Methods of utilizing block copolymers to form patterns

Some embodiments include methods of forming patterns utilizing copolymer. A copolymer composition is formed across a substrate. The composition includes subunits A and B, and will be self-assembled to form core structures spaced center-to-center by a distance of L0. The core structures are contained within a repeating pattern of polygonal unit cells. Distances from the core structures to various locations of the unit cells are calculated to determine desired distributions of subunit lengths.

TECHNICAL FIELD

Methods of utilizing block copolymers to form patterns.

BACKGROUND

Numerous applications exist in which it is desired to form repeating patterns having a small pitch (for example, a pitch of less than about 50 nanometers). For instance, integrated circuit fabrication may involve formation of a repeating pattern of memory-storage units (i.e., NAND unit cells, dynamic random access memory [DRAM] unit cells, cross-point memory unit cells, etc.).

A variety of methods have been developed for creating patterned masks suitable for patterning underlying materials during fabrication of integrated circuit components. A continuing goal of integrated circuit fabrication is to increase integrated circuit density, and accordingly to decrease the size of individual integrated circuit components. There is thus a continuing goal to form patterned masks having increasing densities of individual features. In cases in which the patterned masks comprise repeating patterns of features, there is a continuing goal to form the repeating patterns to higher density, or in other words, to decrease the pitch.

A method showing some promise for creating repeating patterns to high density involves utilization of block copolymer to form the repeating pattern. Unfortunately, there are often numerous defects present in the repeating patterns formed with block copolymers. It would be desirable to develop new methods of forming patterns with block copolymers which enable repeating patterns to be formed to high density, and with fewer defects than are presently formed with conventional methods.

DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENTS

Copolymers are polymers derived from two or more monomeric species, and contain two or more homopolymer subunits linked by covalent bonds. The union of the homopolymer subunits may utilize an intermediate linkage, known as a junction block.

The embodiments described herein may utilize block copolymers. Block copolymers may be in the form of diblock copolymers, triblock copolymers, etc. Example diblock copolymers include polystyrene-b-poly (2-vinylpyridine) (PS-b-P2VP); polystyrene-b-poly(ethylene oxide) (PS-b-PEO); polystyrene-b-poly(methylmethacrylate) (PS-b-PMMA); polystyrene-b-poly(dimethyl-siloxane) (PS-b-PDMS). The “b” utilized in each of the above chemical formulas indicates a block linkage. Other example block copolymers include materials discussed in U.S. Patent Publication No. 2007/0293041.

Diblock copolymers may be generically represented as A-B, where the “A” represents one of the homopolymer subunits, the “B” represents the other of the homopolymer subunits, and the hyphen represents a covalent bond.

A useful property of some block copolymers is that the homopolymer subunits of the copolymers preferentially interact with like subunits, and avoid interactions with dissimilar subunits. For instance, in some diblock copolymers (A-B), the subunits A preferentially interact with other A, the subunits B preferentially interact with other B, and the subunits A and B preferentially avoid interactions with one another; depending on various factors, such as the length of the blocks, the overall volume fraction of each block, Flory-Huggins interactions, etc. The copolymers may thus self-assemble into repeating patterns. For instance, some diblock copolymers may self-assemble into a repeating pattern that may be represented as A-B:B-A:A-B:B-A:A-B. In such pattern, the hyphens represent covalent bonds and the colons represent non-covalent interactions. The self-assembly of copolymers may be utilized to form patterns over substrates.

Base12may comprise, for example, a monocrystalline semiconductor wafer (for example, a monocrystalline silicon wafer), either alone or in assemblies with other materials. If the base comprises monocrystalline silicon, the base may be referred to as a semiconductor substrate. The terms “semiconductive substrate” and “semiconductor substrate” as utilized herein mean any constructions comprising semiconductive material, including, but not limited to, bulk semiconductive materials such as semiconductive wafers (either alone or in assemblies comprising other materials thereon), and semiconductive material layers (either alone or in assemblies comprising other materials). The term “substrate” as used herein refers to any supporting structure, including, but not limited to, semiconductive substrates.

The base12has an upper surface15to which subunit A of the diblock copolymer has more affinity than does subunit B of the copolymer, (for instance, surface15may be more wettable by subunit A than by subunit B). The diblock copolymer is provided over surface15in a solution (or other appropriate mixture) so that the diblock copolymer may assemble in a preferred orientation during subsequent annealing. Accordingly, in the shown embodiment the diblock copolymer orients so that subunits A are directed toward surface15. The first layer of A-B copolymer along surface15may be referred to as a brush layer17(in other embodiments, there may be no brush layer). Additional levels of A-B copolymer are formed over the brush layer during self-assembly of the copolymer.

The self-assembly of the copolymer may be induced by any of various methods known in the art, such as, for example, thermal or solvent annealing of the copolymer. If solvent annealing is utilized, such may correspond to an anneal induced with solvent vapor.

The self-assembly has formed a pattern comprising regions14of A subunits (demarcated by dashed lines19inFIG. 1), surrounded by a region16of B subunits. The regions14may be referred to as “core” structures. The core structures may have any of numerous shapes. In some embodiments, the core structures may be linear structures (for instance, cylinders) that extend in and out of the page relative to the cross-sectional view ofFIG. 1. In some embodiments, the core structures may be spherical micelles. The outer edges of the core structures (i.e., the boundaries demarcated by dashed lines19) are defined by interfaces where the A subunits of the core structures are directly adjacent the B subunits of the surrounding region.

Although the surrounding region is shown to be the B subunits and the core structures are shown to be the A subunits, in other embodiments the pattern may be reversed so that the surrounding region contains the A subunits and the core structures contain the B subunits.

The pattern ofFIG. 1may be diagrammatically represented with the simplified drawing shown inFIG. 2. A boundary between the brush layer17and the B subunit region16is represented with a dashed line21inFIG. 2. The simplified drawing type ofFIG. 2will be used to describe many of the example embodiments presented herein in order to render the description of such embodiments to be more straightforward than would occur if the more complex drawing type ofFIG. 1were utilized.

As mentioned above, the process of forming a pattern with copolymer (for instance, block copolymer) may involve two specific steps. First the copolymer may be spread across a base (for instance, a semiconductor substrate), and second the copolymer may be treated to induce self-assembly of a pattern within the copolymer (the treatment may utilize any process suitable to induce self-assembly within the copolymer, and may utilize, for example, a thermal anneal, a solvent anneal, and/or a process yet to be developed).

FIG. 3shows a top view of a construction10acorresponding to a desired configuration resulting from self-assembly of block copolymer, and shows a construction10bhaving an undesired configuration formed by the self-assembly of the block copolymer. In the desired configuration of10a, the core structures14are all identical to one another, extend parallel to one another, and extend parallel to an upper surface of substrate12. In contrast, some of the structures14of construction10bhave merged together and formed a pattern defect. The type of pattern defect illustrated in the construction of10bis referred to as a pair of dislocations. The constructions10aand10bare shown to be interchangeable with one another if energy (represented by the symbol “E”) is introduced into the system.

The configuration of10ain which the core structures all extend parallel to one another may be thermodynamically favored relative to other configurations in which some of the core structures are not parallel to others. However, although the favored thermodynamic configuration may correspond to a global energy minimum for the system corresponding to construction10a, there may be other localized energy wells corresponding to configurations in which one or more of the core structures are not parallel to others. An aspect of some embodiments is a recognition that undesired patterns, or pattern defects, (such as the pattern of10b) may be inadvertently induced during self-assembly of block copolymers if excessive energy, or internal stress, is present in a system during the self-assembly; and a recognition of methods for determining formulations of block copolymers that may reduce the internal stresses and defects present in self-assembled block copolymer systems.

Construction10billustrates one of many configurations that may occur in which not all of the core structures formed by self-assembly of copolymers are parallel to one another. Another example configuration is shown inFIG. 4as a construction10c, which is also a pair of dislocation defects, separated by two periods of assembled structures. Other types of defects may form during assembly of energetically frustrated block copolymer systems. For example, disclinations may also form in monolayers of surface-parallel cylinders. When surface-normal cylinders or monolayers of spherical micellular structures are considered, additional defects, such as grain boundaries, may result with greater frequency when entropic chain stretching occurs in order to accommodate the geometric mismatch between the molecular (block) chain lengths and the shape of the final unit cell.

An aspect of some embodiments is a recognition that self-assembly of patterns from block copolymer may lead to a geometric mismatch that resembles a “round peg in a square hole”. For example, in the cross-sectional view of a monolayer of a cylinder-forming block copolymer, the block copolymer may form round core structures within polygonal unit cells. Since the polygonal cells are of a different shape than the core structures contained therein, there are varying distances between the outer surfaces of the core structures (with the “outer surfaces” of the core structures being the locations of the interfaces of the core structures and the surrounding regions) and the inner surfaces of the unit cells. Thus, there is substantial heterogeneity, or distribution, amongst the distances that are to be covered by the blocks of the block copolymer molecules. In other examples, the geometric mismatch may reflect a “round peg in a hexagonal hole” when the cylindrical domains of a cylinder-forming block copolymer are oriented normal (perpendicular) to the substrate surface. When the minor block of a block copolymer composition forms micellular domains, the geometric mismatch may be envisioned as a sphere within a cubic or columnar hexagonal unit cell. An aspect of some embodiments is recognition that if there is not sufficient polydispersity amongst the chain lengths of the majority blocks of a block copolymer to span the range of distances that are to be covered by the assembled block copolymer, then residual internal stresses will be incorporated within the assembled block copolymer system. The residual internal stresses result from the combined effects of minimization of interfacial area and the associated entropic chain stretching that occurs to fill the volume of the unit cells. This reduction in conformational entropy increases the free energy of the assembled block copolymer system, which leads to an observed increase in the frequency of defects in self-assembled block copolymer patterns. A further aspect of some embodiments is a recognition of specific geometric relationships that may be used in formulating block copolymer molecules to have distributions of block chain lengths that are tailored to uniformly fill particular types of unit cells without excessive chain stretching, thereby minimizing the occurrence of pattern defects. An example of the geometric mismatches that may occur when block copolymer self-assembles into polygonal unit cells is described with reference toFIGS. 5-8.

Referring toFIG. 5, such shows a construction30comprising a base32having block copolymer34thereover. The block copolymer is a diblock copolymer containing the subunits A and B. The block copolymer has been provided over the base32, and then subjected to conditions suitable to cause the block copolymer to self-assemble into a pattern over the base.

The base is shown having a horizontal surface33, and a step35extending upwardly relative to such horizontal surface. The pattern formed from the block copolymer comprises a brush layer36that extends conformally along horizontal surface33and step35; with such brush layer including a first portion38corresponding to the A subunit of the block copolymer, and a second portion40corresponding to the B subunit of the block copolymer. The block copolymer used to generate the pattern ofFIG. 5may initially have either the formula A-B or the formula B-A.

The self-assembled block copolymer over brush layer36comprises a plurality of core structures42,44and46composed of subunit A. The core structures42,44and46are over surface33of base32, and may be linear structures that extend along a direction that is in and out of the page relative to the cross-section ofFIG. 5. The core structures42,44and46are analogous to the structures14of construction10inFIGS. 1 and 2, and to the structures14of construction10ainFIG. 3.

The self-assembled block copolymer also comprises regions48,50and52surrounding the core structures42,44and46, with such regions being composed of subunit B. The core structures42,44and46, together with the regions48,50and52surrounding such core structures, form a repeating pattern across the horizontal surface33of base32. Such repeating pattern comprises a unit cell that contains a core structure composed of subunit A and the region composed of subunit B that surrounds such core structure. For instance, the cross-sections of three unit cells60,62and64are shown inFIG. 5, with boundaries of the unit cells being shown with dashed lines61.

The illustrated core structures42,44and46may correspond to cylindrical structures extending into and out of the page relative to the cross-section ofFIG. 5, or to spherical micelles, and accordingly may have the shown circular cross-sections along the plane of the cross-section ofFIG. 5. The circular cross-sections of structures42,44and46are each shown to have a center3, and to have a radius “R” extending from the center of the circular cross-section to the surface of the circular cross-section (with the “surface” of the circular cross-section being the interface of subunits A and B). In some embodiments, the core structures42,44and46may have cross-sections that are shapes other than circular. Regardless, there will be a distance R that corresponds to an average distance from center locations of the cross-sections of the core structures to interface locations of the cross-sections of the core structures. The distance R may be generically referred to as an average center-to-interface distance across a cross-section extending through the core structures. In some embodiments, the core structures may be linear structures extending orthogonally relative to the cross-section ofFIG. 5, and the distance R may thus be determined along a cross-section orthogonal to a primary linear direction of the core structures.

The core structures42,44and46may be considered to correspond to a repeating pattern formed over base32, with such repeating pattern having a center-to-center distance between adjacent core structures of L0; where L0is considered to be a natural pitch of the repeating pattern. In some embodiments, the core structures42,44and46may be ultimately utilized as a patterned mask during formation of integrated circuit structures within a semiconductor construction comprising base32; and it may be desired that all of the core structures be substantially identical to one another, and that the repeating pattern have identical pitch across all of the core structures.

It is noted that unit cell60may be slightly different than unit cells62and64due to the unit cell60being along an edge of step35. However, in the shown embodiment such difference does not alter the pitch between structure42and adjacent structure44.

FIG. 6shows an alternative diagrammatic representation of the unit cells60,62and64fromFIG. 5. Specifically, some B subunit chains are shown extending throughout regions48,50and52of the unit cells; and some A subunit chains are shown extending throughout the core structures42,44and46of the unit cells. There are naturally many more molecular chains involved than are illustrated inFIG. 6. The core structures are shown to have interfaces5, and to have the center-to-interface distances “R” that were discussed above with reference toFIG. 5.FIG. 6Ashows an expanded region ofFIG. 6to assist the reader in visualizing the various features present within a core structure.

FIG. 6illustrates a problem that may result from having round core structures within polygonal unit cells. Specifically, the figure shows that the distance from an interface5of a core structure (for instance, core structure42) to a corner of a polygonal unit cell (for instance, the corner of the square unit cell60) is greater than the distance from the interface of the core structure to the side of the unit cell. Thus, the B subunit chains extend across a greater distance in regions where the B subunit chains extend from the interface of the core structure to the corners of the unit cell, relative to the regions where the B subunit chains extend from the interface of the core structure to the sidewalls of the unit cell. It may assist the reader's understanding ofFIG. 6to contrastFIG. 6with the diagram shown inFIG. 10, (which is discussed below), which shows a representation of the unit cells ofFIG. 6under fictional conditions in which the B subunits do not stretch or contract from a relaxed orientation. The diagram ofFIG. 10is provided only to assist the reader's understanding ofFIG. 6, and does not show an actual structure.

The lengthening of the distance covered by the B subunit chains in some regions of the unit cell relative to others, as shown inFIG. 6, may cause stretching of the chains in the regions where the chains are lengthened. The regions where the chains are lengthened may have B subunit chains stretched relative to a desired relaxed conformation. Alternatively, or additionally, regions where the B subunit chains have less room to stretch (specifically, the regions between the core structure interfaces and the unit cell sidewalls) may cause the B subunit chains to be compressed relative to the desired relaxed conformation. In any event, at least some of the B subunit chains are in a conformation other than the natural relaxed conformation of such chains, and this introduces stress into the system which may cause a self-assembled pattern to deviate from a desired orientation analogous to that described with reference to construction10aofFIG. 3. As discussed above, the stress may increase free energy of the assembled system, due to competing effects of minimization of interfacial area and entropic chain stretching to fill additional volume. An elevated free energy per chain may be associated with an exponential increase in dislocation defect density, due to effective reduction in the potential barrier for defect formation.

The relaxed conformation of the B subunit will have a length LBbased on, among other things, a degree of polymerization within the subunit and the statistical average segmental length of the monomer utilized in the polymerization to form the B subunit. The concept of “length” of given subunit of a copolymer may be subject to interpretation, in that the subunits may be fluctuating through many different conformations in any given environment. For instance, the “length” of a given subunit of a copolymer may be considered an average of several possible conformations that the subunit may adopt in a given environment, rather than being a value corresponding to a rigid conformation of the subunit. Alternatively, the length of the subunit may be based on a model of a rigid conformation of the subunit. For purposes of interpreting this document and the claims that follow, the “length” of a subunit may be determined by any suitable technique that would be chosen by a person of ordinary skill in the art.

FIG. 7shows an alternative diagrammatic representation of the unit cell60, and geometrically illustrates the different distances from a center3of the polygonal unit cell to a corner65of the unit cell, and to a sidewall67of the unit cell. The distance to the corner may be referred to as a distance Dcenter-to-corner, and the distance to the sidewall be referred to as a distance Dcenter-to-sidewall. The distances Dcenter-to-cornerand Dcenter-to-sidewallmay be calculated from the geometry of unit cell60, and may be related to the center-to-center distance L0between adjacent core structures (for instance, the distance between the core structures42and44ofFIG. 6). In the shown embodiment in which the unit cell is a square (in cross-sectional view), the distance Dcenter-to-corneris

22⁢L0
and the distance Dcenter-to-sidewallis

FIG. 8shows a diagrammatic representation of the unit cell60similar to that ofFIG. 7, and geometrically illustrates the different distances from an interface5of the core structure42to the corner65and sidewall67of the unit cell. The distance from center3to interface5corresponds to the distance “R” discussed above. Thus, the distance from the interface5to the corner65is (Dcenter-to-corner-R), and the distance from the interface5to the sidewall is (Dcenter-to-sidewall-R). Using the distances Dcenter-to-cornerand Dcenter-to-sidewalldiscussed above with reference toFIG. 7, the distance from interface5to corner65is

(22⁢L0-R)
and the distance from interface5to sidewall67is

An aspect of some embodiments is recognition that it can be advantageous to prepare a block copolymer composition to have a distribution of B subunit lengths that is polydisperse across a range tailored to fill the various regions of a unit cell containing the self-assembled block copolymer (for instance, the unit cell60ofFIGS. 5-8). Specifically, the B subunit lengths (LB) within a block copolymer composition may be tailored to be distributed across a range defined by Equation 1.
[Dcenter-to-sidewall)−R]≦LB≦[(Dcenter-to-corner)−R]Equation 1

The various parameters of Equation 1 were discussed above with reference toFIGS. 7 and 8. In the particular embodiment ofFIGS. 5-8, the various distances in Equation 1 may be calculated, as described above with reference toFIGS. 7 and 8, to ascertain the Equation 2 specific for structures that have, along at least one cross-section, round core structures in square unit cells.

The lengths LBwithin a composition may be determined with any suitable technique. In some embodiments, the lengths are determined by ascertaining the molecular formulas of the B subunits, and then calculating the lengths based on a rigid model of the B subunits. In other embodiments, the lengths of the B subunits are determined by ascertaining the molecular formulas of the B subunits and then calculating the lengths based on a model that considers statistical variations in the conformations of the B subunits. In yet other embodiments, the lengths of the B subunits may be directly measured with one or more analytical tools.

FIG. 9graphically illustrates a distribution of LBacross the range of Equation 2 as a curve70. Specifically, the curve70inFIG. 9represents a population of diblock copolymer molecules having length LBof the B block distributed across the range of Equation 2. The y-axis value of any point on curve70corresponds to the number of molecules within a population of block copolymer molecules that have the length of the B block corresponding to the x-axis value (LB) at that point. Thus, each y-value may be thought of as a “count” representative of the quantity of molecules in a distribution having a given length.

Although the y-value is chosen to be the number of molecules having a given length, the y-value could alternatively correspond to any parameter that reflects a proportion of a population having a given length, such as a volume fraction, weight fraction, number fraction, etc. Similarly, although the x-value is chosen to be length, the x-value could alternatively correspond to any parameter related to length, such as, for example, degree of polymerization, molecular weight, etc. Regardless of the parameter chosen for the y-axis, the concept that each y-value may be thought of as a “count” representative of the quantity of molecules in a distribution having a given length will remain true.

In some embodiments, the population distribution shown by curve70inFIG. 9may be considered to be diagrammatically representative of a population of diblock copolymers that would be used to minimize the geometric mismatch, and defect occurrence, in a monolayer of assembled surface-parallel cylinders in a cylinder-forming block copolymer system.

Although curve70is illustrated as a continuous function inFIG. 9, in practice, the distribution of block lengths is discretized by the minimum increment of block length, which is related to the size of the individual monomer units.

The embodiment represented by curve70ofFIG. 9shows most of the B blocks of the diblock copolymer molecules having a length LBwithin the range between

(L02-R)⁢⁢and⁢⁢(22⁢L0-R).
However, there is some tailing of the population into the region shorter than

(L02-R),
and also some tailing of the population into the region longer than

(22⁢L0-R).
Such tailings of the population may result from practical limitations of attempting to form a distribution of the B subunit lengths across the desired range.

In some embodiments, the cumulative sum, or “count”, of the number of molecules with B-block chain lengths that are outside of the desired range is small compared to the total number of molecules within the system. In other words, the number (count) of molecules with B-block chain lengths outside of the desired range comprises a small fraction of the overall population of block copolymer molecules. Alternatively, the number (count) of molecules with B-block chain lengths within the desired range comprises a large fraction of the overall population of block copolymer molecules. In some embodiments, the percentage of block copolymer molecules within a given population that have the B subunit lengths within the desired range will be greater than 50 percent of the population so that the lengths LBof such population are “predominantly” within the desired range. In some embodiments, the percentage of block copolymer molecules within a given population that have the B subunit lengths within the desired range will be greater than 90 percent of the population so that the lengths LBof such population are “substantially entirely” within the desired range. In some embodiments, the tailings shown inFIG. 9are eliminated and the percentage of block copolymer molecules within a given population of block copolymer molecules that have the B subunit lengths within the desired range will be 100 percent of the population so that the lengths LBof such population are “entirely” within the desired range.

A curve73is provided inFIG. 9to diagrammatically represent a prior art distribution of lengths LBfor comparison to the embodiment represented by curve70. The distribution represented by curve73is a narrow (low polydispersity) distribution of B-block chain length. The distribution represented by curve73is not sufficient to alleviate the chain stretching due to the geometric mismatch, because the curve73distribution does not provide the appropriate allocation of chain lengths to fill the unit cell in a manner where all of the B subunit chains can have a relaxed configuration.

The distribution represented by curve70ofFIG. 9is one of numerous distributions that may be utilized in various embodiments, and generally any suitable distribution may be used that extends across all, or at least a substantial portion of, the range of Equation 2. In some embodiments, the distributions may be continuous (such as the shown curve70), or discontinuous (as shown and discussed below with reference toFIG. 14). In some embodiments, continuous distributions may correspond to “normal” (i.e., Gaussian) distributions, and in other embodiments the continuous distributions may not be Gaussian distributions. The embodiment shown by curve70ofFIG. 9comprises a distribution that is symmetric across the range of Equation 2. In other embodiments, the distribution may not be symmetric across the range.

The distribution represented by curve70ofFIG. 9may be distinguished from the prior art distribution represented by curve73in that curve70has fairly constant y-values across the entirety of the range of Equation 2, and curve73does not. As discussed above, each y-value may be considered to be a “count” representative of the quantity of molecules in a distribution having a given B subunit length. In some embodiments, a diblock copolymer composition will be provided to have a distribution of lengths LBacross the range of Equation 2 that is uniform to the extent that the “count” of molecules per each of the individual lengths across the range will all be within a factor of 106of one another (with a first value being within a “factor of 106” of a second value if the first value is no less than one-millionth of the second value, and no more than one million times the second value). In particular applications, the diblock copolymer composition may be provided to have a distribution of lengths LBacross the range of Equation 2 that is uniform to the extent that the count of molecules per each of the individual lengths LBacross the range are all within a factor of 105of one another, all within a factor of 104of one another, all within a factor of 103of one another, all within a factor of 102of one another, all within a factor of 10 of one another, or even all the same, or about the same, as one another (which is the case illustrated with curve70inFIG. 9).

The graph ofFIG. 9shows a curve70representing a continuous distribution of lengths across the range of Equation 2, or, in other words, shows that there is a non-zero count (i.e., a y-value greater than 0 in the graph ofFIG. 9) for every obtainable length LBacross the range of Equation 2 (as discussed previously, LBis discretized into integer numbers of monomers, and thus lengths that would require monomer fragments are not obtainable). In some embodiments, the distribution across the range of Equation 2 may be discontinuous (see, for example,FIG. 14, which is discussed below) so that not all of the obtainable lengths LBare present in the distribution.

In the embodiments in which the distribution across the range of Equation 2 is discontinuous, some of the counts (i.e., y-values in the graphs of the types shown inFIGS. 9 and 14) for obtainable lengths LBwill be zero. In such embodiments, the diblock copolymer composition does not have the count of molecules per each of the individual obtainable lengths LBacross the range of Equation 2 all within a given factor of one another. However, such embodiments can still be distinguished from the prior art in that a significant fraction of the range of Equation 2 will be encompassed by fairly constant counts. In some embodiments, the diblock copolymer composition may be provided to have a discontinuous distribution of lengths LBacross the range of Equation 2, and yet the distribution across the range of Equation 2 is uniform to the extent that at least 50% of the counts corresponding to the number of molecules per each of the individual lengths LBacross the range are all within a given factor of one another, at least 60% of such counts are all within a given factor of one another, at least 70% of such counts are all within a given factor of one another, at least 80% of such counts are all within a given factor of one another, or at least 90% of such counts are all within a given factor of one another.

In some embodiments, it can be desired that the distribution of LBacross the range of Equation 2 be appropriate to fill the unit cell (for instance, the unit cell60ofFIG. 8) without requiring chain stretching and imposing stresses on the block copolymer molecules within a population. Such can allow maximization of conformal chain entropy, and hence a reduction in the free energy of an assembled block copolymer system relative to prior art systems. The reduction in free energy may enable access to a lowest possible equilibrium dislocation concentration, which may enable problems analogous to those shown in constructions10bofFIGS. 3 and 10cofFIG. 4to be avoided.

An aspect of some embodiments is an understanding that there is an advantage to utilizing a block copolymer composition having a polydisperse distribution of subunit lengths within the ranges of the types set forth by Equations 1 and 2, rather than having a tight distribution of subunit lengths. It may assist the reader in understanding the invention to compare the geometrical arrangement of assembled block copolymer ofFIG. 6to a fictional arrangement in which the assembled block copolymer molecules have maintained their relaxed chain conformation without stretching to completely fill the volume of the unit cells.FIG. 10shows such fictional arrangement of assembled copolymer relative to the unit cells60,62and64that were discussed above with reference toFIG. 6. In the arrangement ofFIG. 10, the B subunits form cylinders around the core structures comprising the A subunits, and empty spaces72are within corners of the unit cells adjacent the cylinders formed from the B subunits. In reality, empty spaces72do not actually form. Instead, the B subunits stretch to fill the entirety of the unit cell as shown inFIG. 6(due to, for example, interfacial tension and a thermodynamic drive to minimize interfacial area). If the arrangement ofFIG. 10actually formed, then there would be an advantage to having a tight distribution of the B subunit lengths. Specifically, the B subunits lengths inFIG. 10are all the same; and are a distance shown as

(L02-R).
However, since the actual arrangement of assembled copolymer is more analogous to the situation of illustrated inFIG. 6than to the situation ofFIG. 10, it is desirable to have a large amount of polydispersity across the B subunit lengths so that the B subunits can span the different geometrical distances of a unit cell without imposing stresses and strain within the assembled block copolymer system.

FIG. 11compares a tight distribution of B subunit lengths (LB) about the length corresponding to

(L02-R)⁢
(with the tight distribution being shown as a curve74in dashed line) to the distribution of the example embodiment discussed above with reference toFIG. 9(shown as the curve70). The tight distribution of curve74has similar problems to those discussed above regarding the distribution illustrated as curve73ofFIG. 9.

Curves73ofFIGS. 9 and 74ofFIG. 11are provided for illustrative purposes only, and are not intended to be generally representative of all of the prior art. Some prior art processes may form distributions of subunit lengths that are in other locations than those of curves73ofFIGS. 9 and 74ofFIG. 11. Also, the unit L0may be altered by the nature of the block copolymer composition, so that different block copolymer compositions will assemble into structures having different pitches relative to one another. Thus, the L0of an assembly obtained using block copolymer having a prior art distribution of subunit lengths may be different than that obtained using block copolymer having a distribution of subunit lengths corresponding to an embodiment of the present invention. However, the concepts shown inFIGS. 9 and 11that the prior art distributions of subunit lengths are different than the distributions obtained with the various embodiments of the present invention, are accurate.

The graph ofFIG. 11shows the prior art distribution (curve74) at one end of the distribution of Equation 2 (curve70). Thus, the shown prior art distribution has a different median value than does the distribution of Equation 2. In practice, it may be desired that the distribution of Equation 2 have the same median value as the prior art distribution of curve74, but be a wider distribution than the prior art distribution of curve74. Also, in practice the distribution obtained using Equation 2 may have a different value of L0than the prior art distribution of curve74; so the comparison of the curves inFIG. 11may be inaccurate in that such comparison assumes a same value of L0for both the prior art distribution of curve74and the Equation 2 distribution of curve70. In some embodiments, curve70may be configured to have a value of L0that is different from that of prior art curve74, and that enables curve70to have a common median value as the prior art curve while encompassing a broader distribution.

Although the block copolymers described inFIGS. 5-11are diblock copolymers, the invention also includes embodiments utilizing triblock copolymers and other multi-block copolymers that contain more than two basic subunits, or blends thereof. The concepts ofFIGS. 5-11do not change when using multi-block copolymers containing more than two basic subunits. Specifically, there will still be a desired distribution of subunit lengths required to fill the unit cell volume with minimum chain stretch or compression with respect to the chain equilibrium length. Also, such desired distribution may be geometrically calculated using calculations analogous to those discussed above with reference to Equations 1 and 2. For instance, a triblock copolymer having the formula A-B-C will still have a desired distribution of lengths for the various subunits A, B and C; and such desired distributions may be geometrically calculated using concepts analogous to those described with reference toFIGS. 7 and 8.

A block copolymer composition having a desired distribution of subunit lengths may be formed by any suitable method. In some embodiments, the synthesis of a subunit utilized within a block copolymer composition may comprise conditions which vary the degree of polymerization within such subunit to create a desired distribution of subunit lengths. For instance, the synthesis of the B subunit of an A-B block copolymer (or a B-A block copolymer) may comprise conditions which vary the degree of polymerization within the B subunits to create the distribution of LBwithin the range described above in Equation 2. In specific examples, the diblock copolymer polystyrene-b-poly (2-vinylpyridine) may be considered to comprise B subunits corresponding to polystyrene in some embodiments, and to comprise B subunits corresponding to poly (2-vinylpyridine) in other embodiments. If the polystyrene corresponds to the B subunits, the polystyrene may be synthesized under conditions in which varying degrees of polymerization create the distribution within LBof Equation 2 within the block copolymer; and if the poly (2-vinylpyridine) corresponds to the B subunits, the poly (2-vinylpyridine) may be synthesized under conditions in which varying degrees of polymerization create the distribution within LBof Equation 2 within the block copolymer.

Another method for formulating a block copolymer composition to have a desired distribution of subunit lengths is to create the block copolymer composition as a blend of two or more compositions that individually have distributions of LBwithin sub-portions of a desired range of LB.FIGS. 12-14graphically illustrate some example embodiment methods for creating a final block copolymer composition as a blend of two or more individual block copolymer compositions.

Referring toFIG. 12, a desired distribution of LBwithin a final block copolymer composition is shown by the curve76; and a plurality, n, of individual block copolymer compositions are shown to each have distributions of LB,iwithin ranges corresponding to curves78,80,82and84(shown in dashed lines). The individual block copolymer compositions are mixed with one another to form the final block copolymer composition having the distribution of LBof curve76

(i.e.,LB=∑i=1n⁢LB,i).
The individual block copolymer compositions have distributions of LB,iacross complementary regions of a desired range of LBcorresponding to the range of Equation 2, and thus the entire range of LBof Equation 2 can be covered with the mixture of the individual compositions.

Although the individual block copolymer compositions ofFIG. 12are shown to have distributions that are similar to one another in size and shape, in other embodiments the individual block copolymer compositions may have distributions that vary in one or both of size and shape relative to the graph ofFIG. 12. If the individual block copolymer distributions differ from one another, they may differ in an amount of a main component (i.e., a height on the y-axis ofFIG. 12), and/or in the level of polydispersity (i.e., a width on the x-axis ofFIG. 12), and/or in type (i.e., the overall shape of the distribution, which may be, for example, symmetric, asymmetric, Gaussian, etc.). In some embodiments, two or more narrow, prior art-type distributions may be combined with ratios appropriate to form the final block copolymer composition having the desired distribution of LB.

The method shown inFIG. 12creates a very uniform cumulative distribution LBacross the desired range of Equation 2 by combining multiple individual block copolymer compositions. In other embodiments, the number of individual block copolymer compositions may be varied relative to the number shown inFIG. 12to create either a more uniform distribution (by using more individual block copolymer compositions) or a less uniform distribution (by using fewer individual block copolymer compositions). An advantage of a more uniform distribution of LBacross a desired range is that energy within an assembled copolymer system may be minimized, but a disadvantage may be that additional time and materials are required to create the cumulative distribution. In contrast, an advantage of a less uniform distribution of LBacross a desired range is that the distribution may be created with little additional time and materials, but the disadvantage may be that increased internal stresses within the assembled copolymer system leads to the formation of a greater concentration of defects analogous to those of constructions10band10c(FIGS. 3 and 4). In some embodiments, it may be desired to find an appropriate blend which minimizes defects analogous to those of constructions10band10c(FIGS. 3 and 4) to an acceptable concentration, while also avoiding mixing more than a minimum number of individual block copolymer compositions.

FIG. 13graphically illustrates a method similar to that discussed above with reference toFIG. 12, but in which a final copolymer composition represented by curve90is formed by mixing only two individual copolymer compositions that are represented by curves86and88(shown in dashed lines). The final copolymer composition ofFIG. 13is less uniform across the desired range of Equation 2 than the final copolymer composition ofFIG. 12, but in some embodiments the final copolymer composition ofFIG. 13may be adequately uniform to avoid undesired defects in a copolymer assembly (such as, for example, defects analogous to those described above with reference to constructions10band10cofFIGS. 3 and 4).

The distributions of FIGS.9and11-13are represented as continuous across the range of Equation 2, without illustrating the natural discretization that occurs due to a finite length of each additional monomer unit (in other words, the distributions of FIGS.9and11-13are continuous to the extent that every obtainable length LBis represented). In other embodiments, distributions across such range may be discontinuous such that every obtainable length LBacross the range is not represented. For instance,FIG. 14shows a cumulative distribution that comprises five separate individual distributions (labeled as curves91,93,95,97and99) within the range between

(L02-R)⁢⁢and⁢⁢(22⁢L0-R).
The various individual distributions may be referred to as separate components of the cumulative distribution, and thus the cumulative distribution ofFIG. 14may be considered to be achieved as a penta-component assortment of individual distributions. The individual distributions may be each roughly the same size and shape as one another, or may differ in size and/or shape relative to one another. If the individual distributions differ from one another, they may differ in an amount of a main component (i.e., a height on the Y-axis ofFIG. 14), and/or in the level of polydispersity (i.e., a width on the X-axis ofFIG. 14), and/or in type (i.e., the overall shape of the distribution, which may be, for example, symmetric, asymmetric, Gaussian, etc.). Any suitable number of individual distributions may be utilized. The trade-offs involved in choosing the number of individual distributions to utilize will be similar to those discussed above with reference toFIGS. 12 and 13.

In some embodiments, it is recognized that there may be advantages to having a distribution of the subunit A lengths, in addition to, or alternatively to, having the distribution of subunit B lengths. Specifically, it is recognized that a low polydispersity of A-block chain lengths will require significant chain stretching/compression to uniformly fill a cylindrical or spherical core of minor domain features in assembled block copolymer systems. Thus, it may be desired that the lengths LAof the A subunits be distributed across a range such that a significant percentage of the A subunits have a length LAthat is less than R. The length LArefers to a length of an equilibrium conformation of the A subunit, as opposed to a conformation that is stressed by a surrounding environment to induce stretching or contraction of the A subunit.

In some embodiments, the A subunits may be distributed across a range described in Equation 3, where “Lmin” is a length less than R.
Lmin≦LA≦R  Equation 3

The length Lminmay be any suitable length, and in some embodiments may be described as a fraction of R. For instance, in some embodiments, Lminmay be 0.1R, 0.2R, 0.3R, etc.

FIG. 15shows a curve92that graphically illustrates a substantially uniform distribution of A subunit lengths (LA), that spans the range of Equation 3, and in which Lminis 0.2R. The y-axis value of any point on curve92corresponds to the number, or concentration, of molecules within a population of block copolymer molecules that have a length of the A-block that corresponds to the x-axis value (LA) at that point. Alternatively, such distributions of chain lengths within a block copolymer population may be expressed on the y-axis in terms of the number fraction, weight fraction, and or volume fraction of the molecules having a corresponding LAon the x-axis. Although the shown x-axis value is LA, the x-axis values may correspond to any suitable parameters related to LA, such as, for example, the degree of polymerization, the number average molecular weight, the mass average molecular weight, etc.

The embodiment ofFIG. 15shows most of the diblock copolymer molecules of the population having a length LAwithin the range between 0.2R and R. However, there is some tailing of the population into the region shorter than 0.2R, and also some tailing of the population into the region longer than R, for reasons similar to those discussed above with reference toFIG. 9in describing the tailing regions ofFIG. 9.

The distribution of LAacross the range of Equation 3 may be “uniform” in a sense similar to that discussed above with reference toFIG. 9regarding the distribution LB. For instance, in some embodiments a diblock copolymer composition may be provided to have a distribution of lengths LAacross the range of Equation 3 that is uniform to the extent that the “count” of molecules per each of the individual lengths across the range will all be within a factor of 106of one another, all within a factor of 105of one another, all within a factor of 104of one another, all within a factor of 103of one another, all within a factor of 102of one another, all within a factor of 10 of one another, or even all the same, or about the same, as one another.

Although the curve92of the graph ofFIG. 15is continuous across the range of Equation 3 (more specifically, is continuous to the extent that every obtainable length LAis represented, and ignores discretization due to the utilization of only integer numbers of the A blocks), it is to be understood that in other embodiments the distribution across the range of Equation 3 may be discontinuous (i.e., not every obtainable length LAwill be represented, analogously to the discontinuous distribution of LBdiscussed above with reference toFIG. 14). In some embodiments, the diblock copolymer composition may be provided to have a discontinuous distribution of lengths LAacross the range of Equation 3, and yet the distribution across the range of Equation 3 is uniform (analogously to the discussion above with reference toFIG. 9regarding the lengths LB) to the extent that at least 50% of the counts corresponding to the number of molecules per each of the individual lengths LAacross the range are all within a given factor of one another, at least 60% of such counts are all within a given factor of one another, at least 70% of such counts are all within a given factor of one another, at least 80% of such counts are all within a given factor of one another, or at least 90% of such counts are all within a given factor of one another.

FIG. 15also shows an idealized distribution of A subunit lengths (LA) of a prior art process that formed a tight distribution about the length corresponding to R (with the prior art distribution being shown as a curve94in dashed line). The distribution of the example embodiment (shown as curve92) is a much broader distribution than the prior art distribution (shown as curve94). Prior art efforts for “improving” block copolymer compositions may be directed toward tightening the distribution of subunit lengths; which is opposite to the approach described with reference to Equation 3 of creating a broad distribution of subunit lengths.

The relationships of Equations 1-3 may be used to develop a diblock composition which will assemble into the configuration ofFIG. 5with few, if any, defects. In some embodiments, the self-assembled structures (for instance, the core structures42,44and46; and/or surrounding regions48,50and52) may be used as a mask during subsequent processing of the underlying base32ofFIG. 5. Such subsequent processing may include, for example, one or both of etching into base32and of implanting of dopant into base32. For instance, the mask may be used in processing of the type described below with reference toFIGS. 31-34. In other embodiments, the block copolymer domains may form active electronic components within electronic devices like integrated circuits, sensors, optoelectronic, photonic or nanofluidic devices. Alternatively, the block copolymer domains may contain active elements, such as nanoparticles, quantum dots, or nanowires, which have been selectively incorporated within one, the other, or both domains. In yet other embodiments, the block copolymer domains may contain functional precursors, e.g. catalyst species, from which active elements are grown, or on which active elements are deposited.

The various methods described herein may be utilized for any geometry of unit cells, and may be used relative to linear structures and/or micelle structures (for instance, spherical micelles in cubic unit cells, or in hexagonal columnar unit cells).FIGS. 16 and 17diagrammatically illustrate a semiconductor construction100in which block copolymer has assembled to form linear structures (specifically, cylinders) extending normal (i.e., perpendicular) to an upper surface33of an underlying base32. Base32may correspond to a semiconductor substrate, and may have any of the compositions discussed above with reference to the base32ofFIG. 5.

The assembled subunits form core structures102corresponding to A subunits, surrounded by regions104corresponding to B subunits. The core structures and surrounding regions together form a repeating pattern based upon a hexagonal unit cell (with the unit cells being shown inFIG. 17as cells106-112, and with boundaries between the unit cells being shown as dashed lines115).

FIG. 18shows a diagrammatic representation of the unit cell108, and geometrically illustrates the different distances from a center120of the polygonal unit cell to a corner121of the unit cell, and to a sidewall123of the unit cell. The distance to the corner corresponds to a distance Dcenter-to-cornenand the distance to the sidewall corresponds to a distance Dcenter-to-sidewall. The distances Dcenter-to-cornerand Dcenter-to-sidewallmay be calculated from the geometry of unit cell108(similar to the calculations discussed above with reference toFIG. 7), and may be related to a center-to-center distance L0between adjacent core structures (shown inFIG. 17). In the shown embodiment in which the unit cell is a hexagon, the distance Dcenter-to-corneris

33⁢L0
and the distance Dcenter-to-sidewallis

FIG. 18also geometrically illustrates the different distances from an interface130of the core structure102(specifically an interface between A and B subunits that defines an outer edge of the core) to the corner121and sidewall123of the unit cell. The distance from center120to interface130corresponds to the distance “R” corresponding to an average radius of the core structure. Thus, the distance from the interface130to the corner121is (Dcenter-to-corner−R), and the distance from the interface130to the sidewall is (Dcenter-to-sidewall−R). Using the distances Dcenter-to-cornerand Dcenter-to-sidewalldiscussed above, the distance from interface130to corner121is

(33⁢L0-R)
and the distance from interface130to sidewall123is

In the particular embodiment ofFIG. 18, the distances analogous to those in Equation 1 may be calculated to ascertain Equation 4, which is specific for cylinders assembled within columnar hexagonal unit cells.

FIG. 19graphically illustrates a curve140that represents a population of diblock copolymer molecules having length LBof the B-block distributed across the range of Equation 4. The y-axis value of any point on curve140corresponds to the number of molecules within a population of block copolymer molecules that have a length of the B block that corresponds to the x-axis value (LB) at that point. Although the y-value is chosen to be the number of molecules having a given length, the y-value could alternatively correspond to any parameter that reflects a proportion of a population having a given length, such as a volume fraction, weight fraction, number fraction, etc. Similarly, although the x-value is chosen to be length, the x-value could alternatively correspond to any parameter related to length, such as, for example, degree of polymerization, molecular weight, etc.

The embodiment ofFIG. 19shows most of the diblock copolymer molecules of the population represented by curve140as having a length LBwithin a range that extends from

(L02-R)⁢⁢to⁢⁢(33⁢L0-R).
However, there is some tailing of the population into the region shorter than

(L02-R),
and also some tailing of the population into the region longer than

(33⁢L0-R),
for reasons similar to those discussed above with reference toFIG. 9in describing the tailing regions of the curve70ofFIG. 9. The curve140ofFIG. 19represents an example distribution, and other distributions (for instance, distributions analogous to those ofFIGS. 12-14) may be formed in other embodiments.

The relationship of Equation 4 may be used to develop a diblock composition which will assemble into the configuration ofFIGS. 16 and 17with few, if any, defects. The self-assembled structures (for instance, one or both of the core structures102and surrounding regions104) may be used as a mask during subsequent processing of underlying base32(FIG. 16). Such subsequent processing may include, for example, one or both of etching into base32and of implanting of dopant into base32. For instance, the mask may be used in processing of the type described below with reference toFIGS. 31-34. In other embodiments, the block copolymer domains may form active electronic components within electronic devices like integrated circuits, sensors, optoelectronic, photonic, or nanofluidic devices. Alternatively, the block copolymer domains may contain active elements, such as nanoparticles, quantum dots, or nanowires, which have been selectively incorporated within one, the other, or both domains. In yet other embodiments, the block copolymer domains may contain functional precursors, e.g. catalyst species, from which active elements are grown, or on which active elements are deposited.

In some embodiments, relationships similar to those discussed above with reference toFIG. 15may be used to define a distribution of lengths LAof the A subunits in the core structures102.

The distribution of Equation 4 may be formed with any of the methods discussed above for forming the various distributions of Equations 1-3. In some embodiments, the B subunit lengths LBmay be uniform to the extent that the count of molecules per each of the individual lengths across the range of Equation 4 will all be within a factor of 106of one another, all within a factor of 105of one another, all within a factor of 104of one another, all within a factor of 103of one another, all within a factor of 102of one another, all within a factor of 10 of one another, or even all the same, or about the same, as one another.

Although the curve140of the graph ofFIG. 19is continuous across the range of Equation 4 (more specifically, is continuous to the extent that every obtainable length LBis represented, and ignores discretization due to the utilization of only integer numbers of the B blocks), it is to be understood that in other embodiments the distribution across the range of Equation 4 may be discontinuous (i.e., not every obtainable length LBwill be represented, analogously to the discontinuous distribution discussed above with reference toFIG. 14). In some embodiments, the diblock copolymer composition may be provided to have a discontinuous distribution of lengths LBacross the range of Equation 4, and yet the distribution across the range of Equation 4 is uniform (analogously to the discussion above with reference toFIG. 9) to the extent that at least 50% of the counts corresponding to the number of molecules per each of the individual lengths LBacross the range are all within a given factor of one another, at least 60% of such counts are all within a given factor of one another, at least 70% of such counts are all within a given factor of one another, at least 80% of such counts are all within a given factor of one another, or at least 90% of such counts are all within a given factor of one another.

Equations 1-4 are derived relative to planar cross-sections through unit cells, and thus are derived from geometrical relationships determined across only two dimensions of a unit cell. Such equations may be appropriate in applications in which the unit cells are linear sheets or strands extending across an underlying substrate. In some embodiments, however, block copolymer may assemble into unit cells for which it may be more appropriate to consider all three of the dimensions of the unit cells in determining optimal subunit length distributions for the block copolymer. For instance, some block copolymers may assemble into unit cells having spherical cores (which may correspond to micelles) contained within cubic unit cells.

FIG. 20shows a construction150in which block copolymer has self-assembled to form cubic unit cells152over an upper surface33of an underlying base32. Base32may correspond to a semiconductor substrate, and may have any of the compositions discussed above with reference to the base32ofFIG. 5. The unit cells have a center-to-center distance of L0.

The self-assembled subunits of the block copolymer are shown to form core structures154corresponding to A subunits, surrounded by regions156corresponding to B subunits. The core structures and surrounding regions together form a repeating pattern of the cubic unit cells152. Centers153of the unit cells are diagrammatically illustrated with crosses.

FIG. 21shows a diagrammatic representation of one of the unit cells152, and shows three orthogonal axes155,157and159to assist the reader in visualizing the unit cell. The unit cell has edges160,162,164,166,168,170,172,174,176,178,180and182; has corners where various of the edges meet with one another (for instance, the corner184where the edges160,162and182meet), and has surfaces bounded by the edges. Locations where the axes cross the various surfaces of the unit cell are diagrammatically illustrated with the crosses161,163,165,167,169and171. An interface130defines an outer surface of the spherical core structure154.

FIG. 22shows an upper eighth of one of the unit cells152. The axes155,157and159are shown inFIG. 22, together with the locations167,169and171to assist the reader in orienting the portion ofFIG. 22relative to the unit cell ofFIG. 21.

FIG. 22geometrically illustrates the different distances from the center153of the unit cell to the edge182of the unit cell (i.e., a distance illustrated with a segment190), to the corner184of the unit cell (i.e., a distance illustrated with a segment192), and to the location171in the center of a sidewall of the unit cell (i.e., a distance illustrated with a segment194).FIG. 22also illustrates the spherical core154as having a radius “R”.

The length of segment190corresponds to a distance Dcenter-to-edge, the length of segment192corresponds to a distance Dcenter-to-corner, and the length of segment194corresponds to a distance Dcenter-to-sidewall. The distances Dcenter-to-edge, Dcenter-to-cornerand Dcenter-to-sidewallmay be calculated from the geometry of unit cell152(similar to the calculations discussed above with reference toFIG. 7), and may be related to the center-to-center distance L0between adjacent core structures (shown inFIG. 20). In the shown embodiment, the distance Dcenter-to-edgeis

22⁢L0,
the distance Dcenter-to-corneris

32⁢L0
and the distance Dcenter-to-sidewallis

FIG. 22also geometrically illustrates the different distances from the interface130of the core structure154to the edge, corner and sidewall of the unit cell. The distance from center153to interface130is the radius “R” of the core structure. Thus, the distance from the interface130to the edge182is (Dcenter-to-edge-R), the distance from the interface130to the corner184is (Dcenter-to-corner-R), and the distance from the interface130to the sidewall (i.e., the distance to location171) is (Dcenter-to-sidewall-R). Using the distances Dcenter-to-edge, Dcenter-to-cornerand Dcenter-to-sidewalldiscussed above, the distance from interface130to edge182is

(22⁢L0-R),
the distance from interface130to corner184is

(32⁢L0-R)
and the distance from interface130to the sidewall is

The distances discussed above may be utilized to calculate a distribution of lengths of the B subunit (LB) in a manner analogous to that discussed above for determining the range of Equation 2. Specifically, the distribution of lengths LBfor the copolymer that self-assembles into the cubic unit cells ofFIGS. 20-22should be such that the distribution encompasses the shortest distance from the interface130to a surface of the unit cell (which corresponds to the distance to the sidewall of

(L02-R)⁢),
the longest distance from the interface130to a surface of the unit cell (which corresponds to the distance to the corner of

(32⁢L0-R)⁢),
and the distances in between such shortest and longest distances. Thus, an optimal range for the distribution of lengths LBfor a sphere-forming block copolymer that self-assembles into a cubic unit cell of the type shown inFIGS. 20-22may be represented by Equation 5.

A distribution spanning the range of Equation 5 may be formed with any of the methods discussed above for forming the various distributions of Equations 1-4. The distribution of LBacross the range of Equation 5 may be continuous in some embodiments, and may be discontinuous in other embodiments.

In some embodiments, the B subunit lengths LBmay be uniform to the extent that the count of molecules per each of the individual lengths across the range of Equation 5 will all be within a factor of 106of one another, all within a factor of 105of one another, all within a factor of 104of one another, all within a factor of 103of one another, all within a factor of 102of one another, all within a factor of 10 of one another, or even all the same, or about the same, as one another. In some embodiments, the diblock copolymer composition may be provided to have a discontinuous distribution of lengths LBacross the range of Equation 5, and yet the distribution across the range of Equation 5 is uniform (analogously to the discussion above with reference toFIG. 9) to the extent that at least 50% of the counts corresponding to the number of molecules per each of the individual lengths LBacross the range are all within a given factor of one another, at least 60% of such counts are all within a given factor of one another, at least 70% of such counts are all within a given factor of one another, at least 80% of such counts are all within a given factor of one another, or at least 90% of such counts are all within a given factor of one another.

The cubic unit cells ofFIGS. 20-22may be arranged in any of numerous orientations.FIG. 20shows the unit cells arranged as a one-dimensional array. In contrast,FIG. 23shows the unit cells arranged as a two-dimensional array (only some of the unit cells are labeled inFIG. 23). Each unit cell of the two-dimensional array may be considered to have a footprint over the underlying base32corresponding to the square area of the unit cell over the base. In the shown embodiment, such footprint has dimensions of about 4F2, where F is a minimum feature size, or half-pitch, within the repeating pattern of the unit cells. The two-dimensional array may be particularly applicable for fabrication of repeating circuit structures of memory arrays, such as, for example, cross-point memory structures.

The cubic unit cells ofFIGS. 20-23may be considered to have square trench cross-sections. In other embodiments, the chain length distribution of a block copolymer subunit may be modified to accommodate a trench geometry that has a cross-section other than square, such as, for example, a rectangular cross-section or a round-bottom cross-section.

The cubic unit cells ofFIGS. 20-23may be generated by assembling the block copolymer within or over a pre-pattern of appropriate surfaces across base32. The pre-pattern may be topographical (i.e., graphoepitaxy) and/or chemical. In some embodiments, it may be desirable for a surface33of base32(and pre-formed sidewalls if graphoepitaxy is used) to preferentially wet a majority block (the B subunit block in the shown embodiments). In other embodiments, the surface33(and the sidewalls if sidewalls are utilized) may be neutral wetting relative to the majority and minority blocks, or may be preferentially wet by the minority block.

FIG. 23shows a two-dimensional array of cubic unit cells in which the core structures154correspond to spheres. In other embodiments, the core structures may have other shapes. For instance,FIG. 24shows a construction200in which a two-dimensional array of cubic unit cells is formed over base32, but in which the unit cells have cylindrical cores which are oriented perpendicular to the surface of base32. In the shown embodiment, each of the cubic unit cells has about a 4F2footprint overlying the underlying substrate, where F is a minimum feature size, or half-pitch, within the repeating pattern of the unit cells. The two-dimensional array may be particularly applicable for fabrication of repeating circuit structures of memory arrays, such as, for example, cross-point memory structures.

FIG. 24shows a plurality of cubic unit cells202(only some of which are labeled) having cylindrical cores204(only some of which are labeled) contained therein. The unit cells have a center-to-center distance of L0.

In the shown embodiment, the core structures204correspond to A subunits, and are surrounded by regions206(only some of which are labeled) corresponding to B subunits.

FIG. 25shows a diagrammatic representation of one of the unit cells202, and shows three orthogonal axes201,203and205to assist the reader in visualizing the unit cell. The unit cell has edges210,212,214,216,218,220,222,224,226,228,230and232; has corners where various of the edges meet with one another (for instance, the corner234where the edges212,214and228meet), and has surfaces bounded by the edges. Locations where the axes cross the various surfaces of the unit cell are diagrammatically illustrated with the crosses211,213,215,217,219and221. The cylindrical core structure204has a pair of ends240and242, and an interface246defines a lateral sidewall surface extending between the ends.

FIG. 26shows an upper eighth of the unit cell202. The axes201,203and205are shown inFIG. 26, together with the locations217,219and221to assist the reader in orienting the portion ofFIG. 26relative to the unit cell ofFIG. 25.

FIG. 26geometrically illustrates different distances from a center axis250of the unit cell (with such center axis being coextensive with the axis205) to the edge212of the unit cell (i.e., a distance illustrated with a segment252), and to the location221in the center of a sidewall of the unit cell (i.e., a distance illustrated with a segment254). The location221is a location where the sidewall is nearest to the core204.FIG. 26also illustrates the cylindrical core as having a radius “R” within a cross-section through the cylinder.

The lengths of segments252and254may be calculated from the geometry of unit cell202, and may be related to the center-to-center distance L0between adjacent core structures (shown inFIG. 24). In the shown embodiment, the length of segment252is

22⁢L0,
and the length of segment254is

FIG. 26also geometrically illustrates the different distances from the interface246of the core structure204to the edge212of the unit cell (which is a longest distance spanned by a B subunit of block copolymer), and from the interface246to the sidewall location221of the unit cell (which is a shortest distance spanned by a B subunit of block copolymer). The distance from the interface246to the edge212is

(22⁢L0-R),
and the distance from the interface246to location221is

The distances discussed above may be utilize to calculate a desired distribution of lengths of the B subunit (LB) in a manner analogous to the that discussed above for determining the range of Equation 2. Specifically, the distribution of lengths LBfor the copolymer that self-assembles into a cubic unit cell ofFIGS. 24-26should be such that the distribution encompasses the shortest distance from the interface246to a surface of the unit cell (which corresponds to the distance of

(L02-R)⁢),
the longest distance from the interface246to a surface of the unit cell (which corresponds to the distance of

(22⁢L0-R)⁢),
and the distances in between such shortest and longest distances. Thus, an optimal distribution of lengths LBfor a copolymer that self-assembles into a cubic unit cell of the type shown inFIGS. 24-26may be represented by Equation 6.

The distribution of Equation 6 may be formed with any of the methods discussed above for forming the various distributions of Equations 1-5. The distribution of LBacross the range of Equation 6 may be continuous in some embodiments, and may be discontinuous in other embodiments.

In some embodiments, the B subunit lengths LBmay be uniform to the extent that the count of molecules per each of the individual lengths across the range of Equation 6 will all be within a factor of 106of one another, all within a factor of 105of one another, all within a factor of 104of one another, all within a factor of 103of one another, all within a factor of 102of one another, all within a factor of 10 of one another, or even all the same, or about the same, as one another. In some embodiments, the diblock copolymer composition may be provided to have a discontinuous distribution of lengths LBacross the range of Equation 6, and yet the distribution across the range of Equation 6 is uniform (analogously to the discussion above with reference toFIG. 9) to the extent that at least 50% of the counts corresponding to the number of molecules per each of the individual lengths LBacross the range are all within a given factor of one another, at least 60% of such counts are all within a given factor of one another, at least 70% of such counts are all within a given factor of one another, at least 80% of such counts are all within a given factor of one another, or at least 90% of such counts are all within a given factor of one another.

The cubic unit cells ofFIGS. 24-26may be generated by assembling the block copolymer within or over a pre-pattern of appropriate surfaces across base32(FIG. 24). The pre-pattern may be topographical (i.e., graphoepitaxy) and/or chemical. In some embodiments, it may be desirable for a surface33of base32(and pre-formed sidewalls if graphoepitaxy is used) to preferentially wet a majority block (the B subunit block in the shown embodiments). In other embodiments, the surface33(and sidewalls if sidewalls are utilized) may be neutral wetting relative to the majority and minority blocks, or may be preferentially wet by the minority block.

FIGS. 27-30describe another arrangement of unit cells that may be formed by self-assembly of block copolymer, and describe a method of determining an optimal distribution of subunit lengths of the block copolymer.

FIG. 27shows a top view of a construction300in which a two-dimensional array of hexagonal unit cells302is formed over base32(the base is not visible in the top view ofFIG. 27). The unit cells have spherical cores304corresponding to an A subunit of the self-assembled block copolymer, and such cores are surrounded by regions306corresponding to a B subunit of the block copolymer. The unit cells have a center-to-center distance of L0corresponding to a pitch of the repeating structures of the self-assembled configuration.

One of the unit cells302is illustrated in three-dimensional view inFIG. 28. The unit cell is hexagonal columnar in shape, and has the spherical core304contained therein. The spherical core has a radius “R”.

FIGS. 29 and 30shows a top view cross-sectional view and side cross-sectional view, respectively, of the unit cell302, and geometrically illustrate different distances from a center311of the unit cell to surfaces, edges and corners of the unit cell.

Specifically,FIG. 29illustrates distances from the center of the unit cell to a surface308(i.e., a distance illustrated with a segment310), and to an edge312(i.e., a distance illustrated with a segment314).FIG. 30illustrates distances from the center of the unit cell to an edge316(i.e., a distance illustrated with a segment318), and to a corner320(i.e., a distance illustrated with a segment322).

The lengths of segments310,314,318and322may be calculated from the geometry of unit cell302, and may be related to the center-to-center distance L0between adjacent core structures (shown inFIG. 27). In the shown embodiment, the length of segment310is

L02,
the length of segment314is

33⁢L0,
the length of segment318is

33⁢L0,
and the length of segment322is

216⁢L0.
Thus the longest segment is322, and the shortest segment is310.

An interface301defines an outer boundary of the core structure304, and the distances from the interface301to the various edges, corners and surfaces of the unit cell are the lengths of the segments310,314,318and322minus R. Such distances from the interface301to the various edges corners and surfaces correspond to the distances spanned by a B subunit of block copolymer. Accordingly, the longest distance spanned by a B subunit of block copolymer in unit cell302is

(216⁢L0-R),
and the shortest distance spanned by a B subunit of block copolymer in unit cell302is

The distances discussed above may be utilize to calculate a desired distribution of lengths of the B subunit (LB) in a manner analogous to the that discussed above for determining the range of Equation 2. Specifically, the distribution of lengths LBfor the copolymer that self-assembles into hexagonal columnar unit cell ofFIGS. 27-30should be such that the distribution encompasses the shortest distance from the interface301to a surface of the unit cell (which corresponds to the distance of

(L02-R)⁢),
the longest distance from the interface301to a surface of the unit cell (which corresponds to the distance of

(216⁢L0-R)⁢),
and the distances in between such shortest and longest distances. Thus, an optimal distribution of lengths LBfor a copolymer that self-assembles into a hexagonal columnar unit cell of the type shown inFIGS. 27-30may be represented by Equation 7.

The distribution of Equation 7 may be formed with any of the methods discussed above for forming the various distributions of Equations 1-6. The distribution of LBacross the range of Equation 7 may be continuous in some embodiments, and may be discontinuous in other embodiments.

In some embodiments, the B subunit lengths LBmay be uniform to the extent that the count of molecules per each of the individual lengths across the range of Equation 7 will all be within a factor of 106of one another, all within a factor of 105of one another, all within a factor of 104of one another, all within a factor of 103of one another, all within a factor of 102of one another, all within a factor of 10 of one another, or even all the same, or about the same, as one another. In some embodiments, the diblock copolymer composition may be provided to have a discontinuous distribution of lengths LBacross the range of Equation 7, and yet the distribution across the range of Equation 7 is uniform (analogously to the discussion above with reference toFIG. 9) to the extent that at least 50% of the counts corresponding to the number of molecules per each of the individual lengths LBacross the range are all within a given factor of one another, at least 60% of such counts are all within a given factor of one another, at least 70% of such counts are all within a given factor of one another, at least 80% of such counts are all within a given factor of one another, or at least 90% of such counts are all within a given factor of one another.

The hexagonal columnar cells ofFIGS. 27-30may be generated with any suitable method, such as, for example, by creating a pre-pattern of appropriate surfaces across a base. The pre-pattern may be topographical (i.e., graphoepitaxy) and/or chemical.

Although the A subunit distributions were not specifically described during the discussions above regarding the various embodiments ofFIGS. 20-30, the A subunit distributions may be any suitable distributions, and in some embodiments may be of the type described above with reference to Equation 3 andFIG. 15.

The various patterns of unit cells described in the figures above may be used to create patterned masks. Such masks may be used in any of numerous applications, including, for example, in semiconductor processing. An example method of forming and using a patterned mask is described with reference toFIGS. 31-34. In other embodiments, the block copolymer domains may form active electronic components within electronic devices like integrated circuits, sensors, optoelectronic, photonic, or nanofluidic devices. Alternatively, the block copolymer domains may contain active elements, such as nanoparticles, quantum dots, or nanowires, which have been selectively incorporated within one, the other, or both domains. In yet other embodiments, the block copolymer domains may contain functional precursors, e.g. catalyst species, from which active elements are grown, or on which active elements are deposited.

FIG. 31shows a portion of the construction200that was described above with reference toFIG. 24. The construction200has alternating regions204and206of A subunits and B subunits, respectively, of self-assembled block copolymer. One of the regions204and206may be selectively removed relative to the other to form a patterned mask. For instance,FIG. 32shows a patterned mask401resulting from the selective removal of regions206. The patterned mask401comprises spaced apart regions204.

Referring toFIG. 33, the patterned mask may be used during implanting of dopant403into base32, to create a patterned of doped regions400within the base. Alternatively, or additionally, the patterned mask may be used in accordance with a process ofFIG. 34whereby the mask protects regions of base32during etching into base32. The mask is thus used to create a pattern of recessed regions402within the base.