Finite element method as applied to the study of gratings embedded in complementary metal-oxide semiconductor image sensors

We present a new formulation of the finite element method (FEM) dedicated to the rigorous solution of Maxwell's equations and adapted to the calculation of the scalar diffracted field in optoelectronic subwavelength periodic structures [for both transverse electric (TE) and transverse magnetic (TM) polarization cases]. The advantage of this method is that its implementation remains independent of the number of layers in the structure, the number of diffractive patterns, the geometry of the diffractive object, and the properties of materials. The spectral response of large test photodiodes that can legitimately be represented in 2-D has been measured on a dedicated optical bench and compared to the theory. The validity of the model as well as the possibility of conceiving in this way simple processible diffractive spectral filters are discussed.

[1]  Ki-Dong Lee,et al.  Color filter based on a subwavelength patterned metal grating , 2007 .

[2]  Shanhui Fan,et al.  One-mode model for patterned metal layers inside integrated color pixels. , 2004, Optics letters.

[3]  Caroline Fossati,et al.  The finite element method as applied to the diffraction by an anisotropic grating. , 2007, Optics express.

[4]  T. Gessner,et al.  Characterization of Sputtered Ta and TaN Films by Spectroscopic Ellipsometry , 2006, 2006 8th International Conference on Solid-State and Integrated Circuit Technology Proceedings.

[5]  H. Macleod,et al.  Thin-Film Optical Filters , 1969 .

[6]  H. Lezec,et al.  Effects of hole depth on enhanced light transmission through subwavelength hole arrays , 2002 .

[7]  Brian A Wandell,et al.  Integrated color pixels in 0.18-microm complementary metal oxide semiconductor technology. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[8]  Jean-Pierre Berenger,et al.  A perfectly matched layer for the absorption of electromagnetic waves , 1994 .

[9]  Masanori Koshiba,et al.  Analysis of anisotropic dielectric grating diffraction using the finite-element method , 1996 .

[10]  Haijun Wu,et al.  Adaptive finite-element method for diffraction gratings. , 2005, Journal of the Optical Society of America. A, Optics, image science, and vision.

[11]  Sébastien Guenneau,et al.  On the use of PML for the computation of leaky modes , 2008 .

[12]  Roger Petit,et al.  Electromagnetic theory of gratings , 1980 .

[13]  A. Sommerfeld.  Partial Differential Equations in Physics , 1949 .

[14]  K. Hane,et al.  Fabrication of Transmission Color Filters Using Silicon Subwavelength Gratings on Quartz Substrates , 2006, IEEE Photonics Technology Letters.

[15]  Christophe Geuzaine,et al.  Modelling of electromagnetic waves in periodic media with finite elements , 2004 .

[16]  S. Guenneau,et al.  Foundations of Photonic Crystal Fibres , 2005 .

[17]  W. Barnes,et al.  Surface plasmon subwavelength optics , 2003, Nature.

[18]  R. Tsai,et al.  Crosstalk and microlens study in a color CMOS image sensor , 2003 .

[19]  Eric R. Fossum,et al.  CMOS image sensors: electronic camera-on-a-chip , 1997 .