The window layers effect on the hardness improvement of space solar cells exposed to the 1 MeV electron irradiations

Because of their state of art technology, GaAs solar cells are generally preferred for spatial applications. Exposure to proton and electron irradiations, solar cells suffer significant degradation in their performance such as short circuit current and open circuit voltage. Adding a window layer helps in effectively reducing the surface recombination at the emitter surface of the solar cell without absorbing the useful light required for the device. It remains to study the physics of the window-emitter hetero-interface in order to understand how the window layer presence increases the minority carrier lifetime of the solar cell exposed to particles irradiation. In this work Numerical simulation has been used to study the AlxGa1-xAs window composition effect on the current–voltage characteristics of a GaAs solar cell under AM0 illumination and exposed to 1 MeV electron irradiation. To predict the effect of window layers on solar cells degradation, the current voltage characteristic are evaluated for different electron irradiation fluences. The findings are supported by experimental data. They lead us to get to know how the window layer improves resistance to electron irradiation through its own parameters.


Introduction
Window layers help in effectively reducing the surface recombination at the emitter surface of the solar cells, without absorbing the useful light required for the device, resulting in significant improvement in energy conversion efficiency (Jain 2003). Various window layer materials have been investigated for III-V compound semiconductor based solar cells. To systematically reach this end, it will be important to understand the physics of the windowemitter hetero-interface as well as growth related issues (Lammasniemi et al. 1997).
In the case of Ga As solar cell, it has been demonstrated with efficiency near to 25 % at one sun illumination and high efficiency Ga As solar cells all use a wide band-gap window layer on the surface to reduce front surface recombination losses (Vernon et al. 1990). One of the more critical design areas in high efficiency Ga As solar cell is AlGa As window layer and in order to minimize its optical absorption, high aluminium content alloys are favoured ones (Gee and Drummond 1990). In previous work, new approach, justified theoretically and experimentally is used, allowing to deduce the relationship between electron and hole minority-carrier lifetime then we have shown, by using this method, the effect of the device parameters, i.e. the thickness X p and X n respectively of emitter and base, and the level doping N A and N D on each side of the junction of the emitter and the base and the front surface recombination velocity, on how is the variation of characteristics and the electron irradiation resistance of solar cells (Idali Oumhand et al. 2008, 2009). In addition, the validity and accuracy of this approach has been justified by the fact that the degradation parameters, τ n0 , τ p0 , K σ n and K σ p which fit the experimental data are the same for both the short circuit current J SC and the open circuit voltage, V OC in the case of p + /n − I nGa P and n + / p − I nGa P solar cell (Idali Oumhand et al. 2008, 2009. This paper is a suite of the study and prediction of solar cell device parameters. We rewrite the calculation principle of new approach by taking into account the physics of the windowemitter hetero-interface and we apply this approach to p − AlGa As p + /n − Ga As solar cell under AM0 illumination and exposed to 1 MeV electron irradiation and then a comparison between both calculated and measured values would be studied (Friedman and Olson 2001). Moreover, we will show how the effect of window layer p − AlGa As on p + /n − Ga As through three parameters, absorption coefficient α w (λ) at a given wavelength λ and effective hetero-interface recombination velocity S n e f f and its thickness variation X w on variation of J SC and V OC versus the fluence of the irradiation, φ (Yoshikawa and Kasai 1981;Ueda et al. 1998 ;Nakayama et al. 2008). The comparison between p − AlGa As and p − I nGa P window-layers effects on degradation of J SC and V OC are investigated.

Experimental results and principle of degradation parameter calculation
The p − AlGa As p + /n − Ga As structure studied is MOCVD epitaxially grown and it has been irradiated with increasing fluences, in the range 10 14 -10 17 electrons cm −2 , at energy of 1 MeV. The irradiation was performed at room temperature with a scanned beam in order to ensure the uniformity of the fluence over the area of the cell (1-4 cm 2 ). The intensity of the beam (2 µA) was chosen to keep negligible the temperature increase. The cell is placed in a Faraday cup allowing accurate measurement of the fluence with a current integrator. Current-voltage measurements were performed in situ in the accelerator under a 1 AM0 illumination provided by a Xe arc lamp (Bourgoin and Zazoui 2002). Defects induced by electron irradiation in n-and p-type materials have been extensively studied (for a review see Pons and Bourgoin 1985). These studies demonstrated that the defects introduced by room temperature irradiation are primary defects, resulting from the displacements of As in the As sub-lattice (Stievenard et al. 1986).
For simplicity it is assumed that the series resistance R S and shunt resistance R Sh have negligible effects and that there is no shadowing effect on the illuminated surface (Walters et al. 1998).
The calculated effective hetero-interface recombination velocity S n e f f assumes that the window layer effectively passive the solar cell front surface by reducing surface recombi-  Table 1 Physical parameter values of p − AlGaAs − p + /n − GaAs cell (Makham et al. 2005) Solar cell parameters 0.035 0.44 3.1 1.2 × 10 18 6.7 × 10 16 nation at the emitter surface of the solar cells without absorbing the useful light required for the device and that the large band discontinuities at the hetero-interface provide a great potential barrier for the minority carriers, as it is illustrate in Fig. 1, and then well improving the performance of the solar cell (Jain and Landis 1991;Nelson 2003). When calculating the contribution of each side of the junction and the depletion region to current in presence of window layer, the incident flux, ϕ(λ), and the electron recombination velocity, S n , should be modified respectively to ϕ(λ)e −α w (λ)X w and to S n e f f which is expressed as (Nelson 2003;Hovel 1979), E g and E w g are the energy gap in GaAs and in window respectively .

Mechanism of degradation
The calculation of degradation parameters τ n0 , τ p0 , K σ n and K σ p of p − AlGa As p + /n − Ga As solar cell will be possible, when the thickness of window layer and doping respectively of the emitter and base are given further information in (Idali Oumhand et al. 2009). The parameters of the studied cell are listed in Table 1 below (Makham et al. 2005). The knowledge of J exp SC0 and V exp OC0 under given illumination, prior irradiation is also necessary in order to derive the minority carrier lifetimes τ p0 and τ n0 . Table 2 Calculated degradation parameters of p-AlGaAs-p + /n-GaAs cell (Makham et al. 2005) p − AlGa As p + /n − Ga As Degradation parameters 1.23 × 10 −11 1.37 × 10 −8 1.12 × 10 −12 7.57 × 10 −14  Makham et al. (2005) Once the initial values of the minority carrier lifetimes are determined, we inject them into calculation (Idali Oumhand et al. 2009).
The knowledge of J exp SC φ and V exp OC φ under given illumination and amount of irradiation φ allow it to deduce the values of τ nφ and τ pφ and hence K σ n , K σ p , for more detailed information see (Idali Oumhand et al. 2009).
Then from the parameters τ n0 and K σ n in emitter, and τ p0 and K σ p in base, see Table 2, we derive the calculated values of J SCφ and V OCφ as shown in curve Fig. 2a , b respectively.

The window-layer parameters effect
Now the degradation parameters,τ n0 , τ p0 , K σ n and K σ p of p − AlGa As − p + /n − Ga As are calculated with the help of our calculation method, and we proceed to study the effects of parameters For instance, thickness X w and effective hetero-interface recombination velocity S n e f f on the variation of J SC and V OC versus the fluence of the irradiation φ, then a comparison between p − AlGa As − p + /n − Ga As and p − I nGa P − p + /n − Ga As is investigated by using variation of absorption coefficient α w (λ).
The variations of the short-circuit currents and open circuit voltages versus fluence of this cell are given in Fig. 3a, b, under 1AM0 illumination, versus the fluence of 1 MeV electron irradiation, calculated for different values of the thickness x w . When we vary the thickness x w from 10 to 35 and to 70 nm the curve of the short-circuit current J SC versus the fluence of the irradiation φ leads to significant reduction in J SC . Indeed, when the window layer thickness x w will be large, the attenuation becomes pronounced which causes a reduction of the spectral response and therefore a diminution of the value of J SC . At high fluence of irradiation, we note a fast decrease of the curves representing the cells of which the thickness x w is large. On the contrary, the V OC curve exhibits no significant reduction at the time of the increase of x w .  The Fig. 4a shows an important effect of variation of the effective hetero-interface recombination velocity on J SC while, this effect remains a little weak on the variation of the Voc parameter as is exhibited in Fig. 4b.
By comparing the degradation parameters of p/n-GaAs junction, as τ p , τ n , J SC and V OC we find that the short circuit current J SC is sensitive to degradation. Moreover, the minority carrier lifetime τ p in base is degraded faster than τ n , in emitter, as shown in Fig. 5.
Whereas, the degradation of V OC is less pronounced relatively to that of minority carrier lifetime. In addition, the study degradation of a series of solar cells technologically similar but differs in their effective front surface velocity was achieved. It can be seen from Table 3, that the degradation parameters τ n0 , τ p0 , K σ n and K σ p of solar are sensitive to variation of effective hetero-interface recombination velocity S n e f f , when the value of this later is greater than a limit value of 5 × 10 6 cm/s. While these degradation parameters become non sensitive to this variation, if the values of S n e f f are smaller than a limit value. This explains why the optimum value of S n e f f must be smaller than a limit value of 5 × 10 6 cm/s. Finally, the Fig. 6a, b exhibit the comparison between p − AlGa As − p + /n − Ga As and p − I nGa P − p + /n − Ga As solar cells, by using the absorption coefficient α w (λ) and the effective hetero-interface recombination velocity S n e f f . We note for both curves, Fig. 6a, b, that the variations of Jsc and Voc are clearly important in the case of p-AlGaAs than that of p InGaP and consequently AlGa As window layer structure is good candidate for solar cell.

Conclusion
In this paper we have investigated the effect of the window layer through three parameters, absorption coefficient α w (λ), effective hetero-interface recombination velocity S n e f f and its thickness variation x w , on the variation of J SC and V OC versus the fluence of the irradiation, φ. We have demonstrated that the short circuit current J SC is sensitive to variations of the thickness of the window-layer, and the effective surface recombination velocity but the open voltage V OC remain little sensitive to these variations.
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