Hi everyone Joe for jaspyscasebrakes.com coming at you with jaspys 11 box Chasing the cup hockey mixer random team break number four Remember cup hockey is a six-box break so we can run this mixer back six times break five already in the store with a couple Fillers all card ship everyone gets a team in the NHL If there's any cracking cards will randomize them as one lot to one person in the break pretty nice boxes in here as well big Thanks to this group Just gotten was too eager to start this break Big was wait for it big thanks to This group for making it happen. Congrats to the people who won spots in the fillers Thanks to the people who bought their spots straight up Britney with last spot mojo But I didn't fill in the teams as well. No, I did not so let's take the cracking out So there should be 31 on each list And let's roll it. Let's randomize names and teams two and a five seven times each one two three four five six and seventh and final time We got Adam on the pole down at Tristan in the 31 spot two and a five seven times for the teams one two three four five six and seventh and final time Vegas down to Anaheim All right Adam with Vegas Steve with the Canucks and the flames Shawn with Dallas Brittany with Pittsburgh Todd with the New York Rangers Dale with the Flyers Todd with the Arizona Coyotes Brittany in New Jersey Devils Last spot mojo Kevin with the Leafs Jason with the Bruins Rob with the Predators Ryan with the Blackhawks Brittany with the Islanders Rob with the Lightning Jake with the Capitals Todd with the Panthers Steve Burch You got my Kings Todd with the Sabres Kevin with the Sharks Ryan with the Wild Brittany with the St. Louis Blues Shawn with the Senators Steve Burch Hurricanes Avalanche We've got some natural disaster teams right there Steve Lockheed got the Oilers Adam with the Blue Jackets Ryan with the Red Wings Kevin with the Jets Steve with the Canadians and Tristan with the Anaheim Ducks Let's alphabetize by team We are going to pause the video just for a little bit when we come back We're gonna see if there's any trades and then we'll have the break so stick around BRB All right. Hi TWC trade window closed No deals are done here on a Monday night. Thanks for chasing the cup with me on Monday night. Appreciate it So the list right here officially printed out remains the same And we've got one two three four five six seven eight nine ten and the cup it makes eleven All right. Good luck everybody We'll do the kind of base heavier stuff first. We'll go work through the three skybox Boxes then a few synergy boxes and work our way into SP game use the black diamond Certified diamond dealer exclusive and of course we'll close with the club the club the cup hockey. There's Cole Caulfield We want to make an appearance here Big hockey guy Pretty happy He's got some Bruins Oilers starting up and the cup break Got another mixer in the store right now if you want to check it out to ask these case breaks calm All spots are in right now. I think we don't have any more of those fillers The hockey puck for the filler breaks. I'm gonna dig around Look for a different filler pack or box to use This will represent the the randomizer that will do for all the cracking stuff All right, and let's roll so pretty much here we're All-card ships you're gonna get all this stuff, but we're looking for The jambalaya's the PMG's Precious metal gems that's that's what we're looking for here in the skybox. That's some fun die cuts as well Gilo's waiting for the sporting KC MLS opener. That's right. I'm less is starting. I think the the opener for the galaxy against Lafc was Canceled and I don't because of oh and the autograph occasion law to grab Adam Beckman for the Minnesota wild Ryan Hoth with Minnesota My hockey knowledge not super strong. I hope this is a good player 171 out of 399 Yeah, I don't know when they're rescheduling that MLS game though Is that Bruins Oilers game? Is that a nationally televised game? Oh? The KC game was rescheduled to know in the UK in England I've seen Premier League matches play it like in the snow Unless there's any lightning feel like those guys should just go out there and play another box. Oh Right, right, right. So it's gonna be on Nessan for you. Should we We whip around the Lee. Oh, there's really not much going on today. We got only one game in progress red wings at Senators and Senators up three two Scoring three in the second period and there's still five minutes left for the Senators Clodgeru, maybe Clodgeru, Batherson and Sanderson are your goal scorers Perone and Bertuzzi are your goal scorers for the red wings Canucks stars coming up We should be Puck drop soon. Yeah, same with Bruins Oilers That's on the NHL network Oh, okay, so I might be able to watch that Golden Knights are in Colorado That's at the top of the hour And then an hour after that will be Blackhawks at Anaheim Right, Gilo says is that set with a clear card in this one? I think so those cards are cool But I don't know anything about hockey not a big hockey guy a small hockey guy Yeah, I've been learning but I'm still I'm still I'm still a small hockey guy As well, let's see as much as I enjoy Monday night raw Maybe I could find some NHL right here Just to have on the background Do we have an hl network on our direct TV? I think we do Bruins at Oilers nice All right onwards We've got planet metal When is the uh NHL trading deadline? I feel like that's Coming up soon. Has there been any big deals made? That I should be aware of That's sort of a casual fan Neon icon Conor McDade. I don't know how short printed these inserts are but it is Conor McDade. It does look pretty cool Terry saying Timo Meyer to the devils. That's a big deal. That looked like a different parallel and an autograph Sample ranta. I don't think autographs are guaranteed one per box, but in these two We got autos That is 227 out of 399 for Colorado Steve Birch with the abs Is it Tuesday? Maybe tomorrow? You're the clear card here. I think this is what gabe was talking about ice carvings leon drissel dry sidle Dry stall all right one more of those sky boxes friday. It's friday at three o'clock It looks like they're warming up here Bruins at Edmonton Both teams doing well Bruins doing amazing Do they still have their amazing home record? Yeah, they're they are 24 two and three At home And they're on a they're on a six game winning streak. They got a plus 95 goal differential Plus 95 goal differential the next closest Are the maple leaves at plus 49 I mean in the west the best goal differential is Dallas stars plus 37 They've got a plus 95 goal differential Geez They've got 95 points already. How many uh, how many How many more games are left? I mean they're easy and get What a season Uzi will bowman bonanza be tonight If you want it to be Actually, that reminds me. Sorry guys and gals. I got to post the last filler for that because The second to last filler sold out already Did I put that on the schedule? Yeah, that's on the schedule and let's post the last one. So we got a chance at getting that done tonight Use easy and everybody else if you want to if you want to fill up the last filler Simple as that the choice is yours All right, so go to jaspys case breaks.com. The last filler has been posted and it is part of the promo promo deadline is not until tomorrow People acting like the promo deadline tonight. No, it's not. We got until tomorrow 24 games left. What? Are they are the Bruins approaching any sort of Single season like points or win record. I don't know what that is in the nhl So steve's thinking the the points single season points are going to 133 So if they have like 24 some odd games left I mean We got plenty of plenty of games to get there Now it's numbered look different 12 out of 96 alexander barkoff Nice that cool looking die cut going to florida that'll be for tot Another ice carvings quintin biofield for the kings. We're having a pretty solid season Wow, there's I blinked and there's two goals already in this oilers Bruins game Then the game just start two shots for edmonton a goal and the Bruins just scored On their second shot That was quick From from distance to no not from distance bounce off the back curls around Wow, that was a nice little pass All right synergy everyone has the over on this game, right? Conor mcdavid with a quick goal assisted by leon Dry saddle Tom Tomas no sec is your goal score for the Bruins Hathaway and orlov On the uh Hathaway and orlov on the on the assists there You're over under on the game was six and a half if you're into that sort of thing. There's jonathan huberto to What is that to eight ninety nine? There's gonna be a lot of numbered cards here We've got lassie Thompson to four forty nine Matthew barzall to seven forty nine The exceptional futures coal lind to one ninety nine We've got two conucks here to three ninety nine Eliza lindholm to one ninety nine We've got caprizov roaring 20s Luke is raymond to 275 And an autograph jake neighbors Like the television show If you're into that sort of thing Uh saint louis blues britney with the blues. I guess that's why they call it the blues All right, so we got co-petar and kempay to nine ninety nine for the king steve birch the point for tampa bay rob Alexander holds to Three ninety nine for new jersey. That's for for britney luke is raymond for detroit. That's going to go to brian Eliza lindstrom for calgary That's going to go to steve birch Canucks duo for steve birch exceptional future. That's going to be part of that randomizer. This is kraken randomizer Islanders that will be for britney Ottawa that'll be for shawn And florida that'll be for For tot and then make david guys. Okay terry terry's wondering who's going to get the dart big hockey guys thinking what a bad team as uh, nationals gm trots plans on quote resetting and quote the preds Injured miller week to week for struggling canucks blackhawks deal mckay blaffordy to the leafs Rangers miller spitting on dowdy an accident Is it? I don't know.  I have no idea Is there a suspension coming lightning lan geno from downsizing credit geno? The downsizing spreaders abs bring back Uh defenseman johnson from cut winning club devils acquire all star four admirer from the sharks That's what terry was mentioning a little bit earlier. All right onwards at austin matthews We'll go through all those numbered cards in a second breeze through these first And we've got an autograph riley damiani for the dallas stars Sean matty with dallas, right? So here are all of your numbered cards. We got Zegras for the ducks that's going to be for tristan claudieru for the flyers to 275 that's going to go to dale There's a shifling kachuk for winnipeg Kevin There's a quinhues For vancouver that'll be for steve a couple ducks here going to tristan Neighbors for the blues that'll be for britney halibut for winnipeg kevin vasily For vancouver that's for steve awesome mercer for new jersey it's going to be for britney And there's joep welski for dallas. That's the 299 that'll be for sean. All right your third synergy box Yeah, I agree nathan. Maybe maybe someday they'll They'll make a play back into uh back into the industry terry misses the panini sets You know some of those some of the panini hockey back in the day wasn't wasn't too bad Just looking at some stanley cup Winning odds Not surprisingly the bruins are five to one.  Where are my kings? 32 to 1 they're right next to the penguins and the kraken We're having a really nice season Devils are 12 to 1 Rangers lightning and devils are currently 12 to 1. All right, so another synergy box down a bunch numbered cards here Sean has dallas. You'll get uh rube heintz to 749 And we've got jeremy swayman to 299 For boston That's going to be for jason k We got it out of 12 Trevor zegras Rookie for anaheim that'll be for tristan. Nice low number there tristan We've got shersirkin to uh, not 899 for the rangers. That'll be for todd It's a copetar bifield duo to 799 for my king steve birch Troy tarry for the devils to 299 devils ducks different d team tristan with the ducks For detroit mort cider to 749 brian hayman There's new hook to 799 not like the old hook There's steve birch in colorado We've got patrick cane to 499 For chicago, that'll be ryan hawk Here's a connor mcdave to 275 for edmonton steve lock It's pretty good And then for dallas. We got riley damiani to 449 right now. Let's get into some sp game used Thanks, steve lock. Yeah It only took a number of years Breaking hockey, but i'm i'm i'm Doing better with the names i've been trying to catch some more kings games at the very least so So i'm kind of absorbing some some knowledge there. There's sampo ranta to 999 Joey keen to 205 colorado. That'll be for steve birch Hurricanes i think is also steve We got jeremy swam and frameworks It's pretty cool It's going to be for boston that'll be four For jason k and the ruins We got rookie blends 148 out of 150. That's vasily uh padoulton pot colson Either way, that's going to go to vincouver that goes to steve Got kailyn adison authentic rookie relic For the while that'll be for ryan Got ryan yohansen for nashville for the prez. That's going to be for rob And a cool uh tuka rask banner years relic For bossam chason k Next sp game used The blank card to slow play some of these guys here authentic rookies to 999 For the devils that'll be for britney We've got seven stonkos to 205 for the lightning. That'll be for rob And we got jeremy drivesdale 28 out of 35 draft day marks Tristan with the ducks And we got for the blue jackets rookie sweaters coal cylinder To 249 Adam with columbus Got logan thompson for vegas That'll be for adam as well And we got purity dug gilmore to 150 with the cool Punch-outs in the card there One more to 999 jacob brison For buffalo Todd with the sabers That sets joggers for the hurricane. That's for steve birch It's got some natural disaster teams and We got matt sundin Hall of fame legend sweaters That's a nice patch nice autograph 23 out of 25. Who's got toronto? That's for kevin m. There you go kevin nice Then some relics we got we got leon driestoff or drysidle The other way banner year for edmonton. That's going to go to steve lock Authentic rookies philipe gustafson for ottawa. That's going to be for shon matik And another purity card john la claire for the flyers All right now black diamond certified diamond dealer exclusive. All right. We got some rookie gems 59 out of 99 Got rock besser on top 279 out of 349 Vancouver that'll be for steve birch The swayman will go to boss and that's for jason k And we got a brent burns black diamond autograph sparkling scripts For my rivals the sharks kevin with san jose Hey, no worries kevin. Thanks for getting in We got mario lemieux cup winners patches That's for pittsbury. That'll be for britney We got jeremy swayman again diamond debut relics boston that's going to go to jason k zach jones at 399 rookie gems For the rangers that'll be for todd and the last one here is quinton bifield. Nice exquisite rookies 117 out of 299 Quentin bifield for the kings He's been evolving growing his game looking pretty good steve birch with the kings and now the big stuff here 2020 2021 The cup hockey a little behind that's okay Better late than never Like I said, we got another mixer in the store. So if you want to run this back jaspyscasebreaks.com We got anzei kobitar 117 out of 249 steve birch and the kings Thanks, jonasia All right, that'll be steve birch and the kings Yeah, that's right mic tower Upper deck is lagging a little bit All right, then we got rookie auto patch steven lorenz 100 out of 249 That's for carolina steve birch The hurricanes Yeah, that'd be great. Thank you Oh, yeah, there were there was some zah talk in the chat and then so I had to I had to get some zah Eighth out of 49 yegor Sharangovitch Rookie signatures quad relic and autograph. How's he doing? Is he good?  We've got tim stutzel. I think he's pretty good signature renditions That's for auto that'll go to shawn Got bruins with another goal here They're up to one now 454 left in the first Then we got I think a couple relics keith yandle Three-color quad relic for florida That'll be for todd All right, terry saying nice stutzel So yeah, I think he's a pretty good one to hit there you go shawn And then the last one here is jason robertson 46 out of 249 rookie class Jason robertson that'll be for dalis and that's going to go to shawn And there you go boys and girls a nice cup mixer Another one in the books another one in the store jasby's case breaks.com. Check it out now Let's see who's going to win all those kraken cards little extra bonus Let's flip back to the list here. Let's gather everybody's names one through 31 And name on top will get all those seattle cards After Four or two six times One Two Three Four five and six in final time After six jake smith I don't think I called your number too often in this break jake But you'll get a You get a little consolation prize some seattle kraken cards that go in your way. Thanks for watching everybody I'm joe for jasby's case breaks.com and I will see you next time for the next hockey break. Bye. Bye


It goes around 22,000 Hertz as the maximum, but most of the frequencies we have, you don't need up to 22,000 Hertz. Most of the frequencies, even Dr. Royals frequencies, most of them are under 20,000 Hertz. Like the higher Hertz doesn't mean that's going to work better. How close do you need to be? About three feet, right? Just three feet. Probably the ideal. You can wear it. You have these lanyards that you can get. You can wear it on yourself, on your person, or you can just put it on the table and you'll get that magnetic energy. If you have the gold orchids, then you can connect this to Bluetooth. So you see this tablet is connected to this Bluetooth wirelessly. And then this Bluetooth is connected to the coil with the wire. You need the wire. You can't be wireless, but this is wireless. So you have the black one, the black version, which comes with the Chico Mini here. This one is not wireless. This one needs to be connected to your device. It could be your laptop, computer, tablet, or phone. So you'll be able to use Bluetooth if you have the right equipment. Also the high power kit has Bluetooth as well. So if you want to increase your power 11 times, you can get that one. And that will super energize your coils and make them so powerful they can reach a lot further. If you read the reviews like on Amazon on terahertz frequency ones, they're not that good. I did some research. The results are not that good. And terahertz frequency, they only have one frequency in there. And they use some kind of looks like a hair dryer application. I mean, there's some people that say it works great. But from my experiences, it's not that effective. So with G coils, you have a way more frequencies of over $10,000 frequencies. And we have a measurable field. And you have the toroidal energy field, spiraling energy field, which actually makes the difference. There's a lot of PMF or magnetic field devices, but they don't have the proper shape. They don't have the toroidal spiraling energy shape, which is how energy is supposed to interface with your body. If you think about how your chakra system works, your chakras actually are vortexes. So they actually emit energy in spirals. We studied Kundalini, like Kundalini is in the spiral, right? And your Kundalini actually spirals in a certain way. So you go in different directions, you get a different experience with the energy field. That's why we have the in and yang coils. A lot of these stuff out there, like the terahertz frequencies, wands or PMF devices, they don't, they miss this.


Good afternoon everyone. Today in this video we will discuss about one of the microwave component isolator, myself Piyusha Shedgar, assistant professor Valchand Institute of Technology, Solapur. These are the learning outcomes for this session. At the end of this session students will be able to explain the working of isolator. At the end of this session students will be able to explain different applications of isolator. These are the contents for this session. Before going to start actual topic isolator you can pause video here for a second and recall that what are ferrite devices. Yes the ferrites are non-metallic materials with high resistivity. They are a mixture of metallic and ferric oxide. So if you are taking the example of the metallic we are considering that MnO and the ferric oxide is nothing but the Fe2O3. So by mixing these two components we can find the ferrite components. In microwave devices ferrites find the application to reduce the reflection, the modulation purposes and in switching circuits. So wherever the high frequency is required that is more than 100 gigahertz applications ferrites are used because of the high resistivity property. Now what is isolator? An isolator is two port non-reciprocal device which produces a minimum attenuation to wave propagation in one direction and very high attenuation in opposite direction. So here the figure is given as a isolator which having the three ports port 1, 2 and 3 port. This third port is terminated thus it can be worked as a isolator so that isolator provides only the one way direction of the signal. If the input signal is applied to this port 1 you are getting the output at port 2 without any reflection towards the generator side. Again consider this is one of the example of the isolator. This isolator is having the two ports port 1 and 2 and if the circulator which having the three ports port A port B and port C the circulator can be worked as a isolator when the third port is terminated. When the third port that is C port is terminated it having only the two ports port A and port B. So it is the property of the isolator when the input is applied to this A port you are getting the output at port B with the reflection is equal to 0. Now consider the block diagram for the transmission system. So in several microwave generator circuit there will be the frequency and the amplitude variation at the generator load because of the reflection from the load side towards the generator side and the reflection from the load towards the generator will happen only when there is a mismatching of the impedance from the load to the generator side and therefore there may be the signal when transmitting from this microwave source towards the load due to mismatching of the impedance at the load side there will be some part of the reflection from this load towards the microwave source side. Thus there the system becomes unstable because of the variations at the generator side. Now if the isolator is placed between this generator and the load that is when the signal is applied from this generator towards the load side it will pass from this isolator towards the load side and if there any reflection from the load side due to mismatching of the impedance in load and the generator side whatever is the reflection is absorbed by this isolator. Now this is one of the block diagram of the isolator used in transmission system. So here the signal generator and the output side you can connect any type of a load and the third port is terminated. So here isolator maintains the one way direction of the signal flow. Now let us discuss about the construction of the isolator. Now this is the construction of the isolator. This is the rectangular wave guide which having the two ports port 1 and port 2. Near to port 1 the resistive card is placed when the plane of the wave of the propagation having the perpendicular plane to that of the resistive card then only the wave will pass through this resistive card. When the wave which having the plane of the polarization is parallel to the plane of that of resistive card then this wave is totally absorbed by this resistive card. This is the property of the resistive card. Another at the center of this rectangular wave guide Faraday's rotation ferrite rod is placed which is used to rotate the signal in clockwise direction by 45 degree. Again near to the port 2 another resistive card is placed which having the same property as that of the first resistive card. At the input side 45 degree twist is used for rectangular wave guide again this twist is in anticlockwise direction. Now let us discuss about the working of the isolator. In working of the isolator let us assume that T10 mode is applied to port 1. When the signal is applied to port 1 the signal is passed through this rectangular wave guide. When it comes to this resistive card the plane of the polarization of this T10 mode is perpendicular to the plane of the resistive card and therefore this wave is passing through this resistive card. When the wave out of this resistive card comes near to this 45 degree twist the wave is twisted by 45 degree in anticlockwise direction because of this 45 degree twist. Again when this wave is comes towards this 45 degree rotation because of this ferrite rod the wave is rotated by 45 degree in clockwise direction. Now this wave becomes perpendicular to the plane of the resistive card and that wave is passing towards this port 2. Now in this case whatever is the wave passing from this port 1 is obtained at port 2 without any reflection. Now consider that the input is applied to port 2. Now when the input is applied to this port 2 initially the plane of the polarization of the wave is perpendicular to the plane of the resistive card and therefore the wave is passing through this resistive card. When it comes to the center of the rectangular wave guide the wave is rotated by 45 degree in clockwise direction. Again when the wave passing through this near to this 45 degree twist is provided in rectangular wave guide. So therefore the wave is again twisted by 45 degree in clockwise direction. So here now the wave becomes parallel to the resistive card that is the plane of the obtained wave guide wave is becomes parallel to the plane of the resistive card and therefore whatever is the wave passing through this port 2 is totally absorbed in this resistive card and therefore no any wave is obtained at the port 1. So output at port 1 is equal to 0. Thus you can say that when the wave is applied to port 1 you are getting the same wave at the port 2 without any reflections and when the input is applied to port 2 at that time the output at port 1 is equal to 0. Now in practical session this is nothing but the microwave test bench practical setup. Here the power supply is used here you can generate the microwave signal which can be passed through this generator side towards the load side. At the load you can connect the CRO or VSWR meter. So whatever is the microwave signal pass from this transmission system transmitted signal is passing through this rectangular wave guide. So here this is nothing but the isolator. Isolator is used to provide a single path one way transmission of the signal from this generator towards the load side. So this is nothing but the variable attenuation. The attenuation of the signal can be changed by using this variable attenuator whereas this is nothing but the frequency meter is used to measure the frequency of the transmitted signal. This section is the slotted section. This slotted section is used to measure the VSWR and all the parameters of the microwave signal and through this rectangular wave guide whatever is the transmitted signal is received at this receiver side. These are the advantages of isolator. Isolator eliminates variation in source power output. It blocks reflection going towards the load. It avoids frequency pooling due to load changing. These are the different applications of the isolators. Isolator used in RF circuit design. Isolator used in test and measurement. Isolator used in RF chain as a component to prevent any undesired reflection. Isolator used in high voltage devices. It can be used in substation that is when a fault occurs in a substation then isolator cuts out the portion of a substation. Isolator used for the isolation purpose that is the input and output signals are isolated and therefore the reflection will be less. These are the references for this session.


We start with the new module, module 3 of the non-classical MOSFET series and this will be on the metal semiconductor contacts and metal source drain junction MOSFETs. That is instead of P N junction, we have metal semiconductor junctions as the source and drain. Now, here we will discuss the properties of Schwarzky junctions in silicon, germanium as well as in compound semiconductors. How they are different? All of them are similar, but there are slight differences are there. Then, Fermi level pinning effect on this Schwarzky barrier on the working of these metal semiconductor contacts. Then, of course, MOSFETs using these metal source drain junctions. So, the first question comes to anybody's mind is why do we need this type of change from the conventional P N junction to metal source drain junctions. Particularly, when you go for small scale or nano scale MOSFETs. For this purpose, I have put here the pinning effect which we discussed last time. In fact, the idea is this is the diagram which I showed last time. Now, a simplified version of the three dimensional picture of the looking from the other side, you can see it is like this. Now, you can see you have got the source drain and this is the pin which connects the source and in fact, the channel is found there. If I have the gate only in this portion, this is the oxide and the polysilicon or metal gate that is in this. I am not showing multiple fins, only one pin. If I want to have multiple fins that will come parallel to these fins and the gate will be formed around that. So, the inversion layer is formed just below this gate. That means, the channel length is from here to here. That is the channel length. Wherever, gate is there below that there is a channel. The width will be that portion which is surrounding that channel like that. So, that is the width. It is not all round. Sometimes, they call it also all round gate. It is there from all the three sides and here as I have already pointed out the thickness. See, this is the back gate. This is the front gate you can think of. Usually, you have it like this, top gate and back gate. Now, you have it like this. You can call this as back gate, this as front gate. In addition, you have got on the top, but that is very thin. So, that means, you have got the soil layer. This whole thing is a soil layer. You have prepared the whole thing by etching the soil layer here.  You have etched this portion and you have realized the transitter like this. One device has hole. So, the width is whatever is surrounding that channel is a width of that. That is h twice height plus the thickness of the width of the fin. So, whatever analysis that you do for double gate MOSFET holds good front gate and back gate you can use it. And the thickness of that soil layer in that formula will be the width of this layer. So, that is the thing. Now, what I have brought this out is this fin portion is very narrow and between the, the channel actually starts from here. This is not inverted or anything. This is, this will be endless looped up to that point, but because this is very thin, you will have lot of resistance coming into here. Rho L by A, area of cross section to the current flow is less. You have to make it thin because you want this, that layer to be very thin when the gate comes in on that. So, you cannot make it wider. So, that is where the series resistance comes into picture. That is where the problem is there when you go to smaller and smaller scale MOSFETs for which this pin fit is relevant. Now, if you take a look at the conventional MOSFET, there also you have the problem. There you have this implanted region at an angle of implant to change the doping concentration there and this thickness of the source region is less here. Even here, you would like to use shallower and shallower junctions because if you are scaling down in the lateral direction, vertical direction also you must scale down. Otherwise, there will be lateral junction formation will be there. So, you, that is a, it will spread laterally also. If you diffuse deeper, it will diffuse laterally also. If you implant, afterwards you are annealing, that will move down, it will move also laterally. So, you are making it shallower and shallower junctions. So, you make it shallower and shallower. Again, you see current flows in this direction. I will just show that here. See, this particular portion again I have put here, there is a metal contact. From the metal contact, which is may be silicide, this n plus region flows into this channel here. Channel is here. This is a gate. This is the special layer, that layer. I have expanded it and so on. This small region, I have put it like this. To magnify the impact of this resistance, I have put it there. So, this diagram is same as what we have taken here. Junctions are made shallower, especially at the gate edge here to reduce their encroachment into a channel. That introduces a lot of series resistance in this portion. Now, how can you reduce the series resistance? You can reduce the series resistance by reducing the sheet resistance. Sheet resistance is defined as resistivity of the layer divided by thickness of the layer. What is resistivity rho? 1 by sigma. 1 by sigma is resistivity and sigma is q mu n into n d and x j is the depth of which is going. So, if I want to reduce that r, that is this resistance that comes in here, I can reduce the rho or I can increase x j. But, increasing x j is not allowed because while scaling down the devices, you want to scale down in the vertically also. So, x j you cannot increase to reduce the thing. You want to keep it low. The only parameter that you can manipulate is rho. Rho depends upon 1 by n d doping. So, you can increase the doping. Already you are at 10 to power 20 doping concentration, the source chain regions. So, you cannot go beyond that point because the upper limit on this doping concentration is decided by the solid solubility limit. Means, there is a limit up to which the material for example, silicon can absorb the dopants without losing the crystallinity. That is the solid solubility limit. For example, if you put phosphorus, you may get something like 5 times 10 to power 20 per centimeter cube. If I am using phosphorus, boron or p type, you will get something like 10 to power 20 solid solubility. So, there is upper limit on that. So, the only way you can reduce that resistance is go to a different material. Changeover from the semiconductor there, changeover to metal. Metal will have lot of carrier concentration, 20 to power 22 or even more of that order. So, you can increase the carrier concentration very much. You can reduce the resistivity. You can reduce the series resistance. That is the goal. So, shallow junctions increase the external resistance and also in the case of this type of junctions, because the profile goes something like that gradually, it is not abrupt. If it is abrupt, you have got entire layer has same doping right through. So, you have got a region where the doping is getting down to lower level. So, that is why if you put a metal, the whole thing can be thin. At the same time, it will be just one sheet there. You can put thicker metal if you like. So, that is the idea. Now, further metal source drain contours have further benefits. One is parasitic resistance of source drain regions of conventional scaled down MOSFET. Whatever I have told, I have written here. It is primarily responsible for reduction in the drive current. How does this happen? This equation. Whatever gate voltage you apply, part of it goes to the resistance in the source. What is available for creating the channel is less for a given voltage. So, drive current gets reduced. So, speed of the device gets hurt. If you cannot drive a capacitor fast, the speed will be slowed down. All these MOSFETs are required to drive the capacitors and charge them. So, they must have higher transconductance g m. g m is delta i d by delta v. For a small change in the input signal, the current should change quite a bit. That is the indication of g m. Now, I do not know whether you remember this. If not, I will just put that.  That is, transconductance without the series resistance and r s. It is related like this. Let us quickly, maybe I can just go through that. See, for example, if I take the MOSFET, I have a resistance there r s. That is the source resistance. Now, I have the v g s applied.  What we are trying to find out is, if I have delta v g s here, how much is the delta v g s here? How much is the delta v g s here? This is actually delta v g s 0. If r s is 0, delta v g s equal to delta v g s 0. This drop is delta i d into r s.  Now, divide right through by delta i d.  So, delta v g s by delta i d is equal to delta v g s and writing is divided by delta. Oh my God, that is really bad. So, that is delta i d plus r s. So, this quantity first term is 1 by g m that you get. And the second quantity is 1 by g m 0. g m you would have got if these were equal and plus r s. Now, you can see, you can now go back and see that the g m. So, this is actually equal to g m 0 1 plus g m 0 times r s. So, now you can see g m is equal to g m 0 by 1 of that. So, this is what we have said there. So, what happens is now your g m becomes like that, but it comes up by that. So, you can see if r s is large, g m is correspondingly reduced.  So, the need, there is a need for reducing that r s to increase the i d and also to increase the transconductance, to increase the driving capability. So, replacing source chain regions of the transistor with the metal can reduce the series resistance effect. Now, we should see what it is going to be. Now, there are other benefits. One is series resistance gets reduced, other one is in a conventional transistor you have got N P N. That is a bipolar transistor coming into picture. Particularly, if you in the soy device, if you do not have the ground contact, that is very much dominant. So, if I replace the junction with the metal semiconductor contact, you do not have the trans attraction, bipolar trans attraction is not there. So, that we will understand better when we, after we discuss the how that eliminates that, when we discuss the metal semiconductor contact. So, and also because there is no P N junction, there is no minority carrier injection there, which to the substrate. All those effects which you do not like are eliminated by putting a metal semiconductor contact. Still, you have got to see how whether it works like a transistor in a MOSFET. So, you can use abrupt, atomically abrupt junction by using a metal on the surface. So, all those limitations of shallow junctions etcetera goes off with this. Further, if I am replacing this junction with a metal semiconductor contact, your processing temperature goes down because you are just evaporating metal. At the most, you may do some sort of annealing at about 400 degree centigrade. So, that way your thermal budget on the wafer is reduced. That is one of the very important things people worry about. Try to process at as low temperature as possible to keep for a bigger wafer, wafer bar page etcetera is reduced if you process at low temperatures. You have to work worry more and more about this. If you go to 8 inch, 12 inch, all that effects you try to minimize. So, lower temperature, do not be carried by a low temperature. Usually, when you have to go to a physics person specialist, low temperature, he will immediately think ravagenic temperature. But we are talking of low temperature, if it is 500, 600 degree centigrade, it is low for processing. So, this is actually just to show that really that type of devices have been fabricated. You can take a look at one of the papers which has come, which gives a very good review even as 5 years back. Even now, that is a classic paper which people refer. So, that is why I put it here. In IEEE Transactions Alternative Devices, it is a long paper which gives some sort of review of the devices. This is the cross-section, TM cross-section of a 20 to the nanometer short key barrier source T metal contact. This is the gate and you have the, you can see this, I do not know, you can see the dark portion there. This is shown here by this portion. This is a platinum silicide, which acts as a metal simulator to contact. There is no junction. In the previous case, you put some silciding etcetera, you do, how do you do? You have that there, N plus is there. Junction is different, but now use that as the, use platinum silicide as the metal semiconductor to contact. There you can get a junction like this, which goes underneath that. You can get self aligned structures. We will come back to this when we go to transit traction. Right now, what we want to take a look at is the schematic of the short key barrier. These are all the depletion layer bits. Let us not worry about it at this moment. We will have occasion to discuss details of this when we come to transistor. So, main thing that focus is, you can get the metal semiconductor of this shape. You can get abrupt junctions here and you can get this gate, which is polysilicon and you have got the spacer layer on both sides that I am sure it has been elucidated in the previous lectures. So, you have got the spacer layer. So, there is no shorting effect when you put this platinum. You can just lift off that from there and you have the platinum only here. Till side, it will spread laterally under these into that, but it will not be like spreading with the junction. It will just, small spreading. Now, what are the requirements here? This metal semiconductor contact should form a very low barrier here. If it is a N channel device to the N type region, it should form a very low barrier. Why it should form a very low barrier? It should be able to inject electrons to that barrier, to the barrier. Also, if it is a P type substrate, it should form a rectifying contact. So, there is requirements. It should make a good omicontact on to N type material. It should make a good rectifying contact on to P type material. So, when we have an inverted channel here, that will form an omicontact there. So, these are the requirements which I have put here. They are summed up in all whatever I have said, they are summed up here. CMOS, you have got N channel and P channel both. When you put a metal, you will have N channel there. So, you must have an omicontact on to the N channel. If it is P channel, you will have N type substrate, P channel here. That should make omicontact to that. So, there are conflicting requirements here which can be met by how we will see. The idea may not be very clear right now, but when we talk about the metal semiconductor contact, it will become clearer. In fact, few years back, people were not talking much about metal semiconductor contact. It was only a part of syllabus where somewhere they put one 10 minutes discussion on that and proceed, but today it has become a matter of research, lot of discussion going on that. Now, let us get on to quickly on to, these are very simple concepts. You can go through that rather easily by discussing. First, when you say you need to have a low barrier height means it should be omicontact. So, on to channel, you would prefer a metal making omicontact. On to substrate, you would have a rectifying contact. What are they? Omicontact, low barrier height. Rectifying contact forms high barrier height. In MOSFET, metal semiconductor contact at the source should form an omicontact to the channel. Short key barrier junction leads to fundamentally different mechanism. That is what I am just alerting right away. Now, omicontact, high characteristic like that, whoever knows. Ideally, it should be vertical, 0 voltage drop, but you can never get to 0. There will be finite resistance. Rectifying should have block current flow in this direction and it should have current flow easily. Ideally, it should be vertical here, 0 there. You never get there. So, now, let us get down to discussion on the, all of you are familiar about the energy band diagram. So, it becomes easy to analyze this metal semiconductor contact with the metal semiconductor with the energy band diagram. This is a metal block. This is an anti semiconductor. They are two are separated. They are not connected. They are neither physically in contact nor electrically in contact. So, metal has got the permeable there and that is the vacuum level. So, what you do is, you have the term called the work function difference, which actually is the energy difference between the vacuum level and the permeable. Virtually, it gives an idea how much energy you must supply to the electrons to take it away from the metal. See, for example, if you take a metal, if you heat up red hot, it emits electrons. That is, you are giving energy much more than that 4, 4.5 electron volts energy by heating with red hot. If you see the old vacuum tubes, you will see that there is a filament, which is heated, which is the source of electrons. So, that is the work function. Now, semiconductor if you take, the vacuum level is same here. Conduction band, balance band, n-type. So, permeable is closer to conduction band. That is the term called the electron affinity that is chi. That is the energy difference between the vacuum level and the conduction bandage. And the work function of semiconductor phi s is the gap between the vacuum level and the permeable. Now, next what we do is, so we are taking a case where phi m is greater than chi s phi f like this. So, you can immediately say that if you join these two metals, need not join, keep them close by, connect these by external wire. It becomes a complete system. These are the definitions. So, when I connect them together, there is a gap. That may be a small gap. This is a complete system. So, what happens is, because the here, because the permeable is above this and there are lot of electrons at a higher level here, occupied, because it is n-type. There is lot of states available here. The electrons, like the p-n junction, electrons will get transferred from the n-type region to this metal. So, leaving back a depletion layer, plus charges behind here like that. The plus charge is the depletion layer, a finite width here and the electrons have gone transferred on to this. I have put these negative charges here. One negative charge I have put here. If there are 10 charges here, there will be 10 charges here. So, many electrons have transferred. Now, this is what happens to the energy band diagram. This layer is depleted. Metal, the number of electrons are very high. There will not be a layer. There will be a charge sheet of large concentration of electrons on the very surface itself. That is why you do not have a depletion layer or accumulation layer. There is a charge sheet there. Now, if you take the energy band diagram, this is n-type. This is depleted and plus charges are there. Through this gap, the electric field will terminate on to the minus charge, because plus charges will look for negative charges. They are here, because they have been transferred from here. So, you have got an electric field from the semiconductor to the metal surface. Here it is distributed charge. Here, on the metal, it is a charge sheet completely. So, because there is electric field from this side to this side, the energy band diagram will be moving in this fashion, because this is negative, this is positive. So, if I have to take an electron from this side to this side further, it is more difficult, because plus minus. Electric field is from right to left. Therefore, it becomes difficult to take the electron from the right to left. That means, the energy band diagram will be moving up. This is getting back again to the basics. Similarly, the electric field will be maximum here, but it will be varying here. It will be linearly varying. Potential will be parabolic, like all the discussions that we have been doing. So, you have got the n-type material here. As you move from here to here, more and more depletion, it becomes less and less n-type. So, you can see the conduction band moves away from this formulable. So, conduction band moves away from the formulable, telling that this is depleted. And this energy band diagram is bent up here, telling that the electric field is in the direction. So, and delta is a gap. Now, what I do is, these are standard textbooks everywhere. You see these types of diagrams, including the book, which we had written at Chotham but that also all the diagrams are there. So, I reduce this gap. The charge transferred to me is the same thing, because this has happened till the formulable has equalized. You do not draw the formulable here in this insulating portion. You do not, that is not happening. Meaning, you stop it there. They are equalized. So, if I reduce the gap, the charge here and charge here is not changed, but the gap is reduced. So, what will happen if the voltage is reduced? Field lines are same. Number of charges here, number of charges are same thing, because that has helped me to transfer and bring the formulable equal. So, because the charges are same, the gap is reduced, the voltage drop is reduced. See the chi, this is the vacuum level. Whatever potential change is there in the energy band diagram here is reflected on the vacuum level also. Further reduced, I reduce it further. The voltage drop is reduced further. There is a small voltage drop in that layer. If there is this layer could be a small monolayer of oxide even present there, which usually is present. So, that is the thing. We have got electric field here. Electric field here, there is a drop B i across this layer. Now, psi m is that per function difference here to the vacuum and there is a drop here or voltage rise here. This is the conduction bandage in the semiconductor. Chi is here. So, the vacuum level is slightly dipping here, because there is a voltage drop. All the energy band diagrams bend. Only this, which does not bend is the formulable thermal equilibrium situation. So, phi m and this particular height, energy difference, this is I pointed it, written it as phi B n, which is in electron volts. I call this as a barrier height for electrons. I call this as barrier height, because if the electrons have energy greater than phi B m, after all in the metal at room temperature, there will be electrons beyond this point. They will be above the formulable. They will not only be here. At 0 degrees, of course, there will not be electrons above that, but at room temperature, there will be electrons from here up to certain height. Now, all those electrons, which are having energy is above this phi B n, find a very thin layer. They can cross this by tunneling. If it is 1 nanometer or of that order, those electrons, which have energy greater than that can tunnel. So, phi B n is the electrons, which are having energy less than this. That is phi B n. They cannot cross, because there is a, this region, there are no states. There is an energy gap. There is a band gap here. So, but here, immediately it sees the available states in the conduction band of this. So, they can tunnel. Similarly, electron present here can tunnel from here to here. So, we can discuss this. Ideally, when you talk of the Schottky barrier or metal semiconductor contact, you do not show this layer, because that is not really coming into picture, because carriers can tunnel from here to here and here to here. So, phi B n is phi m minus chi. If that drop is negligible, it is phi m minus chi. So, normally do not show this gap. So, that is what is shown. So, wherever you see the energy band diagram for metal semiconductor contact, you will see only for n type like this. So, formula level of metal aligned with respect to formula level of silicon and there is depletion layer here. Depleted n type material has got plus charge and the minus charges are present here on the surface, which will terminate on this. So, entire voltage drop is across the depletion layer here. So, here to here, that is what we talk. So, phi B n is that barrier height, whichever what we have discussed, that is phi m minus chi. Phi m minus chi is the phi B n. That is 0 level. Now, wherever there is a depletion layer here under thermal equilibrium conditions, you have got what is known as the built-in potential. Just like in the p n junction. In the p n junction, that is shared between the p-type region and n-type region. Here, it is entirely on the n-side. There is no voltage drop in the metal. So, this is a built-in voltage. So, built-in voltage is actually the voltage rise from here to here like this. If I know phi m, work functional metal and if I know chi, chi, electron affinity, it is known for a given semiconductor. For example, for silicon, it is 4.0 for electron volts. For gold, it may be close to about phi electron volts, phi m. So, phi m minus chi is known because of materials there. You can even measure it from the characteristics of the device. So, otherwise you can say once you know phi m and chi, you know what is phi b n is. Now, once you know the doping in a semiconductor, you know what is the energy difference between the conduction band and the permeable.  So, built-in potential is related to the barrier height and the doping. If the doping is higher and higher, this will not change, but the e c minus c f will decrease. Therefore, your built-in potential will become closer and closer to phi b n. This is the idea. Now, let us just go further into things. This is the, we will see that a structure like this, a metal semiconductor contact, n type material with phi m larger than chi will act as rectifying contact because there is large barrier for electrons from either side. How does it work out? Let us see. Thermal equilibrium situation, I do not know whether you understand this type of diagram. I have redrawn whatever I have drawn here, I have redrawn here. Instead of putting this plus minus, I just put depleted here and there is negative charge here. On the left hand side, I have shown the distribution of electrons because there will be in a metal energy levels will be there continuously, but the probability of occupation goes down as you go from the Fermi level up. Let me just see whether I can and put that diagram. See, what is happening in a metal is, in a metal. You have got the Fermi direct distribution. How is the Fermi direct distribution? Energy versus probability of occupation, if you take, that is 1, the E F. Now, if you draw the Fermi direct distribution like that, it is half there at room temperature. At 0 degree, how is it? At 0 degree is like this. I just redraw that. At 0 degree, it is F p is 1 here. It is like this. Below Fermi level, all the levels are occupied. Above that, they are not occupied. Now, let me just go back to this and see where you can remove that. So, just to make it, everything on. Let me just clear out everything. Just redraw that once again F e and energy. That is 0, Q E F. So, above room temperature, it is, this is 1. So, you will have it going like that. Probability of occupation is half there. That means, there are, if there are levels there, the implication is the Fermi function. You write it as 1 by 1 plus e to the power E F minus E minus E F by k T. That is the plot there. That is the Fermi function, probability function. So, when you write like this, meaning is, if there are levels present above that, that will be occupied. So, in a metal, what I have drawn is, that is like that. In fact, it will not be precisely like that. It will be something like this. That is, it will be going down something like this. Below that, I am not showing. That means, these electrons are, they have got energy above the Fermi level. So, if there is a barrier, if there is a barrier like this, like this, if there is a barrier in this fashion, that is a barrier 5 B n, these electrons above that can cross. There is nothing which brings it from going from there to there. And if there are electrons on this side, they can cross on that side. Now, how is it in the conduction band? Semiconductor, you have the Fermi level here. You have the Fermi level here. Your Fermi direct distribution may be, how will that be? I will put it like that. E f is here. Your Fermi direct distribution may be something like this. The problem of not drawing it beforehand. So, if this is one there, I am taking a bit time. I hope you do not mind this. So, I have this. Just one minute. Take it once again. See, what I am trying to draw is the Fermi direct distribution on this graph, where that is the Fermi level.  This will be half here, like that, probability of occupation. That is the f e. What about density of states? In the conduction band, it is continuous. But the density of states is something like this. 0 there and goes like that. So, the n at any e is equal to, if I call this as g times e, density of states, g times e into f e. So, if I draw the, that is, this is a probability. This is the density of, that is, at the conduction band, this probability of density of states is 0. It keeps on increasing, but probability keeps on increasing. So, your net distribution comes like this, something like that. See, this is 0. Probability is there, but so the, the, if I go from here to here, if I draw the product, these two things together, that will be 0 here. It will increase and go down like that. It is, even though you find out effective density of states with respect to conduction band, the actual distribution will be like this. The 0 here, number of atoms, as you go away from the conduction band, it will slightly increase, then fall down to 0. See, product of probability, because the probability increases, I am sorry, probability decreases, density of states increases. Product actually goes through a peak somewhere here.  Now, I have drawn that here. This is the electron distribution here. When you integrate the whole thing, you get that N c. You find out effective density of electron. When you find out, you integrate the whole thing there. So, here you can see now, under thermo-equilibrium conditions. You have got the distribution like this, which is above that here. So, all those electrons here can move that side. All those electrons from the metal here, under thermo-equilibrium, when the Fermi level has equalized, definitely number of electrons which are able to cross from here to here, must be equal to number of electrons crossing from this side to this side. I can write, say that the current density due to the electrons moving from the semiconductor to the metal, because they have got energy above the barrier. This is the barrier. I can write it as Q for the charge of electrons N. Density of electrons here, whatever electrons are available here, will have thermal energy or thermal velocity v x in that direction, because we are taking one-dimensional case. So, across that barrier, how many electrons per second are crossing? That will give rise to current density. So, I can find out this current I naught. If I know how many electrons are present here, because all of them can move here. If you plot the electron density from this end to that end, we put it as a depleted layer. When we say it is a depleted layer, the implication is there are no electrons. But from here to here, if you go, there is a potential variation. If there is a potential variation like this plus minus, that means electron concentration is decreasing exponentially with respect to that. So, if the drop from here to here is V B I, from that point to that point, if it is V B I, the electron concentration just at the edge of this junction, metal semiconductor junction, will be whatever electron concentration there in the semiconductor bulk multiplied by the bulk is N N electron concentration N region multiplied by e to the power of minus V B I is the potential drop built in potential N N into e to the power of minus V B I by V T. V T is K d by q. This is the Boltzmann's law. When there is no current flow, I can say that carrier concentration is that. Now, all those electrons are having thermal energy there. Because of that, they are above this barrier. So, those electrons can cross from here. If they are, if you have a directed field, they will move in that direction or it will be moving up and down. So, we are considering that the electrons are moving here with the velocity V f x. So, the current is q N into V. That I think that is a basic equation which we use even by deriving the MOSFET equation charge into charge density into velocity. That is the current density. I multiply by area, I get the current. So, from the semiconductor to the metal, there will be current I naught. What is the current flowing from here to here? You do not have to calculate, because you know the current net current is 0. So, from here, all these electrons which have high energy should give exactly opposite current. So, what we are saying is when the energy band diagram is like this under thermo equilibrium conditions, there is exchange of electrons, free exchange from this side to that side. And since the net current is 0, whatever is injected from metal to semiconductor is balanced by whatever injected is from semiconductor to the metal. So, this is the energy band diagram under thermal equilibrium conditions. Now, let us see what happens when I have bias condition. How does it work out as rectifying junction? So, I hope the diagram is all clear. Electron distribution of function of energy here and here. Now, what we have shown is whatever I have discussed there, put it in terms of equation. We are considering only this now. That is, N of x is like this. J naught from metal to semiconductor to the metal is this, Q N into V of x and N s is equal to N N into V to the power minus V V of V t, K t. We are trying to make it compact. So, what is N N? In an entire material, the electron concentration is equal to effective density of states into E c minus E f by K t minus. This is the standard formula. So, that is the standard formula, which is substituted for N N, this term, into V to the power minus V by K t. I have restated what I have written there by substituting for N N. Now, what is this quantity? E to the power minus E c minus E f into E to the power minus Q V V b i by V t. What is that quantity? E c minus E f is this, Q V b i is this and E c minus E f plus Q V b i is this quantity. That quantity is nothing but phi b n. So, what we are telling is this whole thing can be put as N c into E to the power of minus phi b n by K t because sum of these two is that. That is phi b n. So, that makes it simple. That means, electron concentration there here is equal to N c e to the power of minus phi b n by K t. Now, the J naught. What was J naught? We said Q N s into V of x. N s is this one. Q is there, Q is there, I substitute for N s from here. The 1 and 2 N s is given by this. So, that is Q N c into E to the power minus phi b n by K t by V s. Same thing I have read it up. So, this quantity inside here is decided by the density of states and the thermal velocity of atoms in that direction. So, J naught. Now, you can see usually what you refer to in the diode J naught. You will see that this also for the diode also that is the reverse saturation current. We will see how it is.  So, J naught will be low. So, it depends upon phi m minus lower if phi b n is larger. J naught will be higher if phi b n is reduced. Low barrier height J naught will be higher. Now, you can see that if you have a diode which is J naught is very large. It looks like a very leaky diode. It will look like a omicontact. So, you can straight away say that if I make a device where the phi b n is low, it will look closer to a omicontact. If I make a device with the phi b n large, J naught will be low. It will look it will be closer to a rectifying contact. We will see how it is. So, now I just rewriting this again. J naught is equal to that quantity. Now, we have to recall some of the formulae that are available already in the basic device physics that you have studied earlier. N c is related to the effective mass of electrons k t and Planck's constant and this 2 3 by 2. So, N c is that quantity. I am just substituting now for this and V of x for the electron gas, the thermal energy is root k t by 2 pi m n star. Multiply these two together and simplify. You get some constant a star. All these things will have to be constant. Here, t to the power 3 by 2 is there. Here, t to the power half, you get t square. Other things are constant that I pulled it out as a star. A star is this quantity. What is m n star? Effective mass. Effective mass is mass of electrons in the semiconductor which will be different from the mass of electron in free space because of the presence of built in electric fields when the atom moves, when the electron moves from one location to another location. So, to make life easy for us, so that you can still use Newton force, loss of force. You make use of force is equal to mass in the acceleration. Talk of effective mass. So, that is effective mass. So, it is a star that is constant. t squared comes from here into the same thing. What I have written there is here. J naught will be a star t square e to the power minus 5 P n by k t. And a star when you substitute for all these quantities q, k, pi, etcetera, you will get 120 m n star by m naught ampere per centimeter square per degree kelvin square. Why I put it in the form is the m n star by m n m naught depends upon the semiconductor. If you take silicon, it will be almost close to 1. Slightly different. If you take gallium arsenide, it will be 0.067. That is very, very small. So, this a star in the case of silicon will be close to 120, slightly smaller. But in the case of gallium arsenide, it will be 120 into 0.067. It will be about 8 or so. So, that a star will be 8 amperes per centimeter square per k square for gallium arsenide. So, that is why I put this. Because you do not have to remember every time all the whole thing, 120 m n star by m n ampere. So, you know the effective mass in terms of mass usually. You can get that constant. Calculation becomes ready for you, this square into this, pi b n pi minus chi. So, that is what we get for we have calculated. This is the value that current that will be transferred from here to here and here to here. That is J naught, net current is 0, thermal equilibrium. Now, reverse bias. I will at least be able to finish this. In the reverse bias, what happens? If you see here, the permeable was here. In the reverse bias, what happens to that? How do you reverse bias? Like in the p n junction p and n, if you have, here you have metal and n. I make this n side plus. I apply voltage V r into that. The applied voltage will not appear across the metal, where the huge current will flow through the thing. So, because it is like a metal and as insulating layer here, depletion layer. So, the entire voltage adds on to the built-in potential across this. Depletion layer widens. The voltage drop across this layer increases, becomes equal to V B i. V B i, what was the polarity? Plus here, minus here, plus minus. You can see that. Plus here, minus here. Band is like that. It adds on to that depletion layer widens. That is the reverse bias situation. So, this portion I am keeping it as it is. With respect to that, the voltage has increased here. That means, the band bending has taken much more. So, this earlier, the Fermi level was coinciding with that, but now it has moved down by an amount equal to V B i, V r. So, entire energy band diagram, originally whatever was coming up here in this portion has come down by equal to V B i. So, if you go beyond the depletion layer, the charge distribution remains the same thing. I do not know where you can go quickly back. See, whatever was here, this portion has been pulled down. This in the neutral region, this equilibrium diagram, whatever I have drawn holds good. But beyond that point, I do not draw the Fermi level. That has no meaning really. You call it as passive Fermi level. So, I just draw it here. And here, in this portion, the band moved down because the voltage has increased. That is moved down. Now, what has happened to the charge distribution now? On the left-hand side, the barrier has not changed. That is a key thing. The P N junction, the barrier will change on the P side as well as on the N side. Here, the barrier does not change because there is no voltage drop in the metal. So, the barrier remains the same thing. So, all these electrons which are able to give rise to J naught or I naught from due to transfer of electrons from here to here, they will be there. So, I have put a current here in this direction, implying electrons are flowing in that direction. See, if the electrons are crossing from metal to semiconductor, current is from the semiconductor to the metal. So, there is that I naught component is still present to transfer of electrons from the metal to the semiconductor. But what has happened to the electrons here? The electron distribution from the bulk is the same thing. Number of electrons available in the semiconductor in the neutral region that has not changed. That distribution remains the same thing. Since you have pulled the potential energy down, this actually is the energy distribution from here up to this point only. So, the maximum number of the electrons are available only up to certain height in the energy. Beyond this, there are no electrons. So, when we apply sufficient reverse bias, they are not able to cross from right to left. So, whatever J naught was there from the right to left or whatever electrons were there from right to left is brought down to 0. But whatever electrons transporting from metal to semiconductor are still there. That means there is a net transfer of electrons from the metal to semiconductor. There is no transfer of electrons from the semiconductor to the metal. So, whatever was transferred from the metal to semiconductor was I naught. But I have put the I naught as the physical direction. Physical direction is the opposite to the transfer of electrons. So, you will have a current in the direction for this supply voltage to the metal giving rise to that same J naught whatever you have calculated. So, with that I think we have just gone through the basic principles involved in the reverse bias operation or the thermal equilibrium situation of the metal semiconductor contact. More details we will discuss in our forward base, how it works, the great fair we will discuss in another discussion.


Welcome to the third video in the series, Data Science for Beginners. In this one, you'll get some tips for formulating a question you can answer with data. You might get more out of this video if you first watch the two earlier videos in this series. The five questions data science can answer, and is your data ready for data science? We've talked about how data science is the process of using names and numbers to predict an answer to a question. You can also call names, categories, or labels. Now the trick here is that it can't be just any question. It has to be a sharp question. A vague question doesn't have to be answered with a name or a number, but a sharp question must. Imagine you found a magic lamp with a genie who will truthfully answer any question you ask. But it's a mischievous genie, and he'll try to make his answer as vague and confusing as he can get away with. You want to pin him down with a question so airtight that he can't help but tell you what you want to know. If you were to ask a vague question like, what's going to happen with my stock? The genie might answer, the price will change. It's a truthful answer, but it's not very helpful. But if you were to ask a sharp question like, what will my stock sale price be next week? The genie can't help but give you a specific answer and predict a sale price. Now once you formulate your question, check to see whether you have examples of the answer and your data. So if your question is, what will my stock sale price be next week? Then we have to make sure that our data includes the stock price history. If our question is, which car in my fleet is going to fail first, then we need to make sure that our data includes information about previous failures. These examples of answers are called a target. A target is what we are trying to predict about future data points, whether it's a category, a name, or a number. If you don't have any target data, you'll need to get some. You won't be able to answer your question without it. Now to take this to the next level, sometimes you can reword your question and get a more useful answer. The question is this data point A or B predicts the category of something, and to answer it we use a classification algorithm. The question of how much or how many predicts an amount, and to answer that we use a regression algorithm. To see how we can transform one of these into the other, let's look at the question, which news story is the most interesting to this reader? It asks for a prediction of a single choice from many possibilities. In other words, is this A or B or C or D? Is it this story or that one or that one or that one? And it would use a classification algorithm. But this question may be easier to answer if you reword it, such as, how interesting is each story on this list to this reader. Now you can give each article a numerical score, and then it's easy to identify the highest scoring article. This is a rephrasing of a classification question into a regression question. How you ask a question is a clue to which algorithm can give you an answer. You'll find that certain families of algorithms, like the ones in our news story example, are closely related. You can reformulate your question to use the algorithm that gives you the most useful answer. But most importantly, ask the sharp question, the question you can answer with data, and be sure you have the right data to answer it. We talked about some basic principles for asking a question that you can answer with data. Be sure to check out the other videos in Data Science for Beginners, from Microsoft Azure Machine Learning.