Bohr quantized the atom…An atom has a set of energy levels

Some (but not all) occupied by electrons

Not really dealing with isolated atoms, but 3D solids

As atoms approach each other, each affects the other

Energy levels are altered, splitting into bands

Each atom in the system produces another energy level in the band structure

Broadening of energy levels as atoms approach

Degenerate: All electrons in an orbital have the same (lowest) energy

Electronic structure of Solids

Ele

ctro

n en

ergy

gas

Outer levels begin to interactOverlapping levels

N=5N=4

E=0

N=3

N=2Ele

ctro

n en

ergy

3.67Å Internuclear distance

GasSolid

Ele

ctro

n en

ergy

E=0

N=2

N=3

N=4

continuum

Overlapping bands

Energy bands for solid sodium at internuclear distance of 3.67Å

N=5N=4

E=0

N=3

N=2Ele

ctro

n en

ergy

3.67Å Internuclear distance

GasSolid

Immediate implication for X-Ray microanalysis…

Electron transitions from split levels (bands) will result in photon emission energies that do not reflect the discrete degenerate level…

Conduction band:

First empty band above the highest filled band

Valence band:Outermost band containing electrons

nucleus

Conduction band

Valence bandOutermost band containing elelectrons

Electron energy

Bandgap

Bandgap

Bandgap

Partially full

Full

Full

Empty band

Transitions from the valence band involved in characteristic X-ray emission will be energy shifted depending on bond lengths, etc.

Resulting X-Rays will not be monochromatic

These will be Kα X-rays for ultra-light elements nucleus

Conduction band

Valence band

Electron energy

Bandgap

Partially full

Empty band

N=1 (K)

N=2 (L)

Classification of solids:

Conductors

Insulators

Semiconductors

Conductors:

Outermost band not completely filled

Essentially no band gapoverlaplots of available energy states if field is applied

Metals and Alkali metals

Insulators:

Valence band full or nearly full

Wide band gap with empty conduction bandEssentially no available energy states to which electron energies can be increased

Dielectric breakdown at high potential

Conduction band Empty

Valence band Full

Eg Wide bandgap

Semiconductors:Similar to insulators but narrow band gap

At electrical temperatures some electrons can be promoted to the conduction bandMost are cubic Diamond FCC (single element)

Some common band gaps:Element gap (ev)

Ge 0.6Si 1.1GaAs 1.4SiO2 9.0

Conduction band Almost Empty

Valence band Almost Full

Conduction band Empty

Valence band Full

T > 0K T = 0K

Eg bandgap

SZn

Mark McClure, UNC-Pembroke

Zinc blende (FCC ZnS)

Semiconductors are either intrinsic or extrinsicIntrinsic Semiconductors: Pure state

Example: Covalently bonded, tetravalent Si lattice

Promotion of an electron to the conduction band leaves “hole” in the valence band = electron-hole pair

Apply an electric field and the electron will migrate to +

The hole will migrate to – (that is, the electron next to the hole will be attracted to the +, leaving a hole toward -)

Net propagation of hole

Ec

Ev

Eg

- +

Extrinsic Semiconductors:Doped with impurity atoms

p-typen-type

n-typeDope Si with something like pentavalent antimony (5 valence electrons)

Narrows the band gap relative to Si

easy to promote Sb electron

Majority carriers are electrons in conduction band

Minority carriers are holes in valence band

Lattice doped with donor atoms

localized energy levels just below conduction band

Si

Sb

Ec

Ev

Ed

Si lattice with n-type dopant

p-typeDope Si with something like trivalent indium (3 valence electrons)

Incomplete bonding with SiNearby electron from Si can fill hole

Majority carriers are holes in the valence band

Minority carriers are electrons in the conduction bandLattice doped with acceptor atoms

localized energy levels just above valence band

Si

In

Ec

Ev

Ea

Si lattice with p-type dopant

Fermi Level:

That energy level for which there is a 50% probability of being occupied by an electron

Conduction band

Ec

Ev

Eg

Valence band

Ec

Ev

Eg

Valence band

Conduction band

Ef

Ef

Intrinsic

n-type

Recombination

Electron-hole pairs not long lasting

Electron encountering hole can “fall” into it

Free time = microsecond or less

The p-n junction

Single crystal of semiconductor

Make one end p-type (dope with acceptors)Make the other end n-type (dope with doners)

The junction of the two leads to rectification

Current only passed in one direction (diode)

In the region of the junction

Recombination = depletion of region with few charge carriersResults in “built-in” electric field

++++++

Depletion width W

Space-charge layers

Direction of built-in field

-------

p n

Energy band diagram for p-n junction at equilibrium

++++++

Depletion width W

Space-charge layers

Direction of built-in field

-------

p n

Ecp

Evp

Ecn

Evn

EfnEfp

eV0

Apply eV0 to get diffusion

Energy band diagram for p-n junction – applied forward bias

++++++

Depletion width W

Space-charge layers

Direction of built-in field

-------

p n

Ecp

Evp

Ecn

Evn

EfnEfp

eV

Apply small V to get diffusion

Depletion width reducedBuilt-in field reducedBarrier height reducedDiffusion current increased

If Vforward = V0

No barrierPass large current in one direction

+ -

Energy band diagram for p-n junction – applied reverse bias

++++++

Depletion width W

Space-charge layers

Direction of built-in field

-------

p n

Ecp

Evp

Ecn

Evn

eV

Depletion width increasedBuilt-in field increasedBarrier height increased - Diffusion current decreased

Becomes CapacitorNo current passed

+-

So:Can use reversed bias p-n junction as voltage regulator

Zener diodeVoltage too high? Overcome gap energy and pass current

Can use forward bias p-n junction for rectificationAC → DCtransformerAnalog-to-digital conversion

LEDRecombination – “tune” bandgap to achieve photon emission

at the required wavelength GaAs (IR) GaInN (blue) GaAsP (red) YAG:Ce (white)

Ternary and quaternary compounds allow precise bandgap engineering

PIN diode (p and n sections separated by high resistance material)light detectionX-ray detectionelectron detection

-Each of these serve to excite electron-hole pairs -Bias properly and get amplification rather than simple propagation

Bipolar transistor = pair of merged diodes - NPN or PNP

N P N P N P

collector emitter collector emitter

base base

Three voltages (NPN)

Collector = + relative to base (collects electrons)

Emitter = - relative to base (emits electrons)

Small adjustments of the current on the base results in large changes in collector current.

= current amplifier

Amplify weak signals

Use small currents to switch large ones

Simple optical encoding:Generate sine wave by LED passing ruled slidePhototransistor sees varying light intensitycurrent output varies with base current

Diode rectifies

AC→DC

Square waves

Digital output to counter