Biomedical Engineering Reference
In-Depth Information
Table 4.2
Values of the Breakdown Voltage for Some Typical Materials
Material
Paraffin
Oil
Teflon
Glass
Mica
Critical electric filed EBD [MV/m
or V/
m
m]
10
15
59
100
197
Note that the values indicated here are given for perfect materials. Real values are usually less than that.
even destroys, its insulating capability. The detailed physical explanation of dielec-
tric breakdown is not the subject of this topic and is well documented in [22]. For
a dielectric of thickness
d
, the critical electric field
E
BD
is related to the dielectric
breakdown voltage
V
BD
by
(4.44)
V
=
d E
BD
BD
Indications of the value of the critical electric field are given in Table 4.2 for
some typical materials. In Section 4.2.2.4, we have developed the notion of sat-
uration potential. Typically saturation potentials are of the order of 80V for a
chip of capacitance
C
~ 2.2 10-
5
F/m
2
, obtained with a total dielectric/insulating
layer of approximately 1.5
m
m thickness. Thus the electric field at saturation is
of the order of 55 V/
m
m. This value is just below the breakdown value of Teflon.
In other words, typical chips have been designed to function unto the saturation
potential.
However, dielectric breakdown is sometimes observed at lower values of the
potential, as shown in Figure 4.20. It seems that breakdown frequently occurs when
there are defaults in the substrate surface or when objects like cells or proteins ad-
here to the substrate. A possible explanation could be the anomalous value of the
electric field at the vicinity of geometrical inhomogeneities.
The contact of an object with the substrate is sketched in Figure 4.21. Assum-
ing that the liquid is perfectly conductive and that the object is insulating—which
is a coarse assumption in the case of a cell or a protein, and if
e
1
and
e
d
denote the
relative permittivity of the object and the solid dielectric, respectively, the electric
potential is given by the Laplacian equation
Figure 4.20
(a) Dielectric breakdown at the vicinity of a spherical object; the breakdown is materi-
alized by the formation of cracks having the shape of tree branches; (b) close up on the “tree effect”;
(c) electrostatic breakdown model [22] showing the growth of “failure tree” due to an electron
avalanche.
