Arsenic diffusion in si: arsenic is diffused into a thick slice of silicon with no previous arsenic in it at 1100ºc. if the surface concentration of the arsenic is 5.0 × 1018 atoms/cm3 and its concentration at 1.2 µm below the silicon surface is 1.5 × 1016 atoms/cm3 , how long must be the diffusion time? (d = 3.0 × 10-14 cm2 /s for as diffusing in si at 1100ºc.)

Diffusion time is 7.42 h

Solution:

As per the question:

Temperature, T =

Surface concentration of arsenic,

Surface concentration below Silicon surface,

D =

x =

Initial concentration at t = 0,

Now, by using Flick's second eqn:

Thus by putting appropriate values:

             (1)

Now,

Now, from error function values tabulation:

For z = 2.0, erf(z) = 0.998

For z = 2.2, erf(z) = 0.995

Now,

With the help of linear interpolation method:

z = 2.12

Now, using eqn (1) and above value:

= 26700 s

t =

the chart show the masses and velocities of two colliding objects that stick together after a collision.

according to the law of conservation of momentum, the momentum of the object after the collision is  

answer

1,500

kg • m/s.