SEMICONDUCTOR PHYSICS

BAND THEORY OF SOLIDS

 Ge and Si are pure semiconductors  Electronic configuration of Si is  1S 2, 2S 2, 2P 6, 3S 2, 3P 2  P level is partially filled with 2 electrons  Let N be the number of atoms in Si crystal  Out of the 4 valence electrons,2N electrons are in 2N S states and 2N electrons are in the available 6N P states  In an isolated atoms the energy levels are as shown  When the atomic distance is reduced the 6N states spreads out and forms an energy band. Band theory cont……d

 Similarly the 2N electrons forms another band  The two bands are separated by a gap  When the atomic distance is further reduced, the energy gap decreases and the upper and lower bands merges into one  Finally when the inter atomic distance is very small, the energy bands again split apart and are separated by an energy gap E g  Here total number of 8N states are distributed equally- 4N in upper and 4N in lower band.  Lower band is completely filled with valence electrons and is called valence band  Upper band is empty and is called conduction band. Band theory cont…..d

There are 3 bands in solids.

INSULATORS  poor conductors  Forbidden Band is vey wide (6 to 19 eV), V.B is completely filled up, C.B is vacant  Electrons closely bound to the atom, cannot jump from valance band to conduction band even if a large E.F is applied CONDUCTORS  C.B and V.B are overlapping each other  No forbidden band in conductors  There is a large no of free electrons  Conduction is due to these free electrons  Electrons can move freely from valence band to conduction band and they conduct electricity.A very small E.F is enough for this.

SEMICONDUCTORS  Conductivity- between conductors and insulators.  Forbidden band is very small ̴1 eV( eg.Si=1.1 eV and Ge=0.7 eV) and hence many electrons can jump from the valence band to the conduction band by acquiring energy required  At 0 K, V.B is completely filled up, C.B empty  When temp. increases electrons gain K.E and cross the F.B and reach the C.B  So negative temperature coefficient of resistance.

CLASSIFICATION OF SEMICONDUCTOR Semiconductors are classified in to two types (i) Intrinsic semiconductors (ii) Extrinsicsemiconductors n – type semiconduct or p – type semiconduc tor

Si  Intrinsic semiconductors

Si FREE ELECTRON HOLE

 A semiconductor in an extremely pure form is known as an intrinsic semiconductor.  As temp increases, some electrons cross forbidden gap and reach conduction band this accounts for electrical conductivity of the semiconductor n e = n h = n i  Its conductivity is called intrinsic conductivity. Ge and Si are best examples At 0K,no free charge carriers.(V.B filled,C.B empty)

FERMI LEVEL AND FERMI ENERGY

In a crystal, it is not necessary that all levels in a band is occupied by an electron The level occupied by an electron of maximum energy at zero Kelvin is called Fermi level. The energy corresponding to this level is called Fermi energy. Fermi level is the highest energy level of an electron in the valence band of a crystal in its ground state FERMI LEVEL AND FERMI ENERGY

EXTRINSIC SEMICONDUCTORS INTRINSIC SEMICONDUCTORS N-TYPEP-TYPE

 EXTRINSIC SEMICONDUCTORS  DOPING  CONDITIONS OF DOPING  METHODS OF DOPING

 Doped Semiconductors

Doping is the process of adding impurities to pure semiconductors for increasing conductivity CONDITIONS OF DOPING METHODS OF DOPING Doping and Doped Semiconductors 1.The presence of dopant atom must not disturb the crystal lattice 2.The dopant atom must take the position of the semiconductor atom. 3.The size of dopant atom should be the same as that of crystal atom. 4.Concentration of dopant atoms should not be large. 1.By bombarding the semiconductor by ions of dopant atoms 2.By heating the semiconductor in an atmosphere of dopant atoms 3.By adding the impurity atoms in the melt of semiconductor.

Si

B TRIVALENT IMPURITY P-TYPE SEMICONDUCTOR

 If an atom of 3 valence electrons(trivalent-B,Al,Ga) is added into the pure semiconductor,there is a defficiency of one valence electron in trivalent atom to form covalent bond.  This deficiency of valence electron is called hole(+ve charge carrier).Depending on the impurity concentration large number of holes.  These holes are filled up by neighbouring electrons.In this way hole moves from one atom to another and contribute to the conductivity of crystal.  Majority carriers- HOLES  Minority carriers- ELECTRONS  Since trivalent atom accepts an electron it is called acceptor atom.  n e ≠ n h (n h >> n e )

 In p-type,Fermi level near to valence band

Si

P PENTAVALENT IMPURITY

 If an atom of 5 valence electrons(pentavalen-P,Sb,As) is added into the pure semiconductor,out of 5, 4 valence electrons form covalent bond and one become free.  This -vely charged free electron is responsible for conduction. Depending on the impurity concentration large number of electrons  In N- TYPE,  Majority carriers- electrons  Minority carriers- holes  Since pentavalent atom donates an electron it is called donor atom.  n e ≠ n h (n e >> n h )

 In N-type,Fermi level near to conduction band

DIFFERENCE BETWEEN INTRINSIC AND EXTRINSIC SEMICONDUCTORS???

DIFFERENCE BETWEEN P-TYPE AND N -TYPE SEMICONDUCTORS?

FERMI LEVEL IN INTRINSIC AND EXTRINSIC SEMICONDUCTORS

FERMI LEVEL IN INTRINSIC SEMI CONDUCTORS

Electron and hole concentrations in intrinsic semiconductors at thermal equilibrium

Consider an intrinsic S.C at thermal equilibrium at a temp at T K. The following assumptions are made 1.The energy is measured from the top of valence band 2.The lattice modifies the free electron mass from m to m n in the C.B and the mass of the hole from m to m p in the valence band. 3.The electron density(the number of electrons per unit volume)I the C.B at an energy state E is given by Electron and hole concentrations in intrinsic semiconductors at thermal equilibrium

N n (E)= 4. The hole density in the valence band is given by N p (E)= 5. The probability of filling an energy state E is given by Fermi Function f(E)= Where E F is the Fermi energy and K Boltzman’s con. Assumptions cont….…d

Electron concentration in the C.B of an intrinsic semiconductor

Hole concentration HereE V =0 ( as per assumption 1) Hole concentration in the V.B of an intrinsic semiconductor

Add figure Fermi level E F is exactly at the middle of forbidden band. Fermi level in intrinsic semiconductors

Fermi level in n-type extrinsic semiconductors Fermi level is just below the bottom level of conduction band. When temp. rises Fermi level gets lowered and at very high temp. it approaches the middle level and the conductor behaves like intrinsic semiconductor

In the n type semiconductor,with increasing impurity concentration,Fermi level moves closer & closer to the conduction band & finally moves in to the conduction band

Fermi level in p-type extrinsic semiconductors Fermi level is just above the top of the valence band. When the temp rises Fermi level also rises. At a very high temp, the Fermi level approaches the middle of the forbidden band and it behaves like intrinsic semiconductor.

In the p type semiconductor,with increasing impurity concentration,Fermi level moves down closer to the valence band & finally at very high impurity concentration it will shifts in to the valence band

when an impurity is added to the intrinsic semiconductor for increasing the number of electrons in the C.B, there must be a corresponding decrease in the number of holes in V.B