Energy band theory of silicon

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• ANIL NEERUKONDA INSTITUTE OF TECHNOLOGY
  SCIENCES(A)Department of Electronics and
  Communication Engineering
• ECE 125 Basic Electronics Engineering

• Academic year 2022-23
• Class Section 1/4 ECE-A
• Name of the Faculty Mr.D.Anil Prasad

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Contents

• Introduction
• Band Theory of solids
• Classification of materials based on Energy bands
• Mobility and Conductivity

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Introduction

• There are three types of materials, based on
  their conducting properties
• conductors
• semiconductors
• insulators

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Introduction

• At room temperature the conductivity and
  resistivity of selected materials is shown in
  table.
• Metals and alloys have the highest conductivities
  followed by semiconductors and then by insulators

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Introduction

• Resistivity vs. Temperature

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Band Theory of Solids

• Energy band theory of solids indicate that the
  allowed energy states for electrons are nearly
  continuous over certain ranges, called energy
  bands, with forbidden energy gaps between the
  bands.

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Band Theory of Solids

• When atoms are far apart electron energies in
  atom1 and atom2 are same.
• The force of attraction of electron in atom1 and
  its nucleus is same as the force of attraction of
  electron in atom2 and its nucleus.

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Band Theory of Solids

• When atoms are brought closer to each other the
  columbic force of attraction of electrons changes
  in atom1 and atom2.
• The force of attraction between electron in atom1
  and nucleus in atom2 changes. Similarly the force
  of attraction between electron in atom2 and
  nucleus in atom1 changes.

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Band Theory of Solids

• When force of attraction changes the electron
  energy changes.
• Thus when atoms are brought closer to each other
  the energies of electron in each of the hydrogen
  atom changes or splits into two energy levels.

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Band Theory of Solids

• Si-1s22s22p63s23p2
• Consider N atom system which has
• 2N 1s states,
• 2N 2s states,
• 6N 2p states,
• 2N 3s states,
• 6N 3p states

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Band Theory of Silicon

• As the atoms are brought closer coupling of
  various atoms take place. The energy levels split
  into bands beginning with outer shell(n3)
• The 3s states will tend to spread into range of
  energies. Because there are 2N 3s states there
  should be 2N separate energy states represented
  by lines

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Band Theory of Silicon

• Similarly 6N 3p states are shown by 6N separate
  energy states represented by lines. Since N is
  very large (5x1022 atoms/cm3)for si the various
  levels are so close to each other such that it
  represents a continuous band

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Band Theory of Silicon

• If further atomic separation is reduced we can
  have a single continuous band. As the distance
  between atoms approaches the equilibrium
  interatomic spacing of Si (lattice constant of
  si, r05.43A) this band splits into two bands
  separated by an energy gap, Eg

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Band Theory of Silicon

• The number of states in the lower band and upper
  band are exactly 4N states each. The total number
  of electrons are 4N electrons in 8N states. So
  all 4N electrons will occupy the lower energies
  available. The upper band will be empty at T00K

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Band Theory of Silicon

• Valence Band
• Valence Band refers to the lower band in which
  valence electrons are found in energy levels. It
  may have all the electrons it needs or only some
  of them.
• Conduction Band
• Conduction band refers to the upper band where
  free electrons are not present in any energy
  levels. The following allowed energy band is the
  conduction band. It could be devoid of electrons
  entirely or only partially.

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Band Theory of Silicon

• Forbidden energy Gap
• The Forbidden Energy Gap, Forbidden Band Gap, or
  Band Gap is the name given to the energy gap
  between the valence band and conduction band.
• The amount of energy required by an electron to
  move from the valence band into the conduction
  band is known as the energy gap, or Eg. It's
  expressed in eV.

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Band Theory of Silicon
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Classification of materials based on Energy Bands
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Classification of materials based on Energy Bands

• Insulator
• Material which do not conduct current is called
  insulator.
• The energy band gap in insulator is above 5 eV.
• Conductor
• The energy band gap in a conductor, a material
  that conducts electricity, is zero.

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Classification of materials based on Energy Bands

• Semiconductor
• Semiconductor refers to materials with
  conductivity that is between insulator and
  conductor.
• The energy band gap is quite narrow, around 1 eV.

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Mobility and conductivity

• In any material along with atoms, ions are also
  present.
• In any material impurities are present.
• When two different elements are present then
  their electronic configuration is different. The
  electrons can be taken or given by each of the
  material and hence ions are present.

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Mobility and conductivity

• The ve sign within circle represents the net
  positive charge of nucleus and tightly bound
  inner electrons.
• The dots represent the outer or valence electrons
  in atom. These electrons doesnt belong to any
  particular atom. They have lost their
  individuality and can wander freely about from
  atom to atom in metal.

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Mobility and conductivity

• The electrons in a metal are in random motion and
  on an average there will be as many electrons
  passing through unit area in any direction as in
  the opposite direction in a given time. Hence the
  average current is zero.

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Mobility and conductivity

• In a metal, electrons are in continuous motion
  and collide with atoms and scattered by the
  heavy ions and maintain different velocities.
• When a constant electric field E is applied to
  the metal, due to electrostatic force electrons
  would be accelerated and the velocity would
  increase indefinitely with time. (The increase in
  electron velocity is not due to collisions with
  the ions)

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Mobility and conductivity

• At each inelastic collision with an ion an
  electron loses energy and a steady state
  condition is reached where a finite value of
  drift speed vd is attained
• Drift velocity It is average velocity maintained
  by electrons while moving inside material . Drift
  velocity is in the direction opposite to that of
  the E.
• vdaE
• VdµE

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Mobility and conductivity

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Mobility and conductivity

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References

• Robert L Boylestad, Electronic Devices And
  Circuit Theory, Prentice Hall, seventh
  edition,2021
• Jacob Millman and Christos Halkias, Electronics
  Devices and Circuits, Black edition, October,2017

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Thank you

• for listening