Energy band structure

Question 1

What is the notation of Schrodinger’s wave equation?

Answer 1

look at notes

Question 2

What does each term of the Schrodinger wave equation represent?

Answer 2

On the left, the first term represents kinetic energy, the second is potential energy, and the function enveloping it is the wave function

Question 3

Why is Schrodinger’s wave function periodic?

Answer 3

Since the crystal structure is periodic, the potential energy is also periodic, therefore the wave function is also periodic

Question 4

What does each part of the Schrodinger wavefunction represent? (look at notes)

Answer 4

The wavefunction’s exponential term is a sine or cosine wave, and the u(r) affects its amplitude

Question 5

What is a wavevector?

Answer 5

indicates the direction and magnitude of a wave’s transmission

Question 6

What does the direction and magnitude of a wavevector refer to?

Answer 6

The direction refers to the direction of travel, and the magnitude relates to the wave’s frequency and wavelength

Question 7

What is a Brillouin zone?

Answer 7

The Brillouin zone of a crystal represents the unit cell.

The boundaries of the unit cell can be represented by wave vectors centered at the centre of the cube (eg [1,0,0], [1,1,0])

Question 8

What is an advanced way of representing an energy band diagram?

Answer 8

The energy band diagram can be represented as energy vs k-vectors in the unit cell

Question 9

How are the forbidden region, conduction and valence bands identified in a E vs k diagram?

Answer 9

The forbidden region is a horizontal strip where no energy lies

Above the forbidden region is the conduction band, and below is the valence band