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10Статья поступила в редакцию 27.09.10. Ред. рег. № 893
The article has entered in publishing office 27.09.10. Ed. reg. No. 893
МОДЕЛИРОВАНИЕ И ОПТИМИЗАЦИЯ GaInP, ИСПОЛЬЗУЮЩЕГОСЯ В МЕХАНИЧЕСКИ СОЕДИНЕННЫХ
СОЛНЕЧНЫХ ЭЛЕМЕНТАХ
Ю. Мир, М. Хали, М. Зазу
Лаборатория физики конденсированных сред, научно-технический факультет Мохамеди, Университет им. Хасана II-Мохамеди B.P. 146, Хасан II-Мохамеди, Марокко, e-mail: zazouimimoun@yahoo.fr
Заключение совета рецензентов: 17.10.10 Заключение совета экспертов: 27.10.10 Принято к публикации: 30.10.10
Многоспектральное преобразование дало возможность получить высокоэнергетическую эффективность. В этой работе мы изучали систему двух элементов, соединенных механическим способом: первый элемент - это соединение GaInP, а второй элемент - соединение GaAs. Мы получили оптимальные параметры (легирование, толщину и т.д.) для каждого отдельного элемента. С помощью расщепления солнечного спектра, к которому элемент является чувствительным, был получен коэффициент преобразования 31,99% при комнатной температуре без концентрации и при спектре AM1,5.
Ключевые слова: моделирование, оптимизация, тандем, ограниченная эффективность, солнечные элементы.
MODELLING AND OPTIMIZATION OF GaInP USED IN MECHANICALLY STACKED SOLAR CELLS
Y. Mir, M. Khalis, M. Zazoui
Laboratory of Condensed Matter Physics, Faculty of Sciences and Techniques Mohammedia, University of Hassan II-Mohammedia B.P. 146, Bd. Hassan II- Mohammedia, Morocco, e-mail: zazouimimoun@yahoo.fr
Referred: 17.10.10 Expertise: 27.10.10 Accepted: 30.10.10
The converting multi-spectral permitted to obtain the high energy efficiency. In this work, we are interested to study a system of two cells stacked mechanically, the first is a GaInP junction and the second is a GaAs junction. We extracted the optimal parameters (doping, thickness...) of each individually cell. By separation of the solar spectrum where the cell is sensitive, an overall conversion efficiency of 31.99% was obtained at room temperature without concentration and under the AM1.5 spectrum.
Keywords: Simulation; Optimization; Tandem; Limiting efficiency; Solar cells.
Introduction
Since the last decades [1-4], a new architecture for photovoltaic cells has expanded, it is the cells tandem consisting of stacking two or three solar cells in series. The three materials used in photovoltaic cells have a different band gaps. The absorption spectrums are different, which can cover more fully the emission spectrum of sunlight and limit the thermalization of electrons and improve the performance of cells [5].
Furthermore, as the cells are in series, the open circuit voltage of tandem solar cell is equal to the sum of open circuit voltages of three cells [6, 7]. The major disadvantage is the total current short circuit of the cell is the cell presents the weak short-circuits current. This kind of tandem, can achieve an efficiency of 32% with the triple junction GaInP/GaAs/Ge system under a
standard AM0 spectrum [8]. Because the systems of light concentrators for solar power allows to multiply the cell efficiencies over 40% have been obtained with the same technology that is an absolute record in terms of photovoltaic [9]. The development of high efficiency cells has been motivated primarily by space applications [10]. In fact, the first commercial satellite (HS 601HP) with two junctions GaInP/GaAs on Ge solar arrays was launched in August 1997 [11].
In this work we study the simulation and the optimization of the parameters of GaInP top cell, the optimization of the GaAs bottom solar cell was optimized previously [12]. Then, we propose the study of a tandem GaInP/GaAs stacked mechanically and we will discuss the results obtained and compare them with other results.
International Scientific Journal for Alternative Energy and Ecology № 11 (91) 2010
© Scientific Technical Centre «TATA», 2010
Ю. Мир, М. Хали, М. Зазу. Моделирование и оптимизация Оа!пР, использующегося в механически соединенных солнечных элементах
Theoretical models
For the incident light of the wavelength and intensity or flux, electron-hole generated at distance from the surface at a rate: G(x,A) = oF [1 - ^]exp(-ax) (1)
where a is the local absorption coefficient and R is the coefficient reflectivity .Under low injection conditions 1D stationary equation are written as [13-15]:
1 (dx \ Gp + T 0 '
(2)
Jp (X) = - qDp
d AP„ dx
qF (1 - R) aLp
a2 L2p -1
S-¿L + aLp
v dp p
( ^ cosh
vdp
- exp (-ax,. )
( X. A
vlp
+ sinh
( x ЛЛ yh
cosh
( X,. ^ S„L„
kLp
Dp
sinh
( Xl A
vlp
-a exp (-ax,. )
. (13)
1 ( J1-g„ ^ = о
q ^ dx
(3)
with fyn = Pn - Pno and = np - npo. (4)
Here, expressions for the photo-current contributions in the p and n-region Jn and Jp are therefore given by the diffusive currents.
d Ap
Jp = q^ ppnE - qDp~df;
d An
Jn = q^ nnPE+qDn
dx
(5)
(6)
D
d 2(AP„ )
p 2 + aF (1 -R)exp(ax)--n- = 0. (7)
dx2
APn
Tn
A similar integro-differential equation for the electron distribution in the /»-layer can be written as:
d2 (Am ) Am Dn—-r^- + aF (1 - R) exp( ax)--p = 0. (8)
dx t p
The photo-generated excess electrons density in the p-region is given by.
, d An
Jn (X) = qDtl p
q(1 - R)a2LnF
dx
exp(-a(x,. + w)) x
sh
aLn
a2 L2n -1
H1 ), SnLn„, ( H \ ( Snh
Ln
-chl Dn 1 Ln
Dn
aLn I exp (-aH1 )
chi H11+S^sh( H
Where, q is the electron charge, Dn, Dp is diffusion factor for n+/p region we can obtain integro-differential equation which describes distribution of holes in n-layer.
(14)
In the depletion layer, the electric field aids the collection of photo carriers, resulting in collection of every photo carrier generated there, as calculated by:
JSRC (X) = q(1 - R)F exp(-axy )(1 - exp(-aw). (16)
The total photo-current as a function of wavelength is then given by the sum of diffusion currents in the p, n and depletion region.
Í Jl (X) = Jn (X) + Jp (X) + J SCR (X)
t» X max
J = JX . JL (X)dX
^ v X min
(17)
The following initial conditions:
d AP
Dp—rL = SpAPn at x = 0: dx
d Am
- Dn-p = Sn Anp at x = H :
dx
An = 0 at x = x,. + w ;
Ap = 0 at x = x..
(9)
(10) (11) (12)
Where Sn and Sp surface recombination velocity respectively front and back and w is the width of space charge region. After some manipulation we find that:
The photo-generated excess holes density in the n-region is given by.
To determine the maximum power point Pmax the voltage-current characteristic for a single-junction solar cell has to be considered.
J (V ) = J01 exp
qV kT
-1 - J
ph >
(18)
where J0 is the dark or recombination current q the electronic charge, kT the thermal energy. The open circuit voltage VOC is obtained when no current is drawn from the solar cell. From equation (18)
kT (J ^ VOC =— Lnl —ph + 1l, the short circuit current is
q J0 )
obtained if the solar cell is short circuited, i.e. there is no voltage at the cell. From equation (18) we find that JSC = - Jph, i.e. the short circuit current is equal to
x
x
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the absolute light-current amount. The maximum power point, i.e., the maximum of the power P dependent on the voltage has to be found P = VJ. This point can be calculated by using the derivative equal to zero (dP/dV )V = 0. The efficiency of a solar cell is defined
as the ratio of the photovoltaically generated electric output of the cell to the luminous power falling on it: n = P / P .
I ma^/ tnc
Optimization and simulation of GaInP
Whatever the structure of a solar cell optimization of its parameters it is necessary to have a good efficiency. Usually, the parameters to optimize are the thickness of the cell, the level and doping of emitter and base. Optimization of solar cell thus includes the study of the influence of these parameters on the performance to obtain a structure leading to maximum efficiency. The numerical simulation is commonly used for optimization of solar cell.
Fig. 1 shows the influence of the base thickness on the cell efficiency with varying back surface recombination (Sp = 0 cm/s), where the base doping level is 1017 cm-3. With increasing thickness, first the photocurrent increases due to the increasing of absorption. The Voc decreases with increasing thickness due to an increase in the saturation current density J0. With decreasing substrate thickness the cell efficiency is more influenced by the surface recombination. For a very low surface recombination, the optimum thickness is around 1 ^m, for increased recombination velocity (above 1000 cm/s) at least 1.5 ^m is required to reach the highest efficiency.
Fig. 2 shows the efficiency reaming constant for the doping less than 1018 cm-3 and decreases for the doping more than 1018 cm-3.
Рис. 2. Влияние легирования основы на фотогальваническую эффективность Fig. 2. Influence of the doping of the base on efficiency photovoltaic
Increased doping of the base causes the degradation of the lifetime of carriers and mobility. This causes a significant decrease in performance.
We showed that the surface recombination velocity is one of the parameters that most influence the performance of the cell. The high recombination velocity rear of the cell can completely degrade performance. In contrast, if the rate of recombination at the surface is less than 103 cm-s-1, it has no influence on the efficiency of the cell.
In the Fig. 3, the efficiency photovoltaic decrease rapidly when the thickness of the emitter increased.
Рис. 1. Влияние толщины основы на фотогальваническую эффективность Fig. 1. Influence of the thickness of the base on efficiency photovoltaic
Рис. 3. Влияние толщины эмиттера на фотогальваническую эффективность Fig. 3. Influence of the thickness of the emitter on efficiency photovoltaic
International Scientific Journal for Alternative Energy and Ecology № 11 (91) 2010
© Scientific Technical Centre «TATA», 2010
Ю. Мир, М. Хали, М. Зазу. Моделирование и оптимизация GaInP, использующегося в механически соединенных солнечных элементах
Fig. 4 shows we see the two regions, the first between 1018 cm-3 and 1019 cm-3 remain almost constant and decreases rapidly for more than 1019cm-3. In order to have a better efficiency one may use a doping level of the emitter higher. Indeed, the thickness of the emitter is less than that of the base causing recombination in the emitter is negligible in comparison to the recombination in the base.
Рис. 4. Влияние легирования эмиттера на фотогальваническую эффективность Fig. 4. Influence of doping of the emitter on efficiency photovoltaic
In contrast by rising doping level of the emitter, the height of the potential barrier of the p-n junction increases.
As illustrated above a too high emitter doping level results in an increased efficiency loss due to Auger recombination and band-gap narrowing. Moreover a higher emitter doping will result in increased front surface recombination. As a result, ideally the doping level of the emitter is between 1018 and 1019 cm. The influence of the surface recombination is especially present at lower doping levels, as is shown in Fig. 4.
Optimum cell parameters and cell efficiency:
The optimum GaInP solar cell parameters that have been determined by the described simulations are:
H: 1 to 1.5 ^m; Na: 5-106 to 8-1017 cm-3; xJ: 0.01 to 0.02 ^m; Nd: 1018 to 1019 cm-3
The results obtained are in good agreement with those of Abderrazak and al [16, 17].
Tandem GaInP/GaAs
The majority of the inorganic photovoltaic cells are formed by single PN junction. In this junction, only photons whose energy is equal or more than the bandgap of the material (denoted Eg in eV) are able to create
electron-hole pairs. On the other hand, even if the photon energy is sufficient, the probability of meeting an electron is low. Thus, most of the photons through the material without having to transfer their energy.
The corresponding maximum theoretical efficiency is 24% for a number of air-mass equal to 0 [18]. Currently, the maximum theoretical conversion efficiency is 31% for an energy gap of about 1.4eV. By comparison, the band-gap of silicon, which is now the most common material used to form cells in PV sensors on land, not far from this optimum with 1.12eV. Thus, the theoretical maximum for a single junction Si is about 29%.
The first answer; to limit the loss of long known technological standpoint, just use systems at various levels, by stacking the junctions with decreasing gaps. Thus it is possible to exploit the total solar spectrum with very high conversion efficiencies [19].
In addition, another compromise must be made by the design of PV sensors. If the gap of the material is high, few photons have enough energy to create current, but the terminals of the cell; the open circuit voltage will be great and will facilitate even more exploitation of electric energy. Conversely, a material with a small gap but absorbs more photons have a lower voltage. This compromise was quantified by Shockley and Quessier [20].
In this work multi-junction PV cells based associations semiconductor materials III-V (GaInP/GaAs) are studied. The cells are in series, the GaInP top cell band gap is Eg = 1.86 (eV) and GaAs bottom cell gap is Eg = 1.42 (eV) electrical point of view of optimizing the power generated by the system must be conducted to find the optimum power (Fig. 5).
Рис. 5. Моделирование J-V кривых для тандема GaInP/GaAs Fig. 5. Simulated J-V curves for a GaInP/GaAs tandem
In our case, the current produced by the association is limited by the cell producing the lowest current. According to the results of the electrical characteristic J(v) shows that JSC the set corresponds to that of the cell GaInP JSCmin = min(15; 16.33) = 15 mA/cm2, tension VOC, when to it, corresponds to the added tension VOC of two cells as expected from theory: VOC = VOC1 + VOC2 = = 1.13 + 1.4 = 2.53 V and an overall efficiency ntot =
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= nGainP + nGaAs = (17.49 + 14.5)% = 31.99% this value is the highest ever reported for the 2-junction cells under 1-sun illumination. This result is in good agreement with that found by Takamoto et al [21, 22].
Conclusion
From these studies, the GaInP solar cells was modeled and compared with other authors, we saw that the performances of the studied cells are very sensitive to the variations of the technological parameters of the cell (doping, thickness) enabled us to obtain the values of the physical and technological parameters of an emitter and base its optimized performance 17.9%.
We simulated J-V curves and we calculated the efficiency of the two-junction, series-connected Ga0.5In0.5P/GaAs. The efficiency is more and more sensitive to the values of the gap of the cells top and bottom of the stack. Under the AM 1.5 spectrum, a maximum efficiency 31.99% is reached with band gaps of 1.86 ev top cell GalnP and 1.42 ev bottom cell GaAs.
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