everything starts with atomic structure and bondingringel/331 notes/331_wi11/ece331_wi11… ·...
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Everything starts with atomic structure and bonding
• not all energy values can be possessed by electrons; e- have discrete energy valueswe call energy levels or states. The energy values are “quantized” and not continuous
•Convention: we take the zero reference energy to represent the situation of a fully unbound, or “free” e-. Hence, relative to this condition, a fully bound electron in an orbital requires a certain input of positive energy to reach a free condition of “zero” energy. Thus bound e-are taken to have negative energy wrt the free state.
This is the BOHR ATOMIC MODEL
BUT th B h M d l d NOT di t lit !BUT, the Bohr Model does NOT predict reality!
Why? Because it states that both the energy valueAnd radial position of the e- are known i lt l !simultaneously!
This violates the Heisenberg Uncertainty Principle (later)
L2 – bonding.
Wave Mechanical (quantum mechanical) model of an atom• energy levels of individual electrons are discrete and
i i diff t “ fi ti ” th tevery e- is in a different “energy configuration” that we describe by quantum numbers to characterize size, shape and spatial orientation of the PROBABILITY DENSITY of an e-.
• in chemistry you’ll remember that these are called PQN (principle quantum number), electron shell, electron subshell, and electron spin!
• we will re-visit QM for real when we describe solids instead of atoms!
Quantum # Designationi i l ( l l h ll) K L M Nn = principal (energy level-shell) K, L, M, N,
O (1, 2, 3, etc.)l = subsidiary (orbitals) s, p, d, f(0, 1, 2, 3,…, n -1)
L2 – bonding.
( , , , , , )ml = magnetic 1, 3, 5, 7 (-l to +l)ms = spin ½, -½
Electron Energy Statesgy• have discrete energy states• tend to occupy lowest available energy state.
Electrons...
4p4d
N-shell n = 4
py gy
3d
4s
3s3p M-shell n = 3Energy
Adapted from Fig. 2.4,
2s2p L-shell n = 2
p g ,Callister 7e.
L2 – bonding.
1s K-shell n = 1
Atomic Bonds in Solids• bonding represents the balance between attractive and repulsive forces involving e- and positively charged ionsp y g
• when the net force between attraction and repusion is zero, FA + FR = 0. In terms of energy, we have a stable bond when the potential energy of the system is at a minimum,
dEN/dr = 0, EN is the net energyr = ro in this condition, which is the equilibrium bond lengthEN = Eo in this condition, which is the bond energy
A B
Repulsive energy ER
rA
nrBEN = EA + ER = −−
Interatomic separation r
Net energy EN
separation r
L2 – bonding.
Attractive energy EA
Primary Atomic Bonds in Solids• Ionic bonding occurs between elements with large differences in electronegativity
N Cl• e.g. NaCl• non-directional bonding (i.e. bond strength is very similar in all directions)• electron transfer enables a “closed shell” stable configuration• ionic compounds are relatively stable, hard, electrically and thermally insulating in PURE STATE (l t ill th t th i i i d t d d tPURE STATE (later, we will see that there are ionic semiconductors and conductors that are not pure)
Na (metal) unstable
Cl (nonmetal) unstableunstable unstable
electron
+ -Na (cation) Cl (anion)
C
CoulombicAttraction
stable( )
stable
• Covalent bonding: neighboring atoms share e- to complete a shell
• examples: CH4, Silicon, diamond• can be strong or weak
di i l b di !! V i
L2 – bonding.
• very directional bonding!! Very important for semiconductor technology!
Primary Atomic Bonds in Solids
• Metallic Bond -- delocalized electrons as electron cloud
• Ionic-Covalent Mixed Bondingg
% ionic character =
where XA & XB are Pauling electronegativities
%)100(x
1− e− (XA −XB)2
4
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
where XA & XB are Pauling electronegativities
Ex: MgO XMg = 1.3XO = 3.5
ionic 70.2% (100%) x e1 characterionic % 4)3.15.3( 2
=⎟⎟⎟⎞
⎜⎜⎜⎛
−=−
−
L2 – bonding.
⎟⎠
⎜⎝
Summary: BondingType
Ionic
Bond Energy
Large!
Comments
Nondirectional (ceramics)Ionic
Covalent
Large!
Variable
Nondirectional (ceramics)
Directionallarge-Diamondsmall-Bismuth
(semiconductors, ceramicspolymer chains)
Metallic Variablelarge-Tungstensmall Mercury
Nondirectional (metals)
Secondary
small-Mercury
smallest Directionalinter-chain (polymer)
L2 – bonding.
inter chain (polymer)inter-molecular
Properties From Bonding: Tm
• Bond length, r • Melting Temperature, Tm
EnergyEnergyr
• Bond energy, Eo r o rsmaller TEnergy
larger Tm
smaller Tm
r o runstretched length
Tm is larger if Eo is larger.Eo = “bond energy”
o r
L2 – bonding.
bond energy
Properties From Bonding : α
• Coefficient of thermal expansion, αcoeff. thermal expansionlength, Lo
= α (T2-T1)ΔLLo
ΔLunheated, T1
heated, T2
• α ~ symmetry at ro
r
Energy
unstretched length
•α Follows E vs r slope•α is usually larger if Eo is smaller.
r o rlarger αE
L2 – bonding.
s a esmaller αoE
o
Crystal Structures• Not everything is a crystal!!! We have amorphous and polycrystalline materials. These all canbe big, thick blocks, or ultra-thin layers. Former we refer to as bulk materials, latter as thin films.
• crystalline materials: possess long range periodic order, in which identical “unit cells” are repeated in all dimensions in perfection. We call these type of materials single crystals in electronic materials technology
• polycrystalline materials: most crystalline solids are actually composed of collections of smaller crystals or grains, with each grain or crystal separated by a grain-boundary, which is a 2-dimentional interface. Most solar cells today are polycrystalline silicon!!
• non-crystalline materials have no systematic and regular atomic arrangement over relatively large atomic distances. These are called amorphous materials. Amorphous silicon is a mainstay of several device technologies, and its electronic, optical and structural properties are COMPLETELY DIFFERENT from crystalline forms of silicon – demonstrates how structure dictates properties, even for the same element!
L2 – bonding.
Single crystalpolycrystalline
Crystalline silocon dioxide and amorphous SiO2
L2 – bonding.
Crystalline Structures: DefinitionsLattice: periodic arrangment of points in 3-dimensions.
• defined by a lattice vector T = pa + qb +sc.• basically a translation vector to map out all of space in terms of lattice points
• Around each lattice point there are atoms. An atom can be right on a lattice point or atoms can be arranged around a lattice point. The way in which atoms are arranged around a lattice point is called the “basis” and there is a 3-D basis vector, r, that describes this arrangement.
• So, crystal structure = lattice + basis
L2 – bonding.
Crystalline Structures: DefinitionsUnit Cell: a region of a crystal that can be translated through space to any lattice point to completely build the crystal structure.
• the unit cell is essentially a building block and is fundamental to the prediction of all electronic and optical properties of electronic materials
Primitive Cell: is the smallest possible unit cell that can still be translated by lattice vectors to create a crystal. Tend to be less convenient to use, except for the simplest of crystal structures.
L2 – bonding.
7 Unique Crystal Systems
L2 – bonding.
Cubic Crystal Structures
α, β, γ = 90 degreesa = b = c = lattice constant for cubic materials
Simple cubic (SC)
Body centered cubic (BCC)
Face centered cubic (FCC)
L2 – bonding.
Face centered cubic (FCC)
7 Unique Crystal Systems
L2 – bonding.