LITHOGRAPHIC IMAGING BY ELECTROMAGNETIC INTERACTION

The fundamental theory describing “Electrodynamic Fields” has been developed by James Clerk Maxwell and has not changed since Maxwell’s publication in 1862. However this theory is incomplete and fundamentally wrong. Maxwell’s theory, describing Electrodynamics, has been based on the assumption of the superposition of electric fields and magnetic fields. For this reason Maxwell’s equations are linear differential equations. Images in Lithography are considered to be the superposition of a collection of fundamental images. In this New Theory in Physics a new “Non-Linear Electrodynamic” equation has been developed which describes the mutual interaction between different fundamental images. The final resulting image is not any more the superposition of the fundamental images but the final image becomes the result of the mutual interaction between the separate images. This final image is fundamentally different than the superposition of the original separate images. Lithographic Imaging (Photolithography) represents the border area between the material world (silicon wafer) and the energy world (mutual electromagnetic imaging). Existing theories to describe these material-energy interactions are far from the required necessary theoretical physics to realize mutual imaging interaction processes at the surface of the silicon wafer. The only possibility to describe these complex interaction processes correctly is to develop a new theory in physics which describes the electro-magnetic force density interactions (expressed in N/m3) (equation 8). The integration of these force densities of the total interaction volume describes the total force between separate images which is deforming the final image. In this way it is possible to project line thicknesses on a silicon wafer smaller than the wavelength of the used optical light source (LASER). The superposition of images is valid over distances larger than the wavelength of the used optical light source. The electromagnetic interaction between images (contraction of the final image) is valid over distances shorter than the wavelength of the used optical light source. The new theory will be tested at large cosmic scale: Gravitational RedShift, Black Holes and Dark Matter and at sub-atomic levels. And at small atomic scale: The absorption and emission of light at sub-atomic levels in concentric spheres by an atom at discrete energy levels. Evidence will be demonstrated about the correctness of this new electro-dynamic theory which represents the only theory which connects electro-dynamics in a correct way. Differently than in General Relativity, the electro-magnetic-gravitational-acceleration force density interactions (expressed in N/m3) [35] fundamentally has been based on the divergence of the sum of the “Stress Energy Tensor” and the introduced “Gravitational-Acceleration” Tensor. The theory describes “Gravitational-Acceleration-Electromagnetic” Interaction resulting in a mathematical Tensor presentation for BLACK HOLEs. (Gravitational Electromagnetic Confinements) [1] The “Electromagnetic Energy Gradient” creates a second order effect “Lorentz Transformation” which results in the Gravitational Field of BLACK HOLEs which determines the interaction force density between the confinement of Light (BLACK HOLE’s) and the “Gravitational-Acceleration” Field. Einstein approached the interaction between gravity and light by the introduction of the “Einstein Gravitational Constant” in the 4-dimensional Energy-Stress Tensor (1). In this alternative approach related to General Relativity, the interaction between gravity and light has been presented by the sum of the Electromagnetic Tensor and the “Gravitational-Acceleration” Tensor (2) . The new theory describes the impact of "CURL" [38] within the gravitational fields around Black Holes and the impact on Gravitational Lensing. Gravitational "CURL" (Equation 6) is an effect which cannot be explained and calculated by General Relativity. The new approach presents mathematical solutions for the BLACK HOLEs (Gravitational Electromagnetic Interaction) introduced in 1955 by Jonh Archibald Wheeler in the publication in Physical Review Letters in 1955 [1]. The mathematical solutions for BLACK HOLEs are fundamental solutions for the relativistic quantum mechanical Dirac equation (Quantum Physics) in Tensor presentation (41). Assuming a constant speed of light “c” and Planck’s constant ħ within the BLACK HOLE, the radius “R” of the BLACK HOLE with the energy of a proton, is about 1% of the radius of the hydrogen atom (14). The New Theory has been tested in an experiment with 2 Galileo Satellites and a Ground Station by measuring the Gravitational RedShift in an by the Ground Station emitted stable MASER frequency [2]. The difference between the calculation for Gravitational RedShift, within the Gravitational Field of the Earth, in “General Relativity” and the “New Theory” is smaller than 10-16 (12) and (13). In all “General Redshift Experiments” “General Relativity” and the New Electrodynamic-Gravitational-Acceleration” Theory predict a Gravitational RedShift with a difference smaller than 15 digits beyond the decimal point which is beyond the accuracy of modern “Gravitational Redshift” observations. Both values are always within the measured Gravitational RedShift in all observations being published since the first observation of the gravitational redshift in the spectral lines from the White Dwarf which was the measurement of the shift of the star Sirius B, the white dwarf companion to the star Sirius, by W.S. Adams in 1925 at Mt. Wilson Observatory. Theories which unify Quantum Physics and General Relativity [32], like “String Theory”, predict the non-constancy of natural constants. Accurate observations of the NASA Messenger [11] observe in time a value for the gravitational constant “G” which constrains until ( /G to be < 4 × 10-14 per year) . One of the characteristics of the New Theory is the “Constant Value” in time for the Gravitational Constant “G” in unifying General Relativity and Quantum Physics.