196
B. P. Majee and A. K. Mishra
of the surrounding medium. The second resonance term (
ω
2
FK − ω
2
+ γ
2
FK ) shows
the potential dependent and charge transfer resonance occurring at ω = ω FK . Third
resonance term (
ω
2
IK − ω
2
+ γ
2
IK ) represents the molecular resonance occurring at
ω = ω IK .[35] For further details on charge transfer study on metal–molecule system,
one can go through Ref. [23].
3.3.2 Semiconducting Substrate and Analyte Molecule
In semiconductor-molecule system, mainly three resonances contribute to the SERS
signal enhancement, which are exciton resonance, charge transfer and molecular
resonances [36]. The intensity of a Raman transition depends on the polarizability
tensor of the materials in the following formI =
8π (ω ± ω I I )
4 I L /9C
4
α
2
σρ
(11)
where I L is the intensity of laser at angular frequency ω and the molecular transition
frequency is ω I I between states I and I
. The term ‘α’ is the polarizability of the
molecule and the three directions in space (X, Y, Z) are represented by subscripts
σ and ρ. The polarizability (α) of the molecule is the sum of the three terms and
expressed asα σρ = A + B + C
(12)
Lombardi and Birke discussed the enhancement mechanism in semiconductormolecule system. The charge-transfer transitions moment μ I C represents the charge
transfer from HOMO level to the conduction band edge C of the semiconductor.
Similarly, transition moment μ V K represents the charge transfer transitions from
valence band edge V to the molecule LUMO level. The CT can borrow the intensity
either from the molecular transitions μ KI or from the excitation transitions μ VC . The
SERS intensity is proportional to |R|
2 and the A, B and C terms can be expressed as
follows [36]
A-Term: This term can be written as
R IC (ω) =
μ IC μ IC i|kk| f
(ε 1 (ω) + 2ε 0 )
2
+ ε
2
2 (ω)
ω
2
I C − ω 2
+ γ
2
IC
(13)
R VK (ω) =
μ VK μ VK i|kk| f
(ε 1 (ω) + 2ε 0 )
2
+ ε
2
2 (ω)
ω
2
VK − ω 2
+ γ
2
VK
(14)
where the real and imaginary parts of the permittivity of the materials are ε 1 and ε 2 .
The ε 0 is the permittivity of free space and γ is the damping factor. The first term in
both the equations in the denominator is the plasmon resonance term. The resonance
terms in the above equations can occur via charge transfer either from HOMO level
B. P. Majee and A. K. Mishra
of the surrounding medium. The second resonance term (
ω
2
FK − ω
2
+ γ
2
FK ) shows
the potential dependent and charge transfer resonance occurring at ω = ω FK . Third
resonance term (
ω
2
IK − ω
2
+ γ
2
IK ) represents the molecular resonance occurring at
ω = ω IK .[35] For further details on charge transfer study on metal–molecule system,
one can go through Ref. [23].
3.3.2 Semiconducting Substrate and Analyte Molecule
In semiconductor-molecule system, mainly three resonances contribute to the SERS
signal enhancement, which are exciton resonance, charge transfer and molecular
resonances [36]. The intensity of a Raman transition depends on the polarizability
tensor of the materials in the following formI =
8π (ω ± ω I I )
4 I L /9C
4
α
2
σρ
(11)
where I L is the intensity of laser at angular frequency ω and the molecular transition
frequency is ω I I between states I and I
. The term ‘α’ is the polarizability of the
molecule and the three directions in space (X, Y, Z) are represented by subscripts
σ and ρ. The polarizability (α) of the molecule is the sum of the three terms and
expressed asα σρ = A + B + C
(12)
Lombardi and Birke discussed the enhancement mechanism in semiconductormolecule system. The charge-transfer transitions moment μ I C represents the charge
transfer from HOMO level to the conduction band edge C of the semiconductor.
Similarly, transition moment μ V K represents the charge transfer transitions from
valence band edge V to the molecule LUMO level. The CT can borrow the intensity
either from the molecular transitions μ KI or from the excitation transitions μ VC . The
SERS intensity is proportional to |R|
2 and the A, B and C terms can be expressed as
follows [36]
A-Term: This term can be written as
R IC (ω) =
μ IC μ IC i|kk| f
(ε 1 (ω) + 2ε 0 )
2
+ ε
2
2 (ω)
ω
2
I C − ω 2
+ γ
2
IC
(13)
R VK (ω) =
μ VK μ VK i|kk| f
(ε 1 (ω) + 2ε 0 )
2
+ ε
2
2 (ω)
ω
2
VK − ω 2
+ γ
2
VK
(14)
where the real and imaginary parts of the permittivity of the materials are ε 1 and ε 2 .
The ε 0 is the permittivity of free space and γ is the damping factor. The first term in
both the equations in the denominator is the plasmon resonance term. The resonance
terms in the above equations can occur via charge transfer either from HOMO level