[MUSIC] Now let's learn the excess carrier. Excess carrier is extremely important. A semiconductor device is operate by the excess carrier. Either created by the optical excitation or voltage of a pn junction bias. In chapter four, we store the excess carrier created by the optical absorption. Some of you probably learn the previous lecture in sophomore more like electrons in semiconductor. But excess carrier probably this is the first time that you learn. And this is very difficult later part of this lecture four. And this is because very important, because if you go to the pn junction, they assume that you know the excess carrier equation. And they not explain the where this equation come from, which is the lecture for excess carrier. So you perfectly understand this excess carrier section. If you don't, then you probably don't understand pn junction. If you don't understand pn junction, you probably don't understand MOSFET device. As I said, your MOSFET device operate by the excess carrier of the voltage or current. But we learning the excess carrier from the optical excitation. However, although excitation mechanism is different, their result is exactly the same, either by the optical or current excitation. Let's start the excess carrier. Optical absorption, if there is no light, there are only thermogenerated carriers we call electron-hole pair, EHP. However, if you turn on the light onto the semiconductor, regenerating electron hole pair. Let's say there you are applying the light that has energy over h nu, which is above the band gap of a semiconductor. Then electron in valence band is excited conduction band. They lose energy, bombard with a silicon lattice and equilibrium at just above the conduction band. If this electron and conduction band is recombined with a balance band they emit the luminescence. If excitation done by the proton or light, then this emission called the proton luminescence. If this emission is generate by the high energy electron bombardment, this called cathode luminescence. If this recombination excitation is done by the current, which is most cases of the MOSFET or pn junction, then this called electroluminescence. This luminescence light is depending on the semiconductor material. For gallium nitride, which is around 3 electron volts, 3.4, then emitting the blue, and then gallium arsenide is red, etc. Excess carrier that we are going to learn is the two cases, you need to differentiate these two cases. This is very important. One is one time exposure. The other is, Steady state exposure. As you can tell from the name, one time exposure you shining the light at the one time. Steady state exposure, you shining the light steady state. Equation or phenomenon of the excess carrier will be different between the one time exposure and steady state cases. But semiconductor device operation, you probably applying the voltage at constant time. Then probably this is the one steady state exposure. One time exposure is, This cases. At t equals zero, you shining the light. But above the positive time, you does not shining the light. So you only shining the light at t equals zero, then turning off the light, no light during the positive time. What happened? You was shining the light at t equals zero. Then you generating the excess carriers. Let's say that this is the n type semiconductor 10 to the 17. Then hole, minority hole is 10 to the 3 because np equals 10 to the 20 right? Then if you shining the light, let's say that you generating the excess carrier of the EHP, electron hole pair, 10 to the 14. So, excess carrier is equal electron and hole cases. But electron over the 10 to the 14 excess carrier doesn't influencing the measure of decay of electron which is the 10 to the 17, this is a 1000 to 1 ratio. However, minority carrier hole originally, 10 to the 3 and originally 10 to the 3, but excess carrier by the optical absorption generating 10 to the 14, 10 to the 11th. Orders increase amount of minority carrier excess carriers. What happened next, this is happen at only t equals zero. Then you shut it off the light, then this minority carrier, 10 to the 14 excess carrier, will be go back to the original equilibrium which is 10 to the 3 again. By the combination of the minority hole excess carrier we do measure a t electron carrier concentration. So original 10 to the 14 minority excess carrier will be decreasing, decreasing and go back to 10 to the 3 where the excess carrier equals 0. So as you can tell, the combination is proportional to the electron hole concentration and hole concentration. Majority electron is the 10 to the 17 constant, and if you're increasing more minority carrier hole, then a lot of recombination will occur. In thermal equilibrium where there is no excess carrier existing, the combination and generation is equal, right? If you don't shine in the light if you don't applying the voltage, carrier should be constant, which means that generation equal to the recombination. If generation is higher than recombination in equilibrium, doesn't make sense because more carrier is accumulated. If recombination is higher than generation in thermal equilibrium, then doesn't make sense because the carrier will be reduced. So in thermal equilibrium, recombination equal to the generation. And recombination is proportional to the electron concentration and hole concentration, which is recombination equal to the recombination constant times electron concentration and hole concentration. In equilibrium this np equals a ni squared, which is the 2.25 10 to the 20. So this is the one important equations. For summary, one-time exposure generating minority carrier excess carrier from 10 to the 3 to 10 to the 14 and they will combine and go back to the original state, which is the 10 to the 3. Let's this phenomenon in equation. Order ordinal will have a confusing in explanation of the one time exposure is a semiconductor is the n-type silicon, but the equations are being, we changing the n-type semiconductor to the p-type semiconductor. But the concept is the same except that p-type is majority minority access carrier is n, right? So minority carrier excess carrier instead of the p n zero right delta n zero. So, minority carrier changing over dn per dt is thermal generation minus the combination. So, during positive time, there is only thermal generation, which is the positive increased amount of dm per dt. The negative decreased amount of minority carrier is done the combination. Because if you recombine the excess carrier will be disappear. Is this true, this is very difficult to understand. Palatable factor is only thermal generation. What about the optical generate optical absorption and generating optical generation? Is there optical generation is happening in positivity? Then it should add positive optical generation. Answer is no. Because one time exposure, light rays only shining at t equals 0. Reconsidering is positive time if they're positive time there is no light exposing here. Therefore, there is no optical generation. There is only original thermal generation of the existing and minus factor is the the combination of the excess carrier. So let's start with this, dn/dt is thermal generation. This is thermal generation. In previous slides we learned that thermal generation equal to the combination which is the recombination constant to a ni squared. This is the recombination which is the recombination of constant times the mp np is the time-dependent factor originally n zero plus the excess carrier at t equals zero, right? And, majority hole plus excess carrier, then, This alpha, the combination constant, np n0p, there will be, this will co equal is deleted. So these two factor is deleted final result is. Minus alpha the combination constant surplus, n0 delta p(t) p0 delta p(t) because, This n equal p, excess carrier is equal, therefore n0 p0 delta n t plus delta n delta p which is the delta n squared. Now, let's approach this with a engineering point. This is the p-type semiconductor let's say the 10 to the 17 p-type semiconductor, excess carrier is the 10 to the 14. So, p-type is the 10 to the 17 and 10 to the 14 of the excess carrier which is the 10 to the 31. 10 to the 14 squared is 10 to the 28. 10 to the 31, 10 to the 21, then you can ignore 10 to the 28. So final equation becomes minority excess carrier dm per dt is minus the combination constant, and P0 delta n because these are 10 to the 14 and these are the 10 to the 3 and these are the 10 to the 17 negligible. So final equation of the one time exposure about excess minority carrier which is the delta and t is integration of this equation. Which is the delta n exponential minus the combination constant to P0t. And this, 1 over the combination constant plus the times n0 + p0 is the combination lifetime. The original delta and is the original of excess carrier. So this is the graph of the one time exposure at t = 0 you shining the light in one time generating excess carrier of a minority electron of 10 to the 14. Majority carrier originally, let's say the 10 to the 15 or 10 to the 17. These are the little bit of a changing right? But doesn't changing too much of majority carrier. The minority says carrier at one time exposure, t = 0, they will deduce the excess carrier because of the d combination. And they go back to our original state of the 10 to the 5 decreasing exponentially. This is the excess carrier over one time exposure. We learn that the Fermi level so in Fermi level, is under thermal equilibrium. So n times semiconductor there's a lot of measure of electron and my smaller portion of the minority hole. Though how much majority is existing defined by the fermi energy or fermi level function? And nP = 2.25 10 to the 20 then you can define the minority haul. However, excess carrier, majority carrier in loadable induction in majority carrier of excess carrier, majority carrier of electron has the similar number. But minority excess carrier is hugely increasing. So no more this equation is applied. Low level injection, the majority carrier as same number as the equilibrium, so majority carrier electron in n types. And I conduct this small n means the n types and my conductor, majority carrier and equal to the original topic of the concentration. However, there is choosing increasing amount of minority carrier. Those shows increased amount of minority excess carrier can be defined by another Quasi-Fermi level called F of p. So Pn means minority excess carrier in n type semiconductor can be defined by the ni exponential high minus low Ei minus p per tt. This is the low level injection. But high level injection means they're high excess carrier, then high excess carrier then the electron is more hugely increased by the many excess carrier. The Fermi energy is longer original Fermi energy will be more increasing or close to the Ec. Therefore, high level injection majority electron concentration can be defined and I exponential Quasi-Fermi levels electron minus Ei per kt which is higher than equilibrium electron concentration. Same thing for the minority excess carrier Pn = niE minus Fp. Therefore, Quasi-Fermi level is energy level that used to specify the carrier concentration on the non-equilibrium condition means optical excitation or current excitation.
