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5Статья поступила в редакцию 14.02.12. Ред. рег. № 1214
The article has entered in publishing office 14.02.12. Ed. reg. No. 1214
УДК 662.997
ТЕОРЕТИЧЕСКИЙ МЕТОД ОЦЕНКИ И ПРОГНОЗИРОВАНИЯ ПАРАМЕТРОВ СОЛНЕЧНЫХ ЭЛЕМЕНТОВ
В.В. Харченко, Б.А. Никитин, П.В. Тихонов
Всероссийский институт электрификации сельского хозяйства 109456, Москва, 1-й Вешняковский проезд, д. 2 Тел.: +7(499) 171-96-70, факс: 170-51-01, e-mail: kharval@mail.ru, ptikhonov@inbox.ru
Заключение совета рецензентов: 01.03.12 Заключение совета экспертов: 10.03.12 Принято к публикации: 15.03.12
Для оценки и прогнозирования параметров солнечных элементов предложен и развит подход, основанный на учете важной особенности внутреннего фотоэффекта, которая заключается в том, что фотон солнечного излучения независимо от своего энергетического уровня при взаимодействии с полупроводником образует только одну электронно-дырочную пару, а также на принятии к рассмотрению того факта, что солнечное излучение имеет сложную природу и характеризуется спектральным распределением фотонов различной длины волны.
Основой разработанного подхода является рассмотрение и анализ процесса формирования электронно-дырочных пар в результате взаимодействия фотонов заданного участка солнечного спектра с материалом солнечного элемента. Приведены некоторые результаты такого рода расчетов.
Ключевые слова: полупроводник, солнечный элемент, фотон, солнечная радиация.
THEORETICAL METHOD OF ESTIMATION AND PREDICTION OF PV CELLS PARAMETERS
V.V. Kharchenko, B.A. Nikitin, P. V. Tikhonov
All-Russia Institute for Electrification of Agriculture 2, 1st Veshnjakovsky proezd, Moscow, 109456, Russia Tel.: +7(499) 171-96-70, fax: 170-51-01, e-mail: kharval@mail.ru, ptikhonov@inbox.ru
Referred: 01.03.12 Expertise: 10.03.12 Accepted: 15.03.12
For estimation and prediction of PV solar cell parameters there was suggested and developed the methodology based on acceptance for consideration the important peculiarity internal photoeffect which mind-set in the fact that photon of sunlight can form only one electron-hole pair despite of its energy level and that the solar radiation is characterized by spectral distribution of photons of various length of a wave.
The main point of the methodology is consideration the process of electron-hole pairs formation under influence of photons of given site of solar spectrum with semiconductor (silicon) used as solar cell substrate. Some results of this kind calculation are represented in the paper.
Keywords: semiconductor, solar cell, photon, solar irradiation.
Introduction
Possibility to predict and evaluate parameters of PV solar cells and modules with high degree of accuracy on the all steps of their fabrication and practical use is the essential factor for development of works on perfection of parameters of solar power systems. In connection with this it is necessary to develop new technical means. Well proved metodology, based on theoretical calculations can be very useful for this.
The approach based on the analysis of interaction of an solar cells initial material with photons, amount and energy of which is determined by their position in the spectrum of solar radiation looks to be perspective.
The amount of photons and their energies for each line of spectrum can be obtained from the standard solar radiation of 1000 W/m2, suggested and accepted by the International Electrotechnical Committee and corresponding table of the standard solar radiation spectral structure [1].
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The sunlight spectrum especially at the earth surface is complicated enough and depends on a number of factors, such as a thickness of a layer of air at sunlight passage to a surface of the atmosphere mass (AM), content of gaseous impurity etc. In [2] a number of the factors influencing a spectrum of sunlight are consistently considered. These results were be used when considering processes of sunlight photons and semiconductor interaction.
Results of investigations
At the beginning the above mentioned standard table was supplemented with obtained by calculations values connected to photons energy of respective wavelengths such as spectral photon density of a standard solar radiation, a derivative of energy spectral density and photons energy, and also the density of photon flows in each wavelengths sub-diapason of the considered table. Photons energy was represented as in joule as well in electron-volt equivalent that is very convenient for further investigations. Tables obtained required a lot of space. That's why they were not included in the paper in original form and represented as graphs.
Fig. 1 shows graph of the energy density distribution for the above mentioned standard solar radiation vs wavelength. Fig. 2 illustrates the results of calculation for spectral photon density distribution of the solar radiation flow 1000 W/m2.
Studies in which purposefully processes in solar cells are considered in a context of the above mentioned factors especially concerning to the given photons position in the solar irradiation spectrum, acting in a working zone, and the mechanism of their interaction with component of solar cells (especially directly in the p-n junction area, in the base, doped layer and on contacts) were described earlier [3].
Рис. 1. Энергетическая плотность солнечного излучения АМ 1,5 в зависимости от длины волны Fig. 1. Energy density of solar irradiation АМ 1.5 vs wave length
Рис. 2. Фотонная плотность стандартного солнечного излучения АМ 1,5 в зависимости от длины волны Fig. 2. Photon density for different wave length of standard solar radiation АМ 1.5
Unlike mechanism of the interaction of the high energy quantum of the electromagnetic irradiation with electron (Compton-effect), when energy of the photon could be transmitted to electron partly, at the photo effect photon is absorbed completely. The part of the photon energy spends for breakup chemical link of valence electron in semiconductor (for silicon Ecl = = 1.1 eV), the remain part of energy disperses in the volume and transfer to increase of electrons kinetic energy. Even photons with highest energy (part of spectrum with wavelength about 0.3 mkm) are not capable to form more than one electron-hole pair since specific consumption of energy for creation one electron-hole pair in silicon makes the value 3.55 eV [2].
Some solar cell parameters calculated in view of solar radiation spectral structure are described below.
On the basis of these data there were obtained a number of interesting results. Particularly the diagram of the spectral dependence of a silicon layer thickness in which the radiation flow of the given wavelength diminishes in e time was constructed. There was shown that the share of absorbed photons, for instance, in silicon layer are defined by the layer thickness and absorption coefficient corresponding to length of the waves of the standard spectrum of the solar radiation.
There was calculated solar irradiation absorption coefficient a in silicon vs wavelength (Fig. 3). It was shown that the absorption coefficient in silicon with wavelength increasing falls and becomes lower (a = 10 ^m-1).
In the range of wave's lengths about 1 ^m silicon becomes more transparent for long wave photon. However, for lengths of the waves about 0.3 ^m coefficient of the absorption is enough high (a = 104 ^m-i), that explains high absorbing ability of heavy doped layer of the solar cell in this area of the spectrum.
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7S
Рис. 3. Коэффициент поглощения солнечного излучения
в кремнии в зависимости от длины волны Fig. 3. Absorption coefficient of a solar irradiation a in silicon vs wave length
Physically this parameter shows on what thickness silicon layer weakens light flow of given wavelength in e times. Analysis of this curve shows that for left part of the standard solar spectrum i.e. for photon with wavelength X about 0.3 ^m this value is evaluated as 0.2 nm, but for lengths of the waves around 1 ^m this value makes 100 micron.
Analytical expression for absorption coefficient in silicon according [3] looks like below
a = 0,526367 - U442A"1 + 0,58536X-2 + 0,03995X-3, (1)
where X - wave length, ^m.
Value of inverse absorption coefficient (namely layer thickness) vs wavelength is presented at Fig. 4.
Рис. 4. Толщина слоя кремния, снижающая в е раз плотность светового потока заданной длины волны Fig. 4. Silicon layer thickness decreasing light flow dencity in e time vs wave length
This result enables to value the transmission factor for light flows of different wave's lengths and silicon layers of different thicknesses. The graphs illustrating results of these kind calculations have shown that transmission of the irradiation through silicon layers increases with increase of wavelength and approaches to 1 at the wave length around 1 цт. The transmission factor also increases at reduction of the layers thickness.
Theoretical estimations show that at the thickness of silicon layer equal zero dependency is transformed in vertical direct line that is in good correspondence with requirements of the optimum silicon photoelectric converters operation [4].
These results give an opportunity to realize method of nondestructive control of the "dead" layer thickness in already fabricated wafers after diffusion, i.e. during technologic processes of solar cells fabrication. For this objective it is intended to use results of short circuit current measurements under laser irradiation. The integrated dependence of the predicted value of the solar cell photocurrent on the thickness of highly doped ("dead") layer was constructed on the basis of the analysis of spectral dependence of the solar radiation transmission through silicon layers of different thickness (Fig. 5).
Рис. 5. Зависимость плотности тока короткого замыкания в зависимости от толщины легированного слоя при 1000 Вт/м2 и АМ 1,5 Fig. 5. Short circuit current density vs doped layer thickness at 1000 W/m2 and AM 1.5
Among the parameters representing the greatest interest could be emphasized the efficiency coefficient. However, at work on improvement of this parameter it is very important to imagine clearly and take into consideration those restrictions, which are caused by the nature of an initial semi-conductor material and the nature of the sunlight itself. The approach specified above has been used for a theoretical estimation of extremely possible effectiveness ratio of PV solar cells depending on width of the forbidden gap of an initial semiconductor material.
Expression for efficiency coefficient of a solar cell n looks like below [4]:
n =
i U FF
sc oc_
R
(2)
where isc - density of a short circuit current; Uoc - open circuit voltage of solar cell; FF - fill-factor of I-U curve
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as a factor of filling of area Uos-isc by Uopt-iopt; R - level of light exposure of the photo converter, including standard level of solar radiation AM 1.5 (1000 W/m2).
The parity isc and R is any constant k and thus expression (1) takes a form:
n = kUocFF . (3)
The estimation of efficiency of solar cells is made on the basis of theoretical (idealized) I-V curve under which it is stipulated such interrelation of a current and voltage at which consecutive resistance of a solar cell is equal zero, and its shunting resistance is equal to infinity. The algorithm of an estimation of the efficiency coefficient of a solar cell with given value of forbidden gap width of the semiconductor is reduced to sequence of calculations in each range Ak of the solar irradiation spectrum.
Fig. 6 represent results of calculations of theoretical (utmost) efficiency of solar cell vs width of the forbidden gap of an initial semiconductor [5].
n, %
25 --А
15
-В
0 1 3 E.eV 5
a'
Рис. 6. Теоретические (максимальные) значения КПД солнечных элементов в зависимости от ширины запрещенной зоны исходного полупроводника для стандартного наземного (А) и космического (B) солнечного излучения Fig. 6. Theoretical (utmost) efficiency of solar cell vs width of the forbidden gap of an initial semiconductor for standard terrestrial (A) and space (B) spectrum of solar radiation
0 2 4
Width of forbidden, eV
Рис. 7. Значения КПД солнечных элементов в зависимости от ширины запрещенной зоны полупроводника для различных рабочих температур Fig. 7. Solar cell efficiency coefficient vs width of forbidden zone of semiconductor for different temperature of operation
In addition the similar curves were obtained for different temperatures of solar cells operation. These results, submitted at Fig. 7, show that temperature of
operation is a very important parameter wich should be taken under strong control to provide more efficient mode of operation of solar power plants.
This approach gives an opportunity to estimate an influence of concentrated solar radiation on the efficiency of solar cells.
The FF value for this case could be expressed as below [6]:
FF = = (4)
« «max) 2 _ e k<>R
Fig. 8 represent results of a fill-factor (FF) calculations for low levels of solar radiation [7]. (Calculations have been performed for k0 = 6).
0 2 4 6
R 1000, W/m2
к
Рис. 8. Теоретические значения Фил-Фактора для низких значений солнечного излучения, Rx-103 Вт/м2
Fig. 8. Calculated FF values for low solar radiation levels, Rx-103 W/m2
As follows from Fig. 8, for such converters FF parameter with solar radiation growth smoothly decreases from limiting meaning 1 (corresponding to zero level of illumination) to the minimum value 0.616 at 6000 W/m2. In this range of radiation for photo converters of similar quality the theoretical efficiency should not change, as with growth of level of solar radiation the increase of Uoc will be compensated by adequate decrease of FF factor.
Results of FF calculations for more wide range of solar irradiance could be seen in Fig. 9 [7].
FF
Рис. 9. Теоретическое значение Фил-Фактора для широкого диапазона солнечного излучения, Rx103 Вт/м2 Fig. 9. FF values for wide range of solar radiation levels, Rx 103 W/m2
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At higher levels of solar radiations such converters should have FF meanings like it is shown in Fig. 9. After passage of some minimum (around radiation level about 10 Suns) FF value starts to increase and at ultrahigh levels of incident radiation come nearer to the limit, namely to 1.
Last years a wide circulation have been achieved so-called PVThermal systems, devices, transforming a solar energy in electricity (PV cells) and in a heat (solar collectors). It is important to realize what part of solar radiation could be used for heat and electricity production in such kind of devices. Suggested approach give an opportunity to identify these shares, which can be found from result of calculations represented at Fig. 10.
Energy density of solar radiation, W/m2|im
Wave length, (.im
Рис. 10. Спектральное распределение энергии солнечного излучения в фотоэлектрическом тепловом модуле в тепло
и электричество: 1 - доля энергии, поглощенной фотопреобразователем; 2 - доля энергии, преобразованной в тепло, в структуре фотоэлемента; 3 - энергия длинноволновой части спектра, пропущенного структурой солнечного элемента Fig. 10. Distributions of solar radiation energy in PVT system on heat and electricity: 1 - share of energy absorbed in Pv cell; 2 - share of absorbed energy transformed into heat in the solar cell volume; 3 - long wave part of spectrum passed through silicon and transformed into heat behind cell structure
Conclusion
Presented results especially being approved by additional experiments show that suggested approach can be recommended as a good instrument for practical use.
References
1. Bird R.E., Hulstrom R.L., Lewis L.J. Terrestrial Solar Spectral, data Sets // Solar Energy. 1983. Vol. 30, No. 6. P. 563-573.
2. Poulek V., Libra M. Solar energy. CUA Prague, 2006, ISBN 80-213-1489-3. P. 25-31.
3. Kharchenko V., Nikitin B., Sherban D., Simashkevich A., Bruk L., Usatiy I. Estimation of solar cell parameters in view of solar radiation spectral structure // Mold. Journal Phys. Sciences. 2009. Vol. 8, No. 3-4. P. 387-391.
4. Vasiliev A.M., Landsman A.P. Poluprovodnikovie fotopreobrazovateli., Moscow: Sov. Radio, 1971.
5. Kharchenko V., Nikitin B., Tikhonov P., Adomavicius V. Utmost efficiency coefficient of solar cells versus forbidden gap of used semiconductor, Proceedings of the 5th International Conference on Electrical and Control Technologies ECT-2010, ISSN 1822-5934, Kaunas, Lithuania, 6-7 May 2010. P. 289-294.
6. Arbusov Yu.D. Evdokimov V.M. PV fundamentals. Moscow: UNESCO-BRESCE, VIESH, 2007.
7. Nikitin B., Gusarov V. Dependence of fill-factor for theoretical solar cell I-V curve on illumination level, Proceedings of 7th International scientific technical conference on energy supply and energy saving in agriculture, 18-19 May 2010. Moscow. P. 47-52.
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