Intrinsic Semiconductors

Germanium and Silicon are two important materials used in electronic devices. They are known as intrinsic material Semiconductor. The germanium atoms has a total of 32 electrons of which 28 are tightly bound to the nucleus and 4 are valence electrons.

The tightly bound electrons do not leave the nucleus. Therefore, each nucleus and it’s tightly bound electrons can be represented by a circle as shown in a two dimensional representation in Fig 1.1. Each positive charge shown as +4 depicts the nucleus along with tightly bound electrons (Since 4 valence electrons have been taken out, a charge of +4, measured in units of electronic charge remains in each circle). Since both germanium and silicon have 4 valence electrons, this representation is same for both.

 

          Fig.1.1: Two dimensional representation of a crystal of intrinsic semiconductor

 
Each atom shares its 4 electron with four neighboring atoms and also shares one electron from each of these four neighboring atoms. These shared valence electrons shown by lines in Fig. 1.1. Thus each atom fills its valence orbit with 8 electrons, out of which four are it’s own and four belongs to the neighboring atoms. This forms the covalent bond between atoms. At “0 Kelvin” Temperature there are no free electrons and hence no conductivity. At higher temperatures some of these valence electrons get thermally excited and break the covalent bond. At room temperature the number of such electrons is very small and conductivity is low. The energy required to break the covalent bond is 0.72 ev for germanium and 1.1 ev for silicon. These dislodged electrons are free to move in a random fashion throughout the crystal.

As an electron breaks the covalent bond and leaves the vicinity of an atom, it leaves a positive charge behind. This positive charge, left behind when an electron-hole pair is created, two charge carrying particles are formed. One is negative another positive on the application of an electric field “E” in the semiconductor the holes and electrons drift in the opposite directions and current flows. The holes are positively charged and move in the same direction as the field. The electrons move in a direction opposite to that of the field.

The conductivity of germanium increases by about 6 percent per degree increase in temperature. For silicon the increase is about 8 percent per degree increase in temperature.

Fig. 1.2 shows the apparent motion of holes due to recombination of holes and electrons. Let an electron breaks its covalent bond at position A and drift to position B under the influences of electron field. If a hole existed at position B, the electron would combine with this hole to neutralize the charge. Now there is a hole at position A and no hole in position B. Thus the hole has moved from position B to A. The drift velocity of electrons and holes is proportional to electric field strength. Thermal agitation produces new electron-hole pairs.

 Fig.1.2: Motion of holes in intrinsic semiconductor

Conductor, Insulator, Semiconductor

Conductor:

In a conductor, the conduction and valence bands overlap as shown in Fig. 1. There is no forbidden energy band region. When an external electric field is applied, the electrons acquire additional energy and to higher energy level. These mobile electrons constitute a current. The overlapping of conduction and valence bands gives rise to high conductivity. The resistivity of conductors is of the order of 10^-7

Ω (ohm). Most metals are good conductors.

Fig:1: Conduction Band formation of Conductor

Insulator:

The energy band structure of insulators is shown in Fig. 2. A large forbidden band of several electron volts, exists between valence and conduction bands. The valence band is completely filled at absolute zero temperature. The valence electrons remain tightly bound to the nucleus. As the temperature of the insulator is increased, the added heat energy enables some valence electrons to jump the forbidden gap and occupy the unfilled level above. At room temperature the number of such electrons is negligible and conductivity is very small. The resistivity of an insulator is very high and is around 10¹⁰ to 10¹⁶ Ω (ohm).

Fig:2: Energy Band Diagram

Semiconductor:

In some substances the forbidden gap between conduction and valence bands is small (about 1 ev). These materials are known as semiconductors. Germanium and silicon are the two examples of semiconductor. At 0K temperature the forbidden gap in germanium is 0.785 ev and in silicon it is 1.21 ev. Even at room temperature some valence electrons have enough energy and can move into the conduction band. Therefore, these materials are slightly conducting. The forbidden energy gap decrease with increase in temperature. The resistivity of semiconductors is of the order of 1 ohm-m.

Formation Of Energy Band In Solids

Formation Of Energy Band In Solids:
When a large number of atoms are brought together to form a crystal, interactions occur the proper inter-atomic spacing for the crystal. The discrete energy levels of electrons  of an atom are modified by the presence of other nearby atoms. As the spacing between atoms is decreased, the energy level of each electron is increasingly influenced by the charge distribution of neighboring atoms. The magnitude of influence depend on the spacing between atoms as also the location of the electron in the group. Levels of outer shell electrons are changed consideration of the electrons are shared by more than one atom in the crystal. New energy levels of outer shell electrons can be determined by the principles of quantum mechanics. Pauli's exclusion principle dictates that no two electrons in a given interacting system may have the same quantum state. Thus there must be a splitting of the discrete energy levels of the discrete energy level of the isolated atoms into new levels belonging to the pair rather than individual atoms.

Uni-Junction Transistor (UJT)

A Uni-junction transistor (UJT) is a switching device.It switches from blocking to conducting state when the applied voltage reaches a critical value. It is a bar of high resistivity semiconductor with ohmic contacts at each end. The bar is usually of n-type material. A p-type emitter is alloyed at an intermediate position along the length. (In complementary UJTs the bar is p-type and the junction is n-type). When the junction is open or reverse biased, the resistance between base 1 and base 2 is a few kilo-ohms (fig. 1).

Fig: 1: The Symbol, Construction & Equivalent circuit of UJT 

When a positive voltage VBB is applied between B₂ and B₁ , the potential of point E will be ηVBB. The factor η is known as the intrinsic stand off ratio and depends on internal resistance R_B1 and R_B2 of the bar. If V_E is less than V_C , the p-n junction will be reverse biased, the emitter current will be negative and equal in magnitude to the small reverse saturation current. The V-I characteristics are shown in Fig. 2. When V_E = ηVBB + V_D ,where V_D is the forward voltage drop of the diode, the emitter base junction will become forward biased. The emitter current will become positive. The point A is known as peak point. The corresponding voltage and current are Vp and I_P respectively. The holes injected by the emitter drift towards B₁. Therefore, the number of charge carriers in the lower half region of the bar increases and the resistance R₁ decreases. Therefore, the potential of point C will decrease and the p-n junction will experience a higher forward bias. Therefore, the potential of point C will decrease and the p-n junction will experience a higher forward bias.

 Fig: 2: Characteristics Curve of UJT

Light Emitting Diode (LED)

Light energy can excite an electron into the conduction band. On the other band, when recombination takes place energy is released. In a semiconductor with an indirect band gap, e.g, silicon,germanium etc. recombination releases heat to the lattice. However, in some materials (e.g gallium arsenide), direct transitions occur between conduction band and transition band. In these materials, the radiation is in the visible and infrared regions. This effect, knows as injection electroluminescence, finds important application in digital watches, calculators etc. In a light emitting diode, an electric current causes the injection of minority carriers into regions of the crystal where they can recombine with majority carriers resulting in emission of light. The light output varies as (current)ⁿ , where n varies from 1.2 to 1.5 A wide range of photon energies extending from ultraviolet to infrared are available. The available energies can be increased still further by mixing the compounds. Commonly used displays are red, yellow,green and orange.
Figure-1 shows symbol for LED

Figure:01 LED Symbol

 Figure:02 LED circuit diagram

Figure-2 shows a simple circuit to regulate the current through an LED. The forward current I_f

 given by

I_f = (V-V_f  / R)

Where V_f is the forward voltages across the LED. The LEDs for different colours have different values of V_f and I_f. The diode D₁ is to protect the LED against reverse breakdown voltage. When reverse voltage exceeds a certain value, D₁ starts conducting and protect the LED.

Energy Levels

Energy Levels:
An atom consist of positively charged nucleus which contains almost all it's mass. Surrounding this nucleus are negatively charged electrons moving about in closed orbit. While in states corresponding to these discrete energies, electrons do not emit radiation and are said to be in stationary or non-radiating state. A stationary state is determined by the condition that the angular momentum of the electron in this state is quantized and must be an integral multiple of  h/2π,

Where,
            m= mass of electrons, Kg
             v= speed of electron in its circular path, m/s
              r= radius of orbit, m
             h= planck's constant
       
             n= integer
If n= 1,2,3,.................
We get stable orbits with radius r₁,r₂,r_3,................
For n-1, we get an orbit closest to the nucleus and possessing minimum energy. This lowest energy level is the innermost or K shell of the atom and can accommodate only 2 electrons.
The next higher energy level, known as L shell, can accommodate 8 electrons and so on.
The Outer orbit is generally not completely filled and the electrons in this orbit are known as Valence electrons.
In a transistor from one stationary state (corresponding to energy  W₂) to another stationary state (corresponding to energy  W₁) radiation is emitted.
The frequency of the radiant energy is__

Common Emitter (CE) Connection Of Transistor

The most transistor circuits operate with the emitter terminal as common to the input and output circuits. This is known as CE connection and is shown Figure-1. In this connection the left hand loop is the base loop and the right hand loop is the connection loop. The base circuit controls the collector circuit.

Figure:(01) CE  Connection of NPN Transistor

V_BB   is the base supply voltage and R_B is the current limiting resistance in base circuit. V_BE denote the voltage between the base and the emitter. V_BB is more than V_BE. Typically V_BB lies between 5 and 15 V in most circuits.
By changing V_BB and R_B. We can control the base current. The base current control the collector current. V_CC is the collector supply voltage and V_CE is the voltage between collector and emitter. R_C is the current limiting resistance in the collector circuit. As before the base emitter junction is forward biased whereas the base collector junction is reverse biased. The currents I_B, I_E, I_C are assumed positive when they flow into the transistor.

Figure-02 shows the output characteristics of the CE connection. These characteristics depict the relation between collector current I_C and collector to emitter voltage (V_CE) for different values of base current.
These characteristics are for a n-p-n transistor. These characteristics have three distinct region, i.e. active region, saturation region and breakdown region.

The active region is the region in which the curves are almost horizontal. V_CE is between a fraction of 1V and a few volts. In this region, the collector junction is reverse biased and the emitter junction is forward biased. When a transistor is used as an amplifier, it must operate in this region only. The base current is  I_B = - (I_C+I_E)

Basic Concepts of Amplifier CKT

Introduction:

The collective abbreviation of the two English words 'transfer' and 'resistor' is the transistor.

It basically works on the Resistance Transfer rule. The transistor is called a current driven device. And this current is transfer by resistance. That's why the name of the device is transfer resistor or transistor. Transistor is formed when connecting two Semi-conductor diodes as well. Transistor has three Regions (or Layers) and three terminals or electrodes or leads. The terminals are: collector, base and emitter.

Three scientists of America's Bell Telephone Laboratory invented transistor in 1948. There was a Revolution in the electronic world after the transistor was created.

Picture: John Bardeen, William Shockley and Walter Brattain at Bell Labs-1948

Transistor is the active device. Transistors are usually used for amplification and switching. Transistor has two PN Junctions. Every PN junction has a potential barrier.

Due to the barrier of the transistor, the input supply/signal is not transmitted instantly. As a result, the complete signal is not amplifiable; the part of the original signal is excluded. Particular part of the signal is a major drop in the gap between the faithful operations. To avoid this error and difficulty, the transistor has to be biased. This means that when crossing the signal through a transistor circuit, the circuits have to be biased to maintain the value of the zero signal collector current and collector emitter voltage.

Fig: PNP & NPN Transistor Symbol

Conditions of  biasing are: (1) Base emitter junction forward biasing and (2) Base collector Junction reverse biasing is done.

When the transistors send a small signal to the magnified size of the Output, then it is called amplification.The device is called Amplifier. So Transistor is one kind of Device that works as an amplifier & switching.

Amplifier:
The method in which the weak signal is changed into a strong signal, it is called amplification. The device that is used to amplify the amplification process is called an amplifier.

Resistance, Capacitance & Inductance

Resistance:
Electric current in a conductor consists of movement of electrons. When electrons flow through a material, they collide with other atomic particles and energy is lost in these collisions.
The energy lost per unit charge is the voltage drop across the material. The ratio of voltage drop to current is the resistance of the material.
Thus,
V = IR
Where, v= voltage drop, (v)
             I=current, (A)
             R=resistance (ohms,Ω)

Above equation is known as ohm's law which can be stated as under: "The potential difference between the ends of a conductor is equal to the product of its resistance and current."

The voltage and current may be constant or functions of time. Above Figure shows a schematic representation of resistance. V is the voltage drop in the direction of current or a voltage rise in the opposite direction to flow of current.


Capacitance:
Let us refer again to the elementary capacitor shown in below figure for a given battery voltage a definite number of electrons is attracted into the bottom plate and the same number of electrons is driven out of the top plate of the capacitor. If the applied voltage is doubled, twice as many electrons get accumulated on the bottom plate and get driven out from top plate. The amount of charge is directly proportional in the voltage.

 Q = Cv
The constant of proportionality C is called the capacitance of the capacitor.
The SI unit of capacitance is Farad (F). The Farad is the capacitance of a capacitor that store a charge of 1 Coulomb when the potential difference between its terminals is 1 volt. Farad represents a very large value of capacitance. Therefore the terms µF (Micro Farad) and pF ( pico farad) are commonly used.

Inductance:
A statically induced e.m.f can be self induced too. Whenever the current through a coil changes the flux also changes. The change of flux induces an e.m.f in the coil. Thus a coil can introduce an  e.m.f in itself when the current through it changes. This property of the coil is known as inductance. The self-induced e.m.f can be written as

Where e is the induced e.m.f and di/dt is the rate of change of current. The coefficient L is called the self-inductance or simply inductance.


The SI unit of inductance is Henry (symbol H). The inductance of a coil is 1 Henry if an e.m.f of 1 volt is induced in it by a current changing at the rate of 1 ampere per second. It is evident that every coil or even a single conductors has self inductance. However it comes into play only when the current through the coil (or conductor) changes.

By Len'z law this induced e.m.f is in a direction so as to oppose the external e.m.f which is draining current through the coil.
In applying above equation, the induced e.m.f can be written as a voltage drop (from a to b) or as a voltage rise (from b to a) as seen in figure below.

When it is expressed as a voltage drop e_ab,we write

When this e.m.f is written as a voltage rise, it is necessary to add a negative sign. Therefore

In written circuit equations, the former representation is always preferred and the induced e.m.f is written, without the negative sign, as 

Resistor, Conductor,Insulator, Capacitor & Inductor

Resistor:
Resistance is one of the three passive elements of electric circuits. Every element has some amount of resistance. The resistance of leads capacitors and inductors can usually be ignored.

From circuit point of view a resistor is a device which shows a constant relation between the voltage drop across it and the current flowing through it. Thus it obeys ohm's law. 
From the energy view point the resistance parameter can be thought of as a device capable of converting electrical energy into heat energy. The resistance parameter is a geometric constant as seen in equation below.

Here, 
 R= resistance (ohms,Ω)
 l  = Length (m)
 A = Area of cross section (m²)        




 Resistors of values ringing from milli-ohm are used in a variety of circuits of electrical machines, instruments,electronics and heating devices. They are classified into wire wound and carbon composition resistors.

Conductor:

Capacitor:

A capacitor is a device capable of strong electric charge. It is one of three passive elements of electric circuits. It consist of two insulated parallel metallic plates with air or any other insulating material in between.

Above Fig. shows two conductive parallel plates separated by an air space and connected to a battery/source. It consists of two insulated parallel metallic plates with air or any other insulating materials in between.

• Electrons flow from the negative terminal of battery to the bottom plate A. Since air is an insulator, these electrons can't go further. They accumulate on the plate A giving it a negative charge.
• The negative charge on plate A produces an electrostatic field around it. The direction of this field is to repel electrons towards plate B.
• Electrons flows from plate B to the positive terminals of the battery. This happens due to the attracting force of the positive terminal and the repelling force of the field due to charge on plate A. Plate B acquires positive charge.
• When plates A and B become charged, negatively and positively respectively, a potential difference build up between them. This difference is in opposition to the battery voltage. When this potential difference becomes equal to applied voltage, no more electrons can flow and the circuit reaches static state.
• When the switch is kept closed or opened does not make any difference. Even if the switch is opened, the potential difference between the plates will be maintained. The capacitor has stored the charge. If the switch is opened and the plates short circuited, the surplus electrons on plate A travel to the plate B. This continues till the potentials of the  two plates become equal and the capacitor becomes completely discharged.

EMF/Voltage/Potential Difference & Current

EMF/Voltage/Potential Difference:

Absolute potential of a point is the work done in moving a unit positive test charge from infinity to the point. The potential difference between two points is the work done in moving a unit positive test charge from one point to the other.

If we have two points A and B and it requires work to move a unit positive charge from B to A, then A is said to be at higher potential with respect to B or the potential difference between points. A and B is positive when we move from point B to point A, so experience a rise in potential. Conversely from point A to B there is a fall of potential.

The SI unit of potential of potential difference is volt (symbol V).It is defined as the potential difference across a resistance.

Since the potential difference between two points A and B may be positive or negative, it is more appropriate to write as it as, say V_AB which means potential of point A with respect to that of point B. If A is at higher potential than B, V_AB is positive. Then V_AB (i.e. potential of point B with respect to that of A) is negative. Thus V_BA= -V_AB. The terms potential difference and voltage are synonymous.

 The term emf (electromotive force) is also used instead of voltage. Strictly speaking emf is the total voltage of a source (e.g. a battery or a generator). There would always be some voltage drop in the source itself and the voltage at the terminals of the source would be a bit less than the source emf. The voltage at the terminals is known as output voltage or terminal voltage.

Electric Current:

An atom consists of a nucleus and electrons which are in different orbits around the nucleus. The electrons in the outermost orbit are known as valence electrons. This valence electrons are rather loosely bound to the parent atom. When the different atoms of a conducting material are packed to form a solid, the valence electrons are free to move from one atom to another. 

The motion of valence electrons is in random directions. When a field is applied to the conductor, the motion of electrons gets channelized. More electrons flow in on correction that in the reverse direction. Thus there is occurs the flow of electrons. The rate of flow of electrons is electric current. 

It so happens that the reference direction of flow of positive current is reverse of the direction of flow of electrons. The direction of current was assumed much before the concept of electron was discovered.

Later on it was established that electric current is essentially the flow of electrons. However, the original convention about the direction of positive current is still being used.

When a current is flowing in a conductor having a non-uniform cross sectional area, the current is the same for all cross sections of the conductor. This is due to the principle conservation of charge.

The SI unit of current is ampere (symbol A). 1A is defined as the constant current which, when following in each of the two straight infinitely long parallel conductors, situated in vacuum and

spaced one meter apart, produces a force equal to 2×10^-7 newton per meter length between them. 

1A also means flow of 1C (i.e. 6.24×10⁸ electrons) charge past ant point in a conductor in on second. However, this statement doesn’t indicate the speed at which electrons are moving. This speed known as drift velocity is very small about 1 mm per second. 

Nevertheless, electric signals travel along the conductor at a very high speed. The phenomenon is similar to that in fluid mechanics. The speed of water particles is very slow. However when a pressure flows through at one end of a long pipe full of water, a pressure wave travels rapidly along the pipe.

In solids, the current is solely due to electron. In liquids, the current is due to the motion to positive ions and negative ions. In gasses, the current is due to electrons, positive ions and negative ions. In vacuum tubes, the current is due to electrons emitted from the cathode. In semiconductors, the current is due to electrons and holes.

A current may be direct (dc) or alternating current (ac). A direct current flows continuously in the same direction. However, an alternating current flows first in one direction for a brief instant and then in the reverse direction for another equally brief instant. Thus the direction of an alternating current keeps on changing continuously. The supply of electric power to consumers now-a-days is through alternating current.

The current density is the current per unit area

The units for current density is  A/m²