1. Electrical Properties
ISSUES TO ADDRESS...
• How are electrical conductance and resistance
characterized?
• What are the physical phenomena that distinguish
conductors, semiconductors, and insulators?
• For metals, how is conductivity affected by
imperfections, T, and deformation?
• For semiconductors, how is conductivity affected
by impurities (doping) and T? 1 1

2. View of an Integrated Circuit
• Scanning electron microscope images of an IC:
0.5 mm
(a)
(d)
45 m Al Si
(doped)
• A dot map showing location of Si (a semiconductor):
-- Si shows up as light regions.
(b)
• A dot map showing location of Al (a conductor):
-- Al shows up as light regions.
(c)
Fig. (d) from Fig (a), Callister 7e. (Fig is courtesy Nick Gonzales, National Semiconductor Corp., West Jordan, UT.)
Fig. (a), (b), (c) from Fig. 18.0, Callister 7e. 2 2

3. Electrical Conduction
• Ohm's Law:
V = I R
voltage drop (volts = J/C)
C = Coulomb
resistance (Ohms)
current (amps = C/s) I e - A
(cross
sect.
area) V L
• Resistivity,  and Conductivity, :
-- geometry-independent forms of Ohm's Law
E: electric
field
intensity
resistivity
(Ohm-m)
J: current density
conductivity
-- Resistivity is a material property & is independent of sample
• Resistance: 3 3

4. Electrical Conduction
When an electrical potential V [volts, J/C] is applied across a piece of material, a current of magnitude I [amperes, C/s] flows. In most metals, at low values of V, the current is proportional to V, and can be described by Ohm's law:
I = V/R
where R is the electrical resistance [ohms, Ω]. R depends on the intrinsic resistivity ρ of the material [Ω-m] and onthe geometry (length l and area A through which the current passes): R = ρl/A
In most materials (e.g. metals), the current is carried by electrons (electronic conduction). In ionic crystals, the charge carriers are ions (ionic conduction). 4 4

5. Electrical Properties
Which will conduct more electricity?
Analogous to flow of water in a pipe
So resistance depends on sample geometry, etc. D 2D 5 5

6. Definitions J =   <= another way to state Ohm’s law
Further definitions
J =   <= another way to state Ohm’s law
J  current density
  electric field potential = V/ or (V/  )
Electron flux conductivity voltage gradient
J =  (V/ )
Current carriers
electrons in most solids
ions can also carry (particularly in liquid solutions) 6 6

7. Conductivity: Comparison-1 -1
• Room T values (Ohm-m)
= ( - m)
METALS
conductors
Polystyrene <10
-14
Polyethylene
-15
-10
-17
Soda-lime glass 10
Concrete -9
Aluminum oxide <10
-13
CERAMICS
POLYMERS
insulators
-11 7
Silver
6.8 x 10 7
Copper
6.0 x 10 7
Iron
1.0 x 10
Up to 27 orders of magnitude, possibly widest variation in materials properties
Silicon
4 x 10 -4
Germanium
2 x 10
GaAs 10 -6
SEMICONDUCTORS
semiconductors
Selected values from Tables 18.1, 18.3, and 18.4, Callister 7e. 7 7

8. Conductivity / Resistivity8

9. Example: Conductivity Problem
What is the minimum diameter (D) of the wire so that V < 1.5 V?
100m - - e
I = 2.5A +
Cu wire V
< 1.5V
2.5A
6.07 x 10 (Ohm-m) 7 -1
100m
Solve to get D > 1.87 mm 9 9

10. Energy Band Structures in Solids
Electrical conductivity in materials are strongly related to # of electrons available for conduction
Not all electrons will move in a material under an applied potential difference !
More detail in Quantum Mechanics !
In an isolated atom electrons occupy well defined energy states, as discussed in Chapter 2.
Shells (1,2,3….), subshells (s,p,d,f…..), states in subshells, spin states
When atoms come together to form a solid (N =12 atoms), a bonded regular atomic arrangement, their valence electrons interact with each other and with nuclei due to Coulombic forces.
In addition, two specific quantum mechanical effects happen.
First, by Heisenberg's uncertainty principle, constraining the electrons to a small volume raises their energy, this is called promotion.
The second effect, due to the Pauli exclusion principle, limits the number of electrons that can have the same energy.
As a result of these effects, the valence electrons of atoms at distinct energy states get split into closely spaced electron states and form wide electron energy bands when they form a solid. These bands are separated by gaps, where electrons cannot exist. 10

11. Energy Band Structures in Solids
The extend of energy states splitting depends on inter-atomic distance
Outermost shells start forming bands as atoms get closer, however core shells may not form bands as still far from each other.
Band gaps, depending upon the inter-atomic distances also start forming 11

12. Electronic Band Structures
So the individual atomic energy levels interact to form molecular energy levels
In solids gap between states could be eV apart
Adapted from Fig. 18.2, Callister 7e. 12 12

13. Band Structure Valence band – filled – highest occupied energy levels
Conduction band – empty – lowest unoccupied energy levels
Conduction band
valence band
contains valence electrons from the atoms
Adapted from Fig. 18.3, Callister 7e. 13 13

14. Band Structure defines Electrical Properties
insulator
conductor
>2eV
<2eV
Metals, single s valence electron N atoms => 4s band capable of 2N electrons => but only one s electron means half filled band structure.
Metals with overlaping bands. Eg. Both s valence electrons exists in s subshell. In x’tal structure s and p subshells overlap, but p shell is empty.
the valence band is filled, and no more electrons can be added (Pauli's principle). Electrical conduction requires that electrons be able to gain energy in an electric field. This is not possible in these materials because that would imply that the electrons are promoted into the forbidden band gap. 14

15. Energy States: Insulators & Semiconductors
-- Higher energy states not
accessible due to gap (> 2 eV).
• Semiconductors:
-- Higher energy states separated
by smaller gap (< 2 eV).
Energy
filled
band
valence
empty
filled states
GAP ?
Energy
filled
band
valence
empty
filled states
GAP 15 15

16. Semiconductors and Insulators
In semiconductors and insulators, electrons have to jump/move across the band gap into conduction band to find conducting states above Ef
The energy needed for the jump may originate from heat, or from irradiation at sufficiently small wavelength.
The difference between semiconductors and insulators is that in semiconductors electrons can reach the conduction band at ordinary temperatures, where in insulators they cannot. Eg is too large for insulators to have thermally or optically exited electrons promote to the conduction band.
The probability that an electron reaches the conduction band is about exp(- Eg/2kT) where Eg is the band gap. If this probability is < one would not find a single electron in the conduction band in a solid of 1 cm3. How come ? Remember NAv ~ 1024
This requires Eg/2kT > 55. At room temperature, 2kT = 0.05 eV, Eg > 2.8 eV corresponds to an insulator.
An electron promoted into the conduction band leaves a hole (positive charge) in the valence band, that can also participate in conduction. Holes exist in metals as well, but are more important in semiconductors and insulators. 16

17. Charge Carriers Two charge carrying mechanisms
Adapted from Fig (b), Callister 7e.
Two charge carrying mechanisms
Electron – negative charge
Hole – equal & opposite positive charge
Move at different speeds - drift velocity
Higher temp. promotes more electrons into the conduction band
  as T
Electrons scattered by impurities, grain boundaries, etc. 17 17

18. Conduction & Electron Transport
• Metals (Conductors):
-- Thermal energy puts
many electrons into
a higher energy state. + -
• Energy States:
-- for metals nearby
energy states
are accessible
by thermal
fluctuations.
filled
band
Energy
partly
valence
empty
GAP
filled states
Energy
filled
band
valence
empty
filled states 18 18

19. Conduction in Metals
In metals, highest occupied band is partially filled or bands overlap.
Conduction occurs by promoting electrons into conducting states, that starts right above the Fermi level. The conducting states are separated from the valence band by an infinitesimal amount (~10-10 eV).
Energy provided by an electric field is sufficient to excite many electrons into conducting states. => High conductivity. 19

20. Summary Energy Band Structures and Bonding
(metals, semiconductors, insulators)
Relation to atomic bonding:
Insulators – valence electrons are tightly bound to (or shared with) the individual atoms – strongest ionic (partially covalent) bonding. Remember electro-negativity.
Semiconductors - mostly covalent bonding somewhat weaker bonding. Sharing of electrons.
Metals – valence electrons form an “electron gas” that are not bound to any particular ion. 20

21. Electron Mobility
The force acting on the electron is -eE, where e is the electric charge and F=ma. As long as the electric field is present, in the absence of obstacles the electron is expected to speed up continuously in an electric field.
So, is the case in vacuum (e.g. inside a TV tube) or in a perfect crystal .
In a real solid, electrons motion are hindered by defects (dislocations, impurities, vacancies, etc), and even thermal vibrations of atoms. Electrons scatter by collisions with imperfections and due to atomic thermal vibrations.
“frictional forces” => resistance => a net drift velocity of electron motion is established:
where μe – electron mobility [m2/V-s]. The “friction” transfers part of the energy supplied by the electric field into the lattice as heat. That is how electric heaters work. 21

22. Electron Mobility σ = Ne |e| μe
Electrical conductivity is proportional to number of free electrons and electron mobility:
σ = Ne |e| μe
Ne - number of “free” or conduction electrons per unit volume
e is the absolute charge on a free electron x C 22

23. Metals: Resistivity vs T, Impurities Read pages 621- 623
• Imperfections increase resistivity
-- grain boundaries
-- dislocations
-- impurity atoms
-- vacancies
These act to scatter
electrons so that they
take a less direct path.
deformed Cu at%Ni
T (°C)
-200
-100
Cu at%Ni
Cu at%Ni 1 2 3 4 5 6
Resistivity, 
(10 -8
Ohm-m)
Cu at%Ni
“Pure” Cu
• Resistivity
increases with:
-- temperature
-- wt% impurity
-- %CW
 = thermal impurity deformation
Adapted from Fig. 18.8, Callister 7e. (Fig adapted from J.O. Linde, Ann. Physik 5, p. 219 (1932); and C.A. Wert and R.M. Thomson, Physics of Solids, 2nd ed., McGraw-Hill Book Company, New York, 1970.) 23 23

24. Estimating Conductivity
• Question:
-- Estimate the electrical conductivity  of a Cu-Ni alloy
that has a yield strength of 125 MPa.
Adapted from Fig. 18.9, Callister 7e.
wt. %Ni, (Concentration C)
Resistivity, 
(10 -8
Ohm-m) 10 20 30 40 50
Yield strength (MPa)
wt. %Ni, (Concentration C) 10 20 30 40 50 60 80
100
120
140
160
180
125 30
21 wt%Ni
Adapted from Fig. 7.16(b), Callister 7e.
CNi = 21 wt%Ni
From step 1: 24 24

25. Pure Semiconductors: Conductivity vs T
• Data for Pure Silicon:
--  increases with T
-- opposite to metals
electrons
can cross
gap at
higher T
material Si Ge
GaP
CdS
band gap (eV)
1.11
0.67
2.25
2.40
Selected values from Table 18.3, Callister 7e.
Energy
filled
band
valence
empty
filled states
GAP ?
electrical conductivity, 
(Ohm-m) -1 50 10 1
000 -2 2 3 4
pure
(undoped)
T(K)
Adapted from Fig , Callister 5e. (Fig adapted from G.L. Pearson and J. Bardeen, Phys. Rev. 75, p. 865, 1949.) 25 25

26. Semiconductivity
Semiconductor do have a lower conductivity than metals but unique properties of semiconductors make them very useful materials.
Electrical properties of semiconductors are very sensitive to the presence of impurities:
Intrinsic semiconductors - electrical conductivity is based on the electronic structure of pure material.
Extrinsic semiconductors - electrical conductivity is dictated by impurity atoms.
WHY ? 26

27. Conduction in Terms of Electron and Hole Migration
• Concept of electrons and holes: + -
electron
hole
pair creation
no applied
applied
valence
Si atom
pair migration
electric field
electric field
electric field
• Electrical Conductivity given by:
# electrons/m 3
electron mobility
# holes/m
hole mobility
Adapted from Fig , Callister 7e. 27 27

28. Intrinsic Semiconductors
Number of electrons in conduction band increases
exponentially with temperature:
C is a material constant
Eg is the bandgap width
Thermally excited conductions electrons Eg
Holes left behind
0 K
RT ~ 300 K
An electron promoted into the conduction band leaves a hole (positive charge) in the valence band. In an electric field, electrons and holes move in opposite direction and participate in conduction
In Si (Eg = 1.1 eV) one out of every 1013 atoms contributes an electron to the conduction band at room temperature. 28

29. Intrinsic Semiconductors
Since both electrons and holes conduct the conductivity of an intrinsic semiconductor is
Electrons are more mobile than holes, μe > μh
In an intrinsic semiconductor, a hole is produced by the promotion of each electron to the conduction band. Therefore, n = p and
n (and p) increase exponentially with temperature, whereas μe and μh decrease (about linearly) with temperature.
Conductivity of intrinsic semiconductors increase with temperature (different from metals!) 29

30. Intrinsic Semiconductors30

31. Extrinsic Semiconductors
Extrinsic semiconductors - electrical properties (conductivity) is dictated by impurity atoms.
Example: Si is considered to be extrinsic at room T if impurity concentration is one atom per 1012 (remember our estimation of the number of electrons promoted to the conduction band by thermal fluctuations at 300 K)
Unlike intrinsic semiconductors, an extrinsic semiconductor may have different concentrations of holes and electrons. It is called p-type if p > n and n-type if n > p.
One can engineer conductivity of extrinsic semiconductors by controlled addition of impurity atoms – doping (addition of a very small concentration of impurity atoms).
Two common methods of doping are diffusion and ion implantation. 31

32. n-type Extrinsic SMs
When excess electron carriers are produced by substitutional impurities that have more valence electron per atom than the semiconductor matrix.
Example: phosphorus (or As, Sb..) with 5 valence electrons, is an electron donor in Si since only 4 electrons are used to bond to the Si lattice when it substitutes for a Si atom. Fifth outer electron of P atom is weakly bound in a donor state (~ 0.01 eV) and can be easily thermally promoted to the conduction band.
Impurities which produce extra conduction electrons are called donors, ND = NPhosphorus ~ n
Elements in columns V and VI of the periodic table are donors for semiconductors in the IV column such as Si and Ge. 32

33. n-type Extrinsic SMs n >>p
The hole created in donor state is far from the valence band and is immobile upon the promotion of the donated electron to the conduction band.
n >>p
Conduction occurs mainly by the donated electrons (thus n-type).
σ ~ ND |e| μe 33

34. Intrinsic vs Extrinsic Conduction
# 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)
no applied
electric field 5+ 4 +
Phosphorus atom
valence
electron
Si atom
conduction
hole
• p-type Extrinsic: (p >> n)
no applied
electric field
Boron atom 3 + 4
Adapted from Figs (a) & 18.14(a), Callister 7e. 34 34

35. Intrinsic Semiconductors
Pure material semiconductors: e.g., silicon & germanium
Group IVA materials
Compound semiconductors
III-V compounds
Ex: GaAs & InSb
II-VI compounds
Ex: CdS & ZnTe
The wider the electronegativity difference between the elements the wider the energy gap. 35 35

36. Doped Semiconductor: Conductivity vs. T
• 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 < 100 K: "freeze-out“,
thermal energy insufficient to
excite electrons.
-- for 150 K < T < 450 K: "extrinsic"
-- for T >> 450 K: "intrinsic"
Adapted from Fig , Callister 7e. (Fig from S.M. Sze, Semiconductor Devices, Physics, and Technology, Bell Telephone Laboratories, Inc., 1985.)
conduction electron
concentration (1021/m3) T
(K)
600
400
200 1 2 3
freeze-out
extrinsic
intrinsic
doped
undoped
doped
0.0013at%B
0.0052at%B
electrical conductivity, 
(Ohm-m) -1 50 10 1
000 -2 2 3 4
pure
(undoped)
T(K)
Adapted from Fig , Callister 5e. (Fig adapted from G.L. Pearson and J. Bardeen, Phys. Rev. 75, p. 865, 1949.) 36 36

37. Number of Charge Carriers
Intrinsic Conductivity
 = n|e|e + p|e|e
for intrinsic semiconductor n = p
  = n|e|(e + n)
Ex: GaAs
For GaAs n = 4.8 x 1024 m-3
For Si n = 1.3 x 1016 m-3 37 37

38. p-n Rectifying Junction
• 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: + -
p-type
n-type
Adapted from Fig , Callister 7e.
--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. + -
p-type
n-type
--Reverse bias: carrier
flow away from p-n junction;
carrier conc. greatly reduced
at junction; little current flow. + -
p-type
n-type 38 38

39. Properties of Rectifying Junction
Fig , Callister 7e.
Fig , Callister 7e. 39 39

40. Transistor MOSFET
MOSFET (metal oxide semiconductor field effect transistor)
Fig , Callister 7e. 40 40

41. Integrated Circuit Devices
Fig , Callister 6e.
Integrated circuits - state of the art ca. 50 nm line width
1 Mbyte cache on board
> 100,000,000 components on chip
chip formed layer by layer
Al is the “wire” 41 41

42. Ferroelectric Ceramics
Ferroelectric Ceramics are dipolar below Curie TC = 120ºC
cooled below Tc in strong electric field - make material with strong dipole moment
Fig , Callister 7e. 42 42

43. Piezoelectric Materials
Piezoelectricity – application of pressure produces current
at rest
compression induces voltage
applied voltage induces expansion
Adapted from Fig , Callister 7e. 43 43

44. Summary • Electrical conductivity and resistivity are:
-- material parameters.
-- geometry independent.
• Electrical resistance is:
-- a geometry and material dependent parameter.
• Conductors, semiconductors, and insulators...
-- differ in accessibility of energy states for
conductance electrons.
• For metals, conductivity is increased by
-- reducing deformation
-- reducing imperfections
-- decreasing temperature.
• For pure semiconductors, conductivity is increased by
-- increasing temperature
-- doping (e.g., adding B to Si (p-type) or P to Si (n-type). 44 44

45. ANNOUNCEMENTS
Reading:
Core Problems:
Self-help Problems: 45 45