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ELECTRONIC DEVICES AND
INTEGRATED CIRCUITS (EL2006)
LECTURE 6
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Last Class Compensation and space charge
neutrality : A compensatedsemiconductor is one, whichcontains both donor and acceptortype impurities in the sameregion, po + Nd
+ = no + Na- ,
Degenerate and nondegeneratesemiconductors : If material hasbeen doped too heavily ~ 1020
atoms cm-3. One of theapplications is in Tunnel diode.
Drift of carriers in electric andmagnetic fields :
xx EJ .
xx EJ .*
/. nn mtq
xx Ev / xnx EnqJ ...
J = q( n n + p p) . EX
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Todays class
# Drift of carriers in electric and magnetic fields Drift and resistance : Evaluating expression for resistivity
Effect of temperature and doping on mobility : Effect of impurityand lattice scattering
High field effects : What happens, if field is increased beyond alimit.
Hall Effect : Useful effect, which helps in getting to know acouple of parameters
# Invariance of the Fermi level at equilibrium
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Drift and Resistance
If this barcontains bothtypes of
carriers, then Iget value ofconductivity i.e.
xpnx EpnqJ)..(
Now, we know that
1
..
.
tw
L
tw
LR is the
resistivity
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Two basic types of scattering mechanisms thatinfluence electron and hole mobility areLattice scattering Impurityscattering
A carrier moving through the crystalis scattered by a vibration of the
lattice , resulting from the
temperature. Collective vibration of
atoms in the crystal are termed as
phonons. Thus lattice scattering isalso known as phonon scattering.
Due to the
scattering from
crystal defects such
as ionizedimpurities
EFFECT OF TEMPERATURE AND
DOPING ON MOBILITY
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Temperature Frequency of
lattice scattering
events
Mobility
Temperature
(At higher
temperatures)
(At lower
temperatures)
Frequency
of impurity
scattering
Mobility
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The approximate temperature dependence
for lattice and impurity scattering is T-3/2
andT3/2 respectively.
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Hence , the mobilities due to two or more
scattering mechanisms add inversely .
1 = 1 + 1
1 2
So, that is why, the mechanism causing
the lowest mobility value dominates.
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Mobility and impurity concentration :
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Material Mobility(Cm2 / V sec)
Intrinsic silicon at 300 K 1350
Silicon with a donor concentration 700
Of about 1017 Cm-3
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HIGH FIELD EFFECTS
Jx = . Ex
While writing down this eq. it was assumed that the drift
current is proportional to the electric field and that the
proportionality constant ( ) is not a function of E. This
assumption is valid over a wide range of E
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The current density resulting from the net drift of carriers is justthe number of electrons crossing a unit area per unit time( n < vx > ) multiplied by the charge on the electron ( - q ) :
Jx = - q. n . < vx >where < vx > is the average velocity
So, this term velocity is very much coming in
the expression for current density.
HIGH FIELD EFFECTS ( Contd.)
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This dependence of upon E is an
example of hot carrier effect, which
implies that the carrier drift velocity vx is
comparable to the thermal velocity vth (
~ 107
cm / sec).
HIGH FIELD EFFECTS (Contd.)
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HIGH FIELD EFFECTS ( Contd.)
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HIGH FIELD EFFECTS ( Contd.)
Point of saturation represents a situationat which added energy imparted by the
electric field is transferred to the lattice
rather than increasing the carrier velocity.
The result of this scattering limited velocity is
a fairly constant current at high field.
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Hall Effect
Ix
Ix
(+) (-)
Bz
Ex
EyA B
D
E
t
w
L
magnetic field applied to directionof hole drift (p-type bar).
Path of holes deflected in -y direction.
x
y
z
Fy = q(Ey - vxBz)
To maintain flow of holes
down the bar, an electric field
(Ey) needs to be established tobalance force.
Ey = vxBz
VAB
=Eyw
Hall voltage
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Hall Effect
0,
0
1
qpRBJRBqp
J
E HzxHzx
y
AB
zx
AB
zx
y
zx
H qtV
BI
wVq
BwtI
qE
BJ
qRp
)/(
)/(10
wtL
IV
L
Rwtcm xCD
/
/)(
H
H
p
R
qRqqp
)/1(
/1
0
Hall coefficient
Hole
concentration
Measurable
quantities}
xx vqnJ
Current density
Drift velocity
conductivity
mobility
Applications
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Invariance of the Fermi level
at equilibrium
## Technologically very important
section
Basically tells us that what will happen,
when two materials with their Fermi levelsat different position will be brought in closeintimacy.
I i f th F i l l t ilib i (
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We consider two materials in intimate contactsuch that electrons can move between the two as
shown below :
Material 1
Density of states N1 ( E)
Fermi distribution f1 ( E)
E
X
N2 ( E)
f2( E)
Ef
Invariance of the Fermi level at equilibrium (
Contd.)
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I i f h F i l l
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At Equilibrium , these two must be equal :
N1(E).f1(E). N2(E) [ 1f2(E) ] = N2(E).f2(E). N1(E) [ 1f1(E) ]
Rearranging terms , we have at energy E :
N1.f1.N2N1. f1.N2 . f2 = N2. f2 .N1N2. f2. N1. F1
Invariance of the Fermi level
at equilibrium ( Contd.)
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f1 ( E) = f2 ( E )
Hence , we can state that the Fermilevel at equilibrium must be constant
through materials in intimate contact.
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Thanks
