
100 Nanosensors: Physical, Chemical, and Biological
giving
v
qE
m i m
0
0
=
−
e e
Γ ω
(2.12)
The resulting electric current is
j qnv=
(2.13)
where n is the number of electrons per unit volume. In terms of the peak
value j
0
, the electric current is expressed as
j j i t= −
0
exp( )ω
(2.14)
where
j qnv
q n
m i m
0 0
2
0
0
= =
−
=
E
E
e e
Γ ω
σ ω( )
(2.15)
Here σ(ω) is the conductivity of the metal and Equation 2.15 expresses the
Joule’s law. Equations 2.7 and 2.15 are combined together to relate the dielec-
tric constant ε(ω) in terms of known constants ε(∞), n, q, m
e
, ε
0
, frequency ω,
and damping constant Γ as (Moores and Floch 2009):
ε ω ε
ω
ω ω
ε
ω
ω
ω
ω ω
( )
( )
= −
+
= −
+
+
+