Question

(a) The crystal structures of Si is shown below. The side length of the unit cell is 0.54 nm. (1) Based on the structure of this unit cell, calculate the number of atoms in 1 cm3 of silicon. (ii) Explain qualitatively what you would expect to happen to the dimensions of this unit cell if the temperature should increase ? (ii) 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

i) According to the structure given,

Length of one side, a = 0.54nm

Number of atoms in given volume = 18

So, the number of atoms in 1nm³ = 1³ / (0.54)³ x 18 = 114

Number of Si atoms in 1cm³ of silicon = (1e+7)³ / (0.54)³ x 18 = 1.143e+23

ii) The Si atoms are very sensitive to temperature. While increasing temperature the bond between atoms become loose and starts moving apart each other. So the volume of the cell increases lightly

iii) Increases in temperature reduces the bond energy and thus the band gap of a semiconductor. In Silicon, increase in temperaure tends to increase the energy level of electrons and decreases bond energy. Therefore increasing the temperature reduces the band gap.

iv) While increasing the temperature of Silicon cell, the carrier concentration also changed due to the increase in energy level of electrons. The number of free electrons increses with increase in temperature.