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Band Theory & Optical Properties in solids

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Band Theory

where m* is called the effective mass

Useful way to visualize the difference between conductors, insulators and semiconductors is to plot the available energies for electrons in the materials. Instead of having discrete energies as in the case of free atoms, the available energy states form bands

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Electronic properties Energy Bands models for solids

The last completely filled (at least

at T = 0 K) band is called the

Valence Band

• The next band with higher energy is the Conduction Band

• The Conduction Band can be empty or partially filed The energy difference between the

bottom of the CB and the top of

the VB is called the Band Gap (or

Forbidden Gap)SORAN UNIVERSITY

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Energy Bands for Solids

An important parameter in the band theory is the Fermi level, the top of the available electron energy levels at low temperatures. The position of the Fermi level with the relation to the conduction band is a crucial factor in determining electrical properties.

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Most solid substances are insulators, and in terms of the band theory of solids this implies that there is a large forbidden gap between the energies of the valence electrons and the energy at which the electrons can move freely through the material (the conduction band).

Insulator Energy Bands

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In terms of the band theory of solids, metals are unique as good conductors of electricity. This can be seen to be a result of their valence electrons being essentially free. In the band theory, this is depicted as an overlap of the valence band and the conduction band so that at least a fraction of the valence electrons

can move through the material.

Conductor Energy Bands

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Semiconductor

A semiconductor material is one whose electrical properties lie in

between those of insulators and good conductors. Examples are:

germanium and silicon. In terms of energy bands, semiconductors can be

defined as those materials which have almost an empty conduction

band and almost filled valence band with a very narrow energy gap (of

the order of 1 eV) separating the two.

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Types of Semiconductors:Types of Semiconductors:

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Intrinsic Semiconductors

An intrinsic semiconductor is one which is made of the semiconductor material in its extremely pure form.

Examples of such semiconductors are: pure germanium and silicon which have forbidden energy gaps of 0.72

eV and 1.1 eV respectively. The energy gap is so small that even at ordinary room temperature; there are

many electrons which possess sufficient energy to jump across the small energy gap between the valence and

the conduction bands Alternatively, an intrinsic semiconductor may be defined as one in which the number of

conduction electrons is equal to the number of holes. Schematic energy band diagram of an intrinsic

semiconductor at room temperature is shown in Fig. below.

Fermi level" is the term used to describe the top of the collection of electron

energy levels at absolute zero temperature. the highest energy level which an

electron can occupy the valance band at 0k is called fermi energy.

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b. Extrinsic Semiconductors:

Those intrinsic semiconductors to which some suitable impurity or doping

agent or doping has been added in extremely small amounts (about 1 part in

108) are called extrinsic or impurity semiconductors. Depending on the type of

doping material used, extrinsic semiconductors can be sub-divided into two

classes:

(i) N-type semiconductors and

(ii) P-type semiconductors.

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N-type semiconductor:When a small amount of pentavalent donor atoms (e.g., phosphorus (P) and Arsenic (As)) is added, a silicon atom in the lattice may be replaced by a donor atom with four of its valence electrons forming the covalent bounds and one extra free electron. This is an N-type semiconductor whose conductivity is much improved compared to the intrinsic semiconductors, due to the extra free electrons in the lattice, which are called predominant or majority current carriers. There also exist some tiny number of holes called minority carriers.

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P-type semiconductor:When a small amount of trivalent acceptor atoms (e.g., boron (B) and aluminum (Al)) is added, a silicon atom in the lattice may be replaced by an acceptor atom with only three valence electrons forming three covalent bounds and a hole in the lattice. This is a P-type semiconductor whose conductivity is also much improved compared to the intrinsic semiconductors, due to the holes in the lattice, which are called predominant or majority current carriers. There also exist some tiny number of free electrons called minority carriers.

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N-type Semiconductor P-type Semiconductor

1) Doped with pentavalent atoms. Electrons are majority charge carriers. Holes are minority charge carriers.

2) It gives out electrons, hence, known as donor atoms.

3) Bismuth, Antimony, Arsenic and Phosphorus are the elements used for doping.

1) Doped with trivalent atoms. Holes are majority charge carriers. Electrons are minority charge carriers.

2) It accepts electrons, hence, known as accepter atoms.

3) Aluminum, Gallium, Indium and Boron are the elements used for doping.

Comparison of P & N type Semiconductors

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PN-Junction

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P-N Junction Diode •Construction ; It is two terminal devices consisting of a P-N junction formed either in Ge or Si crystal. It is circuit symbol is shown in fig. (3.2-a). The P and N type regions are referred to as anode and cathode respectively. In fig. (1-b) arrowhead indicates the conventional direction of current flow when forwardbiased. It is the same direction in which hole flow takes place.

Fig.3.2•Working; A P-N junction diode is a one way device offering low resistance when forward biased and behaving almost as an insulator when reverse biased. Hence such diodes are mostly used as rectifiers for converting alternating current into direct current.

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For intrinsic semiconductors like silicon and germanium, the Fermi level is essentially halfway between the valence and conduction bands. Although no conduction occurs at 0 K, at higher temperatures a finite number of electrons can reach the conduction band and provide some current. In doped semiconductors, extra energy levels are added. The increase in conductivity with temperature can be modeled in terms of the Fermi function, which allows one to calculate the population of the conduction band.

Semiconductor Energy Bands

There are two cases;· Direct gap; · Indirect gap;