Engineering Physics Viva – …..And Then There Is Physics



Experiment No…..Objective- Using the Hall Effect measurement technique, studies the following properties of p-type semiconductor: Hall voltage and coefficient, The no. of charge carriers per unit volume, and Hall angle and mobility. Apparatus used- Hall 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 used- When 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 y- direction 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).Hall coefficient; RH = tan θ bHz 104 meter3/CoulombNumber of charge carriers per unit volume; n = 1Rh eHall angle; Φ = VHVx.Ixb RadiansMobility; mμ = ΦHz Figure-1 Figure-2Procedure- Measurement of magnetic field Use digital Gauss meter for measurement of the magnetic field.Put ON/OFF switches to ON position and adjusts the reading of the meter to zero by ‘zero adjustment pot’.Put the Gauss probe between poles of the electro-magnet; now connect the constant current power supply to electro-magnet.Switch ON the power supply and vary the currentNote down the readings of magnetic field by Gauss meter at corresponding value in table -1.Measurement of Hall voltage for constant magnetic fieldsConnect 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.Put the switch marked ON/OFF of Hall Board to ON position.Put the meter selector switch towards (0-20 mA) current side and adjust current (not exceeding 5 mA) by current adjust pot.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). Now place the hall probe in a constant magnetic field and note the voltage reading as a (Vx+VH)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 fieldNote-don’t take constant current more than 2.5 Amp. S.No.Current (in Amperes)Magnetic field( in gauss) Hz1.1 Ampere2.1.5 Ampere3.2 Ampere4.2.5 AmpereTable -2: Measurement of Hall voltage for constant magnetic fieldsConstant current to produce magnetic field = ------- Amp Sr. No.Magnetic field(constant)Current, Ix (mA)*Voltage,Vx (volt)(without magnetic field)Voltage, Vx+ VH (volt)(with magnetic field)Hall Voltage, VH (volt)VH / Ix(from graph)1.5 mA21 mA31.5 mA42 mA52.5 mACalculations- 1. 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/Coulomb2. 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-Precautions-Hall voltage developed is very small and should be measured accurately with the help Of a mili-voltmeter Current through the crystal should be strictly within the permissible limits.Do not change the distance between the poles of electromagnet Specification of crystal in our lab-Hall coefficient : 25 ? 103 cm3 coulomb-1Carrier mobility : (25±1) ?102 cm2Volt-1sec-1Carrier density : 2.5 ? 1014 cm-3Resistivity : 10 ohm.cm ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download