Solids, Conductors, Insulators & Semiconductors

Solids: Conductors, Insulators and Semiconductors
•  Conductors: mostly metals
•  Insulators: mostly nonmetal materials
•  Semiconductors: metalloids
AHR, Abril-Julio, 2011
Conductor Insulator Semiconductor
Valence Band
in red
Conduction Band: white
Band gap
No gap

Sodium According to Band Theory
Conduction band:
empty 3s antibonding
Valence band:
full 3s bonding
No gap

Semiconductors
•  Metalloids: semiconducting elements
–  low electrical conductivity at room temperature
–  Electrical conductivity increases with temp.
•  Gap between valence and conduction band is intermediate
in size
•  Semiconducting elements form the basis of solid
state electronic devices.
–  Metalloids (such as silicon or germanium) are semiconducting
elements whose electrical conductivity increases as
temperature increases.
–  A striking property of these elements is that their
conductivities increase markedly when they are doped with
small quantities of other elements.

Semiconductors
•  Semiconducting elements form the basis of solid
state electronic devices.
–  When silicon is doped with phosphorus, it becomes an n-
type semiconductor, in which electric current is carried by
electrons.
–  When silicon is doped with boron, it becomes a p-type
semiconductor, in which an electrical current is
carried by positively charged holes
–  Joining a p-type semiconductor to an n-type
semiconductor produces a p-n junction, which can
function as a rectifier.
–  A rectifier is a device that allows current to flow in
one direction, but not the other.

Figure 13.29: Effect of doping silicon.

7
A p-n junction as a
rectifier.

SEMICONDUCTORS
•  Made from materials that have four valence electrons in
their outer orbits
•  Germanium and silicon are the most common
semiconductor materials used in solid-state devices
•  Silicon is preferred due to its ability to withstand heat
•  When refined into a pure form, the molecules arrange
themselves into a structure called a lattice structure
•  A pure semiconductor material such as silicon or
germanium has no special properties and will make a poor
conductive material.

•  To make semiconductor material useful for solid-state
components, it is doped with an impurity
•  This impurity could be indium or gallium, both of which
have only three valence (trivalent) electrons
•  With the doping of impurity, the lattice structure changes,
leaving a hole in the material where an electron could
reside.
•  Since it now lacks an electron, the material is no longer
electrically neutral, it now carries a net positive charge…
hence P-type material.
•  In a P-type material, designate the holes as the majority
carriers, and electrons the minority carriers
P-type MATERIAL

P-type MATERIAL
Lattice structure of a P-type material

•  Is made by doping semiconductor material with an
impurity that has five valence (pentavalent) electrons
such as arsenic or antimony
•  Now the lattice structure has an excess of electrons,
and a net negative charge… hence N-type material
•  These excessive electrons will enable free electron
movement under certain conditions, much like a
conductor.
•  In an N-type material, they designate the electrons
as the major carriers, and holes as the minority
carriers
N-type MATERIAL

N-type MATERIAL
Lattice structure of a N-type material

•  All solid-state devices are made from a combination
of P and N-type materials
•  The type of device formed is determined by how the
P and N-type materials are connected; the number of
layers; and thickness of layers
•  Examples:
SOLID-STATE DEVICES
The PN junction or
diode
The
transistor

•  In the nineteenth century, scientists were rarely
inventors: Samuel F.B. Morse, Alexander Graham
Bell, Thomas Alva Edison
•  In the twentieth century, scientists invaded the
domain of invention: John Fleming invented the
vacuum diode tube and Lee De Forest invented the
triode tube
•  The transistor can be viewed, as can the laser, as an
invention of physicists.
–  Source: Bunch and Hellemans, The Timetables of Technology,
Simon and Schuster, 1993

William B. Shockley (1910-1989)
•  Known as the Father of the Transistor
•  joined Bell Labs in 1936 in the vacuum tube
department (solid state physicist)
•  Moved to the semiconductor laboratory:
–  It has today occurred to me that an amplifier using
semiconductors rather than vacuum tubes is in principle
possible.

Walter Houser Brattain
•  Experimental physicist who also worked on vacuum
tubes
•  Joined Shockley and Bardeen in semiconductor
research.

John Bardeen (1908-1991)
•  Physicist, Naval Ordnance Laboratory 1941-1945
•  Research Physicist, Bell Telephone Laboratories 1945-1951 (theorist)
•  Professor of Electrical Engineering,
–  University of Illinois, 1951-1978
•  Nobel Prize in Physics: 1956 and 1972
•  transistor (1956) and superconductivity (1972)
–  I knew the transistor was important, but I never foresaw the
revolution in electronics it would bring.

Nobel Prize in 1956
•  Shockley, Brattain and Bardeen start
working with p- and n- type germanium
and silicon semiconductors in 1946
•  Bardeen and Brattain put together the
first transistor in December 1947:
–  a point-contact transistor consisting of a
single germanium crystal with a p- and an
n- zone. Two wires made contact with the
crystal near the junction between the two
zones like the whiskers of a crystal-
radio set.

•  Shockley immediately set out to define the effects that they
had observed, i.e., to explain the physics of transistors
•  A few months later, Shockley devised the junction
transistor, a true solid-state device which did not need the
whiskers of the point-contact transistor.
•  AT&T licensed the transistor very cheaply to other
manufacturers and waived patent rights for the use of
transistors in hearing aids, in the spirit of its founder,
Alexander Graham Bell
Shockley s sandwich
transistor

Manufacturing transistors on a chip
•  Shockley Semiconductor Laboratories,
Palo Alto, CA (1954)
–  the beginnings of Silicon Valley
•  Fairchild Semiconductors founded in Mountain
View, CA (1957) by eight Shockley employees
including Gordon Moore and Robert Noyce
•  Bell Labs had made several improvements in the
manufacturing of crystals of silicon and germanium
with the impurities needed to create semiconductors

Meanwhile….
•  Jack Kilby worked for Texas Instruments
•  Conceived of a manufacturing method that
allowed the miniaturization of electronic circuits
on semiconductor chips, called integrated circuits
or ICs.
•  Kilby had reduced the transistor to the size of a
match head
•  Texas Instruments sold these for $450.

And at Fairchild….
•  Noyce adapted a system called planar
manufacturing, in which all the transistors and
resistors were formed together on a silicon chip
with the metal wiring embedded in the silicon.
•  Noyce filed for a patent five months after TI
•  Lawsuit: TI claimed patent infringement; TI lost
but companies needed licenses from both
companies.
–  source: Shurkin, Engines of the Mind, 1984

Field Effect Transistor (Lucent)

•  Due to improvements in manufacturing, integrated
circuits became smaller and smaller
•  Gordon Moore observed that the number of
transistors on a chip seems to double every year….
–  Moore s Law: the number of transistors on a chip seems
to double every 18 months, while the price remains the
same.
–  Grosch s law for mainframes: every year, the power of
computers doubles while the price is cut in half

A Little Economic Sociology
•  No matter how rich you are working for
someone else, think of how rich you could be
if you worked for yourself!
•  People figured out quickly that one could bolt
from one company, and with enough science,
engineering and venture capital start a new
company down the street.
•  Silicon Valley grew and grew and grew!
–  source: Shurkin, Engines of the Mind, 1984

Bergin s musings….
•  The greatest deterrent to success is success!
•  Large companies tend to be conservative and
bureaucratic with lengthy approval processes which
stifle new ideas.
•  Small companies have no history, they need to take
risks and they have no stockholders to answer to:
Apple, Osborne, etc.
•  Starting technology companies became the new
gold rush (and it was in California!)

Intel
•  Noyce, Moore, and Andrew Grove leave Fairchild
and found Intel in 1968
–  focus on random access memory (RAM) chips
•  Question: if you can put transistors, capacitors,
etc. on a chip, why couldn t you put a central
processor on a chip?
•  Ted Hoff designs the Intel 4004, the first
microprocessor in 1969
–  based on Digital s PDP-8

Microcomputers
•  Ed Roberts founds Micro Instrumentation Telemetry
Systems (MITS) in 1968
•  Popular Electronics puts the MITS Altair on the
cover in January 1975 [nee PE-8, Intel 8080]
•  Les Solomon s 12 year old daughter, Lauren, was a
lover of Star Trek. He asked her what the name of
the computer on the Enterprise was. She said
computer but why don t you call it Altair because
that is where they are going tonight!

Intel processors
•  CPU Year Data Memory MIPS
•  4004 1971 4 1K
•  8008 1972 8 16K
•  8080 1974 8 64K
•  8088 1980 8 1M .33
•  80286 1982 16 1M 3
•  80386 1985 32 4G 11
•  80486 1989 32 4G 41
•  Pentium 1993 64 4G 111

Inter-band absorption (direct gap)
Finite amount of electrons results in filled and empty states
In semiconductor, highest-energy filled states are in the valence band
Lowest unoccupied states are in the conduction band
E
k0 π/a 2π/a 3π/aa -2π/a -π/a
valence electrons
conduction electrons
filled
empty
Egap
Energy difference between valence and conduction band
is called the bandgap of the semiconductor
Material is called a semiconductor if Egap < 4eV, and insulator if Egap > 4eV

Energy levels in real semiconductors
In three dimensions, the dispersion relation depends on direction in the
crystal
source: Optical
Properties of
Semiconductor
Nanocrystals,
Gaponenko

Single atoms are surrounded by bound electrons
In solids: electrons in neighboring atoms can interact:
⇒ electron levels are modified, resulting in energy bands
In semiconductors the highest-energy band that is filled (occupied by electrons)
is the valence band, and the lowest unoccupied states are in the conduction band
strongest optical response if electron transitions can be induced
E
k0 π/a 2π/a 3π/a-2π/a -π/a
filled
empty
Egap valence
states
(usually filled)
conduction
states
(usually empty)
E
k
E
k

Direct-gap semiconductor: highest occupied and lowest unoccupied state occur at
k=0
Light can induce electronic transitions if
energy and momentum are conserved:
Efinal – Einitial = Ephot and Δk = ≈ 0
(Photon: long wavelength compared
to atomic spacing ⇒ kphot « π/a )
photk
E
k
Direct gap semiconductors
Photons with E < Egap have insufficient energy to kick a valence
electron into a conduction state ⇒ absorption starts at Ephot =
Egap
These band-band absorptions have the usual implications for n and κ
(recall Kramers-Kronig relations)

Indirect-gap semiconductor: highest occupied and lowest unoccupied state have
Δk≠0
Direct transitions possible for Δk≈0
⇒ strong direct interband absorption
occurs at E > Egap
Other possibility: momentum and
energy can be conserved by photon
absorption and simultaneous absorption or
emission of a phonon:
Indirect transitions possible with
assistance of a phonon
Shown here are optically induced transitions
- during phonon emission
a phonon is generated in the process
- during phonon absorption
a phonon is generated in the process
Egap
Egap

Excitons
Excitons are combined electron-hole states:
A free electron and a free hole (empty electronic state in the valence band)
exert Coulomb force on each other:
hydrogen-like bound states possible: excitonic states
e
h
Coulomb
force
n=3
n=2
n=1
E
k
Eb
Wave functions of electron and hole look similar to free electron and free hole
Note: exciton can move through crystal, i.e. not bound to specific atom!
Eb is the exciton
binding energy =
energy released upon
exciton formation, or
energy required for
exciton breakup

Excitonic absorption
Light can excite an electron from the valence band and generate an exciton
at energies slightly below the bandgap
⇒ see absorption at Ephot = Egap – Eb (absorption slightly below Egap)
Exciton binding energy on the order of a few meV
Thermal energy at room temperature: kT ~ 25 meV
⇒ exciton rapidly dissociates at room temperature
⇒ absorption lines broaden / disappear for higher temperatures
e
h
Coulomb
force
n=3
n=2
n=1
E
k
Eb

Optical transitions related to dopant atoms
Ga: 3 valence electrons
Si: 4 valence electrons
As: 5 valence electrons

Donor levels
Substitute Si atom with As atom (impurity atom in the Si lattice):
weakly bound extra valence electron
Low T: donors neutral, electron weakly bound
lew energy light can excite donor electron in to conduciton
band
Binding energy Ed similar to kT at room temperature
( RT ):
At room temperature the bound electron is quickly released
⇒ impurity mostly ionized at RT : Arsenic is a donor in Si
At RT such transitions are typically too broad to observe
Low T
RT

Acceptor levels
Substitute Si atom with Ga atom : empty electronic state just above the Si
valence band: at finite temperature, Si valence electron may fill acceptor level
⇒ location of unoccupied valence state (hole) can orbit the charged Ga dopant
Binding energy Ea similar to kT at room temperature ( RT ):
At room temperature the hole can leave the dopant,
producing a free charge
‘hole’ =
available
electron
state

Infrared absorption due to dopants
Dopant binding energies low: donor level related absorptions invisible at RT,
but observable at low temperatures
Example: direct valence band → acceptor level absorption in boron doped Si
Transition at ~40 meV ⇒ absorption at λ≈30 µm : infrared

Dopant related transitions
Possible dopant related transitions:
Typically visible at low T, but not clearly observable at RT

Free carrier absorption (1/2)
At RT, predominant dopant related absorption is free carrier absorption
in which a photon excites an electron into a higher lying state
Example: p-type semiconductors: filled states in the conduction band:
optical transitions possible at Ephot < Egap !
Free electrons:
absorption typically indirect
phonon-assisted transition
Free holes can make direct transitions
form the heavy-hole band
to the light-hole band
⇒ holes cause stronger free carrier
absorption than electrons

Free carrier absorption (2/2)
Free electron absorption can be described by the Drude model
Dopant levels in semiconductors range from ~1014 - 1018 /cm3
which is ~108 – 106 lower than free electron densities in metals
Plasma frequency of doped semiconductors 104 - 103 lower than of metals: IR
3
2
3
2
2
2
)(",1)('
ω
ω
τω
ω
ωε
ω
ω
ωε
Γ
=≈−≈
pp
r
p
r
2
2
2
2
)(")(
p
p
ccc λ
λ
ω
ω
ωε
ω
ωα
Γ
=
Γ
≅≅
At frequencies above plasma frequency,εr and α described by
Electron FCA up for lower energies
Free hole absorption less well defined

Band to band transition

Direct vs indirect gaps

Solids, Conductors, Insulators & Semiconductors

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