Question

(a) The crystal structures of Si is shown below. The side length of the unit cell is 0.54 nm. с (1) Based on the structure of this unit cell, calculate the number of atoms in 1 cm of silicon. (ii) Explain qualitatively what you would expect to happen to the dimensions of this unit cell if the temperature should increase ? (iii) How would such a temperature increase affect the bonding in the Si and how would this then affect that bandgap of Si ? (ii) How would such a temperature increase affect the bonding in the Si and how would this then affect that bandgap of Si ? (iv) Is your answer in (iii) consistent with the changes in carrier concentration expected in Si with increasing temperature ?

Answer 1

a) (i)

Number of atoms in the 1 cm3 of silicon is eaual to,

8 atoms at corners with 1/8 in each cell+6 atoms in face contributing 1/2 with each cell+4 atoms inside the cell=8(1+3+4)

So there are 8 atoms in 1 cm3 of this unit cell.

(ii)For an increase in temperature it is expected that the dimensions of the unit cell will increase. Because atoms will receive more energy and get excited.This will contribute to their atomic vibration. So for the increased temperature we can expect an increase in the unit cell dimensions.

(iii) As we know, bond strength is directly proportional to energy gap. So when temperature increases, atomic vibration increase in the unit cell. This can increase the inter atomic spaces. Now less energy is need for an electron to get in to conduction band. So energy band gap reduces.

So with the relation of band gap and bond strength, bond strength also get reduced.

(iv)With increase in temperature carrier concentration increases. With decrease of bond strength, intrinsic carrier concentration increases. If it was doped, then increase in temperature will produce no change in the concentration as dopant has been ionized.

So our answer in the third option is consistent with carrier concentration.