8.25 Sspd_chapter 6_part 7_introduction to athena 6_process simulator  (Page 3/7)

For a more accurate guideline, see the Chapter 3: “RTA Diffusion Modelling”. Table 3-6 shows the anneal temperature/time combinations required for 95% of the clusters formed during high dose implants to dissolve. Modeling these dopant/defect clusters requires the fully coupled (full.cpl) and cluster damage (cluster.dam) models. Only when these clusters have dissolved can the two.dim model be used without significant loss of simulation accuracy. As a general rule, we recommend that the method statement be changed to method two.dim only after a diffusion time that is at least two or three times as long as the values quoted in the table.

If you wish to be certain of when it’s safe to switch models, the recommended procedure is to save a structure file at the point of interest, load the file into TONYPLOT and perform a 1D cutline. Plot the clusters and interstitials. If the cluster concentration is still visible, it’s too early to switch models.

For power devices, where simulation time is at a premium, the same method already described should be used. But instead of using the cluster concentration as a guide of when to switch models, the interstitial concentration should be used as the guide as to when to switch models one more time from the TWO.DIM model to the basic FERMI model. When the interstitial concentration near the surface during a very long anneal has been reduced to only marginally above the background level at the anneal temperature concerned, the method statement can be switched to METHOD FERMI to greatly reduce the simulation time. The interstitial background level will be the level deep in the substrate where little damage has occurred.

7.7.4: Modelling the Correct Substrate Depth

An important and often overlooked aspect of the correct modeling of dopant diffusion is the choice of substrate depth. It has been mentioned previously that the rate of dopant diffusion is highly dependent on the level of damage in the substrate. Therefore, the accurate modeling of dopant diffusion requires the accurate modeling of substrate damage, particularly the movement of interstitials. In general, the interstitials created directly or indirectly by implantation and oxidation tend to diffuse much greater distances than the dopant. The substrate depth chosen for modeling purposes must therefore be deep enough to allow the interstitial concentrations to return to background levels at the bottom of the simulated substrate, even if no dopant diffusion occurs at this depth.

Figure 7.33. Interstitials can move far into the substrate even after a short 10min anneal

Figure 7.33 shows typical diffusion profiles of interstitials after a 1e15/cm3 20keV Boron implant at various anneal times (as-implant, 6 seconds anneal, 1 minute anneal and 10 minute anneal). After only a 10 minute anneal, the interstitials have diffused 8µm into the substrate.

Interstitials, like dopant, require a concentration gradient in order for overall diffusion to take place. For example, if the concentration gradient of interstitials is removed by having too shallow a substrate depth, the concentration of interstitials will start to pile up because they are no longer being removed through diffusion into the bulk of the substrate. If the level of modeled interstitials becomes too high, the diffusion of dopant, even near the surface of the substrate, will also be too high and the simulation will be inaccurate as shown in Figure 7.34.