The chemical vapor deposition of silane vapor (SiH₄) forms a thin film of solid silicon as described in example 1, Chapter 25. Consider that the simplified CVD unit shown in Figure 25.5 is operating at 900 K and with a very-low-pressure total system pressure of 70 Pa. The diffusion path length (δ) is 5.0 cm, and the silane feed gas diluted in H₂gas to a 

composition of 20 mole% silane. The Lennard€“Jones para meters for SiH₄ are σ_A = 4.08A and ϵA/k  = 207.6 K. 

a. Recall from example 1, Chapter 25 that the steady-state molecular diffusion flux of silane vapor (species A) down to the silicon wafer is 

where y_Ao is the mole fraction of silane in the bulk gas, and y_As is the mole fraction of silane vapor at the surface of the wafer. Assume that surface reaction is instantaneous, so that the rate of silane decomposition to solid silicon is controlled by the molecular diffusion of silane to the silicon surface (e.g., Y_As ‰ˆ 0). Estimate the rate of Si film formation in units of microns (µm) of Si solid film thickness per minute. The density of crystalline silicon is 2.32 g/cm³. 

b. Now consider that the surface reaction is not instantaneous, so that Y_As > 0. The simplified rate equation is given by 

N_A|_z=δ = + k_s C_As

where the (+) sign indicates that the direction of flux for species A is in the same direction as increasing z. At 900 K, ks = 1.25 cm/s. using data provided by Middleman and Hochberg (1993).* Develop a revised model for the flux NA, which does not contain the y term, using the approximation ln( 1 + y) =̇ y. From this model, estimate the rate of Si film formation, and then compare the result to part (a) above. Comment on the importance of diffusion versus surface reaction in determining the silicon thin film formation rate. 

Figure 25.5

Transcribed Image Text:

(1+YAo 1+ YAs c DAB In NA,Z SiH, vapor + H2 gas Diffuser ·Z = 0 SiH,(g) H,(g) Solid Si Quiescent thin film gas -Z = 8 Heated plate SiH, (g) Si (s) + 2 H2 (g) 4.