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1 Concept of Core Conductivity of conductor and semiconductor can also be explained by concept of Core. Core: Core is a part of an atom other than its valence electrons. Core consists of all inner shells and nucleus. Concept of core for a carbon atom is illustrated in figure below. The nucleus consist of 6 protons and 6 neutrons, so nucleus indicates +6 charge and in shell 2 electrons represent -2 charge, so core has net charge of +4. This charge of core will apply attraction force on outermost valance electrons. Comparison of Semiconductor and Conductor (Using core concept): Silicon is a semiconductor and Copper is a conductor. Charge on core of Silicon and Copper is indicated in figure below. Notice that core of Silicon atom has a net charge of +4(14 protons 10 electrons) and core of Copper atom has net charge of +1 (29 protons 28 electrons). The valence electron of Copper atom feels attractive force of only one positive charge compared to silicon atom which fells attractive force of four positive charges. Therefore four times greater power is available in Silicon atom to hold valence electron than Copper. Valence electron of Copper exists in fourth shells and it is at greater distance than Silicon atom which has valence electron in third shell. Page 1

2 This means that it is easier for an electron to escape out from valence band and become free in conduction band of Copper atom than Silicon atom. Therefore Copper atom behaves like conductor and Silicon behaves like an insulator. Comparison of Silicon and Germanium (Using core concept)- We can compare Silicon and Germanium on the basis of atomic structure as shown in figure below. Total Charge on core of both atoms is same but outermost electron in Germanium is at larger distance than in Silicon. The energy required to escape out electron from valence band to conduction band in Silicon will be greater than Germanium. Germanium will be more conducting than Silicon. Page 2

3 Introduction- P-N Junction Diode Page 3

4 If we dope atom with three valence electrons in intrinsic semiconductor material, then we call it p-type semiconductor material. Every doped atom is called acceptor atom and each doped atom creates hole associated with it. If hole shifts to some other atom then particular doped atom will be converted into ion and it will be called accepter ion. We call it accepter because atom accepts or ready to accept electron to satisfied its hole. Hole available in p-type material can be considered as a particle with positive charge because hole represents vacancy for electron. Concentration of hole and accepter atom depends on doping concentration of impurity. Energy band diagram of p- type material shows holes in valence band and some minority electrons in conduction band (due to temperature). If we dope atom with five valence electrons in intrinsic semiconductor material, then we call it n-type semiconductor material. Every doped atom is called donor atom and each doped atom creates free electron associated with it. If this free electron shifts to some other atom, then particular doped atom will be converted into ion and it will be called donor ion. We call it donor because atom donates free electron to semiconductor material. Free electron available in n-type material will be free to move. Concentration of free electron and donor atom depends on doping concentration of impurity. Energy band diagram of n- type material shows free electrons in conduction band and some minority holes in valence band (due to temperature). If one part of an intrinsic semiconductor material is doped with p-type impurity and other part with n-type impurity, then the boundary between these two types of doping is called p-n junction. Formation of Depletion region- In above figure junction between p- type and n-type semiconductor is shown when it is just formed. We can see that on left side of junction in p-type semiconductor large numbers of holes are present, and on right side in n-type there is no hole or can be little amount of hole if some temperature is applied. So concentration difference of holes will be developed on p-side p-n junction. Similarly on the right side of this junction concentration difference for free electrons will developed, because concentration of free electron on n-side will be much greater than concentration of free electrons on p-side. So Page 4

5 diffusion of holes from p-type to n-type and diffusion of electrons from n-type to p-type will be started. Diffusion process-the spread of particles through random motion from an area of high concentration to an area of lower concentration is known as diffusion. The unequal distribution of molecules is called a concentration gradient. Once the molecules become uniformly distributed, dynamic equilibrium exists. Diffusion process can be understood by figure below. In this process some holes and free electrons will come in contact and recombination will be possible. Due to recombination of free electrons and holes accepter atom on p-side will be converted into accepter ion and similarly donor atoms on n-side will be converted into donor ion. So a layer of negative acceptor ion on p-side and a layer of positive donor ion on n-side will be developed near the junction. Due to this layer a potential difference will be developed near the junction, or we can say an electric field will be developed in the direction from donor to acceptor ion near the junction. So an energy barrier will be developed to block movement of holes from p-side and free electrons from n-side. The diffusion of majority charge particles will be blocked by the electric field developed at this layer, so this layer will be depleted of movable charge particles. Therefore this charged layer will be called depletion layer. Page 5

6 P-N junction (energy diagram approach)-formation of energy barrier and depletion region at the junction can also be explained by energy band diagram approach. Energy band diagram of p-n junction diode before diffusion is shown in figure below. From this figure we can see that the valence band of p-type semiconductor is filled by many holes and conduction band is vacant and conduction band of n-type is filled by many free electrons but valence band is vacant. In presence of temperature some electrons in conduction band of p-type and some holes in valence band of n- type can be available. But why p-bands are slightly higher n- bands? The p-type material has trivalent atoms with core net charge of +3 (shown in figure below) on the other hand n-type has pentavalent atoms with core net charge of +5. A +3 core charge will attract electrons with smaller force than +5 does. Therefore the orbits of trivalent atom (p-type) are slightly larger than pentavalent atom (n-type). This is why p-type bands are slightly higher than n- type. Page 6 When p-n junction is just formed, there is no depletion region. In this case free electron from n- side and holes from p-side will start diffusion. From figure it is clear that some part of higher energy range in conduction band of n-side is at equal level of lower energy range in conduction band of p-side. So, free electrons of n-side available in this energy range will be diffused into conduction band of p-side due to concentration gradient. Thereafter these free electrons will loose their energy and will jump into holes available in valence band of p-side and will recombine with holes.

7 Due to this hole will be disappeared and free electron will be converted into valence electron. After this, energy range of rest of the free electrons in conduction band of n-side will be lower than energy range in conduction band of p-side. Therefore diffusion of free electrons from n-side to p-side will be not possible. After this process donor atoms of n-side will be converted into donor ions and acceptor atoms of n-side will be converted into acceptor ions. Due to positive charge layer of donor ion on n-side and negative charge layer of acceptor ion on n-side, an electric field will be developed from n to p. The donor ion layer of n- side will develop higher potential than accepter ion layer of p-side and a potential barrier will be developed near the junction. This potential barrier will block further movement of majority charge particles. So this region will be depleted of movable charge particles and it will called depletion region. Energy Hill: This figure shows energy band diagram of p-n junction after formation of depletion region. The p-bands have moved up with respect to n-bands. Because due to recombination of free electron into hole in p-side valence band an extra electron will be added into trivalent atom. This extra electron will reduce effect of nucleus on conduction band, so conduction band of p-side will be shifted upward. Therefore bottom of each p-band level with top of the corresponding n-band. This means that free electrons in conduction band of n- side no longer have enough energy to cross the junction. For an electron trying to diffuse across the junction, the path it must travel looks like a Hill an energy hill. The electron in conduction band of n-side can not climb this hill unless it receives energy from outside source. Operation of p-n junction diode- Operation of p-n junction diode depends on biasing of diode. For further discussion concept of biasing should be discussed. Biasing- Biasing means providing facility to any device or system to fulfill particular interest. For example if we want to move a car in backward direction then fuel will required to start the car and back gear should be used to move backward. Fuel and back gear are biasing on car to fulfill our interest (backward movement). Page 7

8 From electronics devices point of view, biasing means to provide required energy or condition to fulfill particular interest. Operation of diode depends on the energy hill developed at the p-n junction. Energy hill at junction can be controlled by applying some external source like voltage source, current source etc. Biasing of diode using voltage source can be divided in three parts. 1) No bias condition 2) Forward bias condition 3) Reverse bias condition. To discuss operation of diode in different biasing conditions, knowledge of ohmic contact is required. Ohmic Contact- To apply voltage source across diode, diode should be connected to battery with conducting wire. Contact point between semiconductor and conductor can show different behavior for different direction of current. If this contact point shows same behavior for both forward and reverse current then we call it Ohmic Contact. So we can say that ohmic contact should behave like a resistor. That s mean it should follow Ohm s law. This is the reason to call it Ohmic contact. In this discussion we will consider contact point between semiconductor and conductor as an Ohmic contact. No bias condition- No bias means, any voltage source or external energy is not applied across diode. Due to presence of energy hill across depletion region movement of majority charge particles will be not possible in p-n junction diode. So in no-bias condition current through diode will be zero. Forward bias condition- Forward bias condition means to provide facility to diode for forward current. Current from p to n in p-n junction diode is considered as a forward current. So voltage condition applied across diode for current from p to n is called forward bias condition. Current from p to n will be possible if electron in n-side can be able to cross the energy barrier at the junction. It will be possible if higher voltage is applied at p-side and lower voltage is applied at n-side. This voltage condition can reduce energy barrier, so current can be possible from p to n. Therefore forward bias condition of p-n junction diode will be application of higher voltage to p- side and lower to n-side. Operation of diode in forward bias condition can be divided in three sections. i) Applied voltage is much smaller than voltage barrier at junction ii) Applied voltage is approximately equal to barrier voltage and iii) Applied voltage is greater than barrier voltage. Page 8

9 i) Applied voltage is much smaller than barrier voltage- In this biasing condition majority charge particles will be drifted from ohmic contact towards junction due to applied voltage. The drift velocities of these particles will not enough to reach near the junction. If some charge particles can be present in depletion region due to thermal energy or any other effect then they can cross the junction. So a very small current can be seen in this biasing condition but it can not be measured in lab. If we increase applied voltage then some majority charge particles can be reached near the junction and by diffusion they can cross depletion region and value of current can be increased. In this process majority charge particles can reach in depletion region, so are depleted of movable charge particles will be decreased that means width of depletion region will be decreased. On application of small voltage only majority charge particles can be injected into depletion region. This is called low level injection. It can be understand by analogy with process of injecting medicine by doctor in our body. Doctor injects medicine with some small pressure which can just inject medicine in our body. After this, medicine diffuses in our body due to concentration difference. Page 9

10 ii) Applied voltage is approximately equal to barrier voltage- In this biasing holes in p-side will be drifted from ohmic contact towards junction and electrons on n-side will drifted from ohmic contact towards junction. Drift velocity of these charge particles will be highest near the ohmic contact and will start decreasing on moving towards junction. But if applied energy is equal to barrier voltage then these drifted charge particles can be able to reach near the junction. With of depletion region will be reduced and Energy hill near the junction will also be reduced. Concentration gradient will be developed near the junction and diffusion of free electrons will be started from n to p side and diffusion of holes from p to n side. Diffused charge particles will be attracted towards battery terminal. Holes injected from p-type into n-type will be drifted towards negative terminal of battery and electrons drifted from n-type into p-type will be drifted towards positive terminal of battery. So, most of the currents near the junction will be diffusion current and near ohmic contact will be drift current. Page 10

11 Current components in forward biased diode- From above discussion it is clear that the current through diode will be combination of both drift and diffusion current. Near the ohmic contact dominating part of current is due to drift and near junction dominating part of current is due to diffusion. From figure below it can be seen that near ohmic contact most of the current is due to drifting of charge particles. But on moving towards junction drift current is decreasing, and near junction it is at lowest value. Diffusion current is domination near junction, it is due diffusion of majority charge particles which are collected near the junction. Ipp shows drift current due to holes in p-side Inn shows drift current due to electron in n-side. Ipn shows diffusion current in n-side due to holes which are injected from p-side. Inp shows diffusion current in p-side due to electrons which are injected from n-side. At any position in diode the total current in diode is combination of drift and diffusion. Drift current is dominating near ohmic contact and diffusion current is dominating near the junction. Page 11

12 iii) Applied voltage is greater than barrier voltage- If applied voltage is greater than barrier voltage then holes drifted from p-side and electrons from n-side will cross barrier at junction easily with some velocity. Width of depletion region will be reduced but can not be zero because some recombination may be possible. So contribution of diffusion on junction will be decreased, and effect of drift will be increased. On further increasing applied voltage, current through diode will rise sharply and most of the currents in diode will be due to drift. In this voltage condition diode will show linear behavior. Conclusion: On application of a very small voltage across diode current through diode will be approximately zero. On increasing this voltage a very small current will be possible and dominating current near junction will be due to diffusion and at ohmic contact it will be due to drift. On further increasing, if applied voltage is equal to barrier voltage, width of depletion region will be much reduced and measurable current will be seen through diode. If applied voltage is increased to grater than barrier voltage, a current will be seen and behavior of diode will be linear. Page 12

13 Reverse bias condition- Reverse bias means application of voltage across diode in such a manner that can provide current through diode in reverse direction (current from n to p). For this higher voltage should be applied to n- terminal and lower to p-terminal. In this situation holes in p type will attracted towards negative terminal of battery and similarly electrons in n-type will positive terminal of battery. So the majority charge particles will move away from the junction, width of depletion region will be increased, so there will no current due to majority charge particles. But if minority charge particle is available in p-type that is free electron it will cross depletion region and will move towards positive terminal of battery. Similarly hole available in n-type will move toward negative terminal of battery. So there will be a current from n to p due to minority charge particles. It will be a drift current. For very low biasing voltage only some minority charge particles can be drifted so only small current will be possible. But on increasing reverse biasing voltage this drift current will be increased. The number of minority charge particles is very small, so on increasing reverse bias voltage, initially reverse current will be increased but after a particular voltage, at which all minority charge will start drifting, reverse current can not be raised. This current will be called reverse saturation current. That s means current in diode is in reverse direction and is saturated with respect to applied voltage. This current is due to minority charge particles so its value will be very small and it can be changed by temperature only. Effect of temperature on reverse saturation current- Generally it is seen that for every 1 degree rise in temperature reverse saturation current increases by 7% of its value. If IO is a reverse saturation at temperature t1 then at reverse saturation current IO at temperature t2 (t1+ 1) will be IO1 = IO + 7% of IO= IO (1+ 7/100) = IO (1.07) For 2 degree rise in temperature, IO2 = IO1 + 7% of IO1 IO2= IO1 (1+ 7/100) = IO1 (1.07) =IO (1.07) (1.07) =IO (1.07) 2 Similarly for 10 degree rise in temperature, IO10=IO (1.07) 10 IO (2) Page 13

14 That s means for every ten degree rise in temperature reverse saturation current increases to double of initial value. It can be represented by relation IO2 = IO12 (T2-T1)/10 Page 14

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