This presentation is about the formation of energy band diagram and its formation.the resources used are video from nptel .

1. ENERGY BAND DIAGRAM OF
SEMICONDUCTOR
M.KAVIN YAZHINI
17D039

2. ENERGY BAND DIAGRAM
• A Energy band diagram is a diagram plotting various key electron energy levels as a function
of some spatial dimension
• The bands can be thought of as the collection of the individual energy levels of electrons
surrounding each atom.
• The wavefunctions of the individual electrons, however, overlap with those of electrons
confined to neighboring atoms.
• The main feature of the energy band is that the electron’s energy states of electronics are
stable in different ranges. So, the level of energy of an atom will change in conduction bands
& valence bands.

3. ENERGY BAND DIAGRAM OF SEMICONDUCTOR
• The best examples of semiconductors are Silicon (Si) & Germanium (Ge) which
are the most used materials.
• The electrical properties of these materials lie among semiconductors as well
as insulators.
• The valence band is totally filled however the forbidden gap among these
bands is minute that is 1eV.
• The forbidden gap of Ge is 0.72eV and Si is 1.1eV.

5. E-K DIAGRAM
An E-k diagram shows characteristics of a particular semiconductor material.
• It shows the relationship between the energy and momentum of available
quantum mechanical states for electrons in the material.

6. • The band gap (EG), which is the difference in energy between the top of the
valence band and the bottom of the conduction band.
• The effective mass of electrons and holes in the material. This is given by the
curvature of each of the bands.
• This diagram indicates how the actual electron states are equally spaced in k-
space. Which means that the density of states in E (ρ(E)ρ(E)) depends on the
slope of the E-k curve.

7. ENERGY BAND FORMATION :QUALITATIVE MODEL
• For an isolated atom we assume that the potential well is rectangular of width L and then we
showed that if you solve the energies for the electrons from Schrodinger equation you get
this kind of EK relation.
• This is a Schrodinger equation which depends only on the space we have removed the time
dependent time part because this is how we solved the Schrodinger equation.
• Where this k is related to the electronic energy the solution of this equation is as shown here
consists of a combination of 2 complex exponentials. And if you impose a boundary condition
corresponding to a rectangular well

9. • So therefore they have developed different energies and since there are so
many electrons their energies are very close to each other and so the allowed
energies becomes a band.
• This approach of developing the allowed energy bands from discreet levels of
isolated atoms is referred to as the bloch, tight binding or Linear combination
of atomic orbitals approach.

12. FEATURES OF E-K DIAGRAM

13. • This form of representation of E-k diagram is referred to as period zone
representation.
• So the E-k relation is being shown for several periods even though it is
periodic and you can probably show that information only in one of the
periods and then the same thing will apply to other periods.

14. UTILITY OF E-K RELATION
• The utility of E-k relation is the E-k relation can be used to get crystal momentum because the
force on electron in a crystal is equal to the time derivative of the product h cross K.
• So, this implies hk is conserved in the interaction of electron with a force or other entities
and that is the reason why it is called a momentum namely the crystal momentum.
• However, it is not the true instantaneous momentum. Since the true instantaneous
momentum is mass of the electron multiplied by velocity of the electron.

16. GRAPHICAL ILLUSTRATION

17. ENERGY LEVELS IN E-X DIAGRAM

18. • For the case of Gallium Arsenide similar approach gives you the conductivity and density of states
effective mass. The reason in this case ml and mt are both identical and = 0.067 m0. So, you see if you
compare it with silicon the effective mass of electron in Gallium Arsenide is much smaller.
• So electron feels much lighter in presence of Gallium Arsenide crystal potential as compared to silicon
crystal potential.
• And that is why the mobility of electron in Gallium Arsenide is very high if you apply force because the
mass is small the electron gains a high acceleration or high drift velocity in Gallium Arsenide as
compared to silicon.

20. • So the E0 variation is obtained from the drift efficient modal formula. So, here the relation between E0
and psi is E0/q = constant -psi or gradient of E0/q is E.
• Electron affinity is obtained from the E-k diagram and crystal potential. So, chi can be a function of x if
the crystal potential is varying with x as it happens in a heterostructure or compositionally graded
structure.
• So, if the doping varies in a semiconductor the function of x for example the energy gap can change as
the function of x. Energy gap can also change if the composition is varying as a function of x.