Enhancement type MOSFET - construction, working, characteristic

Enhancement type MOSFET 

In this article , we will learn about the construction,working and the characteristics of the enhancement type of MOSFET. (you can check out for JFET and FET

Construction of enhancement type MOSFET (n channel) 

    Now, if we talk about the construction then in some aspects it is similar to the depletion type of MOSFET. 

Construction of enhancement type MOSFET

    So, if we see the construction of the n-channel enhancement type of MOSFET then the substrate is made up of p-type material and through the metallic contacts, the drain and the source terminals are connected to this n-type material. 
  And similar to the depletion type of MOSFET,the oxide layer isolates the gate terminal and the p-type substrate. But here unlike the depletion type of MOSFET,there is no channel between this drain and the source terminal.
 So, whenever we apply the control voltage,between the gate and the source terminal, then the channel is formed between  drain and the source terminal.
  So, here in this type of MOSFET, basically the application of the control voltage enhances the number of charge carrier . And due to that, the channel is getting created. 
   And that is why this type of MOSFET is known as the enhancement type of MOSFET. 

    Working of then-channel enhancement type of MOSFET 

let's understand how the channel is formed whenever we apply the control voltage. 
   
Working of enhancement type MOSFET

So, initially, here if Vgs is kept is zero and the voltage is applied between this drain and the source terminal ,then due to the absenceof the channel, there will not be any flow of current through this MOSFET. 
   So, whenever Vgs is zero, then this MOSFET will remain in the OFF condition.         when we apply the positive value of Vgs. , the substrate and the source terminals are connected together. And they are connected to the ground terminal. 
    The  positive voltage is applied between the gate and the source terminal. And for a moment, let's assume that  voltage Vds is equal to zero. 
    Now, holes are the majority carriers in the p-type substrate. And whenever we apply the positive voltage at this gate terminal, then the holes which are near the oxide layer will be pushed awayfrom the gate terminal. 
   And at the same time, the electrons which are the minority carriers in the p-type substrate will also get attracted towards the gate terminal.
    But at the lower voltage of Vgs, these electrons will get recombined with the majority charge carriers. 
   Now, as we keep on increasing this voltage Vgs, then the holes will be pushed more and more deeper into the substrate  and the electrons will be able to overcome the recombination with these holes. 
    And they will be rushed towards the gate terminal. But due to this insulating layer, they will not be able to cross this oxide layer. And they will start accumulating near the oxide layer. 
  So, eventually, the inversion layer of free electrons will get created near this oxide layer. And now this inversion layer will act as a channel between this drain and the source terminal. 
     now, suppose if we apply the voltage between the drain and the source terminal, then the current can flow through this channel. 
  So, the value of the gate to source voltage at which this inversion layer is getting created is known as the threshold voltage. below this threshold voltage, there will not be any flow of current through the MOSFET. 
    whenever the Vgs is greater than this threshold voltage, then the width of the channel will increase. So, in this way, due to the application of the voltage Vgs, the channel is formed between the drain and the source terminal. 
   But along with this channel, there will also be a depletion layer around this channel. Because if you observe, there are two PN junctionswhich are reversed biased. So, the first PN -junction is formed between the drain and the substrate. And the second PN - junction is formed between the substrate and the source terminal. And if you observe,  both PN -junctions are reverse biased. So, now we will consider that this voltage Vgs is already greater than the threshold voltage. 
    now let's see what happens when we apply the voltage Vds. 
  So, when we apply the voltage Vds, then through the channel electrons get attracted towards this positive terminal. And in this way, the current will establish in this circuit. 
  And the conventional current will flow from the drain terminal towards the source terminal. But now if you observe, the width of the channelhas been reduced towards the drain side. Because now, due to the positive voltage at the drain terminal, the PN junction will get more reversed biased. And due to that, the width of the depletion region will increase. So, because of that, the effective channel width towards the drain terminal will reduce. 
   And the same phenomenon can be also explained in another way. So, once we apply the drain to source voltage,then the voltage difference between this gate and the drain terminal will reduce. So, the voltage difference between these two terminals will be equal to Vgs - Vds
    as the source or the substrate terminal is grounded, so we can say that the difference will be equal to Vg - Vd. So, as the value of the voltage Vd will increase,then the difference between these two voltages will reduce. On the other end, this source terminal is connected to the ground terminal. So, the voltage difference between the gate and the source terminal will remain as it is. 
   So, due to that, the gate terminal which is towards the drain side will be less positive than the other side. And hence, this region will attract few erelectrons compared to the other side. And due to this reason, the channel width gets narrower as we go from the source terminal towards the drain terminal. 

    And as we keep on increasing the  voltage Vds, then at one particular voltage, the pinch-off condition will occur. So, at that particular voltage, the drain current which is flowing through the circuit will get saturated. So, the voltage Vds, at which this pinch-off condition occurs is known as the saturation voltage. 
saturation voltage can be expressed as
       Vgs - Vt. 
  Where Vt is the threshold voltage. 
   That means the pinch-off condition will occur whenever the difference between the gate and the drain terminal is just equal to the threshold voltage. 
  At  the threshold voltage, the channel is just getting created between the drain and the source terminal. So, for the fixed value of Vgs, if we further increase the value of Vds, the voltage difference between the gate and the drain terminal willbe even lesser than this threshold voltage. And due to that, the channel will not get formed towards the drain terminal. 
    So, it appears that the current through the channel should become zero. But actually if you see, still the currentwill flow through this channel and the current 'Id' will get saturated. Because the electrons which are passing through this channel can still be able to cross this depletion layer due to the electric force.
    So, once the pinch-off condition occurs, then the current Id gets saturated. And even if we increase the value of voltage Vds, still the current through this circuit will remain almost constant.

 Drain curves or the Id vs Vds curves for the different value of Vgs

Drain characteristic


       As the value of Vgs will increase, the current Id will also increase. 
    this parabolic curve shows the locus of the voltage Vds, where the drain current Id will get saturated. 
  In this graph, the left region of curve   is known as either linear of the ohmic region. So, in this region, the MOSFET can be operated as a voltage controlled resistor.    For the fixed value of Vds, as we change the value of voltage Vgs, then the width of the channel will change. Or we can say that effectively the channel resistance will change.
     So, whenever the Vds is less than Vgs - Vt, and Vgs is greater than Vt,  in that case, the MOSFET is operated in this linear region. And in this region, it can be operated as a voltage controlled resistor

    Then if we talk about the next region, thenit is the cut-off region(the axis of Vds region). 
    So, whenever, this voltage Vgs is less thanVt, in that case, the current through the MOSFET is zero. Or we can say that the MOSFET will remainin the OFF condition. 

  Region of operation/ saturation region 

  Whenever the MOSFET is operated on the right-hand side of the locus, then we can say that it is operating in the saturation region. 
    Mathematically we can say that whenever this voltage Vds is greater than or equal to Vgs - Vt, at that time it is operating in this saturation region.
   

 Transfer characteristics

   
Transfer characteristic

Transfer characteristic shows the relationship between the input voltage Vgs and the output drain current Id. 
  So, basically, it shows how the drain current Id changes as we change the value of voltage Vgs.
    While plotting this characteristic the voltage Vds has been kept constant. 
    So, as you can see, up to the threshold voltage,the drain current Id is zero. And after that, as we increase the value of voltage Vgs, then the drain current Id will increase. 
  The relationship between the current and the voltage Vgs can be given as 
       Id = k (Vgs - Vt)^2. 
Where K is the device constant and it depends on the physical parameters of the device.
     So, using this expression, we can find the value of drain current for the fixed value of Vgs. Alright, so far we have discussed the n-channel MOSFET. 
   This is all about n channel enhancement type MOSFET. Thank you. 
Depletion type MOSFET : construction , working and characteristics

 In the earlier article  of the field effect transistor, we have briefly discussed about the different types of FET. And in detail we have already discussed about the JFET.

      So in this article  let discuss  the second type of FET, which is known as IGFET and here this IGFET stands for insulated gate field effect transistor .

     So  in this IGFET, the gate terminal is isolated from the channel using the insulating layer and the MOSFET is the most common type of IGFET. 

    So here this MOSFET stands for metal-oxide-semiconductor field-effecttransistor.  

   Classification of MOSFET 

   MOSFET can be further classified as 

  •  depletion type of MOSFET 
  •  enhancement type of MOSFET. 

 Depletion type  MOSFET 


N channel depletion type MOSFET 

Construction of n channel depletion type MOSFET 

Construction of depletion type of MOSFET

  •       If you see this n-channel depletion type of MOSFET then the channel is made up of n-type material and the substrate is p-type material.  
  •      Through the metallic contacts the drain and the source terminals are connected to this n-channel and similarly the gate terminal is also connected through this metallic contact. 
  •   There is no direct connection between  N channel and gate terminal. And the gate terminal is isolated from the channel using this SiO2 layer. 
  •    MOSFET  is consists of the metallic contacts for  drain, gate and the source terminals, then the  insulating layer and the conducting channel which is made up of the semiconductor material. And that is why this MOSFET is known as themetal-oxide-semiconductor field-effect transistor. 
  •    Now due to this insulating layer there will not be any flow of current through this gate terminal. Or we can say that the input impedance of the  gate terminal is very high and in fact it is even higher than the JFETs. (And that is why these MOSFETs are used inthe application where the minimum power consumption is required). 

 Working of depletion type MOSFET

Working of depletion type of MOSFET

 Initially let us assume that the gate and the source terminals are connected together. And they are connected to the ground terminal, means initially let us assume that Vgs is equal to zero volt. 

When VDS is positive , of depletion type MOSFET 

  • The positive voltage is applied between this drain and the source terminal. So as soon as we apply the positive voltage then the electrons in this N channel will get attracted towards the positive terminal.
  •  the electron starts moving towards the drain terminal from source terminal.  And in this way the current will establish in  N channel. 
  •  if we keep on increasing the voltage between the  drain and the source terminal then the current which is flowing through the channel will increase. 
  • this process will continue until all the electrons in this channel will contributes in the flow of current.And then after if we increase the voltage then the current ,which is flowing through the channel , will become constant.
  •  so if you see the direction ofthe conventional current then it will flow from the drain terminal towards the source terminal. 
  •  For the Vgs is equal to zero, the output or the drain characteristic then it will look like this. 

Depletion type MOSFET output characteristic

That means as we keep on increasing the value of voltage VDS then the drain current ID will increase.And after certain voltage, the drain current ID will become constant.


          The value of the saturation current for Vgs is equal to zero is known as the IDSS.

    

When VGS is negative , of depletion type MOSFET 


Depletion type MOSFET at negative voltage

  •       when the voltage Vgs is negative, the negative voltage , the gate terminal will push the electrons towards the substrate and at the same time the holes in the p-type substrate will also get attracted towards these electrons.
  •  So ,due to the negative voltage at the gate terminal the electrons in the channel will get recombined with this holes. And the rate of the recombination will depend on the applied negative voltage.
  •     so as we increase this negative voltage then the rate of recombination will increase. And that will reduce the number of free electrons which is available in this n-channel. And effectively it reduces the flow of current.

Depletion type MOSFET output characteristic

     So as you can see from the graph, as the value of VGS  will become more and more negative,then the value of drain current will reduce.

[ What is pinch-off voltage? 

     And at one voltage this drain current will become zero. so this voltage Vgs is known as the pinch-off voltage. ]

 So if you see the drain or the output characteristic of the MOSFET then it looks quite similar to the JFET. But this MOSFET also works for the positive values of  Vgs. 

   what happens when we apply the positive voltage (VGS) ?

Whenever we apply the positive voltage at the gate terminal then the electrons which are minority carriers in p-type substrate will also get attracted towards this n-channel. And due to that,the number of free electrons in this N channel will increase. so effectively we can say that the flow of current in this n-channel will increase. so for the positive value of voltage Vgs the drain current ID will be even more than this IDSS

Transfer characteristic of depletion type MOSFET 

       Transfer characteristic is defines as  the relationship between the input and the output quantity. so basically it defines the relationship between the drain current ID and  VGS for the fixed value of VDS

     so if you see the transfer characteristic then it will be similar to the JFET. But now you will also get the value of current ID for the positive values of VGS.  So due to that the curve will get extended towards the right-hand side.

Transfer characteristic of depletion type MOSFET

      Now as we have seen whenever this  VGS is positive then the number of free electrons in the channel will increase and due to that this region where the VGS is positive, is known as the enhancement region and the region where the  VGS   is negative is known as depletion region.

     But still the relationship between this current ID and the voltage VGS can be expressed by the same expression 

Expression for transfer characteristic


       So using this expression we can find the value ofdrain current ID for the given value of VGS . 

P channel depletion type MOSFET 

P channel depletion type MOSFET

So similarly let us briefly discuss about the p-channel type of MOSFET . So in case of a p-channel depletion type MOSFET the channel is made up of p-type semiconductor material and the substrate is n-type.  

     For the P channel MOSFET, now the polarity of the applied voltage will also get reversed that means this voltage VDS will be negative and this voltage VGS will be positive .

    let us see how the current will flow whenever  VGS is equal to 0. So when Vgs is equal to 0 and Vds is applied in this fashion that means when Vds is negative then the holes in this p-type channelwill get attracted towards the negative terminal and the flow of holes will be established in this fashion.

P channel depletion type MOSFET

 And in this case the conventional current will also flow in the same direction. now whenever we apply the positive value of voltage VGS then the holes will be pushed towards the n-type substrate and at the same time the electrons in this n-type substrate will also get attracted towards the p-type channel.

        Due to that this holes and the electrons will get recombined and as we keep on increasing this voltage VGS  then the number of holes in this p-type channel will reduce and effectively the flow of current in this p-type channel will reduce.

Output characteristic of p channel depletion type MOSFET

      So if you see the drain or the output characteristic of this p-channel MOSFET then it will look like this. buthere this voltage VDS is negative and the voltage VGS is positive. So as you can see as we keep on increasing this voltage VGS then the drain current ID will reduce and at the pinch off voltage this drain current  will become zero. and whenever this VGS is negative then the value of drain current will be even higher than the VDSS


Transfer characteristic of p channel depletion type MOSFET

        similarly if you see the transfer characteristic then it will look like this. 

Symbol of depletion type MOSFET 

      So now let us seethe electronic symbols of this n-channel and p-channel MOSFETs. 

Symbol of depletion type MOSFET

So if you see the symbols of depletion type of MOSFET then they resembles the actual construction of the MOSFET. 

     it consists of a three terminals that is gate, drain and the source .

 there is a space between this gate terminal and this channel.

    line which connects the drain and the source terminal represents the channel. 

 the space between this gate terminal and the channel represents that the gate terminal is isolated from the channel. 

   Now if you observe the n-channel and the p-channel MOSFETs then the only difference between the two symbol is the direction of the arrow. 

    If it is going inward then it indicates the n-channel MOSFET and if it is going outwards then it represents the p-channel MOSFET. 

basically it indicates the direction of the flow of current whenever the PN Junction which is formed by the channel and the substrate is forward biased. 

      So incase of the N channel MOSFET whenever this PN Junction is forward biased then the current will flow in this direction and similarly for the P channel MOSFET whenever this PN Junction is forward bias then current will flow in the outward direction. So basically by the direction of the arrow we can differentiate these two symbols. 

  So I hope in this article  you understood the construction, working and the different characteristic of this depletion type MOSFET. So similarly in the upcoming articles we will learn about the enhancement type of MOSFET. So if you have any question or suggestion do let me know here in the comment section below. If you like this article hit comment below  and do email  subscribe  for more such amazing article.  

Junction field effect transistor

Here   we will learn about the JFET in detail.  we will see

      the construction 

      the working of this JFET.
        Now, in the previous video we have seen thatin case of a field effect transistor, the path through which the charge carrier flowsis known as the channel. And if this channel is made up of n-type materialthen the field effect transistor is known as the n-channel FET. And likewise, if the channel is made up ofp-type semiconductor material, then the field effect transistor is known as the p-channelFET. So, in the case of n-channel JFET, the channelis made up of n-type material. And two small p-type regions are fabricatednear this channel. And if you see the structure, this n-typematerial is the major part of the entire structure. So, through the ohmic contact, the top ofthe n-channel is connected to the drain terminal and the bottom of the n-channel is connectedto the source terminal. And two p-type regions are connected togetherto the gate terminal. So, in this n-channel JFET, due to this p-typeregions two p-n junctions are formed. And due to that, the depletion region is alsoformed near this junction. Now, whenever we apply the voltage betweenthe drain and the source terminal, then the current starts flowing through the devicebetween the drain and the source terminal. And by applying the voltage between this gateand the source terminal, this current can be controlled.
      So, the working of the JFET can be explainedusing the tap-water analogy. So, as we know, in case of a tap-water thewater flows from the source towards the drain. And the flow of water can be controlled usingthis knob. So, similarly, in case of this JFET, the voltagebetween this gate and the source terminal controls the current which is flowing betweenthe drain and the source terminal. So, now let's exactly see how this JFET worksby taking the example of the n-channel JFET. And let's also see what should be the exactpolarity of the voltages between this drain and the source as well as between the gateand the source terminal. So, first of all, let's assume that this gateand the source terminals are connected together. So, as you can see over here, the source terminalis connected to the ground and the gate and the source terminals are connected together. 
        Now, here in case of this n-channel JFET,the voltage between this drain and the source terminal should be positive. So, here let's say this voltage Vdd is appliedbetween this drain and the source terminal. So, this voltage Vds should be positive. That means the drain terminal should be morepositive than this source terminal. So, now once we apply this voltage then theelectrons start flowing from the source terminal to the drain terminal. And if we see the conventional current, thenthe current starts flowing from the drain terminal towards the source terminal. so, here let's say Id is the current whichis flowing into the drain terminal. And the Is is current which is flowing outof the source terminal. And as you can see, this current Id is equalto Is. So, instead of defining these two currentsas a separate current, we will only define this drain current Id. So, now considering this Vgs is equal to zeroand Vds is positive, let's see how this n-channel JFET works. So, whenever this Vds is positive, then thesetwo PN junctions will become reversed biased. And due to this reverse bias connection, thewidth of the depletion region will increase.
         Now, if you notice over here, the depletionregion is wider at the top of this p-type region. And it is narrower at the bottom of this p-typeregion. So, first of all, let's understand the reasonbehind it. Now, during the operation, this n-channelact like a resistor. And let's assume, the uniform resistance throughoutthis n-channel. So, this n-channel can be modeled as a seriesof distributed resistors between the drain and the source terminal. And whenever this drain current Id flows,then there will be a voltage drop across each resistor. So, let's say the voltage at the top end isequal to 2V. And as we move towards the source terminalthen there will be a voltage drop across each resistor. And due to that, the upper region of the p-typematerial will be more reverse biased compared to the lower region. And we had seen in the earlier videos, aswe increase the applied reverse bias voltage, the width of the depletion region will increase. So, due to that, the depletion region is widerat the top portion. And it is narrow at the bottom portion. So, in short, due to the applied voltage Vdd,these two PN junctions will become reversed biased. And due to that only a small amount of reversesaturation current will flow through this PN junction. And for the practical cases, we can considerthat the current Ig through this gate terminal is equal to zero. So, due to this reverse biased PN junctions,the input impedance of this JFET is very high. So, now as we increase this voltage Vds fromzero to few volts, then the current which is flowing through the channel will increase. And if we plot this current Id versus Vds,then initially it will almost look like a straight line. So, this curve of Id vs Vds is known as theoutput characteristic of this JFET. Or sometimes it is also known as the draincurves for the JFET. So, as you can see, for the low voltages,this curve is an almost straight line. Meaning that for the low voltages, the resistanceof the channel remains constant. But if we keep on increasing this voltageVds then the width of the depletion region will become wider. And due to that, the channel will become narrowerand the narrower. So, due to this reduced channel width, nowthe channel resistance will increase. And that is also evident from the graph. So, if you see this region of the graph, theslope of the line changes and it becomes more and more horizontal. So, basically, it indicates that as we increasethe voltage Vds, then the channel resistance will increase. And now if we further increase the voltageVds, then at one particular voltage, the depletion regions will touch each other. So, this condition is known as the pinch-offcondition. And the voltage at which this occurs is knownas the pinch-off voltage. So, let's denote this pinch-off voltage asVp. So, whenever this Vds is greater than or equalto Vp, then this pinch-off condition will occur. So, the name pinch-off suggests, once thiscondition occurs, then the current Id should drop to the zero. Because now, there is no path for the chargecarriers to flow from this side towards this side. But in reality, if you see, that is not thecase. And in fact, once the pinch-off conditionis reached, the current Id reaches the saturation level. So, let's understand why is it so. So, first of all, let's assume that once thepinch-off condition is reached, then this Id is equal to 0. 
     So, if that is the case, then the absenceof the drain current would remove the possibility of the different potential levels across thisn-channel. And due to that, the reverse bias across thePN junction would be removed. And that would result in the loss of depletionregion which causes the pinch-off at the first place. So, basically, this current Id will not becomezero. And in fact, at the pinch-off condition, thiscurrent Id is the maximum current. So, this saturation current is denoted asIdss. And Idss is the maximum current of the JFETwhenever the Vgs is equal to zero and Vds is more than pinch-off voltage. So, whenever this Vds is more than this pinch-offvoltage then the current which is flowing through the device is almost constant. And in this region of operation, the JFETworks as a constant current source. So, basically, under this region of operation,we will get a constant current through this device. Now, so far in our discussion, we have assumedthat the voltage Vgs is equal to zero. But as discussed earlier, this gate to sourcevoltage can control this drain current.
        So, now let's see, how the voltage level ofVgs can control the drain current. Or in a way, how it can affect the drain curvesor the output characteristic of this JFET. So, now what we will do, we will make thisVgs more and more negative with respect to zero volts. And we will find the drain currents for thedifferent values of the Vgs. So, first, let's assume that the Vgs is equalto -1V. So, due to this negative voltage now the depletionregion will get created across this PN junction. And as we keep on increasing this voltageVds, between the drain and the source terminal, then the width of the depletion region willincrease. But now, the pinch-off condition or the saturationof the drain current will be reached at the lower voltage of Vds. Because due to this negative voltage of Vgs,the PN junction is already reverse biased.  
         So, in case of this Vgs is equal to -1V, ifwe see the drain curve, then it will look like this. So, as you can see, at Vgs is equal to -1V,the saturation value of the drain current has been reduced. And in fact, it will continuously reduce,once we reduce the value of Vgs below this zero volt. So, as you can see, if we reduce the valueof Vgs, from -1V to -2V, then further this saturation value of the drain current willreduce. And whenever, this Vgs is equal to -Vp thenthe saturation current will essentially become zero. So, this region of operation is known as thecut-off region of operation. Or we can say that whenever this Vgs is equalto -Vp, at that time the device is turned off. 
        So, in this way, this JFET can be operatedin the three different regions. The ohmic region, the saturation region, andthe cut-off region. So, in this ohmic region, the JFET will workas a resistor. And for the fixed value of Vgs, it providesalmost constant resistance. But as we reduce the value of this Vgs, thenthe resistance of the channel will increase. So, basically in this region, the JFET canbe operated as a variable resistor. And by changing the voltage between the gateand the source terminal, we can control the resistance of this JFET. Then the second region of operation is thesaturation region. So, in this region, whenever this drain tosource voltage or Vds is more than this pinch-off voltage Vp, at that time the drain currentwill almost remain constant. And the third region of operation is the cut-offregion. So, whenever this Vgs is greater than or equalto Vp at that time, this drain current Id will be approximately equal to 0. And we can say that the device is turned off. 
     So, apart from these three regions, thereis one more region. And it is known as the breakdown region. And like a diode, this region of operationshould be avoided. So, in this saturation region of operationif we increase this voltage Vds beyond a certain limit, then there is a vertical rise in thisdrain current. Or we can say that the breakdown has occurred. And now the current is limited solely by theexternal circuit. So, generally in the datasheet, the maximumvalue of the Vds has been defined. So, during the operation, the value of thisVds should be less than this rated value.
        So, this all about the output characteristicsor the drain curves of the JFET. Now, so far in our discussion, we have onlydiscussed about the n-channel JFET. But the p-channel JFET also works in a similarway. So, in case of this p-channel JFET, the channelis made up of p-type semiconductor. And two small n-type regions are fabricatednear this channel. And in case of p-channel JFET, now the polarityof the biasing voltage also reversed. So, now in case of this p-channel JFET, thedrain to source voltage should be negative and the gate to source voltage should be positive. Apart from that in case of this p-channelJFET, now the charge carriers will be holes. 
     And when we apply the voltage between thedrain and the source terminal, then they will start moving from the source towards the drainterminal. So, now if we see the Id versus Vds curveor the output characteristics of the p-channel JFET, then it will look quite similar to then-channel JFET. But in this case, this voltage Vds is negative. That means if you see the voltages on thishorizontal axis, they will be negative. So, now in case of this p-channel JFET, aswe increase the voltage Vgs, then the saturation value of the drain current will reduce. And whenever this Vgs is equal to Vp, or thepinch-off voltage, then the drain current Id will be approximately equal to zero amperes. 
      And similarly to the n-channel JFET, thereis also a breakdown region in case of this p-channel JFET. That means if we go beyond the certain valueof this voltage Vds, then the drain current will increase drastically. So, this is all about the output characteristicsof the p-channel JFET. Alright so now let's see the electronic symbolof this n-channel as well as the p-channel JFET. So, these are the symbols of the n-channeland p-channel JFET.
            And if you see these symbol, it has threeterminals. The gate, drain, and the source terminal. And in fact, if you see these two symbols,they almost look identical. But the only difference between the two symbolsis the direction of the arrow. So, in case of an n-channel JFET, the arrowis going inwards. While in case of a p-channel JFET, the arrowis going outwards. And basically, these arrow indicates the directionof the flow of current whenever the PN junction is forward biased. So, in the case of p-channel JFET, wheneverthe PN junction is forward biased, then the current will flow in the outward direction. While in case of n-channel JFET, wheneverthe PN junction is forward biased, then the current will flow in the inward direction. And apart from these symbols, sometimes thissymbol is also used for the n-channel and the p-channel JFT. So, I hope in this video, you understood theconstruction as well as the working of this JFET. So, in the next video, we will find the relationshipbetween the voltage Vgs and the drain current Id. And we will find the transfer characteristicsof this JFET. So, if you have any question or suggestion,do let me know here in the comment section below. 
Flow of fluid : streamline flow and turbulent flow

 Flow of liquid 

          A flowing liquid may be regarded as consisting of a number of layers one above the other. 
Flow of liquid can be divided into two categories 
  1. Streamline flow 
  2. Turbulent flow 

Streamline flow 

    Streamline flow is also known as laminar flow. 

   What is Streamline flow of liquids? 

Flow of liquid said to be streamline if the velocity of a molecule, at any point, coincides with that of the preceding one. 
     
What is streamline flow of liquid

 Consider a liquid flowing through a tube of non uniform area of cross section. If all the molecules while at A, B and C posses value v1, v2 and v3 respectively, the motion is said to be streamline or laminar flow or steady flow or orderly

 Characteristics of streamline flow 

  • The velocity of any molecule ,at a point, is independent of time.
  • The layer of liquid in contact with the solid surface is at rest. 
  • The liquid in streamlined flow can be supposed to be in the form of parallel layers one above the other. This is also called laminar flow. 
  • Motion is governed by Newton's law of viscosity. 
  • In this flow, the loss of energy varies as the first power of velocity. 
    The path of molecule, in such a flow, is called a streamline. 

Why two streamlines can never intersect each other? 

    A streamline may be strength or curved. Direction of motion of any molecule, at any point, on a streamline is given by the direction of tangent draw at that point. For this reason no two streamlines can ever intersect each other. 

What is tube of flow? 

   A bundle of streamlines having same velocity of fluid elements , over any cross section perpendicular to the direction of flow, is called a tube of flow. 

Turbulent flow 

    Definition of turbulent flow 

Whenever the velocity of a fluid is very high or it rushes past an obstacle so that there is a sudden change in its direction of motion, the motion of fluid become irregular, forming eddies or whirlpools. This type of motion is called turbulent flow. 
  
          A fluid moving in turbulent flow exerts greater thrust on an obstacle in its path. 
It depends on how suddenly the direction of motion of fluid, is changed by the obstacles. 
A comparative study of thrust on three different bodies is 
 A flat disc feels maximum thrust 
Streamline flow and turbulent flow

 Ball feels lesser 
Turbulent flow

 While a pin pointed obstacle feel minimum thrust 
Turbulent flow of liquid

Here the motion of fluid remains streamlined. That is why the body is said to be possessing a streamlined shape. 

   This is all about streamline flow and turbulent flow. If you have any queries you can ask .

Qualitative description of phonon spectrum in solid

 We have studied so far that the crystal can not propagate all the frequencies, they allow only those frequencies which fall in allowed band. These allowed bands are separated from each other by forbidden band. 

   If there are N number of atoms per Premitive cell the allowed frequencies split into N bands. 

   The field of elastic wave treated like a gas made up of quanta of the normal modes of the lattice or of phonons having the energy E = hw/2(pi)

And momentum of phonons is given by 

     p = hw/v2(pi)

Where v = velocity of sound 

     Whenever a crystal is heated it behaves as a box with phonon gas. Phonons are described by Bose-Einstein distribution function as photons. 

The energy density E(f) of electromagnetic radiation consisting of photons lying between frequency f and f+df  is given by 

Phonon spectrum in solid

Where h is plank's constant, f is frequency, kB is Boltzmann's constant, c is the velocity of electromagnetic radiation and T is the temperature. 

   Every oscillating atom represents the normal modes of the lattice in which all the atoms of the crystal take part vibrating with the same frequency w. 

   The energy of quantum oscillator is expressed as 

Where n = 0,1,2,..........       is the quantum number. 

Energy of quantum oscillator

 It consist of set of discrete level spaced at the interval hw/2(pi) .

     The minimum portion of energy that can be absorbed or emitted by the lattice in the process of thermal vibrations corresponding to the transition of the normal mode being excited from the given level to the adjacent level and equal to E=hw/2(pi)

      Depending on the immensity of excitation of the normal mode, the crystal can emit a definite number of phonons. Hence if some mode is excited to the third level, in the above fig, the energy becomes 7E/2 .v

   It means that the normal mode has produced three identical phonon each with an energy of E. 

The graph between energy density and energy is this 

Graph between energy density and energy
The vibration spectrum of the phonon waves occupy a wide range of frequency from 10'4 Hz to 10'13Hz . Although there is not direct proof energy of an elastic wave quantised, but experimentally it is proved that phonon do exist. 


This is all about qualitative description of phonon spectrum in solids. 






Field effect transistor notes

In this article  we will  learn about the field effect transistor(FET) .

1. What is field effect transistor? 

2. Types of FET 

3. Application of FET 

4. Why it is known as field effect transistor? 

5. Junction field effect transistor (JFET) 

6. Metal oxide semiconductor field effect transistor (MOSFET) 

7. Difference between bipolar junction transistor (BJT) and field effect transistor  (FET )

   

Field effect transistor notes


What is FET (field effect transistor)? 

      The field effect transistor or FET is a three terminal device, which uses the electric field to control the flow of current through the device. 

         it is very useful in many applications. In fact today most of the integrated circuits including the computers are designed using this FETs. 

Field effect transistor (FET)

characteristics and working of FET 

      The three terminals of the FET are known as 

1.gate

2. drain

3. source

    so in FET, the current used to flow between the drain and the source terminal. And this current can be controlled by applying the voltage between the gate and the source terminal.         

      So these applied voltage generates the electric field within the device and by controlling this electric field or in a way by controlling this voltage we can control the flow of current through the device.

   Basically in this field effect transistor, by controlling the electric field we can control the flow of current. And that is why it is known as the field effect transistor.

Difference between BJT and FET 

  1. This field effect transistor is the voltage control device that means the input voltage between the gate and the source terminal controls the output current. 

      On the other end if you look at the BJT or the Bipolar Junction Transistor, it is a current controlled device, where the input base current controls the output collector current. 

    2.  FET is a unipolar device, while the BJT is bipolar device. Meaning that the BJT relies on the two types of charges, the free electron and the holes. But the operation of the FET relies on either holes or electron. 

3. The input impedance of the field effect transistor is very high and due to that they are used as a buffer amplifier in many applications.

4. If we talk in terms of the power consumption the power consumption of the FET is less than BJT.And that's why they are preferred in many high power applications as well as in the computing applications, particularly where the required power consumption should be minimum. 

Application of FET (field effect transistor) 

        Now in terms of the application, the FETs are used in almost all the applications where the BJTs are used. For example they are used as a amplifier or oscillator in many applications and apart from that also used as analog switch in many applications.        

         FETs are smaller in size compared to the BJTs. And that's why they are commonly used in the integrated circuits. 

 Types of field effect transistor (FET)     

       Basically there are two types of FETs.  

1. junction field effect transistor (JFET)

2.  IG-FET. or it is known as the insulated gate field effect transistor (MOSFET is the most common type of IG-FET)

       so let us discuss about these two types of FETs. Now as we know  the FET has three terminals. The gate, source and the drain. And the current flows between the drain and the source terminals. 

      Now in this field effect transistor the path through which these charge carrier flows is known as the channel and if this channel is made up of n-type semiconductor then the field effect transistor is known as the n-channel FET.  

            Likewise, if the channel is made up of p-type material then it is known as the p-channel FET. And in this FET, the gate terminal is placed very close to this channel, so that it can control the flow of current through this channel. 

JFET (junction field effect transistor) 

     

Junction field effect transistor (JFET)

In JFET this gate terminal is provided using this PN Junction. So if you see the n-type JFET,two small p-type regions are fabricated near this channel. 

       And due to that the PN Junction is formed near this channel and whenever this PN Junction is reversed bias then the depletion region of this PN Junction isolates the gate terminal from the channel. And only a small amount of reverse saturation current used to flow between these two regions.

       So in a way this reverse bias PNJunction isolates the gate terminal from the channel and that is why this type of field effect transistor is known as the JFET or the junction field effecttransistor

Types of JFET 

     there are two types of JFET. 

 1. n-channel JFET

2. p-channel JFET.

      Now as we discuss earlier if this channel is made up of n-type semiconductor then it is known as the n-channel JFET

       And likewise if it is made up of p-type semiconductor then the JFET is known as the p-channel JFET.

IG-FET 

       IG-FET uses an insulated layer between the gate terminal and the channel. And typically this insulated layer is formed from the oxide layer of the semiconductor.

       Now here the name IG-FET refers to the any type of FET which has an insulated gate. And the most common form of IG-FET is the MOSFET.

MOSFET

         

MOSFET

So in this MOSFET, the gate is made up of a metal layer and the insulating layeris made up of silicon dioxide

          this MOSFET can be further classified into two types. 

   1. The depletion type

    2. The enhancement type. 

    so let us understand briefly about these two types. now when we apply the voltage at the gate terminal then due to the electric field it can either deplete or enhance a number of charge carriers in this given channel.

        So by the application of the voltage if the number of charge carriers gets depleted in this channel then it is known as the depletion type of FET. and if the number of charge carrier increases then it is known as the enhancement type of FET.

        So above structure which is shown in this diagram is the depletion type of MOSFET where the applied voltage at the gate terminal depletes the charge carriers inthis n channel. 

     

Enhancement type MOSFET

While this structure which is shown in the diagram is the enhancement type of MOSFET. so in this type of MOSFET the channel is formed between these two n- regions whenever we apply the voltage at the gate terminal.

    So these are the two types of MOSFETs. and these two types of MOSFETs can be further classified either as n-channel or p-channel MOSFETs. so these are the basic types of a FETs. And of course there are other types of FETs like Fin-FET and the CMOS, but we will discuss about it in the separate article . 


Acoustical and optical phonons

 Here we will discuss about acoustical and optical phonons in details. 

Today we will  cover 

1. Vibration of diatomic chain 

2. Dispersion relations for one dimensional diatomic lattice 

3. What is acoustical branch? (in details) 

4. What is acoustic phonons?  (in details) 

5. Graph of acoustical and optical phonons 

6. What is optical branch? (in details) 

7. What is optical phonons?  (in details) 

Vibration of diatomic chain 

     Let us take one dimensional diatomic lattice which has two atoms per primitive cell as in case of sodium chloride or the diamond structure.

Vibration of diatomic lattice
     Let m1 and m2 be the mass of these two atoms and suppose m1 < m2. The distance between two nearest neighbours be a. 

    Suppose the atoms are arranged along X axis and are placed at lattice sites 2n-3, 2n-2, 2n-1, 2n ,......... etc. The atom having small mass are placed at even numbered sites and atom with larger mass are placed at odd numbered sites.

       The assumption are supposed to be same as that for monoatomic lattice except that let x2n represent displacement of atom at 2n th site. 

  The equation of motion of two atoms can be written as 

Equation of motion of two atom


     Where alpha is the interatomic force constant. 

 The solution of both equation can be written as this respectively. 

Solution of equation


    In diatomic lattice, the two masses are not identical, so their amplitude of vibrations are taken to be different. Since both the both atoms are vibrating in identical manner, the frequency of both the atoms are taken same. 

 Now differentiate the solution of equation, we get 

Differentiate equation

After simplify these two equation we can write it in determinant form and it determinant is given by equation : 

Determinant

From this equation we can calculate two value of w² as 

Solution of angular momentum

    This above two equations are called dispersion relations for one dimensional diatomic lattice. 

Acoustical and optical phonons 

    The graph between the w and gives us two branches of the dispersion relations curve. 

One curve corresponding to w_ is called acoustical branch and other corresponding to w+ is called optical branch. 

Acoustical and optical phonons


Acoustical branch 

    The lower branch of the dispersion curve in the fig is known as acoustical curve or acoustical branch

For  k=0 ,sin(ka) = 0

   Hence  w_ = 0

For k<<1 , sin(ka) = ka 

    w_ = alpha [ 1/m1 + 1/m2 ]

In acoustical branch  the value of propagation constant k is restricted to the range between -(pi) /2a and +(pi) /2a as shown in fig. 

   For k = +-(pi) /2a, the frequency 

Acoustical branch frequency

  The amplitude of vibration for the acoustical branch are equal. 

   The vibration in the acoustical branch can be excited by force which compels the atoms in the crystal to move in the same direction. 

  As an example we may force a beam of longitudinal wave such as sound wave to be directed at the surface of a crystal to produce the desired effect. Because of this, the vibrations are termed as acoustical vibration and so on dispersion relations ,the acoustical branch is constituted. 

Discuss the case ,when acoustical beach vanishes 

      The acoustical branch vanishes when heavy particle of mass m2 tends to infinity. Then the mid point between each atom is tied down, thus isolating the atoms from one another. Physically each atom is independent of each other. 

   The acoustical branch remains unchanged when light particle of mass m1 tends to zero and the result of monoatomic lattice is obtained. 

What is acoustical phonon? 

When the atoms of lattice vibrate with the same phase and amplitudes about their mean position, the phonons are said acoustical phonons

    Acoustic phonons exhibit a linear relationship between frequency and phonon wave vector for long wavelength. The frequency of acoustic phonons tends to zero with longer wavelengths.

  Optical branch 

The upper beach of the dispersion curve is called optical curve. 

For k tends to zero, sin(ka) also tends to 0. 

that is neglegeble. 

   Now we can calculate value of w+ by putting sin(ka) =0 

  For ka tends to pi/2a and sin (ka)  tends to 1, we get 

Optical branch frequency


The optical branch has small vibrations over the entire range of k. Since the mode of the optical branch can be excited with visible light in solid which are partly ionic, we name the branch as optical branch. 

   The ratio of the amplitude is negative over the entire range of frequencies by the optical branch. 

What is optical phonons and why this is celled so? 

   Optical phonons are out of the phase movements of the atoms in the lattice. During vibrations, if one atom move towards the left then other atom move towards right. These phonons are called optical phonons because in most of ionic crystals such as NaCl, phonons are excited by infrared radiation. 

The electric field component of electromagnetic radiation compels positive sodium ion along the direction of the field and every negative chlorine ion moves in opposite direction to make the crystal vibrate.

       At Brillioun zone ,the optical phonons have a non zero frequency. Near the long wavelength limit, optical phonons show no dispersion. 

Optical phonons are responsible for the intersection of a solid with light because they have higher frequency. 

Forbidden band 

     There is a band of frequencies between the two branches acoustical and optical, which can not propagate. This band is called forbidden band. 


  This is all about acoustical and optical branch and its explanation. If you have any queries you can ask . Thank you. 

Linear Monoatomic vibration

Let us assume that 

1. Atoms are arranged linearly in a straight line. 

2. The interatomic spacing (a) is constant. 

3. The mass (m) of each atom in crystal is same. 

4. The atom supposed to be a rigid sphere. 

5. The crystal is under the influence of short range forces where the interactions between atoms are confined to only the nearest neighbour. 

6. Each atom in one dimensional monoatomic lattice is connected with a spring having spring constant a and the spring is massless. 

7. The force on the atom is directly proportional to the extension or contraction of its nearest neighbouring distance. 

8. All atom in linear array obey Hook's law. 

9. For simplicity we consider only the longitudinal mode of vibrations.

10. A linear chain of identical atoms extended along the X axis as shown in figure. 

Linear monoatomic vibrations


    At mean position, the distance of nth atom from the origin is (na). When the crystal lattice starts vibration, the atom get displaced by a small magnitude. 

    Here we discuss the result according to fig. 

Here w is angular frequency of atom and k is propagation constant .

 Here relation between them is 

        w = w(o) sin(ka/2)

This relation is called as dispersion  relation. For simplicity we consider only there positive root of above equation so as to have real frequency.

    Here w(o) is maximum angular frequency. 

Knowing the mass of the atom from standard values , we can obtain the expression for the frequency f, called the Einstein's frequency 

     f = (1/2pi) (a/m)-½

Here a is interatomic spacing constant. 

   If we plot a graph between propagation constant or a wave vector k along X axis and corresponding value of angular frequency along Y axis for a longitudinal wave of a linear one dimension lattice, then the dispersion curve will look like as 

Normal mode


   Normal mode 

 A correlated motion of the atoms which has a characteristic wave vector k and angular frequency w is known as normal mode of a lattice. 

   Once this motion get started, it will go on continuously, provided the dissipative forces such as friction are negligible. 

  The powerful bonds transmit the vibration of one atom to other atom so as to have a collective motion in the form of an elastic wave. 

   This collective motion of atoms is referred as the normal mode of a lattice. The number of normal modes coincides with the number of degree of freedom. The degree of freedom is equal to 3N where N is the number of atoms constituting the crystal. 

    This is all about linear monoatomic vibrations.