intrinsic and extrinsic semiconductors

8/13/2019 Intrinsic and Extrinsic Semiconductors

1/7

Fermi Distribution Function

It is a probability Distribution function. The Fermi function, F(E) , gives the

probability that a state at energy E is occupiedby an electron, given that E is

an allowed energy level.

Here EFis the Fermi energy, k is Botzmann constant and T is temperature in

Kelvin.

Fermi Energy:

TheFermi energy is the maximum energy occupied by an electron at 0K. By

the Pauli exclusion principle, we know that the electrons will fill all available

energy levels, and the top of that "Fermi sea" of electrons is called the Fermi

energy or Fermi level.
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/fermi.html#c1http://hyperphysics.phy-astr.gsu.edu/hbase/solids/fermi.html#c1


2/7

Throughout nature, particles seek to occupy the lowest energy state possible.

Therefore electrons in a solid will tend to fill the lowest energy states first.

Electrons fill up the available states like water filling a bucket, from the

bottom up. At T=0 , every low-energy state is occupied, right up to the Fermi

level, but no states are filled at energies greater than EF.

FF(E) = 1 for T = 0 K and E < E and

FF(E) = 0 for T = 0 K and E > E

FFor T 0 K and E = E

1F(E) =

2


3/7

For T>0 , some electrons can be excited into higher-energy states. This is

similar to a bucket of hot water. Most of the water molecules stick around the

bottom of the bucket. The Fermi level is like the water line. A fraction of water

molecules are excited and drift above the water line as vapor, just as

electrons can sometimes drift above the Fermi level.


4/7

Intrinsic and Extrinsic semiconductors

All semiconductors in their pure form are called intrinsic semiconductors. For

example Germanium, Silicon and various combinations from table below.

Combinations of column III V and II VI are also called semiconductors.

Extrinsic Semiconductors:


5/7

The electrical and optical properties of semiconductors can be substantially

altered by adding small controlled amounts of specially chosen impurities, or

dopants, which alter the concentration of mobile charge carriers by many

orders of magnitude. Dopants with excess valence electrons (called

donors)can be used to replace a small proportion of the normal atoms in the

crystal lattice and thereby to create a predominance of mobile electrons; the

material is then said to be an n-type semiconductor.

Thus atoms from group V (e.g., P or As) replacing some of the group IVatoms in an elemental semiconductor.

Atoms from group VI (e.g., Se or Te) replacing some of the group Vatoms in a III-V binary semiconductor, produce an n-type material.

A p-type material can be made by using dopants with a deficiency of valence

electrons, called acceptors. The result is a predominance of holes.

Group-IV atoms in an elemental semiconductor replaced with somegroup-III atoms (e.g., B or In).

Group-III atoms in a III-V binary semiconductor replaced with somegroup-II atoms (e.g., Zn or Cd), produce a p-type material.

Group IV atoms act as donors in group III and as acceptors in group V,and therefore can be used to produce an excess of both electrons and

holes in III-V materials.

The concentrations of mobile electrons and holes are equal in an intrinsic

semiconductor, n = p = ni, where n i increases with temperature at an

exponential rate.

Fermi Level

"Fermi level" is the term used to describe the top of the collection of electron

energy levels at absolute zero temperature. This concept comes fromFermi-

Dirac statistics. Electrons arefermions and by the Pauli exclusion principle

cannot exist in identical energy states. So at absolute zero they pack into the
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/disfd.html#c1http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/disfd.html#c1http://hyperphysics.phy-astr.gsu.edu/hbase/particles/spinc.html#c2http://hyperphysics.phy-astr.gsu.edu/hbase/pauli.html#c2http://hyperphysics.phy-astr.gsu.edu/hbase/pauli.html#c2http://hyperphysics.phy-astr.gsu.edu/hbase/particles/spinc.html#c2http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/disfd.html#c1http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/disfd.html#c1


6/7

lowest available energy states and build up a "Fermi sea" of electron energy

states. The Fermi level is the surface of that sea at absolute zero where no

electrons will have enough energy to rise above the surface.

At higher temperatures a certain fraction, characterized by theFermi function,

will exist above the Fermi level. The Fermi level plays an important role in

theband theory of solids. In doped semiconductors,p-typeandn-type, the

Fermi level is shifted by the impurities, illustrated by theirband gaps.

The illustration below shows the implications of the Fermi function for the

electrical conductivity of asemiconductor.Theband theory of solids gives the

picture that there is a sizable gap between the Fermi level and the conduction

band of the semiconductor. At higher temperatures, a larger fraction of theelectrons can bridge this gap and participate in electrical conduction.

Note that although the Fermi function has a finite value in the gap, there is no

electron population at those energies (that's what you mean by a gap). The

population depends upon the product of the Fermi function and theelectron
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/fermi.html#c2http://hyperphysics.phy-astr.gsu.edu/hbase/solids/band.html#c1http://hyperphysics.phy-astr.gsu.edu/hbase/solids/dope.html#c4http://hyperphysics.phy-astr.gsu.edu/hbase/solids/dope.html#c3http://hyperphysics.phy-astr.gsu.edu/hbase/solids/dsem.html#c1http://hyperphysics.phy-astr.gsu.edu/hbase/solids/intrin.html#c1http://hyperphysics.phy-astr.gsu.edu/hbase/solids/band.html#c5http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/disene.html#c2http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/disene.html#c2http://hyperphysics.phy-astr.gsu.edu/hbase/solids/band.html#c5http://hyperphysics.phy-astr.gsu.edu/hbase/solids/intrin.html#c1http://hyperphysics.phy-astr.gsu.edu/hbase/solids/dsem.html#c1http://hyperphysics.phy-astr.gsu.edu/hbase/solids/dope.html#c3http://hyperphysics.phy-astr.gsu.edu/hbase/solids/dope.html#c4http://hyperphysics.phy-astr.gsu.edu/hbase/solids/band.html#c1http://hyperphysics.phy-astr.gsu.edu/hbase/solids/fermi.html#c2


7/7

density of states.So in the gap there are no electrons because the density of

states is zero. In the conduction band at 0K, there are no electrons even

though there are plenty of available states, but the Fermi function is zero. At

high temperatures, both the density of states and the Fermi function have

finite values in the conduction band, so there is a finiteconducting population.

Fermi level in Intrinsic Semiconductor

The Fermi level in intrinsic semiconductor is given by

c v vF

c

E E N1E = ln( )

2 2kT N

Ncand Nv are density of holes and electrons in conduction and valance band,

respectively. Since hole and electron density are equal in intrinsic

semiconductor so Fermi energy is the average of the valance and conduction

band energy.

Therefore Fermi level lies in mid of band.

Fermi level in Extrinsic Semiconductor
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/disene.html#c2http://hyperphysics.phy-astr.gsu.edu/hbase/solids/fermi.html#c4http://hyperphysics.phy-astr.gsu.edu/hbase/solids/fermi.html#c4http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/disene.html#c2

intrinsic and extrinsic semiconductors

Documents