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05.14.08 ЭНЕРГОУСТАНОВКИ НА ОСНОВЕ ВОЗОБНОВЛЯЕМЫХ ВИДОВ ЭНЕРГИИ
SOLAR ELEMENTS BASED ON NONCRYSTALLIC SILICON WITH NANOSTRUCTURED IMPACTS
Jalalov Temur A., doctor philosophy PhD, Senior Lecturer, Tashkent Institute of Information Technologies. Tashkent, Uzbekistan. E-mail: [email protected]
Imаmov Erkin Z., doctor of physical and mathematical sciences, professor, Tashkent Institute of Information Technologies. Tashkent, Uzbekistan. E-mail: [email protected]
Muminov Ramizulla A., doctor of physico-mathematical sciences, academician of the Academy of Sciences of the Republic of Uzbekistan, Physico-Technical Institute of the SPA «Physics-Sun», Academy of Sciences of Uzbekistan. Tashkent, Uzbekistan. E-mail: [email protected]
Sabirov Habibulla, candidate of Technical Sciences, Physico-Technical Institute of the SPA «Physics-Sun», Academy of Sciences of Uzbekistan. Tashkent, Uzbekistan. E-mail: [email protected]
Atoev Shokhzhahon Sh., PhD student, Physico-Technical Institute of SPA «Physics-Sun» Academy of Sciences of Uzbekistan. Tashkent, Uzbekistan. E-mail: [email protected]
Annotation. The article considers new physical models, technological methods for the formation of high-efficiency cheap solar cells based on non-crystalline silicon with nanostructured impregnations, in particular, nanoheteroclausters with characteristic contact properties.
The features of the electrophysical and optical properties of an individual nanodimensional р-л-junction, the effective absorption spectrum of solar radiation have been studied. In general, the efficiency factor of a solar cell based on non-crystalline silicon with nanostructured impregnations was estimated.
Keywords: solar cell, spectrum, silicon, nanotechnology, р-л-junction, nanoheterostructure, nanoclusters, volt-ampere characteristic.
СОЛНЕЧНЫЕ ЭЛЕМЕНТЫ НА ОСНОВЕ НЕКРИСТАЛЛИЧЕСКОГО КРЕМНИЯ С НАНОВКЛЮЧЕНИЯМИ
Джалалов Темур Асфандиярович, д-р физ.-мат. наук, старший преподаватель Ташкентского университета информационных технологий. Ташкент, Узбекистан. Е-mail: [email protected]
Имамов Эркин Зуннунович, д-р физ.-мат. наук, профессор, профессор Ташкентского университета информационных технологий. Ташкент, Узбекистан. Е -mail: [email protected]
Муминов Рамизулла Абдуллаевич, д-р физ.-мат. наук, академик Академии Наук Республики Узбекистан, Физико-технический институт НПО «Физика-Солнце» при Академии Наук Республики Узбекистан. Ташкент, Узбекистан. Е -mail: [email protected]
СабировХабибулла, канд. техн. наук, Физико-технический институт НПО «Физика-Солнце» при Академии Наук Республики Узбекистан. Ташкент, Узбекистан. Е -mail: [email protected]
Атоев Шохжахон Шухратович, базовый докторант, Физико-технический институт НПО «Физика-Солнце» при Академии Наук Республики Узбекистан. Ташкент, Узбекистан. Е -mail: [email protected]
Аннотация. В статье рассмотрены новые физические модели, технологические методы формирования высокоэффективных и дешевых солнечных элементов на основе некристаллического кремния с наноструктурированными вкраплениями, в частности, наногетерокластеры с характерными контактными свойствами.
Изучены особенности электрофизических и оптических свойств отдельного наноразмерного р-л-перехода. Проведена оценка спектра эффективного поглощения и КПД солнечного элемента на основе аморфного кремния с наноструктурированными компонентами.
Ключевые слова: солнечный элемент, спектр эффективного поглощения, кремний, нанотехнологии, р-л-переход, наноге-тероструктура, нанокластеры, вольт-амперная характеристика.
Jalalov T.A., Imamov E.Z., Muminov R.A., Sabirov H., Atoev Sh.Sh.
World practice of development recommends silicon1 as the most suitable substrate material for a solar cell.
In nature in a free state, silicon in the earth's crust practically does not occur (although it is the most common element after oxygen - more than 25%). It can be obtained in pure form from silica only after a series of 7 highly energy-intensive and expensive technological operations2. And immediately after the first stage of technological operations, silicon (technical) is obtained with a purity degree of about 95-99%. After the 4th - polycrystalline and only after the 7th stage - monocrystalline pure Si is grown. The complexity of isolation, purification and growth strongly limits the efficiency of single-crystal silicon [1, 2].
Technical silicon has a very low degree of purity (of the order of 95-99%) and contains practically all substances of the periodic table as impurities3. Among them there are:
• in a small amount (1017-1019 cm-3) background residual impurities forming cmall acceptor or donor levels in the band gap (from the III or V groups of the table of chemical elements)4,
• in a large number (1023-1024 cm-3) randomly distributed structural defects forming in the bandgap almost mutually compensating local deep levels of acceptor and donor nature.
Naturally, technical Si does not have strict crystallinity and therefore it most likely belongs to the category of a disordered noncrystalline semiconductor. This means that no energy band theory can be applied to such materials, one should not introduce the concept of a forbidden (or allowed) band, that is, one can not use the characteristic electrophysical and optical characteristics of crystals. However, a comparison of the spectral dependences of the intrinsic light absorption of crystalline and technical (disordered, noncrystalline) silicon yields an almost identical spectrum manifestation: in both materials, a sharp increase in the photoresponse at photon energies (fiw) exceeding the AEg value of the band gap of crystalline silicon (fiw > AEg and fiw ? AEg).
The peculiarity in the absorption spectrum of light of noncrystalline silicon is also manifested at low photon energies: light absorption by electrons of localized energy states is observed, practically analogous to impurity absorption of light in single-crystal silicon.
The above mentioned analogies of the optical properties of crystalline and non-crystalline substances make it possible (with a mass conversion of solar radiation into electricity) to use technical silicon as a substrate for solar cells. It is cheap, stable, strong, and in the field of its own light absorption, moreover, it has optical properties similar to monocrystalline silicon. The efficiency of the mass process of converting solar radiation into electricity under long-term aggressive atmospheric conditions is determined by special requirements for the technical characteristics (strength, stability of solar cells and solar panels) of the materials used, and also by the necessity of long-term preservation of their electrophysical and optical properties.
Electrophysical properties
of the separate «nanosized p-n-transition»
In work [3] two fundamentally new approaches to increasing the efficiency of solar cells are proposed:
• the need to divide a single continuous p-n-junction into many parts;
• the expediency of using a sufficiently strong defect silicon as a substrate for a solar cell.
In this paper, both proposals formed the basis for the idea of creating solar cells of increased efficiency. At the same time, the proposal to divide one substrate into many cmall contact cells was extended by us [4-8] to nanoscale scales.
Such a division can be achieved by applying nanoclusions (with an average transverse dimension R of the order of 5-35 nm) from another semiconductor to the surface of a silicon substrate (technical, cheap, highly defective), followed by the formation of nanoheterostructures (or nanoscale «p-n-junctions») on their basis.
The number of nanoheterostructures is ND2/3 - the surface concentration of residual impurities (that is, at least hundreds of millions per square centimeter). When the substrate is illuminated with similar nanoheterocluster, electromotive forces of a valve character appear in them, which indicates the manifestation of contact phenomena.
A separate nanosized «p-n-junction» - an essentially new contact structure consists of a local negative (almost point) p-region and a long positive n-region. The length of the n-region is d = bN, that is, it is a multiple of b = ND~1/3 - the average distance between the residual impurities. The surface area of the substrate surface «nanosized p-n-junctions» does not exceed 5-8%.
Below are the results of calculating [4] the electrophysical parameters of the «nanosized p-n-junction»: Ek (r) is the stress vector and <$k (x) is the potential of the electrostatic field.
Vector of the intensity of the electrostatic field. The negative charge of the solar cell is concentrated on all the nanotubes, which are uniformly distributed over the entire illuminated surface of the substrate with the density aN = q/ND-2/3 = e-N/b2. Each charge is concentrated by the charge q = e- N. Uniform distribution of aN on the surface of the substrate and on other N parallel planes (located behind it), concentrating the positive ones is necessary for their consideration in the model of uniformly charged infinite planes (Fig. 1). Then the calculation of the flux of the vector of the electrostatic field intensity Ek (r) through an arbitrary closed surface is carried out by the Gauss-Ostrogradsky theorem.
At the point with the coordinate x along the axis of the «n-di-mensional p-n-junction», the total vector of the electrostatic field intensity Ek (x) from each N parallel uniformly charged infinite planes (k - number N planes and change 0 < k < N) is based on the superposition principle fields. The figure shows the scheme for the formation of Ek (x) in each k-th interplanar space. The dotted lines of force refer to the negative plane aN.
1 In the USA, besides silicon in heliostations, CdTl is also used (up to 40%) [5].
2 Seven technological operations for obtaining silicon:
a) production of technical Si from natural raw materials;
b) preparation of an easily volatile Si compound;
c) purification of the highly volatile Si compound;
d) production of polycrystalline semiconductor Si from a purified volatile Si compound;
e) metallurgical purification of polycrystalline Si;
g) growing single crystals of Si;
h) alloying.
3 Al, F, Fe, Ti, Ni, Mg, B, As, etc.
4 For example, if the donor is an impurity, then in the form of an ionized donor and a free electron, since the solar cell is constantly at temperatures of the order of 300K and above. It is important to note that this is not a question of doped impurities, but of natural residual (background) impurities.
E = 0 E* О E* О E*0 E* О E = 0 k = 0 Jt = 1 k = 2 k= 3 <r = 4
Fig. 1. Model of uniformly charged infinite planes
Elementary calculation in the one-dimensional model of the resulting field Ek (x) in the k-th interplanar space leads to the relation:
Ek (x) = - (Y/b)(W - [xj).
(1)
Here y = 4nKe+/(eSib); [xk] - in units of b, the integer part of the x-coordinate.
At the end of the space-charge region, the resultant field is zero (after N parallel planes): Ek(x = d = Nb) = 0.
In Fig. 2 (using the example of 8 planes), the calculated coordinate dependence Ek (x) is given. In this case, the electrostatic field from each plane is uniform, the field lines of force are collinear with each other.
ОД. 0
lb 2b 3b 4b 5b 6b 7b 8b 9b 10b lib x
—I-1-1-1-1-1-1-1-1-1-1—
Relations (1 and 2) are obtained under the following boundary conditions:
EN (x = xN = d) = 0; (xk) = (x = xN = d) = 0 for x = xN = d.
E0 (x = 0) = E0 = -YN/b; (xk) = (x = 0) = for x = 0.
Here, E0 = E0(x = 0) and = ^k(x = 0) are the values on the illuminated surface of the substrate, respectively, the vector of the electrostatic field intensity and the contact potential difference.
At the end of the space-charge region (after N parallel planes), the vector of the electrostatic field intensity EN (x = xN = d = Nb) and the contact potential difference (x = xN = d = Nb) are zero.
The amount of charge on one on-off. The vector of the intensity of the electrostatic field, and its potential, and the number of charged planes, and the electrical capacitance of the nano-cluster, and d = bN is the length of the space-charge region, contains the parameter N. Numerically, its value corresponds to the amount of charge of the leveling of the Fermi levels in the thermodynamic process A|) of the contacting materials, that is, characterizes the number of electrons that can take one nanoinclusion in the process of thermodynamic leveling of the Fermi levels.
The value of N can be estimated from the definitions of the electrical capacity of the contact region C = q/^0, the charge q = eN concentrated on it, respectively, the difference between the Fermi levels (A|) and the work of the outputs (AN and ASi) of the contacting materials A| = q^0 = AN - ASi. As a result, to determine the value of N, we obtain the relation:
N--
C Ац
„2
1/2
C (a n a si)
12
(3)
An estimate of N for the same parameters as for | E0 gives a value on the order of 13-15. And this means that for b of the order of |im, the length of the space-charge region will be 13-15 |m (d = bN).
The drift velocity of an electron in the electrostatic field of a nanosized «p-n-junction.» In the process of light generation of photocarriers in a solar cell with nanosized «p-n-junctions,» they immediately find themselves in a contact electrostatic field. Under the action of this field, photocarriers begin to drift to the corresponding electrodes at a rate:
v = = eTp —= 2e
Tp N -
Cbm* N +1
(4)
Pic 2. The coordinate dependence of Ek (x)
A numerical estimate of the modulus of the intensity vector at the surface of the substrate, E0| = YN/b, for example, for N = 15 for one spherical nanoinclusion from PbSe-lead chalcogenide (C = 4ne0 sNR, eN = 250, R = 10 nm, A| = AN - ASi = = 0.1 eV) gives a value of the order of 2.25 • 104 V/m. This value of the field strength is not so great, but within its limits, it can accelerate the electron to energies of 0,15 eV.
Potential of electrostatic field. According to the equation of the electromagnetic field Ek (r) = - grad (x), the coordinate dependence ^k(x) of the contact potential difference at the point x along the axis of the «n-dimensional p-n-junction» is also calculated. In a one-dimensional model, it is equal to:
Фк (x) = -i Ek (x)dx; фк (x = 0) = ф0 = yn (N + 1)/2.
(2)
where and m* are the mobility and effective masses of photocarriers in the zones, t is the momentum relaxation time.
' p
An estimate of the relaxation time of the electron with respect to the momentum Tp in the contact field of the n-dimensional «p-n-junction» for the same parameters as for E0 gives the value Tp = 6 • 10-10 s. In this case, for the value of the drift velocity, we obtain a value of the order of v == 105 m/s, which fully corresponds to the drift velocities of electrons in traditional p-n-structures.
Spectrum of effective absorption of light
The transformation of solar radiation into electricity is carried out by successive four microprocesses: the absorption of a photon, the creation of an electron-hole pair, the separation of a pair into constituent charges and the transfer of charges to the corresponding electrodes.
Jalalov T.A., Imamov E.Z., Muminov R.A., Sabirov H., Atoev Sh.Sh.
The number of such cycles, successively realized micro-processes, is determined (Fig. 3) by the features of two spectral dependences.
Fig. 3. dE/E - the spectrum of the distribution of radiation by energy, a red line with squares; dN/N is the emission spectrum in terms of the number of quanta, a blue line with circles
Both distributions are obtained from the formulas of Planck for the energy density and the density of the number of quanta of the thermal radiation of the source at temperature T and are5:
dE _ dE/V _ 15 3
E ~ ' " '
n
dN N
E/V dN/V
"ÑjV _ 2^(3)'
dx
ex31
= 0.159 x3
dx
1
2
dx
= 0.416 x2
dx
(S)
Here x = ftw/(kT), ;(3) = 1,202 is the zetta Riemann function with argument 3.
It can be seen from the figure that the maxima of both distributions are shifted relative to each other and therefore in the region of effective light absorption optimal for silicon (from 1.08 to about 2 eV)6, the distribution of radiation with energy dE/E is7 32.57%, and the number of quanta dN/N -41.81% of the whole spectrum. It can be seen that the efficiency of solar cells is determined only by a certain narrow band of the spectrum, which is called the effective absorption spectrum of light.
The distribution dE/E shows the energy boundary of the production process of the electron-hole pair (hu should be greater than AEg, where AEg = 1.08 eV is the width of the Si forbidden band). And the distribution dN/N - determines the number of electron-hole pairs produced in the region of effective absorption of light that is optimal for silicon.
The spectrum of effective light absorption is the range of energy of solar radiation (photon energy) that causes electricity generation.
Four microprocessing transformations:
• absorption of radiation;
• the birth of an electron-hole pair;
• separation of the vapor into an electron and a hole in the contact field;
• charge transfer to the corresponding electrodes.
The magnitude of the photocurrent is proportional to gs, the rate of generation of electron-hole pairs in the number of quanta (i.e., dN/N is 41.81% of the number of quanta in the spectrum). This means that the efficiency of a solar cell with nanoscale contact structures is determined precisely by this figure.
Optical properties of the «nanosized p-n-transition»
Volt-ampere characteristic (VAC). The main characteristic of any solar cells is its current-voltage characteristic (VAC). Naturally, therefore, it is important to determine this characteristic of contact structures in a fundamentally new solar cell with nanosized «p-n-junctions».
The general form of the equation for the current-voltage characteristic is the same for any contact structures, including for a solar cell with separate nanosized «p-n-junctions». The difference is only in the features of the quantities entering into the equation, as well as in the varieties of the solar cell.
Fig. 4. Equivalent circuit:
a - of an ideal FE; b - of a real solar cell
For an ideal solar cell (Fig. 4a), the equation of the current-voltage characteristic has the form:
If = I + Id = I - Is (eaU - 1),
where I is the current through the load resistance R, If=If = egsPS is the current generated in the current generator, S is the illuminated area, gs is the generation rate of electron-hole pairs (or the light intensity in the number of quanta N:
N
(m-2s )
5 L = kT4(hc)3 — = ta3^c3 (e*kT -1);
V 15 V n
N = 2i;(WklV dN = ffl2 dm c3 tT -1)
V n2 t hc) V n2 '
6 In the near-Earth space (AM0), the equator, the sun at the zenith.
7 And with it the theoretical limit of the efficiency of the solar cell.
P is the fraction of non-recombined pairs, Id = Is (eaU - 1) and If - currents, respectively, diffusion and opposite to it - light, Is -saturation current, a = e/kT, U = a-1 ln (1 + If/I) is the photo-emf.
If U = 0, then the light current is equal to the short-circuit current (I = I ).
v f sc'
In the equivalent circuit the current-voltage characteristic of a real solar cell contains an additional, directly proportional to the value of the photo-emf (U), the term-leakage current (I):
= I + I + L -y d
I + I - I (eaU - 1).
(6)
The leakage current Iy ~ U is directly proportional to the magnitude of the photo-emf: I = Z IsU.
Here Z is the coefficient characterizing all losses:
• on the resistances of the R - contacts of the solar cell
pn
(including the on-off resistance and the space-charge region in the substrate),
• losses due to thermal and recombination processes.
Resistance of the contact area R can be determined at U = 0,
pn
when Isc - the short circuit current becomes equal to the light current generated in the current generator (If = Isc). This equality also implies that the short-circuit current is directly proportional to the illumination, observed in a wide range of gs, Isc = If (gs).
However, at very high illumination, the Isc increase becomes weaker, since the short-circuit of the external contacts on the solar cell itself is not equal to zero, but is equal to IRpn. The potential on the surface of the substrate (in the p-region) turns out to be positive relative to the n-region, which causes the appearance of a diffusion current oppositely directed to the light current and a corresponding decrease in the short-circuit current.
The equivalent circuit consists of a current generator and in parallel with it a connected ideal diode
With increasing illumination (by increasing I) the EMF increases, but is not proportional to I., but according
I = AI
If,
and for U = Ui the current is zero and eaUxx = A + 1 - ZUi.
For the convenience of analyzing the current-voltage characteristic, we give the basic equation of the current-voltage characteristic to the dimensionless form by introducing dimensionless parameters: a = aUi, b = ZUi, y = I/Is, B = A + 1, If/Is = A.
In this notation, the equation of the current-voltage characteristic has the form:
- = y = fl - b-U. - e I U..
pU/U,
(7)
It can be seen that the parameter, a, characterizes the temperature dependence of the I-V characteristic in the process of solar-light transformation.
The parameter b = ZUi is proportional to the leakage current (determined by all the resistances of the contact areas R , including the rate of recombination processes in the contact areas of the solar cell). For an ideal photocell, we can set b = 0.
Efficiency of the solar element with
nanodimensional «p-n-transitions»
The output power produced by the solar cell (Fig. 5) is equal to: N = UI = UIs (A + 1 - ZU - eaU). (9)
Using the dimensionless parameters (a, b, y = I/Is, P = N/Is), it is reduced to the form:
P = N = Uy = U B-bU-e°Uu■
I 1 U„„
(10)
Tok, A
is not proportional to to the logarithmic law, until the height of the potential barrier is equal to kT.
The boundary conditions for (3) or (4) - the equations of the current-voltage characteristic are the values U = 0 and U = Ui, where Ui is the idling voltage. At U = 0, the short-circuit current is determined completely by the photocurrent:
10 15 uv
HanpflweHne, B
Fig. 5. The current-voltage characteristic according to (6) and the power dependence on the photo-emf value (8) with allowance for (12)
From the condition: dP/dU = 0 we find in the dimensionless quantities P - the maximum output power. It is equal to:
Pp = ypup =(b + aB - abz )-
(1 + az )
(11)
Here, y is the dimensionless current at the maximum,
U is the voltage at the maximum, z
Up/Ui (0 < z < 1),
whose value is determined from the extremum condition by the transcendental relation (dP/dU = 0):
7 B - 2bz
1 + az
The real coefficient of efficiency of the solar cell r| is:
P„
IPUP
Po Isc"x,
where ea = B - b.
We define the physical meaning of the parameters a and b. According to the definition:
a = aUx
eU
kT
Ap, ' kT '
A - A
N S
kT
(8)
Or through dimensionless parameters it can be represented as:
n = (K - Lz )
1 + az
(12)
where A| = (AN - ASi) is equal to the difference of the Fermi levels of the contacting materials and is determined by their work
outputs (AN and ASi).
where K = a + (b + a)/A; L = ab/A; P0 = IxUxx = U.A.
From the expression (11) for r| - the coefficient of efficiency of a solar cell with nanoscale «p-n-junctions», the role of various factors: leakage current, substrate resistances and
.
ea
sc
Jalalov T.A., Imamov E.Z., Muminov R.A., Sabirov H., Atoev Sh.Sh.
the contribution of recombination processes, temperature effects and other losses is clearly visible.
For silicon solar cells with a traditional p-n-junction, r| is in the range 0.75-0.85, and for solar cells based on GaAs, in the range 0.79-0.87. The coefficient of efficiency of a solar cell with nanosized «р-n-junctions» can be in the range 0.49-0.98, depending on the ratio of the short-circuit current to the temperature factor.
Conclusion
The problem of increasing the efficiency of solar cells obtained on the basis of non-crystalline silicon with nanostructured impregnations is considered. The innovative nature of the proposed approach is that the possibility of using a radical change in the transforming properties of the solar cell and a significant decrease in the cost characteristics of solar energy through the use of nanotechnology (nanophysics) is shown. Unique possibilities of using nanotechnology (nanophysics) on the nature of the course of electrophysical and optical phenomena on non-crystalline silicon are disclosed.
It is shown that the use of a non-crystalline, disordered, sufficiently strongly defective and cheap silicon capable of prolonged functioning in an open space with a continuously changing thermal regime is possible as a substrate material for
solar cells. This possibility is associated with the growth of a large number of nanoheterocluster (nanosized contact structures or nanoscale «p-n-junctions») on the substrate surface.
The calculation of the electrophysical properties of nano-scale «p-n-junctions» and their volt-ampere characteristics is performed. It follows from the calculations that the pho-tocurrent in one nanosized «p-n-junction» is determined by 41.81% of the light absorption spectrum (in the number of quanta).
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