(Lab Copy)Four-Probe Experiment

Object: (1) To measure resistivity of semiconductor at different temperatures by Four Probe Method.(2) To plot a graph of resistivity as a function of inverse temperature for a semiconductor.(3) To determine Band Gap of the semiconductor.

Apparatus Used: The Four Probe Set-Up (Model DEP-03 # 70) consists of the following:

(i) Four Probes Arrangement : It has four individually spring loaded probes. The probes are collinear and equally spaced. Whole arrangement is mounted on a suitable stand. Colour Codes: Voltage Probes – Yellow & Green, Current Probes- Red & Black.

(ii) Sample : Ge Single Crystal type (n-type) in the form of a chip of thickness=0.50mm.

(iii) Oven : For variation of temperature from room temperature to about 200˚C (max.) SpecificationsHeater Resistance : 36 ΩMaximum Temperature : 200˚COperating Temperature : 175˚C (Note: Don’t go above this temp.)

(iv) Thermometer (0-200˚C) : For measuring temperature.

(v) Four Probe Set-Up : Consiting of the following in cabinet.

(a) Constant current Generator : To provide a constant current to outer probes. Variation in current is achieved by a potentiometer provided.SpecificationsOpen Circuit Voltage : 18VCurrent range : 0-20mAResolution : 10μAAccuracy : ± 0.25 % of the reading ± 1 digitLoad regulation : 0.03% for 0 to full loadLine Regulation : 0.05% for 10% changes

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(b) Oven power supply : Suitable voltage (64 V) for the oven is obtained through a step down transformer with a provision for low & high rates of heating. A glowing LED indicates, when the oven power supply is ‘ON’

(C) Digital panel meter (for measuring voltages & current).SpecificationVoltage range : 0-200mV & 0-2VCurrent range : 0-20mA (min I=0.01mA, max I=20mA)Resolution : 100μV at 200mV range.Display : 3 ½ digit, 7 segment LED (12.5mm height) with auto polarity and decimal indications.Over load indication : Sign of 1 on left and blanking of other digits.

(d) Mains ON/OFF Switch, Fuse and Jewel light.

Formula Used: ρ0 = (V / I) x 2πS

ρ = ρ0 / G7(W/S)

G7(W/S) = 2S/W (loge2)

From the relation ρ = ρ0 exp (Eg/2kT) we can write, Eg /2kB = logeρ / (1/T)

Where, V= voltage; I= Current; S= Distance between probes 2mm in our case ; W= Thickness of the crystal 0.5mm in our case ; T=Temperature of sample; kB = Boltzman constant = 8.6 x10-5 eV/deg;Eg = Energy band gap;

Procedure:

(1) Connect the outer pair of probes Red & Black leads to the constant current

power supply) and the inner pair Yellow & Green leads to the probe voltage

terminals.

(2) Switch on the ac mains of Four Probe Set-up and put the digital panel meter

in the current measuring mode through the selector switch. In this position LED

facing mA would glow. Adjust the current to a desired value (Say 5mA).

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(3) Now put the digital panel meter in voltage measuring mode. In this position

LED facing mV or V would glow depending on position of switch and the meter

would read the voltage between the probes.

(4) Connect the oven power supply. Rate of heating may be selected with the

help of a switch –Low or High as desired. Switch on the power to the Oven. The

glowing LED indicates the power to the oven is ‘ON’.

Observations:

Constant Current (I) = ……….. (mA)

Distance between probes (S) =……….. mm (2mm in our case)

Thickness of the crystal (W) =……….. mm (0.5mm in our case)

S. No. Temperature(K)

Voltage(volts)

ρ (Ohm cm) T-1 x 10-

3

log10ρ

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Circuit Diagram: (Should be on left page by pencil)

Calculations: (Should be on left page by pen)

ρ0 = (V / I) x 2πS

ρ = ρ0 / G7(W/S)

G7(W/S) = 2S/W (loge2)

Eg /2kB = logeρ / (1/T) = 2.303 log10ρ / (1/T)

Results: Band Gap of the given semiconductor found to be =…………………eV

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Maximum Probable Error: (Should be on left page by pen)

Eg /2kB = logeρ / (1/T)

Taking log of both sides and differentiates

ΔEg / Eg = ?

Sources of error and precautions:

(i) The probes must be gently placed otherwise Germanium crystal can break.

(ii) Temperature must be taken carefully.

(iii) An insulating sheet must be placed between the Germanium sample and

base on which it is kept.

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