Download Semiconductivity

Semiconductivity
Band theory is able to account satisfactorily for the properties of semi
conductors such as Si & Ge. In certain transition metal compounds, it is not applicable, mainly
because the outer valence orbitals on adjacent atoms do not overlap strongly to form bands. For
ex. MnO, FeO, CoO are semiconductors.
Band structure of inorganic solids: Transition metal monoxides
Among the first row transition metal monoxides, early metal oxides, TiO & VO are
metallic conductors, the others MnO, FeO, CoO are semiconductors & NiO is an insulator.
The O 2p orbitals form a filled band. The 4s orbital form another filled band
.Then the remaining is 3d orbitals. In compounds of transition metals the conductivity is due to
partly filled d orbitals on the metal ions
The symmetry enables 3 t2g orbitals of the 5 d orbitals on different metal atoms
to overlap. Because the atoms are not nearest neighbours, the overlap is not large as in pure
metals & the band is thus narrow. The other two d orbitals (eg) overlap with orbitals of adjacent
oxygen atoms to form another narrow band. The lower band ie, the t2g band can accommodate
6N electrons & the upper one eg can 4N electrons divalent Ti has 2d electrons & so there are 2N
electrons to fill the 3N levels of t2g band. For VO also, the t2g band is parly filled. As in the
case of pure metals, a partly filled band leads to metallic conductivity. Consequently TiO & VO
have metallic conductivity. On this basis one would expect MnO, CoO, NiO which also have
partly filled bands to be metallic. But actually these oxides are semiconductors.
The explanation of the variation in properties is that, on progressing across
the transition metal series, the d orbitals experience an increased nuclear charge with increasing
at. number. Consequently the d electrons are more tightly held to individual atoms & become
localized. Then the semi conductivity is due to hopping. ie, semiconductors for which band
theory is not applicable are termed hopping semiconductors. In these, the electrons are
localized but are able to hop to adjacent atoms provided they gain sufficient energy.
In the case of NiO , it is an insulator . Here the t2 g band capable of containing 6N
electrons is full. The 2 extra electrons in Ni2+ are in eg level, These eg orbitals are point directly
at the oxide ions. Because of the intervening oxide ions , the eg orbitals on adjacent Ni2+ ions
cannot overlap to form a band . Hence eg electrons remain localized on individual Ni2+ ions .
(refer A.R West p.117) Figure
There are some guide lines to predict whether a good overlap of d orbitals is likely to occur or
not . So the d band formation is likely to occur if
(a) The formal charge on the cation is small.
(b) The cations in the early transition series
(c) The cations in the second & third transition series
(d) The anion is reasonably electropositive
The following experimental observations can be explained on the basis of
above guide lines.
1. TiO is metallic whereas TiO2 is an insulator . SimilarlyCu2O & MoO2 are
semiconductors whereas CuO & MoO3 are insulators. .Here the d band formation is easy
for TiO, Cu2O & MoO2 because of the small charge on metal cation. (a)
2. TiO & VO are metallic whereas NiO & CuO are poor semiconductors - due to the
reason (b) explained earlier.
3. Cr2O3is a poor conductor whereas lower oxides of Mo, W are good conductors - due to
reason ( c) .
4. NiO is a poor conductor whereas NiS ,NiSe ,NiTe are good conductor - due to reason
(d)
Metallic conductivity has the following characteristics
(a) A significant portion of the valence electrons are free to move throughout the structure
and are completely delocalized.
(b) Collisions between these electrons and phonons (lattice vibrations) occur & are
responsible for the decrease of conductivity with temperature.
(c) Metallic conductivity can be treated in terms of band theory.
(d) Metallic conductivity is not confined to elemental metals & alloys but occur in a variety
of inorganic solids such as metal oxides and sulphides. It also occur in certain
conjugated organic systems such as doped poly acetylene & poly aniline
Semi conductivity has the following characteristics
(a) It is also associated with electronic conduction.
(b) Intermediate between conductors and insulators.
(c) It is very common & occurs in transition metal compounds ,Si, Ge & some organic solids.
(d) It is regarded either as an electron hopping process or may be treated using band theory.
(e) The number of electrons contributing to semi conductivity depends upon temperature &
impurity level.
Some Questions & answers
1. Explain why poly acetylene is an electrical insulator whereas polyethylene is not .
Organic solids are usually insulators. Electrons can not move freely within
molecules or from one molecule to another in a crystal. Exceptions are conjugated systems that
contain a skeleton of alternate double & single C-C bonds. Polymers such as poly ethylene are
insulators because even though the monomer
CH2 = CH2 contains a double bond, the
polymer poly ethylene is saturated & contain only single bond . Poly acetylene is a conjugated
long chain polymer with alternate double & single bonds
H
H
H
C=C
H
H
C=C
C=C
C=C
H
H
C=C
H
H
H
To be conducting , the polymer must have electrons delocalised along the chain length
. In small conjugated alkenes like butadiene the π electrons are delocalised over the molecule.
Then for a long conjugated olefin, it is possible to obtain a band of π levels & if this band were
partially occupied, we expect conductivity. Poly acetylene is such a conjugated polymer & the
trans form has higher conductivity than cis form.
The conductivity is quite low because the π electron system is not
completely delocalized in poly acetylene. It has a band gap of 1.9 e.v . The conductivity of poly
acetylene can be increased by doping. If an electron acceptor dopant such as bromine is added
to poly acetylene , it takes electron from the lower π band forming [CH Br ]n. The doped poly
acetylene now has holes in its valence band & it behaves as a p type semiconductor. And its
conductivity is greater than that of undoped material. The conductivity of poly acetylene can
also be increased by electron donor dopants such as Li . These dopants add electrons to the
upper π band making this partly full. [ Li CH ]n and so producing n type semi conductivity.
Uses of poly acetylene include s light weight rechargable battery & photovoltaic cell.
2. Magnetite is a semiconductor at room temperature. Why ?
The d electron structure of solid transition metal compounds is sensitive to the crystal structure
of the solid & to any variation in oxidation state of the metal. Some interesting examples are
(a). Both Fe3 O4 and Mn3 O4 have spinal structure .But Mn3 O4 is virtually an insulator ,
whereas Fe3 O4 is a metallic conductor . The structure of
[Fe3+]tetra [Fe2+, Fe3+ ]octa O4 ;
Fe3 O4 may be written as
inverse spinal
For Mn3 O4
[Mn2+]tetra [Mn23+ ]octa O4 ;
normal spinal
Since Fe3 O4 is an inverse spinal , it contains Fe2+ and Fe 3+ ions distributed over
the octahedral sites . These octahedral sites are close together since they belong to edge sharing
octahedra. Consequently positive holes can migrate easily from Fe2+ to Fe3+ ions & hence
Fe3 O4 is a good conductor.
In Mn3 O4, the spinal structure is normal which means that the closely spaced octahedral sites
contain only Mn3+ ions. The tetrahedral sites containing Mn2+ , share corners only with the
octahedral sites . The Mn2+ --- Mn3+ distance is greater ,& hence electron exchange cannot
takes place easily.
(b) A related example is Lithium spinals , LiMn2 O4 and Li V2 O4 .
The structural formulae of these spinals are similar
[Li + ]tetra [Mn3+ Mn4+ ]octa O4 ;
[Li + ]tetra [V3+ V4+ ]octa O4 ;
A mixture of +3 and +4 ions are present in the octahedral sites of both , but since the d
orbital overlap is greater for vanadium than for manganese & is reflected in the electrical
properties . Li Mn2 O4 is a hopping semiconductor , whereas LiV2 O4 has metallic conductivity.
3. TiO & NiO both have rock salt structure ,but TiO is metallic whereas NiO is an
electrical insulator .Explain (discussed earlier)
Applications : The main use of semiconductors is in solid state devices such as transistors,
silicon chips, photocells etc. (for further details read A.R West. Page. 299)
Conductivity
Conductivity has been defined by
σ = e. nc .µ
where e is the electronic charge , nc is the number of charge
carriers . & µ is their mobility.
In an n type semiconductor, electrons are called the majority carriers of current , & the holes are
the minority carriers. If a crystal is doped with an acceptor type impurity, the holes become the
majority carriers & is called p type semiconductor. Electronic conductivity takes place by means
of transitions of electrons in the conduction band & the hole conductivity takes place by
transitions of holes in the valence band.
Mobility of charge carriers
One of the factors affecting the conductivity of a semiconductor is the mobility of
charge carriers. Mobility was defined as the drift velocity per unit electric field . As the electrons
move through the crystal , they are scattered by inhomogenities in the crystal. These
inhomogenities are caused by the following
1. Thermal vibrations of the atom
2. Impurity atoms
3. Interstitial atoms
4. Other imperfections
The time that an electron spends between collisions is called mean free
time Tr. Then the average drift velocity in the direction of the field is given by
V= - e .Tr ./ m . €
where € is the electric field . The minus sign indicates that
the velocity vector is opposite to field vector. Then the mobility is given by µ = V/-€
ie,
µ = e .Tr ./ m .
Then conductivity σ = e. nc .µ
= nc . e2. Tr ./ m
Or by knowing σ & nc , mean free time Tr can be calculated.
Hall effect
It has been shown by Hall that both mobility & mean free path of an electron
can be determined experimentally. The so called Hall effect is observed when a mag. field
is applied at right angles to a conductor carrying current . This produces a potential
difference across the conductor, in a direction that is mutually orthogonal to the direction of
the current & that of the mag. field. The reason for the above effect is that , an electron in an
electric field € is acted on by a force that acts in the direction of the field & is proportional
to the field strength & charge of the electron. Ie, F = e. € . If a transverse mag. field is then
applied, the electron is also acted on by a mag. force which is proportional to the electron’s
charge , velocity & to the applied mag. field. And is given by V.B.e. So the total force on
the electron is F = e. € + V.B.e. -------------(A)
This force therefore causes the electrons moving down the wire to be deflected in a
direction that is transverse to both fields. When such electrons reach the surface of the
conductor, they build up a charge at the surface which inturn produces an additional electric
field inside the conductor . After a while an equilibrium condition is attained between the
force due to this field & the force (A) & electrons can again move freely along the
conductor. The magnitude of this new transverse field € must be equal to the magnitude V.B
ie, € = V.B
The velocity can be expressed in terms of current density J & the no. of electrons per unit
volume V = J / nc . e
Substituting this value in the above equation € = J / nc . e .B where 1/ nc . e = R called
Hall constant Then € = J .R .B
University question
1. Discuss the conductivity of pure metals with temperature and mag. field .
References
1. Azaroff . p. 327
2. Lessly Smart
3. A.R West