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!”


Altair 8800 Computer

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/a-3π/a -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-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

eh

Coulomb force

n=3n=2n=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

eh

Coulomb force

n=3n=2n=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

ωωε

ω

ωωε

Γ=≈−≈ pp

rp

r

2

2

2

2

)(")(p

p

ccc λλ

ω

ωωε

ωωα

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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