Page 63 - Multifunctional Photocatalytic Materials for Energy

52 Multifunctional Photocatalytic Materials for Energy

E
CB
CB
Phonon Direct
Direct transition Absorption coefficient/α
Indirect In-direct

VB k
0.0 0.1 0.2 0.3 0.4 0.5
(A) (B) (E ph –E )/eV
g
Fig. 4.2 (A) Band energy level alignment and optical transitions, and (B) wavelength-
dependent light absorption coefficient α for direct and indirect band gap semiconductors,
respectively.

between them is the alignment of VB/CB in the Brillouin zone, as shown in Fig. 4.2A.
If the VB and the CB align with the same K-vector, that is called direct band gap
semiconductor. Otherwise, it is an indirect band gap semiconductor. In the former, an
electron can be directly excited to the CB and then decay by directly emitting a pho-
ton. Whereas in the latter, such excitation and emission processes must pass through
an intermediate state and transfer momentum to the crystal lattice, which requires the
assistance of a phonon transition [19–21].
Such a difference in electronic structure leads to completely different light absorp-
tion for direct and indirect band gap semiconductors (Fig. 4.2B). For a direct band gap
transition, the light absorption coefficient is given as
(
a ~ E - ) / 12 (4.4)
E
g
ph
whereas for an indirect band gap transitions, it is given as
(
a ~ E - ) 2 (4.5)
E
g
ph
where E g is the band gap, and E ph is the photon energy. For a comparison, as shown
in Fig. 4.2B, the absorption coefficient is considerably smaller for indirect band
gap semiconductors. As a result, light with a photon energy close to the band gap
can penetrate much farther before being absorbed in an indirect band gap semi-
conductor than in a direct band gap one. Based on the light intensity decay trend
(Eq. 4.3), an indirect band gap semiconductor needs a much thicker film to absorb
more light than a direct band gap one, which theoretically can absorb most of the
light within a small range beneath the surface [19,22]. Consequently, the charge
carriers generated deep in an indirect semiconductor with a short charge diffusion
length have a high risk of recombining before they reach the surface [6]. This fact
is very important in designing solar energy devices like photovoltaics and photo-
electrochemical solar cells.