Semiconductor testing: practical steps involved in semiconductor testing:

Aim: 1. To determine the values of the energy gap E_g, for a given thermistor for two different values of current passing through it. 2.  To determine the limiting value of the resistance Ro.

thermistor

Conventional carbon and wire wound resistances have very less effect of temperature on their values of resistance. There is about 0.4 % change in the resistance value per degree change in the temperature. They are also linear i.e. they obey Ohm’s law. However, there is a class of resistances which are temperature sensitive and show a significant change in their resistance values with temperature. Such resistances are called thermistors. A change of about 6% to 8 % in their resistance values is observed with change in temperature. They are non-linear resistances. Thermisters are used as current limiters, temperature sensors, self-resetting overcurrent protectors and self-regulating elements. The first NTC thermistor was discovered in 1833 by Michael Faraday, who reported on the semiconducting behavior of silver sulfide

Apparatus: Thermistor, heating mantle, thermometer, toluene in a test tube and constant

                      current source/ thermister kit.

Formula:   1.   E_g = 0.1725 x m   (eV)

                   2.   R_o = e^C    (Ω)

 Where m is the slope of the straight line graph between ln R and 10³/T and

             C is the Y-intercept.                                                                                                                                                             

Introduction: Conventional carbon and wire wound resistances have very less effect of temperature on their values of resistance. There is about 0.4 % change in the resistance value per degree change in the temperature. They are also linear i.e. they obey Ohm’s law. However, there is a class of resistances which are temperature sensitive and show a significant change in their resistance values with temperature. Such resistances are called thermistors. A change of about 6% to 8 % in their resistance values is observed with change in temperature. They are non-linear resistances. Thermisters are used as current limiters, temperature sensors, self-resetting overcurrent protectors and self-regulating elements. The first NTC thermistor was discovered in 1833 by Michael Faraday, who reported on the semiconducting behavior of silver sulfide.

 Thermistors are subdivided into two groups viz:

1.   Those having positive temperature coefficient (PTC) of resistance where the resistance increases with temperature. Metals generally have PTC. For metals; an increase in temperature; results in greater thermal motion of ions, due to which mean free path of the electrons decreases and  consequently the resistance increases.

2.   Those having negative temperature coefficient (NTC) of resistance where the resistance decreases with temperature. Semiconductors like Si, Ge show NTC. However they are not used commercially because they show much change in their resistance. Commercial thermistors are made up of sintered mixtures of Mn₂O₃, NiO₂, and CO₂O_3.

Electronic devices are temperature sensitive showing much change in their characteristics. For example; the collector current in the transistor gets doubled for every ten degree rise in junction temperature. This increase in collector current produces heat (Joule’s effect) which increases temperature further.  This regenerative phenomenon   results in thermal runaway in which transistor may burn. To avoid this; thermistors are used to compensate for the change in current due to temperature variation. Thermistors also find extensive use as sensing elements in microwave power measuring equipments and electronic thermometers.

lnR

Theory: The variation of the resistance for NTC thermistors can be explained on the basis of the band theory of the solids. Band picture of any solid in general can be given as shown in the fig.1. A solid is formed when large number of atoms comes in close proximity. Due to their interactions; energy levels splits and bands are formed. The valence band (V.B.) is formed due to overlapping of valence shells of atoms. The conduction band (C.B.) is band of the empty shells which lie above valence shells. The valence band and conduction band may be separated by energy gap; E_g. Conductivity of the material depends on the number of the electrons in conduction band. (This is the reason for designating it as C.B.).In case of semiconductors and insulators they are separated by an energy gap (Eg). The energy gap is different for different materials and is characteristic of that material; its value in semiconductors being small as compared to insulators. The electron from valence band can go to conduction band only after overcoming this energy gap. For every electron going into C.B. a vacancy is created in the V.B. This vacancy is termed as `hole’ and is treated as positive charge carrier. The holes also contribute towards the conductivity. For intrinsic i.e. pure semiconductor; the number of electron in C.B. is equal to number of holes in V.B. The product of the concentrations of holes and electrons is termed as intrinsic carrier concentration and is denoted by n_i. The raw materials used for preparing the NTC thermistors are generally oxides of metals viz. Fe, Mn, Co etc. However the main mixture being an intrinsic semiconductor; the relevant theory of semiconductors can be applied to thermistors without any hesitation. At lower temperature the number of electrons in C.B. in the NTC thermistors is very less and hence the conductivity is less i.e. resistance is very high. At elevated temperatures some of the electrons get sufficient energy to jump into the C.B. Consequently, the electron density in C.B. increases and thus the resistance decreases. The variation of resistance with temperature for NTC as well as PTC thermistors is shown below. Plot of ln R and 1/T is a straight line.  

 
V-I characteristics of NTC thermistors: The I-V characteristic curve of the NTC thermistor is as shown in the fig. It can be explained as:

At sufficiently small values of current and voltage, the power dissipated is too small to increase its temperature. Therefore initially it obeys Ohm’s law i.e. a straight line is obtained. At increased values of the currents the power dissipated increases and its temperature starts increasing. This results in the decrease in its resistance. Hence for a given value of the current; voltage across thermistor decreases. Thus for this region it exhibits negative temperature coefficient and Ohm’s law is not obeyed. Hence thermistors are nonlinear resistances device.

As explained above; the conductivity σ of the material depends on the intrinsic concentration and temperature. It is given by; 

σ = σ₀ exp {- Eg / 2 kT };

Where k is Boltzman constant & its value is 1.38x10 ^{- 23} J/C

                          σ₀  is the conductivity at known temperature.

Hence resistively ρ (reciprocal of σ) is given by ρ = ρ₀  exp { E_g / 2 kT }

and the resistance at temperature T is given by  

                                            R = R_o  exp {E_g / 2 kT } ------------------- (A)

where, R_o is the limiting value of resistance at infinitely large temperature.

Taking log of both sides of above equation;

                        ln R = ln R_o + E_g / 2kT      or       ln R = C + (E_g / 2k x 10³)(10³ /T )

   where C is the Y intercept of the straight line graph between ln R and 10³ /T   (see fig.). Hence the slope `m’ of this line is given by (E_g / 2k x10³ ) and thus ;

                            E_g= m  x 2 x 1.38 x 10 ^{- 23} x 10³ / 1.6 x 10 ^{– 19} in  eV           

                                    = 0.1725 x m          in  eV.

The temperature coefficient of resistance (α) is defined as the change in resistance per unit degree rise in temperature.                           

 From this definition;   α = dR / R dT= (E_g/ 2k) (- 1 / T²)     [from (A)]

                                    = - 0.1725 m  

     = - (1000 x m)/T²    per   K 

Thus the value of coefficient of resistance can be determined at different temperatures by substituting value of E_g in the above equation. The value of limiting resistance; R₀ is calculated as e^C.

Applications

• NTC thermistors are used as resistance thermometers in low-temperature measurements of the order of 10 K.
• NTC thermistors can be used as inrush-current limiting devices in power supply circuits. They present a higher resistance initially which prevents large currents from flowing at turn-on, and then heat up and become much lower resistance to allow higher current flow during normal operation. These thermistors are usually much larger than measuring type thermistors, and are purposely designed for this application.
• NTC thermistors are regularly used in automotive applications. For example, they monitor things like coolant temperature and/or oil temperature inside the engine and provide data to the ECU.
• Thermistors are also commonly used in modern digital thermostats and to monitor the temperature of battery packs while charging.

PROCEDURE:

1. Insert the thermometer and thermistor inside test tube containing toluene. Place the assembly inside heating mantle using retort stand. 

 2.  Set the current at 30 mA by shorting the power supply terminals and set the voltage  

       knob so that it shows maximum reading(15V).

 3. Set temperature knob at 50⁰ C and wait till thermometer reads 70⁰ C.

4. Switch off heating mantle, remove assembly from it and allow thermometer reading to settle down.

5. Make connections as shown in fig.

6. When temperature settles down; note down its value and corresponding reading of

     voltage across thermistor (V_TH).

7. Note down the value of V_TH for every 2⁰ C fall in temperature till it attains room

     temperature.

8. Repeat the above steps for another value of constant current say 40 mA.

Before setting new value of current; disconnect the terminals of thermistor.

Procedure for Kit

1. Set the voltage constant to 3Volts.

2. Set the temperature knob at mid position and switch ON the heater.

3. Allow the oven temperature to increase upto 60⁰C .

4. For every 2⁰C fall in temp. note down the value of current

RESULT :

1. Value of energy gap E_g at two different constant currents is

            1. ------------------                      2. -------------------

2. Limiting value of resistance Ro at two different constant currents is

1. ------------------                      2. -------------------

PRECAUTIONS:

 1. Assure that the current remains constant.

 2. Do not let temperature of thermistor to increase more than 75⁰ C.

 3. Make connections properly to ensure that voltmeter reads

     Thermistor voltage V_TH.

                                

Answer the following

Q1. What is the liquid in the test tube? Can any other liquid (water, HCl, CHCl₃) be used instead?

Q2. What is the meaning of limiting resistance of thermistor? Is it defined similar way for both NTC and PTC?

Q3. Does thermistor obey Ohm’s law?

Q4. What is meant by temperature coefficient of resistance? Does it depend on temperature?

Q5. From your observations can you guess about type of the thermistor?

Q6. Can you use a metal instead of a thermistor?

Q7. Mention the applications of thermistor.

Q8. What is the material used for making thermistor?

Q9. Why does resistance of metal increases with temperature?

Q10. Why there is a fast change in resistance in the range of 75⁰ c to 45⁰c while  there is slower drop in the range 45⁰ c to 35⁰ c?

Q11. The resistance falls exponentially with the temperature for thermistor used by you. Is this correct?
Q12. Explain what is physical meaning of Eg?
Q13. Draw V-I characteristics of thermistor.
Q14. Why in case of NTC thermistors resistance decreases with rise in temperature?
Q15. What do you mean by linear and non linear resistances?

Semiconductor testing: practical steps involved in semiconductor testing:

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