Physics

2. Electron configuration of atoms:-
The four quantum numbers specify the electron state in atom.
• Principal quantum number, (no. of electrons, e- = 2n2)
n = 1,2,3,4 i.e. K, L, M, N….
• Orbital quantum numbers l= 0, 1, 2….. (n-1) i.e. S, P, d, f.
Electrons in sub shells s=2 ,p= 6 ,d=10 , f= 14
• Magnetic quantum numbers ml= 0, ±1, ±2
• Spin quantum numbers (ms) or (s) by ± 1/2
Pauli’s exclusion principle
“No two electrons in an atom can have the same set of four
quantum numbers n, l, ml & ms ”
UNIT –IV :SEMICODUCTOR PHYSICS

3. law which relates the thermal conductivity (κ) and the electrical conductivity(σ) of a
material which consists of somewhat freely moving electrons in it.
Thermal Conductivity (κ): It is the degree (measure) of capacity of a material to
conduct heat.
Electrical Conductivity (σ): It is the degree (measure) of capacity of a material to
conduct electricity.
Definition:- “The ratio of the thermal conductivity of a material to the electrical
conductivity of a material (metal) is directly Proportional to the temperature.”
Wiedemann-Franz law

4. Classical free electron theory

5. Failure of Classical free electron theory

6. Band theory of solids:-
•A single isolated atom has discrete energy levels .but if two atoms come closer to each other,
they interact & significant change in their energy levels observed.
•To form a solid, large numbers of atoms are required; they are close to one another.
•Every atom’s energy levels are affected by neighboring atom energy levels.
•Inner shell energy levels of atoms are not affected much more by neighboring atom.
•But outer energy levels of atoms are changed considerably, since these electrons are shared by
more than one atom of crystal.
•As per Pauli’s principle, not more than two interacting electrons have same energy levels.
•Therefore new energy levels must be established, which are discrete but infinitesimally
different.
•This closely spaced group of discrete energy levels is called an energy band.
•Thus in solids ,the allowed energy levels of an atom are modified by nearness of other atoms.
•Every discrete level of an individual atom gives rise to a band in solids ,i.e. in a solid
containing N atoms, there are N possible levels in each band & they can be occupied by 2N
electrons. Image for Understanding only

7. valence band, conduction band & forbidden band:-
Valence band: -
Definition: “A band which is filled by the
valence electrons” or” a band having highest occupied
band energy “OR” The bond formed by the series of
energy levels containing valence electrons.”
[Valence electrons: The electrons present in outermost
orbit of shell of atoms]
A valence band is completely filled at O K.
It may be partially fulfill or completely fulfill with
electrons.
ii) Conduction band: -
Definition: - “The next higher permitted energy
band” OR “Lowest unfilled permitted energy band”
It may be either empty or partially filled with
electron.
iii)Forbidden band:-
Definition : “conduction band & valence band
are separated by a region or a gap known as forbidden
band/gap” OR “band collectively formed by a series of
non permitted energy levels above the top of valence
band to bottom of conduction band”[suffix-> Eg]
It is always empty.

8. Give classification of Insulator, semiconductor &conductors on energy band
diagram:-
Insulators:-
•V.B. tightly bound to nucleus &
no free electrons.
•For electron in V.B. required high
energy to go to C.B.
•Resistivity= ρ= 1012Ω - cm
•C.B. Vacant
•V .B. Completely filled
•Energy Band gap= 5 ev to 15 ev
•R α 1/T (Negative Temperature
coefficient))
•e.g. Mica, diamond, quartz.
•No conductivity at normal
conditions/supply
Semiconductor:-
•Electrons loosely bound to nucleus
require less energy to separate out.
•Resistivity =ρ = 106Ω in between
conductor & insulators
•Band gap 1-2eV
•CB – empty VB – completely
filled.
•R α 1/T ((Negative Temperature
coefficient))
•Small energy required for e- to go to
VB from CB
•e.g. Gallium arsenide (GaAS) ,
Cadmium supplied(CdS)
Conductors:-
•Free electrons in CB at N.T.P.
free to move in specimen.
•Resistivity =ρ = 10-6 Ω-cm
(10w)
•R α T (Positive Temperature
coefficient)
•Low energy for electron to
give conductivity.
•C.B. & V.B. overlaps on one
another.
•e.g. Cu,Al,Ag,….

9. Explain types of semiconductors in detail :-
INTRINSIC SEMICONDUCTOR

10. Influence of external factors on conductivity:-

11. Define
Mean Free time;- “ average time between
collisions is called mean free time”
Mean free path:- “ length of the path
during this free time is called mean free
path”
Drift Velocity:-
Valence electrons are not attached to atoms in conductors but free to move in all
directions called conduction electrons & forms free electrons cloud or free electron
gas or Fermi gas.
In absence of external electric field electrons move randomly in all directions, but
in presence of electric field electron get directed to specific direction called “drift” &
having drift velocity (with which they move) which depends on electron mobility &
applied electric field E.
Drift velocity is given by
µe - mobility of charge carrier/Electron
E - Electric field intensity

12. Derive expression for conductivity of semiconductor :-
In semiconductor current flow is due to e-
flow of electron & hole. The conductivity of
conductor is given by σ = neμ
A = cross section area
V= applied voltage
I=n e v A
E= V
l
Important
Formulae

13. Conductivity of Intrinsic Semiconductor:-
For the intrinsic semiconductor ,the electron concentration is equal
to hole concentration
i.e. n= p = ni (Intrinsic charge carrier concentration)
Hence Conductivity of Intrinsic semiconductor is
Therefore Neglecting hole concentration ,the
conductivity of n-type semiconductor can be
written as
Conductivity of Extrinsic Semiconductor:-
i)N-Type Semiconductor
For the Extrinsic N type semiconductor ,the electron
concentration is much more than hole concentration
i. e. n >> p
ii ) P-Type Semiconductor :
In P-Type Semiconductor ,Electron
Concentration is Negligibly small in
comparison with hole concentration
i.e. p >> n
a=concentration of acceptor atoms
Conductivity of
conductor

14. Fermi level in conductor: - Ef
Definition:-
“The highest filled state in the highest energy band which contains electrons in a metal, at 00K
called the Fermi level & its corresponding energy is called Fermi energy.”
Significance -
•At o k all energy states up to Ef are occupied & all above states are empty .
•At high Temperature, the random thermal energy can excite electrons to higher energy states &
there may be some empty states below Fermi level.
Fermi level in semiconductor: - Ef
Definition:-
“The energy which corresponds to the centre of gravity of conduction electrons & holes weighted
according to their energies.”
Significance -
•Ef lies in between conduction band & valence band
•For intrinsic semiconductor, Ef lies exactly at middle of conduction band & valence band.
•For each electron in conduction band, there is a hole in valence band.
Conduction
band
Conduction
band
Valence
Band
Valence
Band
intrinsic semiconductor

15. Fermi Dirac probability distribution function: -
the distribution of electrons over a range of allowed energy
level of thermal equilibrium is given for conductors by FD
statics. As per this, the probability that energy state of energy
E will be occupied by an e- at temp. T0K is given by
K : Boltzmann constant , P(E): Probability of Energy level having electrons
EF : Fermi energy
P (E) = 1 => at o0K all energy levels between
zero & EF are completely filled.
P (E) = 0 => all energy levels E > EF are completely empty
P(E) = ½ => at E= EF. Energy levels
has 50% probability of being occupied .

16. Fermi level in intrinsic semiconductors:-
Probability of an electron occupying a state of energy is E .
Width of V.B. & C.B are small compared to Forbidden Band (Energy
Band Gap) i.e. Eg
Conduction Band => EC & Valence Band => EV
At 0oK semiconductor acts as insulator.
Conduction Band is completely empty at any temperature say ToK
Let NC= no. of e-s in Conduction Band (C.B.)
NV = no. of e-s in Valence Band (V.B. )
N= NC + NV = total no. of electrons in both bands
Fermi level of intrinsic semiconductors is exactly at middle of C.B. & V.B. or
at centre position of F0rbidden Band (F.B.)

17. Position of Fermi level in extrinsic semiconductors:-
Concentration of free e-s in C.B. is much higher
than that of free holes in V.B. Hence Fermi level
get shifted towards C.B. at 0oK the EF lies
between conduction band energy level EC (Close
& Below of Conduction Band)& donor energy
level Ed.(Above Of donor energy level )
With increase in temperature, the
Concentration of free e-s & holes changes & also
Fermi level changes .at T > 0oK, the EF shift below
donor level, but always well above centre of
forbidden band. Typical position of Fermi level at
300 oK is
ii) Position of EF in p-type
semiconductor:-
i) Position of EF N- type
semiconductors:-
Hole concentration in V.B. is greater than the e-
concentration in C.B., hence Fermi level is lies
above the top of V.B. At 0oK, the Fermi level
lies between the valence band energy Ev (Close
& Above Valence Band)& acceptor energy level
Ea (Below of acceptor energy level )
As temp. rises , e-s are intrinsically
available in C.B. , hence Fermi level may be shift
above acceptor level, but is always well below
the centre of forbidden band. Typical position of
Fermi level at 300o K.
EC > EFn >Ed >EFi >EV
Donor Energy Level -Ed
EC > Ed >EFn >EFi >EV EC > EFi >Ea >EFp >EV
Acceptor Energy Level -Ea
EC > EFi >EFp >Ea >EV

18. Explain energy band diagram of P-N junction diode:-
I) Zero bias: - let us consider a P-N junction formed by fusing P- type & N- type
semiconductors. In this case, after fusing the solids, the electrons in the total system
become one family & the Fermi levels will have to align so that there exists a single
Fermi energy level for the entire specimen.
In P- type, the Fermi level is close to top of valence band & in N- type it is close
& below of conduction band. The e-s moves across the boundary to the P- side &
equalize the Fermi levels. The band edges in the two specimen shifts themselves to
make the alignment of Fermi level s, & the energy band diagram changes.
Conduction band-p Conduction band -N
Valence band-p
Valence band-N
EF i-Intrinsic
fermi
EFN
EFp

19. ii) Forward bias :- In forward bias p- connected to
positive & N connected to negative of battery . Hence
equilibrium conditions are disturbed, hence energy
bands, & Fermi levels are altered. The band picture of
P-N junction diode in forward bias as below.
As –ve terminal of battery is connected to N,
the e-s energy in N side increases by an amount eV, ( V
is applied voltage) due to this Fermi level rises by eV
& position of the energy bands are adjusted so as to
match with the elevation of Fermi level. due to
increase in energy on the N- side, the potential barrier
is reduced to e(VB-V) , therefore the e-s crossing the
junction from N-side into P-region will now see a lower
potential barrier as compared to the zero bias
potential is greater than barrier potential, then
conduction takes place in P-N junction diode when.
eV ≥ eVB
iii) Reverse bias:-
In case of reverse bias, N connected to
+ve &P to –ve of battery, energy of e-
decreases by eV, Fermi level on N lower
by amount eV. Increasing the potential
barrier height to e(VB + V) & also
depletion region increases .
If majority e-s on N face larger
potential barrier increasing the
junction(Depletion region), hence
decrease in no of e-s Crossing from N-
side to P-side because of this current is
reduced to a lower value.
Explain energy band diagram of P-N junction diode:-
Zero Bias /Unbiased Forward Bias Reverse Bias

20. Hall effect:- “If a piece of conductor (metal or semiconductor ) carrying a
current is placed in a transverse magnetic field, an electric field is produce inside
the conductor in a direction normal (perpendicular) to both the current &
magnetic field. ”
This phenomenon is known as “Hall effect” & voltage generated is called
“Hall Voltage”.
VH = Hall voltage
RH = 1 ….. Hall coefficient.
ne
VH = RH . BID = RH B JD
A
J
J= I Current Density
A
Hall coefficient:-If W is width of sample then
A = D x W
VH = RH BID = RH BI
DW W
RH = w VH = 1
BI nq

21. Applications of Hall effects:-
i)Determination of type of semiconductor:-
If VH &RH (hall coeff.) is –ve N type of semiconductor
If VH & RH (hall coeff.) is +ve P type of semiconductor
Sign decides type of semiconductor
ii)Calculations of charge carrier concentration: - Hall voltage is measured by placing
two probes at the centers of top & bottom faces of sample.
If B = mag. Flux density = wb/ m2
n= 1 [ RH = 1 ]
e RH ne
& RH = VH W RH & n can be calculated
BI
iii) Determination of mobility:-
If conduction is due to one type of charge carriers. e.g. e-s then
σ = n e μ e
μ e = σ
ne
μ e= σ . VH W
BI
Knowing σ & RH we can determine mobility of e-s.

22. Barrier Potential of PN junction Diode:-
V0=VB=
e=
VT =
VT= Volt Equivalent of Temperature = Temperature Equivalent

23. Ideal Diode Equation :-
J
But
Above Equation can Be written as …Ideal Diode Equation
Io -Reverse saturation current

24. DENSITY STATES:-
“The number of available states per unit volume per unit energy interval
centered around E.”
OR
“The number of possible electron quantum energy states between E & E+dE per
unit volume ”
g(E) dE =4π(2m)3/2 E1/2dE
h3

25. Effective Mass :- Effective Mass of an electron in a band with a given (E,K)
relationship can be given by
m = h2
d2E/dk2

26. Photovoltaic effect :-the emf is generated across an open circuited P-N junction called
photovoltaic effect.
Solar Cells:-Light energy converted into electrical energy
I-V characteristics of solar cell:-
Open circuit voltage (Voc) :- If RL ∞, Output voltage is Voc .
Short circuit current (ISC) :- if RL 0, output current is known as ISC.
Vm & Im :- Vm : maximum voltage & Im : maximum current.
Fill factor;- the ratio of maximum useful power. To Ideal power.
Max. useful power Im Vm Efficiency = output power
F.F. = = Input power
Ideal power ISC Voc
•Solar cell made up of semiconductors like Si + Boron /
phosphorous.
•P- type is thin layer (≈ 0.2 to 0.5 μm) with anti reflecting coating.
•P thin e- hole pair reach junction quickly.
•In between P&N semiconductors ,PN junction is their having
potential barrier Eg
•If terminal short => ISC
•If photon energy i.e. h v > Eg => conduction across cell.
•I α light intensity & I α A (surface area).

29. Some of Applications of solar energy
1. Power plants: In conventional power plants non-renewable energy sources are used to boil
water and form stream so that turbines can rotate and water to produce electricity. But with
application of solar energy heat of sun can boil that water to create steam and rotate turbines. To
convert sunlight into electricity solar panels, photoelectric technologies and thermoelectric
technologies etc are used.
2. Homes: Use of solar energy is increasing in homes as well. Residential appliances can easily
use electricity generated through solar power. Besides this solar energy is running solar heater to
supply hot water in homes. Through photovoltaic cell installed on the roof of the house energy is
captured and stored on batteries to use throughout the day at homes for different purposes. In this
ways expenditure on energy is cutting down by home users.
3. Commercial use: on roofs of different buildings we can find glass PV modules or any other
kind of solar panel. These panels are used there to supply electricity to different offices or other
parts of building in a reliable manner. These panels collect solar energy from sun, convert it into
electricity and allow offices to use their own electrical power for different purposes.
4. Ventilation system: at many places solar energy is used for ventilation purposes. It helps in
running bath fans, floor fans, and ceiling fans in buildings. Fans run almost every time in a
building to control moisture, and smell and in homes to take heat out of the kitchen. It can add
heavy amount on the utility bills, to cut down these bills solar energy is used for ventilation
purposes.
5. Power pump: solar power not just help in improving ventilation system at your homes but with
that it can also help in circulating water in any building. You can connect 6- power pump with solar
power supply unit but you must run it on DC current so that water circulate throughout your home.
6. Swimming pools: swimming pools are great joy for kids and adults in all seasons. But during
winters it is tough to keep water hot in these pools with minimum power usage. Solar energy can
help many in this matter as well. You can add a solar blanket in the pool that will keep the water
hot with energy generated from sunlight. Besides this you can install a solar hot water heating
system with solar hot water heating panels.

30. 7. Solar Lighting: these lights are also known as day lighting, and work with help of
solar power. These lights store natural energy of sun in day time and then convert
this energy into electricity to light up in night time. Use of this system is reducing
load form local power plants.
8. Solar Cars: it is an electrical vehicle which is recharged form solar energy or
sunlight. Solar panels are used on this car that absorb light and then convert it into
electrical energy. This electrical energy is stored in batteries used with the car, so
that in night time as well we can drive these vehicles.
9. Remote applications: Remote buildings are taking benefit of solar energy at vast
scale. Remote schools, community halls, and clinics can take solar panel and
batteries with them anywhere to produce and use electric power.
Points to remember:-
i) Fermi of N- type:-below & close to CB above EFin
ii) Fermi of P- type:- above & close to VB &below EFin
iii) In forward bias:-energy of e-increases by eV, EC & EV increases by eV
fermi increases by eV& potential barrier decreases by eV
iv) In reverse bias: - of e-decreases by eV, EC &EV &EFN decreases by eV &
potential barrier increases by eV.