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Lecture 1 - Review
Kishore Acharya
Agenda
• Transport Equation (Conduction through
Metal)
• Material Classification based upon
Conductivity
• Properties of Semi Conductor
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Electrical Conduction through a Conductor/Metal
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Simple transport equation
Drude’s Method for conduction in Metals
Mq (dv/dt) = q E
Mq is the mass of the charge q, E is the electric field
v = (q E t)/Mq + c
At the instant of collision t=0 and v =0
Velocity change in between collision
v = (q E t)/Mq
The average velocity between collision is called drift velocity (Vd)
Vd = (q E t)/Mq m/sec
where t is the mean time between collision
Vd =  E Where mobility  = (q t) / Mq m2/volt sec
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Conductivity and Resistivity
Vd
W
T
L
Electric current I is the amount of charge crossing area A = WT in a second
Total Charge Q = nqAVd contained within the Parallalopiped P will cross the marked
area A in 1 sec. Where n is the number of particle with vharge q per unit volume.
Therefore,
I = nqAVd or J = I/A = nqVd = nq (q t / Mq) E
Noting that J =  E from the theory of Electro magnetic field theory it is seen that the
conductivity
 = nq  and the resistivity  = 1/(nq )
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Effective Mass Concept
Modern interpretation Mq must be replaced the effective mass Mq* and t
is calculated based upon Quantum Mechanics
Mq* is based upon the curvature of the energy band and is therefore
depends upon the crystal structure of the material. Since Mq* is smaller
for Ge, GaAs than Si the drift velocity Vd is higher for Ge and GaAs than
Si
The collision of the conductive particle is with the lattice and therefore t
depends upon lattice vibration and the concentration of defects and
impurities that distorts the shape of the lattice. Thus t  1/T and 1/Nimp
where T is temperature and Nimp is the concentration of the impurities
Mq* = ħ2/(2E/k2)
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Variation of carrier density with Temparature
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Variation of electron mobility with temperature and impurity
concentration
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A Note on Device Performance
Specification
• Since mobility decreases with increased
temperature
• Since drift velocity decreases as the electric
field decreases
• Device speed is stipulated at a temperature
of 120 C and 4.5 Volts
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Conductivity based Material
classification
Conductivity
Range
Carrier
Concentration
Band Gap
(ev)
Conductivity
Variation
Carrier Type
Conductor/
Metal
106 mho
1022
/cc
0
Decreases as
temperature is
increased
Electron
Semi
Conductor
10-2 to 102
mho
1010
/cc
0.7 to 1.6
Increases with
temperature.
Electron and
Holes
Insulator
10-6
 104
 2.0
NA
NA
Type
mho
/cc
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Properties of Semi Conductor
Group II
Group III
Group IV
Group V
Group VI
B*
C
N
O
Al*
Si
P*
S
As*
Se
Sb*
Te
Zn
Ga*
Ge
Cd
In
Sn
Elemental Semi Conductor: Si, Ge (elements from Group IV)
Alloy Semi Conductor: InP, GaAs, ZnS, CdS, CdTe
* Elements used for Doping intrinsic semi conductor
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Energy Bands and Interatomic Spacing
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Derivation of Effective Mass
• E = p2/2Mq* p = momentum, E= Energy
E = (ħk)2/2M*q since p = ħk where ħ=h/(2)
or E/k = ħ2k/M*q
or 2E/k2 = ħ2/M*q
or M*q = ħ2/ 2E/k2
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A note regarding Effective mass
Effective mass depends on curvature of the E-k curve a
fundamental property of the material based upon atomic
spacing and crystal structure.
In 0.09 m Silicon technology the curvature is manipulated
by stressing the silicon. The stressed silicon has flatter
curvature than standard silicon. The flatter curvature lowers
the effective mass in stressed silicon resulting in higher speed
device.
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Formation of Strained Si
Strained Si
Si
150A
SiGe
400A
Typically 70% Si and 30% Ge
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Mobility Enhancement
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Building Devices
• Insulator cannot be used for building devices
– Not enough charge carriers
• Conductors/ Metals cannot be used for building
devices
– No internal field for carrier flow control
• Semiconductors can be used for building devices
– Supports internal field for carrier flow control
– Carrier concentration must be increased to  1014/cc
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Intrinsic Semiconductor
ni = n = p = 1010/cc
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Impurities used for Semiconductor Doping
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Semiconductor Doping
N type Semiconductor
P type Semiconductor
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Increasing Carrier concentration
by Doping
• np = ni2
– n- elrctron concentration, p- hole concentration
– ni = Intrinsic carrier concentration=1010/cc for silicon
• For N type semi conductor
– n = Nd donor concentration [1014 to 1018 /cc] – majority carrier
– p = ni2 /Nd – minority carrier
• For P type semi conductor
– p = Na acceptor concentration [1014 to 1018 /cc] – majority carrier
– n = ni2 /Na – minority carrier
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Practice Problem
• Given Nd = 1016/cc determine n and p for a N type
semiconductor
– n = Nd = 1016/cc – majority carrier
– p = ni2 /Nd = (1010)2/1016 = 104/cc – minority carrier
• Given Na = 1014/cc determine n and p for a P type
semiconductor
– p = Na = 1014/cc – majority carrier
– p = ni2 /Nd = (1010)2/1014 = 106/cc – minority carrier
Note: As the concentration of majority carrier increases
Concentration of minority carrier decreases
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