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