1.1) Energy bands in solids:
(i) In solids, the group of closely lying energy levels is known as energy band.
(ii) In solids the energy bands are analogous to energy levels in an atom.
(iii) In solids the atoms are arranged very close to each other. In these atoms there are discrete energy levels of electrons. For the formation of crystal these atoms come close together, then due to nucleus-nucleus, electron-electron and electron-nucleus interactions the discrete energy levels of atom distort and consequently each energy level spits into a large number of closely lying energy levels.
(iv) The number of split energy levels is proportional to the number of atoms interacting with each other. If two atoms interact then each energy level splits into two out of which one will be somewhat above and another will be somewhat below the main energy level. In solids the number of atoms is very large (>>1023). Hence each energy level splits into large number of closely lying energy levels. Being very close to each other these energy levels assume the shape of a band.
(v) In an energy band, there are 1023 energy levels with energy difference of 10–23 ev.
(vi) Curve between energy and distance i.e. U-r curve.
(a) When two atoms are interacting:
(b) When 1023 atoms are mutually interacting:
2) THREE TYPES OF ENERGY BANDS IN A SOLID, VIZ.
(a) Valence energy band
(b) Conduction energy band
(c) Forbidden energy gap.
Conduction Energy Band
In this band there are valence electrons.
No electrons are found in this band
In this band the electrons are rarely found
This band may be partially or completely filled with electrons.
This band is completely empty.
This band is either empty or partially filled with electrons.
In this band the electrons are not capable of gaining energy from external electric field.
In this band the electrons can gain energy from electric field.
The electrons in this band do not contribute to electric current.
Electrons in this band
contribute in this band
contribute to electric current.
In this band there are electrons of outermost orbit of atom which contribute in band formation,
In this band there are electrons which are obtained on breaking the covalent bands,
This is the band of maximum energy in which the electrons are always present.
This is the band of minimum energy which is empty.
This band can never be empty.
This band can be empty.
3) MORE ABOUT ENERGY BANDS:
(1) The conduction band is also known as first permitted energy band or first band.
(2) As there are energy levels f electrons in an atom, similarly there are three specific energy bands for the electrons in the crystal formed by these atoms as shown in the figure
Fig: Energy bands
(3) Completely filled energy bands: The energy band, in which maximum possible number of electrons are present according to capacity is known as completely filled bank.
(4) Partially filled energy bands: The energy band, in which number of electrons present is less than the capacity of the band, is known as partially filled energy band.
(5) Electric conduction is possible only in those solids which have empty energy band or partially filled energy band.
(6) Energy gap or Band gap (Eg):
(a) The minimum energy which is necessary for shifting electrons from valence band to conduction band is defined as band gap (Eg)
(b) The forbidden energy gap between the valence band and the conduction band is known as band gap (Eg). i.e. Eg = Ec – Ev
(i) On the basis of band structure of crystals, solids are divided in three categories.
(ii) Difference between Conductors, Semi-conductors and Insulators:
Electrical conductivity and its value
Between those of conductors and insulators i.e. 10-7 Ω/m to 10-13 Ω/m
Negligible 10-13 Ω/m
Resistivity and its value
Negligible Less than 10-5Ω-m
Between those of conductors and insulators i.e. 10-5Ω-m to 105Ω-m
Very high more than 105Ω-m
Energy gap and its value
Zero or very small
More than that in conductors but less than that in insulators e.g. in Ge, ΔEg =0.72 eV is
Si, ΔEg =1.1 eV in Ga As ΔEg =1.3 eV
Very large e.g. in diamond ΔEg = 7 eV
Current carriers and current flow
Due to free electrons and very high
Due to free electrons and holes more than that in insulators
Due to free electrons but negligible.
Condition of valence band and
conduction band at ordinary temperature
The valence and conduction bands are completely filled or conduction band is some what empty (e.g. in Na)
Valence band In somewhat empty and conduction band is
Valence band is completely filled and conduction band is completely empty.
Behaves like a superconductor.
Behaves like an insulator
Behaves like an insulator
Temperature coefficient of resistance (α)
increasing temperature the number of current carriers
On mixing impurities their
Current flow in these takes place
Does not take place
Cu. Ag, Au, Na, Pt, Hg etc.
Ge, Si, Ga, As etc.
Wood, plastic, mica, diamond, glass etc.
(a) Semi conducting elements are tetra-valent i.e. there are four electrons in their outermost orbit.
(b) Their lattice is face centered cubic (F.C.C.)
(c) The number of electrons or cotters is given by:
i.e. on increasing temperature, the number of current carriers increases.
(d) There are uncharged.
Fig: Example of different semi-conductors
(e) Holes or cotters:
(1) The deficiency of electrons in covalent band formation in the valence band in defined as hole or cotter,
(2) These are positively charged. The value of positive charge on them is equal to the electron charge.
(3) Their effective mass is less than that of electrons.
(4) In an external electric field, holes move in a direction opposite to that of electrons i,e. they move from positive to negative terminal.
(5) They contribute to current flow.
(6) Holes are produced when covalent bonds in valence band break.
Fig: Transfer of electrons from valence band to conduction band
(i) The semiconductors are of two types:
(a) Intrinsic or pure semiconductors
(b) Extrinsic or dopes semiconductors
(ii) Difference between intrinsic and extrinsic semiconductors:
Pure Ge or Si is known as intrinsic semiconductor
The semiconductor, resulting from mixing impurity in it, is known as extrinsic semiconductors.
Their conductivity is low (because only one electron in 109 contribute)
Their conductivity is high
The number of free electrons (m in conduction band Is equal to the number of holes pi in valence band.)
In these ni ≠pi
These are not practically used
These are practically used
In these the energy gap is very small
In these the energy gap is more than that in pure semiconductors.
In these the Fermi energy level lies in the middle of valence band and conduction
In these the Fermi level shifts towards valence or conduction energy bands.
(a) At absolute zero temperature (0 K) there are no free electrons in them.
(b) At room temperature, the electron-hole pair in sufficient number are produced.
(c) Electric conduction takes place via both electrons and holes.
(d) The drift velocities of electrons and holes are different.
(e) The drift velocity of electrons (Vdn) is greater than that of holes (Vdp).
(f) The total current is I = In + Jp
(g) In connecting wires the current flows only via electrons.
(h) The current density is given by
Where Vdn = drift velocity of electrons
μn = mobility of electrons
Vdp = drift velocity of holes
μp = mobility of holes
(i) The electric conductivity is given by s = nq(mn + mp)
(j) Mobility of electron mn = Vdn / E
k) Mobility of holes mp = Vdp/E
(l) At room temperature sGe > sSi because nGe > nSi
where nGe = 2.5' 1013/cm3 and nSi = 1.4' 1010 /cm3
(a) Doping: The process of mixing impurities of other elements in pure semiconductors is known as doping.
(b) Extrinsic semiconductors: the semiconductors, in which trivalent and pentavalent elements are mixed as impurities, are known as extrinsic semiconductors.
(c) The extrinsic semiconductors are of two types:
(i) N-type semiconductors
(ii) P-type semiconductors.