Conductivity
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Conductivity Charge carriers follow a random path unless an external field is applied. Then, they acquire a drift velocity that is dependent upon their mobility, n and the strength of the field, V d = - n The average drift velocity, v av is depende Upon the mean time between collisions, 2
description
Conductivity. Charge carriers follow a random path unless an external field is applied. Then, they acquire a drift velocity that is dependent upon their mobility, m n and the strength of the field, x V d = - m n x . The average drift velocity, v av is dependent - PowerPoint PPT Presentation
Transcript of Conductivity
ConductivityCharge carriers follow a random path unless an external field is applied. Then, they acquire a drift velocity that is dependent upon their mobility, n and the strength of the field,
Vd = -n
The average drift velocity, vav is dependentUpon the mean time between collisions, 2
Charge Flow and Current DensityCurrent density, J, is the rate at which charges, cross any plane perpendicular to the flow direction.
J = -nqvd = nqn
n is the number of charges, and
q is the charge (1.6 x 10-19
C)
OHM’s Law: V = IR
Resistance, R() is an extrinsic quantity. Resistivity, (m), is the corresponding intrinsic property.
= R*A/l
Conductivity, , is the reciprocal of resistivity: (m)-1 = 1/
The total current density depends upon the total charge carriers, which can be ions, electrons, or holes
J = q(nn + pp)
Polystyrene <10-14 Polyethylene 10-15-10-17
Silver 6.8 x 107 Copper 6.0 x 107 Iron 1.0 x 107
METALS
Silicon 4 x 10-4 Germanium 2 x 100 GaAs 10-6
SEMICONDUCTORS
Soda-lime glass 10-10 Concrete 10-9 Aluminum oxide <10-13
CERAMICS
POLYMERS
conductors
semiconductors insulators4
• Room T values (Ohm-m)-1CONDUCTIVITY: COMPARISON
As the distance between atoms decreases, the energy of each orbital must split, since according to Quantum Mechanics we cannot have two orbitals with the same energy.
The splitting results in “bands” of electrons. The energy difference between the conduction and valence bands is the “gap energy” We must supply this much energy to elevate an electron from the valence band to the conduction band. If Eg is < 2eV, the material is a semiconductor.
Simple representation of silicon atoms bonded in a crystal. The dotted areas are covalent or shared electron bonds. The electronic structure of a single Si atom is shown conceptually on the right. The four outermost electrons are the valence electrons that participate in covalent bonds.
Portion of the periodic table relevant to semiconductor materials and doping. Elemental semiconductors are in column IV. Compound semiconductors are combinations of elements from columns III and V, or II and VI.
Electron (-) and hold (+) pair generation represented b a broken bond in the crystal. Both carriers are mobile and can carry current.
Simple band and bond representations of pure silicon. Bonded electrons lie at energy levels below Ev; free electrons are above Ec. The process of intrinsic carrier generation is illustrated in each model.
Simple band and bond representations of doped silicon. EA and ED represent acceptor and donor energy levels, respectively. P- and N-type doping are illustrated in each model, using As as the donor and B as the acceptor
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• Metals:-- Thermal energy puts many electrons into a higher energy state.
+-
net e- flow• Energy States:-- the cases below for metals show that nearby energy states are accessible by thermal fluctuations.
Energy
filled band
filled valence band
empty band
fille
d st
ates
CONDUCTION & ELECTRON TRANSPORT
filled band
Energy
partly filled valence band
empty band
GAP
fille
d st
ates
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• Insulators: --Higher energy states not accessible due to gap.
• Semiconductors: --Higher energy states separated by a smaller gap.
Energy
filled band
filled valence band
empty band
fille
d st
ates
GAP
Energy
filled band
filled valence band
empty band
fille
d st
ates
GAP?
ENERGY STATES: INSULATORS AND SEMICONDUCTORS
• Imperfections increase resistivity --grain boundaries --dislocations --impurity atoms --vacancies
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T (°C)-200 -100 0
Cu + 3.32 at%Ni
Cu + 2.16 at%Ni
deformed Cu + 1.12 at%Ni
123456
Resis
tivity
,
(10-
8 Oh
m-m
)
0
Cu + 1.12 at%Ni
“Pure” Cu
These act to scatterelectrons so that theytake a less direct path.
• Resistivity increases with: --temperature --wt% impurity --%CW
thermalthermaldef
METALS: RESISTIVITY VS T, IMPURITIES
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• Data for Pure Silicon: -- increases with T --opposite to metals
undoped e Egap /kT
Energy
filled band
filled valence band
empty band
fille
d st
ates
GAP?electronscan crossgap athigher T
materialSiGeGaPCdS
band gap (eV)1.110.672.252.40
PURE SEMICONDUCTORS: CONDUCTIVITY VS T
electrical conductivity, (Ohm-m)-1
50 100 100010-210-1100101102103104
pure (undoped)
T(K)
• Electrical Conductivity given by:
nee peh
11# electrons/m3 electron mobility
# holes/m3
hole mobility
• Concept of electrons and holes:
+ -
electron hole pair creation
+ -
no applied electric field
applied electric field
valence electron Si atom
applied electric field
electron hole pair migration
Adapted from Fig. 18.10, Callister 6e.
CONDUCTION IN TERMS OF ELECTRON AND HOLE MIGRATION
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• Intrinsic: # electrons = # holes (n = p) --case for pure Si• Extrinsic: --n ≠ p --occurs when impurities are added with a different # valence electrons than the host (e.g., Si atoms)• N-type Extrinsic: (n >> p)• P-type Extrinsic: (p >> n)
nee peh
no applied electric field
5+4+ 4+ 4+ 4+
4+4+4+4+4+
4+ 4+
Phosphorus atom
no applied electric field
Boron atom
valence electron
Si atom
conduction electron
hole
3+4+ 4+ 4+ 4+
4+4+4+4+4+
4+ 4+
INTRINSIC VS EXTRINSIC CONDUCTION
Behavior of free carrier concentration versus temperature. Arsenic in silicon is qualitatively illustrated as a specific example (ND = 1015 cm-3). Note that at high temperatures ni becomes larger than 1015 doping and n≈ni. Devices are normally operated where n = ND
+. Fabrication occurs as temperatures where n≈ni
Fermi level position in an undoped (left), N-type (center) and P-type (right) semiconductor. The dots represent free electrons, the open circles represent mobile holes.
Probability of an electron occupying a state. Fermi energy represents the energy at which the probability of occupancy is exactly ½.
Fermi-Dirac statisticsConductivity in semiconductors is described by
Fermi-Dirac statistics. In general, for both extrinsic and intrinsic, the conductivity formula is:
nkTE
oe
n-type: E = Ec-Ed , n=1
P-type: E = Ea-Ev , n=1
IntrinsicE = Eg, n=2
doped 0.0013at%B
0.0052at%B
elec
trica
l con
duct
ivity
,
(Ohm
-m)-1
50 100 100010-210-1100101102103104
pure (undoped)
T(K)
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• Data for Doped Silicon: -- increases doping --reason: imperfection sites lower the activation energy to produce mobile electrons.
• Comparison: intrinsic vs extrinsic conduction... --extrinsic doping level: 1021/m3 of a n-type donor impurity (such as P). --for T < 100K: "freeze-out" thermal energy insufficient to excite electrons. --for 150K < T < 450K: "extrinsic" --for T >> 450K: "intrinsic"
cond
uctio
n el
ectro
n co
ncen
tratio
n (1
021 /
m3)
T(K)60040020000123
freez
e-ou
t
extri
nsic
intri
nsic
dopedundoped
DOPED SEMICONDUCTOR: CONDUCTIVITY VS T
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• Allows flow of electrons in one direction only (e.g., useful to convert alternating current to direct current.• Processing: diffuse P into one side of a B-doped crystal.• Results:--No applied potential: no net current flow.--Forward bias: carrier flow through p-type and n-type regions; holes and electrons recombine at p-n junction; current flows.
--Reverse bias: carrier flow away from p-n junction; carrier conc. greatly reduced at junction; little current flow.
++ +
++
--
--
-p-type n-type
++
+++
- ---
-p-type n-type
+ -
+++
++
--- -
-p-type n-type
- +
P-N RECTIFYING JUNCTION
