Pre-deposition:

Pre-deposition is also known as constant source diffusion.

In IC processing a two-step diffusion process is commonly used in which pre-deposition diffused layer is first formed under the constant surface concentration condition.

Here surface concentration of dopant is always constant.

It is given by complementary error function.

$N(x,t)=N_0 erfc \frac{x}{2\sqrt{Dt}}$

Where,

N = volume concentration of dopant and it is assumed to be function of x and t.

x = direction in which movement of dopant atoms is taking.

D = diffusion coefficient

Total amount of impurity that has been introduced during diffusion is

$Q≅1.13 N_0 \sqrt{Dt}$

The longer the period of diffusion more impurity is being introduced.

Drive-in step:

Drive-in process is also known as limited source diffusion.

Here finite quantity of diffusing matter is first placed on the wafer.

Diffusion proceeds from this limited source & it is assumed that all of this matter is consumed during process.

Diffusion of this type is known as Gaussian profile.

As drive in progresses surface concentration decreases and dopants move further.

Gaussian distribution is given by –

$N(x,t)=\frac{Q}{\sqrt{πDt}} e^{-x⁄4Dt}$

For most practical cases the diffusion length $\sqrt{Dt}$ for pre-deposition diffusion is much smaller than the diffusion length for drive in diffusion.

Therefore, pre-deposition profile can be considered a delta function at surface 7 extent of the penetration of pre-deposition can be regarded as negligibly small compared to that of final profile that results from drive in.