o12.7 Simulation of Silicon Dioxide from TEOS for Power MOSFETs

Figure 12.2: (a) One of the images of a vertical trench for a power MOSFET approximately 2 micrometer wide and 4 micrometer deep. (b) A simulation result showing initial, intermediate, and final surfaces. The resolution of the underlying level set grid was 80x160. The coarsening algorithm was applied twice, coalescing at most four surface elements into one, and the threshold angle was 3 degrees. This result is nearly identical to the one achieved when no coarsening was applied.

SEM image.

Simulation result.

Figure 12.3: The level set function after the last step of the simulation whose result is shown in Figure 12.2. The active narrow band around the zero level set retains the signed distance function, whereas other grid points have not been updated.

Figure 12.4: The extended speed function in the narrow band in the last step of a simulation. (a) In this simulation, no coarsening was performed, but apart from that it is identical to the one leading to Figure 12.2. (b) The coarsening can clearly be seen at the side walls of the trench.

Without coarsening.

With coarsening.

Table 12.1: Comparison of the speed of the visibility test and of the calculation of the fluxes on surface elements by radiosity both with the coalescing algorithm and without. The computation time relative to the conventional algorithm (equaling $1$) is shown.

Coarsening	Visibility	Flux
Steps	Test	Calculation
0	1	1
1	0.29	0.10
2	0.12	0.02

All of the following simulations were performed using the ELSA simulator (cf. Section 13.8), which is a general topography simulator based on the level set method (cf. Chapter 13).

SEM images of several filled trenches in test structures were provided by an industrial partner for a SiO$_2$ deposition process from TEOS. Different initial trench shapes were produced for different technologies and filled under different process conditions. In experiments SiO$_2$ layers were deposited into trenches roughly $4\,\mathrm{\mu m}$ deep and $2\,\mathrm{\mu m}$ wide, where the final layer thickness was in the range of $1\,\mathrm{\mu m}$ for the flat wafer surface.

The computation time of the level set algorithm with narrow banding (cf. Figure 12.3 and Section 13.6) is negligible compared to the evaluation time of the physical models. This, however, is not the case when narrow banding is not employed. Table 12.1 lists the relative computation time of testing for visibility and the actual radiosity calculation both with and without the coalescing algorithm (cf. Figure 12.4). The simulation result with coarsening in Figure 12.2 is nearly identical to the one yielded when no coarsening was applied. Accuracy is hardly affected, but the simulation time considerably decreased.