted point spread functions in

6424-481: The other cut mask cuts the remaining lines made of the other material. This technique has the advantage of patterning double pitch features over lines at the minimum pitch, without edge placement errors. Cut-friendly layouts are processed with the same minimum number of masks (3), regardless of using DUV or EUV wavelength. Although EUV has been projected to be the next-generation lithography of choice, it could still require more than one lithographic exposure, due to

6512-430: The other hand, allow the detailed calculation of the PSF for various imaging conditions. The most compact diffraction limited shape of the PSF is usually preferred. However, by using appropriate optical elements (e.g., a spatial light modulator ) the shape of the PSF can be engineered towards different applications. In observational astronomy , the experimental determination of a PSF is often very straightforward due to

6600-420: The periphery could use annular illumination. This situation applies to any set of patterns (half-pitch < 0.5 λ/NA) with different pitches or different feature arrangements, e.g., rectangular arrays vs. staggered arrays. Any of the individual patterns is resolvable, but a single illumination cannot be used simultaneously for all of them. A minimum pitch may require an illumination that is detrimental to twice

6688-407: The pitch between features to alternate, a phenomenon known as pitch walking. The positioning of the spacer also depends on the pattern to which the spacer is attached. If the pattern is too wide or too narrow, the spacer position is affected. However, this would not be a concern for critical memory feature fabrication processes which are self-aligned. When SADP is repeated, an additional halving of

6776-496: The pitch is achieved. This is often referred to as self-aligned quadruple patterning (SAQP). With 76 nm being the expected minimum pitch for a single immersion lithography exposure, 19 nm pitch is now accessible with SAQP. Self-aligned contact and via patterning is an established method for patterning multiple contacts or vias from a single lithographic feature. It makes use of the intersection of an enlarged feature resist mask and underlying trenches which are surrounded by

6864-658: The previous exposure pattern. The overlapped regions of two polygons of opposite polarity do not print, while the non-overlapped regions define locations that print according to the polarity. Neither exposure patterns the target features directly. This approach was also implemented by IMEC as two "keep" masks for the M0A layer in their 7nm SRAM cell. Self-aligned blocking or cutting is currently being targeted for use with SAQP for sub-30 nm pitches. The lines to be cut are divided into two materials, which can be etched selectively. One cut mask only cuts every other line made of one material, while

6952-410: The quality as determined by the normalized image log slope was insufficient (NILS<2), while only 36 nm pitch was barely satisfactory for bidirectional single exposure. Point spread function The point spread function ( PSF ) describes the response of a focused optical imaging system to a point source or point object. A more general term for the PSF is the system's impulse response ;

7040-458: The second mask dividing the gap into two features. Tilted ion implantation was proposed in 2016 by the University of Berkeley as an alternative method of achieving the same result as spacer patterning. Instead of core or mandrel patterns supporting deposited spacers, an ion masking layer pattern shields an underlying layer from being damaged by ion implantation, which leads to being etched away in

7128-417: The second mask to cut lines, the overlay relative to the first mask needs to be considered; otherwise, edge placement errors (EPE) may result. If the line pitch is already near the resolution limit, the cut pattern itself may have imaging difficulty, from reduced dose or focus window. EUV stochastic variability causes random shaping of the cuts. In this case, more than one cut mask would have to be used, or else

7216-468: The spacer profile is acceptable, and whether the underlying material is attacked by the etch removing the material attached to the spacer. Pattern transfer is complicated by the situation where removal of the material adjacent to the spacers also removes a little of the underlying material. This results in higher topography on one side of the spacer than the other. Any misalignment of masks or excursion in pre-patterned feature critical dimension (CD) will cause

7304-431: The specific case of hole arrays (minimum half-pitch < 0.6 λ/NA), three well-known cases require three entirely different illuminations. A regular array generally requires Quasar illumination, while the same array rotated 45 degrees results in a checkerboard array that requires C-quad illumination. Different from both cases, an array with close to triangular or hexagonal symmetry requires hexapole illumination. Sometimes

7392-419: The use of PMMA-PS block copolymers to define sub-20 nm patterns by means of self-assembly, guided by surface topography (graphoepitaxy) and/or surface chemical patterning (chemoepitaxy). The key benefit is the relatively simple processing, compared to multiple exposures or multiple depositions and etching. The main drawback of this technique is the relatively limited range of feature sizes and duty cycles for

7480-432: The value of f at the location of the impulse, i.e., at the point ( x , y ) . The concept of a perfect point source object is central to the idea of PSF. However, there is no such thing in nature as a perfect mathematical point source radiator; the concept is completely non-physical and is rather a mathematical construct used to model and understand optical imaging systems. The utility of the point source concept comes from

7568-404: The various components in a complex optical system. A complete description of the PSF will also include diffusion of light (or photo-electrons) in the detector, as well as tracking errors in the spacecraft or telescope. For ground-based optical telescopes, atmospheric turbulence (known as astronomical seeing ) dominates the contribution to the PSF. In high-resolution ground-based imaging, the PSF

7656-482: The vias were separated by less than the single exposure pitch resolution limit, the minimum required number of masks would be reduced, as two separate masks for the originally separated via pair can now be replaced by a single mask for the same pair. In self-aligned double patterning (SADP), the number of cut/block masks may be reduced or even eliminated in dense patches when the spacer is used to directly pattern inter-metal dielectric instead of metal features. The reason

7744-533: Was first demonstrated in 1983 by D. C. Flanders and N. N. Efremow. Since then several double patterning techniques have been developed such as self alignment double patterning (SADP) and a litho-only approach to double patterning. Pitch double-patterning was pioneered by Gurtej Singh Sandhu of Micron Technology during the 2000s, leading to the development of 30-nm class NAND flash memory. Multi-patterning has since been widely adopted by NAND flash and random-access memory manufacturers worldwide. There are

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