LED & Crystal Structures Summary PDF

## TOPIC 2 - From Crystals to LED ### INTRODUCTION - LED & OTHER LAMPS The energy consumption for light contributes to a total of 4% CO2 emission and consumes 22% electricity in the world. | Name | Incandescent light bulb | Halogen lamp | Compact fluorescent lamp | LED | |:---|:---|:---|:---|:-...

## TOPIC 2 - From Crystals to LED ### INTRODUCTION - LED & OTHER LAMPS The energy consumption for light contributes to a total of 4% CO2 emission and consumes 22% electricity in the world. | Name | Incandescent light bulb | Halogen lamp | Compact fluorescent lamp | LED | |:---|:---|:---|:---|:---| | Life time | 1000 h | 2000 - 4000 | 10'000 h | 50'000 h | | Intensity | 16 Lumen per watt | 20-30 Lumens/Watt | 50-70 Lumin/Watt | 200 Lumin/Watt | | Surrounding | Inert gas or vacuum | Add lodin or Br improve lifetime | Contain Hg | | | Negativ Companson 6h light/Day | ½ year | 23 years | | | ## CRYSTALS * **What is a crystal?** * A crystal is a solid in which atoms, molecules, or ions are arranged in a highly ordered, repeating pattern extending in all directions. * **Lattice Structure:** regular, repeating arrangement of atoms or molecules * **Unit Cell:** smallest repeating unit within lattice ### Difference between SQUARE - 2 HEXAGONAL - Packing (2D) | | Square packing (cubic lattice) | Hexagonal - packing | |:---|:---|:---| | Coordination number (CN) | CN = 4 | CN= 6 | | Efficiency | 80% | 90% | | Proof | $ \frac{πr^2}{4}$ *4 = $πr^2$ = 78.5% | $ \frac{πr^2}{4} *6 = \frac{3}{2} πr^2 \approx 90.7%$ | **3D How to pack most efficient** Solid state structures packing of spheres * Layer A (2D & hexagonal) * Efficiency is the same for both variants, but crystal-structure won't be the same **Close - packed structures: FCC & HCP → packing efficiency of about 74%** | | hcp | CCP | |:---|:---|:---| | Koordination number | 12 | 12 | | Other names | | fcc (face centered cubic) | | Unit cell | ABA | ABC | **Voids in the close packed structures** | | Octahedral hole | Tetrahedral hole | |:---|:---|:---| | Koordination number: | 6 | 4 | | How many holes per constituting atom in a FCC- lattice | 1 | 2 | * The FCC - lattice structure has two different voids ## Non-close-padding structures: Simple Cubic (SC) & Body-Centered Cubic (BCC) | | Simple cubic lattice (SC) | Body-centered cubic lattice (bcc) | Comparison FCC | |:---|:---|:---|:---| | Efficiency | 52% | 68% | 74% | | Numbers of atoms in a unit cell | $8 * \frac{1}{8} = 1 $ Atom | $ 8*\frac{1}{8} + 1 = 2 $ Atoms | $(6*\frac{1}{6}) + (8 * \frac{1}{8}) = 4 $ Atoms | | Calc. | | | | * **Prototypical crystal structure** Use the diagram of the unit cell for sodium amide to confirm the 1:1 Na": [NH2] ratio. * Space for 8 tetrahedral holes for every unitcell, but 4 are filled * 2 per conc. atoms 1:1 stoichio * foc -structures ### Lattice systems | Crystal family | Lattice system | Point group (Schönflies notation) | Bravais Lattices | |:---|:---|:---|:---| | Triclinic (a) | | C1 | p | | Monoclinic (m) | | C2h | mP; mS | | Orthorhombic (o) | | D2h | oP; oS; oI; oF | | Tetragonal (t) | | Dah | tP; tI | | Rhombohedral | | D3d | R | | Hexagonal (h) | Hexagonal | Dah | hP | | Cubic (c) | | Oh | cP; cI; cF | ### **Lattice parameter** → dimensions of unit cell * All crystals fall into one of the seven lattice Systems. They are related but NOT the same * The lattice is written as: $\frac{a}{b} \frac{c}{c} α, β, γ$ * For cube the following applies: $ α = β = γ = 90° $ $ a = b = c $ → Every edge is the same **However** * if a = b + c & α = β = γ = 90° → tetragonal * if a= b + c & α = β = γ = 90° → orthonormal * if a b c & α = β = γ → monoclinic * if a b c & α β γ → triclinic ## Prototypical crystal structure → NaCl & similar * NaCI-lattice = NaCI-Gitter * Cl (fcc sublattice) * Na (filling octahedral holes) **Examples with same structure:** * LiH * LiF, LiCl, LiBr, Lil * NaH * NaF, NaCl, NaBr, Nal, * KH * KF, KCI, KBr, KI * RbH * RbF, RbCl, RbBr, Rbl * CsH * CsF * Cs to big so CSF, Cs Br 1 CSI looks like : Radius Cs+ = 170 pm Radius Cl = 181 pm **Unit cell of CSCI** * body centered cubic * CN-8 * → 2 Inter penetrating cubic systems ## Prototypical crystal structure → Ca Fz & Similar * fluorite * Ca (fcc) * F (in tetrahedral holes) * CN= 4 * →every hole is filled! * L> 2 in every constituting atom * Ls 8 per unitcell **Ca & F => 1:2** * CaF2, SrF2 and BaF2 * CeO2 and ZrO2 ## Prototypical crystal structure → CaTiO3 & similar * **Perovskite** → Important Crystal Name **General:** * CN (Ca) = 12 * CN (Ti) = 6 * Perovskite = ABO3 (A2+, B4+, O2-) * Ca does not connect with Ti due to distance & O being bigger than Ti. **Pytagoras:** ($\frac{a}{2}$)² + ($\frac{a}{2}$)² = (a + ro)² ⇒ a² = 2 (ra + ro)² = a = √2 (ra + ro) * **Assumption:** All atoms touch each other (perfect touch) ⇒ a = 2 (r₃ + ro) ⇒ $\frac{a}{2} = (r₃ + ro)$ **(Goldschmidt tolerance - factor)** to determine whether the atoms can form a perovskite ↳ Between 1- 0,9 for perovskite **eg:** * For BaTiO3 ⇒ Ba is to big for Perovskite (+ > 1, trigonal) * Sn TiO3 ⇒ +=1 * Ca Ti Os ⇒ + < 0,964 * ! But + < 0,9 destabalizes structure ### Different perovskites "structures" * (A2+, B4+, O2-) ↳ till now * (A*, B2+, O) ↳ New ⇒ CsPb Br₃, CsPbI₃, CH₃ NH₃PbІз, ↳ Solar cells built from these peroxides (Hype, 2015) ## Prototypical crystal structure → β-Cristobalite (SiO2 & Diamond in comparison **→fcc** * Diamond = hardest natural substance * ↳ covalent Bond * polymorph * **Diamond** →4 hybind orbitale ### Graphite : * **Conductivity (example):** * Graphite C-C- ⇒ sp² C ↓ C . . . . . "Sheets" . . . * T-orbital perpendicular to plane * **denocalize** * **thermodynamikly Graphite is more Stabel** * (Diamond turns into graphite) * but very slow * CN=3 → sp' ## Prototypical crystal structure → Zinc blende (ZnS, sphalerite) & wurtzite ! Polymers! **• FCC** * ** 2 tetrahedral holes per constituting atom** * L↳ for every Zn Atom there are 2 holes filed with IS-atom each * > Structure similar as Diamond (C-C bond stronger than ionic Dond of ZnS) * **Other Crystals:** InP, ZnSe, Cdse, Ca * **CN = 4** for zn & S * **Wurtzite** * Polymorph of ZnS * Hexagonal * Similar structured: ZnS, Cds, Gaw * CN (Zn) = 4 * I unit cell is of the hexagonal ## Prototypical crystal structure → Corundum * **Corundum:** * **Corundum (a-alumina)** Al2O3 is extremely hard. * **RUBY:** Trace amounts of Cr(III) substitutes in the crystal for Al(III) * **SAPPHIRE:** Trace amounts of Fe(III) or Ti(III) substitutes in the crystal for Al(III) * **o: hcp** * Al: octahedral holes * => Every 3 O-Atoms there are 루시 Al * **Sapire has a hexagonal structure & due to this it is possible to grow Galiumnitrate (GaN) on the sapire substrate to use the GoN in LED** * **(Extremly resistant to acid)** ### Activated aluminia * **γ-alumina** Al2O3 * Less dense than a-alumina * More open structure = "activated alumina" * More reactive than a-alumina **Spinel :** * A2+ B2+ O4 * Mg Al2O4, Fez 04 * (Fe Fe O4) * Magnetic form of Iron * fcc * A tetrahedral holes * B octahedral holes * But Al 03 there is no Al3+ / selten * **Prototypical crystal structure → rutile (Ti Oz) ⇒ Not needed for the Exam** * **Triangle cristal structure** ## Estimation of the lattice energy: Energy needed to break the molecules into lons (g) ### The Born-Haber cycle **Estimation of lattice energy** * Law of Hess: the way is not important as long as you sumup all the ways used. | Process | ΔΗ/kJ mol | |---|---| | M(s) + "/2X2(g) → M(g) + nX(g) | | | M(g) + nX(g) → M²+(g) + nX (g) | ΣΙΕ(M, g) + ΠΔΕΑΗ(Χ, 8) | | M²+(g) + nX (g) → MX(s) | - Alattice H (MX, S) | | MX(s) → M(s) + "/2X2(g) | ΔΗ°(ΜΧ, 5) | * **ΔΗ°(Μ, s) = Enthalpy of atomization of metal: M(s) → M(g)** * **ΔΗ°(X, g) = Enthalpy of atomization of X: 12X2(g) →X(g)** * **ΣΙΕ(Μ, g) = Sum of the ionization energies for the processes M(g) →M²(g) → M²+(g) ... → M"+(g)** * **ΔΕΑΗ(Χ, 8) = Enthalpy change associated with the attachment of an electron: X(g) + eX(g) ** * **ΔΗ°(ΜΧ, 5) = Standard enthalpy of formation** * **Alattice H°(MX S) = Lattice energy change (see text and eq. 6.7)** **Example: lattice energy of NaH:** 1. **fill in the values (kJ/mol):** Na (s) + ½ Hz (g) => Na (g) + H(g) => NaH (5) * **Da H° (Na, s) (g) = 108** * **Da H° (H2, g) (g) = 218** * **Da H° (NaH, s) (g) = - 56** => -56 2. **calculate of lattice** Na (s) => Na (g) => NaH (5) * **Da H° (Na, s) (g) = 108** * **Da H° (H2, g) (g) = 218** * **Da H° (NaH, s) (g) = - 56** => -496 **Of latice = -496 + 73-108-218 - 56 = -805 kJ/mol** * Since we go in the opposit direction of the arrows signs need to be changed. ## Exam Question: Compaire with electrostatic model ### The electrostatic model * For an isolated pair to ions: $ΔU = - \frac{e^2}{4πε0 r}$ * For a lattice of ions: Born-Landé equation $ΔU(0K) = -\frac{L x A x Z+ x Z- x e²}{4 x χπx εορ} x (1-\frac{1}{n})$ * **Unit conversions:** for distance: pm → m ### Exam Question : Interaction Energy of different Atoms **Example: Electrostatic model of NaH** * rH = 135 pm * rNa = 102 pm * n = 5 * r = * $ \frac{102 + 135}{2} $ pm = 2.73 x 10-10 m * nNat = $\frac{7}{2}$ * **average n = 6** * Nah has Nall structure = A = 1,7476 $(6 * \frac{1}{6} ) * (\frac{1.60 x 10^{-19} * 1.60 x 10^{-19}}{ (4 \pi * 8.854 * 10^{-12})(2.73 x 10^{-10}) }) * ( 1-\frac{1}{6} ) = -852, 000J = -852 \frac{kJ}{mol}$ * **↳ A perfect lonic Structure** ## (Metal organic) chemical vapor deposition (MOCVD) ### (Metal organic) chemical vapor deposition * Methode to produce single or polycrystalline thin films * chemical reaction of metal - organic precursors in the gas phase to deposit a material into a substrate * used in the production of optoelectronic devices (LED,..) * This methode allows to create smoth linear surfaces even if the starting surface is uneaven ### Reakhon Metal-organic compounds are introduced into a reaction chamber along with a carrier gas. The chamber is heated to a high temperature, causing the precursors to react & form a solid material that deposits onto the substrate. **Two flow - Reactor** * **epitaxial ↑ growth**(growing different cristals with the same structure ontop of it) * **lattice matching** * -Call wurtsite (hexagonal) * Saphire (substrate) ALL 03 * **Colundum** * • hexagonal ## ALD Atomic Layer Deposition * **↳ self limiting half reaction** **1.nd half reaction** * AI (CH3)3 → AI * -CHL * Does not react with it * → self therefore *-H20 (9)** *→ Build cristall on flat surface **2.nd half reaction** * H2O → HO. * -HO (g) ## Metals, Insulators & Semiconductors ### Bonding in metals and semiconductors: metals: band theory * Limetal with simplest electronic configuration: valence 2s¹ * Band of MOS * unbonding Orbital 2s * Bonding orbital * Li₂ Lig Liy ... Lis... Lig... Lin * See chapter 6 ### S and P orbital separation * Atomic orbital energy/kJmol-1 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * Li * Be * B * C * N * O * F * Atomic number * Background information: chapter 2 * 2p * 2s ### Bonding in metals and semiconductors: s and p bands * → measured in [eV] ### Bonding in metals and semiconductors: s and p bands * Energy * Conduction band * Band gap = Bandlücke * p-band * s-band * Valence band * ↳ filled with * (a) * (b) * (c) * →Semiconductor * LTT = ↓ conduchity * L) ↑T = ↑ conductivity * L↳ Si & Ga ## Fermi Level * An imaginary "energy marker" that tells you where the e in a material are located at a given temp. I how they might behave * → alle below Fermi level (100% 10%) * @ OK * @OK Material warms up, e è gain energy & jump to higher levels * L↳ Fermi level = midpoint /"average" around which the è move * Bonding in metals and semiconductors * **s and p bands** * (50%/50%) * @ 2984 * take lover è and transfer to above * ⇒@ fermy lul 50% under & 50% above * **Bolzmann distribution** ## Intrinsic semiconductors in Group 14 * **⇒ values for jump inbetween band** * Conduction band * Valence band * C * Si * Ge * a-Sn | | values for jump inbetween band | |:---|:---| | C | 520 kJ mol-1 | | Si | 106 kJ mol-1 | | Ge | 64 kJ mol-1 | | α-Sn | 8 kJ mol-1 | * No e jump * 5.39 eV * Semi conductor * 1.10 eV * 0.66 eV * 0.08 eV * Bandgap very smal metal * (behaves like a metal) ## Doping of semiconductors * A process of intentionally adding small amounts (≈1%) of impurities to a semiconductor (extrinsic) to change its electrical properties (control number of charge carriers & improve Conductivity). * Intensic when there is no doping * Pure Semiconductors dont conduct electricity very well @ room temp * Why? * **Types of Doping** * **N-Type doping (negative-type)** * Doping with an impurity which has extra electrons leading to more free electrons than holes * **p-Type doping (Positive type)** * Doping with an impurity which has fewer electrons leading to more holes than electrons * **Effect of doping on Fermi level** * n-type: Fermi lul. shifts closer to the conduction band. * p-type: Fermi lul. shifts closer to the valence band. ## Dopants create extrinsic semiconductors * **P-type (LED)** * Si enhanced with Ga * Ga takes a e, creating a hole which can be filled with another e * **N-type (LED)** * The hole is @ the dopant * **P doped Si** * holes Le wander throug the whole system ## P-n junction * when the two regions of p-1 n- junction come into contact, è from n-type diffuse into the p-type region, filling holes & holes from p-type diffuse to n-type. * As è & holes recombine near the Junction, a depletion region forms in which all free charge carriers have recombired, leaving behind only the cho charged dopant electric field created that opposes further movement of charge carriers. * Under no external Voltage (eq.) the electric field depletion region prevents further diffusion of I holes & a built-in potential forms across the junction which balance the diffusion force of e & holes. ### P-N-Junction in a blue LED (light emitting diode) * **P-Type:** GaN doped with Mg * **n-type doped with si } Can be dopeden with any other element the 2. or 4. group** ### Emission of white light with Blue - LED + Phosporus * **with YAG: Ce Phosphor** * Ls (Yittium Aluminium garnet doped with Cerium): * Yz Als Oiz: Ce³+ * When blue light shines onto the YAG: Ce phosphor, blue light gets absorbed & is re-emited as a mixture of yellow, green & blue light which will be percived as white light ## Why does a LED only emitt light when current is applied from only one side? ### There is a forward Bias. * The current flows through a p-n junction where p has positive charge carriers (holes) 1 n has negative charge carriers (e) giving different results when current is applied from one or the other side. * **Current flow in forward bias** * Ls Current flows from (+) → (-) (pn) * Is eletrones move holes from n p side * = light emission * (when moving e from n-top-side the e drop from higher energy to lower = light) **Current flow in reverse bias = no light** * ↳ Current flows from negative to positive (flow of charge carriers across junction is prevented) * **E- > hc or X = 1240 / E(ev)** * **electric field** * at interface, it's empty, but charges still there * Lo be of that it's delocalized and has an electrical field **=> https://youtu.be/AF8d72mA4\M?si=79980Jgya Ty4IGZZ! Ls Video about blue LED** **colour: bandgap** * **GaN: 3,45 ev → 360 nm** * **InGaN2: 2,tev → 450 nm bblue** * **Si 1.1 ev = 1127,27 → Infrared** * **GaN 3.45 ev 359,42 UV-Vis** ### Calc. of bandgap: * X = 1240 * E(ev) * $\frac{1240}{1127,27} = 1240$ * $\frac{1240}{3,45} = 359,42$ ## Similar for Solarcell * Silicon is essetial to solar cells * **P Θ n** * **A single pure Silicone cristal is essential** * **Methode:** Si must be a single crystal * Zone melting * Start polycrystalline rod * Partial meling of small section * Careful cooling * End-Si single crystal * Czochralski process * Polysilicon in quartz crucible * Heat unti meting point * Addition of seed Si crystal * Stow withdrawal of seed ## Silicon is essential to solar cell at least in the current technolgy **Best Research-Cell Efficiencies** * → **CH3NH3PbІз (lausanne)** * → **2+ 4+ 2-** * **ADX3 / AB O3 (perovskite, CaTiO3) Structure** ## Quantum Dots * Nanosale semiconductors (2-10nm = 100 -10'000 atoms) with unique optical & electronic properties due to quantum confinement * L↳ depend on extensive properties (mass, entropy, volume, ...) * **Nanocrystals are different from bulk** * dot colum of atoms * ordved * TEM image (2D projection) * Organic ligand shell * Inorganic core * **↳ Size of the dots determine colour** * **Nanocrystals:** While all quantum dots are nanocrystals, not all nanocrystals are quantum dots. * Quantum Dots refers to semiconductor nanacrystals that exhibit quantum mechanical behaviour while Nanocrystals refer to any crystalline material @ nm scale (1-100nm) including material like metals (gold, silver), ceramics, oxides & semiconductors. * L↳ exited with UV light ### How do Quantum Dots Work **The bandgap is visualized by the color** * hote, cools until its @ bottom of conduction band * σ* (Cd 2+) * Cd (5s) * E * electron * σ hole * Se (4p) * σ (Se²) * Absorbance = 0 (long wavelength = Small energy) * L↳ no absorbance due to non-existing orbital to put e in * First excitonic peak (band band transition) * (band gap energy) * e- * h+ * Absorption of many wavelengths produces the same luminescence wavelength. * **Quantum dots (gd) confine e I holes within a small region, resulting in discrete energy levels** * The smaller the ad the larger the band gap * (↑ energy light emitted blue / green) while large ad have smaller band gaps (↓ energy, yelbu/red) ### Light emission process: * **Excitation:** A photon exites an e from valance band to conduction band, creating electron-hole pair * **Recombination:** è recombine with the hole, releasing energy as photon (light) * **Tunable Emission:** The emitted wavelength of emitted light depends on the size of the ad ### Broad Absorption & narrow Emission: * L↳ Qd absorb a wide range of light wavelength but emit in a narrow spectral peak→ highly pure colours ## Qd & Particle in a Box * Qd behave like particle in a box! * è are confined in 3 dimensions, creating quantized energy levels. * ΗΨ = ΕΨ * Giv: LE * n→ qualisation * m→ mass * a size of the box (~10mm) * E= $\frac{n^2 h^2}{8ma²}$ * **→Confinement energy: additional to the energy a particle already has** * **E pap = Ebulk + E confinement** * **→ & hole are both confined** * **The smaler the nanocrystal the more confined energy is needed (smaller wave length)** ## Lead sulfide and lead selenide QDs ### Small particle * Absorbance (a.u.) ### Big particle * (3) * Se * 3f * 3d * 3c * 3b * 2 * 1 * 500 * 1000 1500 * 2000 * 30 nm * Wavelength (nm) * (7) * Se * 30 nm * (8) * Se * 30 nm ## Phosphorous in the context of semiconductor Nanocrystals * In some lighting applications, semiconductor nanocrystals are used as phosphor substitudes / combined with phosphors to convert light into specific wavelength ### Phosphorous Coatings with semiconductor Nanocrystals * Traditional phosphor are maksial that absorbs high energy photons ( blue luv) & re-emit them as low Energy Photons (green, yellow or red light) & less in IR ### Phosphorous - Doped Semiconductor Nanocrystals: * Phosphours is introduced into semiconductor nanocrystals to modify ther electronic & optical properties leading to presice colouring (altering band gap for tailored optical propertie), Decrease IR Radiation due to improved charged carrier mobility & reduce defects in the crystal lattice for more stable light emission. ### Problems that core with phosporus-doped nanocrystals: * **Sensitivity to high temprature:** that may lead to structural degradation, causing changes in its electronic & optical properties * **Degradation over time:** phosphorus-doped nanocristals can experience photodegradation or thermal degradation, which leads to reduced performance in light-emitting application: * Photo bleaching: loss of fluorescence or light emission * Surface degradation: degration of surface over time when not well-passivated, leading to decreased quantum efficiency