ELECTRON AND PHONON TRANSPORT The Hall Effect General Classification of Solids Crystal Structures Electron band Structures Phonon Dispersion and Scattering Electron Emission and Tunneling Electrical Transport in Semiconductor Devices

The Hall Effect z y x + - I d V electron Electron: a fundamental subatomic particle that carries a negative electric charge Hole: An electric charge carrier with a positive charge, equal in magnitude but opposite in polarity to the charge on the electron

magnetic field V d I z y x q : charge of each carrier u d : drift velocity of the carrier l : length of the conductor

FE I - B n : number density of free electron z y x d l

Klitzing constant Hall coefficient Hall resistance Hall resistivity J x : current density Hall coefficient p – type semiconductor (+) n – type semiconductor (-) Magneto resistance - The change in resistance of a material - The Giant Magneto resistance (GMR) → magnetic hard disk

General Classification of Solids  periodic table of elements by the number of proton

s 1 2 K 2 3 0, 1, 2 0, ± 1, ±2 s, p, d 1, 3, 5 2, 6, 10 M 18 …..n ….(n-1) …..± l g, h…. (2l+1) 2(2l+1) O, P….. n l m Subshell designation Orbital in subshell Subshell capacity Principal shell capacity 4 0, 1, 2, 3 0, ±1, ±2, ±3 s, p, d, f 1, 3, 5, 7 2, 6, 10, 14 N , 1 0, ±1 s, p 1, 3 2, 6 L 8 Electrons in Atoms The number of quantum states

incorrect  Pauli’s exclusion principle Each quantum state can have no more than one electron. At most only two electrons can share the same orbit. (one with +1/2, the other with -1/2 spin)  Aufbau principle Electron fills the lowest energy states first.

incorrect  Hund’s rule Every orbital in a subshell is singly occupied with one electron before any one orbital is doubly occupied and all electrons in singly occupied orbitals have the same spin.

4s orbits are filled before the 3d orbits - The associated energy level of a 3d orbit is higher than that of 4s orbit

A half-filled or filled ‘d’ subshell is more stable than the ‘s’ shell of the next level.

Ionization energy: the energy required to separate an electron from the atomic nucleus easily lose He: 24.6 eV, Li: 5.4 eV

 Classification of solids arrangement of atoms in the solid crystallinepolycrystallineamorphous electrical conductivities - insulators, semiconductors, conductor chemical bonds - ionic, covalent, molecular, hydrogen bond metallic bond Insulators, Conductors, and Semiconductors

 Band structure free electron gas Electron energies are limited to a nearly continuous band from the zero energy level up to the Fermi energy electrons in single atom Electron energies are in various discrete energy levels Allowable band Forbidden band Allowable band

 Insulator (Dielectric) conduction band valance band band made up of the occupied molecular orbitals conduction band band free to move about the crystal E g = 5 ~ 15 eV SiO 2 : 8 eV Transparent to visible light Valence electrons can not be excited.

 Metal & Semimetal conduction band valance band conduction band valance band metalsemimetal Ex) Bi, Sn … Metals interact with electromagnetic radiation [→ free electrons ] strong absorption by thin metallic films, high reflection from polished metal

 Semiconductor conduction band valance band E g ~ 1 eV diamond: 5.5 eV, Si: 1 eV Pure or intrinsic semi-conductor Low Temperature → insulator High Temperature → conductor Band gap absorption interaction semi-conductor with optical radiation Doping the semi-conductor with impurities → electrons ≠ holes

 n-type vs p- type Semi-conductor n – type semi-conductor p – type semi-conductor - increase the number of free (negative) charge carries - group V element - produce an abundance of mobile or "carrier" electrons in the material - phosphorous (donor ) - increase the number of free (positive) charge carries - group III element - create an abundance of holes - boron (acceptor)

Atomic Binding in Solid Cl _ Na + Cl _ Na + Ion crystals (ionic) C C C C C Covalent crystals (covalent) AA A AA AA Crystals of inert gases (van der Waals) F _ H+H+ Hydrogen bond Na + Metal (metalic)

 Ionic bond Alkali & alkaline earth metal [ H, Li, Na, k, Be, Mg, Ca ] - Valance electron are loosely bonded The elements in group VIa & VIIa [ F, Cl, Br..] - Gain additional electrons Cl _ Na + Cl _ Na +

Ionic crystals (NaCl, CsCl..) – hard, high melting point Transparent Insulator Some these crystal is soluble → the solution become conductive The interaction energy between ion i and j Cl _ Na + a0a0 electrostatic force contribution of the Coulomb attraction contribution of the repulsive force NaCl m = 6 ~10

 Covalent bonds Nonmetallic element The attractive force, very strong binding High melting point & thermal conductivity CC linearPlanarTetrahedral

C C CCC Diamond tetrahedron melting point 3820 K k = 2300 W/mK No absorb radiation at frequencies lower than that of the corresponding E g III-V semiconductor ( GaN, GaAS, InSb ) II-IV semiconductor ( ZnO, CdS ) → covalent bond characteristics ( 30% ) SiC (dipole form) → some ionic bond characteristics

 Molecular bonds Inert gases can be solidified at low temperature Electron distribution is very close to that of the free atoms The atoms induce dipole moments in each other (Bound together by Van der Waals forces) Lennard-Jones Potential Transparent insulator Weakly bound Low melting temperature Crystal structures are FCC except He 3 and He 4

 Hydrogen bonds An atom of hydrogen is attracted by strong forces to two atoms. Largely ionic in character Formed only between the most electronegative atoms ( F, O, N ) Important part of the interaction between water molecules and ferroelectric crystals H2H2 FF

 Metallic bonds Some valance electrons leave the ion cores and are shared by all the crystal. Supplemented by covalent and molecular bond Metallic crystals are more flexible. Weaker binding than others Bond formed by conduction electron is not so strong. Na + electron sea