Constant-Source Diffusion

 

 

Fig 2 Constant-source diffusion results in a complementary error function impurity distribution. The surface concentration N0 remains constant and the diffusion moves deeper into the silicon wafer as the Dt product increases. Dt can change as a result of increasing diffusion time, increasing diffusion temperature, or a combination of both. [1]

 

A constant-source diffusion or constant surface concentration or solid solubility limited predeposition / diffusion results in a complementary error function impurity distribution. The surface concentration N0 remains constant and the diffusion moves deeper into the silicon wafer as Dt product increases. Dt can change as a result of increasing diffusion time, increasing diffusion temperature, or a combination of both.

 

Initial Condition:

 

At time t=0, impurity concentration at depth x and time t, that is, N(x,t) is given by,

 

N (x, 0) = 0

 

Boundary Conditions:

 

At surface we have N(0,t) = N0 and N(,t) = 0 for x=

 

The solution of Fick's second law that satisfies the initial and boundary conditions is given by

 

 

Where N0 is the surface concentration (atoms/cm2)

D is constant diffusivity in cm2/s

x is the distance in cm

t is the diffusion time in seconds

 

The table below gives some values of z= x/2(Dt)1/2 and erfc(z)

z

erfc(z)

0

1.0

0.5

0.5

1.0

1.7

1.5

0.35

2.0

0.005

2.5

0.0004

3.0

0.00002

0