electron and phonon transport the hall effect general classification of solids crystal structures...
TRANSCRIPT
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 Effectz
y
x+-
Id
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 fieldV
-
- - - - - - - - - - - -
+ + + + + + + + + + +
l
dI
zy
xHV
B
d F qu B lI B
q: charge of each carrierud: drift velocity of the carrier l: length of the conductor
FF
F E
I
-
B
d F qE qu B
d- 0 0
0 0
x y z
y y
e e e
qE e q u
B
.- 0y d x z yF q E u B e
d. , y x zE u B E V
H d, y x zV E t u B t
d d, I I
I nqu A unqA nqd
H IB
Vnqd
n: number density of free electron
zy
x
d
l
Klitzing constant
H IB
Vnqd
Hall coefficient HH
1
V d
IB nq
Hall resistance H HH
V BR
I d
Hall resistivity HH H
y
x
EV dr B B
IB J Jx: current density
Hall coefficientp – type semiconductor (+)n – type semiconductor (-)
Magneto resistance - The change in resistance of a material - The Giant Magneto resistance (GMR) → magnetic hard disk
2K / 25,812.807449 0.000086 R h e
General Classification of Solids
periodic table of elements
by the number of proton
100
s
1
2
K
2
30, 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
Subshelldesignation
Orbital in subshell
Subshellcapacity
Principal shellcapacity
40, 1, 2, 3
0, ±1, ±2, ±3
s, p, d, f
1, 3, 5, 7
2, 6, 10, 14
N
32
20, 1
0, ±1
s, p
1, 3
2, 6
L
8 22n
Electrons in Atoms
The number of quantum states
incorrect
incorrect7
2N
1s
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.
2s 2 p
incorrect
N
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.
72N
1s 2s 2 p
03d63 p 24s23s62 p22s21s
Ca
20Ca
4s orbits are filled before the 3d orbits - The associated energy level of a 3d orbit is higher than that of 4s orbit
93d63 p 24s23s62 p22s21s
63 p 14s23s62 p22s21s 103d
29Cu
A half-filled or filled ‘d’ subshell is more stable than the ‘s’ shell of the next level.
2 2 6 2 6 2 10 6 2 10 6 2 14 10 6 2 14 101 2 2 3 3 4 3 4 5 4 5 6 4 5 6 7 5 6s s p s p s d p s d p s f d p s f d
2 He 10 Ne 18 Ar 36 Kr 54 Xe 86 Rn
11 Na
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
crystalline polycrystalline amorphous
electrical conductivities - insulators, semiconductors, conductorchemical bonds - ionic, covalent, molecular, hydrogen bond metallic bond
Insulators, Conductors, and Semiconductors
Band structure
free electron gasElectron energies are limited to a nearly continuous band from the zero energy level up to the Fermi energyelectrons in single atomElectron energies are in various discrete energy levels
Allowable band
Forbidden band
Allowable band
FE
Insulator (Dielectric)
conduction band
valance band
gEFE
valance bandband made up of the occupied molecular orbitals
conduction bandband free to move about the crystal
Eg = 5 ~ 15 eV
SiO2: 8 eV
Transparent to visible light Valence electrons can not be excited.
Metal & Semimetal
conduction band
valance band
conduction band
valance bandFE FE
metal semimetal
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
FEgE
Eg ~ 1 eVdiamond: 5.5 eV, Si: 1 eV
Pure or intrinsic semi-conductor Low Temperature → insulator High Temperature → conductorBand 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 )
cEFE
iE
VE
cE
FEiE
VE
- increase the number of free (positive) charge carries- group III element- create an abundance of holes - boron (acceptor)
Atomic Binding in Solid
Cl _
Na+Na+
Cl _
Cl _
Cl _
Cl _
Na+
Na+
Ion crystals(ionic)
C
C
CC
C
Covalent crystals(covalent)
AA
A AA
AA
Crystals of inert gases
(van der Waals)
F _
H+ F _
Hydrogen bond
Na+
Na+Na+
Na+Na+
Metal(metalic)
Ionic bond
Alkali & alkaline earth metal [ H, Li, Na, k, Be, Mg, Ca ] - Valance electron are loosely bonded
NaNa
The elements in group VIa & VIIa [ F, Cl, Br..] - Gain additional electrons
Cl Cl
Cl _
Na+Na+
Cl _
Cl _
Cl _
Cl _
Na+
Na+
Ionic crystals (NaCl, CsCl..) – hard, high melting pointTransparent InsulatorSome these crystal is soluble → the solution become conductiveThe interaction energy between ion i and j
Cl _
Na+
a0 1 22
q qF
r
electrostatic force
contribution of the Coulomb attraction
1-
r
contribution of the repulsive force1mr
NaCl m = 6 ~10
Covalent bonds
Nonmetallic elementThe attractive force, very strong bindingHigh melting point & thermal conductivity
C C
linear Planar Tetrahedral
C
C
C CC
Diamond
tetrahedronmelting point 3820 Kk = 2300 W/mKNo absorb radiation at frequencies lower than that of the corresponding Eg
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 temperatureElectron distribution is very close to that of the free atomsThe atoms induce dipole moments in each other (Bound together by Van der Waals forces)
12 6
0 00( ) 4ij
ij ij
r ru r
r r
Lennard-Jones Potential
Transparent insulatorWeakly boundLow melting temperatureCrystal structures are FCC except He3 and He4
Hydrogen bonds
An atom of hydrogen is attracted by strong forces to two atoms.Largely ionic in characterFormed only between the most electronegative atoms (F, O, N)Important part of the interaction between water molecules and ferroelectric crystals
H2F F
Metallic bonds
Some valance electrons leave the ion cores andare shared by all the crystal.Supplemented by covalent and molecular bondMetallic crystals are more flexible.Weaker binding than othersBond formed by conduction electron is not so strong.
Na+
Na+Na+
Na+Na+
electron sea