Growth and physical properties of crystalline rubrene - BOA Bicocca ...

3.2 Sample characterization 39
Figure 3.9: AFM tapping mode images of a 3 × 3 µm 2 region of the surface of a
sample consisting of a rubrene thin film grown on top of a quatertiophene thin film.
(a) Height image. (b) Phase contrast image collected at the same time as (a).
order to minimize the tip-sample electrostatic interaction. The resulting
voltage between the tip and the sample then is:
∆V = ∆ϕ − Vdc + Vac sin(ωt) (3.3)
where ∆ϕ is the work function difference (or contact potential difference)
between the tip and the sample, Vdc is the DC potential applied to the tip
and ω is the frequency of the applied Vac bias. If the tip-sample distance is
smaller than the tip radius, then the tip-sample system can be considered as
a parallel plate capacitor whose energy U is given by
U = 1 2
C∆V
2
where C is the capacitance of the tip-sample system.
(3.4)
The electrostatic force between the tip and the sample is then given by
F = − ∂U
∂z
∂C
= −1
2 ∂z ∆V 2 = Fdc + Fω + F2ω
where the three components of the force are
Fdc = − 1
∂C
(∆ϕ − Vdc)
2 ∂z
2 +
V 2
ac
2
(3.5)
(3.6)