Lecture handout including QS - Department of Materials Science ...

BH24 Course B: Materials for Devices BH24
If an electric field, E, is applied to a sample of a dielectric material, there is a resultant total charge
density, D:
D = εE = κε 0
E (units of C m -2 )
ε = permittivity of the material (‘polarisability’) ε 0 = permittivity of free space (8.85 x 10 -12 F m -1 )
The Dielectric Constant of the material, κ , is defined as: κ = ε (dimensionless)
ε0
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D (which is sometimes called a displacement field), is made up of 2 components:
D = ε 0
E + P P = polarisation of the material
therefore, polarisation of the material,
P = D − ε 0
E = κε 0
E − ε 0
E
Capacitance
(units of Coulomb / volt: C V -1 , or Farads)
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A capacitor, which is made of a dielectric, stores energy in the form of an electrostatic field, or charge
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P = ε 0
E( κ −1)
Capacitance, C, depends on the dielectric material & the geometry: C = Q V
(a) For an empty parallel plate capacitor (i.e. with a vacuum between the plates):
_ _ _ _ _ _ _
+ + + + + +
+
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A = surface area of plates
L = distance between plates
applied voltage, V = E × L
E = field
⇒ charge density (free space) = ε 0
E and charge on plates, Q = ε 0
E × A
C = Q V
= ε 0 EA
EL
= ε 0
A
L
(b) If a dielectric is placed between the plates, the electric field polarises the dielectric and leads to a
charge density on its surface, P. There is now a higher total charge density on the plates (D):
-
+
_ _ _ _ _ _ _ _ _
+ _ + + + + +
- - - - - -
+ + + + + + + + +
+ +
-
+
D = ε 0
E + P & hence
capacitance,
ʹ′ C = Q V
C ʹ′ is increased:
= ( ε 0
E + P) × A
E × L
ʹ′ C = ε 0
κ A L
= ε A L