Simulations

The used samples had an iron concentration which was laterally homogeneous. This reduced the diffusion to a one-dimensional problem (diffusion perpendicular to the SiC layer).

The calculation of the diffusion was performed by a software that solved the First Fickian law numerically. The total diffusion time t was therefore divided into intervals dt and the total layer thickness was divided into very small cell units. From the difference in concentration between two of these cells, the stream of particles in the time period dt was calculated. This sequence increased, respectively decreased, the concentration in the unit cells. These calculations were computed for all cells and repeated iteratively.

As a starting point both, a constant concentration level and a concentration profile can be used. In our case the measured profile of the as-implanted sample was used as the starting condition. The variable parameters were the segregation coefficient between the materials, the diffusion constant and the thickness of the layers. By a

change of the diffusion constant in the SiC layer, the simulated profile had to be fitted to the profile measured with SIMS.

6.2.3 Results

When interpreting the SIMS measurements one has to consider that the standard SIMS setup can only measure the e/m-ratio. That means a decrease in resolution when the analysed element has the same or a multiple atomic mass as the substrate material. Iron (⁵⁶Fe) has almost exactly double the mass of the silicon (²⁸Si) atom. At different grades of ionisation we get therefore the same e/m-ratio. To avoid this situation we used the ⁵⁴Fe isotope. For other details concerning the SIMS analyses see Appendix A. The electrical isolating SiO₂ capping layer had to be removed with hydrofluoric acid (HF) before the SIMS measurement to avoid a charging of the sample’s surface.

Table 6.3: Diffusion temperatures and times for the 4 samples measured with SIMS.

sample

The reference was the first sample to measure. In Figure 6.4 one can see the comparison of the simulated and the measured Fe concentration profile. Two differences have to be noticed. The measured FWHM value of the implanted curve is surpassing the simulated one by 12%. On the other side the maximum concentration of the implanted curve (1x10¹⁹ cm^-3) is significantly higher than that of the simulated one (7x10¹⁸ cm^-3). The integration over the whole areas below the two curves leads to the result, that the implanted dose surpasses the simulated one by around 50%.

118 Diffusion Barrier Performance

Figure 6.4: Simulated implantation profile of Fe in SiC (with SRIM) and the profile measured with SIMS.

As the layer thickness of the different samples was not exactly the same, the curves had to be shifted into the right position. As an indicator a carbon measurement (monitor signal) parallel to the iron measurement was used. Between the two SiC layers a small carbon peak can be found. This can be explained by a possible damage of the layer during implantation. In Figure 6.5 one can find all SIMS measurements of the different iron concentration profiles.

One significant feature of all measurements is the sharp bend between the two SiC layers. No simulation supposing a two layer system with two identical layers could approximate this trend. We came to the conclusion that network defects caused by iron implantation are the best explanation for this behaviour.

As it was quite difficult to simulate the whole curve from silicon substrate into the SiC capping layer we divided the total profile into different regions. They can also be found in Figure 6.5 and were as follows: (1) plateau in the implanted SiC layer, (2) transition between the two SiC layers and (3) slope in the SiC capping layer.

After many simulations for the different regions in the different layers we had to accept, that the data could not be conciliated. The layers have significantly differing diffusion behaviour which, from our point of view, can only be explained by cracks in the layers. Depending of the measured position on the sample it is not guaranteed

that the measured area is crack free. When hitting a crack the diffusion constant is extremely increased because of the enormous diffusion velocity of metallic impurities along these cracks.

Figure 6.5: SIMS measurements of the iron concentration profiles in the layer stack before (black square) and after annealing at 1200°C for 5 min (dark grey circle), 15 min (grey triangle) and 60 min (light grey triangle).

Nevertheless the following conclusions of all these results can be made:

• The diffusion in region 1 is very fast and leads to diffusion constants in the range of 10^-12 cm²/s. That could be explained by an already cracked SiC layer during implantation and a damage of the layers network during the implantation.

• In region 2 the diffusion constants for the experiments for 15 min and 60 min differ by one order of magnitude. This can be explained by more cracks inside the measured area of the 15 min sample.

• In region 3 the diffusion constants differ again (but at a lower level) by one order of magnitude. Here the different damage generation or again cracks can be a possible explanation.

120 Out-diffusion of Boron at High Temperatures

Table 6.4: Overview of all results concerning the diffusion constant of iron in SiC for the different regions in the layer stack.

region

Nevertheless, the diffusion constant for crack free regions is most probably in the range of 10^-15 to 10^-16 cm²/s. This is an excellent value when comparing it to other amorphous layers (see Table 6.4) like SiN_x (3x10^-14 cm²/s) and SiO₂ (7x10^-13 cm²/s).

It is true that the diffusion experiments did not run as well as expected but after understanding the cracking behaviour of the SiC layer at high temperature (see chapter 5) we are able to use the SiC layer for its original application in the recrystallised wafer equivalent (see chapter 7). Just by reducing the SiC thickness below 400 nm, cracking of the layers can be prevented (on polished surfaces). On rough substrates like our RBSiC ceramic substrates the SiC layer can even be processed (without cracking) with thicknesses up to 1000 nm. This thickness should be highly sufficient to avoid transition metal diffusion from the contaminated substrate into the silicon cell bulk material.