Scaling and Universality of Roughening in Thermal Oxidation of Si(001)

By analyzing atomic force microscopy images, we derive a continuum equation that quantitatively explains the roughening at the $\mathrm{Si}(001)\mathrm{\text{−}}{\mathrm{SiO}}_2$ interface during thermal oxidation at the temperature at 1200 °C in an Ar atmosphere containing a small fraction of ${\mathrm{O}}_2$. We also show that there is a phase transition in the universality class from a disordered to step-terrace structure at the interface at oxidation temperatures between 1150 and 1380 °C with the miscut angle of the substrate as the scaling parameter.

Figure 1

AFM images of the Si(001) surface after annealing for (a) 1.0 and (b) 6 h at 1200 °C followed by chemical etching. The image size is $2\mu \mathrm{m}$ by $2\mu \mathrm{m}$. The full topographic scale, 5.0 nm, is shown.

Figure 2

Root mean square roughness, $W(L,t)$, vs length scale; (a) and (b) were determined from the AFM images in Figs. 1a, 1b, respectively. (c) and (d) PSD curves were obtained from AFM images in Figs. 1a, 1b, respectively.

Figure 3

Log-log plots of $W(L,t)$ vs oxidation time. The slope of the solid line is $\beta =0.23\pm 0.02$. Thermal silicon oxidations were performed in 0.20% ${\mathrm{O}}_2$–99.80% Ar atmosphere at 1200 °C.

Figure 4

Plots of interface structure as a function of mean terrace width with various miscut angles and thermal silicon oxidation temperatures. Solid circles and open squares represent step-terrace and disordered structures at the interface, respectively. Some plots for the 0.5° miscut Si (001) are derived from Ref. 10.