Radiology Physics CH 2 : Conductors, insulators and semiconductors
ELECTRIC CHARGE
The term electric is derived from the Greek word electron. Electric bodies said to possess electric charge (q) and it is a basic property of any matter. There are two types of charges, namely, (i) positive charge and (ii) negative charge. Two like charges repel each other and two unlike charges attract each other. The unit of charge is coulomb. One coulomb (C) is defined as the quantity of charge which when placed at a distance of 1 meter in air or vacuum from an equal and similar charge experiences a repulsive force of 9 × 10–9 N. The amount of charge in an electron is equal to 1.6021 × 10–19 coulombs.
The charges can neither be created nor be destroyed, and the total amount of charge in the system does not change. While calculating the total charge in a system, the signs of the charges should be taken into account.
ELECTRICAL FORCE AND FIELD
The force between two charged particles is directly proportional to the product of the magnitude of the charges and inversely proportional to the square of the distance (r) between them.
ELECTRICAL POTENTIAL
The electric potential (V) at a point in an electric field is the work done (W) in taking a unit positive charge (q) from infinity to that point,
i.e. V = W/q
Positive charges flow from a point of higher potential to point of lower potential and negative charges flow in the reverse direction. The unit of potential is volt and one volt is equal to 1 joule per coulomb. The potential is a scalar quantity and the potential of earth is taken as zero. In practice, kilovolt (kV) and megavolt (MV) are used as units, 1 kV = 1000 volts and 1 MV = 106 volts.
CONDUCTORS, INSULATORS AND SEMICONDUCTORS
Substances in which electric charge moves freely are known as conductors. Substances, which do not allow charge to move freely through them, are known as insulators or dielectrics. The term insulator or conductor is only a relative term and nobody is perfectly insulating or conducting. Substances, which are having their conductivity intermediate between conductor and insulator, are known as
semiconductors.
As per the band theory of conduction, matter is made up of three energy levels, namely, filled band, valence band, and conduction band. Valance band is the highest energy band whose electrons are tied up to individual atoms. It corresponds to the valence shell of a single isolated atom. The filled bands are below the valance band, and they do not contribute to electrical conduction. Hence, it is normally not included in the energy band diagrams.
The conduction band is above the valance band and the electrons are not tied to particular atoms. Hence, it offers free electrons for electrical conduction. The gap between the valance and conduction band is called forbidden gap, which is responsible for the conduction properties of materials. Based on the forbidden gap width, materials may be classified as conductor, insulator and semiconductors.
CONDUCTOR
In conductors, the highest electron energy levels are partially filled and hence its electrons are free to move. There is no forbidden gap between valance and the conduction band, hence electrons move easily from valance band to conduction band. Metals, such as copper, silver and aluminium are good electrical conductors.
INSULATOR
In insulators, the forbidden gap is large, > 9 eV and the electrons unable to flow to the conduction band. Hence, the conduction band is empty and no flow of electric current, e.g. oil, glass, rubber and plastic. At very high temperature, few electrons may move from the valance band, but the material undergo breakdown. This breakdown depends on the applied voltage and the thickness of the material. Hence, X-ray cables are made up of higher thickness of insulation material.
SEMICONDUCTOR
In semiconductors, the width of the forbidden band is 1 eV, e.g. germanium and silicon. At low temperatures, there is no electron flow from valance to conduction band due to lack of sufficient energy and they behave like an insulator. However, at room temperature, they utilize the internal energy of the system and gain > 1 eV energy. This is sufficient to offer electron flow from valance to conduction band, but in a limited way. As the temperature increases, number of electron also increases, resulting higher conductivity. As the electron leaves the valance band, holes are created, which also act like charge carriers. This type of conduction that takes place in a pure semiconductor is called intrinsic conduction.
The conducting property of a semiconductor can be modified by adding impurities to it, which is called doping. By doing so it is possible to create additional energy levels in the forbidden band, resulting higher conductivity. This type of conductivity made out of doping is called extrinsic conductors. There are two types of extrinsic conductors, namely, N-type and P-type (Fig. 2.3). In N-type, there are extra-energy levels, which helps the electrons to move from the valance band to conduction band. In P-type semiconductor, the extra-energy level helps the holes to move, and offer higher electrical conduction.
N-type Semiconductor
When a pentavalent impurity such as phosphorous or arsenic is added to a pure silicon in the ratio 1:106, N-type semiconductor is formed. Four out of five valence electrons of the impurity phosphorous atom form covalent bonds with neighboring silicon atoms. The fifth electron is not associated with any covalent bond and it is free, responsible for conduction. In this type, the majority charge carriers are electrons and the minority charge carriers are holes. Since the impurity donates one electron to the conduction band, it is called donor impurity.
P-type Semiconductor
When a trivalent impurity such as boron is added to a pure silicon (Si), P-type semiconductor is formed. The three valence electrons of boron atom form covalent bands with the three neighboring silicon atoms. The fourth electron of the Si atom is unable to form a covalent bond with the boron atom. Hence, a vacancy is available in the fourth covalent bond. This vacancy is called hole (positive charge) which can accept electrons from other atoms. The majority charge carriers are holes and the minority charge carriers are electrons. Since, there is a hole in the impurity, it is called acceptor impurity.
SEMICONDUCTOR DIODE
A semiconductor (solid state) diode consists of a P-type and a N-type semiconductors which are joined together (Fig. 2.4). Such a arrangement is called the P-N junction diode. When a P–N junction is formed, the holes diffuse from P region and electrons diffuse from N region due to thermal energy. As a result, the holes and electrons combine with
each other and neutralize near the junction. After a short interval of time, a potential barrier is setup near the junction with immobile negative and positive ions which stops further diffusion. The above potential barrier which is created, when a P-N junction is formed is called internal potential barrier or depletion layer. The width of this barrier region is about 10–6 to 10–8 m.
TRANSISTORS
A transistor is formed by three semiconductor materials, which are sandwiched together. Schematic symbols for PNP and NPN transistors are shown in Figure 2.5. There are three regions in a transistor and are called emitter, base and collector. The emitter, base and collector are provided with terminals which are labeled as E, B and C. In the schematic symbols, the arrow head is always at the emitter. The arrow head indicates the conventional current direction flow. The junction between emitter and base is called emitter base (EB) junction. The junction between collector and base is called collector base (CB) junction. Hence, a transistor basically consists of two junctions manufactured back to back in a single piece of a semiconductor.
Transistor Applications
Transistors enable a small current to control the flow of a larger current and have applications in switching and amplification, etc. Large number of transistors along with resistors and capacitors are incorporated in a single silicon chip, known as large scale integration (LSI) and very large scale integration (VLSI) circuits that have multiple applications in medicine and industry.
CAPACITANCE
The property of a conductor to store electric charge is known as capacitance. It is defined as the ratio between the charge and its potential. If Q is the charge in a conductor of potential V then, the capacitance C is given by,
C = Q/V
Capacitance also refers the amount of charge that can be transferred per unit change in its potential. The unit of capacitance is farad (F)
and one farad is the capacitance of a capacitor, which requires one coulomb electric charge to raise its potential by one volt. In practice, microfarad and picofarad are used as capacitance units
CAPACITOR
A capacitor is a device, which increases the capacitance of a conductor. It usually consists of two conductors, one is charged and the other is earthed. The space between the plates is filled with some insulating material called dielectric.
Capacitors are used (i) to store electric charges, (ii) to measure potential
difference and small currents, (iii) to reduce voltage fluctuations, generating oscillations, for providing time delay in various electric circuits, and (iv) to obtain required electric field.
ELECTRICAL CURRENT
The flow of electric charge in a conductor is called an electric current. It is equal to the quantity of charge passing a given point in one second. Charge may flow through solid, liquid and gas or vacuum. The unit of current is called ampere (A). The electric current through a wireless called one ampere, if one coulomb of charge flows through the wire in one second. It is found that one ampere current consists of 6.281× 1018 electrons/s. In practice, milliampere (mA) and microampere are used as units, 1 mA = 10–3A, and 1 A = 10–6 A.
OHM’S LAW
The Ohm’s law states that, a steady current flowing through a metallic conductor is proportional to the potential difference between its ends, provided the temperature remains constant. If I is the current in ampere and V is the potential difference in volts then, I V, at constant temperature, i.e. I = V/R, where, R is a constant known as resistance of the conductor. Ohm’s law is applicable only for
metallic conductors.
RESISTANCE
Resistance is the property of a conductor by which it opposes the flow of electric current. It is defined as the ratio of the potential difference applied across a conductor to the current flowing through it:
i.e., R = V/I.
The device which offers resistance to the flow of current is called resister. In a conductor, the atoms are vibrating and the electrons move
randomly. When a voltage is applied, the electrons move towards the positive terminal. During the process, they collide with vibrating atoms, resulting resistance. The unit of resistance is ohm (). One ohm is the resistance of a conductor through which a steady current of one ampere passes, when a potential difference of one volt exists across
it.
ELECTRICAL POWER
The electrical power (P) is the rate at which energy is expended and it is equal to the product of potential difference (V) and current (I) in a circuit, i.e. P = VI. The unit of electrical power is watt, which is equal to one joule per second (Js–1). In practice, kilowatt and kilowatt hour (kWh) are used as units of electrical power and one kilowatt hour
is equal to 3.6 × 106 J.
HEATING EFFECT OF AN ELECTRIC CURRENT
When electric current flows through a conductor having a resistance, certain amount of electrical energy is converted into heat energy. This heat energy will raise the temperature of the conductor. The above heat is produced by the free electrons as they move through the conductor. On their way, they collide frequently with atoms and give some of their kinetic energy to the atoms. The atoms which gains kinetic energy, generate heat in the conductor.
Joule’s law of heating: The heat (H) developed in a current carrying conductor is directly proportional to (i) the square of the current (I) passing through the conductor, (ii) resistance (R) of the conductor and (iii) time (t) of flow of current i.e.,
H = I2Rt joule
If the current is doubled, the heat generated is four times higher. This concept is applied in fuse wires, as the current goes to higher value, the heat generated in the circuit is sufficient to melt the fuse wire. The melting point of the fuse material is very critical, for material selection.
ALTERNATING CURRENT
Current can be classified into direct current and alternating current. A constant current which is flowing in only one direction is called the direct current. Cells or batteries are used to produce direct current in a small quantity. In the cells or batteries, chemical energy is converted into electrical energy. However, the production of large quantity of direct current is very costly.
A varying current, which reverses direction periodically, is called alternating current. This is generated in power stations, making use
of the phenomenon electromagnetic induction. The machine used in the production of alternating current is called AC generator or alternator. Alternating currents are widely used because it is less costly.
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