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.