Analysis of Light Scattering Properties about Dent Nanoparticles upon Wafer

2013 ◽  
Vol 464 ◽  
pp. 94-97
Author(s):  
Lei Gong ◽  
Hong Lu Hou ◽  
Jin Long Zou
Keyword(s):  
Light Scattering ◽  
Harmonic Function ◽  
Cross Section ◽  
Spherical Harmonic ◽  
Theoretical Foundation ◽  
Scattering Process ◽  
Differential Scattering Cross Section ◽  
Scattering Coefficients ◽  
Vector Spherical Harmonic ◽  
Spherical Harmonic Function

The light scattering properties of the dent nanoparticles upon wafers is discussed in this paper. Taking the advantage of the Bobbert-Vlieger (BV) theorem, the scattering model between wafer and dent nanoparticles is established. The scattering process is analyzed and the scattering coefficients are derived by using of the vector spherical harmonic function. The differential scattering cross section (DSCS) of the dent nanoparticles upon the wafer is calculated which is compared with the extended Mie method proved the validity of the method and the influences of the dent position, dent scale and scattering angle on the DSCS are analyzed numerically in details. The result is shown that the effect of the dielectric is smaller than the metal. Therefore, the material of the defect and the shape can be extracted by calculate the DSCS, which provide strong theoretical foundation to the nondestructive detector engineer.

scholarly journals Non-classical integrals of Bessel functions

1981 ◽  
Vol 22 (3) ◽  
pp. 368-378 ◽  
Author(s):  
S. N. Stuart
Keyword(s):  
Harmonic Function ◽  
Potential Theory ◽  
Spherical Harmonic ◽  
Bessel Functions ◽  
Delta Function ◽  
Generalized Function ◽  
Definite Integrals ◽  
Spherical Harmonic Function ◽  
Image Position ◽  
Fourier Integrals

AbstractCertain definite integrals involving spherical Bessel functions are treated by relating them to Fourier integrals of the point multipoles of potential theory. The main result (apparently new) concernswhere l1, l2 and N are non-negative integers, and r1 and r2 are real; it is interpreted as a generalized function derived by differential operations from the delta function δ(r1 − r2). An ancillary theorem is presented which expresses the gradient ∇2nYlm(∇) of a spherical harmonic function g(r)YLM(Ω) in a form that separates angular and radial variables. A simple means of translating such a function is also derived.

Growth and Approximation of Entire Harmonic Functions in 𝑅𝑛, 𝑛 > 3

2008 ◽  
Vol 15 (1) ◽  
pp. 99-110
Author(s):  
Devendra Kumar
Keyword(s):  
Harmonic Function ◽  
Spherical Harmonic ◽  
Harmonic Functions ◽  
Approximation Error

Abstract We study the growth of functions which are harmonic in any number of variables. The results are expressed in terms of spherical harmonic coefficients as well as by the approximation error of the harmonic function with (𝑝, 𝑞)-growth.

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