PHYSICS INVESTIGATORY PROJECT
By-Ayush Dowerah
[SEMICONDUCTORS] Class-12 A
This project aims to throw a light on subject of semiconductor and their uses in our life and its N.P.S International School working principles.
ACKNOWLEDGEMENT First of all I am thankful to my teacher Mr. Rajesh Kapoor for giving me the opportunity to do this wonderful project on Semiconductors and also guiding and helping me to complete this project. I would also like to thank my school for allowing us the opportunity to undertake such projects and also providing us with the requisite facilities for the same. Lastly i would like to thank my parents and all my friends who have helped and have been there with me and supported me to complete this project within the given time frame.
INDEX Sl.No . 1. 2. 3. 4.
Topic
Introduction Semiconductor-Definition and Theory Types of Semiconductors Electrical Resistivity of Semiconductors
Page No. 1 2 4 8
INTRODUCTION Most of the solids can be placed in one of the two classes: Metals and insulators. Metals are those through which electric charge can easily flow, while insulators are those through which electric charge is difficult to flow. This distinction between the metals and the insulators can be explained on the basis of the number of free electrons in them. Metals have a large number of free electrons which act as charge carriers, while insulators have practically no free electrons. There are however, certain solids whose electrical conductivity is intermediate between metals and insulators. They are called ‘Semiconductors’. Carbon, silicon and germanium are examples of semiconductors. In semiconductors the outer most electrons are neither so rigidly bound with the atom as in an insulator, nor so loosely bound as in metal. At absolute zero a semiconductor becomes an ideal insulator
SEMICONDUCTORS-THEORY AND DEFINITION
Semiconductors are the materials whose electrical conductivity lies in between metals and insulator. The energy band structure of the semiconductors is similar to the insulators but in their case, the size of the forbidden energy gap is much smaller than that of the insulator. In this class of crystals, the forbidden gap is of the order of about 1ev, and the two energy bands are distinctly separate with no overlapping. At absolute “0” temperature, no electron has any energy even to jump the forbidden gap and reach the conduction band. Therefore the substance is an insulator. But when we heat the crystal and thus provide some energy to the atoms and their electrons, it becomes an easy matter for some electrons to jump the small ( 1 ev) energy gap and go to conduction band. Thus at higher temperatures, the crystal becomes a conductors. This is the specific property of the crystal which is known as a semiconductor.
Image showing the energy band structures in different materials
Effect of temperature on conductivity of Semiconductor At 0K, all semiconductors are insulators. The valence band at absolute zero is completely filled and there are no free electrons in conduction band. At room temperature the electrons jump to the conduction band due to the thermal energy. When the temperature increases, a large number of electrons cross over the forbidden gap and jump from valence to conduction band. Hence conductivity of semiconductor increases with temperature.
TYPES OF SEMICONDUCTORS INTRINSIC SEMICONDUCTORS
Pure semiconductors are called intrinsic semiconductors. In a pure semiconductor, each atom behaves as if there are 8 electrons in its valence shell and therefore the entire material behaves as an insulator at low temperatures. A semiconductor atom needs energy of the order of 1.1ev to shake off the valence electron. This energy becomes available to it even at room temperature. Due to thermal agitation of crystal structure, electrons from a few covalent bonds come out. The bond from which electron is freed, a vacancy is created there. The vacancy in the covalent bond is called a hole. This hole can be filled by some other electron in a covalent bond. As an electron from covalent bond moves to fill the hole, the hole is created in the covalent bond from which the electron has moved. Since the direction of movement of the
hole is opposite to that of the negative electron, a hole behaves as a positive charge carrier. Thus, at room temperature, a pure semiconductor will have electrons and holes wandering in random directions. These electrons and holes are called intrinsic carriers.
As the crystal is neutral, the number of free electrons will be equal to the number of holes. In an intrinsic semiconductor, if ne denotes the electron number density in conduction band, nh the hole number density in valence band and n i the number density or concentration of charge carriers, then ne = nh = ni
extrinsic semiconductors As the conductivity of intrinsic semiconductors is poor, so intrinsic semiconductors are of little practical importance. The conductivity of pure semiconductor can, however be enormously increased by addition of some pentavalent or a trivalent impurity in a very small amount (about 1 to 106 parts of the semiconductor). The process of adding an impurity to a pure semiconductor so as to improve its conductivity is called doping. Such semiconductors are called extrinsic semiconductors. Extrinsic semiconductors are of two types : i) ntype semiconductor ii) ptype semiconductor
N-type semiconductor When an impurity atom belonging to group V of the periodic table like Arsenic is added to the pure semiconductor, then four of the five impurity electrons form covalent bonds by sharing one electron with each of the four nearest silicon atoms, and fifth electron from each impurity atom is almost free to conduct electricity. As the pentavalent impurity increases the number of free electrons, it is called donor impurity. The electrons so set free in the silicon crystal are called extrinsic carriers and the ntype Sicrystal is called n type extrinsic semiconductor. Therefore ntype Sicrystal will have a large number of free electrons (majority carriers) and have a small number of holes (minority carriers). In terms of valence and conduction band one can think that all such electrons create a donor energy level just below the conduction band as shown in figure. As the energy gap between donor energy level and the conduction band is very small, the electrons can easily raise themselves to conduction band even at room temperature. Hence, the conductivity of n type extrinsic semiconductor is markedly increased. In a doped or extrinsic semiconductor, the number density of the conduction band (ne) and the number density of holes in the valence band (nh) differ from that in a pure semiconductor. If ni is the number density of electrons is conduction band, then it is proved that ne nh = ni2
P-type semiconductor If a trivalent impurity like indium is added in pure semi conductor, the impurity atom can provide only three valence electrons for covalent bond formation. Thus a gap is left in one of the covalent bonds. The gap acts as a hole that tends to accept electrons. As the trivalent impurity atoms accept electrons from the silicon crystal, it is called acceptor impurity. The holes so created are extrinsic carriers and the ptype Sicrystal so obtained is called ptype extrinsic semiconductor. Again, as the pure Sicrystal also possesses a few electrons and holes, therefore, the ptype sicrystal will have a large number of holes (majority carriers) and a small number of electrons (minority carriers). It terms of valence and conduction band one can think that all such holes create an accepter energy level just above the top of the valance band as shown in figure. The electrons from valence band can raise themselves to the accepter energy level by absorbing thermal energy at room temperature and in turn create holes in the valence band. Number density of valence band holes (nh) in ptype semiconductor is approximately equal to that of the acceptor atoms (Na) and is very large as compared to the number density of conduction band electrons (ne). Thus, nh Na > > ne
ELECTRICAL RESISTIVITY OF SEMICONDUCTORS Consider a block of semiconductor of length l1 area of cross section A and having number density of electrons and holes as ne and nh respectively. Suppose that on applying a potential difference, say V, a current I flows through it as shown in figure. The electron current (Ic) and the hole current (Ih) constitute the current I flowing through the semi conductor i.e. I Ih
= (i)
Ie +
It ne is the number density of conduction band electrons in the semiconductor and ve, the drift velocity of electrons then
Ie = eneAve Similarly, the hole current, Ih = enhAvh From (i) I = eneAve + enhAvh I = eA(neve + nhvh) (ii)
If is the resistivity of the material of the
semiconductor, then the resistance offered by the semiconductor to the flow of current is given by : R = l/A (iii) Since V = RI, from equation (ii) and (iii) we have V = RI = l/A eA (neve + nh vh) V = le(neve + nhvh) (iv)
If E is the electric field set up across the semiconductor, then:
E = V/l (v) From equation (iv) and (v), we have E = e (neve + nhvh)
1/ = e (ne ve/E + nh vh/E)
On applying electric field, the drift velocity acquired by the electrons (or holes) per unit strength of electric field is called mobility of electrons (or holes). Therefore, mobility of electrons and holes is given by : e = ve/E and h = vh/E 1/ = e(ne e + nh h) (vi)
Also, =1/ is called conductivity of the material of semiconductor = e (ne e + nh h) (vii)
The relation (vi) and (vii) show that the conductivity and resistivity of a semiconductor depend upon the electron and hole number densities and their mobilities. As ne and nh increases with rise in temperature, therefore, conductivity of semiconductor increases with rise in temperature and resistivity decreases with rise in temperature.
P-N JUNCTION A p–n junction is a boundary or interface between two types of semiconductor material, p-type and ntype, inside a single crystal of semiconductor. The "p" (positive) side contains an excess of holes, while the "n" (negative) side contains an excess of electrons. The p-n junction is created by doping, for example by ion implantation, diffusion of dopants, or by epitaxy (growing a layer of crystal doped with one type of dopant on top of a layer of crystal doped with another type of dopant).
A p–n
junction circuit symbol is shown: the triangle corresponds to the p side.
If an external potential is applied to the terminals of PN junction, it will alter the potential between the P and N-regions. This potential difference can alter the flow of majority carriers, so that the PN junction can be used as an opportunity for the diffusion of electrons and holes. If the voltage applied decreases the width of the depletion layer, then the diode is assumed to be in forward bias and if the applied voltage increases the depletion layer width then the diode is assumed to be in reverse bias. If the width of depletion layer do not alters then it is in the zero bias state.
Forward Bias: External voltage decreases the built-in potential barrier. Reverse Bias: External voltage increases the built-in potential barrier. Zero/No Bias: No external voltage is applied.
PN Junction Diode When No External Voltage is applied In zero bias or thermal equilibrium state junction potential provides higher potential energy to the holes on the P-side than the N-side. If the terminals of junction diode are shorted, few majority charge carriers (holes) in the P side with sufficient energy to surmount the potential barrier travel across the depletion region. Therefore, with the help of holes, current starts to flow in the diode and it is referred to as forward current. In the similar manner, holes in the N side move across the depletion region in reverse direction and the current generated in this fashion is referred to as reverse current. Potential barrier opposes the migration of electrons and holes across the junction and allow the minority charge carriers to drift across the PN junction. As a result of it, a state of equilibrium is established when the majority charge carriers are equal in concentration on either side of the junction and when minority charge carriers are moving in opposite directions.
A net zero current flows in the circuit and the junction is said to be in dynamic equilibrium. By increasing the temperature of semiconductors, minority charge carriers have been continuously generated and thereby leakage current starts to rise. In general no conduction of electric current takes place because no external source is connected to the PN junction.
Forward Biased Diode With the externally applied voltage, a potential difference is altered between the P and N regions.When positive terminal of the source is connected to the P side and the negative terminal is connected to N side then the junction diode is said to be connected in forward bias condition. Forward bias lowers the potential across the PN junction. The majority charge carriers in N and P regions are attracted towards the PN junction and the width of the depletion layer decreases with diffusion of the majority charge carriers. The external biasing causes a departure from the state of equilibrium and a misalignment of Fermi levels in the P and N regions, and also in the depletion layer. So an electric field is induced in a direction converse to that of the incorporated field. The presence of two different Fermi levels in the depletion layer represents a state of quasi-equilibrium. The amount of charge Q stored in the diode is proportional to the current I flowing in the diode.
With the increase in forward bias greater than the built in potential, at a particular value the depletion region becomes very much thinner so that a large number of majority charge carriers can cross the PN junction and conducts an electric current. The current flowing up to built in potential is called as ZERO current or KNEE current.
Forward Biased Diode Characteristics With the increase in applied external forward bias, the width of the depletion layer becomes thin and forward current in a PN junction diode starts to increase abruptly after the KNEE point of forward I-V characteristic curve. Firstly, a small amount of current called as reverse saturation current exists due to the presence of the contact potential and the related electric field. While the electrons and holes are freely crossing the junction and causes diffusion current that flows in the opposite direction to the reverse saturation current. The net result of applying forward bias is to reduce the height of the potential barrier by an amount of eV. The majority carrier current in the PN junction diode increases by an exponential factor of eV/kT. As result the total amount of current becomes I = Is * exp(eV/kT), where Is is constant. The excess free majority charge carrier holes and electrons that enter the N and P regions respectively, acts as a minority carriers and recombine with the local majority carriers in N and P regions. This concentration consequently decreases with the distance from the PN junction and this process is named as minority carrier injection.
The forward characteristic of a PN junction diode is non linear, i.e., not a straight line. This type of forward characteristic shows that resistance is not constant during the operation of the PN junction. The slope of the forward characteristic of a PN junction diode will become very steep quickly. This shows that resistance is very low in forward bias of the junction diode. The value of forward current is directly proportional to the external power supply and inversely proportional to the internal resistance of the junction diode. Applying forward bias to the PN junction diode causes a low impedance path for the junction diode, allows for conducting a large amount of current known as infinite current. This large amount current starts to flow above the KNEE point in the forward characteristic with the application of a small amount of external potential. The potential difference across the junction or at the two N and P regions is maintained constant by the action of depletion layer. The maximum amount of current to be conducted is kept limited by the load resistor, because when the diode conducts more current than the usual specifications of the diode, the excess current results in the dissipation of heat and also leads to severe damage of the device.
Reverse Biased Diode When positive terminal of the source is connected to the N side and the negative terminal is connected to P side, then the junction diode is said to be connected in reverse bias condition. In this type of connection majority charge carriers are attracted away from the depletion layer by their respective battery terminals connected to PN junction. The Fermi level on N side is lower than the Fermi level on P side. Positive terminal attracts the electrons away from the junction in N side and negative terminal attracts the holes away from the junction in P side. As a result of it, the width of the potential barrier increases that impedes the flow of majority carriers in N side and P side. The width of the free space charge layer increases, thereby electric field at the PN junction increases and the PN junction diode acts as a resistor. But the time of diode acting as a resistor is very low. There will be no recombination of majority carriers taken place at the PN junction; thus, no conduction of electric current. The current that flows in a PN junction diode is the small leakage current, due to minority carriers generated at the depletion layer or minority carriers which drift across the PN junction. Finally, the result is that the growth in the width of the depletion layer presents a high impedance path which acts as an insulator.
In reverse bias condition, no current flows through the PN junction diode with increase in the amount of applied external voltage. However, leakage current due to minority charge carriers flows in the PN junction diode that can be measured in micro amperes. As the reverse bias potential to the PN junction diode increases ultimately leads to PN junction reverse voltage breakdown and the diode current is controlled by external circuit. Reverse breakdown depends on the doping levels of the P and N regions. With the increase in reverse bias further, PN junction diode become short circuited due to overheat in the circuit and maximum circuit current flows in the PN junction diode.
Reverse Biased Diode Characteristics:
V-I Characteristics of PN Junction Diode
In the current–voltage characteristics of junction diode, from the first quadrant in the figure current in the forward bias is incredibly low if the input voltage applied to the diode is lower than the threshold voltage (Vr). The threshold voltage is additionally referred to as cut-in voltage.
Once the forward bias input voltage surpasses the cut-in voltage (0.3 V for germanium diode, 0.6-0.7 V for silicon diode), the current spectacularly increases, as a result the diode functions as short-circuit. The reverse bias characteristic curve of diode is shown in the fourth quadrant of the figure above. The current in the reverse bias is low till breakdown is reached and therefore the diode looks like as open circuit. When the reverse bias input voltage has reached the breakdown voltage, reverse current increases spectacularly. PN Diode Ideal and Real Characteristics
For ideal characteristics, the total current in the PN junction diode is constant throughout the entire junction diode. The individual electron and hole currents are continuous functions and are constant throughout the junction diode. The real characteristics of PN Junction diode varies with the applied external potential to the junction that changes the properties of junction diode. The junction diode acts as short circuit in forward bias and acts as open circuit in reverse bias.