The number of silicon atoms per m3is 5 × 1028. This is dopedsimultaneously with 5 × 1022 atoms per m3of Arsenic and 5 × 1020per m3atoms of Indium. Calculate the number of electrons and holes.Given that ni= 1.5 × 1016 m–3. Is the material n-type or p-type?
Number of silicon atoms, N S = 5 × 10 28 atoms/m 3 .
It is doped with arsenic and indium. Number of arsenic atoms, N As = 5 × 10 22 atoms/m 3 .
Number of indium atoms, N In = 5 × 10 22 atoms/m 3 .
It is given that the number of thermally generated electrons, n i = 1.5 × 10 20 atoms/m 3 .
The number of electrons in the semiconductor will be difference of the number of electrons in arsenic and number of thermally generated electrons.
n e = 5 × 10 22 − 1.5 × 10 16 = 10 22 ( 5 − 1.5 × 10 − 6 ) ≈ 4.99 × 10 22
Let n h be the number of holes in the semiconductor.
The relation between the number of holes and number of electrons in a semiconductor at thermal equilibrium is given by,
n e ⋅ n h = ( n i ) 2
Substitute the values in the above formula and find the value of number of holes.
n h = ( n i ) 2 n e = ( 1.5 × 10 16 ) 2 4.99 × 10 22 = 4.51 × 10 9
Thus, number of holes is 4.51 × 10 9 and number of electrons is 4.99 × 10 22 .
Since the number of electrons in the semiconductor is higher than the number of holes, the material is an n-type semiconductor.
Number of silicon atoms,
It is doped with arsenic and indium. Number of arsenic atoms,
Number of indium atoms,
It is given that the number of thermally generated electrons,
The number of electrons in the semiconductor will be difference of the number of electrons in arsenic and number of thermally generated electrons.
Let
The relation between the number of holes and number of electrons in a semiconductor at thermal equilibrium is given by,
Substitute the values in the above formula and find the value of number of holes.
Thus, number of holes is
Since the number of electrons in the semiconductor is higher than the number of holes, the material is an n-type semiconductor.
