
61Introduction to Nanosensors
f E
E
k T
( ) exp= +
⎛
⎝
⎜
⎞
⎠
⎟
⎧
⎨
⎩
⎫
⎬
⎭
−
1
1
B
(1.30)
Though the predominant tunneling current ow for negative sample voltage
−V is directed from sample to tip, there exists a smaller reverse tunneling
current of electrons from tip to sample. The governing equation for this cur-
rent is written in an identical manner. By summation of these currents, and
integration over all energies E, the total tunneling current from sample to tip
becomes
I
E F
A
E E qV
f E f E qV
E
total s t
F
= −
⎛
⎝
⎜
⎞
⎠
⎟
⎛
⎝
⎜
⎞
⎠
⎟
+
× − +
−
∞
∫
4
1
2
π
ρ ρ
( ) ( )
( ) ( )) ( ) ( )
{ }
− −
{ }
+
{ }
⎡
⎣
⎤
⎦
1 f E f E qV dE
(1.31)
This basic equation can be simplied by applying various ...