1

Section 4(M&T Chapter 7)

Structure and Structure and EnergeticsEnergetics of of

Metallic and Ionic SolidsMetallic and Ionic Solids

Bonding in Solids

• We have discussed bonding in molecules with three models:

– Lewis

– Valence Bond

– MO Theory

• These models not suitable for describing bonding in solids

(metals, ionic compounds)

• The structures of many solids (e.g. NaCl(s), Fe(s)) are best

described by a lattice model, in which atoms (ions) of the

lattice are placed in highly ordered arrangements (crystal

lattices)

• Arrangement yields maximum net attractive force with other

ions/atoms in the lattice and minimum repulsive forces

Close-Packing

• Treat the atoms of a metal (or ions of an ionic

substance) as spheres (e.g. marbles).

• Fill a tray until its surface is covered with a layer

of marbles, get a picture that looks something like

this:

• In this model, all spheres are touching the surface of six

other spheres (except those on the edges/corners) – a

hexagonal arrangement

• This arrangement is one layer of what is called a “close-

packed” arrangement

• See that there are also six spaces around each sphere

• If we were to pile another layer on top of this, it would

appear as follows…

Close-Packing

Around each sphere, there

are a total of six spaces Put next layer

of spheres into

three of them

Close-Packing

• So far, the levels are different (the spheres are not located inthe same space directly above the first level), so we have an “AB-type” arrangement for the two layers

• Note the spaces (hollows) that are now present – two types:

– “A” – located above a sphere

– “C” – located above a space

When the next closeWhen the next close--packed level is added, only threepacked level is added, only three

of the spaces surrounding each sphere can be occupiedof the spaces surrounding each sphere can be occupied

A

A AC

C

C

2

Close-Packing

If we were to add another closeIf we were to add another close--packed level on top, we could do so in two ways:packed level on top, we could do so in two ways:

Put 3rd layer

into A hollows

Put 3rd layer

into C hollows

AC

C CCA

Close-Packing

• In the upper figure (ABA-type) the top level was created

by putting spheres into the spaces labeled “A” of the

second layer

• The top level here is thus the same as the first (bottom)

level (the spheres in this level are located directly above

those of the first level) – an “ABAB…” arrangement

ABA arrangement

Close-Packing

•In the lower figure (ABC-type), the top layer was

constructed by placing spheres in the spaces labeled “C” of

the second layer

•This results in a level that is different than either of the

first two levels (an “ABC…” arrangement)

ABC arrangement

Close-Packed Arrangements

• These two arrangements shown below, are represented

as ball-and-stick arrangements, and not meant to imply

that spheres are not touching

• Which is which?The coordination number (CN)

in each of these lattices is 12.

Top layer different

than bottom

Close-Packed Arrangements• The unit cells are called:

a) hexagonal close-packed (hcp) – describing

an “ABABAB…” arrangement

b) cubic close-packed (ccp) – this describes an

“ABCABC…” ordering

hcp ccp

(this is also known as a “face-

centered cubic” arrangement)

Close-Packed Arrangements

• The unit cells are shown below as spherical models

– Cubic close-packed (ccp) (face-centered cubic)

– Hexagonal close-packed (hcp)

3

Interstitial Holes

• The spaces between spheres in the close-packing

arrangements are called interstitial holes or

interstitial spaces

• Two types:

– Tetrahedral (four point cavities)

– Octahedral (six point cavities - larger)

Crystal Structures

Amorphous: no long-range pattern

Crystalline: long-range order

Unit Cell

Holes in Crystals Unit Cells in the Cubic Crystal System

Non-Close Packed Arrangements

• In many solids, the percentage of occupied space is less

than 74% - these solids assume non-close packed

arrangements

• Arrangements below depict the simplest model that

incorporates all the information of the lattice (a unit cell)

What are the

coordination

numbers in

these lattices?

Simple cubic Body-centered cubic

52% of space used 68% of space used

Number of Atoms in a Unit Cell

Face centered unit cell

contains 8 corners @ 1/8 atom + 6 faces @ ½ atom = 4 atoms

4

Counting Cell Occupancy

2 atoms 4 atoms 1 atom

circle = bcc

diamond = hcp

+ = ccp (fcc)

Data quoted for T = 298 K

X-Ray Diffraction : Crystallography

Diffraction of X-Rays

Constructive interference of the x-rays only when the

pathlength in the crystal is a whole multiple of the wavelength

Bragg Equation: nλλλλ = 2d sin θθθθ, n = 1, 2, 3, …

Polymorphism

• The lattice structure adopted by an element may change

as the temperature and/or the pressure is changed

• A substance that can exist in more than one crystalline

form is said to be polymorphic

• Next slide – a phase diagram for Fe

• Phase diagram – lines (phase boundaries) separate

different phases of a substance

• On a line, have both phases present in equilibrium

5

Phase Diagram for Iron

Non close-packed

At ambient temperature (~ 300 K) and pressure (1 atm),

iron adopts a body-centered cubic (bcc) ordering (αααα-Fe)

Phase Diagram for Iron

Look at Fe at 1000 K, 1 atm (αααα-Fe). Increase the pressure.

What happens? (γγγγ-Fe)

Fe at 200K, 1 atm – increase

pressure to 100 atm. What

happens?

Phase Diagram for Iron

• Sometimes, we can heat an element, changing its

packing, and rapidly cool it to retain the higher

temperature structure (quenching) – this allows

higher temperature structures to be studied at

ambient temperatures

Alloys and Intermetallic Compounds

• Alloys are intimate mixtures (solid solutions) of

metals/elements, or a distinct compound consisting

of these elements, with physical properties that

differ from those of the elements that make it up

• The aim of alloying is to endow the mixture with

desirable properties that are inherent to the

metals of the mixture (e.g. hardness, ductility)

Alloys and Intermetallic Compounds• Everyday examples of alloys: (solute(s), solvent)

– Solder (Sn, Pb); low melting point

– Stainless steel (Cr, C, Fe); anti-corrosion, strength

– Sterling silver (Cu, Ag); doesn’t tarnish

Alloys

• Substitutional alloys: created from metals having similar rMet (radii), similar coordination number

• Metals are mixed in the molten state (high temperature) and allowed to cool gradually

• The solute atoms occupy sites in the lattice that would normally be occupied by solvent atoms

• Sterling silver is created from 92.5% Ag, 7.5% Cu – both adopt ccp lattices

– rMet(Ag) = 140 pm

– rMet(Cu) = 124 pm

rMet = metallic radius: half the distance between

nearest neighbor atoms in a solid-state metallic

lattice

6

Substitutional Alloys Alloys

• Interstitial alloys: solute atoms occupy the

interstitial spaces (cavities) of a host lattice (e.g.

carbon steel)

– Low C steel: 0.03 – 0.25% C (steel sheeting)

– Medium C steel: 0.25 – 0.70% (bolts, screws, etc.)

– High C steel: 0.8 – 1.5% (cutting, drilling tools)

Intermetallic Compounds

• Some melts (combinations of metals in the molten

state) will solidify in arrays that are different than

either of the components that make up the mixture –

these compounds are called intermetallic

compounds

• Brass (Cu, Zn) is an intermetallic compound -

γγγγ-brass has a formula of Cu5Zn8

Alloys and Intermetallic Compounds

• Alloys are intimate mixtures (solid solutions) of

metals/elements, or a distinct compound consisting

of these elements, with physical properties that

differ from those of the elements that make it up

• The aim of alloying is to endow the mixture with

desirable properties that are inherent to the

metals of the mixture (e.g. hardness, ductility)

Diamond

• In diamond, C-atoms take

on a fcc-type arrangement

• Each C-atom is four-

coordinate (tetrahedral)

and so possesses a

complete octet of electrons

through covalent bonds

• Also adopted by Si, Ge, Sn

and Pb (other C-group

elements)

Graphite

• The most thermodynamically stable

form of carbon (diamond is

metastable), graphite consists of

layers of carbon sheets that are built

from fused, 6-membered carbon rings

• The bonding that exists within a layer

is covalent (and delocalized), but

between planes, dispersion forces

(non-covalent) hold the rings together

(weak intermolecular force)

7

Unit Cells• The smallest collection of spheres that describes a lattice

(when it is repeated) is the unit cell

• Some of the atoms in a unit cell are shared with other cells,

and so they do not belong entirely to one cell

Example, the atoms at the corners of the

cell shown on the right are shared with

seven other cells

Each contributes 1/8 of an atom to the

cell shown, and is called a “corner site”

Corner site

Face-centered site

A face-centered cubic unit cell

Unit Cell Contributions

• Corner sites each contribute 1/8 of a

sphere to a cell

• Edge sites contribute ¼ sphere to the

cell

• Face sites contribute ½ sphere to the cell

• Sites contained in the cell (e.g. the

center site of a bcc cell) contribute 1

each

Face-centered site

How many spheres (atoms/ions) occupy

- a simple cubic unit cell?

- a body-centered cubic cell?

- a face-centered cubic cell?

Ionic Solids

Particles: Cations (+) – small size

Anions (-) – large size

UNIT CELL dimensions usually determined by the

arrangement of the large ANIONS.

Cations fit into the “holes” within the anion structure

Holes in Crystals

(2R)2+(2R)2 = (2R+2r)2

••••

••••

r = 0.414R

Radius Ratios• A rough guide for predicting structures of salts

(cations and anions). Use rcation/ ranion, or r+/r-)

Value of r+/r-Predicted

Coordination

Number of

Cation

Predicted

Coordination

Geometry of

Cation

<0.15 2 Linear

0.15-0.22 3 Trigonal Planar

0.22-0.41 4 Tetrahedral

0.41-0.73 6 Octahedral

>0.73 8 Cubic

Sodium Chloride

rNa+/RCl- = 102 pm/ 181 pm = 0.56,

expect Na+ to occupy octahedral holes.

8

Holes in Crystals

Four types of holes:

trigonal < tetrahedral < octahedral < cubic

too small

for any

cation

Final arrangement depends on relative sizes of

cations and anions plus the required stoichiometryThis is an example of a binary solid (two elements involved) – what is its formula?

Dimensions of Cubic Lattices• For cubic unit cells, it is possible to determine cell lengths (edge) and

dimensions of lattice spaces

• For example, a simple cubic cell will have an edge length of 2r, where

r is the radius of a sphere

• It can be shown that the corner-to-corner length indicated in the

picture will be √√√√3××××a

Each sphere has a radius of r

Each edge length (length of the edge of the

unit cell) is then 2r (spheres in contact)

Can also be shown that

- a sphere of radius up to 0.73r can fit

in the center

-the atoms occupy 52% of the available

space of the unit cell

a

√√√√3××××a

Simple cubic unit cell

In this diagram, let a = 2r

√√√√2××××a

Rock Salt Lattice (NaCl)

• Interpenetrating fcc lattices of Na+ ions and Cl- ions (rem: fcc = ccp)

• Cl- ions are much larger then the Na+ ions (Cl-: 181 pm; Na+: 102 pm).

• Na+ ions are occupying octahedral holes in the unit cell shown

• Each Na+, Cl- ion is octahedral (six coordinate)

• NaCl-type lattice structures exist for many ionic compounds (NaF, NaBr, NaI, NaH, LiX, KX, RbX (X = halide), AgF, AgCl, AgBr, MgO, CaO, SrO, BaO, MnO, CoO, NiO, MgS, CaS, SrS, BaS)

Binary Lattices

CsCl Lattice

• Eight coordinate ions (cations and

anions) – body centered cubic

• Interpenetrating simple cubic-type

lattice

• Adopted by CsBr, CsI, TlCl, TlBr

CaF2 (Fluorite) Lattice• Eight-coordinate cations (Ca2+, grey spheres)

• Four-coordinate anions (F-, blue spheres)

• Six cations are face-positioned, shared between adjacent cells.

• This lattice type adopted for group II metal fluorides, BaCl2, and f-block metal dioxides

• Exchanging the cations and anions in this structure would yield an antifluorite lattice – M2X stoichiometry. Adopted by some group I metal oxides and sulfides (e.g. Na2S).

9

Zinc blende, ZnS (diamond type) lattice

• Similar to the fluorite lattice, with removal of half of the

anions (so MX2 to MX stoichiometry).

• Looks something like the structure shown for diamond –

each atom is in a tetrahedral environment

How many Zn, S

atoms exist in thisstructure?

Zn: grey

S: blue

Wurtzite (ZnS) lattice

• Wurtzite formed by high

temperature transition

from zinc blende

• Hexagonal prism unit cell

with all ions tetrahedrally

sited

• How many Zn2+, S2- ions

exist in this structure?

β-cristobalite (SiO2) lattice

• Again, much like diamond

structure, but with oxygen

ions between the

tetrahedral Si ions.

• Si-O-Si bond angle in

figure is 180o, while in

practice, it is found to be

147o (bonding in SiO2 is

not purely electrostatic).

In a pure ionic model, electrostatic attraction would be the only factor that

would be expected to hold an ionic lattice together

Rutile (TiO2) structure

• Oxygen ions (white) are

trigonal planar while

titanium centers (black)

are octahedral.

• Four oxygen ions are face-

oriented, while two are

contained in the cell

Perovskite (CaTiO3) lattice

• A double oxide (oxygen atoms are coordinated to both

Ca2+ and Ti4+)

• Ca2+ ion is at center of cube unit cell

• Ti4+ ions at corners of the cube (eight of these)

• O2- ions at each edge of the cube (twelve of these)

CdCl2, CdI2 Lattices

• Common for MX2 structures to crystallize in this structure

• Can observe the layers as ABAB (layered lattices)

• I- ions (gold) are arranged in a hcp format with the Cd2+ ions (white) occupying octahedral holes.

• In CdCl2, the arrangement is ccp

• Attractive forces that exist between these planes is weak (dispersion forces), and so fracture of a crystal of this kind usually produces cleavage planes

CdI2 lattice

10

Energy Changes in the Formation of Ionic Crystals

Na(s) + ½ Cl2(g) →→→→ NaCl(s)

∆∆∆∆Hreaction = ∆∆∆∆Hf(NaCl(s))

Energy Changes in the Formation of Ionic Crystals

Lattice Energy

Born-Fajans-Haber Cycle

sublimation

bond energy

ionization energy

electron affinity

(Ionic Bond Strength)

Lattice Energies

• We have already looked at bond dissociation

enthalpies (energy required to break bonds in

homonuclear and heteronuclear diatomics)

• Energy is also required to break apart ionic

lattices, due to the large amount of electrostatic

forces that exist between the ions in the lattice

• Coulombic forces (attractions, repulsions)

• Born forces (electron-electron, nucleus-nucleus)

Energy Between Two Point

Charges• Consider what happens if we bring two point charges

from an infinite separation to form an ion pair:

Mz+(g) + Xz-(g) MX(g)

• We can calculate the change in internal energy (∆∆∆∆U) as:

• Z-, Z+ are the charges of the ions in electron units

• e is the charge of an electron (1.602 x 10-19 C)

• εo is the permittivity of a vacuum (8.854 x 10-12 C2/J.m)

• r0 is internuclear separation

=∆ −+

0

2

0 4 επe

r

ZZU

• Because oppositely charged ions are attracted to one

another, energy is released in this process

• Consider the attractions and repulsions that exist in a rock

salt lattice (between oppositely-charged and like-charged

ions)

=∆ −+

0

2

0 4 επe

r

ZZU

11

A Summary of Attractions and Repulsions

• The attractions experienced by the Na+ ion are summarized as follows:

• 6 Xz- ions, each at a distance d (the ions at the face sites)

• 12 Mz+ ions, each at a distance (√√√√2)d (the ions at the edge sites)

• 8 Xz- ions each at a distance (√√√√3)d (the ions at the corner sites)

• 6 Mz+ ions each at a distance of (√√√√4)d (imagine the next set of pink spheres in figure beyond the face gray spheres)

Madelung Constants

• We must factor these attractions and repulsions

into the expression:

• Convergent series, which yields a number for each

lattice type that is called the Madelung constant, M

( )

−

+

−=∆ +−++−+ ...

4

6

3

8

2

126

4

222

ZZZZZZd

eU

oπε

Madelung Constants

• If we sum the interactions (attractive and repulsive) between the ions of this lattice, we get a convergent term (for this lattice, the value converges to a value of ~1.7476). This valueis obtained regardless of the actual charges on the ions.

• Madelung constants (M) are unique for each coordination environment (i.e., for each type of crystal lattice).

=∆ −+

0

2

0 4 επe

r

ZMZU

Table 7-2, M. & T.

Lattice Energy (almost there…)

• The internal energy change for the formation of one mole of an ionic lattice in this arrangement is then calculated as:

• N = Avogadro’s number (6.022 x 1023 mol-1)

• but what about Born forces? (nuclear-nuclear, electron-electron forces)

=∆ −+

0

2

0 4 επe

r

ZNMZU

Lattice Energies

• If we consider electrostatic and Born forces, we

arrive at the Born-Mayer equation (evaluated at

equilibrium internuclear separation, ro)

• ρρρρ corrects for repulsions at short distances.

Typically, a value of 30 pm is used for ρρρρ.

•Lattice energy can also be defined as the energy required to pull apart an ionic latticeinto its gas-phase ions, as defined in M&T, in which case, it is a positive energy

Correction for

Born forcesThis equationwill enable us

to predict latticeenergies (calledthe calculated

lattice energy

( )

−

=∆ −+

00

2

0

1 4

K 0r

e

r

ZNMZU

ρεπ

Lattice Energies

• Lattice energy can be defined as the internal energy change associated with the formation of one mole of the solid from its constituent gas phase ions at 0 (zero) Kelvin. Thus, at 0K, the lattice energy corresponds to the process:

Mn+(g) + nX-

(g) MXn(s)

Lattice energies may be estimated by assuming an electrostatic model (ions are point charges) – a good approximation in some cases. In others, not so good.

12

Sample Calculation: Lattice Energy

• Calculate the lattice energy for NaCl (rNa-Cl = 283 pm)

( )( )

molkJ

molJ

pm

pm

mmJC

CKU

/767

/766871

283

301

)10283)(10854.8(4

)10602.1(11)7476.1)(10022.6()0(

121.1.212

21923

−=

−=

−

××

×−+×=∆

−−−−

−

π

rNa+ = 116 pm

rCl- = 167 pmAppendix B

( )

−

=∆ −+

00

2

0

1 4

K 0r

e

r

ZNMZU

ρεπ

Lattice Energies

• We see there is only a minor discrepancy between the value

obtained with the Born-Mayer equation (-767 kJ/mol) and

the Born-Fajans-Haber thermodynamic cycle (-787 kJ/mol)

• For NaCl, there’s only a ~2% difference between the

calculated and experimental energies (an ionic model

provides a good approximation of NaCl)

Lattice Energies• Since the calculated values agree so well (2% error), we see the

electrostatic model is a reasonably good assumption for the type of

bonding which exists in a NaCl(s)

lattice

• Not true for layered structures like CdI2(s) – recall the forces that exist in

this structure

• We also see that for silver halides, the calculated and experimental

energies differ greatly, in the order AgF<AgCl<AgBr<AgI. The bonding

with larger halide ions has more covalent character, and thus an ionic

approximation does not hold

F Cl Br I

CHEM 245

Interactive 3-D Crystal Structures:

http://www.chemtube3d.com/solidstate/_table.htm

Radius Ratios

• These guidelines often yield incorrect predictions – example: LiBr(r+/r- = 0.38; tetrahedral)

• Predict only one coordination geometry for a given combination of ions (not helpful for polymorphic samples)

• Examples:

– What is the coordination number of Ti in rutile? (rTi3+ = 75 pm; rO2- = 124 pm)

– What is C.N. of Ca in fluorite? (rCa2+ = 126 pm; rF- = 117 pm)

– What is C.N. of Zn in zinc blende? (rZn2+ = 77pm; rS2- = 170 pm)

Electrical Conductivity in Metals,

Semiconductors, and Insulators

• Electrical conductivity is a property displayed by metals and some inorganic and organic materials

• Loosely defined as the ability of a substance to permit movement of electrons throughout its volume

• On a molecular level, electrons can be passed around (atom-to-atom) by being promoted into empty orbitals on otheratoms

• For solid structures a modification of Molecular Orbital Theory called Band Theory is used to explain conductivity

13

Electrical Conductivity and Resistivity

• Resistivity (ρρρρ) measures a substance’s electrical

resistance for a wire of uniform cross-section

• Resistance is measured in ohms (ΩΩΩΩ)

• Conductivity is 1/resistivity. Units of conductivity

are ΩΩΩΩ-1m-1 or S/m (S = Siemens; S = ΩΩΩΩ-1)

( )( )( )2/_sec

//

mareationalcross

mlengthmyresistivit

a

lR

−

Ω==

ρ

Electrical Conductivity and Resistivity

• The resistivity of a

metal increases

(conductivity

decreases) with

increasing

temperature

“electrical resistivity”Ωm

Electrical Conductivity and Resistivity

• The resistivity of a

semiconductor decreases

(conductivity increases) with

increasing temperature

Resistivity with temperature for a semiconductor

MO Theory Approach to Band Theory

• Consider a line of H-atoms that interact through their valence s-orbitals.

As more H-atoms interact, more MO’s are created

In the infinite structure, there is a continuum of energy states - a “band” (non-quantized)

Valence orbitals overlap to create a “valence band”

Band Theory of MetalsIn order for electrons to be able to move through a material, they must jump

from an occupied molecular orbital to an unoccupied orbital. In a metal, this

should be easily accomplished (metals are highly conductive).

Lithium (and other alkali metals) have a half-filled valence s-orbital (occupied).

In the infinite solid, there will be a half-full band. Electrons can move into an

unoccupied MO with minimal energy cost (small applied potential)

density of

states isgreatest

in themiddle of

the band

Band that is created from occupiedorbitals is called “valence band”

unoccupied orbitals produce

a “conduction band”

Band Theory of Metals• For the metal, Be (2s2), how does electron

movement occur? (valence band is full)

• The energy separation of 2s and 2p orbitals in Be is small enough that the conduction band (band that derives from unoccupied orbitals) overlaps the valence band

electron movement canelectron movement can

occur by an electron jumpingoccur by an electron jumping

from the valence band into anfrom the valence band into an

energyenergy--matched unoccupiedmatched unoccupied

conduction band orbitalconduction band orbital

14

Semiconductors and Band Gaps

• In many materials (e.g. diamond), there is an energy gap (band gap, Eg) between the valence band and the conduction band

• For C, the energy separation that exists between the 2s and 2p valence orbitals is not small enough for valence band-conduction band overlap to occur in the bulk material (e.g. diamond)

– Metals have either partially filled valence bands or overlapping valence and conduction bands (e.g. Na)

– Insulators have fully occupied valence bands that are separated from the conduction band by a significant energy gap (e.g. diamond)

– Semiconductors have fully occupied bands that are separated from the valence band by a small energy gap (e.g. Si)

Band Theory

overlapping valence

and conduction bands

conduction

conduction

valence valence

band gap

Semiconductors

• For semiconductors, thermal energy will enable

electrons to move into the empty conduction band,

creating “holes” in the valence band (orbitals that

were occupied by electrons). The mobile electrons

(and holes) give rise to electrical conductivity.

• Pure materials that are electrically conductive

called intrinsic semiconductors

Extrinsic Semiconductors

• Certain semiconductors exhibit enhancedelectrical conductivity when small quantities of another element are present in the semiconductor lattice (called doping).

• The band structure of silicon involves a band gap of approximately 106 kJ/mol (1.11 eV)

• Introduction of either gallium or arsenic in very small quantities creates an extrinsic semiconductor, with a band gap of only about 10 kJ/mol (0.10 eV)

Si adopts a diamond lattice

Semiconductors

s2 p2

Semiconductors

Ga

Ga

15

Band Theory

overlapping valence

and conduction bands

conduction

conduction

valence valence

band gap

n-Type Semiconductors

• Arsenic-doped silicon contains atoms having an additional valence electron (As is gr. 5A, Si Gr. 4A). As in a Si lattice use four of its electrons in bonding (one left over)

• Even a small number of As atoms in the Si matrix creates a “donor band” with an energy just below the energy of the Si conduction band (~10 kJ/mol below)

• Thermal energy can excite electrons from the donor band into the Si conduction band, yielding mobile charge carriers

The charge carriers in the Si band structure are electrons: “n-type” semiconductor

Si is n-doped by introducing P or As atoms

p-Type Semiconductors

• Ga has one less valence electron than Si

• Introduction of a small number of Ga

atoms (Gr. 3A) into the Si lattice

structure creates a hole (nothing for

silicon’s fourth electron to bond to)

• The energy of these holes creates a

band just above the valence band

energy (by ~ 10 kJ/mol), an “acceptor

band”

• Electrons can occupy this new band,

leaving holes in the Si valence band

The mobile holes in Si band structure yield conductivity The mobile holes in Si band structure yield conductivity –– a a ““pp--typetype”” semiconductorsemiconductor

Semiconductors

• Semiconductors can be inorganic or organic

• Inorganic semiconductors consist of main group elements

(Si, Ge, Ga, As, In,…)

• Organic semiconductors consist of conjugated carbon

structures, typically oligomers or polymers

**

n

* *n

S

* *n

N

* *n

H

N

* *n

Semiconductor Devices

• Thermal population of unoccupied states makes these

materials conductive; at 0 K, electrons occupy lowest

possible energies

p-type semiconductor at 0 K (left)

and at 298 K (right)

n-type semiconductor at 0 K (left)

and at 298 K (right)

The Fermi energy is energy at which an electron is

equally likely to be in occupied and unoccupied bands

Semiconductor Devices• The Fermi level serves to set the relative energies of the p-

type and n-type interfaces, and is the energy at which an e- is

equally likely to be in the valence or conduction band.

• In an intrinsic semiconductor, this lies in the middle of the

bandgap of the host semiconductor

• Doping:

– lowers the energy of the Fermi level to the region between

the acceptor band and the top of the host’s valence band

– raises the energy of the Fermi level to between the donor

band and the bottom edge of the host’s conduction band

intrinsic p-type n-type

16

Semiconductor Devices• When n- and p-type semiconductors

contact, mobile electrons in the n-type

layer near the interface can migrate

into the p-type layer, resulting in

recombination

• The extra electrons in the p-type layer

raise its energy and new holes in the n-

type layer lower its energy. Charge

movement ceases nearly immediately, as

the p-type layer accumulates negative

charge and the n-type layer positive

charge

• Recombination results in the formation

of a depletion zone at the junction. This

depletion zone is accompanied by its

own potential

p,np,n--junctionjunction

Diodes

When this kind of device is connected to a DC power source, a connection can be made in two ways:

1. Negative terminal to n-type layer, positive terminal to p-type layer (forward bias): as the potential at the negative terminal is made more negative (and the positive terminal more positive), the potential difference of the depletion zone can be overcome and a current flows (e-’srepelled by – terminal; holes repelled by + terminal)

-+ powersupply

Diodes

2. Negative terminal to p-type

layer; positive terminal to n-

type layer (reverse bias):

electrons and holes are pulled

away from the depletion zone.

Charge cannot move across

the junction and there is

essentially zero current

+- powersupply

Diodes

• Diodes are semiconductor devices

which permit current to flow in one

direction but not the other (current

rectifying), made through

combinations of p-type and n-type

semiconductors

• Such devices are useful in

electronics (e.g. in common

circuitry)

Photovoltaic Cells

• In the absence of an applied

potential, electrons can be made

to jump from valence to

conduction bands by absorbing

radiation (e.g. sunlight) and

through external connections,

can be used to power electronics

(solar calculators, solar panels)

Photoswitches

• Under reverse bias conditions, if the bandgap is small enough, visible radiation may be sufficient to promote electrons from the valence band to the conduction band (thus current flows in the presence of light – a photoswitch)

• Used in sensors (photodetectorsfor UV, visible, infrared radiation), automatic lights, etc.

17

Light Emitting Diodes (LEDs)

• Under forward bias conditions, electrons move from the n-

type layer (conduction band) into the p-type layer (valence

band)

• This movement results in recombination (releases energy).

When electrons fall into the holes of the p-doped layer, if the

energy change is of the right magnitude, visible light will be

emitted (luminescence)

• The color of the radiation emitted will depend on the

bandgap (Eg), so by varying the bandgap (by controlling the

composition of the semiconductor material), different colors

can be produced

Microscopic to Macroscopic

(Atomic Properties to Bulk Properties)

atoms, molecules

•discrete orbitals,

energy states

bulk solids

•bands, non-quantized

Quantum Dots

< 10 nmEnergy levels depend

strongly on size

Quantum Dots

Photoluminescence of

colloidal ZnSe Quantum Dots