you can follow along with this presentation using printed slides from the nano hub visit www.nano hub.org and download the PDF file containing the slides for this presentation print them out and turn each page when you hear the following sound enjoy the show okay so let's get started today today we'll be talking about bulk recombination and this means that if you have a bulk of semiconductor on which let's say you have part of the equilibrium by some means let's say by shining light then how the equilibrium is restored now bulk could be bulk of many things gallium arsenide silicon and all other that type of things but as you know silicon is sort of the dominant material indirect bandgap material that derivation is a little complicated and that's why I want you to guide you through that gallium arsenide and other direct bandgap material very easy so I'll keep it to for the end when you are a little tired maybe towards then so we'll begin by derivation of Shockley Reed Hall formula now three names are associated Shockley and Reed these are the two people very famous they wrote a paper I guess in 1954 deriving the formula and hall in fact one year earlier I think he derived the formula independently and so there is often called SRH formula short for Shockley Reed Hall formula and I'll show you how to use Shockley Reed Hall formula for various special cases now remember Shockley Reed Hall formula only applies to indirect bandgap material trap assisted recombination this type of thing for silicon and many other indirect bandgap material it's not a general formula that applies everywhere and then we'll talk about OJ recombination and direct recombination remember we said in direct bandgap material this is very important OJ is when two electrons bump against each other one electron goes down the other electrons goes up very high in energy so we'll talk about that and then we conclude now let's think about it slowly we are talking about an electron red electron that dotted line is a trap I have a generally I used to draw it short here I have drawn it long because I'll have to draw a few more things but remember that's a localized state at one point right it's a defect or a trap now what we see here the electron is coming down to the trap being captured by the trap waiting there till a hole shows up and then dropping into the hole at the end of the process an electron is lost from the conduction band a hole is lost from the valence band and nothing has stayed in the trap the trap it has returned to its original position so this is going down we'll call that process 1 and 3 just to give it a name because we'll be using this later on we'll just call this process 1 and 3 now there is always an inverse process that where an electron from the valence band now jumps up to the to the trap and from that electron eventually goes up to the conduction band so at the end of the day the net result is one extra hole generated in the valence band and one extra electron generated in the conduction band and nothing left behind in the trap so trapped temporarily hold it held it the electron but at the end of the day it is not really holding anything and we'll call that process 2 and 4 and many times when I'm working out this math it will be helpful if you consider the dotted line in analogy of the USA remember I had these boxes for USA Mexico and India that type of thing so you can think about conduction band being let's say India the valence band being Mexico and the trap level being let's say USA so then you can clearly see the analogy I'm talking about in that context okay now this view that I just told you about is fine but for mathematical purposes a slightly different point of view is often useful so you see what happened in the left hand side picture the left and the right are exactly the same picture but treated in a slightly different way in the left picture as I told you is a recombination process one electron from the conduction band was lost through the trap eventually one holes from the valence band was lost so at the end of the day one electron gone one hole gone that's the status of that look at the right hand side where I have drawn the process three process one is exactly the same but I have drawn the process three in a slightly different way what I have said here that instead of the electron coming down from the trap to the hole in the valence band instead what we'll think that as if a hole has jumped up hole has jumped up to the trap and they have met at the trap the electron and hole they have met at the trap now you see what the consequence of this at the end of the day one electron is gone right it came down to the trap one hole is also gone because it jumped up from the valence band to the trap and there they recombined so at the end of the day the trap is also gone there's no electron and hole left in the trap also exactly the same process right in terms of as far as electron number and hole number is also exactly the same process now what about the other process two and four so let's think about that two and four remember what happened one electron jumped up from the valence band to the trap and then eventually from the trap to the electron how do they get this energy by the way they may string up a bunch of phonons and then get a help of a photon to eventually go up there remember going up is very difficult coming down is very easy it's like getting good rates getting a D is probably easier than getting an A now the equivalent process on the right hand side is something like this I have put together you can see a red and a white on the right hand side so I have one electron and one hole but they are together at the end of the day one electron goes up from there it started from there both of them and the hole jumps down look at what happened at the end of the day isn't it exactly the same as it is from the left hand side for two and four why is it exactly the same because at the end of the day I have one extra electron in the conduction band one extra hole in the valence band right and nothing left behind in the in that trap level so these are exactly the same process so instead of the physical picture physically what is happening will work on this picture because then you can see the things will get in and out of the trap level and that will be easier to keep the book keeping up okay now let's think about it the first is we want to look at the number of electrons so we're focusing on let's say India the conduction band on the top and we want to see how many people come out and how many people go in now the one the state that conduction band communicates with it changes electrons and holes with let's say is the trap it doesn't know as far as compared for the previous picture starting for the previous picture it doesn't even know holes I bear valence band exists right because valence band is only talks to through the trap so therefore only thing I need to draw when I'm thinking about how many electrons getting in and out of the conduction band I just need to think about the trap and that's it so how many electrons in the conduction band and how is it changing with time so I have to consider process 1 and 2 right and that's why I have written the subscript 1 comma 2 so these are the two processes I have to think about now think about the first process first process so remember in the last class I told you about these electrons are swimming around this black electron swimming around and then there is this trap sitting fixed in the real space and once in a while they capture if they are empty then they can capture an electron and then become filled right in the last class we told you about that and this is exactly that process look at that N N is number of electrons if you have more electrons of course it will get captured more P sub T P sub T is number of traps that are empty of course it has to be empty otherwise how is it going to catch in electron and C sub and that is the capture coefficient proportional to the velocity because if it is running around quite a bit then the probability of getting captured is more right so proportional to the thermal velocity you saw that in the last class why is there a negative sign the negative sign is because of process 1 the number of electron is reduced because anytime they are captured as far as electrons are concerned it has lost a partner so the number is reduced what about the process 2 well process 2 is you can see that first I'll explain what is E sub N is but NT is the number of electrons that can jump from the trap to the conduction band remember it was the process 2 just a little bit before that is proportional to the number of traps that has electron if it has no electrons how is it going to give up anything so it's proportional to N sub T and 1 minus FC means that when it's wants to jump to a state that state must be empty because because poly exclusion principle remember if it is not empty then it cannot jump so it's 1 minus FC and an E N is the rate at which it goes up it's a emission coefficient now we don't know we haven't given any physical explanation of E sub N we'll do it in a second we told you about C sub N in the last class why plus sign well electrons are coming back so I have it as far as conduction business concerned I have more electrons now plus sign okay now remember okay so and correspondingly I will not explain this a great deal but you can convince yourself that between valence band and the trap you can write the same thing 3 and 4 I'm focusing on the number of holes this time again C P P and N sub T P is number of holes N sub T is whenever they are occupied because holes are captured by occupied traps remember that's when it has large cross section in the last class and correspondingly it has the emission probability so I hope that you will try to understand this one that's it I don't need any more equation I will manipulate this equation a lot but this is the basic equation and I'm actually done so now think about this word look at the title detailed balance in equilibrium of course it's redundant because detailed balance can only happen in equilibrium out of equilibrium it cannot happen right what is detailed balance every country every pair of countries in that case India and Mexico let's say everybody has individually the net rate is zero that's detailed balance steady state doesn't have detailed balance remember so every state pair wise they exactly cancel each other so since these things in equilibrium I'm assuming since it's in equilibrium I will turn out the on the light a little bit later but since it is now in equilibrium sitting on your desk without any external stimulation then I can write this DN DTA because of detailed balance what should the result be there should not be any net change in the number right number of electrons should exactly remain the same independent of time so I should set the left hand side to zero I can only do it only do it in equilibrium cannot do it any any other time now do you notice that I have done something which is a little fishy here I have taken out one minus FC do you see the second term had the one minus FC I can only do it I cannot do it in general I can only do it if the semiconductor is non degenerate that Fermi level is way down you have few electrons in the conduction band remember ni is 10 to the power 10 so it's most of the places are empty anyway f is very close to zero so I have dropped it in general if I give you a new problem where the level is degenerate Fermi level is up in the conduction band don't take this make this extra step right now once I have this you see here I know if I if I somehow could find out this n sub t and p sub t all those quantities and I'll show you how to then a beautiful relationship between these two and detail balance says that e sub n the emission coefficient is actually related to the capture coefficient you see it has to be if the total thing has to be balanced then the rate at which you capture must have some relationship with late at you which emit and this detail balance will allow you to connect the two coefficients in fact detail balance is a way in which in any rate equation this is semiconductor physics you can take anything you can take geophysics you can take astrophysics anywhere this notion of detail balance is so powerful it will always connect two processes or couple of processes in equilibrium right to each other and thereby reduce the coefficient by a factor of two is a very powerful technique so one thing you see that emission is related to the capture coefficient multiplied by a bunch of constants and we'll think about what those bunch of constants are then I put a zero there why because this is in equilibrium so that's why all these numbers have carry a zero around okay and the whole thing n0 p sub t0 and the numerator together I will call give it a name called n1 I'll just give it a name it's no physical significance nothing I'll just call it so that I don't have to write too much and in general you see as soon as en and c7 emission and capture are related in the previous equation instead of having to carry around e7 I'll insert n1 multiplied by cn you see I haven't done anything so long I don't know n1 I haven't just a substitution haven't really done any made any progress yet but we will okay so 3 and 4 is your homework you should be able to see the same thing and again notice on the top line for the whole rate I have eliminated f sub v because that was the number of holes in the valence band I haven't written that because this is non degenerate had it been degenerate I must carry that around right and again you see exactly the same thing but this time whole emission and whole capture these two coefficients are related to each other and the valence band only talks to the trap level so they are four on the right hand side I have just kept them to I haven't even written up the electron number here right now let's think about it I just defined n1 I didn't know what it is it looks like a bunch of constants and I also will get correspondingly a values of p sub 1 now look at the magic here that if I multiply ends n1 and p1 I don't know what they are I don't know but if I multiply you will notice amazingly that everything cancels only thing that remains is n0 and p0 do you see that how it cancels the trap trap occupation how it cancels and n0 and p0 why am I writing it ni-squared because remember this is in equilibrium this is in equilibrium so the number of electron concentration and the number of hole concentration regardless of whether there is trap or not if there is trap good if there's no trap that's even fine it's always equal to ni-squared that's the mass action right remember that's why I said it's very important it really doesn't depend on whether it's doped undoped whether accept a donor trap doesn't matter this is always true and therefore since n0 and p0 in equilibrium is equal to ni-squared somehow if I can calculate n1 I'm done because I can calculate p1 by using this relationship remember right this is why the quantum mechanics hides ni-squared because it is effective density of state nc and nv and the band gap expand the exponential do you remember that so this is why the quantum we are carrying along the quantum mechanics just it's in a disguise so you don't see it but everything is coming with us okay so now I want to calculate n1 because once I calculate n1 I'll be in good shape so first of all in order to calculate and so on n1 I want to know how many traps are occupied now if I want to know how many traps are occupied did I write it correctly I should have multiplied f0 okay let me double check on this one I think I must have written it correctly but let me double check on this one but mt0 let's say I multiplied by f00 which is the number of when it's empty so this is fine when it is occupied means when it's not empty and f00 means when it's nothing is there right no electron is there so this is fine 1 minus f0 means when it is occupied and when it's occupied that's n sub t so I multiply remember the derivation from before for the donor level remember there's no difference between a donor and a trap a trap is a donor in the mid-gap why is it why they have different name I'll tell you a little bit later in the next class but I should be used able to use the same formula for donor had it been below the conduction band I should be able to use the same formula for the acceptors so it's the same same formula so I put some put that in g sub d do you remember what is that degeneracy factor right for conduction band for silicon it is 2 and for valence band for silicon 4 right so we remember that quantity here we know beta is 1 over kt and e sub t is a trap level we know that copper where is it or gold where that level is in silicon we know that so we can put it in now let's try to calculate this thing now do you agree with this statement that p multiplied p sub t is when the trap is empty when the trap is empty means it doesn't have any electron that means n sub t is a total number the fraction which has lost both its electron is multiplied by f 0 sub 0 0 which is the blue f sub 0 0 so that's the numerator and in the denominator I also have the expression for n sub t okay and these are all in equilibrium remember that's why I am carrying around the 0 on there in the denominator in the subscript okay now you already know the expression for f 0 0 so let me not worry about it you just insert the whole thing n and once you do you see you get an expression for n sub 1 what is that do you see you whether you know everything on this one n i do you know that you know that 10 to the power 10 right that you know g sub d you know degeneracy factor what about e t well you look at the table whatever the e t is do you know e i e sub i the intrinsic level do you know that you know that because remember we said in equilibrium n is equal to p and from that we calculated the value for e f and e f is e i for the intrinsic material do you remember that it's close to the mid gap I have e i this whole thing I know and therefore I know n 1 where is silicon hiding is in here silicon hiding is in n i because if you change it to germanium n i will be different g sub d this is where e these are various places the material constants are hiding if I know n 1 do I know p 1 well of course because of this and because of that I know p 1 as well I'm done you see this is math there's no deep physics in here just have to keep track of a few lines of algebra okay I'm done with this one n 1 I know p 1 I know I can go forward now now this time I look at USA which is sort of the trap level previously I looked at the conduction band and the valence band this time I'm looking at the yellow region that how the electrons are coming in the trap and getting out of the trap same for the holes right so how would you do that so let's look at this so I'm looking at how the trap concentration is changing trap occupation is changing as a function of time first of all see whether you agree with this I have written is a minus of the change in the electron concentration is this does it sound right it is right because anytime a electron is lost from the conduction band that loss is the trap levels gain because trap got one when the electron conduction band is unhappy but trap is happy it got an extra one they have a negative sign what about holes the holes the same way because I'm looking at occupied number of traps anytime the whole concentration went up right how did it go up because the electron jumped up to the conduction band that's why its whole concentration went up because it jumped up as a result I will have a plus sign for this one please try to convince yourself that this is a correct statement right if I give you two trap level in exam I should not that complicated perhaps but you should be able to do this detail balance right the equation at least of the trap level right instead of having one level now I already know the expressions for dndt I just derived it in the last few slides I know that and I also know that for the dp dt I'll just flip the sign and put it in here right and the en and cn e p and cp well they are all related so I'll put them all in here so I'm getting an expression here I essentially know everything do you see that look at this equation cn I will calculate it multiplying by sigma the capture cross section from the last class and the thermal velocity do you remember last class cn I know if I know cn I also know c sub p now n and n1 I know I just calculated and n sub t is what I'm trying to calculate and p sub t is one minus n sub t or nt minus so except from nt I know everything on this equation I should be able to solve this so now I'm talking about that's the general case if I solve that one I should be able to solve in every case transient steady state I should be able to do any problem that is a general equation always true single trap level non-degenerate always true that equation but if I insist that it's in steady state then what's going to happen in steady state what will happen that although the trap level talks to the conduction band and to the valence band right it talks to many different people individually they will not be balanced anymore why because this is no longer in equilibrium right they are no longer in equilibrium so they will not be individually balanced however globally they will be balanced that there will be no net change in the population in the trap as a function of time so I said that thing to zero so now I can solve for n sub t this I can easily solve for this you can just work out the algebra this is one line of algebra I will not go through that and let me just look at the net rate of recombination so remember this is in steady state that means all rates are the same the number rate now rate at which electrons are disappearing the same rate at which the holes are disappearing right net it has to be the same so if I just wanted to calculate the flux that is at which it is disappearing I will just say the recombination is minus dp dt and from the previous expression if I substitute the value from the previous slide substitute the value of n sub t I have the whole thing very complex looking equation this is what terrorizes solid state students but it's not that bad I will show you do I know everything here in order to calculate the trap number if somebody gave me n and p if somebody did then everything else is known n sub t n sub t the number of traps right I know the number of traps I know all the capture coefficients n i squared I know so I should be able to calculate this and that is I will be going to give you some example but before I proceed let me quickly ask you something you see in this one it says in equilibrium if I wanted to look at equilibrium in equilibrium the rate must be zero right and then the only way this whole thing can be zero is if np is equal to ni square so this is an important statement when we derive them a law of mass action we just multiply two things and it came ni squared came out and it didn't really say how violently electrons are moving around but you can see actually np equals ni squared actually comes from a detailed balance condition like this here the electrons are coming down from the trap they are going up through the trap they are all around and at the end in equilibrium np is ni squared see so that is somehow is getting reflected in this expression so equilibrium is not a retired person's life equilibrium is a very active person's life but all the processes are balanced it looks stationary and this instead of carrying it around we will call this whole quantity tau sub n this is minority carrier recombination time for electrons and tau sub p this whole thing in the bracket just to look it make it look nice that is the whole recombination time okay let me show you a few examples derivation done so let me show you a few examples how to use it let us consider a semiconductor in which you have shine light on it right on line on but not very strong light just a few extra electron hole pairs so let's say on the order of maybe 10 to the power 12 10 to the power 13 in silicon ni is 10 to the power 10 right per centimeter cube very weak light i have that's why the word low level injection so the number is not very high how will i know how the electron and hole after i turn it off how will it disappear let's look at this the way it will disappear is by something like this so i have this electron and holes now i have written n as n naught plus delta n now delta n here does not mean it is small in general don't always assume that if i have a delta it always means small in our context it will not be so in general i can always write it n naught equals n equals n naught plus delta n and p equals p naught plus delta n why do i write delta n not just delta p because i shine light in it and the number of electrons that was generated must have left behind is same number of holes and so the number of electrons and number of holes in the spatial case is exactly the same so therefore i write delta n and delta p equal to each other that's what i have written now it can be simplified a little bit more and let's say whether you agree the first term on the numerator n naught multiplied by p naught what is that ni square and you can see that will take care of the last term on the numerator ni squared is gone and you can see if you cross multiply this then you will have a delta n multiplied by a constant and delta n square and you have the same bunch of things on the denominator now if it is small low level injection if delta n is small delta n squared is even smaller right so i'll get rid of that similarly if this is a p type material p type means it has a lot of acceptors then it has a few electrons right relatively few electrons and so which term can i get rid of i can get rid of n naught why because it's a p type material lots of holes few electrons and that's why i get rid of the n naught compared to p naught you see you'll have to make relative comparison and once i have done that i will simplify in every case for example i can get rid of n naught from here and delta n is small compared to p naught right and so i'll get rid of that the whole term and only thing that remains is p naught because p naught is much larger than delta p because of it's a low level injection so i'll get rid of this now this step you'll have to follow step by step when you go home follow step by step but at the end of the day look at that expression delta n divided by tau 7 so how will it decay as a function of time this is dn dt right that's the rate of change this proportional to delta n over tau n so it will go down exponentially as a function of time right that's that's how it will going to decay so the few electrons you have pumped up in the conduction band they see a sea of holes all around it because it's a p type and they bump in the holes all the time through the traps and recombinates keeps recombining so therefore you don't see the expression for anything related to the holes here you see there's delta n over tau n because holes are so numerous anytime it wants a hole it will get a hole so as a result i do not have anything in the final expression related to the holes you see that's not a rate limiting supply you have to understand the meaning of the equation so that you remember it exactly high level injection same procedure but now you have shown a very strong light let's say you have put a laser on a bunch of say a little piece of semiconductor semiconductor was intrinsic to begin with huge number of electron hole pairs so therefore what are you going to do you will expand it the same way but this time unfortunately you cannot leave out delta n square in fact delta n square is much larger than the first term around right because ni let's say 10 to the power 10 or so and i delta n if it is 10 to the power 18 then this whole second term will be significantly larger the number t tiny amount of electrons and holes you had in the beginning doesn't matter because the light has generated so many and so you will put it in and this time you'll see that instead of just tau sub n you sub have tau sub n plus tau sub p why is this why is does it physically is like this because now the electron and hole number are almost equal to each other right they are nobody is dominant so therefore it will depend on how quickly they can find each other it is not that anytime electron once there is always a hole or the vice versa it is here both are limiting you have to have find both at the same time in order for the recombination to occur so therefore you serve have tau sub n plus tau sub p high level injection right okay and the previous one was low level injection by the way this very quickly so in organic solar cells a topic i am working on recently this type of processes are very important organic solar cells are essentially intrinsic right but the sunlight comes in and it generates a huge number of electron hole pairs when they recombine this is the process with which they will recombine not the the low level injection process now let me ask you this is which one is higher in one case i have a delta n in the numerator and another case i have the you know a little bit bigger numerator a denominator compared to the other one but you see high case has a bigger denominator does it mean at a higher level of injection you have lower recombination that makes no sense so what's wrong exactly right so the delta n for high level injection although they are both delta n one delta n is 10 to the power 18 another delta n maybe 10 to the power 12 so although it looks like that the first case is actually looks like smaller actually first case is orders of magnitude higher because they will recombine very quickly right there's lots of electrons and holes so that's why the expression looks funny but it is correct now what happens if somehow and this will come later on when we talk about diode somehow you can take out all the free electron holes take them all out now if you take them all out then n is 0 p is 0 because i took them all out so if i take them all out then i have n i squared on the top and i you can see that i have taken out n and p from the denominator and this is a constant i know the important point i want to show you here is in the previous cases i always had a plus sign r was delta n divided by tau n in this case i have a minus sign what does it mean it means the previous case there are lots of electron hole pair they were recombining and they were going away the number was going away this time this is being generated because there's no electron and hole it wants to go back to the 10 to the power 10 right so it will keep generating until it can reach the equilibrium and therefore i have a minus sign here it is inverse of recombination generation so that is what i have here now this again i'll show you in devices everything i'm doing every step will be used in the subsequent lectures so it's important to know how it works now the two remaining processes i'll talk about is direct and og recombination direct recombination i'll not even try to may i'll just make an analogy and let it let it go with that you see in the recombination generally what we had in the denominator we had sorry numerator we all had n p minus n i squared that says in equilibrium that thing must vanish in the denominator for the shock lead hall we had things proportional to the trap concentration right n t capture cross section and all those when you have direct recombination and electron coming in recombining with holes i don't have any traps or anything so the whole thing that i had in the denominator i'll just replace it with something called a b now of course i can derive it properly this depends on the band gap and other things but that's another class maybe 659 they will will derive it properly but for now let's assume that it's a simple formula or life is simple and if you want to handle low level injection in gallium arsenide direct band gap material then you will just do this it's a p dope material let's say you'll expand it and you will drop terms you will say delta n is equal to delta p the second order square term you will drop and eventually you will get an expression for proportional to delta n the excess generation you have what is tau direct by the way tau direct is a rate so this first term b multiplied by p naught that is the rate or time constant with which the extra electrons and holes will disappear this time you see it has a number of holes because if you have more number of holes of course that allows you to recombine faster similarly you can say what what happens if i completely remove electrons and holes from this from a given region okay this is this is no problem n and p is zero so there is a net generation upwards and given by b and i squared why do you find b well this is listed in the tables in every material somebody if you just look up a handbook they will tell you what the value of b is for a given material oj recombination again by analogy look look whether you can understand does it look right let's start with the red one the red first term i write it as n squared p first focus on that n squared p does it look right because two electrons have to bump in against each other n squared and p well it has to find a hole in order to get in right so therefore it's multiplied by p now in principle i should have written a one minus fc for the second electron to go up but that that level everything is empty so therefore only thing i have is n squared p right now why do i write n i squared n on the right hand side on the second term the reason is this term must vanish in equilibrium does it vanish in equilibrium do you see because in equilibrium n will be replaced by n not n not by multiplied by p not what is that n i squared and you can see that this term will vanish in equilibrium so this is necessarily it's not a derivation but it looks right do you see on the other hand on the second term we're multiplying c sub p that there is a p squared multiplied by n this says two holes bouncing each other so it's so much energy one electron going in the conduction band and another going deep down in the valence band that's the second term and that's where it comes from these constants are measured people and in fact i spend many years i've not placed few years in my life working on semiconductor lasers and i really have to go through the intricacies of the physics here but for you one slide is more than enough hopefully low level injection you should work it out again put these conditions in and once you put this condition in you will see that if it is a p-doped material you will see that p squared will become n a squared because p is equal to n a the number of holes equals to the acceptors so you can put it in and you will see that the recombination in this case the og recombination if the doping is very high n a is very high in that case og recombination would be the dominant recombination mechanism in many semiconductors right because you see n a square why did the n a squared come from because that's the p squared over there you need two holes and when you have high values because it doesn't have to consume momentum directly remember that was the problem same wavelength that was the problem so when you have lots of electrons you can bypass that conservation problem and therefore have very rapid recombination through the og process so let me i think let me show you just one slide and then i will end because i think the i will pick it up in the next in the next class so now consider we have all this complicated derivation so let's take a step back the semiconductor doesn't know that you are grouping things into shock lid hall direct og when an electron goes up yeah when you shine light it will go down in any path it can find direct available good if it doesn't have a direct path it will take the shock lid hall path it will take any way it can go it will go down so when you shine light and let the light be off turn it off then it's going to go down from experiment i'm saying and in experiment if you look at the output light that is coming out you will see it is decaying as a function of time so x axis is time y axis is delta n and i am t equals zero in this one is when i have turned the light off just light turned the light off and i'm looking how the photons are coming out so from experiment what i will get is something called a tau effective that's how i'll see the whole thing decaying now from that how am i going to understand get this various coefficients c sub n the capital B for direct recombination how am i going to do that so in order to do that you'll have to understand how these recombinations actually depend on various things so as i said every all processes will work simultaneously and this all recombination rates will be together but i just told you that for each one of them remember this is low level injection so every one of them is proportional to delta n i have a shock lid hall time constant i have a direct time constant and i have a oj time constant this i just derived in the previous three slides and this each one of them has a certain dependency the first term the shock lid hall it depends on the number of traps the direct it doesn't care about number of traps because no trap is involved only thing it cares about is the number of dopant atoms right why because it gives you a certain number of holes or certain number of electrons oj yes it depends on the number of dopant atoms but as a square because two of them have to bump against each other so they have different dependency so if i do a set of experiments in which i'm changing the dopant level systematically then this decay will be different for each one of them and from that i should be able to pick out what these different coefficients are you see so this is what it is let's this is from your book and i want to explain how did they get this one so y axis is tau effective so from experiment somebody shine light on it on silicon dioxide and they saw how the whole thing is decaying and they just put one data point on each one of them x axis number of dopants so that's the x axis so on the left hand side is close to intrinsic on the right hand side heavy doping effect remember heavy doping effect we talked about so that's happening on the the right hand side let's see whether we can understand this the tau effective should be the sum of all these things now in the left hand side n sub d is close to zero right it's close to intrinsic so that means the second and the third term will drop out at the low low side it will it will drop out so from there if i know the number of traps i should be able to calculate c sub n that's that's good now if you go at a very high doping side then you see the first and second term will drop out why because these are actually smaller terms the third term will now be humongous because it's n d square now remember this is a log log plot so if you take a log log on the tau effective on on this on the right left and right hand side what should be the slope of that line minus two right log if you take a log and if you look at this curve you will see exactly minus two is exactly the value on this curve uh the slope and the high sign is exactly the value on this curve and experimentally people have seen exactly very similar that's theory that's the theory so you put various values of n d you can generate the curve but experimentally i have shown you from two different papers that indeed at high density this is 10 to the power 20 very high density right one atom in every hundred uh host atoms very high density and you can see how the things are falling off so from here if i give you a curve like this from here by looking at the slope and looking at the intercept you should be able to calculate back the oj recombination constant is that right and from our lower values you should be able to calculate the number of traps because actually from that you should be able to deduce all this okay all right so this is all about recombination that how equilibrium is restored we perturbed it with light and we said that the shock lid hall recombination this is one of the things you have to learn unfortunately in order to earn a six-figure income later on but hopefully this was not too painful and this is an important recombination mechanism that's a dominant thing that's how you design your anytime you carry a stick memory stick many are or DRAM memory you buy for your computer all of them actually if the people who design them understand how the this recombination mechanism work because you are allowed to lose only one electron in every 10 years because some of the memory that has so few electrons in it that you cannot lose any electron because if you lose one in a year or one in a few years that's also even too many so this recombination mechanism somehow or other you have to have extreme control over before you can have a viable product that you can sell it is looks a little complicated but if you follow through the steps and why don't you do this exercise where instead of having one trap level you have a pair of trap levels and see whether you can derive the detail balance for this you know it's no rocket science here very simple very simple thing now direct band to band and og recombination I use the very similar formula they have their independent derivation but generally for direct band gap material shock treated hall is not that important this direct band gap and og recombinations are the dominant are the dominant things especially for laser og is is the dominant dominant process and this is not just some theory for last 50 years hundreds and hundreds maybe thousands of engineers and physicists have done beautiful measurements you know those looks like few data points but who did it really had to work hard to set up the experiment shine laser on it get the electron hole pair out and see how they are decaying as a function of time a beautiful experiment that has been done hopefully some other course will have an opportunity to discuss them okay all right thank you


What's going on everyone? Sam here with late in sports cards and I'm ripping one 2022 series one baseball and one 2022 Panini Donrest baseball hobby for Kevin A. So good luck Kevin See we got in here for you man. It's full of wander out of that pull the wander last time I opened this So that won't be too bad. Let me just swiffer off the chrome dust really quick We just opened up a full case of optic football. So chrome dust is a little bit prevalent, I would say Empty Here we go. Good luck here, Kevin. Tell Marte Got Louise Robert that is to 999 for the white socks Lou Bob and Jared Walsh I haven't opened any series one, so I'm actually kind of excited for that I started like just after series one was big Jonathan India blue foil Jose of Reu Independence day on Moncada Romeo Gonzalez on the blue foil Lance Lynn and Clayton Kershaw Lance Lynn is to 2022 Blue foil Madison Bungarner Frank Thomas and Jim tommy. I didn't need her until today to be honest Got gold to 99 Robert Poisson on the rated prospect. That is 86 of 99 ease nice Poisson and Blue foil Marcus Strowman Liberty Jake Meyers rookie nice one there one per box on the Liberty and Unleash that is your don Alvarez to 999 Stroze your don and Carlos Rodin on the blue foil. We've got lightning Tyler O'Neill to 25 Cardinals nice Tyler O'Neill Got Starling Marquis blue foil stars and stripes Adola scarcia and Seth beer blue foil rated rookie Diamondbacks Jake McCarthy red Jacob the grumblou Here I believe Got Jamison Tyone that is for the Yankees to 99 on the Tyone nice Pitch today, I believe actually that is player worn Nice Jamison Tyone Hit Whitmerfield or Jersey, I should say Ozzy Alvy's red diamond Kings Joey Votto blue foil when Otto and Brendan Crawford on the blue foil Stars and stripes you won. Yep as Louise Heel blue foil Yankees got Lou Brock to 125 for the Cardinals Nice Lou Brock and blue foil Teosca Hernandez First auto is Andy young For the Diamondbacks Not numbered on the Andy young auto Nice one there Louise Urius Diamond Kings Louise Robert to 2022 both flows blue foil unleashed Mike Piazza to 349 Mets that is a met Piazza and Blue foil will ya domus brewers diamond Kings America to 50 that is Matt Olson ease Wilson is still an A in this product and Cabrion Hayes blue foil Independence Day Fran Milraeus and blue foil Jake McCarthy rookie Brandon Lau to 2022 Justin Turner The second autos in here the captain dock is amazing. We've got nice Louise Robert on the Superstar scribbles white socks. There you go Kevin congrats on that. That's awesome. Nice Lou Bob Not numbered that's really cool each year old blue foil and last pack of Don Russ and then we'll go into some series one baseball Tom Siever and Pete Alonzo blue foil on to some series one baseball hobby Good luck here Kevin. I believe those are the silver packs. I'm not mistaken Again, I have not ripped series one. I've not really watched any series one It's been a while before or since we've opened any of it. So bear with me I know who I'm looking for but you man Troy. Hey, Amber G Obviously looking for the wander got Tommy Pham I'm the foil not numbered I didn't watch the yet actually Chavez. I want to for sure. I gotta when I have like a day off I'm not doing anything. I think that's what my plan is gonna be to watch the dock Sonny Gray Yankee legend Sonny Gray There's a wander There you go It's wander Franco rookie a home run challenge of Bryce Harper Alex Wells That manning rookie on the back Johnny Quaidoo Williams Miguel Cabrera Austin Riley Jazz Cheslem, Jr. Future stars. That's cool. Tony Gwynn base Jake Myers Patrick Wisdom with the Got Denver pride Charlie Blackman on the manufactured patch cool one there City flag patch card Patrick wisdom or Charlie Blackman Patrick wisdom on my mind for some Eric Hosmer Turnbull Randy Rosarino Ozzie Smith base with all Bruhan Stuart Fairchild rookie 2022 Hingin Ryu gold border for the Blue Jays This one there Andrew Vaughn future stars Sammy Long rookie Ricky Henderson base Hendricks see it's another wander out of this. Why not Andre Jackson rookie? Xander Bogarts Willie Castro, Kevin Sheets rookie on top Connor Wong Brian De La Cruz Brandon Marsh rookie angels So used to seeing all these guys and unlicensed jerseys because I haven't opened really any 2022 products So it's just funny seeing them and in like their licensed jerseys Like oh, that's Brandon Marsh actually in an angel jersey. Oh, it's Brian De La Cruz actually in a Marlins Jersey doesn't just say Miami on it Josiah Gray in a Nationals uniform at least heel rookie Josiah Gray base Austin Meadows on top foil future stars Alex Kearlaw of not numbered base Free Galvis as a Philly Will Clark base waters new bar rookie Cal Raleigh rookie Drew Ellis and the city connect Jersey Luis Robert Manoa future stars Miguel Cabrera base Nina foil Tyler McGill rookie Tyler McGill base rookie behind that two packs to go then we got our series one Silver packs Jackie Robinson base Drake burger we're both with Castro Base got one so do Anthony Rendon Chris Bryant and Fernando Tothi's junior home run challenge That'll do it for your break there Kevin congrats on the hits. We'll get those right out to you. Thanks again, buddy


These sweet bananas are all clones of each other. They're genetically identical. And they actually have susceptibility to different diseases and fungal diseases. And so we're using nuclear techniques to improve the disease resistance of bananas. What happens is we treat the plant material with ionizing radiation. In the case of this project, we're using gamma radiation. And it's similar to, like, X-rays, right?  It's energy that's coming in, and it's affecting the DNA. And afterwards, the material's completely safe. And that's a big advantage, because the seed or material that we can irradiate in our laboratories and cybersdorf can immediately be handled completely safely and immediately grown in the ground.


is going to turn tide changing power of hope. Welcome to Hope Today. I'm Amy Schaefer. I'm here with Corey and Sydney. This is an amazing day with an incredible topic. Yes it is. You know how do hardship and hope go hand-in-hand? Well coming up in a moment on Hope Today, Benjamin Wendell will explain how real hope only comes from chaos and challenges. It's gonna help you shift your perspective that your greatest moments begin at your deepest point of pain. You know Corey I am so excited about this conversation because I think it is time a lot of us are going through hardships, we're facing certain things, we want to get out of it but this is a way that we navigate through life storms and Benjamin is going to give us a really good blueprint of how we walk through life and look at it in a different way. You know I really love that word Sydney navigation right? Navigating through some very tough terrain in the waters and you know we always say you know where is the light at the end of the tunnel? Well many times we have to go through the process with God and that bonding experience that we have with God in the darkness in the midst of that so being able to do this and talk about these things is very important and Pastor Benjamin has some great insight on these dark spaces and how to experience God through that so I am excited about this conversation. You know I am not a huge fan of pain and suffering and troubles and trials and tribulations. It's not my favorite thing but here's what I know. It happens and life happens and guys you know we're getting ready for my son to graduate high school and you know right now he's under that mama bear he's in he's in the cave he's under the wing of my shelter and I know that he's going to go into the world and he's going to make a difference but he's going to face suffering he's gonna face hard times he's gonna run into problems and I just know because of who God is that God is faithful and that no matter what he goes through that he can come through it and he can win. Sydney yay though we walk through the valley of the shadow of death I will fear no evil and I do know that victory is our ultimate finish line we will finish strong we will win and we can do that because of hope. I just appreciate your transparency Amy about like not liking to talk about pain and I think it's an uncomfortable subject for a lot of us but I think it's important that we dive into it and this conversation that we're gonna have with Benjamin is going to shift our paradigm of how we think about it and what real hope looks like you know Benjamin Whittle is an innovative and empathetic author and speaker and as a pastor for more than 20 years he's walked many people through dark shadows and valleys of the human experience in his book Good Catastrophe he provides a blueprint for people to weather their way through the storms of life. Pastor Benjamin we are so grateful to have you with us. Hey guys it's a real joy to be having this talk with you. So Benjamin before we dive into what it means to be a good catastrophe can you tell us a little bit about yourself and where you're from. Well you will tell from the accent that I ain't from around here so I'm from Australia now in the US and yes I've pasted for over 20 years and you get to walk with people through a lot of lived experience. I've also been married for 20 years and I have three awesome sons so my hands are full you know what I mean. Definitely you're like a busy husband busy dad but you know one thing I just love is like your passion and your heart when you were writing through this and I have to say this is one of my favorite books that I've ever read you know being on part of this program and so can you talk to us about good catastrophe because where it comes from because sounds like an oxymoron it doesn't seem like they should coexist as the same phrase. Well I think that many of us live out that oxymoron in the way we approach life and challenges but that's being challenged by a unique cultural moment. I know for my life I don't think I've ever lived through a season that's had as much cultural upheaval or complexity. In fact the CDC recently did a survey and they found that 57% of teenage girls in the United States feel persistently sad or hopeless not just occasionally not just every now and then and that's just a pluck one number out but I'm sure for each of you and every listener that's not just a number if we did a quick hope audit many people would say it's been a while since I've let the light in or felt optimism or really dreamed of a better tomorrow somewhat even say it's been a while literally since I laughed and just had the ability to smile at life so there is a desperate need for the kind of transcendence that hope brings to us in a modern and complex world. You know one thing I love that you just said about letting the light in because a lot of people there are a lot of darkness that they're walking through and sometimes it feels like in life that we can pray all we want we feel like we get like hands laid on us all stuff and sometimes it just doesn't let up so what would you say you know when it comes to this idea of like what real hope is in the midst of that what does that truly look like? Yeah I mean for me this idea this concept of a good catastrophe actually comes from the writings of J.R.R. Tolkien the book looks at Job but I had to go back I could not find an English word that even described that good can come from bad but Tolkien coined this term you catastrophe EU catastrophe meaning good catastrophe and his philosophy was when he was writing books like Lord of the Rings and the Hobbit that when the main character reached a point where all seemed lost everything went dark there was no way out there would be a sudden turn towards joy I think in our world we often put these experiences in completely different categories we're either going through challenges or we're experiencing joy and fulfillment and light I'm trying to present that hardship and hope work together in our life and they do something for us that a problem free life never good so take us a little deeper into that because I think a lot of people it's hard to say okay I'm going through a hardship and then there's hope and it's almost like they're separate so what does that look like the mending and the blending of the two when it comes into our lives well I write about this little concept called the bicycle and if you think about riding a bicycle you know which I'm doing that a little bit right now in Southern California you you are always riding on both wheels both wheels are turning and if you think of one wheel as being the divine wheel goodness joy laughter fulfillment and the other wheel being hardship challenge pain suffering I used to think that if I could just only have the good things then I would be happy and have hope what I've discovered is you're always riding on both wheels every day of your life you won't have a single day that's so good that you won't have any bad and chances are it's not like you'll ever have a day that's so bad that there's no good the lived human experience is always and constantly riding on both wheels and here's the kicker it's not just that we experience challenge at the same time as what we experience good things but that there is a symbiotic relationship between our challenges and our growth and God uses the challenges God uses the pain to bring about our greatest flourishing and our greatest growth it's so true that it's like it's hand in hand that no matter what we're going through the challenges God uses it all and one thing I love that you bring up is this whole story of the book of Job and you give it a like the way you wrote about it of just explaining I mean a lot of us have read the story of a Job we know what's happening but to really take a good look at what he was experiencing as he lost all his children lost his livelihood and then the book also permeates from this place of understanding from out of that pain and brokenness there's a concept that you bring up that's based on the book of Job and it's the scent of water can you talk to us about that I I have come to just be fascinated by this old story Job and what it represents like the obvious is it represents a man who suffered but actually it speaks to us at a more fundamental level of how God interacts with the human experience and Job was incredibly successful he had 10 children and in a single day a perfect storm trespasses into this man's life it arrives unannounced it doesn't send a calendar invite and it brings with it devastation sufficient to say the man basically loses everything including the death of his 10 children and the storyline of this man ends up with Job and it's as if his world went silent there's no more little footsteps in the home there's no more laughter and he has to figure out how do I rebuild who I am and how do I create a new future when I've lost everything and Job makes this dramatic claim he says this it's it's a metaphor he paints his life as a tree that's been just brutally cut down to a stump in the ground now I'm not sure about you guys but I like taking photos of trees I never walk past and take a photo of a dead stump in the ground but Job makes this claim he says at just the scent of water even a stump that for all intents and purposes looks dead in the ground can live again thrive again but again and grow again he wasn't just talking about trees he was making a claim about the human experience when it encounters the dynamic of hope just even at the scent of water that's where we have hope and Benjamin just want to ask you you know you're really touched and triggered by the book of Job can you just share with us the moment in your life where you felt like all hope was lost but you encountered that scent of water the scent of the Holy Spirit the scent of God being with you in the midst of a hard time well I'll tell you this Sydney it's certainly a lot easier writing about it than living it and I wrote this book Good Catastrophe and in the last 12 months I'm like God where's the good it feels like I'm only experiencing catastrophe I lost my older brother to a devastating cancer journey he was just 18 months older than me I lost two grandparents this is all just in the in recent months I went through the biggest life transition I've been through and it felt like I fell into a dark hole and just couldn't figure a way out so what do we do when it feels like circumstances conspire against us if our hope is linked to outcomes it's always going to be a fragile version of hope I had to learn again this concept of the scent of water that I don't need an ocean I don't need a bucket I don't even need a single drop of water all I need is the scent the smallest intervention of God in my life to bring about a dramatic turn and I've had to rest on that I've had to embrace that and I've seen how hope can reach us even when we feel unreachable thank you for just sharing that transparency of loss because I know you talk about it in your book especially with your brother so sorry about your brother and your grandparents as well and I know something that is really deep on your heart is this whole concept of the broken piano can you tell us about that story and how it applies to our lives well the year is 1975 you guys are gonna love this little story I mean it's something that's just so fascinating to me Keith Jarrett is driving from Switzerland to the Cologne Opera House in Germany he arrives late he has back pain and he has requested a specific piano he's a musician the Bosendorfer 290 Imperial Concert Grand but to his surprise when he gets there the staff put out the wrong piano instead of the Bosendorfer 290 it's a small undersized piano some of the keys and get stuck the pedals don't work properly and to make matters worse the piano was terribly out of tune he has a decision to make he courageously steps out in front of 1400 people and decides to play on this broken piano while the Cologne Concert has gone on to sell more than four million albums it's the best-selling instrumental album of all time now one would presume the best-selling instrumental album is recorded in the best studio with the best microphones and yet it's this unusual midnight concert in Cologne on an undersized broken piano and here's the message for all of us none of us get the Bosendorfer 290 Imperial Concert Grand in the concert of life we all have a broken piano but god brings the most beautiful masterpieces out of broken pianos and for every person that feels like my piano was broken feels like my whole life all i got was a flawed instrument i want people to know this you still have a song to sing and the most beautiful masterpieces come out of flawed instruments i love that so much of just being i can just see all of us are like broken pianos or these broken instruments but we make such a beautiful and unique melody based out of the pain and the traumas that we've walked through and i like a quote that i want to share with our audience that you have in the book it really struck out to me you said this if i view my pain from a materialistic comfortable vantage point it will appear disastrous but when i see it through an internal filter it will give me a wide enough perspective to include the multiple layers of human experience can you just speak into the heart of somebody that is going through just utmost tragedy is trying to figure out this playing this dance of trying to find hope in the midst of hard times can you just take a moment and to minister and to speak to the heart of someone watching out there when we're sitting in moments of great challenge and adversity i think it's so important that we take that one step back and we actually look at the vantage point in which we're approaching life from this is a part of the gift that adversity brings into our life and i'm convinced that in today's world we need to fundamentally reframe the way we see our troubles and here's what i want people to see that with hope the storyline of our life always curves toward a redemptive purpose the life if your faith is following Jesus that life is not a promise that you will live a problem free life we do not see that in the characters in scripture we do not see that in the life of Jesus we do not see that in the life of the apostle paul and the disciples so what the christian faith provides us is not immunity from pain or perfect circumstances it gives us a world view through an eternal ultimate hope that gives a lens or a perspective through which we can see every challenge or problem and instead of just experiencing the pain of what a circumstance brings i can begin to see that god goes to work in the midst of my challenges and some of my most game-changing lessons and growth will come out of storms not just good times but through navigating through trauma anxiety depression and lust god is at work there if not the most out of anywhere in life he's at work in our challenges to bring about our deepest growth wow i love that viewpoint about having an eternal mindset and view as you're going through pain and trouble and suffering what do you mean by the phrase that hope needs human skin well thank you for the for the question amy i've been asking myself this question is there a link between hope and friendship and i have come to believe because i thought this for many years that hope is like a personal virtue or feeling that just happens in my heart i've started to now see hope as a communal experience that hope comes to us in the form of friendship and where this originates from is the life of joe because infamously he has these three friends that walk into his life at his low point and give him bad advice but what people miss because these guys have become almost villainous in this narrative they miss this moment it's so beautiful joe has lost everything three friends leave their families their businesses they're not going on a vacation they're not going on a cruise ship they're coming to pain joe is on the ground covered in dirt and through tear stained cheeks he looks up at the horizon and he sees the outline of three people their friends they walk into his pain and sit with him for seven days and seven nights and they may have gone on to give some poor advice but the beauty in that moment i don't think that loneliness and hope are compatible we we need to let the light in by letting people in and the primary tool that god uses as the delivery mechanism of hope is other human beings so if you're going through challenges we've got to get outside of our homes we've got to put our devices down we have to re-engage in people and understand hope comes through human skin it's a relational experience not just an emotional virtue this is amazing topic and i want to go into that a little bit more when you talk about joe's friends but i want to go back a little bit when he was experiencing the grief of his children there was also the grief of the loss of bond that he had with his wife who we know in scripture says you know curse god and die i feel that certain circumstances bring out characteristics of someone you may love that you never thought was going to happen until that was introduced how do you feel like joe interpreted the grief of losing that covenant with his wife not necessarily their marriage but they're bond with god through her grief processing her grief and then processing his own that level of loneliness in that moment i know that was a lot but how do you feel yeah yeah go ahead and share it's it's it's a great question cori and and you know i think when we go through adversity um you know cori in our life or or loss or or even just major change you know what's really interesting it's interesting the way that people around us respond and that can be more difficult than the actual loss is the uh disappointment that people weren't there for us when we needed them the most and i know what that feels like and i think that's where we've got to got to reimagine hope and what it means to build lives that are highly connected relationally i mean you look at my generation millennials one out of every four millennials say they don't have a single friend uh to turn to when they go through a storm gen z 79 percent say they're lonely these are staggering numbers and so for joe it was you know he went through so much complexity but three friends came and sat with him and maybe we get to be that person for somebody else we get to be the hope with human skin that walks into somebody's life i put it this way pain needs to be diffused through our friendships to come out the other side as hope it means we have to let people in to those places of our life that are not comfortable the places of pain and when people disappoint when people don't call when i mean i've again i've gone through this it's so difficult the best i can say is this we all get to make a choice to be that for somebody else and if we ultimately believe in the principle of sowing and reaping if we give our lives away as hope ambassadors i believe we're creating a net of hope that exists when we go through our own falls and we go through our own trials i just want to like snap right now on that point and say say luck as the three of us gory abe and i we were all like what you just said about when we have our pain and like able to diffuse it through friendships and other people y'all just need to sit on that i feel like well we can close the show and sit there i'll just say thank you so much that's your benjamin so much for just your wisdom and your insight and what you poured out today it is so rich and we're just so thankful for who you are in the kingdom of god and who you are that you are a gift truly a gift to the world his book is called good catastrophe the tied turning power of hope i highly highly recommend this book thank you so much pastor benjamin hey thank you i really appreciate it guys being a great conversation wow wow what can we say about this i mean we we say these cliche things like you know your test will become your testimony god will take you know the ashes and make something beautiful but they're not just cliches it is really true that no one is perfect no one has a perfect life no one has a life that all things are going perfect in every area at all times that's just not reality if you think about jesus as he was talking about friends jesus is about to suffer the most brutal execution ever known to man he's about to be crucified beaten and whipped and he is praying it out and he needs he needs help he needs some friends now he calls on some disciples now they might have fallen asleep but jesus the son of god needed men to be with him to suffer with him to pray with him how much more you know quarry do we need people that will put hope on and help us in times of great need and you know we touched on this a little bit today we touched on this scripture but just so that you can marinate on this throughout your day and throughout your week we're going to read jobe 14 7 through 9 and it says this for there is hope for a tree if it be cut down that it will sprout again and that its shoots will not cease though its root grows old in the earth and its stump die in the soil yet at the scent of water it will bud and put out branches like a young plant that word there the scent of water he said that today not even a drop but the scent of water and i know that sometimes in the midst of depression and agonizing pain and you might be going through grief or you might be going through a divorce or you might be an economic place where you don't know how things are going to get paid or whatever the scent of god's presence that would descend in gives you hope gives you clarity gives you peace that surpasses all understanding and that hope and you might feel like that tree that's cut down all the way to the stump says and there's no branches in my life there's no growth there's no fruit in my life but the scent of god's presence is going to begin to permeate into your life in a way and you will begin to grow again through this amy sydney you can just sit on the scent of water piece like something that benjamin actually wrote in his book and i've been on this i'm a plant mom i love plants and there's actually a study that says plants when they hear water they hear the water that's how the roots start growing towards the water so it's amazing that what we see in the natural is mimicked it's in the the spiritual that maybe today just like what kori was saying and aim is saying that you need the scent of the presence of god the scent of the spirit just take a moment if you need to sit somewhere if you need to go outside and walk but i only tell you when you get that scent of water it's so amazing what god begins to do what god begins to show you and reveal you you know something i just want to share that god spoke to me in this season as i think even the scent of water the water of the word it's the wisdom of god god told me his wisdom is your way out in this season don't look to the ways of the world but look to his wisdom because the fear of the lord is the beginning of wisdom and we just thank you so much for today joining us for this really special conversation and we pray and we hope that you get the scent of his water in his presence today have a good one


Ukrainian forces destroy Russian triad electronic warfare station near Bakhmut. Ukraine's Special Operations Forces Aerial Reconnaissance Unit has tracked down and the defence forces have destroyed nine Russian targets including electronic warfare systems on the Bakhmut front using artillery. Special Operations Forces Press Service reported this. The triad and LIA-2 radio electronic warfare systems were destroyed thanks to aerial reconnaissance from the Special Operations Forces Unit. Soldiers from Special Operations conducted reconnaissance of the Russian soldiers positions and, after identifying the targets, successfully aimed and adjusted the artillery fire of the defence forces. The Press Service reported that a total of nine Russian targets were hit by accurate fire in a short period of time. In addition to electronic warfare systems, Ukrainian forces destroyed artillery pieces and Russian armoured vehicles. The Special Forces add that the operators of FPV drones also work out their tasks together with the reconnaissance team, adding that FPV drones strike not only at equipment and manpower but also destroy Russian observation equipment. It should be noted that electronic warfare has emerged as a critical and increasingly important component on the battlefield due to the growing reliance on interconnected systems and communication networks. As a result, electronic warfare has become a vital element for militaries worldwide, enabling them to gain a competitive edge and protect their assets in the face of emerging threats. The ability to blind an enemy, overwhelm or disable air defences and radar and deny an adversary the ability to communicate or target could determine victory in the war.


We're going to be running the ultimate frog fishing challenge today. I'm going to be taking you guys along. I love frog fishing, guys. Probably one of my favorite top waters to throw. One of my favorite baits to throw at all times. Something about throwing a frog, watching the fish just come up under it and slam that thing.   And sometimes they just come all the way out of the water. It's just so exciting. And we're going to be getting on some big frog fish today. If you guys are new to the channel, please hit that subscribe button. Hit the notification bell. Also, hit that like button if you guys have been enjoying the content. I really appreciate the support. Let's go ahead and look in this box right here. This is actually Fletcher's. I sadly didn't bring mine out for some reason. It just came to mind when I was driving over to Fletcher's house. I was like, let's go catch them on some frogs. We have a bunch of different baits in here. Let's go ahead and pull a few out and see what we're going to throw today. Regular hollow body frog, rivet frog, lunker hunt frog, hollow belly sunfish, a smaller sunfish, a standard sprow popping frog. And lastly, we have the old popping pickle that's already tied up on my rod. You guys know I've caught a ton of big bass this last year on the popping pickle. We're going to be starting off with that one today. Let's go ahead and catch you on the water. By the way, I have Fletcher behind the camera. He's going to join in on the video today. He's going to pick out, you know, a frog to throw as well. Let's go ahead and get on the water and catch some big bass. This one's going to be good. Like I said, guys, we are starting off with the pickle, the popping pickle. And we're going to, we're going to be fishing a bunch of, it's very sunny today. We're going to be fishing, you know, some shade lines under those trees, skipping this frog up in the trees. This is going to be an amazing video. I'm so pumped. I've never been this excited for a video in a long time.  I already feel it. We're going to be casting any shade lines. Just stay tuned. Don't skip through. This is going to be good.  I'm going to be honest with you. I've been dying to catch just a megalodon on a frog. Dude, it hit the water from the limb. I never saw him eat it. I was over the limb popping it and I just felt him pull. That was the weirdest frog bite I've ever had. There you go. He's not big, but yeah, dude, I casted over the limb. It hit the water and I was like watching the limb, trying to get my line off it. You know how you barely pop it to get it off? Yeah. And like, when I was popping, I felt him pull back. I was like, what? I never saw it. That was awesome. I'm a little tiny guy. Nothing big, but we're going to keep on trying. Oh my gosh. Oh, nice. Yeah, that's a good one. Nice. You choked it too. Look at me skirting. What? Look at that fish. That is one of the weirdest looking bass. What is this? Dude, that is the weirdest looking bass I have ever caught. I thought he was big because of his head, but he's, what in the world I would not want to catch him in a tournament. Imagine if he didn't get the length. Dude, he choked that frog though. Look at that bass right there. That is crazy looking. Never in my life have caught a fish like that. He's got a jacked up spine. Beautiful guy. We're going to get a picture.  Second frog fish today. That is the weirdest looking bass. Just got a picture of him. That is so crazy, man. The head of like a three pounder and he's just, I don't even know what. He's got some strange stuff going on. I mean, it's like, I don't know. He's really flappy down here. Usually they feel like more firm. See that? Yeah, it's like he's definitely got a messed up spine. It's like he doesn't even have a spine on this tail. Let's see how he swims off. Oh, fine. He swam off fine. Let's get back in there guys. There's two on the popping pickle. That was a good bass. He slurped it, bro. He slurped it. Look at the freaking boil that put in the water. I don't think he was quite forward, but he was pushing it. Wow. Dude, he slurped it, never saw him hit it. He just went. I watched it happen, but he didn't come just hitting at it. That's crazy. This corner did look too good. Did he get all the way back there yet? I did not. Not all the way. That's the bad thing about a frog. Sometimes I hook them so hard and they come flying in the air. And I freaking lose so many because of that. I might take a couple. That one I lost. Dude, that was a big one, Fletcher. I saw him roll on it.  Never saw him eat it. Oh my god. He ate all of them.  That's not good. That was annoying. I never had one do that on this thing. All right, guys, I think I'm going to be going with this regular brown frog right here. We tried the popping frog, and that was like in specifically like a popping perch. But now we're going to go with this frog, see if we can get destroyed on it. Frogs skip so much better than that popping one. I was about to say, I can't believe there's not one in there. He finally ate. I would do the words we're about to come out of my mouth. Guys, we just tied this brown frog on and freaking we slurped it up on that tree. This frog, I can skip a little bit better. And I can also walk it a little bit better. But I love the popping frog. Just I can work it a lot slower. I feel like under the trees, if I'm fishing pads and stuff, normally a regular frog, that's a pretty fish. Nothing big. He's a thick, chunky guy. Look at that fish. Oh, yeah, he's got some meat on his back. It's a little fatty. Ever caught any under this dog? I think there just might not be enough water on these dogs. Oh, that was so awesome. Oh, my gosh, that was so awesome.  Skipped it under the dock, freaking hammered it. Dude, they're slurping it. It's so weird. You never even hit it.  What in the world, Fletcher? Spot looked too good. Oh, dude, my rod did not move. This is a different one. This is a different fish. This one's a little bigger. Yeah, dude. Look at that. That's not a bad fish. Oh, yes, I love it. No, that was a different fish, bro. He looked bigger when he swirled on it. That is a beautiful bass about the two number, right there on the brown frog. There's two on the brown frog now. That is awesome. I actually had two bites right before that. I don't think it was this fish. I thought it was a smaller one. I mean, it could be, but I think it was a different bass. Beautiful, right in that shade line, where you should be. Beautiful markings, beautiful colors. I love that right there. They've been bedding around these trees real good. You're about to get slammed. Yep. No! Dude, it was a dangler. It was a dangler. Oh, that is too much slack. You landed on that bed. Yeah. At the second I set the hook, that, there it is. There it is. Yep. Oh, gosh. Oh, baby. I lost you the other day on a swim bait. Oh my God, it is. It is what we were saying.  That is the fattest. Just a meaty, just a meatball. Look at that right there on that frog.  I wouldn't trade it for anything right now. I wouldn't trade that frog bite for nothing. Not any other top water, not a big swim bait, nothing.  That is the fattest bass today by far. We're gonna get that beauty back in the water. But that is a chunky bass right there. Look at that right there, guys.  It's a straight pancake. There she goes. That was so cool right there. Should be one right there. Dude, this is what I was talking about, losing frog bit. I don't know how you didn't come off. He choked that thing, freaking small one too. Look at that. It's the best ones eating it all day.  Look at that.  Whew, pretty guy. Gosh, dude, that's actually, oh, he's stuck in the duck. Oh, there's your double up. You got it, Noah? Yeah. On the frog? Oh, man. I thought he was a lot bigger. I'm solid too, but I thought he was freaking three plus. Look at that pretty bass. Gorgeous. Ah! Double trouble? Yeah. And you got me beat by it, just a good bit. Thanks, pal. Gosh, that was awesome. We rolled on that freaking frog.  Beautiful markings on that fish. Thank you, bud. Dude, that looks so good. Gosh! Dude, that's a decent one, too. Oh, that is a good one. Oh, that might be the heaviest one yet. He's barely hooked, freaking annihilated. That's what I said, too. I was like, look, he's about to destroy it. Look at him pissing. That is a thick bass right there. Heat, that was one of the best blow-ups all day. Oh, easy. And by far, you gotta love that right there. Frog fishing at its finest. Another double-up. Is that a good one? Oh! Those are about the same size. Dang it. Well, let's get this baby back in the water, saw the two and a half here. Maybe two and three quarters.  Dang it, Fletcher. You're supposed to double up with me. I know, I'm sorry. They are eating so good here.  See, all these bass, there's a lot on bed in here. The other places that we fish, like the big lake that we fished, earlier they're not. And if they are, they're on the whole other side of the lake where we fished the other day. But in here, there's a lot that are pushed up on the bank, right by their beds. We'll probably get another one right here. Oh! Oh gosh, Fletcher. That's a big one. Like, actually. Dude, like big. So here's the one I literally just missed. Noah got back in there. I was trying to fix my hook, he bent it straight out and I can see why. Oh my gosh. So I try to set the hook into a big old chunk. That's almost a four pounder. That's a tank. Dude, look at him eat that frog. Annihilated it. Holy cow, we're getting a weight on this girl. This is a high three number. Oh yeah. Did that frickin' frog bite. Look at that bass right there. I know the beautiful one, that's it right there. Pretty markings on that bass. All right, let's see what she weighs. She might be close to four. She might be close to four. Oh, she is four. What is she weigh? 4.03. That's a four pounder, baby. We got us a big one today. Yes, sir. We got us a good bass today.  Right there. We're gonna get her right back in the water. Try to catch another one. All right, baby. Let's get her right back in. That is a solid four pound bass right there. Gotta love that. Topwater action with big fish. You cannot complain about that. There she goes. Another good one. Gosh. Freaking crushing this frog. I don't even wanna put another one on. Two number. Get you right up here, girl. Look at that. Munched. I'm munched. They're eating this frog so good I can almost not get it out of their mouth. Oh yeah. Little guy. Not a little guy. That's a quality fish. But compared to that last one, you're not a lot. Thank you, bud. Watch this. That's a big one. There it is. You mind getting the camera out of there? Oh. That's bigger than that other one.  Oh. That's a big girl. Ah. That's a beautiful three number though. Gosh. They're just eating it too good. I don't even know what to say about that. You can throw anything you want right now and this will outbeat a worm. This will outbeat a drop shot. This will outbeat anything. I'm telling you, there's eatin' top water that good. That is a healthy fish. Let's get her right back in. That was so much fun. Thank you so much, fish. She goes. That was right where I got him. Right when it got to the edge of that grass. Oh. That sounded like a good one, bro. There is another one there. There's probably a couple beds up on that.  Holy cow. It's about time that I put on a different frog. I think I'm actually gonna do the sunfish. Similar to a frog, they've been eating it with the walking action and I think they're going to destroy this thing. I don't even think there's gonna question asked that they're about to eat this. So this is exactly what I'm about to throw. I think we're gonna catch some giants on it. They're just munching top water right now. Sun's coming down too. This is insane. This is a little like... That's a good one. Oh yeah. Oh yeah. On the sunfish.  The walking of it. That's what they can't stand. Gosh. That's the first one on the sunfish. Pretty two pounder.  I can already feel that one coming. Yep.  Oh my gosh, that was close. Oh my gosh, that was a close one. Oh man. Let's see if he'll bite the sunfish. Skipped it under that tree. Got it. He ain't big. He ain't big, but he ain't bad. You know why he ain't bad? Because he's a top water fish. Bats with an X. Yep. You got one? Oh.  They're all rusty. Oh, watch him eat that. Dude, that was crazy. I've never seen a bass come up from behind like that and eat something. That is awesome. On the sunfish. Freaking good one, too. Look at that bass. Gosh, that's a good bass. On the sunfish, as you guys can see. Freaking things. Getting munched. I mean, munched. Look at that fatty. Thank you, buddy. Dude, he came up like this. Towards the frog I watched him put it in his mouth or towards the sunfish. That was so cool. You might be able to see it on the GoPro. Dude, like, what is going on? Oh, yeah. Dude. Dude. Yep. Dude, I literally don't know, bro. Every time. Oh. That's on this corner. Get on him that time. Oh.  I said, if I miss my next one, I'm cutting it off. Freaking baby. A little twinkie. A little one-pounder. Oh, this frog or this sunfish. I'm a fan of it. It's just, I think the one that I got's a little defective. Just a little defective, but pretty fish. Needless to say. I'm gonna catch this dang fish. Oh, there you go. He ain't that big. I thought he was big. What did I say? I said, I'm gonna catch this fish. We're about to freaking take out. Said, I'm gonna catch this fish. I got you. I got you, bud. You weren't going nowhere. Oh yeah, I need some attention on that one.


Here's how you can generate more than $500 in a week by doing options on this wonderful company called Meta. If you want to generate passive income using the power of options safely, especially during volatile time like this, then keep on watching. Hi, this is Chloe and welcome back to my channel. The only one place for you to learn about stocks, investing, as well as options. If it's the first time of you coming to my channel, remember to hit the subscribe button as well as the notification bell so that you will not miss out any of my future investment insights. An early thumbs up is also appreciated because it will tell YouTube algorithm that you find this video helpful, and it will actually help to push out to more people to inspire them to start investing safely. In the past one month, Meta has dropped more than 35%. With the recent massive sell-off in Meta, it actually presents investors like you and me a great opportunity to school up some shares really, really undervalued at the current market condition. But apart from buying shares directly from market, there's actually another way for you to generate additional income using this powerful option strategy called BOSS, which is also the exact option strategy that Warren Buffet has been using for the past 30 years to increase his wealth. And with just a few click of buttons, you can actually generate more than $500 in a week. Now let's log into Moomo platform and see how you can execute that for yourself as well. So once you come into the Moomo platform, all you need to do is to go to quotes and actually search for the company that you want to invest. So in this case, I'm actually wanting to invest in Facebook, which is Meta, because it's such a great company at undervalued right now. And once you're done with that, you can actually go to this column called options to execute this strategy. And over here, you can see that actually there are many different expiration dates. What I want to choose is one week later. So from now until one week, it's until 25th of February, I'm going to choose this. And under here, I want to choose put option, because when I sell a put option, which is BOSS option strategy, it basically means that I want to promise to buy 100 shares of Facebook at the strike price that I want to buy. So in this case, I really don't mind owning Facebook at $207.50, because really it's a no-brainer price to buy for the long-term. Long-term Give It Time Facebook is definitely going to be way more than the current share price right now. So what I need to do is under the big option, I just right-click once and I view detail quote. And you'll see that over here, the screen starts to change a little bit. And you just click on the trade button over here. And remember the quantity, depending on your portfolio size. I'm just going to set it at one first, because just by selling one put option, you already need about $20,000. And because my account has it, I will be able to execute this BOSS option strategy safely. So make sure you do have enough money before you execute this strategy as well. So by doing that, I will actually be able to make about $565 in just one week time. This is a premium that I will get to collect by selling away my promise. And once you're done with that, you just have to click unlock trade. And FUTU will actually send you the password going to do is to actually execute it accordingly. So think about it, because you promised to buy 100 shares of Facebook. And in return, you get more than $500 in terms of premium. Isn't that a win-win situation for both scenarios? If you want to find out why do I think Meta is such a strong business and what exactly is my exact entry price, then do check out the video right here. And if you look at Meta's stock price closely, right now Meta has actually dropped back to its pre-COVID level. It's almost as if the market is perceiving that Meta as a company has not grown for the past two years, which is ridiculous. But exactly due to the ridiculous emotions felt by so many investors out there, now it presents us great opportunities to buy these companies at a great price. But make sure you do your due diligence before investing in any company. By the way, if you have not set up a brokerage platform yet, then do consider Moomoo because it's a globalized platform backed by tech giant Tencent, and it's actually regulated by MAS, which is Monetary Authority of Singapore. Apart from being able to invest in stocks and options in the US market, you can also buy and sell shares in Hong Kong, China, as well as Singapore market. On top of that, you will even get an additional $50 cash bonus and a free Apple share worth more than $200 as long as you sign up your account via my link below and fund $2,700 Singapore dollars inside. And when you buy your first share, you will even get an additional $40 cash back into your account. If you think about it, all the bonuses add up to more than $315, which means that the moment that you fund your account with $2,700, your return on investment is already more than 11%. But you may be thinking, Chloe, I'm not sure what kind of company should I start investing. Well, I just shared a wonderful company in this video, but fret not, I have other company choices for you to choose from as long as you sign up via my link below, I will personally send you my latest private portfolio watchlist where I share with you what companies am I looking at, what price am I looking at, and most importantly, what are the options strategies will I be executing on these companies as well. Once you sign up, all you need to do is to submit your Moomoo ID to the Google Form link below so that I will be able to send you my private portfolio watchlist to your inbox. And this offer is only valid until the end of this month, so if you want to get additional 11% ROI into your investment, then make sure you grab the chance right now before it's gone. If you want to learn exactly how you can use options to accelerate your return and generate income consistently regardless of the market condition, then do join me in my upcoming Options Foundation class where I will be sharing with you 3 powerful option strategies that you can take advantage of during this volatile time. All you need to do is to register for your free spot via the link below. If you find this video helpful, remember to give it a thumbs up and share it out to your friends so that you can inspire more people to start investing safely. With that, happy investing, and I will see you in the next video. Mada, laishu, bye bye.


Next, you want to go onto the website of your targeted journal and obtain the author guidelines. It is so essential for you to read the directions. I have to say one of my greatest frustrations as an editor is that the majority of papers that are submitted, the author, has never read the directions. The directions will tell you the referencing format. The directions will tell you what length of paper you can submit. The directions usually tell you that all tables and figures are to be placed at the end of the paper, not embedded in the paper. The directions will tell you what should be on the cover page, the title page, the contact information. The directions may tell you whether they need an abstract copyright release forms. So I highly encourage you, before you get writing, read the directions to know all the guidelines that you're supposed to follow as you write your paper. It's very, very important. One time I got a paper that was so beautifully written. It followed every, every direction and it's so rare that I get a paper like that. I actually called up the author and I said, Anne, hi, I'm Trish. I'm the editor. I'm thrilled to see that you followed the directions. I think Anne thought I was crazy. She was quite amused that I called her and she said to me, well, I always followed directions. Well, I pointed out to Anne that she's a rare person and that I really appreciated that she followed the directions and I asked her for tips of how can I get other authors to follow directions. So we had a great chat, but I would again encourage you, read carefully. We try to make it as clear as we can as the editor. If you have any questions about the directions, contact the editor and get that cleared up before you write the paper.