Incidence critical angle

In Total Reflection X-Ray Fluorescence Analysis (TXRF), the sutface of a solid specimen is exposed to an X-ray beam in grazing geometry. The angle of incidence is kept below the critical angle for total reflection, which is determined by the electron density in the specimen surface layer, and is on the order of mrad. With total reflection, only a few nm of the surface layer are penetrated by the X rays, and the surface is excited to emit characteristic X-ray fluorescence radiation. The energy spectrum recorded by the detector contains quantitative information about the elemental composition and, especially, the trace impurity content of the surface, e.g., semiconductor wafers. TXRF requires a specular surface of the specimen with regard to the primary X-ray light. 

The primary X-ray beam is directed onto the solid surface in grazing incidence. The angle of incidence is kept below the critical angle at which total reflection occurs. The critical angle is given by... 

Agglomerated impurities, such as particles or droplet residues, do not participate in the interference phenomenon leading to total reflection their fluorescence intensity is independent of the angle of incidence below the critical angle, and drops by a factor of 2 if the critical angle is surpassed due to the disappearance of the reflected component in the exciting beam nonreflecting impurities and residues). 

If M]>M2, then, if 6 2 = 90°, sin 6 1 =M2/mj. The incident angle at this moment is called the critical angle, designated by 9. If the incident angle is larger than the critical angle (6 1 >0c), then the incident wave will be totally reflected back to Medium 1. This is known as total reflection. 

Fig. 9.1. Principle of total internal reflection. Light propagation and refraction in a system with different refractive indices separated with a smooth surface is shown. Left The incident light is entering from the high refractive index medium under an angle 61 which is less than the critical angle 0C. Right total internal reflection because the incident light angle 61 is larger than 6C.

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