# Structure of Solids

Document Sample

```					     Section 4
(M&T Chapter 7)

Structure and Energetics of
Metallic and Ionic Solids
Bonding in Solids
► We have discussed bonding in molecules with three
models:
 Lewis
 Valence Bond
 MO Theory
► The above models aren’t 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
Close-Packing
► Treat    the atoms of a metal (or ions of an
ionic substance) as spheres (e.g. marbles).
► If fill a tray until its surface is covered with
a layer of marbles, we get a picture that
looks something like the figure
Close-Packing
► 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 six spaces around each sphere
also
► 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
Close-Packing
When the next close-packed level is added, only three
of the spaces surrounding each sphere can be occupied

►   So far, the levels are different (the spheres are not located
in the 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
Close-Packing
If we were to add another close-packed level on top, we could do so in two ways:

ABC arrangement

ABA arrangement
Close-Packing
► In the top 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)
► In the bottom 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
Close-Packed Arrangements
►   These two arrangements are shown below, are
represented as are 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

(this is also known
as a “face-centered
cubic” arranegment)

hcp                 ccp
Close-Packed Arrangements
unit cells are shown below as spherical
► The
models
 Cubic close-packed (ccp) (face-centered cubic)
 Hexagonal close-packed (hcp)
Interstitial Holes
► The  spaces between spheres in the
close-packing arrangements are called
interstitial holes/interstitial spaces
► Two types:
 Tetrahedral (four point cavities)
 Octahedral (six point cavities - larger)
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)
52% of space used   68% of space used
What are the
coordination
numbers in
these lattices?

Simple cubic      Body-centered cubic
circle = bcc
diamond = hcp
+ = ccp (fcc)   Data quoted for T = 298 K
Polymorphism
► The  lattice structure adopted by an element
may change as the temperature and/or the
pressure is changed
► A substance that exists in more than one
crystalline form is said to be polymorphic
► Look at figure on 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
Phase Diagram for Iron

Non close-packed
Phase Diagram for Iron
► At ambient temperature (~ 200 K) and pressure (1
atm), iron adopts a body-centered cubic (bcc)
ordering (a-Fe)
 look at Fe at 1000 K, 1 atm (a-Fe). Increase the
pressure. What happens? (g-Fe)
 Fe at 200K, 1 atm – increase pressure to 100 atm.
What happens?
► 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)
► 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
 rMet(Ag) = 140 pm
 rMet(Cu) = 124 pm   rMet = metallic radius: half the distance between
nearest neighbor atoms in a solid-state metallic
lattice
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)

►   Tetrahedral holes can contain atoms up to 0.225r,
where r is the radius of the spheres that make up the
close-packed lattice
►   Octahedral holes can accommodate larger atoms (e.g.
C in carbon-steel) – up to 0.41r
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
► g-brass has a formula of Cu5Zn8
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 don’t completely belong to
one cell            Corner site

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”

Face-centered site
A body-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

How many spheres (atoms/ions) occupy   Face-centered site
- a simple cubic unit cell?
- a body-centered cubic cell?
- a face-centered cubic cell?
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      In this diagram, let a = 2r

It can be shown that the corner-to-corner length 3 a
1/2
►
indicated in the picture will be 31/2a
Each sphere has a radius of r
Each edge length (length of the edge of the
unit cell) is then 2r (spheres contact at surface)
Can also be shown that                                                         a
- 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
21/2a
Simple cubic unit cell
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)
Binary Lattices

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)
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).
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 this
structure?

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, a lot like a 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 (grey) are arranged in a
hcp format with the Cd2+ ions
(blue) 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
Lattice Energies
► We   have already looked at bond dissociation
enthalpies (energy required to break bonds in
homonuclear and heteronuclear diatomics) when
we looked at Pauling electronegativities
► 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 (DU)
as:
 z z e 2 
DU  
 4e d 

     o     
►   z is the magnitude of the charge of an ion; |z+/-| is the
absolute value of this quantity (the modulus)
►   e is the charge of an electron (1.602 x 10-19 C)
►   eo is the permittivity of a vacuum (8.854 x 10-12 C2/J.m)
►   d is internuclear separation
► 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)

 z z e 2 
DU  
 4e d 

     o     
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 (21/2)d (the ions at
the edge sites)
► 8 Xz- ions each at a distance (31/2)d (the ions at
the ions at the corner sites)
► 6 Mz+ ions each at a distance of (41/2)d (imagine
the next set of blue spheres in figure beyond the
face gray spheres)
► We must factor these attractions and
repulsions into the expression:

              12   2  8         6   2 
6 z z   
e2
DU                              z    z z    z ...
4e o d               2       3         4     

► Convergent  series, which yields a number
for each lattice type that is called the
► Ifwe 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 value is
obtained regardless of the actual charges on the
ions.                           Table 7-2, M. & T.
► Madelung constants (A) are unique for each
coordination environment (i.e., for each type of
crystal lattice).
 A z z e 2 
DU  
 4e d 

      o      
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:
 LA z  z e 2 
DU  
 4e d 

        o      

►L  = Avogadro’s number (6.022 x 1023 mol-1)
► but what about Born forces? (nuclear-nuclear,
electron-electron forces)
Lattice Energies
► If  we consider electrostatic and Born forces,
we arrive at the Born-Mayer equation
(evaluated at equilibrium internuclear
separation, do)                        Correction for
This equation                                                           Born forces
will enable us
to predict lattice                 LA | z || z | e 2    r
energies (called    DU (0 K )                       1  
 d 
the calculated                      4e o d o           o 
lattice energy

►r    corrects for repulsions at short distances.
Typically, a value of 30 pm is used for r.
•Lattice energy can also be defined as the energy required to pull apart an ionic lattice
into its gas-phase ions, as defined in M&T, in which case, it is a positive energy
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.
Sample Calculation: Lattice
Energy
► Calculate        the lattice energy for NaCl (rNa-Cl =
283 pm)
LA | z || z | e 2    r
DU (0 K )                       1  
4 o d o  d o      

(6.022x1023 )(1.7476) | 1 || 1 | (1.602 x1019 C ) 2     30 pm 
DU (0 K )                                                         283 pm 
1        
4 (8.854 x10 C J m )(283x10 m) 
12 2 . 1. 1             12

 766871J / mol
 767kJ / mol
rNa+ = 116 pm
Appendix B
rCl- = 167 pm
Sizes of Ions
► Ions of ionic lattices are treated as hard spheres in
these models
► Think of the ions (of opposite charge) as just
touching in this model, thus internuclear
separation (do), determined experimentally, yields

d = rcation + ranion

► This pure, electrostatic model is a (sometimes
poor) approximation of structure. It assumes zero
electron density between ion spheres (at odds
with MO theory)
Lattice Energy and Born-Haber
Cycle
► The  Born-Mayer equation calculates an
estimate of the lattice energy by considering
various interactions in an electrostatic
model.
► We can also determine the lattice energy by
employing experimental values (e.g.
enthalpies of formation, bond dissociation
enthalpies, etc.). This procedure is called
the Born-Haber cycle
Relevant Reactions For Sodium Chloride, NaCl

► Atomization
Na(s)  Na(g)
► Bond Breaking     Cl2(g)  2Cl(g)       Appendix
► Ionization        Na(g)  Na+(g) + e-      B-2

► Electron Affinity Cl(g) + e  Cl (g)
-     -         B-3

► Lattice Energy
Na+(g) + Cl-(g)  NaCl(s)

Na(s) + ½Cl2(g)  NaCl(s)
► Formation

Bond enthalpy, DCl2 corresponds to DH for Cl2(g)  2Cl(g) process
Born-Haber Cycle
 DHof(MXn,s) = DaHo(M,s) + n/2D(X2,g) +
ΣIE(M,g) + nDEAH(X,g) +
DHolattice(MXn)
DHolattice(MXn) = DU(0K)
►   Rearranging, we get

DHolattice(MXn) ≈ DHof(MXn,s) - DaHo(M,s) - n/2D(X2,g)-
ΣIE(M,g) - nDEAH(X,g)

Born-Haber cycles are often called “experimental” lattice
energies, since they are derived from thermochemical
data.
Sample Calculation
► Use the Born-Haber cycle to calculate the lattice
energy of NaCl, given DHof(NaCl,s) = -407.6
kJ/mol

► DaHo(Na,s)  (sublimation of Na) = 108 kJ/mol
► D(Cl2,g) (dissociation of Cl2) = 242 kJ/mol*
► ΣIE(Na,g) (appendix B-2) = 495.8 kJ/mol
► DEAH(Cl,g) (appendix B-3) = -349 kJ/mol*

* Defined for Cl2(g)  2Cl(g)
* Defined for Cl(g) + e-  Cl-(g)
Sample Calculation
► Thus,   the lattice energy is:

   DU(0K) ≈ DHof(MXn,s) - DaHo(M,s) - n/2D(X2,g)-
ΣIE(M,g) - nDEAH(X,g)

   DU(0K) ≈ (-407.6 kJ/mol) – (108 kJ/mol) - ½( 242
kJ/mol) – (495.8 kJ/mol) – (-349 kJ/mol)

= -783.4 kJ/mol
Lattice Energies
► Wesee there is only a minor discrepancy
between the value obtained with the Born-
Mayer equation (-767 kJ/mol) and the Born-
Haber cycle (-783 kJ/mol)

NaCl, there’s only a ~2% difference
► For
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
►A   rough guide for predicting structures
of salts (cations and anions). Use
rcation/ ranion, or r+/r-)
Value of r+/r-     Predicted      Predicted
Coordination   Coordination
Number of      Geometry of
Cation         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
►   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
conductivity is a property displayed by
► Electrical
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 other atoms
► Band theory is used to explain conductivity
Electrical Conductivity and Resistivity

► Resistivity(r) measures a substance’s electrical
resistance for a wire of uniform cross-section

R
rl

resistivity / Wm length / m 
a        cross  sectional _ area / m 
2

► Resistance is measured in ohms (W)
► Conductivity is 1/resistivity. Units of conductivity
are W-1m-1 or S/m (S = Siemens; S = W-1)
Electrical Conductivity and Resistivity

“electrical resistivity”
Wm

► The resistivity of
a metal increases
(conductivity
decreases) with
increasing
temperature
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 Metals
In 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 is
greatest
in the
middle of
the band

Band that is created from occupied
orbitals is called “valence 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

electronic movement can
occur by an electron jumping
from the valence band into an
energy-matched unoccupied
conduction band orbital
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)
 Semiconductors have fully occupied bands that are
separated from the valence band by a small energy gap
(e.g. Si)
 Insulators have fully occupied valence bands that are
separated from the conduction band by a significant energy
gap (e.g. diamond)
metal with
half-filled
valence band
insulator                metal with
(e.g. diamond)              overlapping
valence and
conduction bands

semiconductor
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
enhanced electrical 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
►   Introduction of either gallium or
arsenic in very small quantities
creates an extrinsic semiconductor,
with a band gap of only about 10         Si adopts a diamond lattice
kJ/mol
Extrinsic Semiconductors
n-Type Semiconductors
►   Arsenic-doped silicon contains
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

Si is n-doped by introducing P or As atoms
The charge carriers in the Si band structure are electrons: “n-type” semiconductor
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 – a “p-type” semiconductor
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

H
N
S             N
*                          *           * *       n
*   *           *
n   *   *     n   *           n                             n
Semiconductor Devices

►   Thermal population of unoccupied states makes these
materials conductive; at 0K, electrons occupy lowest
possible energies
The Fermi energy is energy at which an electron is
equally likely to be in occupied and unoccupied bands

p-type semiconductor at 0K (left)                 n-type semiconductor at 0K (left)
and at T = 298K (right)                           and at T = 298K (right)
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
 Raises the energy of the Fermi level to between the donor band
and the bottom edge of the host’s conduction band
 Lowers the energy of the Fermi level to the region between the
acceptor band and the top of the host’s valence band

intrinsic            p-type              n-type
Semiconductor Devices p,n-junction
►   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
Diodes
+   power    -
supply
►    When this kind of device is
connected to a DC power
source, a connection can be
1. Negative terminal to n-
type layer, positive
terminal to p-type layer
(forward bias): as the
potential at the negative
more negative (and the
positive terminal more and
more positive), the
potential difference of the
depletion zone can be
overcome and a current
flows (e-’s repelled by –
terminal; holes repelled by
+ terminal)
Diodes
-   power    +
supply
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
Diodes
►   Diodes are semiconductor
devices which permit
current to flow in one
direction but not the other
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
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
to promote electrons from
the valence band to the
conduction band (thus
current flows in the
presence of light – a
photoswitch)
►   Used in sensors
(photodetectors for UV,
automatic lights, etc.
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

```
DOCUMENT INFO
Shared By:
Categories:
Stats:
 views: 109 posted: 6/23/2011 language: English pages: 83