 Tukaj je napravil s mojem brzim, Aleksandr Efrasovim, in taj poslednji doktor. Vseč, kvantom doce in vse obtikalne vseženje, na kvantom doce, je vseženje obtikalne elektronike. z pridem vseh doličenih, in jeznik način. Res, Kvantum Dots je zvedal v Leningrad, tudi na St. Petersburg, v 1981. Vsih je zvedal v Alešej Ekimov, V malo, zelo zelo z Kvantum dot. En jasnj izgleda. To je zelo, da je zelo z American Physicist Bruce. En jasnj izgleda, nekaj jasnj izgleda, je bilo najbolj konferenci v Parisu, tudi 30 jasnj iz Kvantum dot, izgledajte z toga eventa. V svoju koncijnenju je konferencija izgleda, ker kvantem doti je več, več, več important. V kvantem doti je, kaj sem zelo, dimenzionalne opentizacije, kaj prejmiči začnega radiečnja in začnega rečenja. Simpl kvantem docega je napravljati, zelo početno početno, zelo početno početno, In zelo se koutilo s surfikantem, če je polemera. Zelo se pošlo v vesele in prišlo. To je vse technoločno. To je vse surfikant. Kadmium selenite je najbolj stavljena, colloidal semikonduktor nanocrystal. Now the next step after quantum dots. Pretty recent step. Yes, the advantage of quantum dots is that depending on the size, depending on the size, they change color. Here is fluorescence result for cadmium selenite. And on the right is big nanocrystal, on the left is small nanocrystal with strong quantization. There are many such, it's called tunable fluorescence. There may be many types and even more beautiful picture of fluorescence of quantum dots, depending on size. So the idea is very simple that if you have a small size, then you have strong quantization and you have ultraviolet shift of line. It can be seen also on tunable absorption, the same thing that the absorption is shifted to the red side with increasing of the size of the dot. So you can tailor absorption, maybe different semiconductor and has wide scope of application. And now we come to a pretty recent object, quantum dot crystal. That's the device that consists of a crystal. It has usually base centered structure, but instead of atoms there are quantum dots. And this paper is probably the first theoretical paper in this direction. The motivation of this paper is that there was another event that happened recently, couple years ago, that they obtained quantum dots with metallic type conduction. Before that it was pure hopping. And a few years ago they obtained quantum dots, quantum dot crystal with metallic type conductivity. It's pretty large mobility and definitely metallic type conductivity probably close to Anderson transition. It's interesting that since that time, since that time the mobility, many groups obtained mobility of this order. But since that time, it's about three years, nobody did better, substantially better. So it's very difficult. And of course it's very important for devices, because to make devices with big conductivity is much better than with hopping conductivity. What was interesting for us is the theory of metallic conductivity in quantum dots. And also the following fact that photoconductivity in nanocrystal photoconductivity exceeds two, three order of magnitude, dark conductivity. Exceeds three dark conductivities, two or three order of magnitude. And it's relatively less, relatively small excitation generation. So that excitation generation is much less than one electron per whole, one electron per nanocrystal. So the only idea that can be said that if current is represented as a sum of dark current and photocurrent, then density is more or less the same and it means that mobility of photocurrent is much, much larger, few orders of magnitude larger than mobility of dark current. Kualitative explanation is very simple. It's connected with low conductivity because of small overlap between neighboring dots. In our theory we assume that in each dot there is potential well and potential so-called wood sucks and potential that come from nuclear theory. And this deviation from straight line, this value of lambda is very important when we speak about very short wavelength slide. So that's theoretical potential well. Then periodic potential have this form and first we consider optical excitation and this is typical big binding, big binding scheme where the gaps are two UKS square modulus, two UKS, the width of the gap, the width of the bend is this and it's, this is the width of the bend and it's much larger than the gap. So actually this parameter of near free electron, near free electron approximation. Then the theory of transport is very simple, may just use Boltzmann transport equation and scattering, we consider scattering on fluctuations of radius and interatomic distance. Small fluctuation of radius, reduces of quantum dots and interatomic distance. Actually the energy of photoelectron is very high because the process, as far as we understand, that create photo current, photo carriers is Ager processes. So the energy is very high. It's about 10 electron volt and therefore the relaxation time is pretty large. It's difficult to calculate exactly mobility because you should know distribution of charges in energy but the estimation of mobility may be get from, just from tau k that may be calculated from the above equation. And this mobility will be 2000 cm2 volt per second. Now I come to the dark conductivity, the lowest energy of bend and dark transport. There is some problem with this, some theoretical problems with this. The point is that in this material the spectrum is very nonparabolic. And you should take into account nonparabolist. Parameter of dots is mass, effective mass at zero energy, then mass at function of energy. And the residual parameter which ionization threshold, that's the energy of the quantum well. Actually it's not good enough but we assume it's in this range. And radius of nano crystals. So to do this it's pretty difficult stuff because to do that we should use model for gallium arsenide and dimak and right model for lead selenite. Actually this equation above is strongly transcendental equation because m star is expressed in this model by this equation. So it's strongly transcendental equation and it's not parabolic at all. If you solve this, you should solve this equation and then with this equation you should solve quantum well to find the energy level in this quantum well. That's the most difficult part of this problem. Let's wave function in the quantum well. And probably I will not tell you all the algebra. The result is usual tight binding approximation. Tight binding approximation and the overlap c is exponent. A minus B. B is distance between dots and A is radius of one quantum dots. Now there is some calculations which I probably omit and I better show you the results. The calculation actually should be done numerically here. That's the energy in cadmium selenite as a function of radius. The energy definitely fall with increasing of radius. That's kappa A is the distance in the tunneling. And that's the hopping integral. And we see actually the most important fact that the hopping integral becomes larger for smaller dots. It happens due to very simple reason that the level is higher and overlap is stronger. And that's important for all. That's more or less the same. Now width of the band. Width of the band is strongly depend on radius. Look here, cadmium selenite. That's 1.5 and 1 nanometer. And 1.5, the width of the band is much less than for one nanometer. The less the quantum well is, the more overlap between them and the more mobility is. And it contains the exponent. It stands in the exponent, this A. So mobility is expressed by this equation. And again you see mobility may be calculated for just from Boltzmann equation in this heavy band. For degenerate gas it's independent on temperature. And if the temperature is higher than the width of the band, then this energy is much larger than kBt. And you can just use scaling to get expression for relaxation time and temperature dependence is 1 over T. That's mobility as a function of radios. Mobility for cadmium selenite is a function of radios. As you see mobility becomes larger and smaller radius. It's very strong dependence. Because it's exponential dependence, it stands in the exponent of overlap. Therefore it's so important to make very small dots. Schematic temperature dependence looks like this. Now dark conductivity and localization. Actually we consider Anderson transition in this crystal of quantum dots. This crystalline structure. As in the case when I forget to say that when we calculate mobility we consider scattering by the fluctuation of radios and fluctuation of distance between dots. And the same thing leads to an Anderson transition. We may calculate the change of the energy of each dot using this equation where xiA is a random variable that characterizes the fluctuation of the radios. If you assume rectangular distribution of delta energy, then we use for the criteria of Anderson transition, which is delta epsilon o divided by the width of the band, 2, 6, 7. It was checked by computer simulation many times. And also this result of percolation approach to Anderson transition. So this is the Anderson transition. And we were able to draw the diagram for lead selenite and cadmium selenite. And this line separates localized state from delacalized state for different ionizations rational to u. This is shown here in different radios. For smaller radios delacalized states, delacalized states has more pronounced. States are more delacalized. And let's face diagram separating localized and delacalized states due to Anderson transition. Also possible mod transition, which can be calculated with Hubbard model. It's also possible in this dot extra electron. And electron-electron interaction, if it's stronger than the width of the energy band, then it leads to mod transition. And then there is an interesting fact that we mentioned, that there is negative correlation of dark conductivity and photo conductivity. And this correlation has the following reason. You know that Ajay effect, which plays the most important role in this photo excitation, is actually atomic phenomena. And in white band it will be absent. It's pure atomic phenomena. But mobility, dark mobility in white band will be larger. So between photo current and dark current there is anti-correlation. If you have very white band, you have good mobility, good dark mobility, but bad photo conductivity due to small amount of photo electrons. Because Ajay effect doesn't work. Ajay effect is the main effect in this process of generation. So discussion of experimental result. The light high increase of photo current much larger than you should obtain is result of Ajay effect. Because Ajay effect put electron very high in the band. And their mobility is at least order of magnitude higher than mobility of electrons in the ground state. And that explains the difference between light current and dark current. That's experimental data obtained by group by Klibov. And that's how it looks like. Number of photo electrons per incident photon. And we see here that the burst at o9 electron volt is connected with photo excitation of resident electron in quantum bell. Burst at 1.5 is the most important burst. Is Ajay effect, Ajay photoenization. It's this scheme. Burst at 2.2 can be explained by direct edization from the valence band. And additional feature at 3.3 can be explained by excitation from below the valence band. The largest dark mobility 27 centimeter square volt second was reported in the area of closely packed cadmium selenite nanocrystal is to A3.9 nanometer. Such mobility indeed could be reached in theoretically in order at array of nanocrystals with nanocrystals size dispersion of the order of 5%. And confinement potential of one electron volt. In summary, we develop a theory of photo and dark conductivity in order at arrays of nanocrystals. Electron transport properties were calculated for scattering by structural defects of supercrystal, namely small fluctuations for radii and positions of nanocrystals. For dark conductivity we found the diagram in axis A and B separating Anderson localized states with hopping conductivity and bent states with metallic type conductivity. We propose a new mechanism for the conductivity triggered with very efficient recombination of electron hole pairs in bent H of nanocrystal, which transfers electron localized nanocrystal into high energy quasi free states in nanocrystal array. This leads to two for orders of magnitude increase of the photo current because the mobility of the states is 4 pi orders of magnitude larger than mobility of electrons in ground state. Concentration is less. Our theory predicts anticorelation between dark and photo conductivity. And now I want to finish my talk with the following. I am probably the oldest person here who knows Boris. I remember very well how Arkady Aronov came to me and sent me with triumph that he had found a genius student. He was recommended to him by Volody Griebov. Very soon I met this genius student and now look there is unfortunately there is no Volody Griebov nor Arkady already and I am the only person that probably remembers this time and I congratulate this genius student with his 60th birthday. Thank you.