Bonding
•  Bonding is primarily by valence electrons
•  Bonding is electrostatic
•  The “chemist’s” model
–  Chemical bonds are localized between atoms
•  The “physicist’s” model
–  Electrons wander through the solid
–  Electron states are gathered into “bands”
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Electron States in Atoms
•  Pauli exclusion principle
•  Quantum numbers
–  n = orbit
–  l = angular momentum [0(s)1(p)2(d)3(f)…n-1]
–  m = z-component of l [-1,…,l]
–  s = spin (1/2,-1/2)
•  Configuration
–  1s22s22p63s23p64s23d104p6...
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Electron States in Atoms
•  Pauli exclusion principle
•  Quantum numbers
–  n = orbit
–  l = angular momentum [0(s)1(p)2(d)3(f)…n-1]
–  m = z-component of l [-1,…,l]
–  s = spin (1/2,-1/2)
•  Configuration
–  1s22s22p63s23p64s23d104p6...
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
The Periodic Table
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Core and Valence States
•  Valence electrons are outer-shell sp states
–  Govern bonding
•  Configurations
–  H:
–  C:
–  Si:
–  Fe:
–  Cu:
MSE 200A
Fall, 2008
1s1
(z = 1)
[1s2]2s22p2 (z = 4)
[1s22s22p6]3s23p2 (z = 4)
[1s22s22p63s23p63d6]4s2 (z = 2)
[1s22s22p63s23p63d10] 4s1 (z = 1)
J.W. Morris, Jr.
University of California, Berkeley
Interatomic Bonding
•  Electrostatic interaction
–  Electron-nucleus
Ze 2
φ =−
r
•  Molecules or solids
–  Electrons see multiple nuclei
–  Interact with all
€–  Potential energy decreases
⇒  bonding
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Bonding
dΦ
F(r) = −
dr
•  Electrons between nuclei
see both
=> attraction
•  Closed inner shells overlap
=> repulsion
A B
Φ(r ) = m − n
r
r
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Chemical Bonding
Shared Electron Bond
covalent
metallic
+
Ionic bond
+
-
-
+
Dipole bond
•  Types of bonding
– 
– 
– 
– 
MSE 200A
Fall, 2008
Covalent => shared electron, saturated
Metallic => shared electron, unstairated
Ionic => electrons exchanged to charge ions
Dipole (Van der Waals) => transient or permanent dipoles
J.W. Morris, Jr.
University of California, Berkeley
Covalent Bonding
^^ ^^ ^^
^ Si ^ Si ^ Si ^
:^ Si
:^Si
^ Si
^
..
..
^ ^ ^ ^ ..^ ^
^ Si
:^ Si :^Si ^
^ ..Si ^ ..Si ^ ..Si ^
^^ ^^ ^^
Si : Si : Si
•• •
•
••
••
•  Valence electrons are shared to fill outer shell
•  Examples:
–  CH4
–  C, Si, Ge (4/4); GaAs (3/5); ZnS (2/6)
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Properties of Covalent Materials
^^
^ Si ^:
^ Si
^
..
^^
Si
^:
^ Si
..
^
^
^Si
^ :
^^ ^^
^ Si
Si
:
Si
Si ^^
^ ..
..
^^
^^
Si
:
Si
Si
Si ^^
.. ^^ ..
^^
^ ^ : Si
Si
•• •
•
••
••
•  Electrical:
–  Semiconductors or insulators
•  Mechanical:
–  Hard, brittle
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Metallic Bond
= ion core
sea of
= valence
electrons
•  Shared electrons, bonds unsaturated
–  Excess electrons or excess neighbors
•  Model:
–  Ion cores float in a sea of electrons that glue them together
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Properties of Metallic Materials
= ion core
sea of
= valence
electrons
•  Electrical
–  Good conductivity by electron flow
•  Mechanical:
–  Relatively easy to deform
–  Ductile, not brittle
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Ionic Bonding
= Na+
= Cl
-
•  Electrons are transferred to create ions
–  Common for “almost filled” and “almost empty” shells
•  Large difference in “electronegativity”
–  Opposite charges bind together
•  Ionic and covalent bonding can be mixed
–  Dissimilar atoms always “transfer” some charge
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Properties of Ionic Materials
= Na+
= Cl
-
•  Electrical
–  Insulators
–  Ionic conductors (diffusion of ion => current)
•  Mechanical
–  Tend to be brittle
–  Slip forces unlike ions together
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Dipole Bonding
=O
+
=H
-
•  Dipoles bond by alignment
–  No charge transfer
•  Permanent dipoles (H2O)
–  “Hydrogen bonding” in organics
•  Transient dipoles (He)
–  “Van der Waals” bonding is always active
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Properties of Dipole Bonded Materials
=O
+
=H
-
•  Electrical
–  Insulators
–  Weak conductors (“hopping” mechanisms)
•  Mechanical
–  Low strength
–  Deformable (e.g., thermoplastic polymers)
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Interatomic Bonding
•  Electrostatic interaction
–  Electron-nucleus
Ze 2
φ =−
r
•  Molecules or solids
€
MSE 200A
Fall, 2008
–  Electrons see multiple nuclei
–  Interact with all
–  Potential energy decreases
⇒  bonding
J.W. Morris, Jr.
University of California, Berkeley
Bonding
•  Bonding is primarily by valence electrons
•  Bonding is electrostatic
•  The “chemist’s” model
–  Chemical bonds are localized between atoms
•  The “physicist’s” model
–  Electrons wander through the solid
–  Electron states are gathered into “bands”
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Discrete Electron States in an Atom
•  In an atom electron states have
–  Particular energies (Ei)
–  Separated by energy gaps
unbound
states
E
electron
potential
MSE 200A
Fall, 2008
bound
states
•  Electrons confined to “potential
energy well” around nucleus
–  Ei > V = - Ze2/r
J.W. Morris, Jr.
University of California, Berkeley
Why Atomic States Become
Energy Bands
There are four-and-twenty ways
To make up Irish lays
And-every-single-one-of-them-is-right
- Rudyard Kipling
•  There are many different models,
all of which are basically correct
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
The Physicist’s Model:
Atomic States Become “Energy Bands”
free
states
E
excited
states
valence
states
core states
•  Overlap decreases potential between atoms
–  Valence electrons travel through the solid
•  Atomic states become “bands” of allowed states
–  Separated by “energy gaps”
–  Gaps are the energies electrons cannot have
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Why Atomic States Become
Energy Bands
• 
Pauli exclusion principle
⇒  electrons in different states
–  even electrons from the same atomic
level
free
states
excited
states
E
valence
states
core states
• 
Electrons from the same state differ in
momentum
E = E0 + p2/2m*
–  p-values fixed by structure
–  m* is “effective” mass
–  m* lower for higher E0
⇒  high-E bands are broader
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Change of Band Width with Separation
•  Atom states spread into bands as r decreases
•  Valence bands broaden and overlap
–  m* decreases as overlap makes electron motion easier
•  Core bands remain narrow until cores overlap
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Band Structure Determines
Electrical Behavior
•  Electrons fill low-energy states
–  To “Fermi energy”, EF
•  EF within a band => metal
–  Empty states are accessible
–  Electrons can flow with field
•  Filled to band top => non-metal
–  Must excite electrons across gap
–  Small gap => semiconductor
–  Large gap => insulator
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Change of Band Width with Separation:
Different Modes of Behavior
•  In sodium, s and p-bands simply overlap
•  In carbon, the s- and p-bands interact
–  Create a new gap
–  4 states/atom in lower band, 4 in upper
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Drawing the Band Structure
free
states
excited
states
E
E
EG
valence
states
core states
EF
EF
x
x
•  Show energy bands as a function of position
–  Leave out potential
•  Band identification
–  Valence band contains valence electrons
–  Conduction band is first band of excited states
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
The Band Structures of Metals
EG
E
EG
EF
EF
x
x
EF
x
•  Natural metals - EF within band
–  Electron states are paired (spin up, spin down)
–  Almost all odd-valence elements are natural metals
•  Exceptions are “molecular” solids with even total valence
•  “Overlap” metals - EF in band overlap
•  Transition metals - EF in partially filled d-band
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
The Band Structure of Non-Metals
•  Valence electrons fill band
-  EF in center of band gap
-  Poor conductor
•  EG small (< ~ 2 eV)
-  semiconductor
•  EG large (> ~ 3 eV)
-  insulator
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Microstructure
•  Microstructure:
–  Type and location of all atoms in solid
•  All atom positions known in only two ideal cases
–  Perfect order (“crystals” or “quasi-crystals”)
–  Perfect disorder (“amorphous solids” or “glasses”)
•  Almost all solids prefer the crystalline state
–  But perfect crystals are not possible in nature
–  Describe by basic crystal structure + “crystal defects”
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Atomic Resolution TEM Image:
Two Crystals (Grains) of Al
grain
boundary
-Eric Stach
NCEM/LBNL
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley
Atomic Resolution TEM Image:
Two Crystals Meet at an Interface
NiSi
Silicon
-Eric Stach
NCEM/LBNL
MSE 200A
Fall, 2008
J.W. Morris, Jr.
University of California, Berkeley