TimeDomain CVD, Inc.
Along the Tube
How do gases move around within a tube reactor? How is heat transported? To get some ideas, we'll perform a simplified transport analysis: rough estimates of the relevant velocities and characteristic times for the system. We'll consider a typical geometry and conditions for processing e.g. 150 mm diameter wafers, e.g. for deposition of polysilicon.
We assume as usual that the gases are ideal, with transport properties close to those of nitrogen. In this case, we take into account thermal expansion of the gases as they enter the reactor tube. To start with, let's examine transport of gases through the tube; we correct the tube cross-sectional area for for the wafer area, assuming negligible flow between the wafers.
What do these results tell us?
Let's look at some plausible values for a polysilicon process running in the tube reactor above.
That is, 70% of the silane put into the reactor is consumed! This is a starved reactor. Depletion along the tube is very important. The diffusion length is comparable to the tube length, so axial diffusion has a modest but beneficial effect on axial uniformity.
Improvements in axial uniformity can be achieved by:
Between the Wafers
Convective flow between the wafers will be essentially negligible if the spacing is much less than the radius, which is normally the case. (As we've seen, convection plays little role in transport over small distances anyway.) Thus transport of reactants in the space between the wafers is essentially due to diffusion only.
Since this is a CVD process whose purpose is to deposit a film on the wafers, it may also be assumed that the precursor is consumed on the wafer surfaces. Therefore transport between the wafers is described as simultaneous diffusion and consumption: Thiele diffusion. Recall that the solutions in the linear case are exponentials with a characteristic length:
where Ks is the surface reaction rate constant. (In cylindrically symmetric geometries, the solutions will be modified Bessel function Io; these functions behave much like exponentials and don't change the qualitative conclusions.) If the Thiele length is much longer than the wafer radius, the concentration of the precursor will change little with radius and the film thickness will be fairly uniform along the radius of the wafer. In the other extreme film deposition will occur only on the outer ring of the wafer, for a distance roughly equal to Lth.
Let's consider a numerical example: for a typical polysilicon deposition process operating at the parameters shown above, a reasonable value of the reaction constant might be about Ks = 0.12 cm/second. Then for a 3 mm wafer spacing, Lth is about (1740*0.3/0.12)^1/2 = 66 cm. The modified Bessel function Io is approximately (1+0.25x^2) for small x=(r/Lth). Thus for a 150 mm wafer, r=7.5, x=7.5/66 = 0.11, and Io -1 = 0.003, i.e. about 0.3% variation in thickness to the wafer edge. A process running under these conditions is quite uniform. We can also see that if we increased the pressure to e.g. 5 Torr with the same molar flow and absolute silane concentration (i.e. reduced silane mole fraction), the Thiele length would increase about 3-fold, and a much larger variation (about 3%) in thickness would result.
[reference: T. Badgwell et al J. Electrochem Soc 139 p. 524 (1992) ]
Since Lth controls the film uniformity, we can improve film uniformity by:
We should note that more complex situations can arise in practice, in which deposition may depend on gas phase reactions taking place between the wafers, or be inhibited by reaction products. In such cases, the wafers are frequently enclosed in a "cage" of quartz with perforations, the size of which is empirically adjusted for optimal uniformity.
For a more detailed discussion consult "Fundamental Conceptions Modeling the Thickness Distribution of (LPCVD) Deposited Films on Wafers and within Narrow Trenches" , J. Schlote, K. Schröder, and K. Drescher , J. Electrochem. Soc. 138 p. 2393 (1991).