optical electronics presentation files based on chapter 2 of book harold kolimbiris

7/27/2019 optical electronics presentation files based on chapter 2 of book Harold kolimbiris

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Chapter 2: Fundamentals ofSemiconductor Theory

Presenter: Saransh Malik

School of Electronics and Computer Engineering

Chonnam National University

2013. 09. 23


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Contents

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Semiconductor Theory2.1

N-Type Semiconductors2.2


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2.1 Semiconductor Theory

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Elements of Atomic Theory

Ancient philosopherDemocritiuss Hypothesis all matter compose of ATOMS

Atoms Smallest unit of Matter.

Atoms combined to form molecules.

Non-Element Atoms compose of same molecules.

Substance Atoms compose with different molecules.

Electrons Negatively charged particles orbiting the nucleus with fixed numb

er for each element. Discovered by JJ Thomp son

Nucleus Extremely massive central core part contains subatomic particles

Protons (positive charge) and Neutrons (Neutral Charge).

Protons - Positive charge particles with charge of+1.602x10-19 C; Mass

1.643x10-27 Kg. Discovered by Ernest Rutherford

Electromagnetic Forcesand Gravitational forceswere better known for

holding the structure of Atom.

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H Yucawa in 1935 discovered existences ofNuclear Force.

Neil Bohr In 1813 discovered the spherical approximated model for Atom asshown in figure below .

Sum of total +ve charge is equal to total sum for negative charge in an atom ;

which makes an atom electrically neutral.

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Based on Atomic Number periodic table elements are assigned based on Hydrogen.

Atomic Weight Sum of total no. of Protons and neutrons in the nucleus of atom

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Niels Bohr uses the emission spectrum of hydrogen to develop a quantum model

for H. Central idea: electron circles thenucleus in only certain allowed circular orbitals.

Bohr postulates that there is Coulombic (C) attraction between e- and nucleus.

Electrons orbit the nucleus in circular paths of fixed energy (energy levels).

Indicates main energy levels

n = 1, 2, 3, 4

The maximum number of electrons in a

principal energy level is given by:

Max no. of electrons = 2n2 ,

n= the principal quantum number

Shell closest to nucleus have lowest energy,

labelled as K,L,M

K is closest to nucleus

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Bohr model for the H atom is capable of reproducing the

energy levels . The electrons in an atom as per Schrdingerare given as

quantum numbers

Energy of the emitted photon=Difference in energy

between two states.

Example , n =1 shell contains one orbit with one or two

electron

Thus the 3rd sub shell contains 18 electrons and the 4th

contains 32 electrons.

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Force of attraction between electrons and protons within atom

F: Force of attraction; qn& qp: mass of neutron & proton, respectively.

Valence Shell : The valence shell is the outermost shell of an atom.

Electrons in this shell make up its valence electrons, these electrons

determine how the atom chemical properties will be. Relationship between Position of Shell in Atomic model and the number of

electrons occupying Shell is given as

Ne: Maximum no. of electrons; n: Position of shell in the atom.

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Example 2-1 Calculate Maximum number of electrons occupying each

of the four shells in a balanced atom

Solution:

First Shell:

Second Shell:

3rd orbit, by 18 electrons and 4th by 32 electrons.

Shell which has electrons less than max. is valance shell.

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Thus, Maximum number of electrons occupying

the first energy orbit is two.

Thus, the max. number of electrons occupying

the second orbit is eight.


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Example of Atomic model ofSilicon(Si) and Germanium(Ge) are shown below in

Figure 2-4 and 2-5.

Si : 14 Protons & 14 Neutrons in nulceus, surrounded by 14 electrons

So, the first and second shell are complete, but only 4 electrons are there in valence

shell.

In fig 2-5 for Germanium , composed of 32 Protons in nucleus and 32 electrons,

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Figure 2-4 An atomic model of silicon (Si) Figure 2-5 An atomic model of Germanium (Ge)


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Electrons belonging to the same shell occupy different energy levels as shown in

Table 2-1 At a specific temperature the atom of element is said to be neutral

Atoms absorbs thermal energy

The electrons in this valence shell absorbs energy. If the energy level is higher than

the threshold energy electron leave the atom and become a free electron

Ifatom deprive and electron it gains positive charge and if it gains one it attains

negative charge.

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Principle of Semiconductor Theory : Insulators,Conductors and Semiconductors

Energy Bands

Basic categories of elements :

Insulators : Dont conduct Electric current

Conductors : Conduct Electric current

The conduction band is the range of electron energies enough to free an electron from binding

with its atom to move freely within the atomic lattice of the material as a 'delocalized electron.

The valence band is the highest range of electron energies in which electrons are normallypresent at absolute zero temperature.

Fig 2-6a: Energy gap of an insulator is very large and of very high energy order 3eV will have to

be absorbed by an electron order to elevate it from the valence band to conducting band.

Fig 2-6b: In conductors some electron move freely from valence bond to conducting band at

room Temp. .

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Energy Gap: Amount of energy required by an electron to be able to

transfer from valence band to conducting band.

Band Gap Width : Band Gap energy (Eg) is based on the temperature.

Given by equation (2-3)

where Eg : band gap energy at Tx; Eg (T0) is the band gap energy at 0 K and

(,) are coefficients.

Band gap Energy of silicon is higher than germanium as in Table 2-3.

Also, with an increase in operating temperature, the band gap energy is

correspondingly decreases, thus increasing probability that electrons fromthe valence band will transfer to the conducting band to become free

electrons.

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i i l f i d h l


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Table 2-3 Band Gap Energy

Table 2-4 Band Gap Energy Levels for Si, Ge and GaAs at

differencet temp.

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Semiconductor Eg/0K(eV) Eg/300K(eV) (eV/K) /K

Germanium (Ge) 0.7437 0.66 4.774x10-4 235

Silicon (Si) 1.170 1.12 4.73x10-4 636gAllirum Ars

Gallium Arsenide(GaAs)

1.519 1.42 5.405x10-4 204

i i l f S i d h l


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Band Gap Energy :

Conductor : 0.1 eV Insulator : Larger than 5 eV.

Semiconductor: approx. 1eV.

Example 2-2 Cal. Band gap energy (eV) of silicon, germanium and GaAs for

temperature ranging from 0K to 400K, and plot the corresponding graphs

Sol.: At

At

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P i i l f S i d Th I l


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The Fermi Dirac Distribution : This distribution helps to get the hole density in the

valence band and the electron density in the conduction band in a semiconductormaterial , given by equations

Pc(E) : Density of state function in the conduction band

Pv(E) : Density of state function in the valence band

fn(E) : Fermi Dirac Distribution function in electrons in conduction band

fp(E) : Fermi Dirac Distribution function in holes in valence band.

The density state function for both conducting and valence bands are given as-

Ev : Energy at the top of the valence band; Ec : Energy at the bottom of the conducting band

me :Density of state effective mass of electrons ; mh : Density of state effective mass of holes

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P i i l f S i d Th I l


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Fermi Dirac Functions are given by :

Where, EFn: Fermi Energy for electron; EFp : Fermi Energy for hole;

K: Boltzman Const.; T: Absolute Temperature

Evident sum of probabilities =>1,

In terms of eV reference to kT,

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Probability that electron occupies available energy (E)

Probability that Hole occupies available energy (E)

P i i l f S i d t Th I l t


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The Concentration of Electrons and Holes in Intrinsic Semiconductors

Electrons and hole distribution in an intrinsic semiconductor material is defines

as product of density of state and Fermi Distribution.

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Electron Concentration in the Conducting Band

It is defined by the Fermi Dirac density of state distribution function

Substituting this into Equation (2-14) and solving yields (2-15)

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Differentiating both sides, gives

Substituting, (2-17) to (2-16), gives (2-18)

Fermi Efficiency F,

F0.5 (F) is Fermi integral of half order; Nc is given by:

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(2-20)



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An approx. solution is required for F much larger than one.

For Non degenerate Semiconductors: Fermi Level Within Band Gap First approx. Limitation:

This shows : Fermi Level must lie within the gap and away from the bottom

of the conducting band by several kT. By applying Second Approx.

2-26 is evident of the reason why, semiconductors electrical props. Are similar to

that of conductors.

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First Approximation : Intrinsic properties of semiconductors, so based on

Maxwell-Boltzman Statistics.

Hole Concentration in the Valence Bond

Hole: Empty space that e- leaves behind at valence bond anf provides +ve charge.

Hole concentration uses same procedure as with the electrons in the

conduction band is applied.

So, Integrating Fermi-Dirac distribution function of equation (2-5) from

in valence band yields (2-28)

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pv(E) and fp(E) Equation (2-28) yields Equation (2-29)

Differentiating both sides

Equation (2-29) and (2-30).

Fermi Efficiency

Fermi Integral of Half Order

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Nv Effective densityof states in valence bonds

Principle of Semicond ctor Theor : Ins lators


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As, (2-33) is not closed so a relationship is required for Fermi Efficiency.

For Non Degenerate Semiconductors: Fermi Level Within the Band

Gap

By using the approximation,

This shows Fermi level must be within the band gap and must be away from

the top of the valence band (kT)

Hole concentration in the valence band is given as:

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Principle of Semiconductor Theory : Insulators


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A new kind of material that show electrical property of both conductors and

insulators. The band gap energy level is higher than conductor and lower than insulator.

Basic Semiconductor materials are Silicon and Germanium.

In germanium, electrons occupying the valence shell are at higher energy levels thus

absorbs less energy.

In Silicon, it is opposite as in case of germanium.

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The figure shows Silicon structure as crystalline form, held together by a covalent

bond which is formed when electrons occupy valence shell, as in fig 2-9.

Crystalline structure share e- with adjacent atom makes it more chemically stable.

When e- at valence shell acquires enough thermal energy/electric field, it can

transfer from the valence shell to conducting band

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After losing the thermal energy it also retrieve back to its valence shell make it

neutral again. This process continues as long as the right conditions external to the atom continue

to exist this is referred as electron hole generation.

At absolute temp. 0K, Si exists in crystalline structure.

Crystalline structure exists in a neutral state: no free electrons.

At room temp. : No. of free electrons and holes remains constant for a condition that

makes it best for fabrication.

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Other Semiconductors used are as: Gallium Arsenide (GaAs) & Iodium Phoshide

(InP). Intrinsic semiconductor : At state of equilibrium, The concentration of electrons and

holes is equal.

With the injection of certain impurities in molecular structure, the extrinsic properties

can be altered, this can be done through doping.

The new types of Semiconductors then produced are : N- type and P-Type varying

with Conductivity.

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2.2 N-Type Semiconductors

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N-Type semiconductor is created by adding pentavalent impurities like :

Phosphorus (P), Arsenic (As), Antimony (Sb), Bismuth (Bi).

4 As (DONOR) valence electrons are used to make covalent bond with Si(ACCEPTOR) atom, while the 5th electron becomes free.

This free electron contributes to the conducting properties.

Since electrons are negative charge carriers, the resultant material is called N-

type (or negative type) .

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In N-type semiconductors materials that ratio ofmajority (Electrons) and Minority

(Hole).

The product of electron and hole can be defines by the relation:

Intrinsic Semiconductor n is equal to p, thus, above equation can be

In an intrinsic Semiconductor, Ec-Ev=Eg. Thus , the above equation can be given as,

Ec: Conducting band energy level, Ev : Valence band energy level, Eg : band gap energy

level.

Product of electron/hole density is independent of the Fermi Level and

dependent on the operating temperature.

Eg For Si at room temperature 300K electron/hole density is 2.4x1017 carriers/m3 for Ge it

is1.51017 carriers/m3

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optical electronics presentation files based on chapter 2 of book harold kolimbiris

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