Silicon Epitaxy Modeling & Control
SC Solutions provides controls and physical modeling solutions to its customers for silicon epitaxy. SC Solutions’ engineers have designed temperature controllers for a RTCVD equipment manufacturer for their next-generation, single-wafer epitaxy chamber. The dynamic finite-volume heat transfer model, and the model-based, multiple-input, multiple-output, feedback controllers were computer tested for performance (temperature ramp-up and ramp-down rates, wafer temperature uniformity, etc). Multiple design iterations were explored quickly, and suitable modifications were made to the chamber design before constructing a prototype. This integrated approach, with an eye towards design-for-controllability, resulted in considerable time and money savings for our customer. Apart from real-time feedback controllers, we also provide run-to-run controllers for increased repeatability of wafer properties.
In addition, SC Solutions develops reactor-scale CVD models for the industry using CFDRC’s popular simulation software, CFD-ACE. These models provide insight into a variety of issues such as performance limits, troubleshooting, design improvements, etc. The graphic above describes a physical model of a horizontal, hot-wall reactor for silicon epitaxy. This relatively simple 2D case study was taken from the literature solely to show SC Solutions’ modeling capabilities.
Hot Wall Epitaxial Reactor
Two-dimensional Reactor-scale Transport Model
Figure 1 shows the geometry used in the 2-D model obtained from Habuka et al [1]. The end-to-end length of the radiantly-heated chamber is 0.705 m and the total height is 0.4 m. The top part of the left wall and the entire right wall are at 300 K, and the sections of the top and the bottom wall immediately above the susceptor are at specified temperatures. The rest of the walls are adiabatic. The flow enters at atmospheric pressure from the top left corner of the chamber, and exits from the bottom right corner. The 8" wafer is located at the center of the 12" susceptor, 0.205 m from the left end of the chamber.
Figure 1. Schematic of a two-dimensional horizontal CVD
reactor [1]. The figure is not to scale. Shaded walls are adiabatic. The part of
the walls next to the IR heaters are semi-transparent and at elevated
temperatures.
A gaseous mixture, consisting of trichlorosilane (SiHCl3, nominal mass fraction=0.71) and hydrogen, is injected into the chamber at room temperature (300K) and a velocity of 0.67 m/s. The wafer temperature is isothermally elevated to a nominal value of 1423K. The temperatures of the hot sections of the top and bottom walls, Twall, were measured by Habuka et al [1], and expressed as the following linear function of the susceptor temperature, Tsus:
Twall = 730 + (770-730)(Tsus-1393)/(1453-1393) For Tsus = 1423K, Twall = 750K. The other sections on the top and the bottom walls are kept at 300K. The susceptor (and hence, the wafer) temperatures are here assumed to be independently controlled to excellent uniformity.
Figure 2. Mesh for numerical solution using CFD-ACE. The 90 X 53 mesh (with 3399 cells or control volumes in all) is clustered near the walls and near regions of high temperature gradients at the edges of the wafer. For clarity, the vertical dimensions are magnified five times the horizontal dimensions.
Figure 2 shows the mesh generated for the control-volume solution. The solution converged after 600 iterations in about half-an-hour on a Pentium PC. Figure 3 shows the velocity vectors with superposed temperatures for nominal conditions (trichlor mass fraction of 0.71, wafer temperature of 1423K, and top and bottom quartz wall temperatures of 750K). The gas is heated up considerably by the susceptor and the wall, and speeds up along the wafer surface. Figure 4 shows comparison of deposition rate uniformity with Habuka et al [1]. Figure 5 shows that wafer rotation significantly improves deposition uniformity, assuming that the rotation period is much smaller than the deposition period (which is almost always the case). The CFD-ACE results compares quite well with those Habuka et al [1], the average deposition rate difference being about 10%.
Figure 3. Gas velocity vectors with superposed temperature.
Figure 4. Deposition profile along flow direction. Comparison
with Habuka, et al [1].
Figure 5. Effect of wafer rotation on deposition rate
uniformity.
The deposition rates were calculated by varying the trichlor mass fraction. The results are plotted in Figure 6. These results agree well with Habuka’s experimental data. The slight over-prediction of the deposition rate may be attributed be due to two possible causes. First, the temperatures at the adiabatic parts of the wall are relatively high, and in reality, there is probably some deposition on the walls leading to reactant depletion downstream. Second, there is always a small amount of HCL etching of deposited silicon that reduces the overall deposition rate.
Figure 6. Average deposition rate as function of average molecular weight of gas at inlet. Nominal molecular weight is 6.67 kg/kg-mole (when trichlor mass fraction = 0.71).
Several tests were carried out on the model to establish convergence on the basis of mesh refinement and number of iterations needed. The results are shown in Figure 7.
Figure 7. Convergence study using deposition rates and gas temperatures.
We find that reducing iterations from 5000 to 1000 results in an average difference of 0.5% in the deposition rate. Based on this result, it is arbitrarily decided that for this geometry, 1500 iterations are sufficient. Reducing the number of cells from 3399 to 1381 changed the average deposition rate by 0.8%, and the average horizontal centerline temperature by 0.7%. Hence, 1381 cells are deemed sufficient. It is also noted that the time per iteration rises non-linearly for more refined mesh, which is to be expected from this solver.
References
[1] M. Habuka, Katayama, M. Shimda, K. Okuyama, "Numerical Evaluation of
ON Silicon Thin Growth from SiHCl3-H2 Gas Mixture in a
Horizontal Chemical
Vapor Deposition Reactor," Jpn. J. Appl. Phys., 1994.
33: p.1977-1985.