4. METALS AND SEMICONDUCTORS

4.1 Introduction.

4.2 Properties of metallic solids.

4.3 Theories of bonding in metal.

i) Free electron theory.

ii) Molecular orbital theory (Band theory).

4.4 Classification of solids as conductor, insulators and semiconductors on the basis of band theory.

4.5 Semiconductors.

Types of semiconductors - intrinsic and extrinsic semiconductors.

Applications of semiconductors.

4.6 Superconductors:

Ceramic superconductors - Preparation and structures of mixed oxide YBa2Cu3O7 – x

4.7 Applications of superconductors.

4.1 Introduction

The Solid State:

Matter is something that has mass and occupies space .It is characterized by a set

of properties such as shape, size, mass, melting point, boiling point., color,

texture, reactivity, etc. Based on size shape, volume and rigidity, matter is

classified into three categories: solid, liquid and gaseous .There are some

simplifying features of solids which allow considerable insight into their nature.

The solids have definite shape and volume and are rigid. Therefore solids are

characterized by rigidity incompressibility and mechanical strength. .These facts

indicate that the atoms ions or molecules which make up the solids are very

closely packed .They are held together by strong forces of attraction and are not

free to move at random. The solids are, therefore, the outcome of well ordered

arrangement of building units. A good understanding of nature and properties of

solids will provide a wide range of tailor-made materials with specific properties

having uses in the development of science and technology. Much of our recent

progress is no doubt due to the advances we have made in solid state physics and

solid state chemistry.

Types of Solids:

From the state of aggregation the solids are grouped into two categories:

amorphous and crystalline.

Crystalline Solids : The Solids whose constituents are arranged in a regular

geometrical pattern over the entire lattice are knows as the crystalline Solids .This

is proved to be so by X –ray diffraction study .Due to the orderly arranged atoms,

ions or molecules the crystalline Solids exhibit different elements of symmetry

and accordingly belong to either of the crystal systems.

Metallic Crystals: The crystalline Solids having positively charged metal ions in the

lattice points, surrounded by a sea of mobile electrons are known as metallic

crystals. For example: Copper, Silver, gold, sodium, potassium, iron, cobalt, nickel,

etc. Here the binding force is the electrical attraction between positively charged

metal ions and negatively charged sea of mobile electrons. On account of this fact

the metals are characterized by many typical features. They may be soft or hard

sufficiently tough, with moderate to very high melting points, good conductors of

heat and electricity. These are malleable, ductile and elastic with high tensile

strength; exhibit good Iustre on fresh cut etc. (Exception – mercury). In the

present chapter our aim is to discuss crystalline Solids such as metals

semiconductors and super-conductors.

METALS: The most numerous of all the elements are the metallic elements. All

the elements in the s, d and f blocks are metals: aluminium, gallium, indium,

thallium, tin, lead and bismuth of the p-block are considered to be metals.

Further, germanium and polonium are also sometimes taken to be metallic

elements. Thus the metals constitute about eighty percent of the element in the

periodic Table. It appears that the element with too little electrons in the valence

shell but with too many orbitals behave as metals. No doubt, metals are marvels

among elements. The marvelous characteristics such as luster, conductivity,

malleability, ductility, etc of metals have been attributed to the metallic bond.

Metals mean such to modern man. Every amenity of modern civilization depends

heavily on metals. In fact there is no moment when man is not in contact with

metallic objects directly or indirectly. In other words the distinctive applications of

metals are due to the strange nature of forces that exist within the metals .Hence

to understand metals it is wise to make an attempt only through their special

features.

4.2 PROPERTIES OF METALLIC SOLIDS

Metals are characterized by a set of physical properties. Let us take a brief

account of some of these properties to understand, “What the metals exactly

are”.

1. Crystal Structure

The distinctive properties of metals depend on their crystal structure .Metals have

comparatively high melting points ,high boiling points and high densities .These

indicate a close-packing of atoms .X-ray analyses have revealed that the metallic

atoms give closest packed structures namely face centered cubic, body centered

cubic and hexagonal close-packed .See Fig 4.1

Some examples of metallic crystals have been given in Table 4.1

Table 4.1: Crystal structure of Metals

Types of Lattice Co-ordination

number

Metals

1. Cubic closed packed

(ccp) or (fcc)

12 Cu, Ag, Au, Ca, Sr, Fe, Co, Ni, Ru,

Rh, Rd, Os, Ir, Pt, Sc, Y, La etc.

2. Body-centered cubic

(bcc)

8 Li, Na, K, Rb, Cs, Ti, Zr, Hf, V,

Nb, Ta, Cr, Mo, W etc.

3. Hexagonal close-

packed

12 Be, Mg, Ca, Sc, Y, La, Ti, Zr, Hf,

Co, Ni, Ru, Os, Zn, Cd etc

4. Complex structure 12 As, Sb, Bi, Se, Te, Po, Pa, U, Np,

Pu, Ga, In, Ge, Sn etc

2. High Electrical Conductivity :

Conduction is mechanism of transmission of energy without transfer of mass.

Electrical conduction arises due to the flow of mobile electrons through the

vacant space between the metal ions. Conduction is effected by displacement

mechanism. When an electric field is applied across a metal electrons enter at one

end and kicked out form the other as shown in Fig 4.2 Conductivity is a periodic

property. With increase of mobile electrons, conductivity increases.

e.g. Na < Mg < Al . Thus aluminum which contributes three valence electrons is

the best conductor of electricity. With increase of temperature, atomic vibrations

increase.

Electrical conductivity therefore decreases with increase of temperature. There is

an enormous difference in electrical conductivity between metals and the other

kinds of solids .See Table 4.2

Table 4.2 Electrical Conductivity of Solids

Solid matter Bond type Electrical conductivity

Silver

Copper

Sodium

Zinc

Metallic

Metallic

Metallic

Metallic

6.3 × 105

6.0 × 105

2.4 × 105

1.7 × 105

Sodium chloride Ionic 1 × 10-7

Diamond

Quartz

Covalent

Covalent

1 × 10-14

1 × 10-14

In general metals show supreme electrical conductivity.

3. High Thermal Conductivity

Among solid substances metals are by far the best conductors of heat. If metal is

heated at one end, the heat is carried to the other end. Mobile electrons absorb

energy, become more mobile, collide on adjacent electrons and heat is

transported to the other end .See Fig 4.3 similar to the electrical conductivity, the

metals are characterized by high thermal conductivity.

Thermal conduction increases if number of mobile electrons increases e.g. Na <

Mg < Al. With rise in temperature, heat conductivity decreases as the vibrational

motion of metal ions increases.

4. Metallic Lustre: (Reflectivity)

All metals typically have a lustrous shiny appearance .When a beam of light

(i.e. electromagnetic radiations) falls on the surface of metal its electric field sets

the mobile electrons in the surface of the metal into to and fro oscillations. We

know that any moving charge always emits electromagnetic energy. Hence, these

oscillating electrons emits electromagnetic energy in the form of light .Thus when

light falls on the surface of the metal it seems as if light is being reflected .This

reflectivity is known as metallic luster.

In other words it may be commented that when a beam of light falls on a

clean surface the mobile electrons move to some excited state. When these

electrons jump back to ground state, light of all wave lengths is re-emitted. Hence

show luster.

Note: Sodium, magnesium and aluminium being more reactive they react

with atmospheric oxygen and form oxide layer on their surface. Under these

conditions the mobile valence electrons are blocked by ionic bonds. Hence these

metals do not show metallic luster when tarnished.

5. Emissivity : (Emission of Electrons )

Under the conditions of excitation emission of electrons is called emissivity.

When a metal is heated strongly it emits electrons. e.g W at (28000C) 3073 K and

Th at (18000C) 2073 K. On heating the mobile electrons acquire kinetic energy and

get boiled off the electron sea. This is known as thermionic emission. This

property is used in thermionic valves.

On the other hand, the metals like sodium, potassium, selenium etc. emit

electrons when irradiated with UV light. This is known as photoemissivity. This

principle is exploited in photoelectric cells.

6. Melting and Boiling Points :

In metallic crystals the force of bonding between metal and metal is the strong

electrostatic force of attraction between the positively charged metal ions and

the negatively charged sea of mobile electrons. This force is essentially non-rigid

and non-directional. Therefore metals have very high melting points and high

boiling points.

7. Magnetism:

Many metals possessing one or more unpaired electrons especially the d-and f-

block elements, shows considerable degree of paramagnetism.

MECHANICAL PROPERTIES

8. Malleability, Ductility and softness

Metals are malleable i.e. easily flattened into thin sheet and are ductile i.e. easily

drawn into wire .These properties make the metals the most useful materials of

construction.

Metallic elements have a close-packed structure with high coordination

number say 8 to 12. The bonding in metallic crystals is the attraction between

positively charged metal ions and the mobile electrons. These forces holding the

metal ions together are therefore, non rigid and non-directional. On applying

mechanical force one layer of ions slips over the other. As a result metal ions move

easily from on e lattice site to the other. But in terms of crystal lattice, nothing is

changed. The environment of every metal ion remains the same as before since the

delocalized electrons are available everywhere which adjust the positions rapidly

and the crystal lattice is restored See Fig 4.4

Fig 4.4 Sliding to layers of metal ions in a crystal

This explains why the metals are malleable and ductile. The possibility of planes

gliding is found to be greatest in cubic close-packed structures, so these are

generally softer and more easily deformed than hexagonal. This fact further

explains why metals like sodium and potassium can easily be cut with a knife.

Thus the softness of metals can be accounted for.

In these cases, the electron cloud is very much diffused and the bonding is

considerably weaker in the lattices.

Aluminium with ccp is highly malleable and ductile while magnesium with hcp is

less malleable, less ductile and more brittle.

9. High Tensile Strength:

Metals have high tensile strength i.e. metals can resist stretching without breaking.

This is attributed to the strong electrostatic force of attraction between the

positively charged metal ions and the negatively charged mobile electrons

surrounding to them. Thus metallic crystals differ from the covalent crystals or

ionic crystals.

10. Elasticity

Elasticity is a property by virtue of which a substance can regain its original form

as soon as the deforming force is removed .This property is attributed to the ease

with which the metal ions can move from one lattice site to another.

4.3 THEORIES OF BONDING IN METALS

Review:

The metallic bond is a type of binding or linkage or attraction or force that holds

the atoms of two or more metals together in an alloy or it is the force that links

atoms of the pure metal together in a metallic crystal.

The metallic bond cannot be an ionic bond as there is no transfer of electrons from

electropositive element to electronegative element. It cannot be a directional

(covalent) bond since metallic properties persist even in liquid state (e.g. mercury)

or in solution (e.g. sodium in liquid ammonia) etc. See Fig 4.5

Different theories have been suggested for metallic bonding from time to time .The

successful theory of bonding in metals is one which can explain the following to

utmost satisfaction.

a) The great mobility of electrons in metallic solids.

b) The bonding between a large numbers of identical atoms in a pure metal.

c) The bonding between widely different atoms in an alloy and

d) The non-rigid and non-directional bonding in metals which is retained even in

the liquid state (say in ,mercury) or even for the metals which are dissolved in

a suitable solvent e.g. sodium in liquid ammonia .

These are at present three theories to explain the metallic features

1. Free Electron theory or Electron Gas Theory

2. Valence Bond theory (VBT) or Pauling’s Atomic orbital theory and

3. Molecular orbital Theory or Band theory

1. The Free Electron Theory of Metals:

As early as 1900 the free electron theory was first proposed by Drude and was

further refined by Lorentz in 1932. The theory is based upon two assumptions

(a) Mutual repulsion between the negative electrons in absent.

(b) The potential field due to the positive ions is completely uniform throughout the

metallic crystal.

According to Drude metal is a lattice through which electrons move as freely as

molecules of a gas .This idea was used primarily to account electrical conductivity

of metals.

According to Lorentz metal is a lattice of rigid spheres (i.e. positive metal ions)

embedded (fixed) in a gas of valence electrons which could move freely in the

interstices of metal throughout the crystal .

Explanation:

We know that metals are poor in valence electrons and have low ionization

energies. Hence metals lose some of their valence electrons and tend to be

electropositive. The electrons so freed are not bound to any single nucleus but

spread out around several nuclei. Such free electrons are referred to as non

localized or delocalized or mobile electrons and their some total collection is

appropriately termed as electron pool or electron cloud or electron gas according

to the classical electromagnetic theory. For clear understanding take into

consideration Fig 4.6

If many metal atoms are brought close together the outer energy levels of each can

merge together when they begin to overlap. The outer electrons are then in a

position to move not just around one atom but around and between all the atoms.

These electrons have turned to be delocalized or non localized and are therefore

more stable. Thus a block of metal may be visualized as an array of positive ions

located in the crystal lattice, immersed in an ocean of mobile electrons. The

metallic bond is the force of attraction between metal atoms and all the electrons

under their influence.

Illustration:

Consider a simple metal such as lithium. It crystallizes in the body centred cubic

form. Hence each atom of lithium is co-ordinated by eight neighboring lithium

atoms. The electronic configuration of lithium is 1s2 2s1 i.e.

For lithium metal, one cannot expect ordinary covalent bonding which requires

eight pairs of electrons as CN=8 but there is only one such electron per lithium

atom. This means that the single electron utilizes all the four valence orbitals; 2s

and 2p’s available to it .Thus the nine electrons from (1+8) lithium atoms have

freedom to move simultaneously in all the (9x4) thirty six orbitals forming the unit

cell of lithium. The electrons are thus regarded as belonging to the crystal a whole

and not just to any particular atom or atoms.

Since the theory accounts for electron gas or sea of mobile electrons and the non

directional nature of bonding, it can successfully explain the properties of metals

such as metallic lustre, malleability, ductility high thermal and electrical

conductivity high melting and boiling points etc as already outlines.

But the theory fails to explain the following due to the concept of electron gas

in metallic solids namely

i. Semiconductance

ii. Specific heats

iii. Calculations of cohesive energy of metallic crystals quantitatively.

(Another sincere attempt was made to explain metallic bonding by Prof. L.

pauling in 1940. This is known as pauling’s Atomic Orbital of Valence Bond

Theory. He pictured metallic bond to be a dynamic covalent bond which

oscillates through a number of positions between an atom and its nearest

neighbors. e.g. sodium metal may be pictured as :

Na Na—Na Na Na—Na Na—Na Na—Na- Na Na

Na Na—Na Na Na—Na Na—Na Na+ Na Na Na

But the theory fails to explain metallic character in liquid state or in solution.

2. The Band Theory (Molecular Orbital Theory)

The characteristic physical properties as well as the high co-ordination number

(either 8 or 1) suggest that the bonding in metals is quite different from those in

other substances. There is ionic contribution and it is also not possible to have 2c-

2e covalent bonding between all the adjacent pairs of atoms since there are neither

sufficient electrons nor sufficient orbitals. A satisfactory explanation has been

provided for metallic bonding by the so-called band theory or molecular orbital

theory.

The configurational study of elements reveals that the presence of empty AOs in

the valence shell is a prerequisite for metallic properties. The elements which lack

in empty AOs in their valence shell are all non-metals. For example, carbon in

excited state and N, O, F, Ne, etc. lack in empty AOs and are therefore non

metals.

Formation of Energy Bands:

Basis: The band theory is put forward by Bloch in 1928. This theory is an

extension of MOT to metallic structure. According to MOT formation of energy

band may be outlined as follows:

We may recall that AOs combine to form MOs of which one half will be

bonding type and the other half will be of the anti-bonding type .This mechanism

results in the splitting of the original atomic orbital energy levels into different

energy MOs.

Clue: In metal crystal there are numerous atoms which involve several

combinations between their different types of atomic orbitals. Suppose in a metal

crystal there are combinations between n orbitals where n may be considered to be

6x1023 (Avogadro Number) So that there will be 3x1023 bonding and 3x1023 anti-

bonding MOs. If the starting AOs are all of similar energy (say 2s AOs in lithium

crystal), the resulting boding and anti-bonding MOs give rise to series of very

closely spaced energy levels that constitute an energy band .The building up to

such MOs may be represented as in Fig 4.7————

Now to have a clearer picture of band theory and to have a better account to

observed properties of metals let us consider some specific illustrations.

1. Lithium Metal :

The electronic structure of lithium atoms is 1s2 2s1 2p0

When two lithium atoms join, a lithium molecule Li2 is formed .Here the 2 s

AOs on each of the two Li atoms combine to give tow MOs one bonding and

one anti-bonding where the valence electrons occupy the bonding MO and Li2 is

formed see Fig 4.8

Now suppose four Li atoms join to form Li4 molecule. In Li4 four AOs would

form MOs –two boning and tow anti-bonding. The bonding type as shown in Fig

4.9

As the number of atoms is the cluster increases the spacing between the various

orbitals decreases. And thus with a large number of atoms the energy levels of the

orbitals are so close together that the virtually form a continuum i.e. band as

shown in Fig 4.10

The numbers of MOs are always equal to the number of AOs involved in bonding.

Since there is only one valence electron per atom in lithium and a MO can hold

two electrons it follows that only half the Mos in the 2s valence band are filled i.e.

the binding MOs are only filled while the anti-bonding MOs are completely empty.

Note: As the MOs extend in three dimensions over all the atoms in the crystal the

electrons have a very high degree of mobility in crystal lattice. A minute amount

of energy is more than sufficient to perturb (push) an electron to empty levels

where it moves rapidly and readily. This mechanism explains the high degree of

thermal and electrical conductivity of metals.

In absence of an electric field equal number of electrons move in all possible

directions. But if a positive electrode is placed at one end and a negative at the

other then the electrons will move towards the anode (+) much more readily than

in the opposite direction and thus the electric current flows as shown in Fig (4.2)

In metals conduction occurs because MO extend over the whole crystal and

because there is effectively no energy gap between the filled and lithium is

because only half the MO band is filled with electrons. See Fig 4.10 and Fig 4.14

(a)

2. Beryllium Metal:

Be (z=4): 1s2 2s1 2p0

In the valence shell of beryllium atom there are two valence electrons which

would just fill the 2 s valence band of MOs. In the isolated beryllium atom, the 2s

and 2p AOs are some 160 kJ mol-1 different in energy. But in beryllium metal

(say Ben) the 2p AOs form a 2p band of MOs just similar to the 2s band of MOs

formed from the 2s AOs. The striking aspect is that the upper part of the 2s band

overlaps with the lower part of 2p band See Fig 4.11

This overlap causes some of the 2p band occupied while some of the 2s band to be

empty. Thus in metallic crystal the energy gap is absent so easy perturbation of

electrons from the filled valence band to the empty conduction band. Hence

beryllium behaves as a metal.

It should be noted that the energy bands thus produced belong to the crystal as a

whole and act as a measure of the complete delocalization of electron cloud. This

fact will naturally account all the properties of metals that we encounter.

For further understanding of formation of energy bands, another pictorial

presentation may be shown where energy may be plotted horizontally and the

number of electrons that may be accommodated at each value of the energy may

then appear as an envelope on the vertical as shown in Fig 4.12. Here the shading

represents the filling up of the bands with the available number of electrons .These

are called N (E) curves which show the complete distribution of electrons between

the various possible energy states and in turn the distribution of various possible

energy states and in turn the distribution of various energy states over the energy

range within a band.

As an illustration, N (E) curves have been given for Lithium and Beryllium metals

as shown in Fig 4.12

Band Theory and High Conductivity of Metals

According to MOT, energy states extend in 3D over the entire crystal lattice. It

provides a great mobility to electrons under suitable circumstances and imparts

high conductivity to metals.

For alkali metals (ns 1), Li, Na, K etc. the lower half of ns band in filled while

the upper half if completely empty to serve as a conduction band See Fig 4.10 and

Fig 4.12(a) For alkaline earth metals (ns2) such as Be ,Mg etc. the ns band is

completely full while np band is completely empty where the upper np hand

overlaps the lower ns band and as a result there remains no energy gap between the

filled valence band and the empty conduction band. See Fig 4.11 and Fig 4.12 (b).

This is the situation especially at absolute zero. Consequently at any other

temperature the available thermal energy is just sufficient to excite a large number

of electrons form the valence band to the conduction band where they can move

very freely. Hence the metals exhibit electrical and thermal conductivities. See Fig

4.2 and Fig.43.

4.4 CLASSIFICATION OF SOLIDS AND BAND THEORY

(TYPES OF SOLIDS)

On the basis of band theory, by studying the extent of electrical conductivity all

the solids can be classified into three categories.

1. Conductors (Metals)

2. Non –conductors of Insulators (Non -metals) and

3. Semi conductors (Metalloids)

1. Conductors (Metals)

The substances known as metals are classified as (electrical conductors)

Conductors are the metallic solids in which either (a) the valence band is only

partially filled or (b) the valence and conduction bands overlap See Fig 4.11 Fig

4.12 and Fig. 4.13 (A) and (B). Thus there is practically no energy gap between the

filled and unfilled MOs and perturbation of electrons can occur readily hence high

thermal and electrical conductivities.

For example:

(a) Sodium and copper are the typical examples in which 3s and 4s bands

respectively are only half filled.

(b) In magnesium the filled 3s band overlaps the 3p band whereas in nickel the 3d

and 4s bands overlap

2. Non –conductors of Insulators (Non -metals)

Non –metals are classified as non-conductors or insulators.

In Non –metals the valence band is completely filled so migration of electrons

within the band is not possible. Secondly, there is an appreciable difference in

energy (called band gap or energy gap) between the valence band and the next

empty band. Consequently the electrons fail to cross this huge energy gap to reach

to empty level where they could move freely. See Fig 4.13(C) and Fig 4.14 (A)

For example: All ceramic materials (say mica aluminium oxide, porcelain glass

etc) non–metals as well as the covalently bonded polymers (Say nylon 66

polyethylene polystyrene etc.) are essentially insulators.

3. Semi conductors (Metalloids )

The solids which are basically insulators at absolute zero but which can conduct

electricity to certain extent by migration of electrons at room temperature are

called as the semi-conductors. The conductivity of a semiconductor lies between

those of metallic good conductor and non metallic insulator.

Commercially, the best known semi –conductors are silicon and germanium

Semi conductors are the solids in which there is only a small energy gap between

the valence band and conduction band. See Fig 4.13 (d) and Fig (c). At absolute

zero in such solids, all the electrons occupy the lowest possible energy levels (i.e.

valence band) and thus the conduction band is devoid of electrons. At absolute

zero the substance therefore acts as a perfect insulator. However as the temperature

of the solid is increased a finite number of electrons do get promoted thermally

from the full valence band to the empty conduction band. Both the promoted

electrons in the conduction band the unpaired electrons left in the valence band can

conduct electricity .The conductivity of semiconductors increases with temperature

as the number of electrons promoted to the conduction band increases. This

electrical conductivity of a semiconductor is termed as intrinsic conductivity and

the pure semiconductor as intrinsic semiconductor

For example: Silicon and Germanium

The electrical conductivity of intrinsic semiconductors (i.e. pure silicon and

germanium) can be increased by adding small amounts of impurity atoms which

can act as charge carriers between valence band so that electrons may be excited

from the insulator bands to the impurity bands of vice-versa. Such electrical

conductivity produced by doping with a suitable impurity is called extrinsic

conductivity and such doped intrinsic semiconductors are turned to be extrinsic

semiconductors. See Fig 4.13 (E). Both n type and p-type semiconductors are

produced by doping an insulator with a suitable impurity. (The detailed discussion

of semiconductors is given in the following section). The three types of solids are

shown differently in Fig 4.13 and Fig 4.14 for comparison.

Fig 4.14 N (E) Curves for Insulators and semiconductors

Note:

i. For extrinsic semiconductors, refer to fig, 4.17(D) and figure 4.18 (D).

ii. For metals, refer to fig 4.12 (a) and (b).

4.5 SEMICONDUCTORS: TYPES OF SEMICONDOCTORS

The solids act as the semiconductors where there is small energy gap or band gap

(< 200 kj mol-1

) between the filled valence band. See Fig. 4.13 (D), table 4.2 and

Fig. 4.14 (C).

In other words, semiconductors are the solids, which are basically insulators at

absolute zero, but with increased temperature, they can conduct electricity by

migration of finite number of electrons, thermally excited, from the valence band

to the conduction band.

The electrical conductivity of semiconductor lies between metallic good

conductor and non metallic insulator. Such conductivity of a pure semiconductor is

termed as intrinsic conductivity and concerned solid is called an intrinsic

semiconductor.

Commercially, silicon and germanium are known as the most important

semiconductors of this kind.

1. Intrinsic semiconductors:

(Photo-excited Semiconductors and Thermal Defects in solids)

Silicon and germanium both belong to group 14th (Gr. IVA) of the periodic table.

The crystal structures of both are like diamond. In the outermost shell of atoms of

Si and Ge, there are four electrons, which form four covalent bonds to the

surrounding atoms, giving rise to a highly stable tetrahedral structure, as shown in

Fig. 4.15.

As all the electrons are used up in covalent bonding, there are no free electrons, in

the pure silicon or germanium crystal. If cooled to absolute zero, The electrons

occupy the valence band, and the conduction band remains completely empty.

Under these conditions, si and Ge both behave as the perfect insulators and cannot

carry any electric current.

The band gaps in silicon and germanium are only 106 kJ mol-1

and 68 kJ Mol-1

respectively. See Table 4.2. At room temperature, the atoms in the crystal lattice

acquire some energy and start agitation. As a result some of the covalent bonds

break a few valence electrons released and promoted into the conduction band.

Such electrons migrate in a random manner and leave behind ‘holes’ which act as

the positive charges as shown in Fig 4.13 (D). When electric field is applied across

the crystal, the electrons move in opposition to the field and the positive holes in

the direction of the field, and carries a small current to make the Si or Ge crystal

slightly conducting. This type of electrical conductivity is termed as intrinsic

semiconduction and such pure crystals are called intrinsic semiconductors. Thus Si

and Ge act as the semiconductors due to thermal defects in solids.

As the temperature is increased more and more electrons are promoted to the

conduction band, and semiconductivity increases that is the electric resistance

decreases (Not This is an opposite behavior as compared to those of metals) Above

423 K (1500C), too many electrons are promoted to the conduction band in silicon

that the crystal lattice itself disintegrates as the valence band is devoid of bonding

electrons. Similar is the case of Ge crystal above 373 K (1000C). Naturally, such

intrinsic semiconduction is undesirable and one has to take precautions to limit the

working temperature of semiconductors.

Instead of thermal energy if light energy causes excitation of electrons form

valence band to conduction band the phenomenon may be termed as intrinsic

photosemiconductivity. Intrinsic semiconduction may be shown as in Fig 4.13 (D)

and a little crudely in Fig 4.16

(Conductivity is due to slight migration of electrons in the conduction band and of

holes in the valence band).

Table 4.3: band gaps of semiconductors at absolute zero (kj mol -1

)

Solid substances Band gap Solid substances Band gap

PbTe 19 InP 125

Te 29 GaAs 145

PbS 68 Cu2O 212

Si 106 CdS 251

ZnO 328

2. Extrinsic Semiconductors

(Impurity or Defect Semiconductor)

The semiconducting characteristics of pure Si and Ge can be improved by adding

small amounts of either trivalent (Group 13) or pentavalent (Group 15) impurity

atoms which act as charge carriers. Such electrical conductivity is called extrinsic

semiconductivity and such doped intricsic semi-conductors are called as extrinsic

semiconductors or sometimes as impurity semiconductors or defect

semiconductors.

The deliberate addition of impurity atoms to a sample of pure crystal is called

doping. Based on nature of dopant, the semi-conductors can be classified into two

categories as follows:

(a) n-type semiconductors: The intrinsic semiconductors containing pentavalent

(donor) impurity atoms like P As or Sb (of Group VA or Group 15) having 5

valence electrons are termed as p-type semiconductors .

(b) p-type semiconductors: The intrinsic semiconductors containing trivalent

(acceptor) impurity atoms like B, Ga or In (of Group III A of 13 )having 3

valence electrons are terms as p-type semiconductors.

(a) n-type semiconduction: n-type semiconductors: Suppose an impurity of

Group VA (or 15 ) like P As or Sb having five valence electrons (ns2 np

3 ) is

added to the crystal lattice of silicon, some of the Si atoms are replaced by

pentavalent impurity atoms .This process is called ‘doping’ the crystal. Each

doped atom forms four covalent bonds with the surrounding four Si atoms by

using its four valence electrons, and its fifth electron remains unused. See Fig

4.17. In this way an extra electron over and above the number required for

symmetrical structure remains loosely bond in the silicon crystal. Such extra

electrons occupy an energy level called donor (impurity) level just below the

vacant conduction band of silicon crystal .At absolute zero or at low temperature,

the extra electrons remain localized on parent atoms .However at room

temperature, electrons from donor level can be easily excited to the vacant

conduction band (by the application of electrical field or thermal energy) where

they can carry current quite readily. Since the current is carried by negatively

charged electrons it is n-type semiconduction and the silicon (or germanium)

crystal doped with P/As/Sb is called n-type (extrinsic) semiconductor. The

structure for n-type silicon may be depicted as in Fig 4.17 (A) (B) (C) or (D).

(b) P-type semiconduction p-type semiconductors: If an impurity of Group III A (or

13) say B Al, Ga or In having three valence electrons (ns2 np

1) is added to the

crystal lattice of silicon (or germanium) some of the Si (or Ge) atoms are replaced

by the trivalent impurity atoms. Since the impurity atoms contribute only three

electrons some of the sites normally occupied by the electrons in the symmetrical

structure (Fig 4.15) will be left empty. This process of doping creates electron

vacancies called positive holes in the crystal .These occupy the energy level called

acceptor (impurity) level that exists close to the filled valence band of Si (or Ge).

At absolute zero (or at low temperatures) the positive holes are localized

around the doped atoms. However at normal temperatures or when an electric

field is applied, adjacent electrons from the filled valence band are promoted to

the vacant acceptor level of positive holes. In this way new electron vacancy i.e.

positive holes are created in the silicon lattice. By a series of such jumps or hops

the positive holes can migrate across the crystal. This is equivalent to moving an

electron in the opposite direction and thus current is carried. Since the current is

carried by migration of positive hole carriers this is p-type (extrinsic)

semiconductor .The p-type semiconductions may be depicted variously as shown

in Fig 4.20(A) (B) (C) and (D)

To prepare extrinsic semiconductors, extremely pure Si or Ge obtained by

zone refining is used. The pure Si or Ge crystal can be converted to p-type

semiconductor by high temperature diffusion of the appropriate dopant element,

up to a concentration of 1 part in 108. Usually, Ga or In is used to make p-type

semiconductors where In is preferred, because of its low melting point. Similarly

P or As can be used for n-type of semiconductor where As is preferred, because of

its low melting point.

If a single crystal is doped with indium at one end and arsenic at the other end,

then one part is a p-type semiconductor whereas the other is an n-type

semiconductor. It is called as a p-n junction. Such junctions are the important

parts of semiconductor devices used for several purposes.

Applications of semiconductors

Semiconductors have acquired a unique position in modern engineering and

technology. Every day the applications of semiconductors are increasing in

industry both in quantity and in diversity of forms. semiconductor have limitless

applications. We are enjoying today our standard of life only through the use of

semiconductors. As n-type, p-type, p-n junction diodes and p-n-p or n-p-n junction

triodes, semiconductors are used for numerous purposes. They find applications as

calculator, electronic watches, hearing aids solar batteries computers, catalysts,

satellites, radio and T.T sets. Thermocouples, thermistors, for battery charging,

for electroplating, as refrigerators and what not.

In addition the semiconductors find several general applications such as:

(a) To control current intensity and voltage to desired extent.

(b) To protect high voltage transmission lines from over voltage.

(c) To convert sound energy into electrical energy and vice-versa.

(d) To convert heat energy into electrical energy (i.e. solar batteries)

(e) To enhance the rate of chemical reactions in chemical processes thus

semiconductors can act as the catalysts etc.

4.6 SUPERCONDUCTIONS: CERAMIC SUPERCONDUCTORS

Introduction: Metals are good conductors of electricity and their conductivity

increases as the temperature decreases. In 1911 the phenomenon of

superconductivity was discovered by the Dutch scientist Kamerlingh Onnes when

he was studying electrical properties of materials near absolute zero. A

superconductor has zero or almost zero electrical resistance. It can therefore carry

an electric current without losing energy. In other words the current can flow

forever. It was proved that mercury is a superconductor below 4.2 K – (the critical

temperature (T) at which the superconducting state is formed.

Following the discovery, physicists and chemists made slow but steady

progress in the discovery of superconductors with higher values of Tc. After 75

years in 1986 high temperature super conductors were discovered. George

Bednorz and Alex Mueller reported a new type of (mixed oxide) superconductor

of lanthanum barium and copper (La2-x Ba x CuO4-y) which exhibited

superconductivity at 35 K For this significant work Bednorz and Mueller were

awarded the Noble Prize for physics in 1987.

Meanwhile, Meissner and Ochsenfeld found that some low temperature

superconductors exhibit the exclusion of magnetic field below Tc i.e. they do not

allow a magnetic field to penetrate their bulk. This is known as Meissner effect.

See Fig 4.19 Thus superconductors are essentially diamagnetic. Meissner effect

gives rise to ‘Levitation’. Levitation occurs when objects float on air. Here

repulsion is encountered between a permanent magnet and a superconductor.

4.6.1 Ceramic Superconductor

The first non metallic superconductor was found in 1964. This was a metal

oxide with a perovskite crystal structure and found to be quite different type of

superconductor from the alloys.

In March 1987 one of the most significant ceramic superconductor was

reported by Wu, Chu and co-workers. This is a mixed oxide type material based

on the Y-Ba-Cu-O system formulated as YBa2Cu3O7-x which became

superconducting at 93 K. This temperature appeared to be quite significant for

practical reasons. This temperature allowed liquid nitrogen to be used as coolant

rather than the more expensive liquid helium which was used earlier. Such

materials are also called as warm superconductors or high temperature

superconductors as they work at higher temperatures than the temperature of

liquid nitrogen (B.P. = 77 K).

4.6.2 Preparation:

There are different methods to prepare mixed oxide superconductors. For massive

form chemical fusion of sintering is used. For film type, the methods used are

(i) Chemical Deposition Method

(ii) Chemical Vapor Deposition Method

(iii) Electrical Deposition Method

For illustration two different methods have been discussed below.

(1) Chemical Fusion: The synthesis of high temperature super conductors needs a

variety of qualitative considerations. These materials may be prepared by fusing

the mixture of metal oxides say oxides of yttrium barium and copper to 1073-

1173 K (800-9000C), in an open alumina crucible or in a sealed gold tube.

(2) Chemical Vapor Deposition Method: In electronic devices superconductors

are used in the form of thin films. For this purpose the best suited method is

chemical vapor deposition. The general procedure is to from a thin film by

decomposing a thermally unstable compound on a hot solid substrate material

See Fig 4.21

In this method, volatile complexes of metals Cu Y and Ba are held at

temperatures T1 T2 and T3 which provide desired vapor pressure of each

reactant. The reactants are then swept into the reaction chamber by a reactive

carrier gas mixture: Argon, oxygen, and water vapor through traps as shown in

Fig 4.23. When conditions are properly controlled, the desired YBa2Cu3O7-x film

is deposited on the wedge shaped block, heated to a high temperature by an IR

lamp. After deposition, the film may be amorphous it is annealed at high

temperature to get the desired crystallinity of the film.

4.6.3 Structure

Informally this, YBa2 Cu3 O7-x ceramic super conductor, is called “123” (or

‘1-2-3’) superconductor from the proportions of metal atoms in the compound. Its

structure is similar to perovskite but with some missing ‘O’ atoms, hence (7-x) in

its composition.

Its structure comprises three cubic perovskite units stacked one on top of the

other giving an elongated (tetragonal) unit cell See Fig 4.21.

From the figure it is clear that the lower and upper cubes have Ba2+

ions at the

body centre while the smaller Cu+2

ions at each corner. The middle cube had Y3+

ion at the body centre. A perovskite has formula ABO3 and the stoichiometry of

the compound would be YBa2Cu3O9. But the actual formula being YBa2Cu3O7-x.

There is a massive deficiency of oxygen where about one quarter of the oxygen

sites are vacant in the crystal. The copper atoms are surrounded by oxygen

polyhedra which are in square –planar and square-pyramidal environments i.e.

CuO4 and CuO5 units as shown in Fig 4.20(C)

4.6.4 Properties

(i) Ceramic superconductors have mixed oxide system and are called high

temperature superconductors or warm superconductors or mixed

superconductors. Many of them contain copper which exists in three oxidation

state (+I), (+II) and (+III) where Cu (II) forms many tetragonally distorted

octahedral complexes.

(ii) They have perovskite structure.

(iii) They exhibit critical deficiency of oxygen.

(iv) Superconductivity in the YBa2Cu3O7-x is thought to be associated with ready

transfer of electrons between cu (I) Cu (II ) and Cu (III)

(v) Below critical temperature (Tc), at which the superconducting state is

formed, the ceramic superconductors show zero electrical resistance.

(vi) Superconductors can repel magnets and are thus diamagnetic and hence

they exhibit Meissner effect below Tc.

4.7 APPLICATIONS OF SUPERCONDUCTORS

1. Ceramic Superconductors show zero electrical resistance. Thus the cables

made of Superconducting materials if used then the 20 % loss of electricity

during its transmission through aluminium or copper wires is avoided. Thus

ceramic superconductors are useful to carry huge amounts of electricity

without much loss.

2. Large magnetic fields can be generated by using the ceramic

Superconductors. This property is applied in superfast magnetically levitated

trains. Trains which can run with speeds of about 500 km per hour have been

built in Japan on the principle of magnetic levitation.

3. Superconductors being diamagnetic they are used in Magnetic Resonance

Imaging (MRI) which is a new diagnostic tool.

4. Superconductors are useful in computers satellites and variety of electronic

devices.

5. Powerful electromagnets using Superconducting windings are quite useful

especially at higher temperatures.

A Few of the new Superconductors along with other Superconductors materials

have been tabulated in table 4.5 for general reference.

Table 4.5

Elements Critical temperature

(Tc) K

compounds Critical temperature

(Tc) K

Zinc 0.88 Nb3Sn 18.0

Cadmium 0.56 K0.4Ba0.6BiO3 29.8

Mercury 4.15 YBa2Cu3O7 95.0

Zinc 7.19 Ti2Ba2Ca2Cu3O10 122.0

Ceramics:

Let us conclude with familiarity to ceramics. This terms is often applied to all

inorganic non metallic non-molecular materials including crystalline as well as

amorphous. The word is derived from Greek word “Keramos” meaning burnt

earth literally potters clay Ceramics comprise different engineering produced

through high temperature processing. They possess greater hardness rigidity and

thermal stability than the metals. Ceramics are composed of both cationic and

anionic species. The basic difference between ceramics and other kinds of solids

lies in the nature of chemical bonding. The typical and traditional examples of

ceramics are white wares, tiles and bricks abrasives, refractories, chemical

stoneware etc.

QUESTIONS

(A)Objective Type Questions

(a) Germanium doped with phosphorus is called n-type Semiconductor.

(b) Boron acts as an acceptor impurity in Semiconductors.

(c) With increase of temperature conductivity of metals decreases.

(d) p-n junctions act as the rectifiers in electronic devices.

(e) Metallic bond is a type of electrostatic attraction between metallic ions and

gas of mobile electrons

(f) Free electron theory of metallic bonding is due to Drude and Lorentz.

(g) Semiconductors have numerous applications in electronics.

(h) Mixed oxide ceramic superconductor has the composition YB a2Cu3O7-x

(i) Ceramic Superconductors have zero electrical resistance.

(j) Superconductors are applied in magnetic levitation.

(Ans: All the statements given above are true )

2. Select the most correct alternative for the following :

(i) Matals are better conductors of electricity because of ………..

(a) free nucleons (b) free protons

(c) free neutrons (d) free electrons

(ii) Bonding in metals is best explained by………..

(a) crystal field theory (b) valence bond theory

(c) ligand field theory (d) molecular orbital theory

(iii) Germanium doped with donor atom is called ………..

(a) mixed oxide conductor (b) superconductor

(c) p-type semiconductor (d) n-type semiconductor

(iv) Metallic solids are………..

(a) insulators (b) superconductors

(c) semiconductors (d) good conductors

(v) Metallic solids are characterized by ………..

(a) low price (b) partially filled orbitals

(c) paired electrons (d) bright lustre

(vi) On the basis of band theory solids are classified as ………..

(a) metals and non-metals

(b) n-type and p-type conductors

(c) crystalline and amorphous solids

(d) insulators semiconductors and conductors

(vii) Idea of superconductivity was introduced by ………..

(a) Drude (b) Bloch

(c) Pauling (d) Kamerlingh Onnes

(viii) The pure crystals which are insulators at low temperature but show

conduction at higher temperatures are known as………..

(a) High temperature superconductors

(b) p- type semiconductors

(c) extrinsic semiconductors

(d) intrinsic semiconductors

(ix) Superconductors show ………..

(a) resonance effect (b) trans effect

(c) Raman effect (d) Meissner effect

(x) Mixed oxide ceramic superconductor has structure called as ………..

(a) Kekule-II structure (b) Lipscomb structure

(c) Lewis double dot structure (d) Cubic perovskite structure

(Ans: Alternative (d) for all )

3. Fill in the Blanks

(a) Conductivity of semiconductors is intermediate between those of ……and

……………

(b) Arsenic is doped in germanium crystal to get ………..type of semiconductors.

(c) …………….is called 1 2 3 superconductor.

(d) ………..and …………are the striking mechanical properties to the metal.

(e) ……….is the most fruitful approach to metallic bonding.

(Ans: (a) metallic good conductors, non metallic insulators (b) n,

(c) YBa2Cu3O7-x (d) Malleability, ductility (e) Band theory

4. Match the following :

Group A Group B

(a) Metals (a)High conductivity

(b) n-type semiconductor (b) Antimony

(c) p-type semiconductor (c) Boron

(d) Drude (d) Free Electron Theory

(e) Meissner effect (e) Diamagnetism

(f) Polyethylene (f) Insulator

(g) Solids (g) Rigidity

(Ans: (a) –a ,(b) –b,(c)- c, ,(d)- d,(e)- e ,(f)- f ,(g)- g

5. Define the following

(a) Metals (b) Semiconductors

(c) Metallic bond (d) n-type semiconductors

(e) Superconductor (f) Meissner effect

B Short Answer Type Questions

(a) Metallic (b) Free Electron Theory

(c)Band Theory (d) Types of semiconductors

(e) p-type semiconductors (f) Semiconductor action

(g) Applications of semiconductors

(h) Ceramic superconductuor (i) N-type semiconductor

7. Distinguish between

(i) Metallic conductors and semi conductors

(ii) n-type and p-type semiconductors

(iii) Insulators and superconductors

8. Give reasons for the following

(a) semiconductors have a negative temperature coefficient of electrical resistance.

(b) Metals show good lustre.

(c) Metals mean much to modern man.

(d) Semiconductors find wide spread applications in diverse fields

(e)Pure silicon crystal con not serve as a semiconductor for practical applications.

(f)Superconductors are used in magnetic resonance imaging (MTI)

(g) Ceramic superconductors are called 123 super conductors.

(h)Sodium gives golden yellow flame.

9. Answer the following:

(a) Give any two important applications of semi conductors?

(b) What do you mean by crystal?

(c) What do you mean by doping of silicon?

(d) Electrical conductivity of p-type semiconductor.

(e) Conducting action of p-type semiconductor.

(C) Long Answer Type Questions:

10. Write a note on metallic structure and metallic bonding. Explain how each

electron belongs to a metallic crystal as a whole.

11. Based on band theory of metallic bond, explain the physical properties of

metals viz. mechanical strength, lustre and emissivity.

12. What are semiconductors? Explain what do you mean by n-type and p-type

semiconduction?

13. Explain the principle of ceramic superconductor? What is meant by 123

superconductor?

14. (a) Discuss the common crystal structures of metals.

(b) Explain the semiconducting action in silicon caused due to the addition of

pentavalent and trivalent atoms.

15. (a) Explain N and P types of semiconductors .Give their applications.

(b) Give an account of theories of bonding in metals.

16. With a neat diagram, explain the structure of ceramic superconductor and give

its important applications.

17. What are solids? How are they classified? Comment on types of

semiconductors with suitable examples.

18. Give precise information on classification of solids on the basis of band theory

giving neat diagrams and specific illustrations.

19. What are metals? Mention their important physical properties. Comment on

their mechanical properties as brief note.

20. With suitable illustrations write precise notes on the following (Any three)

(i) Intrinsic semiconductor

(ii) Extrinsic semiconductor.

(iii) Mixed oxide 123 type superconductor.

(iv) Electron sea model of metallic bond.

(V) Types of crystalline solids.

21. Give a brief account of ceramic superconductor of mixed oxide type with

respect to its meaning, preparation, properties, and important applications with an

illustration of YBa2Cu3O7-x

22. Explain metallic bonding on the basis of

(i) Electron gas theory and

(ii) Molecular orbital theory

23. By using energy level diagrams and the band theory explain the differences

between conductors, insulators and semiconductors.

24. (a) Explain why the electrical conductivity of a metal decreases as the

temperature is raised but reverse is the situation with semiconductors.

(b) On the basis of free electron theory explain the following properties of metals

(i) high melting points

(ii) malleability

(iii) Ability to conduct heat energy

25. (a) On the basis of band theory explain the electrical conductivity of –

(i) alkali metals

(ii) alkaline earth metals and

(iii)Semiconductors

(b) What are mixed oxide types of superconductors? Give structures preparation

and applications of YBa2Cu3O7-x.