Introduction to Nanotechnology

1 meV
10 meV
100 meV
FJ
E
W
1 eV
10 eV
Positronium
Hydrogen
n=5
n=5 - n=4
n=4 - n=3
n=3
n=2
n=2
n=l
n=l
2.3. LOCALIZED PARTICLES 33
n=4
n=3
n=2
n=l
Exciton
Figure 2.20. First few energy levels in the Rydberg series of a hydrogen atom (left), positronium
(center), and a typical exciton (right).
Table B.ll that the relative dielectric constant &/EO has the range of values
7.2 < &/eO < 17.7 for these materials, where c0 is the dielectric constant of free
space. Both of these factors have the effect of decreasing the exciton energy E,, from
that of positronium, and as a result this energy is given by
1 3.6m*/mo
E,, = - m*/mo e’ - eV
(&/Eo)’ 4n&oaon2 - (&/&o)’n’
(2.18)
as shown plotted in Fig. 2.20. These same two factors also increase the effective
Bohr radius of the electron orbit, and it becomes
(2.19)