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SOLID STATE PHYSICS II: 3 UNITS
PHY 432
Dr
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4
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Band theory of metals
Semiconductors and Insulators
Introduction to the properties of materials
(a) Electrical
(b) Magnetic
(c) Optical
5
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Introduction to dielectric properties of materials

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Fundamentals: Conductors – Insulators – Semiconductors
Conductors
Conductors are generally substances which have the property to pass different types of energy
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Materials in general can be classified on the basis of their
conduction of electric current
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Already
with low energy electrons become sufficiently detached from the atoms and a conductivity is achieved
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The lattice is formed of positive atomic ions in the metal
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This is a lot
compared to non-metals
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These electrons form a sea of electrons that are relatively free to move from
one positive metal ion to another
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They have random motion at normal temperatures, often bouncing about
among positive ions but having no uniform direction of motion
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There is no net movement of electric charge in any direction
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The electric field produces a net
velocity of the electrons in the direction opposite to the electric field
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In other words, a current flows
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The speed of the electron movement within the conductor is of the order of 1
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The electron
drift speed is of the order of 1 × 10–5 ms–1
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They simply have a
net drift forward induced by the electric field
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The ions "get
in the way" of the electrons and impede their progress through the metal
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This suggests that the resistance
of a piece of metal should increase with
temperature
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An electrical insulator is a material whose internal electric charges do not flow freely; very little electric current will
flow through it under the influence of an electric field
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The property that distinguishes an insulator is its resistivity;
insulators have higher resistivity than semiconductors or conductors
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In addition, all insulators become electrically conductive when a sufficiently large
voltage is applied that the electric field tears electrons away from the atoms
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Some materials such as glass, paper and Teflon, which have high resistivity, are very good
electrical insulators
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Examples include rubber-like polymers and most plastics which can be
thermoset or thermoplastic in nature
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So
when connecting an insulator to the terminals of a battery,
co current flows through the circuit
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The schema consists of two energy bands (valence and conduction band) and the band gap
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Between the two energy bands there is the band gap, its width
affects the conductivity of materials
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If there are multiple atoms side by side they are interdependent, the discrete energy
levels are fanned out
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The width of the energy bands depends on how strongly
the electrons are bound to the atom
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As a result, the energy bands of the individual
atoms merge to a continuous band, the valence band
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In general, both states occur at the same time, the electrons can therefore
move inside the partially filled valence band or inside the two overlapping bands
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In insulators the valence band is fully occupied with electrons due to the covalent bonds
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To achieve a conductivity, electrons from the valence band
have to move into the conduction band
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Only with considerable energy expenditure (if at all possible) the band gap can be overcome; thus
leading to a negligible conductivity
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More importantly, as temperature increases, the electrical conductivity of a semiconductor increases
while that of a metal decreases
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The energy gap 𝐸 𝑔 is equal to the difference between the energy 𝐸 𝑐 at the bottom of the 𝐶𝐵 and
the energy 𝐸 𝑣 at the top of the 𝑉𝐵
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Once they are in the 𝐶𝐵, these electrons accept further energy and occupy higher levels in the 𝐶𝐵;
thus conduction takes place
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The holes also contribute to conduction
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This increase in conductivity with temperature is exponential
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However, elements with the diamond structure
and compounds with the zinc blende structure have been most thoroughly investigated
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The addition of a pentavalent impurity like phosphorous, arsenic or antimony to germanium
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In the Ge structure each Ge atom is covalently bonded to four neighbouring Ge atoms
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If a pentavalent impurity, say As, is added to Ge, each impurity atom replaces one of the Ge
atoms
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That leaves one surplus electron which is now only
weakly attached to the impurity atom
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Types of Semiconductors
On the other hand, if the impurity is a trivalent atom like B, Al, In, Ga, the three electrons of the impurity atom
bond with three neighbours
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In either case, the
addition of impurities creates additional carriers (electrons or holes) in the host crystal resulting
in larger conductivity
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Such
semiconductors are called ‘impurity semiconductors’ or ‘extrinsic semiconductors’
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If the additional carriers are holes, the semiconductor is called ‘ptype’
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Types of Semiconductors
The energy bands of the donor and acceptor atoms are shown to lie between Ec and Ev
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This may appear
contradictory
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Energy level diagram of a semiconductor containing a donor impurities at energy level Ed and (b) acceptor
impurities at energy level Ea

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Direct Gap Semiconductors and Indirect Gap Semiconductors
Let us consider a semiconductor with a band structure shown in Figure
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e
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When an electron from the 𝑉𝐵 is excited into the 𝐶𝐵 the change in wave
number Δ𝑘 = 0
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The group II-VI and group III-V compound
semiconductors belong to this type
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There are two minima in the CB
/
/
with corresponding energy gaps 𝐸 𝑔 and 𝐸 𝑔
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In this transition Δ𝑘 = 0
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The transition of an electron to this
second 𝐶𝐵 minimum involves change in energy as well as change in 𝑘
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e
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In Fig
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The first transition is possible provided a photon with energy 𝐸 𝑔 is available
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Such
semiconductors are called ‘indirect gap’ semiconductors e
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, Si and Ge

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