Solid State Physics UNIST, Jungwoo Yoo 1. What holds atoms together - interatomic forces (Ch. 1.6) 2. Arrangement of atoms in solid - crystal structure (Ch. 1.1-4) - Elementary crystallography - Typical crystal structures - X-ray Crystallography 3. Atomic vibration in solid - lattice vibration (Ch. 2) - Sound waves - Lattice vibrations - Heat capacity from lattice vibration - Thermal conductivity 4. Free electron gas - an early look at metals (Ch. 3) - The free electron model, Transport properties of the conduction electrons ------------------------------------------------------------------------------- --------------------------(Midterm I) 5. Free electron in crystal - the effect of periodic potential (Ch. 4) - Nearly free electron theory - Block's theorem (Ch. 11.3) - The tight binding approach - Insulator, semiconductor, or metal - Band structure and optical properties 6. Waves in crystal (Ch. 11) - Elastic scattering of waves by a crystal - Wavelike normal modes - Block's theorem - Normal modes, reciprocal lattice, brillouin zone 7. Semiconductors (Ch. 5) - Electrons and holes - Methods of providing electrons and holes - Transport properties - Non-equilibrium carrier densities 8. Semiconductor devices (Ch. 6) - The p-n junction - Other devices based on p-n junction - Metal-oxide-semiconductor field-effect transistor (MOSFET) ------------------------------------------------------------------------------- --------------------------------(Final) All about atoms backstage All about electrons Main character Main applications
Transcript
Solid State PhysicsUNIST, Jungwoo Yoo
1. What holds atoms together - interatomic forces (Ch. 1.6)2. Arrangement of atoms in solid - crystal structure (Ch. 1.1-4) - Elementary crystallography - Typical crystal structures - X-ray Crystallography3. Atomic vibration in solid - lattice vibration (Ch. 2) - Sound waves - Lattice vibrations - Heat capacity from lattice vibration - Thermal conductivity4. Free electron gas - an early look at metals (Ch. 3) - The free electron model, Transport properties of the conduction electrons---------------------------------------------------------------------------------------------------------(Midterm I) 5. Free electron in crystal - the effect of periodic potential (Ch. 4) - Nearly free electron theory - Block's theorem (Ch. 11.3) - The tight binding approach - Insulator, semiconductor, or metal - Band structure and optical properties6. Waves in crystal (Ch. 11) - Elastic scattering of waves by a crystal - Wavelike normal modes - Block's theorem - Normal modes, reciprocal lattice, brillouin zone7. Semiconductors (Ch. 5) - Electrons and holes - Methods of providing electrons and holes - Transport properties - Non-equilibrium carrier densities8. Semiconductor devices (Ch. 6) - The p-n junction - Other devices based on p-n junction - Metal-oxide-semiconductor field-effect transistor (MOSFET)---------------------------------------------------------------------------------------------------------------(Final)
All about atoms
backstage
All about electrons
Main character
Main applications
Solid State PhysicsUNIST, Jungwoo Yoo
What holds atoms together ?
Interatomic forces
The binding energy of the atoms in all solids results from the reduction inenergy of atomic electrons due to the proximity of the neighboring atoms
Type of bondings
1. Ionic bonds
2. Covalent bonds
3. Metallic bonds
4. Van der Waals
5. Hydrogen
There must be some bindings to hold atoms together to form a solid.
Solid State PhysicsUNIST, Jungwoo Yoo
Distance between two atoms
V(r)
r
repulsive
attractive
equilibrium distance
00
rrr
Vequilibrium distance is given by
A typical curve for the potential energy of interatomic interaction
Repulsive force a Pauli exclusion principle prevent the crystal from collapsing
Attractive force a bonding hold atoms together to form solid
Interatomic forcer
rVrF
)(
)(
Type of bondings
1. Ionic bonds
2. Covalent bonds
3. Metallic bonds
4. Van der Waals
5. Hydrogen
Solid State PhysicsUNIST, Jungwoo Yoo
Inoinzation energy: the energy required to remove an electron from a neutral isolated atom to form an ion with one positive charge
Electron affinity: the amount of energy released when an electron is added to a neutral isolated atom to form an ion with one negative charge.
Electronegativity: the average of the first ionization energy and the electron affinity. It is the mea-sure of the ability of an atom or molecule to attract electrons in the context of a chemical bond.
Chemical bonds
1. Ionic
2. Covalent
Chemical bonding between two atoms determined by the difference in electronegativity
Large difference a ionic bonding e.g. Na-Cl (3.16 - 0.93 = 2.23)Small difference a covalent bonding e.g. C-O (3.44 – 2.55 = 0.89) O-O (0)
Solid State PhysicsUNIST, Jungwoo Yoo
Solid State PhysicsUNIST, Jungwoo Yoo
Principle quantum number: n = 1, 2, 3, 4,….Orbital quantum number: l = 0, 1, 2,…..(n-1)Orbital magnetic quantum number: ml = - l, -(l -1), , , , (l -1), l
Solid State PhysicsUNIST, Jungwoo Yoo
Solid State PhysicsUNIST, Jungwoo Yoo
1. Ionic
When the difference in electronegativity between two different atoms is large,
electrons will be transferred from the low electronegative atom to the high electronegative atom.
The low electronegative atom will become a positive ion and the high electronegative atom will be-come a negative ion
(e.g. Na + Cl → Na+ + Cl-).
The energy difference = 7.9 + 3.6 – 5.1 = 6.4 eV
between molecule unit and separated neutral atoms
Solid State PhysicsUNIST, Jungwoo Yoo
2. CovalentWhen the electronegativity between two atoms is small, the two atoms can form covalent bond by sharing a pair of electrons (one from each atom).
The molecular orbital of the two atoms are linear combinations of and
21
21
a
b
1 2
Solid State PhysicsUNIST, Jungwoo Yoo
Most atoms can form more than one covalent bond. For example, C has four outer electrons and hence it can form 4 covalent bonds.
Covalent bond is highly directional and the bonds will repel from each other. So a crystal can be formed even the structure has a low filling factor.
For example, carbon and silicon can have diamond structure, with atoms joined to four nearest neighbors at tetrahedral angles showing only four nearest neighbors. Diamond structure has a filling factor of 0.34 compared with 0.74 of close-pack structure.
Solid State PhysicsUNIST, Jungwoo Yoo
Diamond
Solid State PhysicsUNIST, Jungwoo Yoo
n=1, l=0
N=2, l=1, ml = 1, 0, -1
n=2, l=0
1s
2s
2p
2s22p2 2s12p3
px py pz
s
When one C is surrounded by 4C
sp3 hybridzation
sp3 sp3 sp3 sp3
Carbon’s electron orbital
Solid State PhysicsUNIST, Jungwoo Yoo
How about graphene ?
Solid State PhysicsUNIST, Jungwoo Yoo
How about graphene ?
2s12p3
px py pz
ssp2 hybridzation
sp2 sp2 sp2pz
Solid State PhysicsUNIST, Jungwoo Yoo
3. Metallic
Atoms bounded by free atoms
e.g. alkali metals (Li, K, Na, etc)
Negatively charged free electrons in a metal serve as glue that holds positively charged ions together.
Delocalized electrons induced by the reduction of kinetic energy introduce significant binding energy
px
Heigenberg’s uncertainty principle22
2
L
n
mEn
Q. Get En from de broglie’s matter wave
p
h
Solid State PhysicsUNIST, Jungwoo Yoo
4. Van der Waals
Coulomb attraction can occur between two neutral spheres, as long as they have some “internal charges” so that the neutral spheres can be polarized
Interaction between two inert gas atoms
612
2)(rr
rVLenard-Jones potential
RepulsionPauli exclusion principle
AttractionVan der Waals
Larger molecule a stronger Van der Waals force a higher melting point He Ne Ar Kr Xe Rn
Increase melting point
Solid State PhysicsUNIST, Jungwoo Yoo
1. Hydrogen
Hydrogen ion is just a proton (10-13 cm in radius), 10-5 times smaller than any other ions.
First ionization energy of atomic hydrogen is very high (13.6 eV) because the outset electron is in the first shell without any shielding. It is highly unlikely for hydrogen to form ionic bonding.
The complete shell of hydrogen atom is 2 electrons and a hydrogen atom has only one electron. It can form only one covalent bond and it does not have sufficient bond to bind the whole crystal to-gether with covalent bond.
However, the covalent bond between hydrogen and the other atom (e.g. oxygen) can often be polar-ized, when the electronegativity between these two atoms has a moderate difference.
