Chapter 5, Problem 5.50P

5.50.19 In chemical vapor deposition (CVD), a semiconducting or insulating solid material is formed in a reaction between a gaseous species and a species adsorbed on the surface of silicon wafers (disks about 10 cm in diameter and l mm thick). The coated wafers are subjected to further processing to produce the microelectronic chips in computers and most other electronic devices in use today.

In one such process, silicon dioxide (MW = 60.06, SG = 2.67) is formed in the reaction between gaseous dichlorosilane (DCS) and adsorbed nitrous oxide:

   ${\text{SiH}}_{\text{2}}{\text{Cl}}_{\text{2}}\left(\text{g}\right){\text{+2N}}_{\text{2}}\text{O}\left(\text{ads}\right)\to {\text{SiO}}_{\text{2}}\left(\text{s}\right){\text{+2N}}_{\text{2}}\left(\text{g}\right)\text{+2HCl}\left(\text{g}\right)$

A mixture of DCS and N₂O ?ows through a “boat reactor"—a horizontal pipe in which 50 to 100 silicon wafers about 12 cm in diameter and 1 mm thick are set upright along the reactor length, with about 20 mm separation between each wafer. A side view of the reactor is shown below:

The feed gas enters the reactor at a rate of 3.74 SCMM (standard cubic meters per minute) and contains 22.0 mole% DCS and the balance N₂O. In the reactor, the gas ?ows around the wafers, DCS and N₂O diffuse into the spaces between the wafers, N₂O is adsorbed on the wafer surfaces, and the adsorbed N₂O reacts with gaseous DCS. The silicon dioxide formed remains on the surface, and the nitrogen and hydrogen chloride go into the gas phase and eventually leave the reactor with the unconsumed reactants. The temperature and absolute pressure in the reactor are constant at 900°C and 604 millitorr.

(a) The percentage conversion of DCS at a certain axial position (distance along the length of the reactor) is 60%. Calculate the volumetric ?ow rate (m³/min) of gas at this axial position.

(b) The rate of deposition of silicon dioxide per unit area of wafer surface is given by the formula

   $r\left(\frac{\text{mol}{\text{SiO}}_{\text{2}}}{{\text{m}}^{\text{2}}\cdot \text{s}}\right)\text{=3}{\text{.16×10}}^{\text{-8}}{p}_{\text{DCS}}{p}_{{\text{N}}_{\text{2}}\text{O}}^{\text{0}\text{.65}}$

where $p_{\text{DCS}}$and $p_{{\text{N}}_{\text{2}}\text{O}}$are the partial pressures of DCS and N₂O in millitorr. What is r at the axial position in the reactor where the DCS conversion is 60%?

(c) Consider a wafer located at the axial position determined in Part (b). How thick is the silicon dioxide layer on that wafer after two hours of reactor operation, assuming that gas diffusion is rapid enough at the low reactor pressure for the composition of the gas (and hence the component partial pressures) to be uniform over the wafer surface? Express your answer in angstroms, where $1\text{A}$

˙ = 1.0 × 10 − 10 m . (Hint: You can calculate the rate of growth of the SiO₂layer in $\text{A <mo> ˙ </mo>}$from r and properties of SiO₂given in the problem statement.) Would the thickness be greater or less than this value at an axial position closer to the reactor entrance? Brie?y explain your answer.