# Numerical Studies on the Application of Photonic Crystals for EUV mirrors

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## Abstract

Presently, 193 nm UV radiation is used in lithography. To further reduce
the dimensions of electronic components into the sub-10-nm regime
the wavelength has to be reduced drastically. A promising option is the
use of EUV radiation. A source of particular interest is the Sn plasma
produced by laser pulses which emits radiation around 13.5 nm.
The use of EUV radiation, however, also presents new challenges. It
is no longer possible to simply use the surface of a metal as a mirror.
As the EUV lies beyond the plasma frequencies of metals[1] the real
part of the dielectic constant ε can be < 1but is no longer negative and
therefore the reflection by a single surface is no longer sufficient. It is
necessary to use the constructive interference of many interfaces, e.g.,
alternating layers of Mo and Si are used. This structure can be conside-
red to be a one-dimensional photonic crystal (1D PhC), where theε of Si
is very close to unity while Mo is responsible for the needed contrast in
ε. It is therefore of interest to develop simulation methods to explore
more complex PhC structures.
To simulate the reflectivity of an array of different layers, the multiple
scattering method (MSM) is used. The scattering of the EUV radiation by
each layer is described by a scattering matrix which transforms incident
waves into waves propagating away from the layer. Another matrix, the
transfer matrix, which is calculated from the scattering matrix, relates
the waves incident and travelling away from the layer on one side of
the layer with those on the other side. The transfer matrix of a com-
plex system built up of many different layers is the matrix product of
the individual transfer matrices. From the corresponding scattering
matrix reflectivity and transmissivity of the system are calculated. This
method is the basis for the program MULTEM [2,3] used in the present
work. This program can also handle 3D PhCs made of layers containing
regular 2D arrays of spheres.
For more general systems the FDTD method[4] has to be used. The
reflected field is Fourier transformed and normalized to the Fourier
transform of the field propagating in free space. With this method, any
type of PhC structure can be investigated.
The feasibility of different materials was investigated for 1D PhCs by
calculating the reflectivity of a layer system with Si and another layer
with a range of different real and imaginary parts of ε. It is found that a
large ratio Re (ε) /Im (ε) optimizes the reflectivity as long as the number
of layers is large enough and the small absorption in Si does not domi-
nate. Comparing with actual values for different elements the highest
reflectivities were found for Nb/Si and Mo/Si.
3D PhCs of Mo spheres regularly embedded in Si do not exceed the re-
flectivity of the 1D layers even for a large number of layers. This is due
to the weaker, but still relevant, absorption of the Si matrix. Replacing
Si by vacuum, yields relectivities for small Mo radii exceeding the 1D
reflectivities at the expense of reduced bandwidths.
[1] A.D. Rakic, et al., Applied Optics, 37, 5271 (1998).
[2] N. Stefanou, V. Yannopapas, A. Modinos, Comput. Phys. Commun.
113, 198 (1998).
[3] N. Stefanou, V. Yannopapas, A. Modinos, Comput. Phys. Commun.
132, 198 (2000).
[4] K.S. Yee, IEEE Trans. Ant. Prop. 14, 302 (1966).

## Details

Original language | English |
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Publication status | Published - 29 Sep 2016 |

Event | ÖPG Jahrestagung 2016 - Boltzmanngasse 5, 1090 Wien , Wien, Austria Duration: 27 Sep 2016 → 29 Sep 2016 http://oepg2016.univie.ac.at/ |

### Conference

Conference | ÖPG Jahrestagung 2016 |
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Country | Austria |

City | Wien |

Period | 27/09/16 → 29/09/16 |

Internet address |