The bulk material is a collection of atoms having properties that are from individual atoms.
ELECTRON
DENSITY IN BULK MATERIAL
The
bulk material is a collection of atoms having properties that are from
individual atoms.
The
minute size of nanomaterials gives them unique electronic properties. One of
the major ways in which small-volume materials differ from bulk materials is
the number of available energy states. In a bulk material, the states within
each energy sublevel are so close that they blend into a band.
The
total number of electron states, N, with energies upto E, can be determined
based on quantum mechanics using the following equation
…....(1)
Here,
we represent the volume as V [V being the characteristic dimension of the
solid], m is the mass of an electron and h is the Plancks constant.
The
number of energy states per unit volume is given by
….....(2)
If
we differentiate the above equation with respect E, we get a relation for
density of states Z(E).
Density
of states is defined as number of available electron energy states per unit
volume, per unit energy
…....(3)
We
can write equation (2) as
……....(4)
The
most important thing to note about the density of states equation for a bulk
material is that it is proportional to the square root of energy.
…....(5)
The
specific electrical properties of semiconductors and superconductors will
depend on density of states.
The
most relevant application of density of states is that it provides information
about nanomaterials.
The
existance of energy state itself does not mean that it is occupied all the
time. The Fermi function gives us the probability of occupation by a free electron
in a given energy state.
i.e.,
Fermi function .........(6)
Multiplying
fermi function F(E) with density of states Z(E) will give us the number of free
electrons per unit volume per unit energy
……...(7)
To
be specific, the number of free electrons per unit volume
……..(8)
In
a conductor at T = 0K, [Hint: put F(E)= 1] or electron
density in a conductor at 0K is given by the number of free electrons
……...(9)
Physics for Information Science: Unit V: Nanodevices and Quantum Computing : Tag: : - Electron Density in Bulk Material
Physics for Information Science
PH3256 2nd Semester CSE Dept | 2021 Regulation | 2nd Semester CSE Dept 2021 Regulation