In Situ Observation of Oxidization Process at the Most Upper Surfaces by X-Ray Surface Propagation Waves
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15 Mat. Res. Soc. Symp. Proc. Vol. 591 @2000 Materials Research Society
to 0.2 deg., they are dispersed into three parts
as shown in Fig. 1. The reflection, XSPWs
White X-rays
and refracted waves arise according to their en-
•
41c tZ/•/.-ray
ergies, below, equal or over against the critical
Reflected X-rays (Ec) XSPWs propagating near the surface, and then the energies can be related with the the electron Fig. 1.Dispersion of white x-rays density of the surface material by the following around the total reflection condition. equations. In the complex refractive index gx, 8 and IP =2(dgldq/ are real and imaginary parts (1) (containing f' and f" in M to-8-m _ _ (qA(a) atomic scattering factor ), f A' = Ne2 / m2nc2 respectively, where, p: density, M: molecular weight, Z: atomic number, N: Avogadro's number, 1I: damping factor, (dg/ 2irn 2" 2 e2 Af' dCov)q: density of oscillators of q shell electrons. 8== =2 , fe" f'=1 +-f 2 f', The integral term contains discontinuous anomalous scattering frequancy (wy) in q shell =1 =Cos 1 1- 2 +_-.¢ ..From Snel's law electrons. When the energy of the XSPWs does (0c) 2! c4! not approach to the frequancy ((oy), the anomalus scattering values (Af') in the integral n,= -MZN=h e *E(2) E M=k law, term can be ignored, so that from Snell's we can use the simplified Eq. 2 with sufficient precision for practical usages. In this equation, if the incident/critical angle 4c is measured correctly, we can get directly and very easily the electron density (he) and/or the density(p) of the material,
where k: constant (me: electron mass, h: Planck's con-
Enhanced electric field
stant, e: electron charge).
at just critcal energy
2-2. Enhanced x-rays on the most upper surface
Figure 2 shows the calculated electric field of non
"4
Ec: 022deg.
.1i
propagation wave, that is, evanescent wave, at the most Ec:l .4 keV upper surface of materials and penetration depth for V, .1 the incident x-ray energies normalized by critical energy. There exists the most intense electric field at . i V just the critical energy. This field interacts to the surface irregularity and generates the lateral propagation . "' wave named XSPWs. This interaction has been 0.0 1.0 2.0 3.0 4.0 S.0 Normalized x-ray energy(EIEc) treated as diffuse scattering of x-rays using distorted wave Born approximation (DWBA) theory[ 1]. Ac- Fig. 2. Calculated enhanced electric field at the cording to this theory, it could be thought that the most upper surface and penetration depth vs. XSPWs corresponds with diffuse scattering x rays x ray energy normalized by critical energy. propagating on the surface, so called "Yoneda wing"[2]. It should be emphasized again that our new method based on the principles in x-ray dispersion and enhancement theories offers new abilities of detecting the densities of the materials with high sensitivity at the most upper surface.
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3. EXEMPLARY EXPERIMENTS 3-1. Platinum on Silicon wafer substrate.
SD Figure 3 shows the experimental set-up. The white x rays from Mo target rotating x-ray generator
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