0
Q)
0
Table A.3. Number of electrons M E ) and density of states @ E ) = dN(E)/dE as a function of the energy E for
electrons delocalized/confined in quantum dots, quantum wires, quantum wells, and bulk material
a
Dimensions
Number
Density
Type
of Electrons N
of States D(E)
Delocalized
Confined
Dot
N ( E ) = 2Cdi0(E - EIW)
D(E) = 2Cdi8(E - Eiw)
0
3
Well
N ( E ) =
v 2m ' I 2
379 h2
Bulk
N ( E ) = - (-)
D(E) =- 2: 2 (:)'I2 - @)'I2
1
2
2
1
3
0
"The degeneracies of the confined (square or parabolic well) energy levels are given by d,. The Heaviside step function O(x) is zero for x < 0
and one for x z 0; the delta function 6(x) is zero for x # 0, infinity for x = 0, and integrates to a unit area.