Unit-2
Semiconductor Physics
Prof.K.Surendranath
RVR&JC College of Engineering
What is a semiconductor ?
❖ Semiconductor is usually defined rather loosely as a material with
electrical resistivity lying in the range of 10-2 - 10-9 Ω Cm with
energy gap less than 3eV.
Properties:
1.
2.
3.
4.
5.
6.
Negative temperature coefficient of Resistance (α is -ve)
Photoconductivity
Large Seebeck Coefficient (S)
Large Hall coefficient (RH)
Rectification
Carrier concentration (n= 1015/cm3)
SemiConducting materials:
1.
Elemental Semiconductors: IV group elements
In the periodic table as Si,Ge are most common
used semiconductors.
2 Compound SemiConductors:
a)
Binary SemiConductors: Compounds from III and V or II and VI group
Eg: GaAS, InP, ZnS
SemiConducting Materials:
b) Ternary Semiconductors: Compounds formed from two elements of group III
with one element of group V (or one from group III with two from Group V) are
important ternary semiconductors. (AIx Ga1-x As) for example, is a ternary
compound with properties intermediate between those of AlAs and GaAs,
depending on the compositional mixing ratio x
SemiConducting Materials:
c) Quaternary Semiconductors: These compounds are formed from a mixture
of two elements from Group III with two elements from group V.An example is
provided by the quaternary (In1-xGax)(As1-xPx), whose band gap energy
E, varies between 0.36 eV (InAs) and 2.26 eV (Gap)
Classification of Semiconductors:
Intrinsics Semiconductors:
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❖
❖
❖
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Pure crystalline semiconductors are known as “Intrinsic semiconductors”
Concentration of electrons = concentration of holes ( n=p)
Rate of generation = Rate of recombination ( G = R )
Rate of generation depends on Temperature and material
Rate of recombination depends on concentration of electrons and holes
R= rnp
Classification of Semiconductors:
Extrinsic Semiconductors:
Donor and acceptor energy levels:
According to quantum theory of hydrogen like atom the ground state energy is
given by EH = = -13.6ev and rH =
= 0.53A0
Adopting the same to donor impurity in n-type semiconductor
ED =
for Єr = 11.7 and
, ED = -0.02eV = 20meV and
rH =31A0 . thus donor orbitals overlaps at low concentrations
Carrier concentration in an Intrinsic
semiconductor
Carrier concentration in an Intrinsic
semiconductor
Derivation:
Problems:
Ln ni = C - EG/2kT , Plot Ln ni vs 1/T
ni2 = nop0 is known as law of mass action and it is valid for any
semiconductor at equilibrium
Conductivity equation:
Mobility also depends on temperature but its contribution will not comparable
with the exponential term.
Expressing n0 and p0 to ni and pi
Extrinsic semiconductors: n-type
p-type
problem:
Non Degenerate semiconductors:
Degenerate Semiconductors:
Ionization of Impurity atoms:
Let ND and NA be the concentration of donors and acceptor impurities in
Semiconductor. When donor atoms donate an electron to C.B they ionized as N +D
and acceptors will be ionized as N-A by accepting an electron from V.B.
Let N0D and N0A be the concentrations of unionized atoms.
Then ND = N+D + N0D —------------ 1
NA = N-A + N0A —----------- 2
Statistics of Donors and Acceptors
Then
—--------- 3
where ½ is known as degeneracy factor , due to each donor level occupied by
single electron. Then
Statistics of Donors and Acceptors
In the case of acceptor impurities
Complete Ionization and freeze out
Charge neutrality and Compensated
semiconductor:
At room temperature, all doping impurities are ionized, therfore
Then
Electron and hole concentrations in n and p type
semiconductors:
Problem:
Calculation of Fermi level:
Let
where
is fermi potential
Temperature dependence:
Drift and diffusion
Einstein relation:
At thermal equilibrium:
Recombination and Generation:
Recombination : It is a process in which electron and holes are annihilated or
destroyed.
Generation : A process by which electron and holes are created.
We know that at thermal equilibrium ni2 = n0p0 is valid for any semiconductor.
Excess carriers can be introduced in semiconductor by supplying thermal energy
or illuminating the sample by light causes a non equilibrium condition.
Equilibrium will be restored by recombination of minority excess charge carriers
with majority carriers. In this process heat energy will be dissipated to the lattice.
Recombination and generation:
The continuous thermal vibration of lattice atom
cause bond breakup.In term of energy band this
scenario is represent by enabling valence electron to make an upward transition to
the conduction band leaving hole in the valence band.
This process is called carrier generation and represented by generation rate G.
When the electron makes a transition downward the from the conduction band to the
valence band the electron hole pair is annihilated.
Recombination and Generation
This reverse process is called recombination. Represented by R
The rate of the recombination R is expected to be proportional to the number of
electrons available in the conduction band and number of hole in the valence band.
R = r n0p0 —---------- (1)
Under thermal equilibrium the generations rate should be equal to the recombination
rate.
G= R = r n0p0 —-------(2)
If non equilibrium condition created then the concentration of electrons and holes
will be (n0+Δn) , (p0+Δp) respectively , where Δn , Δp are excess electrons and
holes.
The rate at which excess holes recombine at any instant is
Hall effect:
Def: When a current carrying conductor ( metal/ semiconductor) placed in a
transverse magnetic field , a potential known as Hall potential will be observed
due to Hall fieled perpendicular to both current and magnetic field directions.
Importance of Hall effect:
1)
2)
3)
Sign of Charge carriers (+ve or -ve)
Concentration of charge carriers
Ratio of mobility to conductivity(μ/𝝈)
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Let us consider a sample whose
length is L ,bredth is w and
thickness is d as Shown in the
figure.
Let Current Ix flowing along X
direction due to the application of
P.D VX.
Let BZ be the magnetic field
applied along the Z direction
Let vd be the drift velocity of the
charge carrier.
Vd = vd î for +ve charge carriers
and Vd = - vd î for -ve charge
carriers
A Lorentz force FL = q(vxB) will
be experienced by the charges L/q
●
Due to force FL the positive charge carriers moves in
the -ve Y- direction, where as -ve charge carriers moves
in +ve y direction ,thus charge separation occurs.
This compilation of charges stops when force due to
electric field equals the magnetic force
F E + F B= 0
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qEH + q( vd x BZ) = 0 ⇒ EH = - ( vd x BH )
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—--------- 1
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But the current density J = nevd —-------- 2
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From 1., vd = EH / BZ , substituting in 2 gives J = ne(EH / BZ) —--- 3
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Let us define RH = 1/ne known as Hall coefficient
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From 3., RH = EH/JBZ =/( wd vH )/(Ix BZ w) = vH d/ Ix BZ :
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RH = vH d/ Ix BZ —----- 4
-
+
+
+
- - - -
+
+
●
If VH is +ve then RH is +ve. The charge carriers are holes
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If VH is -ve then RH is -ve. The charge carriers are electrons
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Since n = 1/ eRH , the concentration can be estimated.
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From Ohm’s law J = 𝜎 E = neμE ====> μ/𝜎 = 1/ne = RH —-----5