Model Development Solution

Build a simple model for carbon diffusion in silicon. Use a constant diffusivity: Dc = 1.0 * exp(-3.5 / kT). Set the initial carbon profile to: Cc = 1.0e18 * exp(- (x-0.1)*(x-0.1) / 0.001 ) + 1.0e15

Part 1: Diffuse the profile for 60min. at  900, 30min. at 1000, and 10min. at 1100C. Does it agree with what you expect from a simple estimated hand calculation?

Part 2: Modify the model so the diffusivity it proportional to carbon concentration / 1e16 . Run the same anneals – what happens qualitatively? 

Results for Part 1:

At 900 Celsius for 60 mins:

At 1000 Celsius for 30 mins:

At 1100 Celsius for 10 mins:

Results for Part 2:

At 900 Celsius for 60 mins:

At 1000 Celsius for 30 mins:

At 1100 Celsius for 10 mins: