a) Calculate the polarization of a BaTi03 crystal (See the following Fig.). The structure transforms from cubic to tetragonal below the Curie point with lattice parameters c and conductivity to 4.06A and 3.97 A respectively. The displacement of titanium ion is opposite to that of oxygen ions. The magnitude of displacement is 0.06 A for titanium, 0.06 A for oxygen ions on the side faces and 0.08 A for oxygen ions on the top and bottom faces of the cube. The displacement of barium ions may be neglected.

21 0

Get full Expert solution in seconds

$1.97 ONLY

Unlock Answer

Question:

a) Calculate the polarization of a BaTi03 crystal (See the following Fig.). The structure transforms from cubic to tetragonal below the Curie point with lattice parameters c and conductivity to 4.06A and 3.97 A respectively. The displacement of titanium ion is opposite to that of oxygen ions. The magnitude of displacement is 0.06 A for titanium, 0.06 A for oxygen ions on the side faces and 0.08 A for oxygen ions on the top and bottom faces of the cube. The displacement of barium ions may be neglected.

b) Show a typical variation of conductivity with temperature for an extrinsic semiconductor and explain the different regions.

c) What is piezoelectricity?

EXPERT ANSWER

a) Below the curie temperature the Barium titanate shifts to tetragonal structure, i.e ina unit cell, the oxygen atoms at the top and bottom moves down by 0.08nm, the four oxygen atoms at the side moves by 0.06nm and the Ti moves up by 0.06nm

Therefore the total polarisation per unit cell is,

Here we have plotted conductivity in logarithmic scale v/s 1/T. There are three regions in this graph.

At zero kelvin there are no carriers as there are no thermal generation and contribution from donors. Therefore the material acts as insulator.

As the temperature increases (as we go from right to left in the graph), i.e, at low temperatures the electron contribution due to ionised donors is more compared to that of thermally generated electrons and as the temperature increases it reaches a point where all the donors are completely ionised.

Further increase in temperature will not increase the conductivity as the carrier contribution solely depends on amount of doping. This region is called as extrinsic region. We want the device to work in this region as there is no much fluctuation in conductivity.

At higher temperatures we have an intrinsic region where thethermally generated electrons dominates the carrier generation process.

c)

Piezoelectricity is the property of the material, when subjected to mechanical stress, generates an electical potential across it.The potential generated is proportional to the stress applied. This property is called as piezoelectric effect.

A piezoelectric material converts pressure energy into electricity.

Eg. Gas lighter. When pressure is applied to click the lighter ON, it produces a spark.