The document discusses various topics related to energy band theory:
- Materials have energy bands separated by a forbidden band gap, through which electrons must gain energy to be promoted.
- Insulators have a large band gap that requires significant energy like heat, voltage, or photons to ionize electrons.
- Ionization occurs when the electron gains enough energy, typically the ionization potential, to escape the atom.
- Various ionization mechanisms are described like collisional, thermal, and photo-ionization depending on the energy source.
2. Energy Band Theory:
• Each shell has its own energy level.
• The energy of the outer shell is more as compare to the inner
shell.
• The half-filled/ incomplete shell means the outermost shell,
because there is also some shell present after the last shell and
electrons moves through them by getting energy.
•
3. • For the conduction, the electrons should be in the conduction band
(CB).
• The energy gap between the conduction band and valance band is the
forbidden energy gap.
• In case of conductor, the C.B and V.B are slightly overlap each other.
Because the forbidden energy gap is small/less.
• But in case of insulator, the forbidden energy gap is high between
C.B and V.B
4. • Band gap energy
• Now the minimum energy required to move the electrons from the
V.B to the C.B is called as band gap energy.
• According to Energy Band Theory, the breakdown of insulator
occurs
“ When the external energy is greater than the band gap energy of the
material then the electrons jumps from V.B to C.B.
• External energy > E2-E1
• The voltage ‘V’ is applied across the insulator with ‘n’ number of
the electrons in the ground state as;
neV > or = E2-E1 (to move n es from E2 to E1)
(1ev=1.6×10-19j)
• where E2-E1 (the band gap energy) is the difference of the energy of
the valence band and conduction band
5. • External energy can be provided by any of the following means to
get ionized (to jumps the electrons from VB to CB)
1) Heat/temp
2) Voltage/electric field
3) Due to hitting / bombardment with particle/ collision
4) Light/photons
5) Sound
6) Radiations
7) Pressure
6. Ionization Potential:
• “The minimum energy required to eject the electron from the
outermost shell of gaseous atom is called the ionization potential.”
• External energy> I.P
• Means the K.E of the electron must be greater than the ionization
potential.
Ionization
Collision Ionization
Thermal Ionization
Photo-ionization
7. • Excitation Process
• When the kinetic energy or electron volts (eV) is less than the ionization
potential then excitation will take place.
• i.e K.E/eV < I.P Excitation
• e- + A0 A* + e- + hv
A* shows the excitation of atom.
e- electron having K.E<I.P
A0 stationary target atom.
hv energy in the form of photon
• To move the electron from the lower to a higher shell a certain amount of
energy is required. This energy can be in the form of electric fields.
8. Collision ionization:
• “The production of electron from an atom due to energetic incident
electrons, under the electric field, so the energy of incident electron is
transported to the atom. Resulting in positively charge ion”
• e- + A A+ + 2e-
e- shows fast moving incident electron
A shows stationary target atom
• This process is also called electron pair production
• The ionization is due to collision
• The moving or incident electron possess the K.E which is provided
by applied voltage
• i.e eV =1/2mv2 [ applied voltage provide K.E to moving e]
• so v=√(2eV/m)
• The velocity of the incident e- depend upon the applied voltage
9. • Thermal Ionization:
• The term thermal ionization in general applies to the ionizing in gases due
to high temperatures.
• A + ET A+ + e-
• When a gas is heated to high temperature, some of the gas molecules
acquire high kinetic energy and these particles after collision with neutral
particles ionize them and release electrons (Primary Ionization)
• These electrons and other high-velocity molecules in turn collide with
other particles and release more electrons (Secondary Ionization).
• Thus, the gas gets ionized.
10. • The relationship of electrical conductivity and the temperature is
given by:
• ϭ = A exp(-E/2KT)
• Where
• ϭ = conductivity in S/ms
• A = Arbitrary constant = 3.5 * 10_8
E = bandgap energy in joules
k= Boltzmann’s constant (1.38 x 10-23 joule. 0K-1)
T= absolute temperature in 0K.
12. • E2= hv + E1
• E2= higher energy state.
• E1=lower energy state.
• The energy state depend upon the hf,
• The energy in the form of photons.
• ∆E=hf
• E2-E1=hf
• This energy will release by the electrons when it is de-excited or de-
jumping,
• c=fλ f = c/λ
Where c =3*108 (velocity of light)
13. • This ionization by radiation or photons involves the interaction of
radiation with matter.
• Photo ionization occurs when the amount of radiation energy absorbed
by an atom or molecule exceeds its ionization energy.
• hv the photon energy
• If the photon energy is less than the ionization energy, it may still be
absorbed thus raising the atom to a higher energy level. This is known as
photo excitation.
14. • M + hv M* (photo-excitation)
• M + ET M* (thermal-excitation)
15. Examples
• Q. The energy band in a dielectric is 1.02 eV. find the voltage
required to transport 1012 electrons to the conduction band
• Solution:
• eV> E2-E1 to carry one electron
• neV> E2-E1 to carry n electrons
• V =
E2−E1
𝑛𝑒
=
1.02
1012 ∗1.6∗10−19
• V = .35 MV
E2
E1 1012 electrons
Voltage =?
17. Q. Findthe frequency(Hz) and wavelength
(nm) of the spectralline emittedby the atom
whenelectron jumpsdownfrom 3eV to 1eV
Sol.
E = h.f where h = plank’s constant = 6.63* 10-34
f =
2∗1.6∗10
_
19
6.63∗10
_
34
f = 4.84 * 1014 Hz
C=f.λ
λ=
3∗108
8.84∗1014
= --- ANS
