**4.2 Evaluation of the thickness of the deposition layer by TEM cross-sectional observation**

In the previous section, it was confirmed that the RGB values measured by the color analyzer are equivalent to the reflection rate. To estimate the thickness of the deposition layer from the reflection rate, it is necessary to clarify the relationship between them. The cross-sections of the long-term installation samples were cut by the Focus Ion Beam (FIB), and the thickness of the deposition layer of the longterm irradiated samples was evaluated by TEM observation. **Figure 4** shows the TEM images of each sample. In some samples, it is difficult to identify the interface of the deposition layer, and tungsten is deposited on the surface of the sample to prevent surface damage during FIB cutting. Although, the TEM images show interesting features such as directional structures in the deposition layer and blistering of the substrate, we will only focus on the thickness of the deposition layer in this chapter. **Figure 5** shows the relationship between the thickness of the deposition layer, evaluated from the TEM images, and the reflection rate measured by the color analyzer and spectroscopic ellipsometer.

#### **4.3 Relationship between the experimental results and the single-layer model**

To discuss the relationship between the thickness of the deposition layer and the reflection rate, we consider a single-layer model. In the model, we assume a simple

**Figure 4.** *TEM cross-sectional images of long-term irradiated samples [11].*

*Colorimetry in Nuclear Fusion Research DOI: http://dx.doi.org/10.5772/intechopen.101634*

**Figure 5.** *Relationship between thickness of deposition layer and reflection rate using single layer model [11].*

three-layers: the atmospheric layer, the deposition layer and the substrate layer. The reflection rate, *R*ref, can be expressed as follows [12].

$$\mathcal{Q} = \frac{2\pi N\_{\text{f}} \cos \theta}{\lambda},\tag{2}$$

$$r = \frac{r\_0 + r\_1 \exp(i2\mathcal{Q})}{1 + r\_1 \ r\_0 \exp(i2\mathcal{Q})},\tag{3}$$

$$R\_{ref} = \left| r \right|^2 \tag{4}$$

where *ϕ*, *λ* and *θ* are the phase difference, the wavelength of the incident light and the angle of incidence of the light, respectively. *N*f and *d* are the refractive index and thickness of the deposited layer, *r* is the electric field ratio of the reflected light to the incident light, and *r*0 and *r*1 are the Fresnel reflection coefficients at the air-deposition layer boundary and the deposition layer-substrate layer boundary, respectively. This simple model shows that the reflection rate is nonlinearly dependent on the thickness of the deposition layer. For the polarization of the light, the ratio of S-wave to P-wave is assumed to be 1:1. The refractive index of the deposition layer was set to *n* = 1.24 and *k* = 0.98 based on the results of ellipsometric measurements. The refractive index of the stainless steel substrate is assumed to be *n* = 1.5, *k* = 2.9. The relationship between the thickness of the deposition layer and the reflection rate of the singlelayer model is shown by the solid line in **Figure 5**. A clear dependence of the reflection rate on the thickness can be observed in the range of 10 nm to 100 nm. We now look at the thickness dependence of the reflection rate of the single-layer model. While there is a dependence of the reflection rate between 10 nm and 100 nm, the dependence becomes weaker when the thickness of the deposition layer is below 10 nm or above 100 nm. This may be because the reflection rate of the substrate dominates for the thin layer and the reflection rate of the deposition layer dominates for the thicker

layer. The dependence of the single-layer model is similar to the experimental results of the reflection rate using a color analyzer and spectroscopic ellipsometry. Therefore, the relationship between the reflection rate and the thickness of the deposition layer can be explained by the single-layer model.
