Download ENGINEERING PHYSICS II SEMICONDUCTING MATERIALS

ENGINEERING PHYSICS II
SEMICONDUCTING MATERIALS
2.16 HALL EFFECT
When a conductor carrying a current is placed in a transverse magnetic field, an electric
field is produced inside the conductor in a direction normal to both the current and the magnetic
field. This phenomenon is known as Hall effect and the generated voltage is called “Hall voltage”.
Hall effect in n-type semiconductor
 Let us consider an n type material to which the current is allowed to pass along x-direction
from left to right and the magnetic field is applied in Z-direction, as a result Hall voltage is
produced in y direction as shown in figure.
 Now due to the magnetic field applied the electrons move towards downward direction with
the velocity ‘v’ and cause the negative charge to accumulate at face (1) of the material as
shown in figure
 Here the force due to PD = -eEH
………….. (1)
 Force due to magnetic field = -Bev
………….. (2)
At equilibrium (1) =
(2), we get
…..……… (3)
EH =Bv
..………… (4)
Current density Jx = -neev and v=-(Jx/nee)
Sub eqn (4) in eqn(3) we get
… .……….. (5)
Hall coefficient RH = -(1/nee)
The negative sign indicates that the field is developed in the negative y direction.
Hall effect in P type semiconductor
 Let us consider an p type material to which the current is allowed to pass along x-direction
from left to right and the magnetic field is applied in Z-direction, as a result Hall voltage is
produced in y direction as shown in figure.
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ENGINEERING PHYSICS II
SEMICONDUCTING MATERIALS
 Now due to the magnetic field applied the holes move towards downward direction with the
velocity ‘v’ and cause the negative charge to accumulate at face (1) of the material as shown
in figure.
 Here the force due to PD = eEH
…………….. (6)
 Force due to magnetic field = Bev
…………….. (7)
At equilibrium (1) =
(2), we get
………..…… (8)
EH =Bv
…………… (9)
Current density Jx = nhev and v=(Jx/nhe)
Sub eqn (9) in eqn(8) we get
………….. (10)
Hall coefficient RH = 1/nh e
The positive sign indicates that the field is developed in the positive y direction.
Hall coefficient in terms of Hall voltage
If the thickness of the sample is t and the voltage developed is VH, then
……………… (11)
Hall voltage VH = EH.t
Sub the value of EH in eqn (11) we have
2.17 EXPERIMENTAL VERIFICATION OF HALL EFFECT
 A semiconductor slab of thickness ‘t’ and breadth ‘b’ is taken and current is passed using
the battery as shown in figure.
 The slab this placed between the pole pieces of an electromagnet so that current direction
coincides with x-axis and magnetic field coincides with z-axis.
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ENGINEERING PHYSICS II
SEMICONDUCTING MATERIALS
 The Hall voltage is measured by placing two probes at the centre of the top and bottom
faces of the slab (y-axis).
 If B is magnetic field applied and the VH is the Hall voltage produced, then the Hall
coefficient can be calculated from the formula,
RH =
VH b
Ix B
Mobility of charge carriers
1
 In general the Hall Co-efficient can be written as 𝑅𝐻 = − 𝑛𝑒
 The above expression is valid only for conductors where the velocity is taken as the drift
velocity.
 But for semiconductors velocity is taken as average velocity so RH for an ‘n’ type
semiconductor is modified as
𝑅𝐻 = −
3𝜋
8𝑛𝑒
=−
1.18
………………… (1)
𝑛𝑒 𝑒
We know the conductivity for n type is 𝜎𝑒 = 𝑛𝑒 𝑒𝜇𝑒
μe =
(or)
σe
ne e
………………… (2)
From eqn (1) we can write
1
ne
=−
RH
1.18
………………… (3)
Substituting eqn (3) in eqn (2) we get
μe = −
σe RH
1.18
The mobility of electron is in an n-type semiconductor is
𝜇𝑒 = −
𝜎𝑒 𝑉𝐻 𝑏
1.18𝐼𝑥 𝐵
Similarly for p-type semiconductor, the mobility of hole is
μh = −
σh VH b
1.18Ix B
Hall Angle (θH)
We know if the current (Ex) is applied to a specimen along x direction, magnetic field (B)
along z-direction then Hall voltage (EH) is produced along y-direction.
Here the Hall angle can be measured from the formula
tan 𝜃𝐻 =
𝐸𝐻
𝐸𝑥
………… (1)
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ENGINEERING PHYSICS II
We know
SEMICONDUCTING MATERIALS
𝐸𝐻 = 𝑅𝐻 𝐽𝑥 𝐵
………. (2)
𝐸𝐻 = 𝑉𝑥 𝐵
………. (3)
Sub eqn (3) in (1) we get
tan 𝜃𝐻 = 𝜇𝐵
Thus the mobility can be defined as the velocity acquired by the charge carrier per unit
electric field.
2.18 APPLICATIONS HALL EFFECT
i.
It is used to determine whether the material is p type or n type semiconductor.
ii.
It is used to find the carrier concentration
iii.
It is used to find the mobility of charge carriers
iv.
It is used to determine the sign of the current carrying charges.
v.
It is used to design magnetic flux meters and multipliers on the basis of Hall voltage
vi.
It is used to find the power flow in an electromagnetic wave.
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