1 ENE 325 Electromagnetic Fields and Waves Lecture 5 Conductor, Semiconductor, Dielectric and...
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Transcript of 1 ENE 325 Electromagnetic Fields and Waves Lecture 5 Conductor, Semiconductor, Dielectric and...
1
ENE 325ENE 325Electromagnetic Electromagnetic Fields and WavesFields and Waves
Lecture 5Lecture 5 Conductor, Conductor, Semiconductor, Dielectric and Semiconductor, Dielectric and Boundary ConditionsBoundary Conditions
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Review (1)Review (1)
The electric potential difference Vba is a work done by an external force to move a charge from point a to point b in an electric field divided by the amount of charge moved.
The electric potential is the same no matter which routes are used. Only displacement distance (shortest route) matters
b
baa
WV E dL
Q ����������������������������
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Review (2)Review (2) Conductors and Ohm’s law
Current, I is defined as the amount of charge that passes through a reference plane in a given amou
nt of time. Ampere.
Current density, J is defined as the amount of cu rrent per unit area A/m2
the relationship between I and J , convection current conduction current
dQI
dt
I J S ����������������������������
sI J S
����������������������������
vJ v����������������������������
J E����������������������������
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OutlineOutline
Conductor and boundary conditions Semiconductor and insulator
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Conductors and boundary Conductors and boundary conditionsconditions
charge density is zero inside a conductor. Surface charge density DS is on the
conductor surface. An electric field inside a conductor is zero.
outside charges cause an electric field. Ds=0
E=0
++
+
+
++
+
+
+
+
+
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Tangential and normal fields. Tangential and normal fields.
The electric field on the surface can be divided into two components. tangential electric field, Et, = 0 for an
equipotential surface normal electric field, En
EnEt
E
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Boundary conditions (1) Boundary conditions (1)
Consider a conductor-free space boundary
From
0E dl ����������������������������
a b
cd
h
w
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Boundary conditions (3) Boundary conditions (3)
Consider Gauss’s law
From
D dS Q ����������������������������
s
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Boundary conditions (3) Boundary conditions (3)
For conductor-free space boundary conditions (B.Cs.)
Dt = Et = 0
Dn = 0
En = s
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Ex1Ex1 Let V Let V and let a point and let a point PP(0.1, (0.1, /12, /12, /24) /24) locate at the conductor-free space locate at the conductor-free space boundary. At point boundary. At point PP, determine, determine
a) V
b) E
5100 sin(3 )cos(4 )xV e y z
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c) En
d) Et
e) S
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SemiconductorsSemiconductors
Electron and hole currents conductivity mobility is 10-100 times higher than
conductor. electron and hole density depend on
temperature. Doping is the process of adding impurities
to a semiconductor to alter the polarity.
e e h h
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Dielectric or insulator Dielectric or insulator
no free charge microscopic electric dipoles energy stored capability polar and non-polar molecules
+
-+ - +
+
+
+
+
+
+
-
-
-- -
polar molecules non-polar molecules
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Alignment of dipoles with E Alignment of dipoles with E field field
+
-
+
-
+
-
+
-
+
-
+
-+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
E
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Polarization Polarization
Each dipole has its dipole moment,
where Q is the positive one of the two bound charges is the vector from the negative to the positive charge.
where n = number of dipoles per volume.
Polarization is dipole moment per unit volume,
p��������������
p Qd C m ����������������������������
1
n v
itotali
p p
��������������
2
0 1
1lim /
n v
iv i
P p C mv
��������������
d��������������
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Equivalent polarization Equivalent polarization
The movement of bound charges when induced by an electric field causes changes in surface and volume charge densities.1. Equivalent polarization surface charge density, s
2. Equivalent polarization volume charge density, v
2/ns P a C m ��������������
+-
+-
+-
+-
+-
+-
+-
+-
+-
+-+-
+-+-
+-+-
E
+-
+-+-
+-+-+-
+-+-+-
+-
+-+-+-
+-
+-
an
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Electric flux density in a Electric flux density in a dielectric material (1)dielectric material (1) can be calculated from free and bound charges.can be calculated from free and bound charges.
Net bound charges flowing out of the closed surfaces,
bS
Q P dS C ����������������������������
Let
where QT = total charge Q = free charge
T bQ Q Q
+
-+
-
+
-
D��������������
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Electric flux density in a Electric flux density in a dielectric material (2)dielectric material (2)
From
then
Let
we can write
where is an electric flux density in a dielectric material.
0Ts
Q E dS ����������������������������
0( ) .T bs
Q Q Q E P dS ������������������������������������������
0D E P ������������������������������������������
sQ D dS
����������������������������
D��������������
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Equivalent divergence Equivalent divergence relationshipsrelationships
From
use a divergence theorem, we have
Since
then
We can also show that
therefore
,nbs
Q P a dS ����������������������������
.s vP dS Pdv ������������������������������������������
b vQ dv
.v bP ��������������
0 ,TE ��������������
.T b vD ��������������
20
Electric flux density in Electric flux density in dielectric medium (1) dielectric medium (1)
If the dielectric material is linear and isotropic,the polarization is proportional to the electric
field . P��������������
E��������������
0 eP E ����������������������������
where e is an electric susceptibility. Then 0 0 .
������������������������������������������eD E E
Let 1r e
where r is a relative permittivity or a dielectric constant.
21
Electric flux density in Electric flux density in dielectric medium (2) dielectric medium (2)
So we can write
0rD E ����������������������������
o r
D E����������������������������
where F/m. 0 r.
22
Ex2Ex2 A dielectric material has an A dielectric material has an electric susceptibility electric susceptibility ee =0.12 and =0.12 and has a uniform electric flux density has a uniform electric flux density DD = 1.6 nC/m = 1.6 nC/m22 , determine , determine
.
a) E
b) P
c) Average dipole moment if there are210x 19 dipoles/m3
23
Boundary conditions for dielect Boundary conditions for dielect ric materials ric materials: tangential fields: tangential fields
It is useful to determine the electric field in a dielectric medium.
Dielectric-Dielectric
w
h
1 2
Et1 Et2
Et1 =Et2
and 1 1
2 2
t
t
D
D
24
Boundary conditions for dielect Boundary conditions for dielect ric materials ric materials: normal fields: normal fields
Dielectric-Dielectric
s
Dn1 = Dn2
and
1
En1 = 2
En2.
1 221 ( ) Sa D D
����������������������������
For a free of charge boundary,
21ais the unit vector pointing from
medium 2 to medium 1.
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Use B.C.s to determine Use B.C.s to determine magnitude of magnitude of and and
��������������D
��������������E
Dn1
Dn2
Dt1q1
q2
D t2
D2
D1
12
22 22
2 1 1 121
cos sinD D
q q
22 21
2 1 1 122
sin cosE E
q q
26
Ex3Ex3 The isotropic dielectric medium The isotropic dielectric medium with with r1r1 = 3 and = 3 and r2r2 = =22 is connected as s is connected as s
hown. Given hown. Given V/m, determine and its m V/m, determine and its m
agnitude, and its magnitude, agnitude, and its magnitude, qq11
, and , and qq
22..
1 5 4x y zE a a a
��������������2E
��������������
2D��������������
Z
-Z
r1 3
r2 2x-y
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Boundary conditions for diel Boundary conditions for dielectricectric-conductor-conductor
h
wEt
En
conductor
dielectric
Dt = Et =0Dn = En = s
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ExEx44 - Between a dielectric conductor inter - Between a dielectric conductor inter face has a surface charge density of face has a surface charge density of ss = =
2 10x2 10x -9-9 C/m C/m22 . Given . Given V/m, determine V/m, determine ..
1 30 50 70
��������������x y zE a a a 2E
��������������