Question

(a) If 5 x 10^17 phosphorus atoms per cm3 are add to silicon as a substitutional impurity, determine the percentage of silicon atoms per unit volume that are displaced in the single crystal lattice.

(b) Repeat part (a) for 2 x 10^15 boron atoms per cm3 added to silicon.

Answer 1

The percentage of silicon atoms per unit volume that are displaced in the single crystal lattice = 0.001 %

The percentage of silicon atoms per unit volume that are displaced in the single crystal lattice with boron atoms = 0.4 ×
`10^(-5)` %

Step-by-step explanation:

No. of phosphorus atoms = 5 ×
`10^(17) \ cm^(-3)`

The volume occupied by a single Si atom

`V_(si) = (a^(3) )/(8)`

`V_(si) = (5.43^(3)(10^(-8) )^(3) )/(8)`

`V_(si) =` 2 ×
`10^(-23)`
`(cm^(3) )/(atom)`

`n_(si) = (1)/(V_(si) )`

`n_(si)` = 5 ×
`10^(22)`
`(atoms)/(cm^(3) )`

`PCT = (N_p)/(N_(si)) 100`

Put the values in above equation we get

`PCT = (5 (10^(17) ))/(5 (10^(22)) ) 100`

PCT =
`10^(-3) = 0.001` %

These are the percentage of silicon atoms per unit volume that are displaced in the single crystal lattice.

(b).

No. of boron atoms = 2 ×
`10^(15) \ cm^(-3)`

The volume occupied by a single Si atom

`V_(si) = (a^(3) )/(8)`

`V_(si) = (5.43^(3)(10^(-8) )^(3) )/(8)`

`V_(si) =` 2 ×
`10^(-23)`
`(cm^(3) )/(atom)`

`n_(si) = (1)/(V_(si) )`

`n_(si)` = 5 ×
`10^(22)`
`(atoms)/(cm^(3) )`

`PCT = (N_p)/(N_(si)) 100`

Put the values in above equation we get

`PCT = (2 (10^(15) ))/(5 (10^(22)) ) 100`

PCT = 0.4 ×
`10^(-5)` %

These are the percentage of silicon atoms per unit volume that are displaced in the single crystal lattice.