solid state chemistry che2007 (2026)

unsure terms to review, from lecture notes, don't really have unit 6

vacancy defect

• absence of atom

• not neutral electronically

• stoich not maintained

• Clcl^x → Vcl^.

interstitial defect

• extra atom where not supposed to be

• stoich not same

• not neutral charge

• /o [hole] → Xi^x

kroger-vink notation

Ms^c

• M: v - vacancy, I - interstitial atom letter, e - electron, h - hole

• s: site occupied; i - interstitial site, + - cation, - - anion

• c: difference in charge; ‘ negative, ^. positive, x null charge

  • charge on site - original charge

• eg. Alal^x - Al ion in Al site, neutral charge

• eg. Vcl^. - vacancy where chlorine, +ve

substituition defect

• different atom in crystal site, replacement

• charge: depends

• stoich change, ion change

• Xcl^x

• solid solution

schotty defect

• in material MX vacancy of M and X (both in formula, eg. Na and Cl missing)

• stoich is same

• neutral electric difference

• Vna’ + Vcl^.

frenkel defect

• atom/ion in lattice gets displaced into interstitial site

• stoich same

• not solid solution

• Clcl^x = Cli’ + Vcl

solid solution vs solid with defects

• matrix of 2 atoms w/ interstitial or substitution

• adding a different atom/ion

• defect is a point, with a hole

• vacancy, schotty, frenkel?

amorphous vs crystalline solids

• unpredictable, random spacing of molecule

• turn crystalline into this with high T

• symmetry

• predictable, infinite structure

• perfect 3D order, the same everywhere

fermi level

highest occupied energy level at 0K (HOMO at 0K)

• in doped: between extra level and band

3 types of conductivity, band structures

• metallic: continuous band

• insulating: band gap >4eV

• semiconducting: bandgap <4eV (electrons can jump gap with thermal excitation)

conductivity σ

σ = η x e x μ

• metallic 10^6 S/cm

  • inc T dec σ

• insulating < 10^-12 S/cm

  • inc T inc σ a tiny bit

• semiconducting 10^-2 S/cm

  • inc T inc σ a lot

intrinsic vs extrinsic semiconductors

• pure materials, band structure allows (natural small band gap)

• electrons promoted to conduction band, leaves positive holes in valence band

• electrons move toward positive electrode

• impurity increasing conductivity, use dopants

• extra acceptor/donor levels, leads to conduction

dopants/extrinsic examples

Si + Group III/V dopant

• p type: Ga

• n type: As

p type semiconductor

• Ga in Si

• empty levels above valence band (acceptor levels)

• electrons promoted and leave Positive hole

n type semiconductor

• As in Si

• filled levels just below conduction band

• electrons can easily jump to CB (conduction)

wavelength equation

Eg = hc / λ

• E in J, convert to eV: divde by electron charge

• wavelength in m, convert to nm: nm x 10^-9 = m

how to identify type of conductor of material

• metal: exactly half filled orbitals, jump easily

• insulator: gap between orbital energies too big (eg. 3p → 4s)

• semiconductor: idk

density of states example graphs

look

tuneable bandgap

• bandgap determined by chemistry

• multicell can match different sun spectral lines

• heavier elements → bigger overlap of orbitals, smaller band gap

  • smaller Eg → bigger wavelength λ

biasing

• applying potential to p-n junction

• changes voltage of band bend

• forward:

  • + potential to p type (same)

  • stronger current, flatten the bend

  • large current flow p → n

  • in LEDs: more light

• reverse:

  • - potential to p (opposite)

  • higher potential barrier, wall

  • conduction stopped, tiny current flow n → p

depletion region

• when doped carriers move, leave behind charges and create depletion region

• creates Ve field opposite (points toward -ve instead of +ve)

• once layer created, doesn’t move and incoming charges bounce off

photodiode junction (solar cell function)

• photon absorbed (hv > Eg), creates carriers:

• promotes electron in depletion region, hole and electron swept to sides, creates current (moving charge)

• e- go to n side, h+ goes to p side

photocurrent

• current of carriers from light (photodiode junction)

• flow reverse direction (n → p)

• instant and unreliable

photovoltaic effect

• consequence of photocurrent

• generate extra voltage V across junction??

• forward bias?

• allows solar cell to deliver power

solar cell unit

• ** study image it was on the midterm bruh

• top to bottom layers: n Si layer - depletion zone - p silicon layer

  • n: excess electrons

  • depletion zone: electric field (- on n side, + on p side)

  • p: excess holes

• connect the layers to a circuit, electrons move → +ve (attraction)

• sunlight energy creates holes and electrons which are swept to sides

schokley-queisser limit (limitations of solar cells)

• photon only absorbed if = Eg or bigger (thermal waste if can’t bridge semiconductor gap)

• excess energy if energy is bigger than band gap (lost as heat)

• some carriers recombine and photon emitted

• max efficiency: 33%

multijunction solar panels

• many material layers, each can absorb different wavelengths (image)

• material needs:

  • high light absorption

  • high mobility/lifetime of carriers

  • metal connections for electron flow

  • different band gaps for light to go through

atom quantum numbers

quantum numbers: n l ml ms

• n: principle

• l: n-1

• ml: -l to l values (eg. l = 3; ml = -3, -2, -1, 0, 1, 2, 3 → 7 levels)

  • fill electrons from top (highest number), Hunds rule

• ms: -1/2 or ½ spin

angular momentum J

• angular momentum J = | L + S |

  • half filled: use -

  • L: orbital sum (filled orbitals of ml: add)

  • S: no. of filled ml orbitals x half/full filled

    • eg. 3 × ½ = 3/2

magnetic moment μB

of 1 electron: μB (bohr magnetron)

• unit of measurement for others

spin moment of electron μS

μS = sqroot [4S ( S+1 )]

permeability

μr = 1 + χ

susceptability χ

χ = M/H

• M: moment

• H: magnetic field

diamagnetism vs paramagnetism

di:

• slight repulsion of field

• χ don’t change, -ve

• no unpaired electrons (di = 2)

para:

• moments follow the field applied

• χ small but +ve

• unpaired electron is attracted

ferromagnetism vs antiferromagnetism

ferro:

• moments line up

• decrease with temp, field dependent

• χ »»» 0

• all moments point same direction ↑↑↑↑↑↑↑↑↑

antiferro:

• moments are opposite (antiparallel), net moment = 0

• inc with temp, field independent

• χ close to 0

• ↑↓↑↓↑↓↑↓↑↓↑↓

curie law, curie weiss law

curie: χ = C/T

weiss: χ = C/ (T-ϑ)

• ϑ = weiss constant/temp

• arrangement shifts to ferro/antiferro ordering

for a paramagnet:

• disordered moments locally align with field, harder with increased temp (susceptibility dec)

ferromagnetic ordering

• arrows same direction

• becomes more susceptible

• Tc: curie temp of ferro transition

  • below Tc: ferromagnetic

  • above Tc: paramagnetic

antiferromagnetic ordering

• lowers susceptability, random to opposite arrows

• behaviour diverges at Tn

soft vs hard magnet

soft:

• thin hysterisis curve graph

• high permeability, low coercivity

• ferromagnetic, very accompanying for magnetic field

  • drags flux lines into material, shields inside

hard:

• harder to magnetize → function permanet magnet

• high coercivity: resistance to switching direction

• wide hysterisis curve

• bigger BHmax

permanent magnet

• all hard ferromagnets

• ALNICO, rare earth, ferrites

ferrimagnetism?

• magnetic moments are aligned but slightly unequal, result in slight magnetic moment

• more spin up than spin down → net spin behaviour

ALNICO

• big Tc, can work well in high temp

• not too expensive, popular

• composition: alloy of Al, Ni, Co

• mix of soft and hard magnet (soft shields hard)

rare earth magnets

• strongest, biggest BHmax, highest performance

• expensive

• samarium based

  • SmCo5, Sm2Co17 (rare materials)

  • Tc = 1000K, very expensive

  • strong anisotropy

• neodymium based

  • Nd2Fe14B

  • Tc = 585K (doesn’t work at high T)

  • total magnetic moment: 37 μB per formula unit

anisotropy

• lack of symmetry, opposite of isotropy

• material/crystal structure is longer in one direction

ferrites/hexaferrites

hexa:

• simliar to Nd but cheaper mateiral

• ferrimagnetic

• SrFe12O19

• BaFe12O19

cheap insulating, corrosion resistant

popular (fridge magnets)

spin ice and glass

ice: point in and out, total is 0 (not up and down)

frustrated structure: nothing fits

glass: amorphous like glass, ~0

LED

• use direct band gap

• light emitting diode

• narrow emission spectrum depending on band gap (more efficient than lightbulb)

quasi fermi levels

• fermi splits into 2 qf levels, one at CB/VB

• stronger bias → more split → population inversion

• Efc - Efv > Eg

spontaneous emission

• fluoresence: same spin, short emission

• phosphorescence: need to spin flip, longer relaxation

• electron goes from bottom of CB to top of VB, emits photon

absorption coefficient 𝛼

• log scale

• graph vs photon E (eV) → straight line direct, bend at top indirect

• 𝛼 indirect «« 𝛼 direct

phonon

• vibration of lattice, helps change momentum

• assist transition in indirect band gap

excitonic transitions

• excition/quasi particle: positive hole with electron orbiting

emission losses LED

internal quantum efficieincy: photons generated/carrier injuected

external quantum efficiency: photons emitted externally/carrier injected

edquations??

external quantum efficiency ηex

lower ηex:

• internal reflection

  • solve by textured/round surface

  • angle = sin^{-1} (n1/n2)

  • GaAs = 15.3 degrees

• fresnel loss

  • slow increase of refraction index reduces fresnel loss

  • fraction reflected = ( [n2-n1] / [n2+n1] )^{2}

  • GaAs = 0.34 → 34% reflected

• use heterojunctions to help with reabsorption

LED structure

• layered semiconducting materials

• top to bottom: p - active layer - n

  • active region: GaAs, p- doped p type

    • has a smaller band gap, hetero

    • electrons and holes accumulate there

    • recombine and emit photon

  • light not reabsorbed since the outer layers have a larger band gap

laser

• monochromatic emission (1064nm)

• needs population inversion (more electrons in higher level, for laser emission

• emission needs spin flip, long lifetime

laser examples

ruby:

• Al2O3 with Cr³+; 3 levels

neodymium

• Y3Al5O12 with Nd³+; 4 levels

• f to f transition has long lifetime

semiconductor

• population inversion by more electrons in excited than ground state

• need enough e- and holes in active region hv > Eg

resistivity ⍴

⍴ = 1/σ

• almost linear w/ T

superconductor behaviour

• conducts electricity without resistance below critical temperature Tc

• temp reversible, field reversible

• lose with magnetic field over critical level Hc