EUV MaskΒΆ

Optics for extreme ultraviolet lithography (EUV, EUVL) consist of various reflective elements (multilayer reflectors operated at oblique incidence of light). EUV photomasks consist of a multilayer reflector with absorbing patterns. This example includes project files for simulating light scattering off an EUV line mask.

The mask geometry is defined using a 2D layout with several polygons (please note that for the multilayer reflector there is just the definition of an exterior domain as subspace, with a specific identifier ExteriorDomainId = 10. Please compare the multilayer material and geometry definition in the materials.jcm file):

 1
 2
 3Layout2D {
 4  Name = "EUV_line"
 5  UnitOfLength = 1e-09
 6  MeshOptions {
 7    MaximumSideLength = 7
 8    MinimumMeshAngle = 5
 9  }
10  Objects {    
11    Polygon {
12      Name = "ComputationalDomain"
13      DomainId = 1
14      Priority = ComputationalDomain
15      Points = [-88 0 88 0 88 77.6 -88 77.6]
16      Boundary {
17        Number = 1
18        Class = Transparent
19        ExteriorDomainId = 10
20      }
21      Boundary {
22        Number = [2 4]
23        Class = Periodic
24      }
25      Boundary {
26        Number = 3
27        Class = Transparent
28      }  
29    }
30    
31    Polygon {
32      Name = "Capping layer"
33      DomainId = 5
34      Points = [-88 0 88 0 88 11.5 -88 11.5]
35      MeshOptions {
36        MinimumMeshAngle = 1
37      }
38    }
39    Polygon {
40      Name = "Oxide layer"
41      DomainId = 4
42      Points = [-88 11.5 -44 11.5 44 11.5 88 11.5 88 12.6 -88 12.6]
43    }
44    Polygon {
45      Name = "Buffer"
46      DomainId = 3
47      Points = [-44 12.6 44 12.6 42.2502267295 32.6 -42.2502267295 32.6]
48    }
49    Polygon {
50      Name = "Absorber"
51      DomainId = 2
52      Points = [-42.2502267295 32.6 42.2502267295 32.6 38.7506801884 72.6 -38.7506801884 72.6]
53      CornerRounding {
54        NPoints = 5
55        Point = [3 4]
56        Radius = 5
57      }
58    }
59  }
60}
61

As sources, S- and P-polarized plane waves at oblique incidence are defined:

 1SourceBag {
 2  Source {
 3    ElectricFieldStrength {
 4      PlaneWave {
 5        Lambda0 = 1.34e-08
 6        SP = [1, 0]
 7        ThetaPhi = [4, 0]
 8        3DTo2D = yes
 9        Incidence = FromAbove
10      }
11    }
12  }
13}
14SourceBag {
15  Source {
16    ElectricFieldStrength {
17      PlaneWave {
18        Lambda0 = 1.34e-08
19        SP = [0, 1]
20        ThetaPhi = [4, 0]
21        3DTo2D = yes
22        Incidence = FromAbove
23      }
24    }
25  }
26}
27

The material definitions include a planar layer stack modelling the DBR multilayer reflector (LayeredMedia):

 1Material {
 2  Name = "Material_1_air"
 3  DomainId = 1
 4  RelPermittivity = 1
 5  RelPermeability = 1.0
 6}
 7Material {
 8  Name = "Material_2_absorber"
 9  DomainId = 2
10  RelPermittivity = (0.8703211743, 0.0707916176)
11  RelPermeability = 1.0
12}
13Material {
14  Name = "Material_3_buffer"
15  DomainId = 3
16  RelPermittivity = (0.9498420903, 0.0245814296)
17  RelPermeability = 1.0
18}
19Material {
20  Name = "Material_4_oxide_layer"
21  DomainId = 4
22  RelPermittivity = (0.9498420903, 0.0245814296)
23  RelPermeability = 1.0
24}
25Material {
26  Name = "Material_5_Si_capping_layer"
27  DomainId = 5
28  RelPermittivity = (1.0004767452, 0.0036408736)
29  RelPermeability = 1.0
30}
31Material {
32  Name = "Material_6_Mo"
33  DomainId = 6
34  RelPermittivity = (0.8532399029, 0.011269506)
35  RelPermeability = 1.0
36}
37Material {
38  Name = "Material_7_Si"
39  DomainId = 7
40  RelPermittivity = (1.0004767452, 0.0036408736)
41  RelPermeability = 1.0
42}
43
44LayeredMedia {
45
46  # Si-Mo-Multilayer
47  DomainId = 10
48  LayerThickness = [2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09 2.42e-09 4.48e-09]
49  RelPermeabilityInLayers = [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1]
50  RelPermittivityInLayers = [(0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736) (0.8532399029, 0.011269506) (1.0004767452, 0.0036408736)]
51
52  # Substrate
53  RelPermeabilityInfiniteDomain = 1.0
54  RelPermittivityInfiniteDomain = 0.9585976464
55}
56

The definitions in the project.jcmp file include numerical accuracy parameters as well as the definition of a post process for computing the reflected diffraction orders:

 1Project {
 2  InfoLevel = 3
 3  Electromagnetics {
 4    TimeHarmonic {
 5      Scattering {
 6        Accuracy {
 7          FiniteElementDegree = 3
 8          Precision = 1e-3
 9          Refinement {
10            MaxNumberSteps = 1
11          }
12        }
13      }
14    }
15  }
16}
17PostProcess {
18  FourierTransform {
19    NormalDirection = Y
20    FieldBagPath = "project_results/fieldbag.jcm"
21    OutputFileName = "project_results/reflected_diffraction_orders.jcm"
22    Format = JCM-ASCII
23  }
24}

The example files of the project include a Matlab script and template files for automatic setup of parameterized geometries for this type of EUV mask. The script also allows to compare the results of the computation where a rigorous domain-decomposition approach is used to couple the multilayer mirror to the 2D computational domain to results from a computation where the whole setup is defined in a single computational domain.