Download Lecture 2 - The Dionne Group

Lecture 2
Atoms & Their Interactions
Si: the heart of electronic materials
Intel, 300mm Si wafer
Intel
wafer, 200 μm thick
and 48-core CPU (“cloud computing
on a chip”)
Twin Creeks Technologies,
Technologies San Jose
Jose,
Si wafer, 20 μm thick
Atomic Configuration
The shell model of the atom: electrons are confined within certain
shells and in subshells within shells
Carbon: 1s22s22p2 or [He]2s22p2  insulator, semiconductor, conductor
Silicon: 1s22s22p63s23p2 or [Ne]3s23p2  semiconductor
Aluminum: [Ne]3s23p1  metal
Atomic bonding influences material
properties
ti
q1
r
1. rinfinity:
y
• Particles don’t interact
• Potential energy E(r)
E(r)=0
0
• Force F=dE/dr=0
q2
Atomic bonding influences material
properties
ti
q1
r
q2
2. If the two particles are close enough,
g they
y will attract. This
attraction is governed by electrostatic interactions:
• Potential energy EA(r) = -Cq1q2/r
• C α 1/(4πε0)
Atomic bonding influences material
properties
ti
q1
r
q2
3. If the two particles are too close, they
y will repel.
• Potential energy ER(r) = +B/rm
• m an integer, usually large (for Na+ and Cl-, m=8)
For all separations, the net force exerted on the particles is
p
forces:
the sum of attractive and repulsive
F=dE/dr
Fnet=FA+FR
Force, F(r)
•Net Force FN=FA+FR
•Equilibrium
E ilib i
when
h FN=0
0
•r0=bond length
Potential energy, E(r)
•E0: bond energy or cohesive
energy (energy required to
separate the two atoms)
ER
E
E0
EA
A B
• In general: E (r )   n  m
r
r
Types of bonds
Covalent
Metallic
Ionic
Secondary Bonding (Van der Waals)
Mixed
d Bonding
d
Covalent Bonding
Formation of a covalent bond between two hydrogen atoms leads to the H2
molecule Electrons spend majority of their time between the two nuclei
molecule.
which results in a net attraction between the electrons and the two nuclei.
Covalent Bonding in Methane
Covalent bonding in methane, CH4, involves four hydrogen atoms
sharing bonds with one carbon atom. Each covalent bond has two
shared electrons. The four bonds are identical and repel each other.
In three dimensions, due to symmetry, the bonds are directed
towards the corners of a tetrahedron.
Covalent Bonding in Diamond
The diamond crystal is a covalently bonded network of carbon atoms
atoms. Each carbon
atom is covalently bonded to four neighbors forming a regular three dimensional
pattern of atoms which constitutes the diamond crystal.
Properties of covalently-bonded materials
• due to the strong Coulombic interaction between the
shared electrons and the positive nuclei, the covalent
bond energy is usually the highest among all bond types
• very high melting temperatures
•very hard solids (like diamond)
• insoluble in nearly all solvents
•Non-ductile (or non malleable)
•Exhibit
Exhibit brittle fracture under a strong force
Properties of covalently-bonded materials
• due to the strong Coulombic interaction between the
shared electrons and the positive nuclei, the covalent
bond energy is usually the highest among all bond types
• very high melting temperatures
•very hard solids (like diamond)
• insoluble in nearly all solvents
•Non-ductile (or non malleable)
•Exhibit
Exhibit brittle fracture under a strong force
Properties of covalently-bonded materials
• due to the strong Coulombic interaction between the
shared electrons and the positive nuclei, the covalent
bond energy is usually the highest among all bond types
• very high melting temperatures
•very hard solids (like diamond)
• insoluble in nearly all solvents
•Non-ductile (or non malleable)
•Exhibit
Exhibit brittle fracture under a strong force
•Since all electrons are locked in the bonds between the
atoms, the electrons are not free to drift in an electric field:
Poor Conductors
Metallic bonding
Consider Ag
Electronic configuration:
[Kr] 4d10 5s1
In metallic bonding the valence electrons from the metal atoms form a
“cloud of electrons” which fills the space between the metal ions and
“ l
“glues”
” the
h ions
i
together
h through
h
h the
h coulombic
l bi attraction
i b
between the
h
electron gas and the positive metal ions.
Properties of metallic-bonded materials
• ionic cores tend to pack closely, like stacked oranges, i.e.
hexagonal close
close-packed,
packed, face
face-centered
centered cubic
• bond is non-directional  under an applied force, metal
ions can move with respect
p to each other
• as a result, metals are ductile 
• eelectrons
ect o s ca
can drift
d t freely
ee y with
t aan app
applied
ed electric
e ect c field
ed
high conductivity
• with temperature gradients, electrons can contribute to
energy transfer  Good thermal conductivity
Ionic bonds
• Bond between a positively charged ion (the cation) and a
negatively charged ion (the anion)
•frequently found between metal atoms and non-metals
•i.e., NaCl
N has
Na
h only
l one valence
l
electron
l t
th
thatt can b
be easily
il
removed (1s22s22p63s1)
 Cl has 5 electrons in its 3p subshell,
subshell and can readily
accept one more electron to close this subshell
Ionic bonds in NaCl
The formation of ionic bond between Na and Cl atoms in NaCl. The attraction
is due to coulombic forces.
Potential energy per ion-pair in solid NaCl
Ionization energy: +1.5eV
+1 5eV (energy to
transfer the electron from Na to Cl)
Cohesive energy:
gy -6.3 eV ((energy
gy
required to take solid NaCl apart into
individual Na and Cl atoms)
A schematic illustration of a cross section from solid NaCl. NaCl is made of Cland Na+ ions arranged alternatingly so that the oppositely charged ions are
closest to each other and attract each other. There are also repulsive forces
between the like ions. In equilibrium the net force acting on any ion is zero.
Properties of ionically-bonded materials
• Strong, brittle materials
•High
g melting
g temperatures
p
compared
p
to metals
•Soluble in polar liquids
No free electrons  are all fairly rigidly positioned
•No
within the ions
• electrically
y insulating
g
• poor thermal conductivity
Are there bonds between atoms that have full shells, and
therefore cannot share electrons?
Yes!
•Liquid He (~4K)
•Solid Ar (below -189
189oC)
• Water: although each H2O molecule is neutral, these
molecules attract to form a liquid state below 100oC and
the solid state below 0oC.
Van der Waals Forces
• Electrostatic attractions between the electron distribution
of one atom and the positive nucleus of the other
Dipole: negative and
positive charge of equal
magnitude
Polar molecules (i.e., exhibiting
p ) can attract or repel
p
a dipole)
each other depending on their
relative orientations.
Water & Van der Waals Forces
The H2O molecule is polar and has a net permanent dipole moment
Attractions between the various dipole
p
moments in water g
gives rise to
van der Waals bonding
Van der Waals bonding
• can also occur between neutral atoms based on random motions
of electrons around the nucleus
Van der Waals bonding
• can also occur between neutral atoms based on random motions
of electrons around the nucleus
induced synchronization of electronic motions can lead to attractions
 solid Ne, Ar, liquid He
also responsible for the attractive interactions between C-chains in
polymers
Van der Waals bonding
• can also occur between neutral atoms based on random
motions of electrons around the nucleus
induced synchronization of electronic motions can lead to
attractions
 solid Ne, Ar, liquid He
also responsible for the attractive interactions between Cchains in polymers
• poor thermal conductivity
• electrically insulating
• low
l
elastic
l ti moduli
d li
Mixed bonding
• Bonding in silicon is totally covalent, because the shared
q
y attracted by
y the
electrons in the bonds are equally
neighboring positive ion cores and therefore equally
shared
• However, where there is a covalent-type bond between
different atoms, the electrons become unequally-shared
 GaAs,
GaAs III-V
III V compounds
 “polar bonds”
 in
i GaAs,
G A the
h electrons
l
spend
d slightly
li h l more time
i
around
d
the As5+ ion than the Ga3+ ion
Group Activity
Rank the following materials according to their melting
points, from lowest to highest:
p
g
NaCl
Al
Si
He
H2 O
Group Activity
Rank the following materials according to their melting
points, from lowest to highest:
p
g
Lowest Tm
(weakest bonds)
Van der Waals: He (-272oC)
H-bonding:
g H2O ((100oC))
metallic: Al (660oC)
ionic: NaCl (801oC)
Highest Tm
(strongest bonds)
covalent:
l t Si (1414oC)
Group Activity
What periodic table element do you think has the highest
melting point, at ambient pressure?
Group Activity
What periodic table element do you think has the highest
melting point, at ambient pressure?
Tm=3683K (3410oC)
Note: Carbon has no melting point at atmospheric pressure, but
will sublime around 4000K
Kinetic Molecular Theory
Understanding the relationship between energy of atoms
p
and temperature.
Can be used to explain seemingly diverse topics as the
heat capacity of metals, the average speed of electrons in a
semiconductor, and electrical noise
We’ll start with the kinetic molecular theory of gases.