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EE4209 Instructor: Md. Nur Kutubul Alam Department of EEE KUET

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Analogy of water and current flow Water flows at non-equilibrium condition only.

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Equilibrium situation Arbitrary reference level mgh w mgh g Potential energy, mgh w < mgh g That is why water can not reach to river bank. And at the same time, water has a maximum height or level above which there is no water. This level is called Fermi level Fermi level h w < h g

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Small disturbance to the Equilibrium Arbitrary reference level mgh w mgh g Fermi level Small disturbance like wind or storm can create a wave of water. In this condition, a very small fraction of total river water can go above the fermi level.

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Movement of water Arbitrary reference level mgh w mgh g Fermi level 1 Fermi level 2 If we dig a pond in the river bank, it will be at a larger height than river water. But the pond water also has a fermi level and this level is at a higher position than that of river water until they are disconnected from each other.

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Movement of water Arbitrary reference level mgh w mgh g Fermi level 1 Fermi level 2 Now, if we remove the barrier between pond water and river water, water will flow from pond to river. WHY???? Pond water had a higher potential energy and physical body wants to minimize its energy. In another sense, pond water had higher fermi level and no two system wants different fermi level, when they are connected by appropriate mean. They want a single fermi level which implies the equilibrium.

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Its all about Energy Arbitrary reference level mgh w mgh g Fermi level To be at any geometric position of the land, water needs a minimum amount of energy depending upon that position. For example, at a position where the pond was dug (see few slide back), water needs “mgh g ” amount of energy to be there.

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Its all about Energy Arbitrary reference level mgh w mgh g Fermi level To be at any geometric position of the land, water needs a minimum amount of energy depending upon that position. For example, at a position where the pond was dug (see few slide back), water needs “mgh g ” amount of energy to be there. And the maximum amount of energy that water has is equal to the “fermi level”

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Its all about Energy Arbitrary reference level Fermi level And the maximum amount of energy that water has is equal to the “fermi level”

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Energy profile/diagram Arbitrary reference level Fermi level Energy Position, x Graph of required energy to be somewhere, at position ‘x’ Maximum available energy is the “fermi energy” So, positions where required energy

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Energy profile/diagram Fermi level Energy Position, x Every concept we discussed so far on water, is similar for electron inside a solid. Previously, this was a graph of “required energy” of water on earth. Now consider it is the graph of “required energy” of electron inside a solid. Water always flow downward in energy diagram and so the electron.

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Energy profile/diagram Fermi level Energy Position, x So, just like water, if you put an electron to the left, it will travel to the right side and will be somewhere where the “required energy” is bellow the fermi level. And what does it physically mean?

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Physical meaning of Energy profile Fermi level Energy Position, x Consider a semiconductor bar shown above and let, the diagram bellow is the “Required potential energy” inside it. Now let, a photon strikes to the left of the bar and created an electron.

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Physical meaning of Energy profile Fermi level Energy Position, x

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Water vs Electron (Energy view point) As said previously, Everything we discussed previously for water, is applicable for electron also! You can say river of electron instead of river of water. So- Concept of position dependant energy (or required energy) be the same Maximum energy of electron (at absolute zero temperature) is equal to the fermi level. At non-zero temperature, i,e when electron sea is not calm, some electrons will have energy higher than fermi level.

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Brief about potential energy, or “the band diagram” Electron will go to minimum energy position This potential energy diagram is also known as “band diagram”.

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How to find this potential diagram or band diagram? Answer: Calculate the potential energy some how! Example: Take a semiconductor bar and put a voltage ‘V G ’ as shown. Assume resistance of the bar be R. At x=0, Potential=V G volt At x=L, Potential=0 volt But what in between? To understand easily, assume the total resistance R is composed of many series connected resistance ‘r’ as shown. Now, from right side (x=L), Voltage after 1 st resistor, V 1 =0+ir Voltage after 2 nd resistor, V 2 =V 1 +ir Voltage after 3 rd resistor, V 3 =V 2 +ir and so on x L voltage VGVG V1V1 V2V2 V3V3 VGVG

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How to find this potential diagram or band diagram? x voltage VGVG L Exact Mathematical technique to get this potential profile is to solve the poisson’s equation, For a simpler case here, let n(x)=0. That means there is no charge in the semiconductor bar. (It is true only for intrinsic semiconductor or for insulator) Then, At x=0, V=V G At x=L, V=0 C 2 = V G C 1 = - C 2 /L So V=V G - (V G /L).x VGVG

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How to find this potential diagram or band diagram? x voltage L V1V1 V2V2 V3V3 Now we have the potential (voltage) distribution along the semiconductor bar. And we know, energy required +1C charge at a position is called potential of that point ‘V’. Hence energy required to bring q coluomb chare, E=qV So energy required to bring one electron, E= -eV Energy of electron -eV x VGVG VGVG

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The band diagram x voltage L -eV Strange! At x=0, energy of electron = -eV How energy can be negative??? Actually absolute energy in the system of semiconductor bar is not negative. It means, upon application of voltage, energy of electron at x=0 is reduced by the amount “eV” with respect to the energy at x=L x Energy of electron VGVG VGVG

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Significance of Band diagram x voltage L -eV So what will happen then? If there was an electron at x=L, after application of voltage, electron will see that it will have less amount of energy at x=0. So, it will travel towards the left to have minimum amount of energy. The result is obvious because, The positive voltage of the battery will attract the electron from x=L (rightmost) to x=0 (left most) position. x Energy of electron VGVG VGVG

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Operation of FET Upon application of positive voltage at the gate (+V g ), electrons come close to gate terminal. The more positive V g, the more electron near gate region and vice versa. Then drain current, I d = - nAv y e v y =μE y I d = - nAe μE y I d = - nAe μ(dV d /dy) If V d is fixed, then I d α V g [N.B: This is true only in linear region] Drain Source VGVG

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FET operation One very important question. When we put a positive voltage in the gate, why electron does not come to the gate metal from the semiconductor and produce a current in gate circuit??? Or why does the gate voltage only cause the movement of electron inside the semiconductor only???

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FET operation One very important question. When we put a positive voltage in the gate, why electron does not come to the gate metal from the semiconductor and produce a current in gate circuit??? Or why does the gate voltage only cause the movement of electron inside the semiconductor only???

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FET operation One very important question. When we put a positive voltage in the gate, why electron does not come to the gate metal from the semiconductor and produce a current in gate circuit??? Or why does the gate voltage only cause the movement of electron inside the semiconductor only??? All physical connections are established here. So the circuit is complete. Then should not the electron flow like this?????? Why does not it do so?

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FET operation Answer is for the energy barrier. At x=0, there is a change in energy from lower value to a higher value which was not told previously. It is just like an energy hill, called a “barrier”. This energy hill or barrier opposes the electron to come into the metal from the semiconductor. X=0 X=L X= -a Energy Electron can not overcome this energy barrier and hence can not come into the metal conductor. Now the question is, how to create this energy barrier? VGVG

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Creation of energy barrier Answer is simple! By making a junction of two different materials. So, possible options are- Metal-semiconductor schottky junction Metal-insulator-semiconductor structure Semiconductor-semiconductor heterojunction X=0 X=L X= -a Energy To understand each of these thing clearly, we will pay our attention to the junction (or interface of semiconductor and external gate circuit). VGVG

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