Density of states in quantum well, quantum wire and quantum dot structure

DENSITY OF STATES IN QUANTUM WELL, QUANTUM WIRE AND QUANTUM DOT STRUCTURE

Bulk Structure

The density of state of a bulk material is given by

where, E_c - 'bottom of conduction band energy

m* - effective mass of electron

The density of state curve is parabolic as shown in fig. 5.7(a).

Quantum Well Structure

In quantum well structure, the electrons can move freely in two directions (2D) and confined in only one direction. The density of state of the quantum well structure

The density of state function is constant and it gives step like function with energy as shown in fig. 5.7 (b).

Quantum Wire Structure

The quantum wire structure provides only one non confinement direction, ie., the carrier can move freely along one direction (1D). The remaining two directions are confined for charge carrier.

The density of states of quantum wire is proportional to 1/√E. The density of state for this structure is given as

The density of states function with energy is as shown in fig. 5.7(c).

Quantum dot

In quantum dot all the directions are confined and no direction (OD) in which electron movement is free. The density of state for this structure is given by

Z (E) = δ (E - E_i), i = 1, 2, 3

For quantum dot (OD) or nano particle, the permitted energy values are not continuous but form discrete bunches of varying densities. Thus, density of energy levels appear as discrete line as in fig. 5.7(d).

Table 5.2 gives different quantum structures and their corresponding density of state functions.

Table 5.2

Density of states as a function of dimensionality of the structure