electrical properties of materials
DESCRIPTION
Electrical Properties of Materials. Conductivity, Bands & Bandgaps. Objectives. To understand: Electronic Conduction in materials Band Structure Conductivity Metals Semiconductors Ionic conduction in ceramics Dielectric Behavior Polarization. Definitions. Ohm’s Law V = iR - PowerPoint PPT PresentationTRANSCRIPT
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Electrical Properties of Materials
Conductivity, Bands & Bandgaps
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Objectives
To understand: Electronic Conduction in materials Band Structure Conductivity
Metals Semiconductors Ionic conduction in ceramics
Dielectric Behavior Polarization
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Definitions
Ohm’s Law V = iR
V - Voltage, i - current, R -Resistance Units
V - Volts (or W/A (Watts/amp) or J/C (Joules/Coulomb))
i - amps (or C/s (Coulombs/second)
R - ohms ()
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Definitions
Resistance
ρ= RAl
= VAil
= m2
m = m
Area
Length
i
Consider current moving through a conductor with cross sectional area, A and a length, l
R = V/i
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Definitions
Conductivity, :
Conductivity is the “ease of conduction”
Ranges over 27 orders of magnitude!
= 1/ρ (units: (-cm)-1
ConductivityMetals 107 1/cmSemiconductors 10-6 - 104 1/cmInsulators 10-10 -10-20 1/cm
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Definitions
Electronic conduction: Flow of electrons, e and electron holes, h
Ionic conduction Flow of charged ions, Ag+
Charge carriers can be electrons or ions
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Electronic Conduction
In each atom there are discrete energy
levels occupied by electrons Arranged into:
Shells K, L, M, NSubshells s, p, d, f
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In Solid Materials
Each atom has a discrete set of electronic energy levels in which its electrons reside.
As atoms approach each other and bond into a solid, the Pauli exclusion principle dictates that electron energy levels must split.
Each distinct atomic state splits into a series of closely spaced electron states - called an energy band
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Electronic Conduction
Energy
interatomic separation
1s
2s
Band
Pauli Exclusion Principle - no two electrons within a system may exist in the same “state” All energy levels (occupied or not) “split” as atoms approach each other
1S1 1S1
E 1S11S1
A1 A2
For two atoms For many atoms
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BandingE
nerg
y
1S
3S
3P
2P
2S
4S
3D
Isolated AtomE
nerg
y
1S
3S
3P
2P
2S
4S
3D
Bonded Atoms
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Electronic Conduction
Once states are split into bands, electrons fill states starting with lowest energy band. Electrical properties depend on the arrangement of the outermost filled and unfilled electron bands. “boxes of marbles analogy”
Inter-atomic separation
Equilibrium Separation
BandGap
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Band Structure
Valence Band Band which contains highest energy electron
Conduction Band The next higher band
Insulator
filled
empty
filled
empty
Metal
filledempty Valence
Band
Conduction Band
Semiconductor
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Band Structure
Fermi Energy, EfEnergy corresponding to the highest
filled state
Only electrons above the Fermi level can be affected by an electric field (free electrons)
Ef
E
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Conduction in Metals- Band Model
For an electron to become free to conduct, it must be promoted into an empty available energy state
For metals, these empty states are adjacent to the filled states
Generally, energy supplied by an electric field is enough to stimulate electrons into an empty state
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Resistivity, ρ in Metals
Resistivity typically increases linearly with temperature: ρt = ρo + T
Phonons scatter electrons
Impurities tend to increase resistivity: Impurities scatter electrons in metals
Plastic Deformation tends to raise resistivity dislocations scatter electrons
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Temperature Dependence, Metals
There are three contributions to ρρt due to phonons (thermal)ρi due to impuritiesρd due to deformation (not shown)
ρ = ρi + ρo+ ρd
ρ = ρi + ρo+ ρd
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Electrical Conductivity, Metals
For charge transport to occur - must have:- something the carry the charge- the ability to move
= conductivity = 1/ρ
= ne
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Electrical Conductivity, Metals
= electrical conductivity n = number of concentration of charge
carriers depends on band gap size and amount of thermal energy
= mobility measure of resistance to electron motion - related to
scattering events - (e.g. defects, atomic vibrations) “highway analogy”
= ne
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Temperatures Dependence, Metals
Metals, decreases with T ( = ne Two parameters in Ohm’s law may be T dependent: n and
Metals - number of electrons (in conduction band) does not vary with T. n = number of electrons per unit volume n 1022 cm-3 and
102-103 cm2/Vsec
105-106 (ohm-cm)-1
All of the observed T dependence of in metals arises from
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Semiconductors and Insulators
Electrons must be promoted across the energy gap to conduct
Electron must have energy: e.g. heat or light absorptrion
If gap is very large (insulators) no electrons get promoted low electrical conductivity,
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Semiconductors
For conduction to occur, electrons must be promoted across the band gap
E
EF
Full
Empty
Energy is usually supplied by heat or light
Note - electrons cannot reside in gap
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Thermal Stimulation
P=exp
−ΔEkBT ⎛ ⎝ ⎜ ⎞
⎠ ⎟
Suppose the band gap is Eg = 1.0 eV
P = number of electrons promoted to conduction band
T(°K) kBT (eV) ΔE/kBT
exp
ΔEkBT
0 0 0100 0.0086 58 0.06x10
-24
200 0.0172 29 0.25x10-12
300 0.0258 19.4 3.7 x10-9
400 0.0344 14.5 0.5x10-6
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Stimulation of Electrons by Photons
Photoconductivity
Eg ω ≥ Eg h
Conductivity is dependent on the intensity of the incident electromagnetic radiation
E = h = hc c m(sec -
1)
h Eg
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Stimulation of Electrons by Photons
Provided
Band Gaps: Si - 1.1 eV (Infra red)Ge 0.7 eV (Infra red)GaAs1.5 eV (Visible red)SiC 3.0 eV (Visible blue)
(If incident photons have lower energy, nothing happens when the semiconductor is exposed to light.)
h Eg
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Intrinsic Semiconductors
Intrinsic Semiconductors Once an electron has been excited to the
conduction band, a “hole” is left behind in the valence band
Since neither band is nowcompletely full or empty,both electron and hole canmigrate
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Conductivity of Intrinsic S.C.
Intrinsic semiconductor pure material
For every electron, e, promoted to the conduction band, a hole, h, is left in the valence band (+ charge)
Band GapSilicon - 1.1 eVGermanium - 0.7 eV
Total conductivity = e + h = nee + neh
For intrinsic semiconductors: n = p & = ne(e + h)
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Extrinsic Semiconductors
Extrinsic semiconductors impurity atoms dictate the properties
Almost all commercial semiconductors are extrinsic
Impurity concentrations of 1 atom in 1012 is enough to make silicon extrinsic at room T!
Impurity atoms can create states that are in the bandgap.
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Types of Extrinsic Semiconductors
In most cases, the doping of a semiconductor leads either to the creation of donor or acceptor levels
n-Type
p-Type semiconductorsIn these, the charge carriers are positive
p-Type
n-Type semiconductorsIn these, the charge carriers are negative
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Silicon
Diamond cubic lattice Each silicon atom has one s and 3p orbitals that hybridize
into 4 sp3 tetrahedral orbitals Silicon atom bond to each other covalently, each sharing 4
electrons with four, tetrahedrally coordinated nearest neighbors.
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Silicon
n-type semiconductors: Bonding model description:
Element with 5 bonding electrons. Only 4 electrons participate in bonding the extra e- can easily become a conduction electron
p-type semiconductors: Bonding model description:
Element with 3 bonding electrons. Since 4 electrons participate in bonding and only 3 are available the left over “hole” can carry charge
Si Si
Si Si
Si P
Si Si
Si Si
Si Si
Si Si
Si Si
Si Si
Si Si
Si Si
Si Si
Si Si
Si Si
B Si
Si Si
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In order to get n-type semiconductors, we must add elements which donate electrons i.e. have 5 outer electrons. Typical donor elements which are added to Si or Ge:
Phosphorus
Arsenic
Antimony
Typical concentrations are ~ 10-6
Doping Elements, n-Type
Group V elements
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Doping Elements, p-type
To get p-type behavior, we must add acceptor elements i.e. have 3 outer electrons. Typical acceptor elements are:
Boron
Aluminum
Gallium
Indium
Group III elements
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Location of Impurity Energy Levels
Typically, ΔE ~ 1% Eg
Eg
ΔE
ΔE
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Conductivity of Extrinsic S.C.
There are three regimes of behavior:
Temperature
impurity excitation
all impuritiesionized
Excitation across band gap
It is possible that one or more regime will not beevident experimentally
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n-Type Semiconductors
Band Model description: The dopant adds a donor state in the band gap
Band GapDonor State
If there are many donors n>>p (many more electrons than holes)
Electrons are majority carriers“n-type” - (negative) semiconductor
= e + h = nee + neh
≈ neu
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p-Type Semiconductors
Band Model description: The dopant adds a acceptor state in the band gap
Band GapAcceptor State
If there are many acceptors p>>n (many more electrons than holes)
holes are majority carriers“p-type” - (negative) semiconductor
= e + h = nee + neh
≈ peu
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III-V, IV-VI Type Semiconductors
Actually, Si and Ge are not the only usuable Semiconductors Any two elements from groups III and Vor II and VI, as long as
the average number of electrons = 4 and have sp3-like bonding, can act as semiconductors. Example: Ga(III), As(V) GaAs
Zn(II), Se(VI) ZnSe Doping, of course, is accomplished by substitution, on either site,
by a dopant with either extra or less electrons. In general, “metallic” dopants will substitute on the “metal” sites and “non-metallic” dopants will substitute on non-metal sites. For the case where the dopant is between the two elements in the compound, substitution can be amphoteric (i.e. on both sites)
Question: Give several p-type and n-type dopant for GaAs and ZnSe. What kind of dopant is Si in InP?
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