# SEMICONDUCTOR PHYSICS Class 1

## SEMICONDUCTOR PHYSICS Class 1

Hello friends this is Divakar, today I’m going to discuss on the topic of SEMICONDUCTOR PHYSICS. This topic has little scope in competitive exams but it’s more useful in viva voice. In order to understand working of semiconductors this topic is very useful.

In electrical point of view there are three types of materials i.e insulators, conductor and semi conductor. Before discriminating these I would like discuss on 3 terms i.e valance band, conduction band and forbidden energy gap.

In case of single atom, there are single energy levels. We know that in case of solids, the atoms are arranged in a systematic space lattice and hence the atom is greatly influenced by neighboring atoms. The closeness of atoms results in the intermixing of electrons of neighboring atoms. So in solid there will be bands of energy levels. A set of such closely packed energy levels is called energy band. The band formed by series of energy levels containing the valence electrons is known as valence band. In certain metals the valence electrons are loosely attached to the nucleus. Even at the room temp, some of electrons left valence band these called free electrons and responsible for conduction of current hence it called as conduction band. It also defined as the lowest unfilled energy band. With empty conduction band current conduction is not possible.

The separation of conduction and valence bands is known as forbidden energy gap (Eg). No electrons can stay in the gap. More the forbidden energy gap, more tightly the valence electron bound to the nucleus. In order to push an electron from valence band to conduction we need some energy which is equal to forbidden energy gap. As the temperature increases energy gap will decreases.

Eg = Eg0– BT where B is a constant depends on material. So energy gap decreases with increasing of temperature.

Eg0-energy gap at 00k                       germanium-0.783ev                       silicon-1.21ev
B-                                                            germanium-2.23×10-4                   silicon- 3.6×10-4

1st:    which one of the following equation represents the energy gap (EG) variation of silicon with temperature (T)? [IES-2006]

EG (T) = 2.21-3.60x 10-4 T
EG (T) = 1.21-3.60x 10-4 T
EG (T) = 1.41-2.23x 10-4 T
EG (T) = 0.785-2.23x 10-4 T

Materials are classified in to three parts as per band gap theory i.e insulators, semi conductors and insulators.

Semi conductors:
Semi conductors are one whose electrical properties lie between insulator and conductor. There are two types of semi conductors

• Intrinsic or pure semi conductor
• Extrinsic or impure semi conductor

Silicon, germanium and Gallium Arsenic (GaAs) are the examples of semi conductors. But silicon and germanium are mostly used than GaAs, because GaAs has higher Eg so it requires more energy to pass energy gap. These materials are tetravalent; each has four electrons in the outermost shell i.e valence. Let us consider the case when the two atoms are brought close to each other, each atom attracts one electron from the other atom and the electrons are shared by two atoms and forms electron pair it called as covalent bond is shown in figure.

### Mechanism of conduction in semi conductors:

At very low temperature (00k), the semi conductor crystal behaves as a perfect insulator since the covalent bonds are very strong and no free electrons are available. There is a large energy gap between valence band and conduction band. Here valence band is filled but no electrons can reach conduction band to become free electron. At room temp some of the covalent bond broke due to the thermal energy. So some electrons are free and available for conduction. When the electrons are liberated on breaking the covalent bond, they move randomly. These free electrons are not attracted by the nuclei of the atoms and also repelled by the electrons in covalent bonds because their electrical nature completely engaged in covalent bonds. Whenever electrical field applied, these free electrons move towards positive terminal, it leads to electric current. For one electron set free, a hole is created. So no of free holes are equal to no of free electrons.

2nd:    The bonding forces in compound semi conductor, such as GaAs arise from? [IES-2002]

A) Ionic bonding

B) Metallic Bonding

C) Covalent Bonding

D) Combination of ionic and covalent bonding.

Reason: In semi conductors every atom is in covalent bond but ionic bonds are due to in GaAs there is difference in Ga and As in periodic table i.e ‘Ga’ is 3rd group where as ‘As’ is in 5th group.

Most possible viva-voice question from this chapter is—

Why semi conductor has negative temperature co-efficient?

Answer:  As temperature increases the no of free holes and free electrons are increases by breaking covalent bond, so conductivity of semi conductor increases and resistivity decreases. Finally resistivity inversely proportional to temperature, it’s called negative temperature co-efficient.

#### Intrinsic Semi conductor:

A semi-conductor which is in pure form is known as intrinsic semi conductor.
p- Concentration of electrons/cm3
n- Concentration of holes/cm3

n = p = ni (intrinsic carrier concentration)

3rd:      Assertion: The intrinsic carrier concentration of si at room temperature is more than that of GaAs
Reason: Si is an indirect bandgap semi conductor while GaAs is a direct band gap semi conductor. [IES -2002]

Answer:  here both statements are correct but reason is not correct explanation of assertion because there is no relation between bandgap and intrinsic carrier concentration.

##### Extrinsic Semi conductor:

Intrinsic semi conductor has little conduction capability. In order to use this into electric device, its conduction properties should be increased. The electrical conductivity can be increased by adding some impurities in the presence of crystallization. The added impurity is in the order of one atom per million atoms of the pure semi conductor. The process is called as Doping. Usually doping materials are two types

1. Pentavalent-Donor (bismuth, antimony, arsenic, phosphorus) which have five valance electrons. When small amount of pentavalent impurity is added to a pure semi conductor crystal is called as N-type extrinsic semi conductor. Here electrons are majority carries and holes are minor carriers. It has positively charged donor ions.

2. Trivalent-acceptor (gallium, indium, aluminum, boron) which have three valance electrons. When small amount of trivalent impurity is added to a pure semi conductor crystal is called as P-type extrinsic semi conductor. Holes are majority and electrons are minor. It has negatively charged acceptor ions.
Note: one major difference between P and N type is, in P-type conductivity the valence electrons move from one covalent bond to another covalent bond unlike the N-type where current conduction is by free electrons.

4th:    The concentration of minority carriers in an extrinsic semiconductor under equilibrium is [IES-2012]

(A)  Directly proportional to doping concentration

(B)  Directly proportional to intrinsic concentration

(C)  Inversely proportional to doping concentration

(D)  Inversely proportional to intrinsic concentration

As doping increases majority charge carriers increases and recombine with minority charge carriers, results decreasing minority charge carriers.

The Mass-Action law:
Under thermal equilibrium, the product of concentration of free electrons and concentration of holes is constant and is independent of the amount of doping by donor and acceptor impurities.

In case of intrinsic semi conductor:           n X p =   ni2

In case of extrinsic semi conductor:
Positive charge density = concentration of donor atoms + concentration of holes (ND + p)
Negative charge density= concentration of acceptor atoms+ concentration of free electrons (NA + n)
As per the law of electrical neutrality, semi conductor is electrically neutral i.e the magnitude of positive charge density must be equal to negative charge density.

ND + p = NA + n

In N-type semi conductor NA=0 and nn>>p so Nn = ND subscript denote type of semi conductor
Nn X  Pn =ni2,     ND X Pn = ni2
In p-type semi conductor     PP = NA      NP x PP = ni2,    NA X NP = ni2

5th:     A specimen of intrinsic germanium with the density of charge carriers of 2.5X 1013 /cm3, is doped with donor impurity atoms such that there is one donor impurity atom for every 106 germanium atoms. The density of germanium atoms is 4.4x 1022 /cm3. The hole density would be?  [IES-2001]

A) 4.4x 1016 /cm3                B) 1.4x 1010 /cm3                    C) 4.4x 1010 /cm3                D) 1.4x 1016 /cm3

ni = 2.5X 1013 /cm3
ND = 4.4x 1022 / 106 = 4.4x 1016 /cm3
Doping with donor impurity nothing but n-type semi conductor where n= ND
As per mass action law n.p=ni2
P=(2.5X 1013)2 / 4.4x 1016 = 1.4x 1010 /cm3

6th:    in a p-type silicon sample, the hole concentration is 2.25x 1015 /cc. if the intrinsic carrier concentration is 1.5x 1010/cc. what is the electron concentration in the p-type silicon sample?  [IES-2005]

A) Zero                  B) 1010/cc                           C) 105/cc                                D)1.5x 1025 /cc

P = 2.25x 1015 /cc
ni= 1.5x 1010 /cc
n.p = ni2
n = ni2/p = 105/cc

7th:  for a n-type semi conductor having any doping level, which of the following hold(s) good?

1)   ND X Pn  = ni2                 2)    Pp x ND = ni2                3)    nn  x ND = ni2              4)    nn X Pn  =ni2

Select the correct answer using code given below [IES- 2006]

A) 1 and 4                    B) 2 and 4                        C) 3 and 4                 D) only 4