UNIVERSITY OF CALIFORNIA SANTA BARBARA DEPARTMENT OF CHEMICAL ENGINEERING

CHE 142 and ChE 242: Microelectronics Processing

Spring 2003 Homework # 4 (Due May 14, 2003)

Problem #1

Consider the deposition of material A on a solid surface (substrate) from decomposition of gaseous reactant AB via the overall reaction

AB(g) → A(s) + B(g).

The reactant, AB, is fed into the reactor diluted in an inert gas. The reactant gas flows over the surface and a stagnant layer with thickness δ forms above the substrate as shown in Figure l. The boundary layer thickness, δ, is inversely proportional to the square root of the gas flow rate Q. In a series of experiments, deposition rate as a function of substrate temperature, T, was determined to vary as shown in Figure 2. There are two different hypotheses for the deposition mechanism. Your objective is to determine which deposition mechanism is consistent with the data in Figure 2. I will lead you to the answer through a series of questions.

Both hypotheses agree that the important reactions do not occur until AB enters the stagnant layer, but they differ in where the decomposition occurs.

Hypothesis 1

There are no gas phase reactions. AB diffuses through the stagnant film and decomposes on the substrate surface to yield A via the reaction

AB

sk→ A + B.

The reaction rate is given by R = ks CAB

where ks is the surface reaction rate constant (e.g., in cm/s) and CAB is the AB concentration (e.g., in mole/cm3) immediately above the surface.

Hypothesis 2 AB decomposes in the gas phase via the reaction

AB gk→ A + B.

The reaction rate is given by

R = kg CAB

where kg is the gas phase reaction rate constant (e.g., in s-1) and CAB is the AB bulk phase concentration (e.g., in mole/cm3). A diffuses to the surface and reacts infinitely fast to deposit A. Flux of AB at the surface is zero.

Questions:

Assume that the reactor is isothermal. Assume that the diffusion coefficients of all the species are the same

1) Without solving any equations, using the data on Figure 2 what can you say about the deposition rate limiting step? Explain your answer briefly.

For questions 2-4 assume hypothesis 1 is correct.

2) Using the mechanism in hypothesis 1 write down the governing differential equation for AB concentration in the boundary layer and the appropriate boundary conditions, assuming steady state conditions.

3) Solve the equation in (2) to show that the deposition rate (e.g., flux of AB to the surface in moles cm-2 s-1) is given by

F = ( )1ABD Cφ δ

∞

+ where AB

s

Dk

φδ

= ,

C∞ is the AB concentration at the boundary layer edge and DAB is the diffusion coefficient of AB in the inert gas. What is the physical significance of φ?

4) From the data in Figure 2 and using the result from (3), what can you say about the magnitude of φ for T < To, T > To and T ≈ To?

For questions 5-7 assume that hypothesis 2 is correct.

5) Assuming steady state conditions, write down the governing differential equations for A and AB concentrations in the boundary layer and the appropriate boundary conditions.

6) Without solving the equations sketch A and AB concentrations in the boundary layer. Outline the steps you need to go through to solve the equations in (5).

7) If you were to integrate the equations in (6) you would find that the deposition rate is given by

F = ( )( )1 sech DaABD Cδ

∞ − where 2

Da g

AB

kD

δ= .

What is the physical significance of Da?

8) Based on the experimental data in Figure 2 comment on the probability of hypothesis 1 and/or 2 being correct. Explain your reasoning. (Recall that sech x = 1/cosh x and cosh x ≈ l+ x2/2! ....).

Problem #2 Consider an LPCVD reactor used to deposit polysilicon films operated under the following conditions: Pressure = 0.5 Torr Temperature = 623 oC Wafer diameter = 5 cm Reactor Diameter = 10 cm Wafer thickness = 0.05 cm Number of wafers = 25 Gas flow rate and composition = 1000 sccm (3% SiH4 in H2) Viscosity = 0.035 cp at reactor conditions. Consider that an engineer has collected the following data and your job is to design a reactor for 30 cm diameter wafers. Without solving any differential equations answer the following questions but be as quantitative as you can be.

1) What is the mean free path of the hydrogen molecules assuming that they collide with each other most of the time? Collision cross section for H2 is 0.27 nm2. Is the continuum assumption valid?

2) Is the flow in the annular space laminar or turbulent? 3) Using the attached data and assuming that the deposition is first order in SiH4 concentration

estimate the sticking coefficient of SiH4. What is the first order surface reaction rate constant, k?

4) Using the attached data estimate the diffusion coefficient of SiH4 in H2.

For questions 5-8, suppose that the reactor was being operated with wafer spacing of 3 cm and that there were 25 wafers loaded into the reactor.

5) What is the pressure drop from the first wafer to the last? 6) What process controls (i.e., slowest) the transport and reactions of reactants along the length of

the reactor? What about in between the wafers? Calculate the relevant dimensionless numbers and explain physically the important processes based on these numbers.

7) Do you expect good wafer-to-wafer uniformity? Propose two or three methods to improve wafer-to-wafer uniformity.

8) Would you expect uniform film growth on individual wafers? Would this depend on where the wafer is located in the reactor?

9) Based on the above analysis and data, design (i.e., suggest dimensions and wafer spacing) for a reactor that needs to handle 30 cm diameter wafers while keeping the throughput approximately constant. Would you change operating pressure and flow rate of gases? How and why?

In figure with data labeled A assume that the the reactor was operated such that there was only a few wafers in the reactor separated far apart. In B, the wafer spacing was 0.15 inches.