Four probe Method.pptx

IGNTU

1. FOUR PROBE METHOD Presentators: JATIN MAHATO, M.Sc. III Sem (1801168007) SUDIPTA MAHARANA, M.Sc.III Sem (1801168016) Department of Physics

2. PLAN OF TALK HISTORY TWO PROBE METHOD FOUR PROBE METHOD THE EXPERIMENT APPARATUS REQUIRED FORMULA USED PROCEDURE OBSERVATION RESULTS PRECAUTIONS APPLICATIONS REFERENCES

3. HISTORY: Four-terminal sensing is also known as Kelvin sensing, after William Thomson, Lord Kelvin, who invented the Kelvin bridge in 1861 to measure very low resistances using four-terminal sensing.

4. TWO PROBE METHOD The two thin Cu wires of few microns, called lead wires, were soldered at the two ends (1 and 2). • These lead wires were connected to the constant current power supply. The same lead wires were also connected to the voltmeter (D and C).

5. TWO PROBE METHOD from fig. V DC = V AB + V BC + V DA = IR sample + IR lead + IR lead Here, V DC = IR Hence the measured resistance, R= R sample +R lead +R lead ⇒ R= R sample +2R lead It can make an error of 2R lead if, R sample ≤ R lead. Since range of R lead ( few mΩ ≤ R lead ≤ few hundred Ω ). That is why, two-probe method can be implemented in those situations where R sample >> 2R lead . Hence, two probe method can be comfortably used in cases where sample resistance is more than 1MΩ. However, in case of metallic identities, the resistance range typically falls below 1kΩ .

6. FOUR PROBE METHOD To overcome the error due to lead resistance in our measurements, we chose a collinear equidistant four-probe method. It permits measurements of resistivity in samples having a wide variety of shapes, including the resistivity of small volumes within bigger pieces of semiconductor. Typical probe spacing ~ 1 mm. Each tip is supported by springs on the other end to minimize sample damage during probing.

7. FOUR PROBE METHOD T he two end contacts (1 and 4) are dedicated to pass current and the two middle contacts (2 and 3) are to measure voltage separately. From fig. V 23 = V 14 + V 43 + V 21 No current is drawn by the middle contacts because of the very high internal resistance of the voltmeter (∼GΩ). So, V 43 ∼0 and V 21 ∼0 Therefore, V 23 = V 14 R= V 43 / I =V 14 /I ⇒ R=R sample Thus, we can exclude the error due to lead resistance by using four-probe configuration.

8. FOUR PROBE METHOD AIM OF EXPERIMENT: TO STUDY THE RESISTIVITY OF A SEMICONDUCTOR ( Ge -CRYSTAL ) AND HENCE TO DETERMINE THE BAND-GAP ENERGY (E g) BY USING FOUR PROBE METHOD. APPARATUS REQUIRED : 1. A thin Ge crystal with smooth surface four probe arrangement 2. A digital voltmeter. 3. Constant current source. 4. An oven with power supply . 5.A thermometer range from 0-200°C .

9. WORKING FORMULA At constant temperature , R  L R= resistance  1/A L= length Therefore, R=  L /A In case of slice ,the resistivity is = o/ f(W/S) The function f(w/s) is a divisor for computing resistivity if w>s then =(V/I) × 2 π S Temperature dependence of resistivity of semiconductor is:

10. PROCEDURE A high impedance current source is used to supply current through the outer two probes. A voltmeter measure the voltage across the inner two probes to determine the sample resistivity.

11. EXPERIMENTAL SETUP

12. OBSERVATION TABLE Constant current is = 2 mA Serial no. Temperature (In K elvin ) Voltage (volt) Resistivity  In (  .cm) 1/T(*10 (In Kelvin) Log 10  1 308 83.8 8.924 3.246 .9505 2 318 83.1 8.850 3.144 .9469 3 328 80.3 8.552 3.048 .932 4 338 71.2 7.581 2.958 .8797 5 348 59.6 6.347 2.873 .8025 6 358 47.7 5.048 2.793 .7031 7 368 36.61 3.8974 2.717 .5908

13. GRAPH b/w 1/T Vs Log 10  Log 10  10 3 /T The slope of the straight line graph b/w log of resistivity and 10/T is: SLOPE = Eg /(2 .3026× 10 3 )×2 =1.747

14. CALCULATIONS Band gap of Germanium sample is: Eg = (2 .3026× 10 3 ) ×2k × slope RESULTs: The band gap for the given semiconductor at room temperature was found to be 0.68ev. CONCLUSION: Resistivity for the given sample decrease with increase in temperature.

15. PRECAUTIONS Current should be constant while performing the experiment. Reading should be taken not only while heating and sample but also while cooling . The sample should be heated to a temperature near about 180-200 degree Celsius. The tip of the thermometer should be well inside the hole and the temperature should be read carefully. The surface of the semiconductor should be flat. All the four probes should be collinear. The adjustment of 4-point probes should be done gently,as the semiconductor chip is brittle.

16. APPLICATIONS 1. Remote sensing areas 2. Resistance thermometers 3. Induction hardening process 4. Accurate geometry factor estimation 5. Characterization of fuel cells bipolar plates

17. REFERENCES Introduction to Solid State Physics by C.Kittel Fundamentals Principles ofElectronics by B.Ghosh Wikipedia Google images