Materials PropertiesMaterials Properties

• Electrical properties

• Magnetic properties

• Optical properties

Electrical propertiesElectrical properties

• Ohm’s law• Resistance, resistivity, conductivity

• Matthiessen’s rule

1

l

RA

IRV

ndeformatioimpuritythermaltotal

Electrical resistivityElectrical resistivity

Energy bandsEnergy bands

K L M

discrete energy levels(Pauli exclusion principle)

splitting into energy bands (N=12)

Electron Band StructuresElectron Band Structures

em p ty

filled

metal (e.g. Cu)

energy

valenceband

bandgap

conductionband

filled

em p ty

metal (e.g. Mg)

EF

EF

filled

em p ty

isolators (Egap>2eV)semiconductors

Egap

ConductorsConductors

EF

Semiconductors (intrinsic)Semiconductors (intrinsic)

band gap

n-type Extrinsic Semiconductorn-type Extrinsic Semiconductor

p-type Extrinsic Semiconductorp-type Extrinsic Semiconductor

The p-n DiodeThe p-n Diode

reverse biasforward bias

Magnetic propertiesMagnetic properties

• Magnetic field strength, magnetic flux density, magnetization, permeability, and magnetic susceptibility

1HMMHB

HB

rmm00

0r

The Magnetic FieldThe Magnetic Field

vacuum atmosphere/material

The Magnetic MomentThe Magnetic Moment

orbital contribution=> mlµB

spin contribution=> +/-µB

Bohr magneton: µB=9.27 x 10-24 Am²

Diamagnetic MaterialsDiamagnetic Materials

Paramagnetic MaterialsParamagnetic Materials

Ferromagnetic MaterialsFerromagnetic Materials

The B-H HysteresisThe B-H Hysteresis

remanent flux density

coercive force

Hard and Soft Magnetic MaterialsHard and Soft Magnetic Materials

soft:alternating magnetic fields

hard:permanent magnets

energy productcoercivity

Magnetic StorageMagnetic Storage

coil:magnetic field in gap

magnetic field:induces electriccurrent

Optical propertiesOptical properties

• Transmission

• Refraction

• Absorption

Electro magnetic wavesElectro magnetic waves

electric field E

magnetic field H (perpendicular to E)

light = electromagnetic wavelight = electromagnetic wave

wave: c=(const. light velocity in vacuum=km/s)photons: E=h(Planck constant, 6.63 x 10-34 J/s)

Light Interaction with SolidLight Interaction with Solid

I0=Itransmitted+Iabsorbed+Ireflected

transparenttranslucentopaque

heat

reflection (metals): absorption (electrons excitation by E) => re-emission of photonscolor (e.g. Au, Cu => only partial re-emission)

refraction: transmission into transparent material => decrease in v (n=c/v), bending at interface

AbsorptionAbsorption

Ireflected

Io

x (transparent medium)

Itransmitted

Iabsorbed

Itransmitted=I0(1-R)2exp(-x)absorption coefficientreflectivity

Photon Absorption in a (Semiconducting) SolidPhoton Absorption in a (Semiconducting) Solid1. hole/electron pair generation

Egap,max=hc/min (>3.1eV no visible light absorption=transparent)

Egap,min (max,visible=700nm) (<1.8eV all visible light absorbed=opaque)

2. hole/electron pair generation

in between colored!!e.g. red ruby Al2O3 with Cr2O3 impurity level in the band gap

Light Transmission in AlLight Transmission in Al22OO33

single crystal: transparent

poly-crystal: translucent

with 5% pores: opaque

internal reflection/refraction at grain/phase boundaries – porespolymers: scattering at boundaries betw. crystalline/amorphous regions

Effects/ApplicationsEffects/Applications

luminescenceabsorbing energy => re-emitting visible light (1.8eV<hv<3.1eV)

fluorescence (<1s)phosphorescence (>1s)

e.g. TV (fluoresc. coating) LED (forward bias diode – recombination=> light)

photoconductivityillumination => generation of charge carrierse.g. light meters, solar cells

optical fibres1/0 impulses – high information density 24000 telephone calls by two wires

e.g. 30000kg Cu corresp. to 0.1kg high-purified SiO2 glass

Laser ConceptsLaser Concepts

1. Xe flash lamp excite electrons from Cr3+ ions2. large number of electrons falls back to intermediate state 3. after approx. 3ms: spontaneous emission – triggers avalanche of emissions4. photons parallel to the rod are transmitted to the semi-silvered end

(light amplification by stimulated emission of radiation)(light amplification by stimulated emission of radiation)

monochromatic, high-intensitycoherent red beam