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Experiment No…..
ObjectiveUsing the Hall Effect measurement technique, studies the following properties of p-type
semiconductor:
a. Hall voltage and coefficient,
b. The no. of charge carriers per unit volume, and
c. Hall angle and mobility.
Apparatus usedHall effect board, A semiconductor crystal (rectangular shape of ~0.5 mm thickness),
Electromagnet, constant current power supply (0-4 A), digital gauss meter with gauss
probe.
Basic principle & formula usedWhen a substrate of conductor (metal / semiconductor) carrying a current (say Ix) is
placed in a transverse (perpendicular) magnetic field (say Hz), an electric field (Ey) is
produced inside the conductor in a direction normal to both the current (Ix) and the
magnetic field (Hz). This phenomenon is known as ‘Hall effect’ and the generated voltage
corresponding to developed electric field (Ey) is called Hall voltage (VH) .
A specimen rectangular slab of solid in which Hall effect is to be studied is shown as
ABCDA’B’C’D’ in Figure (1) with length AB, breath BC, and thickness AA’ as l, b, d
in respectively x, y, z directions . If Ix is the current density in x- direction and Hz is
applied magnetic field in z- direction, then Hall field EH (i.e. Ey) developed in ydirection is proportional to Ix and Hz and is given by:
EH = RH Ix Hz
Hall voltage; VH, is measured with the help of mili-voltmeter (as given in procedure).
𝑏
Hall coefficient; RH = tan θ (𝐻 ) 104 meter3/Coulomb
𝑧
Number of charge carriers per unit volume; n = 𝑅
𝑉𝐻
𝐼𝑥
1
ℎ
Hall angle; Φ = ( 𝑉 ).( 𝑏 ) Radians
Φ
𝑥
Mobility; mμ = 𝐻
𝑧
Figure-1
𝑒
Figure-2
ProcedureMeasurement of magnetic field
1. Use digital Gauss meter for measurement of the magnetic field.
2. Put ON/OFF switches to ON position and adjusts the reading of the meter to
zero by ‘zero adjustment pot’.
3. Put the Gauss probe between poles of the electro-magnet; now connect the
constant current power supply to electro-magnet.
4. Switch ON the power supply and vary the current
5. Note down the readings of magnetic field by Gauss meter at corresponding
value in table -1.
Measurement of Hall voltage for constant magnetic fields
1. Connect the widthwise contacts of the Hall probe to the terminal marked ‘voltage’
and lengthwise contacts to the terminal marked ‘current’ of the Hall effect set-up
board.
2. Put the switch marked ON/OFF of Hall Board to ON position.
3. Put the meter selector switch towards (0-20 mA) current side and adjust current
(not exceeding 5 mA) by current adjust pot.
4. Now put the meter selector switch toward (0-200 mV) Voltage side. There may be
some voltage reading even outside the magnetic field. This is due to imperfect
alignment of the four contacts of Hall probe and is generally known as ‘Zero field
potential’ (or Vx).
5. Now place the hall probe in a constant magnetic field and note the voltage reading
as a (Vx+VH)
6. The difference between with magnetic field voltage (Vx+VH) and without
magnetic field voltage Vx will give you the value of hall voltage VH.
Observations:
Physical dimensions of the crystal
Length; lx = 4 mm, Width; b = 3 mm, Thickness; d = 0.5 mm.
Table -1: Measurement of magnetic field
Note-don’t take constant current more than 2.5 Amp.
S.No.
1.
2.
3.
4.
Current (in Amperes)
1 Ampere
1.5 Ampere
2 Ampere
2.5 Ampere
Magnetic field( in gauss) Hz
Table -2: Measurement of Hall voltage for constant magnetic fields
Constant current to produce magnetic field = ------- Amp
Sr.
No.
Magnetic
field
(constant)
1
2
3
4
5
Current, Ix
(mA)*
Voltage,
Vx (volt)
(without
magnetic field)
Voltage,
Vx+ VH (volt)
(with magnetic
field)
Hall Voltage,
VH (volt)
.5 mA
1 mA
1.5 mA
2 mA
2.5 mA
Calculations1. A graph is plotted in VH and IX (Fig2).
From its slope; tan θ = VH/Ix is found.
Then Hall coefficient is; RH = tan θ (b/Hz) 104 meter3/Coulomb
= ------ meter3/Coulomb
2. The number of charge carriers per unit volume n = 1/RH.e
3. Hall angle, Φ = (VH/Vx).(Ix/b) =…….. Radian
4. Mobility, mμ = Φ/Hz
Result-
VH / I x
(from
graph)
Precautions(1) Hall voltage developed is very small and should be measured accurately with the help
Of a mili-voltmeter
(2) Current through the crystal should be strictly within the permissible limits.
(3) Do not change the distance between the poles of electromagnet
Specification of crystal in our lab1. Hall coefficient : 25 ⤫ 103 cm3 coulomb-1
2. Carrier mobility : (25±1) ⤫102 cm2Volt-1sec-1
3. Carrier density : 2.5 ⤫ 1014 cm-3
4. Resistivity : 10 ohm.cm