Electric Field and Magnetic Field

When charges are separated, a space is created where forces are exerted on the charges. An electric field is such a space. Depending upon the polarity of the charges, the force is either attractive or repulsive. Therefore, we can say that static charges generate an electric field. An electric field influences the space surrounding it. Electric field strength is determined in terms of the force exerted on charges. A capacitor is a reservoir of charge. The two parallel plates of a capacitor, when connected to a voltage source, establishes an electric field between the plates. The positive terminal, or pole of the voltage source will draw electrons from plate 1 whereas the negative pole will push extra electrons on to plate 2. Voltage across the capacitor will rise. The capacitor gets charged equal to the voltage of the source. The capacitance of a capacitor is a measure of its ability to store charge. The capacitance of a capacitor is increased by the presence of a dielectric material between the two plates of the capacitor.

A current-carrying conductor or a coil produces magnetic field around it. The strength of the magnetic field produced depends on the magnitude of the current flowing through the conductor or the coil. There is presence of magnetic field around permanent magnets as well.

A magnet is a body which attracts iron, nickel, and cobalt. Permanent magnets retain their magnetic properties. Electromagnets are made from coils through which current is allowed to flow. Their magnetic properties will be present as long as current flows through the coil.

The space within which forces are exerted by a magnet is called a magnetic field. It is the area of influence of the magnet.

Atomic Structure and Electric Charge

Several theories have been developed to explain the nature of electricity. The modern electron theory of matter, propounded by scientists Sir Earnest Rutherford and Niel Bohr considers every matter as electrical in nature. According to this atomic theory, every element is made up of atoms which are neutral in nature. The atom contains particles of electricity called electrons and protons. The number of electrons in an atom is equal to the number of protons.

The nucleus of an atom contains protons and neutrons. The neutrons carry no charge. The protons carry positive charge. The electrons revolve round the nucleus in elliptical orbits like the planets around the sun. The electrons carry negative charge. Since there are equal number of protons and electrons in an atom, an atom is basically neutral in nature.

If from a body consisting of neutral atoms, some electrons are removed, there will be a deficit of electrons in the body, and the body will attain positive charge. If neutral atoms of a body are supplied some extra electrons, the body will attain negative charge. Thus, we can say that the deficit or excess of electrons in a body is called charge.

Charge of an electron is very small. Coulomb is the unit of charge. The charge of an electron is only 1.602 × 10^–19 Coulomb (C). Thus, we can say that the number of electrons per Coulomb is the reciprocal of 1.602 × 10^–19 which equals approx. 6.28 × 10¹⁸ electrons. Therefore, charge of 6.28 × 10¹⁸ electrons is equal to 1C. When we say that a body has a positive charge of 1C, it is understood that the body has a deficit of 6.28 × 10¹⁸ electrons.

Any charge is an example of static electricity because the electrons or protons are not in motion. You must have seen the effect of charged particles when you comb your hair with a plastic comb, the comb attracts some of your hair. The work of combing causes friction, producing charge of extra electrons and excess protons causing attraction.

Charge in motion is called electric current. Any charge has the potential of doing work, i.e., of moving another charge either by attraction or by repulsion. A charge is the result of separating electrons and protons. The charge of electrons or protons has potential because it likes to return back the work that was done to produce it.

Underground Cable Fault Identification Methods

If a fault occurs in the underground cable, it is essential that the type of the fault and location of the fault should be determined as quickly and accurately as possible. Accuracy is important in order to avoid excessive trenching work. The type of fault which is most likely to occur is single conductor to ground fault. In multi-core cables, the fault current will likely give rise to excessive heating at the fault causing further damage to the insulation and extending the fault to remaining conductors. Open circuit faults may occur occasionally which be usually at cable joints. 

Cable fault type identification:

 Prior to the location of the fault on the power system it is important to determine the type of fault so as to make a better choice of the method to be used for fault location

• Isolate the faulty cable and test each core of the cable for earth fault. One terminal of the insulation tester is earthed and each conductor of the cable is in turn touched with other terminals. If the insulation resistance tester indicates zero resistance during any measurement, conductor to earth fault for the particular conductor is confirmed
• Then check the insulation resistance between the conductors. In the case it is a short circuit fault, the insulation resistance tester will indicate zero resistance
• After the above step, short and earth the three conductors of the cable at one end. Check the resistance between the conductors and earth and between individual conductors (at the other end). This procedure is carried out to check the open circuit faults
• In case in order to test any other faults. the insulation test of the individual cores with sheath or armour and between the cores is essential. The test should also be done by reversing the polarity of the insulation resistance tester. In the case of any difference in the readings, the presence of moisture in the cable insulation is confirmed. The moisture in the cable forms a voltage cell between the lead sheath and conductor because of the difference in the conductivity of these metals and the impregnating compound forms an organic acid when water enters 

Cable fault location Identification:

After the fault type identification, suitable fault location method should be employed to pinpoint the location of the fault. Some of the fault identification methods generally employed are:

• Murray loop test method
• Fall of potential test
• dc charge and discharge method
• Induction test
• Impulse wave echo test
• Time domain reflectometry test

Silicon Carbide (SIC) Lightning Arresters

Silicon Carbide Arresters (SIC):

The Non linear lightning arrester basically consists of set of spark gaps in series with the silicon carbide non linear resistor elements. Lightning arresters are connected between the phase conductors and ground. During normal system operating voltage conditions, the spark gaps are non conducting and isolate the high tension (HT) conductors from the ground. However whenever an overvoltge of magnitude dangerous to the insulation of the apparatus protected occurs ( these over voltages or over surges may be caused due to lightning strikes on the conductors or due to Extra High Voltage (EHV) switching) the spark gap breaks down and allows the high voltage surge current to flow through the ground.

Working Principle of Silicon Carbide (SIC) Lightning Arresters:

The volt-ampere characteristics of the non linear resistor in the lignting arrester can be approximately described by expression V = KI^β. Where K and β are dependent on the composition and manufacturing process of the Non linear Resistor (NLR). The value of β lies generally in the range of 0.3 and 0.45 for modern silicon carbide (SIC) lightning arresters. If the voltage across the Non Linear Resistor (NLR) doubles, the current would increase approximately by 10 times.

Therefore, with multiple spark gaps arresters can withstand high Rate of Recovery Voltage (RRRV). The non-uniform voltage distribution between the gaps (which are in series in lightning arresters) presents a problem. To overcome this, capacitors and non-linear resistors are connected in parallel across each gap. In case of lightning arresters employed for high voltage applications, capacitors and nonlinear resistors are connected across the stock of gaps and NLRs. With the steep voltage wave surge the voltage is mainly controlled by the capacitor and at the power frequency by the non-linear resistors. It is obvious that when the over voltages cause the break down of the series gaps, the current would be very high so as to make the voltage to subside very fast. The highest voltage that appear across the lightning arrester would be either the spark over voltage of the arrester or the voltage developed across the non-linear resistor during the flow of surge current. The lowest spark over voltage of the arrester is called the hundred percent impulse spark over voltage of the arrester. The voltage developed across the non-linear resistor during the flow of surge current is called residual voltage. The lower the value of the voltage developed the better the protection of the lightning arrester.

Disadvantages of Silicon Carbide (SIC) Arresters:

Some of the disadvantages of silicon carbide arresters compared to gapless arresters are given below:

• Silicon Carbide (SIC) arresters have inferior V-I Characteristics compared to Zno arresters (Metal oxide arresters). 
• Decrease in energy absorption (surge wave) capability compared to Zno arresters.
• Probability of sparking between the gaps.  

Advantages of Silicon Carbide (SIC) Arrester :

• Due to the presence of gaps the normal power frequency voltage during normal operation is negligibly less compared to gap less arresters. Hence no leakage current flow between the line and earth in SIC arresters  

Electrical Engineering interview questions and answers Part 17

Why star delta starter is preferred with induction motor?

Star delta starter is preferred with induction motor due to following reasons:
• Starting current is reduced 3-4 times of the direct current due to which voltage drops and hence it causes less losses.
• Star delta starter circuit comes in circuit first during starting of motor, which reduces voltage 3 times, that is why current also reduces up to 3 times and hence less motor burning is caused.
• In addition, starting torque is increased and it prevents the damage of motor winding.

State the difference between generator and alternator

Generator and alternator are two devices, which converts mechanical energy into electrical energy. Both have the same principle of electromagnetic induction, the only difference is that their construction. Generator persists stationary magnetic field and rotating conductor which rolls on the armature with slip rings and brushes riding against each other, hence it converts the induced emf into dc current for external load whereas an alternator has a stationary armature and rotating magnetic field for high voltages but for low voltage output rotating armature and stationary magnetic field is used.

Why AC systems are preferred over DC systems?

Due to following reasons, AC systems are preferred over DC systems:
a. It is easy to maintain and change the voltage of AC electricity for transmission and distribution.
b. Plant cost for AC transmission (circuit breakers, transformers etc) is much lower than the equivalent DC transmission
c. From power stations, AC is produced so it is better to use AC then DC instead of converting it.
d. When a large fault occurs in a network, it is easier to interrupt in an AC system, as the sine wave current will naturally tend to zero at some point making the current easier to interrupt.

How can you relate power engineering with electrical engineering?

Power engineering is a sub division of electrical engineering. It deals with generation, transmission and distribution of energy in electrical form. Design of all power equipments also comes under power engineering. Power engineers may work on the design and maintenance of the power grid i.e. called on grid systems and they might work on off grid systems that are not connected to the system.

What are the various kind of cables used for transmission?

Cables, which are used for transmitting power, can be categorized in three forms:
• Low-tension cables, which can transmit voltage upto 1000 volts.
• High-tension cables can transmit voltage upto 23000 volts.
• Super tension cables can transmit voltage 66 kV to 132 kV.

Why back emf used for a dc motor? highlight its significance.

The induced emf developed when the rotating conductors of the armature between the poles of magnet, in a DC motor, cut the magnetic flux, opposes the current flowing through the conductor, when the armature rotates, is called back emf. Its value depends upon the speed of rotation of the armature conductors. In starting, the value of back emf is zero.

What is slip in an induction motor?

Slip can be defined as the difference between the flux speed (Ns) and the rotor speed (N). Speed of the rotor of an induction motor is always less than its synchronous speed. It is usually expressed as a percentage of synchronous speed (Ns) and represented by the symbol ‘S’.

Explain the application of storage batteries.

Storage batteries are used for various purposes, some of the applications are mentioned below:
• For the operation of protective devices and for emergency lighting at generating stations and substations.
• For starting, ignition and lighting of automobiles, aircrafts etc.
• For lighting on steam and diesel railways trains.
• As a supply power source in telephone exchange, laboratories and broad casting stations.
• For emergency lighting at hospitals, banks, rural areas where electricity supplies are not possible.

Top 5 Electrical Mini Projects For Electrical Engineering

we are providing the list of the top electrical mini projects ideas in this page. As many engineering students are searching for the best electrical projects from the 2nd year and 3rd year, we are providing this list of projects. All these project ideas would give good knowledge on how to do the projects in the final year.

So, we hope this list of electrical mini projects ideas are more helpful for many engineering students. You may write your comments and new projects ideas also by visiting our contact us page.

Top Electrical Mini Projects List:

1.  Auto Night Lamp Using LED: Auto Night Lamp Using High Power LEDs is a circuit which turns ON the LED lights interfaced to it at night time and it turns OFF the lights automatically when it is day.
2.  Anti Bag Snatching Alarm: This is a simple alarm circuit to thwart snatching of your valuables while travelling. The circuit kept in your bag or suitcase sounds a loud alarm, simulating a police horn, if someone attempts to snatch your bag or suitcase. This will draw the attention of other passengers and the burglar can be caught red handed. In the standby mode, the circuit is locked by a plug and socket arrangement (a mono plug with shorted leads plugged into the mono-jack socket of the unit). When the burglar tries to snatch the bag, the plug detaches from the unit’s socket to activate the alarm.
3.  Automatic Plant Watering System: This one of the most useful project in our real life. It helps us in watering plants automatically without any human interference. We may also call it as Automatic plant irrigation system. We know that people do not pour the water on to the plants in their gardens when they go to vacation or often forget to water plants. As a result, there is a chance to get the plants damaged. This project is an excellent solution for such kind of problems.
4.  Water Level Indicator: The Water Level Indicator employs a simple mechanism to detect and indicate the water level in an overhead tank or any other water container. The sensing is done by using a set of nine probes which are placed at nine different levels on the tank walls (with probe9 to probe1 placed in increasing order of height, common probe (i.e. a supply carrying probe) is placed at the base of the tank). The level 9 represents the “tank full” condition while level 1 represents the “tank empty” condition.
5.  IR Remote Control Switch: By using this circuit, we can control any house hold appliance with the help of remote. In this project, there are two parts – one is in transmitting section and the other is in receiving section.

LOAD SHARING BY TWO TRANSFORMERS

Let us consider the following two cases:

• Equal voltage ratios.
• Unequal voltage ratios.

1.39.1 Equal Voltage Ratios

Assume no-load voltages E_A and E_B are identical and in phase. Under these conditions if the primary and secondary are connected in parallel, there will be no circulating current between them on no load.

Figure 1.48 Equal Voltage Ratios

Figure 1.48 shows two impedances in parallel. Let R_A, X_A and Z_A be the total equivalent resistance, reactance and impedance of transformer A and R_B, X_B and Z_B be the total equivalent resistance, reactance and impedance of transformer B.

From Figure 1.48, we have

E_A=V₂+I_AZ_A     (1.71)

and          E_B=V₂+I_BZ_B     (1.72)

∴      I_AZ_A=I_BZ_B

∴    

Equation (1.73) suggests that if two transformers with different kVA ratings are connected in parallel, the total load will be divided in proportion to their kVA ratings if their equivalent impedances are inversely proportional to their respective ratings.

Since    

i.e.,    

i.e.,    

Similarly,    

Similarly, load shared by transformer A,

Similarly,    

Total    S=S_A+S_B=V₂I×10^-3 kVA

∴    

2 Unequal Voltage Ratios

For unequal voltage turns ratio, if the primary is connected to the supply, a circulating current will flow in the primary even at no load. The circulating current will be superimposed on the currents drawn by the load when the transformers share a load.

Let V₁ be the primary supply voltage, a₁ be the turns ratio of transformer A, a₂ be the turns ratio of transformer B, Z_A be the equivalent impedance of transformer A (= R_A + jX_A) referred to as secondary, Z_B be the equivalent impedance of transformer B (= R_B + jX_B) referred to as secondary, I_A be the output current of transformer A and I_B be the output current of transformer B.

The induced emf in the secondary of transformer A is

The induced emf in the secondary of transformer B is

Again, V₂ = IZ_L where Z_L is the impedance of the load

∴    V₂=(I_A+I_B)ZL    (1.80)

From Equations (1.78), (1.79) and (1.80), we have

E_A=I_AZ_A+(I_A+I_B)Z_L    (1.81)

and    E_A=I_BZ_B+(I_A+I_B)Z_L    (1.82)

∴ E_A − E_B = I_AZ_A − I_BZ_B

i.e.,    

Substituting I_A from Equation (1.83) in Equation (1.82), we have

i.e.,    

i.e.,    

Similarly,    

SYNCHRONOUS MOTOR Interview Questions With Answer

1.  State the characteristic features of synchronous motor.
Ans:   a.  the motor is not inherently self starting
          b.   The speed of operation is always in synchronous with the supply frequency irrespective of load   conditions
            c.   The motor is capable of operating at any power factor.

2.  In what way synchronous motor is different from other motors?
All dc and ac motors work on the same principle. Synchronous motor operates due to magnetic locking taking place between stator and rotor magnetic fields.
3.  Name any two methods of starting a synchronous motors
•    By an extra 3 phase cage induction motor
•    By providing damper winding in pole phases
•    By operating the pilot excitor as a dc motor
4.  What is the effect on speed if the load is increased on a 3 phase synchronous motor?
The speed of operation remains constant from no load to maximum load in the motor operating at constant frequency bus bars.
5.  Why a synchronous motor is a constant speed motor
 Synchronous motor work on the principle of force developed due to the magnetic attraction established between the rotating magnetic field and the main pole feed. Since the speed of rotating magnetic field is directly proportional to frequency the motor operates at constant speed.
 6. What is the phasor relation between induced emf and terminal voltage of a 3 phase  synchronous motor?The rotating magnetic field is initially established by the prime source of supply V. The main field then causes an emf e to get induced in the 3 phase winding. Hence when the machine operates as a synchronous motor the emf phasor always lags the terminal voltage phasor by the load1torque angle   .
7. At what load angle is power developed in a synchronous motor becomes its maximum value ?
When its load angle   is equal to the impedance angle   .

8. What are V and inverted V curves of synchronous motor ?
The variation of magnitude of line current with respect to the field current is called V curve . The variation of power factor with respect to the field current is called inverted V curve.

9. What happens when the field current of a synchronous motor is increased beyond the normal value at constant input?
Increase in emf causes the motor to have reactive current in the leading direction. The additional leading reactive current causes the magnitude of line current, accompanied by the decrease in power factor.

10.Distinguish between synchronous phase modifier and synchronous condenser

A synchronous motor used to change the power factor or power factor in the supply lines is called synchronous phase modifier.

A synchronous motor operated at no load with over excitation condition to draw large leading reactive current and power is called a synchronous condenser

Single phase induction motor Interview Questions Part1

Q1: Where do we require single-phase induction motors?

Ans:Single-phase induction motors are required where

(i) 3 phase supply is not available 

(ii) efficiency is of lesser importance

(iii) Rating is less than one H.P. 

(iv) Equipment is portable

Q2: Why is the power factor of a single-phase induction motor low?

Ans:It is due to the large magnetizing current which ranges from 60% to 70% of full-load current. As a result, even at no-load, these motors reach temperatures close to the full-load temperature.

Q3: What is the function of centrifugal starting switch in a single-phase induction motor?

Ans:The centrifugal switch is connected in series with the starting winding. The primary function of the centrifugal switch is to produce rotating flux in conjunction with main winding at the time of starting. When the motor has started and reaches nearly 75% of synchronous speed, it produces its own rotating field from the cross field effect. The starting winding now has no function to perform and is removed from the circuit by a centrifugally operated switch.

Q4: What happens when the centrifugal starting switch fails to open?

Ans:If the starting switch fails to open when needed, then the starting winding will overheat and burn out and motor will not start next time.

Q5: What happens when the centrifugal switch fails to close when needed?

Ans:If the centrifugal starting switch fails to close, the motor will overheat the main winding without any failure of the main winding.

Q6: Why are resistance split-phase inductions motors most popular?

Ans:These motors are most popular due to their low cost. They are used where moderate starting torque is required and where the starting periods are not frequent. They drive fans, pumps, washing machines, small machine tools etc. They have power ranting between 60 watts and 250 watts.

Q7: What is the draw back of the resistance split-phase induction motor?

Ans:The starting winding has a relatively small number of turns of fine wire and its resistance is higher than that of the main winding. Therefore the current density is high and the winding heats up quickly. If the starting period lasts for more than 5 seconds, the winding begins to smoke and may burn out unless the motor is protected by a built-in-thermal relay.

Q8: Why is the starting torque of a resistance split-phase induction motor not high?

Ans:The starting torque is given as, Ts = K Im Is Sin Ф

Where

            K = constant whose magnitude depends upon the design of the motor

(i) The angle between Is and Im is small (approximately 25 degree) in a resistance split-phase induction motor, so the starting torque is small.

(ii) Since currents Is and Im are not equal in magnitude, the rotating magnetic field is not uniform and the starting torque produced is small.

Q9: Why is the starting torque of a capacitor start induction motor high?

Ans:The capacitor C in the starting winding is so chosen that Is leads Im by 75 degree. Since the starting torque is directly proportional to Sin Ф, and it is quite high in capacitor-start induction motor.

Q10: Why do we use capacitor-start induction motors in applications requiring high starting torque in preference to repulsion induction motors?

Ans:Capacitors are easily available, cheaper and reliable. Repulsion-induction motors posses a special commutator and brushes that require maintenance. Most manufacturers have stopped making them.

Q11: What is the principle of operation of shaded-pole induction motor?

Ans:A shaded-pole motor is basically a small single-phase squirrel cage motor in which the starting winding is composed of short-circuited copper ring (called shading coil) surrounding one-third of each pole. The effect of the shading coil is to cause a flux to sweep across the pole faces, from unshaded to shaded portion of the pole, producing a weak rotating magnetic field. As a result, the rotor is set in motion due to induction principle.

Q12: Which type of torque is developed in single phase motors?

Ans:Pulsating torque is produced.

Q13: If a single phase motor is driven in any direction by any means, it starts running in that direction. Explain why?

Ans:Actually a pulsating torque has two components which are equal in magnitude and rotate in opposite direction with synchronous speed at unity slip. Now if the motor rotates in any direction, the slip decreases and the torque component in this direction increases than the other component and hence motor runs in that direction.

Q14: What is a fractional H.P. motor?

Ans:A small motor having H.P. less than unit is called fractional H.P. motor.

Q15: Which type of rotor is used in single phase motors?

Ans:Squirrel cage type

Q16: How the starting winding produce rotation in a single phase resistance start induction motor?

Ans:The starting winding is highly resistive and the main winding is inductive. So the phase difference between the two currents becomes nearly 90 degree and hence the motor start as two phase motor.    

    

Q17: How the starting winding is made resistive?

Ans:It consists of only few turns of smaller diameter.

Q18: How the speed of rotation of a split phase induction motor is reversed?

Ans: The terminal connections of the starting windings are reversed with respect to main running windings.

Q19: What will happen if the centrifugal switch fails to open the starting winding?

Ans:Excessive heat will be produced due to high resistance of the starting winding due to which stator temperature will rise and eventually both windings will burn.

Q20: How speed control is made in single phase motors?

Ans:It is usually controlled by applying a variable voltage from tapped transformers, variacs, potentio meters, and tapped reactors.

Q21: Is there any relation between the capacitances of two capacitors used in two value capacitor motor?

Ans: Starting capacitor has about 10 – 15 times high capacity than the value of running capacitor.

Q22:  What is size of shaded-pole motor?

Ans: These are usually built in small fractional H.P, not exceed 1/4 H.P.

Q23: Why shaded-pole single phase induction motor does not need any special starting technique like capacitors and auxiliary winding etc.

Ans:Because it is inherently self started motor. The construction of the poles is such that they give a sweep to the magnetic flux and motor starts rotating.

Q24: How can a universal motor be reversed?

Ans: By reversing either the field leads or armature leads but not both.

Q25: What are applications of Stepper motors?

Ans:(i) Paper feed motors in typewriters and printers 
(ii) Positioning of print heads 
(iii) Pens in XY-plotters 
(iv) Recording heads in computer disc drives etc.

Q26: Why do we use capacitor-start induction motors in applications requiring high starting torque in preference to repulsion induction motors?

Ans: Capacitors are easily available, cheaper and reliable. Repulsion-induction motors posses a special commutator and brushes that require maintenance. Most manufacturers have stopped making them.

Q27: If a single phase motor is driven in any direction by any means, it starts running in that direction. Explain why?

Ans:Actually a pulsating torque has two components which are equal in magnitude and rotate in opposite direction with synchronous speed at unity slip. Now if the motor rotates in any direction, the slip decreases and the torque component in this direction increases than the other component and hence motor runs in that direction.

Q28: What is a fractional H.P. motor?

Ans: A small motor having H.P. less than unit is called fractional H.P. motor.

Q29: Which type of rotor is used in single phase motors?

Ans:Squirrel cage type

Q30: How the starting winding produce rotation in a single phase resistance start induction motor?

Ans:The starting winding is highly resistive and the main winding is inductive. So the phase difference between the two currents becomes nearly 90 degree and hence the motor start as two phase motor.  

      

Q31: How the starting winding is made resistive?

Ans:It consists of only few turns of smaller diameter.

Q32: How the speed of rotation of a split phase induction motor is reversed?

Ans:The terminal connections of the starting windings are reversed with respect to main running windings.

Conduction in Semiconductors

At room temperature of 300°K, it requires an energy of E_G = 1.12 eV to break covalent bonds in Silicon material and E_G = 0.7 eV to break the covalent bonds in Germanium material and to produce some ‘electron–Hole pairs’.

Even at room temperature, a few of the covalent bonds will be broken, leading to equal number of electrons and Holes in Conduction Band and Valence Band, respectively. Electrons in the Conduction Band and Holes in the Valence Band, in an intrinsic semiconductor, are shown in Fig. 2.12. Small dashes represent free or conduction electrons. Holes are represented by circles in valence band.

Fig. 2.12 Energy-band diagram for an intrinsic semiconductor

Conductivity and Resistivity of Semiconductor Materials

The value of conductivity of a material gives us an estimate of the extent to which a material supports the flow of current through it. Electrical conductivity depends upon the number of electrons available in the conduction process. The concept of conductivity is useful in many engineering applications including medical electronics.

J = nqμE

Equation (2.17) derived in the previous section can also be written as

is called as conductivity of the material.

Thus, electrical conductivity of a material is defined as the ratio of current density J and electric field intensity E.

Conductivity of semiconductor materials increases with temperature, as an increase in temperature causes increase in conduction current. This is due to increase in broken covalent bonds that result in more charge carriers for current flow. So more electrons from Valence Band jump to Conduction Band with increase in temperature. The conductivity of semiconductors varies completely in the opposite way to that of metals.

Here it is found that current density (J) and field strength (E) are proportional to each other with σ as the constant of proportionality: J ∝ I and E ∝ v.

So σ has the dimensions of Siemens/m as shown below:

As already explained, semiconductors contain two types of mobile charge carriers, electrons and Holes. In semiconductors, the conductivity depends upon the concentrations and mobility of both electrons and Holes (Fig. 2.11).

Fig. 2.11 Electrons in a conducting medium

where n is the concentration (number) of electrons, p is the concentration (number) of Holes, μ_n is the mobility of electrons and μ_p = mobility of Holes.

In an intrinsic semiconductor n = p = n_i

If the values for the mobility and concentrations of electrons and Holes are known, the conductivity of the materials can be estimated.

Current Density in a Conducting Medium

Currents in metals are due to the movement of charge carriers ‘electrons’.

where I is the current in Amperes and A is the cross-sectional area of conducting medium in metre². Describing current density J as current per unit area has the advantage, since the dimensions of the conducting medium are not directly involved. Relation between current density and charge density ρ is described in the following:

Current density: Current I (Amperes) through a conductor by definition is Charge (in Coulombs)/Time (in seconds). Current is due to the movement of charges through a conducting medium in a given time. If, 1 C of charge moves through a conducting medium in 1 s, the resulting current is 1 A.

electrons carry 1 Coulomb of charge. So the movement of 6.25 × 10¹⁸ electrons for 1 s contributes to 1 A of current in a conductor.

where q is the charge of an electron and N is the number of electrons in a given volume. If the charge passes through a distance L (metres) in time T (seconds), through a conducting medium, then the velocity v with which the electrons move is L/T.

Substituting the value of T from Eq. (2.13) in Eq. (2.12), we get

where n = N/AL is the concentration of electrons that is the number of electrons per unit volume.

Using v = μE in Eq. (2.16), we get

where μ is the mobility of charge carriers.

Current density J_p due to the movement of Holes = pqμ_pE.

Conduction in conductors and semiconductors

Conduction in conductors and semiconductors

Mobility μ: In good conductors like metals, free electrons exist in abundance. They are supposed to be accelerated under the influence of electric or magnetic field as per ballistic (dynamics) laws. But in practice it is found that the electrons move with a constant velocity proportional to the field. The reason for this is the random nature of the electron movement involved in repeated collisions. The loss of energy during collisions is supplemented due to acceleration caused by the applied field E. Thus it is observed that the random motion of electrons when resolved in the direction of the field, the electrons acquire a constant speed called the drift speed v that is proportional to the field E (V /m) and velocity v is in metres/second.

where μ is the constant of proportionality. μ is called as mobility. It is measured as m²/V-s. Mobility of electrons and Holes due to the influence of electric field is given in Eq. (2.10). Because of the lighter mass of electrons, electrons have large values of mobility μ_n compared to Hole mobility μ_p.

For a given excitation energy to electrons (due to applied field strength), electrons move faster in Germanium semiconductor when compared to Silicon semiconductor, because of small forbidden band-gap energy in Germanium semiconductors. So Germanium semiconductor devices find their use in high-frequency applications.

Conduction (Inverse of Resistance) in Intrinsic Semiconductors

Purest semiconductor is known as intrinsic semiconductor. At 0°K, semiconductor behaves like an insulator, because energies of the order of E_G cannot be acquired from an electric field. At room temperature, covalent bonds in the semiconductor may be broken into a few Hole–electron pairs, contributing to current flow through the material allowing the conductivity to increase.

With respect to energy, if an electron is given additional energy, it breaks away from its covalent bond. When the free electron enters a Hole in a Valence Band, this excess energy is released as a quantum of heat or light. In turn this quantum of energy may be reabsorbed by another electron to break its covalent bond and create a new Hole–electron pair. Thus Holes and electrons appear to move. The moving charge carries form current. Ohm's law governs the conduction phenomena in conductors and resistors.

Conduction by Holes is less when compared to that of electrons because of differences in freedom of movements for Holes and electrons, based on their mobility μ. The mobility of electrons μ_n is greater than the mobility of holes μ_p because of the differences in relative masses of electrons and Holes.

Typical values of mobility of electrons and Holes in semiconductors

The mobility μ of electrons and Holes is defined as the velocity acquired by these charged particles per unit-applied electric field.

Electrical conduction by electron–Hole pairs generated by thermal energy is called intrinsic conduction in pure semiconductors, of either Silicon or Germanium.

Classification of Materials

When voltages are applied, materials offer different values of electrical resistances to the passage of currents through them. On the basis of electrical resistances, materials are classified as conductors, semiconductors and insulators.

In solids, available energy states for the electrons form ‘bands of energy levels’ instead of discrete energy levels in atoms.

Conductors: Materials with adjacent or over-lapped conduction and Valence Bands with zero forbidden band-gap energy (E_G = 0) are known as conductors. EBD for a conductor material is shown in Fig. 2.7.

Fig. 2.7 Energy-band diagrams for conductors

Initially, the energy levels in the Conduction Band are empty. But, electrons enter the Conduction Band due to increase in temperature or energy acquired from an applied electric field. Then the electrons move freely inside the Conduction Band as charge carriers with each electron carrying an electron charge q_n = 1.6 × 10^–19 C. So in a conductor, electric current can flow freely. Most familiar conductors are metals such as gold, silver and copper.

Semiconductors: Materials with small forbidden band-gap energy (E_G), around 1 eV, re called semiconductors. Silicon, Germanium and gallium arsenide are semiconductor materials. They are also known as intrinsic or pure semiconductor materials.

Semiconductor materials have some of the following features:

• Typical value of resistivity is of the order 0.6 Ω-m at the room temperature.
• The material has negative temperature coefficient of resistance. Resistance of the semiconductor material decreases with increasing values of temperatures.
• The addition or doping of trivalent or pentavalent materials to the intrinsic semiconductors (Silicon or Germanium) modulates the electrical conductivity σ of the semiconductor materials. This is the important feature for the fabrication of P- and N-type semiconductors, which are the backbone materials for semiconductor devices in electronic engineering technology.
• At 0°K, E_G0 = 1.12 eV for a Silicon semiconductor material.
• For Germanium semiconductor, E_G0 = 0.785 eV.
• E_G0 = 1.41 eV for gallium arsenide.
• At room temperature (300°K), E_G = 1.1 eV for Silicon semiconductor.
• E_G = 0.72 eV for Germanium semiconductor.
• Forbidden band-gap energy
  
  
  
  
  
• At very low temperatures, the Conduction Band is practically empty. When the temperature is increased, the electrons in the top of Valence Band acquire sufficient thermal energy and move into the Conduction Band.

E_G is forbidden band-gap energy, E_C is the energy of the lower most energy level of Conduction Band and E^V is the energy of the top most energy level of Valence Band.

Silicon semiconductor has the forbidden bandgap energy E_G = 1.12 eV (Fig. 2.8). EBD for the Germanium semiconductor material is shown in Fig. 2.9. It has band-gap energy E_G = 0.72 eV.

Fig. 2.8 Energy-band diagram for silicon semiconductor

Fig. 2.9 Energy-band diagram for germanium semiconductor

• Silicon has wider forbidden band-gap energy compared with Germanium semiconductor material. This suggests that Silicon devices work up to higher temperatures with stable operation. Silicon devices are preferable for military and tropical country applications.
• Because of smaller forbidden band-gap energy, Germanium devices are limited to lower temperature applications.
• Typical band-gap energy in semiconductors is less than 2 eV.

Insulators: The materials with large forbidden band-gap energy E_G > 6 eV do not support conduction at all. Large forbidden band-gap energy between the Valence Band and the Conduction Band shown in Fig. 2.10 suggests that no electron can reach the Conduction Band. Such materials are known as insulators.

Fig. 2.10 Energy-band diagram for insulator materials

Insulators practically have no free electrons to act as charge carriers to support electrical conduction. Non-metallic solids such as glass, porcelain and mica behave as insulators. Their resistivity is very high, while conductivity is very low.

Energy-band Concepts of Materials

Energy-band Concepts of Materials

• The electron energy levels for a single free atom in a gaseous medium are discrete, since the atoms are sufficiently far apart. So the energy levels of individual atoms are not perturbed.
• The proximity of neighbouring atoms in solid media such as crystals does not appreciably affect the energy levels of inner shell electrons. But, groups of energy levels of outer shell electrons are changed due to the influence of electrons in the neighbouring atoms. They allow sharing of electrons among them to form covalent bonds between neighbouring atoms in the process of getting on to stable ‘8-electron configuration’ in Silicon and Germanium semiconductors.

Sharing of outer shell electrons to form covalent bonds is shown in Fig. 2.5.

• Valence band The coupling between the outer shell electrons of the atoms results in a group or a band of closely spaced energy levels or states instead of the widely spaced energy levels of the isolated atoms. Because of the coupling between atoms in the crystals (As the inter-atomic distance is quite small in solid materials.) completely filled and partially filled energy levels are merged into an ‘energy band’ known as Valence Band.
• Top most energy level of Valence Band is E_V.
• Merging of empty energy levels in atoms form Conduction Band (top energy band).
• Lower most energy level of Conduction Band is E_C.
• Region between Conduction Band and Valence Band is known as forbidden band gap E_G, or band gap equal to (E_C – E_V). It decreases with temperature.
• The magnitude of the band-gap energy E_G predicts the type of the materials, such as conductors, semiconductors and insulators, which is discussed later.
• Energy-band diagrams (EBD) show the energy of electrons (in electron volts) associated with the energy levels on the y axis and the momentum (P) on the x axis. Energy of electrons is measured in eV (electron volts).
• The unit of electron volt (eV) is the energy acquired by an electron while falling through a potential difference of 1 V.

Fig. 2.5 Covalent bonds about silicon atoms

According to quantum-mechanical theory, when the energy band has all filled energy levels; electron there cannot contribute to electrical conduction. There is no open energy level to which they can move after absorbing any energy from the applied electric field. Therefore they do not absorb energy and do not become conduction electrons. Only the band containing the unfilled or empty energy levels is the Conduction band, to which electrons enter to contribute electrical conduction.

Conductivity of a pure semiconductor at ‘Absolute-Zero temperature’ is zero, since lower Valence Band is filled and there are no electrons in the upper Conduction Band.

At the ambient temperature, some electrons may acquire sufficient energy equal to or greater than the forbidden band-gap energy E_G and they will move to energy levels in the upper band. These electrons will be in an incompletely filled band and they can contribute to electrical conduction. While the electrons move to the Conduction Band, they leave Holes in the Valence Band (Holes were formed due to the formation of Hole–electron pairs during the process of breakage of covalent bands in Valence Band). Hole will have positive charge. Formation of Hole–electron pairs is shown in Fig. 2.6.

Fig. 2.6 Formation of hole–electron pair

Conductivity of ‘intrinsic semiconductor’ is due to the Hole–electron pairs formed during broken covalent bonds or due to supply of energy to free electrons to cross the forbidden band gap to enter the Conduction Band.

Resistivity of semiconductor material can be expressed as

where A is a coefficient that varies slightly with temperature, and ρ is the resistivity of the emiconductor material. It is a function of temperature T and forbidden band-gap energy ΔE_G.

Resistance across a standard mass and shape of a material at a given temperature is called the resistivity of the material. The reciprocal of resistivity is conductivity (σ).

Electronic configuration of a Germanium atom

Fig. 2.3 Electron configuration of germanium atom

Germanium semiconductor atom has ‘atomic number’ Z = 32. It has 32 positive charges in the nucleus and 32 electrons in various shells containing 2, 8, 18 and 4 electrons. Germanium atom is electrically neutral. Germanium semiconductor as a whole is electrically neutral.

• First, second and third orbits are completely filled.
• Fourth orbit (shell) is partially filled.
• Energy levels from fifth orbit onwards are empty energy levels.

Germanium atom representation is shown in Fig. 2.4. It is a basis to know the formation of covalent bonds and so on. Germanium is also considered as a ‘tetravalent’ material, as it has 4 valence electrons in its outer incomplete shell. Thus, Silicon and Germanium materials are referred as tetravalent materials with similar electrical and chemical properties.

Fig. 2.4 Representation of germanium atom with four valence electrons