Abstract:
A combination of two lithographically patterned mandrels can be employed in conjunction with sidewall spacers to provide two spacers. The two spacers may intersect each other and/or contact sidewall surfaces of each other to provide a thickness that is a sum of the thicknesses of the two spacers. Further, the two spacers may be patterned to provide various patterns. In addition, portions of at least one of the two spacers may be etched employing an etch mask. Additionally or alternately, an additional material may be selectively added to portions of one of the two spacers.

Description:
BACKGROUND 
       [0001]    The present disclosure relates to a method of forming patterned structures, and particularly to a method of forming patterned structures employing dual mandrel sidewall image transfer processes. 
         [0002]    As scaling of lithographically printable dimensions stagnates due to delays in development of lithographic exposure tools for printing small scale images, methods of forming small dimensions in a manner not limited by lithographic capabilities are desired in semiconductor manufacturing. Particularly, methods of patterning a material layer with a complex and arbitrary pattern are desired. 
       SUMMARY 
       [0003]    A combination of two lithographically patterned mandrels can be employed in conjunction with sidewall spacers to provide two spacers. The two spacers may intersect each other and/or contact sidewall surfaces of each other to provide a thickness that is a sum of the thicknesses of the two spacers. Further, the two spacers may be patterned to provide various patterns. In addition, portions of at least one of the two spacers may be etched employing an etch mask. Additionally or alternately, an additional material may be selectively added to portions of one of the two spacers. 
         [0004]    According to an aspect of the present disclosure, a method of forming a patterned structure is provided. A first mandrel structure is formed on a top surface of a material layer. A first spacer is formed around the first mandrel structure. A second mandrel structure that straddles a portion of the first spacer is then formed. A second spacer is formed around the second mandrel structure. A composite pattern of at least one portion of the first spacer and at least one portion of the second spacer is transferred into the material layer by an etch. 
     
    
     
       BRIEF DESCRIPTION OF SEVERAL VIEWS OF THE DRAWINGS 
         [0005]      FIG. 1A  is a top-down view of a first exemplary structure after formation of a first mandrel structure and a first spacer according to an embodiment of the present disclosure. 
           [0006]      FIG. 1B  is a vertical cross-sectional view of the first exemplary structure along the vertical plane B-B′ of  FIG. 1A . 
           [0007]      FIG. 2A  is a top-down view of the first exemplary structure after formation of a second mandrel structure according to an embodiment of the present disclosure. 
           [0008]      FIG. 2B  is a vertical cross-sectional view of the first exemplary structure along the vertical plane B-B′ of  FIG. 2A . 
           [0009]      FIG. 3A  is a top-down view of the first exemplary structure after removal of physically exposed portions of the first mandrel structure and the first spacer employing the second mandrel structure as an etch mask according to an embodiment of the present disclosure. 
           [0010]      FIG. 3B  is a vertical cross-sectional view of the first exemplary structure along the vertical plane B-B′ of  FIG. 3A . 
           [0011]      FIG. 4A  is a top-down view of the first exemplary structure after formation of a second spacer according to an embodiment of the present disclosure. 
           [0012]      FIG. 4B  is a vertical cross-sectional view of the first exemplary structure along the vertical plane B-B′ of  FIG. 4A . 
           [0013]      FIG. 5A  is a top-down view of the first exemplary structure after removal of the second mandrel structure according to an embodiment of the present disclosure. 
           [0014]      FIG. 5B  is a vertical cross-sectional view of the first exemplary structure along the vertical plane B-B′ of  FIG. 5A . 
           [0015]      FIG. 6A  is a top-down view of the first exemplary structure after formation of a masking material layer according to an embodiment of the present disclosure. 
           [0016]      FIG. 6B  is a vertical cross-sectional view of the first exemplary structure along the vertical plane B-B′ of  FIG. 6A . 
           [0017]      FIG. 7A  is a top-down view of the first exemplary structure after etching physically exposed portions of the first and second spacers and removal of the masking material layer according to an embodiment of the present disclosure. 
           [0018]      FIG. 7B  is a vertical cross-sectional view of the first exemplary structure along the vertical plane B-B′ of  FIG. 7A . 
           [0019]      FIG. 8A  is a top-down view of the first exemplary structure after transfer of the pattern in remaining portions of the first and second spacers into an underlying material layer according to an embodiment of the present disclosure. 
           [0020]      FIG. 8B  is a vertical cross-sectional view of the first exemplary structure along the vertical plane B-B′ of  FIG. 8A . 
           [0021]      FIG. 9A  is a top-down view of a second exemplary structure after formation of a second spacer according to an embodiment of the present disclosure. 
           [0022]      FIG. 9B  is a vertical cross-sectional view of the second exemplary structure along the vertical plane B-B′ of  FIG. 9A . 
           [0023]      FIG. 10A  is a top-down view of the second exemplary structure after removal of the first and second mandrel structures according to an embodiment of the present disclosure. 
           [0024]      FIG. 10B  is a vertical cross-sectional view of the second exemplary structure along the vertical plane B-B′ of  FIG. 10A . 
           [0025]      FIG. 11A  is a top-down view of the second exemplary structure after transfer of the pattern in remaining portions of the first and second spacers into an underlying material layer according to an embodiment of the present disclosure. 
           [0026]      FIG. 11B  is a vertical cross-sectional view of the second exemplary structure along the vertical plane B-B′ of  FIG. 11A . 
           [0027]      FIG. 12A  is a top-down view of a third exemplary structure after removal of the first mandrel structure selective to the second mandrel structure according to an embodiment of the present disclosure. 
           [0028]      FIG. 12B  is a vertical cross-sectional view of the third exemplary structure along the vertical plane B-B′ of  FIG. 12A . 
           [0029]      FIG. 13A  is a top-down view of the third exemplary structure after formation of a second spacer according to an embodiment of the present disclosure. 
           [0030]      FIG. 13B  is a vertical cross-sectional view of the third exemplary structure along the vertical plane B-B′ of  FIG. 13A . 
           [0031]      FIG. 14A  is a top-down view of the third exemplary structure after removal of the second mandrel structure according to an embodiment of the present disclosure. 
           [0032]      FIG. 14B  is a vertical cross-sectional view of the third exemplary structure along the vertical plane B-B′ of  FIG. 14A . 
           [0033]      FIG. 15A  is a top-down view of the third exemplary structure after transfer of the pattern in remaining portions of the first and second spacers into an underlying material layer according to an embodiment of the present disclosure. 
           [0034]      FIG. 15B  is a vertical cross-sectional view of the third exemplary structure along the vertical plane B-B′ of  FIG. 15A . 
           [0035]      FIG. 16A  is a top-down view of a fourth exemplary structure after patterning first and second spacers according to an embodiment of the present disclosure. 
           [0036]      FIG. 16B  is a vertical cross-sectional view of the fourth exemplary structure along the vertical plane B-B′ of  FIG. 16A . 
           [0037]      FIG. 17A  is a top-down view of the fourth exemplary structure after forming a masking material layer according to an embodiment of the present disclosure. 
           [0038]      FIG. 17B  is a vertical cross-sectional view of the fourth exemplary structure along the vertical plane B-B′ of  FIG. 17A . 
           [0039]      FIG. 18A  is a top-down view of the fourth exemplary structure after etching physically exposed portions of the first spacer and the second spacer according to an embodiment of the present disclosure. 
           [0040]      FIG. 18B  is a vertical cross-sectional view of the fourth exemplary structure along the vertical plane B-B′ of  FIG. 18A . 
           [0041]      FIG. 19A  is a top-down view of the fourth exemplary structure after removal of the masking material layer according to an embodiment of the present disclosure. 
           [0042]      FIG. 19B  is a vertical cross-sectional view of the fourth exemplary structure along the vertical plane B-B′ of  FIG. 19A . 
           [0043]      FIG. 20A  is a top-down view of the fourth exemplary structure after transfer of the pattern in remaining portions of the first and second spacers into an underlying material layer according to an embodiment of the present disclosure. 
           [0044]      FIG. 20B  is a vertical cross-sectional view of the fourth exemplary structure along the vertical plane B-B′ of  FIG. 20A . 
           [0045]      FIG. 21A  is a top-down view of a fifth exemplary structure after selective deposition of a material on physically exposed portions of the second spacer according to an embodiment of the present disclosure. 
           [0046]      FIG. 21B  is a vertical cross-sectional view of the fifth exemplary structure along the vertical plane B-B′ of  FIG. 21A . 
           [0047]      FIG. 22A  is a top-down view of the fifth exemplary structure after transfer of the pattern in remaining portions of the first and second spacers into an underlying material layer according to an embodiment of the present disclosure. 
           [0048]      FIG. 22B  is a vertical cross-sectional view of the fifth exemplary structure along the vertical plane B-B′ of  FIG. 22A . 
           [0049]      FIG. 23A  is a top-down view of a sixth exemplary structure after formation of a first mandrel structure and a first spacer according to an embodiment of the present disclosure. 
           [0050]      FIG. 23B  is a vertical cross-sectional view of the sixth exemplary structure along the vertical plane B-B′ of  FIG. 23A . 
           [0051]      FIG. 24A  is a top-down view of the sixth exemplary structure after formation of a matrix layer that complementarily fills an entire space above the underlying material layer up to the top surface of the first spacer according to an embodiment of the present disclosure. 
           [0052]      FIG. 24B  is a vertical cross-sectional view of the sixth exemplary structure along the vertical plane B-B′ of  FIG. 24B . 
           [0053]      FIG. 25A  is a top-down view of the sixth exemplary structure after formation of a second mandrel structure according to an embodiment of the present disclosure. 
           [0054]      FIG. 25B  is a vertical cross-sectional view of the sixth exemplary structure along the vertical plane B-B′ of  FIG. 25A . 
           [0055]      FIG. 26A  is a top-down view of the sixth exemplary structure after formation of a second spacer around the second mandrel structure according to an embodiment of the present disclosure. 
           [0056]      FIG. 26B  is a vertical cross-sectional view of the sixth exemplary structure along the vertical plane B-B′ of  FIG. 26A . 
           [0057]      FIG. 27A  is a top-down view of the sixth exemplary structure after etching of the second mandrel structure, the first mandrel structure, and the matrix layer employing the second spacer as an etch mask according to an embodiment of the present disclosure. 
           [0058]      FIG. 27B  is a vertical cross-sectional view of the sixth exemplary structure along the vertical plane B-B′ of  FIG. 27A . 
           [0059]      FIG. 28A  is a top-down view of the sixth exemplary structure after transfer of the pattern in the first and second spacers into the underlying material layer according to an embodiment of the present disclosure. 
           [0060]      FIG. 28B  is a vertical cross-sectional view of the sixth exemplary structure along the vertical plane B-B′ of  FIG. 28A . 
       
    
    
     DETAILED DESCRIPTION 
       [0061]    As stated above, the present disclosure relates to methods of forming patterned structures employing dual mandrel sidewall image transfer processes. Aspects of the present disclosure are now described in detail with accompanying figures. It is noted that like reference numerals refer to like elements across different embodiments. Elements with the same reference numerals have the same composition across different embodiments unless expressly indicated otherwise. The drawings are not necessarily drawn to scale. 
         [0062]    Referring to  FIGS. 1A and 1B , a first exemplary according to an embodiment of the present disclosure includes a material layer  20 L. The material layer  20 L can include any material provided that the material layer  20 L includes a material that is different from the materials of various structures to be subsequently formed thereupon. The material layer  20 L can be a semiconductor material layer, a dielectric material layer, or a conductive material layer. The material layer  20 L can have a planar top surface. In one embodiment, the material layer  20 L can be provided on a substrate  10 , which can include a semiconductor material, a dielectric material, and/or a conductive material. The material layer  20 L is an optional structure, and as such, variations in which the material layer  20 L is omitted from the various illustrated structures herein are expressly contemplated. 
         [0063]    A first mandrel structure  30  is formed on the top surface of the material layer  20 L, or, if the material layer  20 L is not present, on the top surface of the substrate  10 . The first mandrel structure  30  can be formed, for example, by depositing a first mandrel material layer (not shown) and patterning the first mandrel material layer, for example, by a combination of lithographic methods and an etch, which can be an anisotropic etch or an isotropic etch. The composition of the first mandrel structure  30  may be the same as, or may be different from, the composition of the material layer  20 . 
         [0064]    The first mandrel structure  30  can include a semiconductor material, a dielectric material, or a conductive material, provided that the material of the first mandrel structure  30  is different from the material of the material layer  20 L. In one embodiment, the first mandrel structure  30  can include silicon, a silicon-germanium alloy, germanium, amorphous carbon, silicon oxide, silicon oxynitride, silicon nitride, a dielectric metal oxide, a dielectric metal nitride, a photoresist material, an organic material, an elemental metal, an intermetallic alloy, a metal oxide, a metal nitride, or any other material different from the material of the material layer  20 L. The height of the first mandrel structure  30  can be, for example, from 10 nm to 500 nm, although lesser and greater thicknesses can also be employed. 
         [0065]    A first spacer  40  is formed around the first mandrel structure  30 . The first spacer  40  can be formed by depositing a first spacer material layer (not shown) on the top surface of the material layer  20 L and on the top surface and sidewalls of the first mandrel structure  30 , and removing horizontal portions of the first spacer material layer by an anisotropic etch, such as a reactive ion etch. The remaining vertical portions of the first spacer material layer constitute the first spacer  40 . 
         [0066]    The first spacer  40  can include a semiconductor material, a dielectric material, or a conductive material, provided that the material of the first spacer  40  is different from the material of the first mandrel structure  30  and from the material of the material layer  20 L. In one embodiment, the first spacer  40  can include silicon, a silicon-germanium alloy, germanium, amorphous carbon, silicon oxide, silicon oxynitride, silicon nitride, a dielectric metal oxide, a dielectric metal nitride, an organic material, an elemental metal, an intermetallic alloy, a metal oxide, a metal nitride, or any other material different from the material of the material layer  20 L and from the material of the first mandrel structure  30 . In an illustrative example, the first mandrel structure  30  can include germanium, silicon-germanium alloy, or amorphous carbon, and the first spacer  40  can include silicon oxide, silicon nitride, or silicon oxynitride. 
         [0067]    The thickness of the first spacer  40 , i.e., the lateral dimension between an inner sidewall of the first spacer  40  and an outer sidewall that is most proximate to the inner sidewall, is not limited by lithographic capabilities of available lithography tools. Thus, the thickness of the first spacer  40  can be a sublithographic dimension, i.e., a dimension that is less than the smallest dimension that can be printed by single lithographic exposure. In one embodiment, the thickness of the first spacer  40  can be from 1 nm to 100 nm, although lesser and greater thicknesses can also be employed. In one embodiment, the aspect ratio of the first spacer  40 , i.e., the ratio of the height of the first spacer  40  to the thickness of the first spacer  40 , can be in a range from 2.5 to 100. 
         [0068]    Referring to  FIGS. 2A and 2B , a second mandrel structure  50  is formed on the top surface of the material layer  20 L. The second mandrel structure  50  can be formed, for example, by depositing a second mandrel material layer (not shown) and patterning the second mandrel material layer, for example, by a combination of lithographic methods and an etch, which can be an anisotropic etch or an isotropic etch. The second mandrel structure  50  straddles a portion of the first spacer  40 . A portion of the first mandrel structure  30  can be covered with the second mandrel structure  50 . 
         [0069]    The second mandrel structure  50  can include a semiconductor material, a dielectric material, or a conductive material, provided that the material of the second mandrel structure  50  is different from the material of the material layer  20 L, the material of the first mandrel structure  30 , and the material of the first spacer  40 . In one embodiment, the second mandrel structure  50  can include silicon, a silicon-germanium alloy, germanium, amorphous carbon, silicon oxide, silicon oxynitride, silicon nitride, a dielectric metal oxide, a dielectric metal nitride, a photoresist material, an organic material, an elemental metal, an intermetallic alloy, a metal oxide, a metal nitride, or any other material different from the material of the material layer  20 L, the material of the first mandrel structure  30 , and the material of the first spacer  40 . The height of the second mandrel structure  50  can be, for example, from 12 nm to 1,000 nm, although lesser and greater thicknesses can also be employed. In one embodiment, the height of the second mandrel structure  50  can be greater than the height of the first mandrel structure  30 . 
         [0070]    In an illustrative example, the first mandrel structure  30  can include one of germanium, a silicon-germanium alloy, and amorphous carbon, and the first spacer  40  can include silicon oxide, silicon nitride, or silicon oxynitride, and the second mandrel structure  50  can include a photoresist material, an organic material, or a silicon germanium alloy (which has a lesser atomic germanium concentration than the atomic germanium concentration of the first mandrel structure  30  if the first mandrel structure  30  includes another silicon germanium alloy). 
         [0071]    Referring to  FIGS. 3A and 3B , all portions of the first mandrel structure  30  that are not covered by the second mandrel structure  50  can be removed by an anisotropic etch (such as a reactive ion etch) that employs the second mandrel structure  50  as an etch mask. Further, all portions of the first spacer  40  that are not covered by the second mandrel structure  50  can also be removed by the etch. Thus, the physically exposed sidewalls of the remaining portions of the first mandrel structure  30  and the physically exposed sidewalls of the remaining portions of the first spacer  40  are vertically coincident with overlying sidewalls of the second mandrel structure  50 . As used herein, a first surface is vertically coincident with a second surface if the first surface and the second surface are located within a same vertical plane. The chemistry of the anisotropic etch that removes the physically exposed portions of the first mandrel structure  30  and the first spacer  40  can be selective to the material of the material layer  20 L so that the material of the material layer  20 L is not significantly removed by the anisotropic etch. 
         [0072]    Referring to  FIGS. 4A and 4B , a second spacer  60  is formed around the second mandrel structure  50  and remaining portions of the first mandrel structure  30  and the first spacer  40 . The second spacer  60  can be formed by depositing a second spacer material layer (not shown) on the top surface of the material layer  20 L, on the top surface of the second mandrel structure  50 , and sidewalls of the second mandrel structure  50  and the remaining portions of the first mandrel structure  30  and the first spacer  40 , and subsequently removing horizontal portions of the second spacer material layer by an anisotropic etch, such as a reactive ion etch. The remaining vertical portions of the second spacer material layer constitute the second spacer  60 . 
         [0073]    The second spacer  60  can include a semiconductor material, a dielectric material, or a conductive material, provided that the material of the second spacer  60  is different from the material of the second mandrel structure  50 , from the material of the first mandrel structure  30 , and from the material of the material layer  20 L. In one embodiment, the second spacer  60  can include silicon, a silicon-germanium alloy, germanium, amorphous carbon, silicon oxide, silicon oxynitride, silicon nitride, a dielectric metal oxide, a dielectric metal nitride, a photoresist material, an organic material, an elemental metal, an intermetallic alloy, a metal oxide, a metal nitride, or any other material different from the material of the material layer  20 L, from the material of the first mandrel structure  30 , and from the material of the second mandrel structure  50 . The material of the second spacer  60  can include the same material as, or a material different from, the material of the first spacer  40 . 
         [0074]    The thickness of the second spacer  60 , i.e., the lateral dimension between an inner sidewall of the second spacer  60  and an outer sidewall that is most proximate to the inner sidewall, is not limited by lithographic capabilities of available lithography tools. Thus, the thickness of the second spacer  60  can be a sublithographic dimension, i.e., a dimension that is less than the smallest dimension that can be printed by single lithographic exposure. In one embodiment, the thickness of the second spacer  60  can be from 1 nm to 100 nm, although lesser and greater thicknesses can also be employed. 
         [0075]    In an illustrative example, the first mandrel structure  30  can include one of germanium, a silicon-germanium alloy, and amorphous carbon, and the first spacer  40  can include silicon oxide, silicon nitride, or silicon oxynitride, and the second mandrel structure  50  can include a photoresist material, an organic material, or a silicon germanium alloy (which has a lesser atomic germanium concentration than the atomic germanium concentration of the first mandrel structure  30  if the first mandrel structure  30  includes another silicon germanium alloy), and the second spacer  60  can include silicon oxide, silicon nitride, or silicon oxynitride. 
         [0076]    Referring to  FIGS. 5A and 5B , the remaining portion of the first mandrel structure  30  and the second mandrel structure  50  are removed without removing the first spacer  40 , the second spacer  60 , and the material layer  20 . The removal of the remaining portion of the first mandrel structure  30  and the second mandrel structure  50  selective to the first spacer  40 , the second spacer  60 , and the material layer  20  can be performed by an etch that is selective to the first spacer  40 , the second spacer  60 , and the material layer  20 . The etch can be an isotropic etch or an anisotropic etch. If the remaining portion of the first mandrel structure  30  and/or the second mandrel structure  50  includes a material that can be removed by combination with oxygen, e.g., amorphous carbon, a photoresist material, or an organic material, the remaining portion of the first mandrel structure  30  and/or the second mandrel structure  50  can be removed by ashing, i.e., controlled combustion at a low pressure environment. The remaining portion of the first mandrel structure  30  and the second mandrel structure  50  can be removed concurrently. All portions of the top surface of the material layer  20 L that are not covered by the first spacer  40  and the second spacer  60  are physically exposed. 
         [0077]    Referring to  FIGS. 6A and 6B , a masking material layer  67  is formed over at least one portion of the first spacer  40  and the second spacer  60 . For example, the masking material layer  67  can be a patterned photoresist material layer. In this case, the masking material layer  67  can be formed by applying a blanket photoresist material layer and lithographically patterning the blanket photoresist material layer. 
         [0078]    Referring to  FIGS. 7A and 7B , the first spacer  40  and the second spacer  60  can be patterned employing the masking material layer  67  as an etch mask. For example, physically exposed portions of the first spacer  40  and the second spacer  60  can be etched selective to the material layer  20 L by an anisotropic etch or an isotropic etch that employs the masking material layer  67  as an etch mask. The masking material layer  67  is subsequently removed selective to the remaining portions of the first spacer  40  and the second spacer  60 , for example, by ashing. The combination of the remaining portions of the first spacer  40  and the second spacer  60  provides a pattern as seen in a top-down view, which is herein referred to as a “composite pattern.” 
         [0079]    Referring to  FIGS. 8A and 8B , the composite pattern defined by the first spacer  40  and the second spacer  60  is transferred into at least one underlying material layer such as the material layer  20 L and optionally into the substrate  10  by an etch, which can be an anisotropic etch. After the transfer of the composite pattern through the material layer  20 L by the etch, the remaining portions of the material layer  20 L are herein referred to as material portions  20 . If an anisotropic etch is employed to transfer the composite pattern into the material layer  20 L, the material portions  20  include the composite pattern. In other words, a horizontal cross-sectional area of the material portions  20  has the same shape as the periphery defined by the combination of the first spacer  40  and the second spacer  40  that overlies the material portions  20 . Thus, the sidewalls of the material portions  20  are vertically coincident with the sidewalls of the first spacer  40  and the second spacer  60 . 
         [0080]    The first spacer  40  and the second spacer  60  can be removed selective to the material portions  20  by an etch, which can be an isotropic etch or an anisotropic etch. A non-limiting illustrative example, if the material portions  20  include a semiconductor material or a metallic material and if the first spacer  40  and the second spacer  60  include a dielectric material such as silicon oxide, silicon nitride, and/or silicon oxynitride, the materials of the first spacer  40  and the second spacer  60  can be removed by one or more wet etches for removing dielectric materials selective to the semiconductor material or selective to the metallic material as known in the art. 
         [0081]    Referring to  FIGS. 9A and 9B , a second exemplary structure according to an embodiment of the present disclosure is derived from the first exemplary structure of  FIGS. 2A and 2B  by forming a second spacer  60  without removing physically exposed portions of the first mandrel structure  30  or the first spacer  40 . In this embodiment, the material of the second mandrel structure  50  can be the same as, or can be different from, the material of the first mandrel structure  30 . The material of the second spacer  60  can be the same as, or can be different from, the material of the first spacer  40 . 
         [0082]    The second spacer  60  is formed while the first spacer  40  is present in regions that are not covered by the second mandrel structure  50 . The second spacer  60  surrounds the first mandrel structure  30 , the first spacer  40 , and the second mandrel structure  50 . The second spacer  60  can contact outer sidewalls of the first spacer  40 . 
         [0083]    Referring to  FIGS. 10A and 10B , the first mandrel structure  30  and the second mandrel structure  50  are removed without removing the first spacer  40 , the second spacer  60 , and the material layer  20 . The removal of the first mandrel structure  30  and the second mandrel structure  50  selective to the first spacer  40 , the second spacer  60 , and the material layer  20  can be performed by an etch that is selective to the first spacer  40 , the second spacer  60 , and the material layer  20 . The etch can be an isotropic etch or an anisotropic etch. If the first mandrel structure  30  and/or the second mandrel structure  50  include a material that can be removed by combination with oxygen, e.g., amorphous carbon, a photoresist material, or an organic material, the first mandrel structure  30  and/or the second mandrel structure  50  include can be removed by ashing, i.e., controlled combustion at a low pressure environment. The first mandrel structure  30  and the second mandrel structure  50  can be removed concurrently. All portions of the top surface of the material layer  20 L that are not covered by the first spacer  40  and the second spacer  60  are physically exposed. 
         [0084]    The combination of the remaining portions of the first spacer  40  and the second spacer  60  provides a composite pattern, which includes a first sub-pattern having the same width as the first spacer  40 , a second sub-pattern having the same width as the second spacer  60 , and a third sub-pattern having the width of the sum of the width of the first spacer  40  and the width of the second spacer  60 . 
         [0085]    Optionally, the processing steps of  FIGS. 6A ,  6 B,  7 A, and  7 B can be performed to cut portions of the first spacer  40  and/or the second spacer  60  into arbitrary shapes. Features having three different widths can be formed. 
         [0086]    Referring to  FIGS. 11A and 11B , the composite pattern defined by the first spacer  40  and the second spacer  60  (or any pattern derived therefrom by cutting portions of the first spacer  40  and/or the second spacer  60 ) is transferred into at least one underlying material layer such as the material layer  20 L and optionally into the substrate  10  by an etch, which can be an anisotropic etch. After the transfer of the composite pattern through the material layer  20 L by the etch, the remaining portions of the material layer  20 L are herein referred to as material portions  20 . If an anisotropic etch is employed to transfer the composite pattern into the material layer  20 L, the material portions  20  include the composite pattern. In other words, a horizontal cross-sectional area of the material portions  20  has the same shape as the periphery defined by the combination of the first spacer  40  and the second spacer  40  that overlies the material portions  20 . Thus, the sidewalls of the material portions  20  are vertically coincident with the sidewalls of the first spacer  40  and the second spacer  60 . 
         [0087]    The first spacer  40  and the second spacer  60  can be removed selective to the material portions  20  by an etch, which can be an isotropic etch. A non-limiting illustrative example, if the material portions  20  include a semiconductor material or a metallic material and if the first spacer  40  and the second spacer  60  include a dielectric material such as silicon oxide, silicon nitride, and/or silicon oxynitride, the materials of the first spacer  40  and the second spacer  60  can be removed by one or more wet etches for removing dielectric materials selective to the semiconductor material or selective to the metallic material as known in the art. 
         [0088]    Referring to  FIGS. 12A and 12B , a third exemplary structure according to an embodiment of the present disclosure is derived from the first exemplary structure of  FIGS. 2A and 2B  by removing the physically exposed portions of the first mandrel structure  30  that are not covered by the second mandrel structure  50  by an etch. A portion of the first mandrel structure  30  is covered with the second mandrel structure  50 . Portions of the first mandrel structure  30  that are not covered by the second mandrel structure  50  are removed by the etch, which employs the second mandrel structure  50  as an etch mask. The etch can be an anisotropic etch. The chemistry of the etch is selected such that the physically exposed portions of the first spacer  40  are not removed. 
         [0089]    In an illustrative example, the first mandrel structure  30  can include one of germanium, a silicon-germanium alloy, and amorphous carbon, and the first spacer  40  can include silicon oxide, silicon nitride, or silicon oxynitride, and the second mandrel structure  50  can include a photoresist material, an organic material, or a silicon germanium alloy (which has a lesser atomic germanium concentration than the atomic germanium concentration of the first mandrel structure  30  if the first mandrel structure  30  includes another silicon germanium alloy). In this example, the chemistry of the etch can be selected such that the dielectric material of the first spacer is not removed, while physically exposed portions of the first mandrel structure  30  are removed. 
         [0090]    Referring to  FIGS. 13A and 13B , second spacers  60  are formed by deposition of a second spacer material layer (not shown) and an anisotropic etch that removed horizontal portions of the second spacer material layer. Remaining vertical portions of the second spacer material layer constitute the second spacers  60 . The second spacers  60  are formed after the first spacer  40  is removed in regions that are not covered by the second mandrel structure  50 . A contiguous portion of the second spacers  60  surrounds the remaining portion of the first mandrel structure  30 , the first spacer  40 , and the second mandrel structure  50 . Another contiguous portion of the second spacers  60  contacts inner sidewalls of the first spacer  40  and sidewalls of the remaining portion of the first mandrel structure  30 . Thus, the second spacers  60  can contact outer sidewalls of the first spacer  40  and inner sidewalls of the first spacer  40 . The material of the second spacer  60  can be the same as, or can be different from, the material of the first spacer  40 . 
         [0091]    Referring to  FIGS. 14A and 14B , the remaining portion of the first mandrel structure  30  and the second mandrel structure  50  are removed without removing the first spacer  40 , the second spacer  60 , and the material layer  20 . The removal of the remaining portion of the first mandrel structure  30  and the second mandrel structure  50  selective to the first spacer  40 , the second spacer  60 , and the material layer  20  can be performed by an etch that is selective to the first spacer  40 , the second spacer  60 , and the material layer  20 . The etch can be an isotropic etch or an anisotropic etch. If the first mandrel structure  30  and/or the second mandrel structure  50  include a material that can be removed by combination with oxygen, e.g., amorphous carbon, a photoresist material, or an organic material, the first mandrel structure  30  and/or the second mandrel structure  50  include can be removed by ashing, i.e., controlled combustion at a low pressure environment. The remaining portion of the first mandrel structure  30  and the second mandrel structure  50  can be removed concurrently. All portions of the top surface of the material layer  20 L that are not covered by the first spacer  40  and the second spacer  60  are physically exposed. 
         [0092]    The combination of the remaining portions of the first spacer  40  and the second spacer  60  provides a composite pattern, which includes a first sub-pattern having the same width as the first spacer  40 , a second sub-pattern having the same width as the second spacer  60 , and a third sub-pattern having the width of the sum of the width of the first spacer  40  and twice the width of the second spacer  60 . 
         [0093]    Optionally, the processing steps of  FIGS. 6A ,  6 B,  7 A, and  7 B can be performed to cut portions of the first spacer  40  and/or the second spacer  60  into arbitrary shapes. Features having three different widths can be formed. 
         [0094]    Referring to  FIGS. 15A and 15B , the composite pattern defined by the first spacer  40  and the second spacer  60  (or any pattern derived therefrom by cutting portions of the first spacer  40  and/or the second spacer  60 ) is transferred into at least one underlying material layer such as the material layer  20 L and optionally into the substrate  10  by an etch, which can be an anisotropic etch. After the transfer of the composite pattern through the material layer  20 L by the etch, the remaining portions of the material layer  20 L are herein referred to as material portions  20 . If an anisotropic etch is employed to transfer the composite pattern into the material layer  20 L, the material portions  20  include the composite pattern. In other words, a horizontal cross-sectional area of the material portions  20  has the same shape as the periphery defined by the combination of the first spacer  40  and the second spacer  40  that overlies the material portions  20 . Thus, the sidewalls of the material portions  20  are vertically coincident with the sidewalls of the first spacer  40  and the second spacer  60 . 
         [0095]    The first spacer  40  and the second spacer  60  can be removed selective to the material portions  20  by an etch, which can be an isotropic etch or an anisotropic etch. A non-limiting illustrative example, if the material portions  20  include a semiconductor material or a metallic material and if the first spacer  40  and the second spacer  60  include a dielectric material such as silicon oxide, silicon nitride, and/or silicon oxynitride, the materials of the first spacer  40  and the second spacer  60  can be removed by one or more wet etches for removing dielectric materials selective to the semiconductor material or selective to the metallic material as known in the art. 
         [0096]    Referring to  FIGS. 16A and 16B , a fourth exemplary structure can be the same as the first exemplary structure of  FIGS. 7A and 7B , or can be derived by patterning the second exemplary structure of  FIGS. 10A and 10B  or the third exemplary structure of  FIGS. 14A and 14B , for example, employing a masking material layer and an etch. 
         [0097]    Referring to  FIGS. 17A and 17B , a masking material layer  77  can be formed over the material layer  20 L such that the masking material layer  77  covers a portion of the first spacer  40  and a portion of the second spacer  60 , while physically exposing another portion of the first spacer  40  and another portion of the second spacer  60 . In one embodiment, the masking material layer  77  can be a lithographically patterned photoresist layer. In another embodiment, the masking material layer  77  can be a patterned hard mask layer including a dielectric material, an organic material, a semiconductor material, or a metallic material. The material of the patterned hard mask layer is different from the materials of the first spacer  40  and the second spacer  60 . The patterned hard mask layer can be formed, for example, by depositing a blanket hard mask layer, by applying and patterning a photoresist layer thereupon, and by transferring the pattern in the photoresist layer into the blanket hard mask layer by an etch. 
         [0098]    Referring to  FIGS. 18A and 18B , physically exposed portions of the first spacer  40  and the second spacer  60  are etched by at least one etch process, while the masked portion of the first spacer  40  and the masked portion of the second spacers  60  are protected by the masking material layer  77 , and consequently, are not etched. The at least on etch process can be, for example, at lease one isotropic etch or an etch including a substantially isotropic etch component. 
         [0099]    In one embodiment, the physically exposed portion of the first spacer  40  can be etched at a greater etch rate than the physically exposed portion of the second spacer  60  during the etching of the physically exposed portions of the first and second spacers ( 40 ,  60 ). 
         [0100]    In another embodiment, the physically exposed portion of the second spacer  60  can be etched at a greater etch rate than the physically exposed portion of the first spacer  40  during the etching of the physically exposed portions of the first and second spacers ( 40 ,  60 ). 
         [0101]    Referring to  FIGS. 19A and 19B , the masking material layer  77  is removed selective to the first spacer  40 , the second spacer  60 , and the material layer  20 L. The composite pattern defined by the combination of the first spacer  40  and the second spacer  60  can include four different widths, which can include a first width w1 for unetched portions of the first spacer  40 , a second width w2 of unetched portions of the second spacer  60 , a third width w3 for the etched portion(s) of the first spacer  40 , and a fourth width w4 for the etched portion(s) of the second spacer  60 . 
         [0102]    Referring to  FIGS. 20A and 20B , the composite pattern defined by the first spacer  40  and the second spacer  60  is transferred into at least one underlying material layer such as the material layer  20 L and optionally into the substrate  10  by an etch, which can be an anisotropic etch. After the transfer of the composite pattern through the material layer  20 L by the etch, the remaining portions of the material layer  20 L are herein referred to as material portions  20 . If an anisotropic etch is employed to transfer the composite pattern into the material layer  20 L, the material portions  20  include the composite pattern. In other words, a horizontal cross-sectional area of the material portions  20  has the same shape as the periphery defined by the combination of the first spacer  40  and the second spacer  40  that overlies the material portions  20 . Thus, the sidewalls of the material portions  20  are vertically coincident with the sidewalls of the first spacer  40  and the second spacer  60 . 
         [0103]    The first spacer  40  and the second spacer  60  can be removed selective to the material portions  20  by an etch, which can be an isotropic etch or an anisotropic etch. A non-limiting illustrative example, if the material portions  20  include a semiconductor material or a metallic material and if the first spacer  40  and the second spacer  60  include a dielectric material such as silicon oxide, silicon nitride, and/or silicon oxynitride, the materials of the first spacer  40  and the second spacer  60  can be removed by one or more wet etches for removing dielectric materials selective to the semiconductor material or selective to the metallic material as known in the art. 
         [0104]    Referring to  FIGS. 21A and 21B , a fifth exemplary structure according to an embodiment of the present disclosure can be derived from the fourth exemplary structure of  FIGS. 17A and 17B  by selectively depositing a material on one of the first spacer  40  and the second spacer  60 , while not depositing the material on the other of the first spacer  40  and the second spacer  60  or on the top surface of the material layer  20 L. In this embodiment, the first spacer  40  and the second spacer  60  include different materials. Any known method for depositing a material on one type of surface selective to other types of surfaces can be employed. The deposited material can be, for example, a dielectric material such as silicon oxide or a semiconductor material such as silicon or a silicon germanium alloy. 
         [0105]    The material can be deposited on at least one physically exposed portion of the first and second spacers ( 40 ,  60 ) while no material is deposited on the masked portions of the first and second spacers ( 40 ,  60 ). In one embodiment, the selective deposition of the material can be performed such that the material is deposited on a physically exposed portion of the first spacer  40 , while the material does not nucleate on a physically exposed portion of the second spacer  60  or the top surface of the material layer  20 L. In another embodiment, the selective deposition of the material can be performed such that the material is deposited on a physically exposed portion of the second spacer  60 , while the material does not nucleate on a physically exposed portion of the first spacer  40  or the top surface of the material layer  20 L. 
         [0106]    Referring to  FIGS. 22A and 22B , the composite pattern defined by the first spacer  40  and the second spacer  60  is transferred into at least one underlying material layer such as the material layer  20 L and optionally into the substrate  10  by an etch, which can be an anisotropic etch. The remaining portions of the material layer  20 L after the transfer of the composite pattern through the material layer  20 L by the etch are herein referred to as material portions  20 . If an anisotropic etch is employed to transfer the composite pattern into the material layer  20 L, the material portions  20  include the composite pattern. In other words, a horizontal cross-sectional area of the material portions  20  has the same shape as the periphery defined by the combination of the first spacer  40  and the second spacer  40  that overlies the material portions  20 . Thus, the sidewalls of the material portions  20  are vertically coincident with the sidewalls of the first spacer  40  and the second spacer  60 . 
         [0107]    The first spacer  40  and the second spacer  60  can be removed selective to the material portions  20  by an etch, which can be an isotropic etch or an anisotropic etch. A non-limiting illustrative example, if the material portions  20  include a semiconductor material or a metallic material and if the first spacer  40  and the second spacer  60  include a dielectric material such as silicon oxide, silicon nitride, and/or silicon oxynitride, the materials of the first spacer  40  and the second spacer  60  can be removed by one or more wet etches for removing dielectric materials selective to the semiconductor material or selective to the metallic material as known in the art. 
         [0108]    Referring to  FIGS. 23A and 23B , a sixth exemplary structure can be the same as the first exemplary structure of  FIGS. 1A and 1B . 
         [0109]    Referring to  FIGS. 24A and 24B , a matrix layer  30 L is formed above the top surface of the material layer  20 L and around the assembly of the first mandrel structure  30  and the first spacer  40 . As used herein, a “matrix layer” refers to a contiguous layer embedding at least one heterogeneous material therein. The matrix layer  30 L fills a complementary region that is not occupied by the first mandrel structure  30  and the first spacer  40  over the material layer  20 L. The matrix layer  30 L complementarily fills the entire space above the underlying material layer  20 L up to the top surface of the first spacer  40 . The matrix layer  30 L can include the same material as the first mandrel structure  30 . Alternately, the matrix layer  30 L can include a same type of material as the first mandrel structure  30  provided that the material of the matrix layer  30 L can be removed simultaneously with the removal of the materials of the first mandrel structure  30  and a second mandrel structure in a subsequent etch step. 
         [0110]    In one embodiment, the matrix layer  30 L can be planarized by employing a self-planarizing material applied by a spin-on coating process, and/or by other planarization processes such as chemical mechanical planarization. The matrix layer  30 L embeds the first mandrel structure  30  and the first spacer  40 . In one embodiment, the top surface of the matrix layer  30 L can be coplanar with the top surface of the first mandrel structure  30  and the top surface of the first spacer  40 . Optionally, an etch stop material layer (not shown) may be formed over the matrix layer  30 L and the first spacer  40  so that a pattern subsequently formed above the top surface of the matrix layer  30 L and the first spacer  40  is not transferred below the top surface of the matrix layer  30 L and the first spacer  40 . 
         [0111]    Referring to  FIGS. 25A and 25B , a second mandrel structure  50  is formed over the top surfaces of the matrix layer  30 L, the first mandrel structure  30 , and the first spacer  40 . The second mandrel structure straddles a portion of the first mandrel structure  30  and a portion of the first spacer  40 . The etch stop material layer, if present, can prevent collateral patterning of the matrix layer  30 L and the first spacer  40 . 
         [0112]    Referring to  FIGS. 26A and 26B , a second spacer  60  is formed around the second mandrel structure by deposition of a second spacer material layer and by an anisotropic etch that removes horizontal portions of the second spacer material layer. The remaining vertical portions of the second spacer material layer constitute the second spacer  60 . In one embodiment, the second spacer  60  may straddle the first spacer  40 . The second spacer  60  is formed while the first spacer  40  is present in regions that are not covered by the second mandrel structure  50 . 
         [0113]    Referring to  FIGS. 27A and 27B , physically exposed portions of the first mandrel structure  30  and the matrix layer  30 L are removed selective to the materials of the second spacer  60  and the first spacer  40  by an anisotropic etch The entirety of the second mandrel structure  50  and physically exposed portions of the first mandrel structure  30  and the matrix layer  30 L that are not covered the second spacer  60  are removed during the anisotropic etch that employs the second spacer  60  as an etch mask. 
         [0114]    A remaining portion of the first mandrel structure  30  and a portion of the matrix layer  30 L that are underlie the second spacer  60  is formed after the anisotropic etch. The remaining portion of the first mandrel structure  30  and the portion of the matrix layer  30 L are herein referred to as residual material portions  32 . 
         [0115]    Referring to  FIGS. 28A and 28B , the composite pattern defined by the first spacer  40  and the second spacer  60  is transferred into at least one underlying material layer such as the material layer  20 L and optionally into the substrate  10  by an etch, which can be an anisotropic etch. After the transfer of the composite pattern through the material layer  20 L by the etch, the remaining portions of the material layer  20 L are herein referred to as material portions  20 . If an anisotropic etch is employed to transfer the composite pattern into the material layer  20 L, the material portions  20  include the composite pattern. In other words, a horizontal cross-sectional area of the material portions  20  has the same shape as the periphery defined by the combination of the first spacer  40  and the second spacer  40  that overlies the material portions  20 . Thus, the sidewalls of the material portions  20  are vertically coincident with the sidewalls of the first spacer  40  and the second spacer  60 . 
         [0116]    The first spacer  40  and the second spacer  60  can be removed selective to the material portions  20  by an etch, which can be an isotropic etch or an anisotropic etch. A non-limiting illustrative example, if the material portions  20  include a semiconductor material or a metallic material and if the first spacer  40  and the second spacer  60  include a dielectric material such as silicon oxide, silicon nitride, and/or silicon oxynitride, the materials of the first spacer  40  and the second spacer  60  can be removed by one or more wet etches for removing dielectric materials selective to the semiconductor material or selective to the metallic material as known in the art. 
         [0117]    The various embodiments of the present disclosure enable formation of structures having sublithographic dimensions because dimensions of the spacers are not limited by lithographic methods. Further, structures having multiple widths can be provided by the composite pattern, which can be transferred into underlying layers to provide conductive, semiconducting, or insulating structures having dimensions not limited by lithographic methods. 
         [0118]    While the disclosure has been described in terms of specific embodiments, it is evident in view of the foregoing description that numerous alternatives, modifications and variations will be apparent to those skilled in the art. Each of the embodiments described herein can be implemented individually or in combination with any other embodiment unless expressly stated otherwise or clearly incompatible. Accordingly, the disclosure is intended to encompass all such alternatives, modifications and variations which fall within the scope and spirit of the disclosure and the following claims.