# Using VICTORY Process to Simulate Thermal Oxidation of Silicon at High Pressures of Ambient Gases

**Introduction**

Developing ULSI silicon technology requires good control of dopant diffusion and minimizing defect formation during thermal oxidation. The use of high pressures of ambient gases can have a significant impact on ability to meet such requirements [1]. In particular, high pressure steam (~10atm) allows the growth of oxide films of the order of 1 μm in less then 2.5 hours at temperature as low as 800 C. At such low temperatures dopant redistribution is substantially reduced.

This paper demonstrates the ability of VICTORY Process to accurately model the thermal oxidation of silicon at high pressures. The 3D process simulation software VICTORY Process uses the same physical model as one implemented in ATHENA (2D process simulator). The model is briefly outlined bellow. Numerical results are compared with the experimental ones [1] and the good agreement is demonstrated. If plane silicon is thermally oxidized, both Silvaco’s process simulators (VICTORY Process and ATHENA) give very close results. The paper shows that these results are also close to the results obtained by integration of the 1D kinetical equation obtained by DealGrove and Massoud [2,3]. These comparisons prove that the model is properly implemented in VICTORY Process and can be used to oxidize 3D structures at high pressures.

**Physical Model**

The main physical parameters that determine the kinetics of silicon oxidation are

- linear rate, B/A
- parabolic rate B
- Massoud rate R

These rates are normally measured and specified at pressure equal to 1 atm. To describe the pressure dependence of these parameters VICTORY Process and ATHENA use the relations suggested by R. Razouk, L. Lie and E. Deal [1]. According to their model, all three rates are multiplied by correspondent pressure factors such that the resulting rates become:

where index 1 denotes the terms taken at pressure equal to one atm., l.pdep ≈ p.dep ≈ thinox.p ≈ 1 being calibrating parameters. The resulting rates are used to calculate the microscopical parameters like diffusion and reaction coefficients which are used in 3D mathematical model [4].

**Numerical and Experimental Results**

Using the experimental results from [1] we obtained the following values for the linear and parabolic rates at T=900 C (dry) and P=1atm: (B/*A*)_{1} = 0.00462 μm/min and B_{1} = 0.00247 μm^2/min. The rates are assumed to obey the Arrhenius relations:

with the user specified parameters *lin.h.0, lin.l.e, par.h.0, par.l.e. *The powers describing the pressure dependence are taken as following: l.pdep = 0.8, p.dep=1, thinox.p=1. All other oxidation parameters (e.g. Massoud rate, siliconoxide expansion coefficient etc.) are equal to its default values specified in Silvaco’s material database (smdb). The described values are supplied using the deck command:

MATERIAL material=silicon dry02 lin.h.0 = 0.00462 lin.h.e = 0.0 l.pded = 0.8 \

par.h.0 = 0.00247 par.h.e = 0.0 p.pdep = 1 thinox.p = 1

Different times and pressures are set by using commands like :

DIFFUSE time=30 temperat=900 dry02 pressure=10

To compare our results with the experimental ones, we simulated oxidation of plane silicon at the conditions chosen in the experiment. Namely, at four different pressures (1, 5, 10, 20) atm., times being equal to (0.5, 1, 2, 3) hours. Experimental and numerical results are compared on the Figure 1.

Figure 1. Oxide thickness vs. oxidation time for silicon oxidized in dry oxygen at temperature of 900 C and at pressures of 1, 5, 10 and 20 atm. |

**VICTORY Process, ATHENA and Analytical Results
**

The 3D implementation of the highpressure oxidation model in VICTORY Process can be partly verified by comparing its results with the results obtained by ATHENA (2D) and with the results obtained by integration of the 1D Deal-Grove-Massoud equation:

with the initial condition x (t=0) =x0 and *x*_{0} being initial oxide thickness (20Å in our case). The 1D model uses the same values of oxidation rates. The results are plotted on the Figure 2. The figure demonstrates that for the oxidation of plane silicon the results are very close.

Figure 2. Oxide thickness vs. oxidation time for silicon oxidized in dry oxygen at temperature of 900 C at pressure of 1 and 10 atm. Comparison of the numerical results obtained using VICTORY Process, ATHENA and 1D integration of DealGroveMassoud equation. |

**Conclusion**

In this paper we demonstrated the ability of VICTORY Process to simulate thermal oxidation of silicon at high pressures in 3D.

**References**

- Reda R. Razouk, Liang N. Lie and Bruce E. Deal. Kinetics of High Pressure Oxidation of Silicon in Pyrogenic Steam J. Electrochem. Soc. : SolidState Science and Technology, vol. 128, no 10, pp.22142220, Oct 1981.
- B.E.Deal and A.S.Grove General Relationship for the Thermal Oxidation of Silicon Journal of Applied physics, vol. 36, no 12, Dec 1965.