Gradual Band Energy to Passivate the Window Layer in Solar Cells ()
1. Introduction
The main objectives for developing space solar cells are to improve their radiation resistance and high efficiency solar cells. Among compound semiconductor materials, GaAs is widely favoured for space applications due to its excellent conversion efficiency and radiation resistance [1] [2] . Unfortunately, GaAs solar cells suffer from carrier loss due to a high surface recombination velocity. So to reduce front surface recombination losses, one of the more critical design areas is AlGaAs window layer and in order to lessen optical absorption in this layer, high aluminium content alloys are preferred [2] [3] . Normal window layers are quite important in improving and passivising the solar cell energy conversion efficiency. They help in effectively reducing the surface recombination at the emitter surface without absorbing the useful light required for the device.
In precedent work, taking into consideration the physics of the window emitter hetero-interface, we have investigated the effect of the normal window layer on solar cells degradation through its own parameters [4] [5] . This new approach which has been proved theoretically and experimentally is used to deduce the relationship between electron and hole minority-carrier lifetime.
This paper is an extension and amelioration to what have been tackled about window and prediction of solar cell device parameters [5] . This is through the numerical simulation by rewriting the calculation principle in solar cells with different window structures, by taking into account the gradual band profile window emitter hetero-interface. Both cells have (AlxGa1−xAs/GaAs)-p+ type window/emitter, and n+ type collector layers under AM0 illumination and are exposed to 1 MeV electron irradiation. For the sake of investigation, we will display how this effect can contribute to passivating the solar cells. The gradual band structure diagram of cell p+-AlGaAs-p/n-GaAs is given in Figure 1 through the parameters, absorption coefficient αW (λ) at a given wavelength λ and effective hetero-interface recombination velocity Seff and the field electric due to the gradual band energy of the window layer. The effect of precedent parameters is analysed from studding the variation of short circuit current JSC and the open voltage VOC versus the fluence of the irradiation φ [6] [7] [8] . Then, a comparison between both calculated and measured values would be made. Next of great importance is to analogize it with previous work using the normal window layer [5] .
When calculating the contribution of each current in different sides of the junction in presence of gradual band window layer, the incident flux
, and the electron recombination velocity Sn should be modified respectively to:
(1)
And to 
which is expressed as [9] [10] :
(2)
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Figure 1. Gradual band structure diagram of cell p-AlGaAs-p/n-GaAs.
where the absorption coefficient is:
(3)
A is a constant depending of choice of semiconductor window, Eg and 
are the energy gap in GaAs and in window layer gradual respectively, 
represent the energy of assumed constant band gap where q is the electric charge and ξ is the electric field.
2. Mechanism of Degradation and Optimization of Windows Layer Parameters
2.1. Mechanism of Degradation
This mechanism made it possible to calculate degradation parameters τno, τpo, Kσn and Kσp of p AlGaAs p+/n-GaAs solar cell, just knowing the thickness Xw window layer and doping respectively of the emitter and base which are given [4] .
The parameters of the studied cell are listed in Table 1 [11] .
For the sake of determining the minority carrier lifetimes τno and τpo in the p and n regions respectively, it is of paramount importance to know the short circuit current density 
and open circuit voltage 
measurements under given illumination. In addition, prior irradiation is necessary in order to make the derivation from the initial values of the minority carrier lifetimes and then we inject them into calculation. By so doing along with knowing 
and 
under given illumination and amount of irradiation 
allow it to deduce the values of the minority carrier lifetimes 
and 
to determine Kσn and Kσp; where K is the defect introduction rate, σn and σp are the electron and hole capture cross section. Then from the parameters 𝝉no, Kσn in emitter and 𝝉po, Kσp in base, see Table 2, we can determine the variations of the short-circuit currents 
and open circuit voltages 
versus fluence. More specifically, the degradation parameters, τno, τpo, Kσn and Kσp which fit the experimental data, 
and![]()
, are the same for both the short circuit current ![]()
and the open circuit voltage ![]()
calculated for cell solar p-AlGaAs p+/n-GaAs, more details are given in [4] [5] .
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Table 1. Physical parameter values of p-AlGaAs-p+/n-GaAs cell [11] .
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Table 2. Calculated degradation parameters of p-AlGaAs-p+/n-GaAs cell [11] .
2.2. Optimization of the Window Layer Parameters
2.2.1. Effective Parameter Hetero-Interface Recombination Velocity Sneff Effect
The degradation parameters, τno, τpo, Kσn and Kσp of the cell p-AlGaAs p+/n- GaAs are added up with the help of our calculation method, and we proceed to study the effects of these parameters. the effective hetero-interface recombination velocity Sneff allows us to know the variation of JSC and VOC versus the fluence of the irradiation φ, then we can compare between windows p-AlGaAs normal and gradual band where the electric field ξ = 0 and ξ = −500 V/cm are applied respectively.The degradation is more pronounced when the effective recombination velocity Sneff is smaller. This claim can be justified by the relationship between Sneff and Egw see the expression of Sneff, i.e., the increase of Egw leads to the decrease in the Sneff. Figure 2(a) shows an important effect on the variation of the JSC under 1 AMO illumination versus the fluence for both values of Sneff. This effect remains a little weak on the variation of the Voc parameter as exhibited in Figure 2(b), our design may have the same idea as that of [4] [5] .
2.2.2. Parameter Electric Field ξ Effect
By comparing the irradiation effect on Cell 1 and Cell 2, where the window layer p-AlGaAs on p+/n-GaAs are normal (ξ = 0) and gradual (ξ = −500 V∙Cm−1) respectively, we find that the gradual p-AlGaAs window improves the better resistance to electron irradiation of the short circuit current Jsc for the short fluence. This is more clarified in Figure 3(a) which shows the variation of the short circuit current Jsc versus the fluence of 1 MeV electron irradiation under 1AMO. Also, thanks to the gradual band profile, the internal electric field ξ caused the accelerating photo-generated of the carriers and thereby enhance their collection efficiency; this electrical field helps to reduce the recombination. By contrast, in
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(a) (b)
Figure 3. Variation of the short circuit current Jsc (a), and the open circuit voltage Voc (b), under 1 AM0 illumination, versus the fluence of 1 MeV electron irradiation, calculated for both values of ξ = −500 V/Cm (?) and ξ = 0 V/Cm (?) in p-AlGaAs window gradual and normal respectively.
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Figure 4. Current density-Voltage (J-V) and Power-Voltage (P-V) characteristics of the illuminated solar cells after irradiation by 1014 cm−2 electron fluence, calculated for both values of ξ = −500 V/Cm and ξ = 0 in p-AlGaAs gradual and normal windows respectively.
Figure 3(b), the VOC curve exhibits no significant reduction to the different types of the windows, normal and gradual.
From Figure 4 the J-V and P-V characteristics are confirmed better energy conversion performance of the illuminated solar cells after irradiation by 1014 cm−2 electron fluence for gradual windows.
3. Conclusion
A modeling of an AlGaAs window/GaAs solar cell, operating under AM0 solar spectrum and exposed to 1 MeV electron irradiation is presented. This is to study the effect of the AlGaAs window on the cell sensitivity to the electron irradiation. In the gradual energy gap AlGaAs window, we have demonstrated that the short circuit current JSC is sensitive to variations of this parameter, but the open voltage VOC remains little sensitive to these variations, so the p-AlGaAs gradual window layer structure reduces the surface recombination, and effectively passivates the solar cell. Consequently, the gradual band window layer structure is more effective. Therefore, it is a good candidate for developing the solar cell than normal windows layer.