Xray NanoDiffraction of Si and SiGe

[Karl330]

Hello I am doing research on kinematic and dynamic scattering of xrays on a crystals. I am attempting to simulate the diffraction patterns of a silicon substrate and I have already simulated two other layers of a Silicon Quantum Well and SiGe from which the hetero structure was composed of. In my book called Elements of Modern Xray Physics it tells me that the scattering amplitude squared is the scattered intensity. I understand that dynamical scattering is used for a substrate(infinite amounts of layers) but I am confused how to apply the equations of the Darwin Curve(dynamical under the curve and kinematical outside of the curve) to put into my code apart from using the scattered intensity with the kinematical approximation. The equations that I was given in the book are Intensity Reflectivity = (S_o/T_o)(S_o/T_o)* = (x-√x^2-1)^2 for x≥1, 1 for abs(x) ≤1, (x+√x^2-1)^2 for x≤1. Where x= ∈/g, ∈=mπζ-πζ, g is defined as the amplitude reflectivity for one layer. Sorry for the confusing symbols, I guess that is why I am so confused. Thank you!

 

[BigJDubs]

The Darwin Curve equation is used to describe the behavior of the intensity of a diffracted beam as a function of the angle of incidence. The equation describes the transition between kinematical and dynamical scattering for a substrate, with kinematical scattering occurring outside of the curve and dynamical scattering occurring inside of the curve. To apply this equation in your code, you will need to calculate the wave number (k) of the incident beam, the thickness of the substrate (d), the structure factor (F) of the substrate, and the amplitude reflectivity (g) of the single layer. With these values, you can then plug them into the equation and calculate the scattered intensity.