12

s you have read in Chapter 1, the electronic era commenced with vacuum tubedevices. Later semiconductor devices replaced them. Till today, semiconductor is

the main raw material in the field of electronic devices. Miniature electronic circuitsare fabricated on semiconductor chips as integrated circuits (IC), which will be brieflyintroduced in Chapter-10. Discrete electronic devices like diode (Chapter-3), transistor(Chapter-5) and field-effect transistor (Chapter-8) are also made of semiconductors incombination with metal and insulator, as required. All these materials, viz. metal,insulator and semiconductor are crystalline solids. Therefore, as a part of electronics,you should have some idea on the basic properties of crystalline solids with specialemphasis on semiconductors.

olids have the general features like mechanical strength, rigidity and shape.Liquids have negligible compressibility but no definite shape. Gases can be

compressed. Solids are distinguished from these two. The atoms and molecules insolids are strongly bound together and closely packed. The closely bound atoms insolids may or may not have regular arrangement, which determines whether or not thesolid is crystalline.

Crystals are the solids that have atoms arranged in symmetrical arrays. Thecrystal structure has a periodicity and symmetry in the arrangement of atoms. Allsolids are not crystals. Some solids have no periodic structure at all and are calledamorphous solids. Some solids, known as polycrystalline solids have many smallregions of crystal structure.

Solid state electronic devices involve the transport of electrical carriers throughcrystalline solids. The transport properties depend not only on the properties ofelectron but also on the atomic structure of the solid. Both the mechanical andelectrical properties of the solids are determined by the atomic structure. That is why itis so important.

A

Properties of Crystalline Materials

S

2

SemiconductorFundamentals

13

It is mentioned above that solids have rigid shape. There are three types of solids,

namely metal, insulator and semiconductor. Crystalline arrangement of atoms may be

found in each of these types ; some are amorphous too. The mechanical properties of

solids like elasticity and deformation and electrical properties like conductivity are

often explained on the basis of the atomic structure. Based on the electrical

conductivity, solids are classified into metal, insulator and semiconductor. The

electrical properties of metal, insulator and semiconductor are distinguished by

energy band theory, which stems from the atomic structure of the solid. Therefore, the

study of crystal structure of solid is of fundamental importance. An introduction is

given here.

:

:

14

Studies on crystal structure represent the crystal by lattice and explain the solidproperties with lattice model. Therefore it is essential to get acquainted withparameters related to lattice. Unit cell is the minimum geometric structure repeatedin space so as to form the lattice. Do not confuse it with basis. Fig. 2.2 will clarify theconcept of unit cell.

The same array of points may be composed of repetition of either the rectangle or the parallelogram . Any one can be treated as unit cell for this array. Thus,

various arrangements of atoms in space may be assumed in connection with theformation of lattice. The distance and orientation between atoms may differ. However,repetition of a minimum structure forms the lattice. That structure is unit cell. Theactual lattice is three-dimensional, hence the unit cell is a volume, which is regularlyrepeated throughout the crystal.

In general, a unit cell is the smallest volume, which has all the structuralproperties of the given lattice and which constructs the entire lattice by translationalrepetition in three-dimensions. The length of the side of a unit cell is the distancebetween the atoms of the same kind.

Fig. 2.1: Lattice representation of sodium chloride (NaCl) crystal

ab cd

Fig. 2.2 : Schematic representation of unit cell

15

One can mathematically define lattice in terms of unit cell. Refer to Fig. 2.2 again.

Let be an arbitrary origin and vectors and join two lattice points to this origin.

Therefore all the other points may be defined as the distance given by

where and are integers. The vectors and represent the two sides of the unit

cell. The unit cell of an actual lattice has three sides and any arbitrary lattice point can

be represented by expression like

where the vectors , and are termed as crystallographic axes. These are the

fundamental translational vectors, characteristic of the lattice array. These are chosen

such that these pass through lattice points representing similar atoms. The angles

between the axes are called interfacial angles.

Auguste Bravais (1811–1863), who introduced the idea of lattice identified

fourteen possible types of space lattices depending on the plane of symmetry, axes of

symmetry and center of symmetry. These are known as Bravais lattices. Table 2.1

illustrates them.

Table 2.1 :

1 Cubic 3

2 Trigonal

1

3 Tetragonal 2

O a b

d

d n1a n2b 2.1

n1 n2 a b

d n1a n2b n3 c 2.2

a b c

a b c

90NaCl KI

a b c

< 120 90

Sb As,CaSO4

a b c

90NiSO4 SnO2

16

We may have, as example, the three cubic structures shown in Fig. 2.3. Thestructures are self-explanatory.

Crystal axes have been defined. It is often convenient to define a set of parallelcrystal planes passing through the lattice in terms of intercepts with these axes. The

4 Hexagonal 1,

5Orthorhombic

4,

6 Monoclinic 2

7 Triclinic 1,

[ , ]

Total 14 Bravais lattices

a b c

90

120

Cd Ni

ZnO Quartz

a b c

90

KNO3 MgSO4

BaSO4

a b c

90

FeSO4 Na2SO4,

KClO3

a b c

90

K2Cr2O7

CuSO4 5H2O

Fig. 2.3 : Cubic lattice structures (a) SC, (b) BCC and (c) FCC

(a) (b) (c)

17

crystal planes have practical significance because diffraction of X-ray from theseplanes yield important information on the crystal structure.

British mineralogist William Hallowes Miller (1801–1880) established a notationsystem to describe the orientations of crystal planes in terms of their intercepts on thethree axes. The notations are called Miller indices.

The process of defining Miller indicesconsists of the following steps.

Note the crystal plane interceptunits on the three axes. InFig. 2.4, the -intercept is 2, -intercept is 2 and -intercept is1 unit.

Make the reciprocals of theintercept units. The present caseis and 1.

Multiply the above reciprocalsby a common multiplier toconvert to the smallest wholenumber. For the present case,multiply by 2. the values become1, 1 and 2.

The Miller indices are now indicated as [112].

hese are solid materials having electrical conductivity intermediate between thatof metal and insulator. The notable property of a semiconductor is that its

conductivity increases on increasing temperature, optical excitation and addition ofspecific impurities in controlled amounts (doping). There are both elemental andcompound semiconductors as mentioned in Table 2.2.

Table 2.2 :

Silicon (Si) element IV Majority of semiconductordevices: diode, transistor, IC

Germanium (Ge) element IV Some transistors, nanodevices

Gallium arsenide (GaAs)

compound III-V Light emitting diode (LED)

Fig. 2.4 : Orientation of crystal plane(shaded) in terms of interceptswith the three axes

x yz

12

12

Semiconductor Materials

T

18

The general properties of crystals mentioned in the previous sections hold tometals, insulators and semiconductors. The basic lattice structure for manysemiconductors is diamond lattice and zinc blende, which consist of twointerpenetrating FCC structures displaced by .

Although the above definition qualitatively explains the properties ofsemiconductors, quantification of the wide variation of electrical and opticalproperties and proper distinction from metal and insulator are possible only with theconcept of energy bands.

he electrons in isolated atoms have discrete energy levels. But in the case of solids(metal, insulator or semiconductor), a large number of atoms remain closely

spaced so that the neighbouring atoms affect the energy levels of the electrons in oneatom. However, Pauli’s exclusion principle must be satisfied so that no two electrons ina given interacting system can have the same quantum states. Therefore the energylevel of one atom cannot superimpose on the levels of another. Instead, the levelsremain very close to one another, the difference between two consecutive levels beingvery small, of the order of eV. The collection of such levels may be considered asa continuous energy band.

A discrete atom has only discrete energy levels separated by energy gaps.Similarly, the energy bands of the atoms in a solid may be separated by energy gaps.Also the bands may overlap one another. These conditions determine the electricalproperties of the solids as discussed in section 2.5.4 of this chapter.

Each crystalline solid has its own characteristic energy band structure. It isactually the energy-momentum relationship for the current carriers within thatmaterial. Determination of the exact energy band picture is a matter of rigourousquantum mechanical calculations. However, you can have a qualitative idea on theformation of energy band with the help of Fig. 2.5.

Gallium phosphide (GaP)

compound III-V LED

Aluminium gallium arsenide (AlGaAs)

compound III-V LED, nanostructures

Silicon carbide (SiC) compound IV-IV LED

Zinc sulphide (ZnS) compound II-VI TV screen

14

14

14

Energy Band Theory

T

10 19

19

Fig. 2.5 qualitatively explains the energy state

variations of carbon atoms and it may be used as a

model for semiconductor bands indicated by

shaded region. The atomic number of carbon is 6,

hence it has up to states only. Let there be

atoms of a solid. The available energy states are

states of states of and states of

. Had these atoms been kept isolated, the

and states would be discrete as indicated in the

diagram. When these atoms come closer, the

interatomic distances reduce (moving from right

to left in Fig. 2.5) and energy bands are formed

beginning with and states. These two states

overlap to form a mixture of energy

states. As the interatomic distance further reduces,

the two bands are again separated into two parts

and separated by an energy gap ( ), that has

no available state for electrons. Therefore the electrons must reside either in V-band or

in C-band. Since the V-band consists of lower energy levels, the electrons are more

likely to fill up that band first according to the law of Fermi-Dirac distribution.

However, acquiring energy from light, heat or other sources some electrons may climb

up to C-band also crossing the energy gap ( ).

The above explanation builds up the concept of conduction and valence bands.

The highest energy band filled with electrons is called valence band (V-band in

Fig. 2.5). The next higher available band is called conduction band (C-band in

Fig. 2.5). It may be vacant or incompletely filled up with electrons. These two bands

may overlap or may be separated by a band gap, which contains no allowed energy

levels for electrons to occupy. It is ‘forbidden’ for the electrons. This energy gap is

defined with a lot of synonymous terms like ‘forbidden gap’, ‘energy gap’ and ‘bandgap’. We shall use the term ‘band gap’ throughout the book.

nformation on charged carrier concentration in semiconductor is important to

understand the properties of semiconductor devices. To get information on the

carrier concentration, one must know the law of carrier distribution over the available

energy states.

Electrons in solids obey Fermi-Dirac statistics. The probability that an electron

will occupy an available energy state at thermal equilibrium is given by

Fig.2.5 : Energy states of carbonatoms for isolated andcrystallized states.Energy bands andband gaps are createdon decreasing theinteratomic distance

2p N

2N 1s 2N 2s 6N

2p 1s 2s

2p

2s 2p

2N 6N 8N

C

V Eg

Eg

Fermi Level

I

E