SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

(Greg DeLong) #1
76 CHAPTER 2. ELECTRONIC LEVELS IN SEMICONDUCTORS


E 2

E 1

V(z)



∞ ∞


quantum well


Valence band


POSITIONz


Conduction band


quantum well


E


NERGY

Barrier material
Well
material

W


V 0


Barrier material


Figure 2.32: A schematic of a quantum well formed for the electron and holes in a heterostruc-
ture.


These equations can be solved numerically. The solutions give the energy levelsE 1 ,E 2 ,E 3
...and the wavefunctions,f 1 (z),f 2 (z),f 3 (z),···.
Each levelE 1 ,E 2 , etc., is actually a subband due to the electron energy in thex–yplane. As
shown in figure 2.33 we have a series of subbands in the conduction and valence band. In the
valence band we have a subband series originating from heavy holes and another one originating
from light holes.
The subband structure has important consequences for the optical and transport properties of
heterostructures. An important manifestation of this subband structure is the density of states
of the electronic bands. The density of states figures importantly in both electrical and optical
properties of any system. In Section 2.3 we have discussed how dimensionality alters the density
of states.

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