14.3 Dielectrics
14.3.1 Introduction
Dielectrics seem to be really boring materials for electronics, because an ideal dielectric doesn’t con-
duct. But experimentally everything conducts, if the voltage is high enough. What we exactly want
to have is that they don’t conduct at DC and that they have low losses at AC. It is not possible to
have zero losses at AC, because the dielectric constant always has a real part and an imaginary part.
The real part corresponds to the out-of-phase components of the electric field and the current. The
imaginary part corresponds to the in-phase components, which is the dissipative part, so there always
have to be losses.
Sometimes low dielectric constants are needed for transporting signals (CMOS) and sometimes high
dielectric constants are needed for supercapacitors. This kind of capacitors is used to store the won
energy of braking a car and to give it back when accelerating.
It is possible to use the complex dielectric function to describe the AC losses, but that is not done in
practice. Instead of that, we start with an ideal capacitor, where the current leads the voltage by 90 ◦.
Because of the complex dielectric part, this angle will not be exactly 90 ◦, so we add an offset angle
90 ◦−δ. As we see in eqn. (247), the power loss depends on the tangent of this offset angle and it gets
bigger, when the frequency gets higher.
Power loss=
w 1 V 02
2tan(δ) (247)In fig. 126 many loss tangents for different materials are listed to get a feeling for the size of them. As
we see, they are really small numbers, so it doesn’t matter if someone speaks about the loss tangent
or someone speaks about the angleδ, because they are nearly the same near zero (tan(δ)∼δ,δ 1 ).
Barium titanate is a material which is used in capacitors as a dielectric. It can appear as white powder
or as a transparent crystal. The unit cell is a cube, where the Barium atoms sit on the corners. There
is one titanium in the middle and the oxygens sit on the faces of the cube. This structure is called a
perovskit.
In fig. 127 we can see, that the dielectric constant has several peaks at different temperatures, which
will be explained in the chapter of structural phase transistions. In addition, the dielectric constant
depends on the applied voltage. The developer of an electronic element has to think about the
temperatures inside the element, when the device is working. A typical temperature for the processor
of a mobile phone is about 100 ◦C, which leads to anrof approximately 2000, which is not a bad
value for a dielectric.
When the temperature is increased, it leads to a structural phase transition, which will be discussed
in chapter 14.4.4.