Flow in a CVD Reactor

Consider the laminar flow in a CVD reactor. The governing equation is 

The governing equation for U is then solved with the above boundary conditions to obtain the final solution. Example 4.9 is solved in Maple below  

Maple cannot find the limit as b—Alternatively, the governing equation is solved using the first boundary condition (bcl) only  

The solution is a combination of exponential and Whittaker functions. In the literature this problem is usually left in terms of integrals (Gamma functions). However, Maple is able to solve the differential equation explicitly. Next, the constant C2 is found using the boundary condition bc2. 

Since the limit does not exit, U/ C2 is plotted until r =10. 

---

CVD reactions are most often produced at ambient pressure in a freely flowing system. The gas flow, mixing, and stratification in the reactor chamber can be important to the deposition process. CVD can also be performed at low pressures (LPCVD) and in ultrahigh vacuum (UHVCVD) where the gas flow is molecular. The gas flow in a CVD reactor is very sensitive to reactor design, fixturing, substrate geometry, and the number of substrates in the reactor, ie, reactor loading. Flow uniformity is a particulady important deposition parameter in VPE and MOCVD. 

---