IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 44, NO. 9, SEPTEMBER 1997 1499

Performance of AntireflectingCoating-AlGaAs Window Layer Coupling for

Terrestrial Concentrator GaAs Solar CellsCarlos Algora del Valle,Member, IEEE, and Manuel Felices Alcaraz

Abstract—In this paper, we present the performance of opticalcoating systems coupled with AlGaAs window layers over GaAssolar cells. Single, double, and triple antireflecting coatings andwindow layers with constant and graded aluminum content areconsidered. Comparison between constant and graded windowlayers is established. To better represent reality, practical factorssuch as absorption of materials even for antireflecting coatingsand the oxidation at window layer surface due to its highaluminum content are also included in the calculations. Thedesign criteria to determine the optimum thickness of each layeris the achievement of maximum photogenerated current density.For this purpose and to account for terrestrial concentratorsGaAs solar cells, the inclusion of direct terrestrial solar spectrumtogether with the internal spectral response of the device aretaken into account. Finally, the best antireflecting coating/AlGaAswindow layer couplings for different cases are presented.

I. INTRODUCTION

T HE EFFICIENCY of AlGaAs/GaAs heteroface solar cellsdramatically depends on light that can arrive to the active

layers. Due to reflection losses, the photogenerated currentdensity (and consequently, the efficiency) reaches a levelmuch lower than the maximum for the standard terrestrialspectrums of light coming from the sun (only around 70%of the maximum for Air Mass 1.5 Direct (AM1.5D) solarspectrum). To reduce the reflection of incident light at thesurface of the cell, an antireflecting coating (ARC) can beused over the cell. This coating can range from a simple layerto a multilayer system of many layers having almost zeroreflectance over a wide range of wavelengths. Many studiescontaining the design and optimization of such layers for GaAssolar cells have been published [1]–[3].

Nevertheless, ARC optimization is not a task independentof the rest of solar cell structure. Light, in its path from air toGaAs active p-n junction, and after passing the ARC, arrivesat the AlGaAs window layer (from now on, WL to be usedtogether with the ARC acronym). Consequently, any surfaceoptical optimization of GaAs solar cells must take into accountthe simultaneous design of the ARC/WL coupling. In fact,the achievement of the highest efficiency AlGaAs/GaAs solar

Manuscript received February 7, 1996; revised January 10, 1997. Thereview of this paper was arranged by Editor P. N. Panayotatos. This workwas supported by the Spanish CICYT under Contract TIC96-0725-C02-01and by Iberdrola under Contract 94/350P.

The authors are with the Instituto de Energıa Solar, E.T.S.I. Telecomuni-cacion (U.P.M.), Ciudad Universitaria s/n, 28040 Madrid, Spain.

Publisher Item Identifier S 0018-9383(97)06136-4.

cell [4] (definitively corrected to 27.8%) used a theoreticalstudy including an assumption of this type [5]. Nevertheless,in that study there are not any details about the resultingoptimum ARC/WL, and even in [4] the authors consideredthe enhancement of their ARC as a main factor of improvingthe performance of GaAs solar cells.

Accordingly, in this paper we present the performance ofsingle, double and triple layer optical coating systems coupledwith constant and graded aluminum content AlGaAs windowlayers over terrestrial concentrator GaAs solar cells, takinginto account the AM1.5D solar spectrum and the spectralresponse of the devices. To better represent reality, factorssuch as the material absorption of ARC and the oxidation atwindow layer surface due to its high aluminum content arealso included in the calculations. The physical method usedis based on matrix formulation for the transfer of electricand magnetic fields across the interface between layers. Thedesign criteria to calculate the optimum thickness of the layersis the achievement of the maximum photocurrent density.Finally, the best ARC/WL couplings for different situationsare presented.

II. OPTICAL FUNCTION OF THE AlGaAs WINDOW LAYER

Independently of the meaningful role that AlGaAs windowlayer develops in the performance of a GaAs solar cell fromthe electrical point of view, the presence of window layer alsoaffects the optical characteristics of the cell because part of theradiation is reflected at the interface AlGaAs/GaAs, since theirrefractive indexes are different. Fig. 1 shows that the additionof a window layer of any aluminum composition decreases thereflectivity of the GaAs solar cell.

Traditionally, it has been considered that the reduction ofreflectivity was equivalent to improving the general opticalcharacteristics of solar cells. But not only reflection must beconsidered, the absorption in the AlGaAs window layer canbe also taken into account. If we take into account this effect,the previous assertion that a window layer of any constantaluminum composition improves the energy conversion of thesolar cell is not true. Fig. 1 also shows that all aluminumcompositions produce a lower transmissivity in the ultravioletand only some of them give higher transmissivity in the visiblerange. Particularly, if we consider the AM1.5D spectrum andthe 300–900 nm range, the light power that enters the GaAssurface in the case of no window layer is the 63.4% in compar-

0018–9383/97$10.00 1997 IEEE

1500 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 44, NO. 9, SEPTEMBER 1997

Fig. 1. Calculated spectral transmissivity(T ), reflectivity (R), and absorp-tivity (A) of a 30 nm thickness AlGaAs window layer for different aluminumcompositions,x, over a GaAs solar cell. Also is included the nonexistencewindow layer case,x = 0:0.

ison with the 56.7%, 60.5%, 64.6%, 69.6%, and 71.8% for thecase of presence of a 30 nm thickness window layer with 0.2,0.4, 0.6, 0.8, and 0.9 aluminum composition,, respectively.Therefore, only aluminum contents higher than about 0.5 allowthat the light power that enters GaAs surface be higher that inthe case of the cell without AlGaAs window layer.

Fig. 1 seems to indicate that once the threshold of analuminum composition of around 0.5 is reached, the higher thealuminum content, the higher the transmissivity of the windowlayer. In fact, this is true and only technological considerationssuch as the oxidation of the window layer for , limitthe advisable aluminum content in the window layer to amaximum of 0.85, which we will consider from now on asthe optimum.

Since solves the aluminum composition tradeoff,the determination of the optimum thickness is necessary.Traditionally, it has been thought that the thinner the window,the better its performance. This idea was supported by anabsorption minimization criterion and is only partly true. Infact, [6] shows that the thinnest thicknesses have the bestperformance in the ultraviolet (where absorption becomesimportant) but the worst in the visible and infrared region (dueto reflection considerations). Even so, the possible advantagesin the ultraviolet region vanish when the light received bythe cell comes from the sun since solar spectrum at earthhas the lower irradiance precisely in the ultraviolet region.Therefore, an analysis concerning the determination of theoptimum thickness that includes the solar spectrum influenceis necessary. Accordingly, Fig. 2 shows the mean AM1.5Dspectrum weighted transmissivity, defined as

(1)

Fig. 2. Mean AM1.5D spectrum weightedT , R, and A considered forthe 300–900 nm wavelength range versus the window layer thickness.Both gradual and constant window layers are considered. The aluminumcomposition of constant window layer is 0.85 and the aluminum profile ofgraded window layer is taken from [6].

being the AM1.5D spectral irradiance [7] and thespectral transmissivity. In both magnitudes, wavelength is ex-pressed in nanometers. As can be seen,(transmissivity) and

(reflectivity) exhibit the typical maximums and minimumsof interferential layers. Nevertheless, bothand decreasewith window layer thickness due to the continuous incrementof (absorptivity). The maximum transmissivity 0.7092, isobtained for a window layer thickness of 35 nm.

All these considerations are valid for windows with aconstant aluminum content in the whole layer. However, thisis not the only kind of used window layer. Effectively, there isother kind of window whose aluminum content varies alongthe layer. Specifically, the Isothermal Liquid Phase Epitaxy(ILPE) technology allows the formation of an AlGaAs layergraded in its Al content (that varies from zero at the AlGaAs-GaAs interface to a determined value at the external surface)and with a thickness of some tenths of nanometers over theGaAs surface during its isothermal contact with an, Al-Ga-As liquid phase due to the initial nonequilibrium betweenthe binary GaAs substrate and the ternary Al-Ga-As liquidsolution [8]–[10]. The so-called graded window layers havedemonstrated their effectiveness giving terrestrial concentratorGaAs solar cells with efficiencies as high as 25% [11] and,more recently, their suitability for working at 1300 suns witha 23% efficiency [12]. These values could be increased if anoptimization of such layers were performed and this is justone of the tasks of this work.

For this purpose, we have taken the experimental Al profilein the window layer measured in [6] that it is very similarto that obtained by other workers [9], [13]. Maintainingthe shape of this profile we have varied its thickness inour calculations. The result is presented in Fig. 2. Gradedwindow layers with thickness that ranges from 80 to 140nm exhibit lower reflectivity than constant ones. Nevertheless,

ALGORA DEL VALLE AND ALCARAZ: PERFORMANCE OF ANTIREFLECTING COATING 1501

transmissivity continuously decreases with thickness due toa permanent increment of absorptivity. As a conclusion, theoptimum thickness for graded window layer is the smallestpossible and is higher in constant window layersthan in graded ones for any thickness.

III. OPTIMIZATION CRITERIA FOR ARC/WLCOUPLINGS: THEORETICAL MODEL

The main purpose of an ARC system is to improve the con-version efficiency of the solar cell by means of increasing itsshort circuit current. For this goal the incident spectrum mustbe considered giving different weights to each wavelength.Moreover, the spectral response of the device must also betaken into account. The accurate criteria would consist in theachievement of the highest efficiency, as it was tried in [5].Nevertheless, for this purpose it is necessary a complete under-standing of the electrical behavior of window layer, that thereexist not in the case of graded window layer, and that there issome scare for the constant one (in fact, in [5] window layeris assumed not to contribute to the photocurrent but insteadonly serves to reduce the surface recombination velocity).Therefore, until the knowledge about AlGaAs window layersbecomes more accurate, in our opinion, the best optimizationcriterion consists of the maximization of the photogeneratedcurrent density,

SR (2)

being SR the internal spectral response (current/incidentoptical power) of the solar cell without considering the windowlayer photogeneration.

Nevertheless, the inclusion of SR in the functionto maximize impedes any generalization attempt, becauseto each solar cell has its own spectral response. Hence, ina first step, we will consider the product of the two firstmagnitudes of integral of (2), that is the solar spectrumweighted transmissivity, , and further on we willinclude the effect of spectral response. In this way, we cansee the differences between the two approaches.

In order to calculate the transmissivity, reflectivity, andabsorptivity for a multilayer thin-film stack, the matrix for-mulation [2], [14] of the boundary condition of the filmsurfaces derived from Maxwell’s equations has been used.The procedure we will follow consists of the determinationof thicknesses of an ARC system to maximize wherethe number of layers and materials used are known (themean solar spectrum weighted transmissivity, , was firstpresented in (1) for the AM1.5D case). Therefore, the functionto maximize is

(3)

where are the thicknesses of-layers con-stituting the ARC system. The algorithm used is the down-hillsimplex method of Nelder and Mead [15].

When we want to include the SR the function tomaximize will be

SRSR

(4)

which is the ratio between the photocurrent density one cellgenerates and the photocurrent density the same cell wouldgenerate with a transmissivity of 100% over the whole wave-length range. But (4) also has the meaning of a transmissivity.The difference between (4) and (1) is that first case is the meansolar spectrum and spectral response weighted transmissivity,that is, the mean photocurrent density weighted transmissivity,while in (1) transmissivity is only weighted by the solarspectrum.

For comparative purposes, optimum ARC thickness ob-tained from (1) could be used to calculate . Thenwill be introduced in (4) to obtain . This value is com-parable with the one directly obtained from the ARC thicknessoptimization of (4), so differences between considering or notthe internal spectral response could be established, as we willsee in the following section.

IV. DETERMINATION OF THE OPTIMUM ARC/WL COUPLING

A. Without Including the Internal Spectral Response

Several optical systems with single-, double-, and triple-layer coatings have been studied. The values of the refractionindex for the different materials have been taken from theliterature. In this way, the refractive index of ZnS and TiOare complex [16] and for SiOand Si N are taken as real [2].Similarly, the case of TaO is assumed as nonabsorptant [17],[18]. Real, constant, and independent of wavelength for MgF

[19] has been assumed. The complex refractiveindex of GaAs are taken from the data of Aspneset al. [20]and Pikhtinet al. [21] depending on the wavelength range,while those for Al Ga As (including AlAs) are taken fromseveral authors [22]–[24]. When necessary, these data werenumerically interpolated.

The results of calculations for (in terms of totalincident irradiance in the wavelength range 300–900 nm ofAM1.5D solar spectrum) at the interface AlGaAs/GaAs asa function of constant aluminum content windowlayer thickness for different single- and double-layer opticalsystems are shown in Fig. 3 and summarized in Table I. Ineach window thickness, the ARC thickness is optimum and iscalculated by the procedure described in Section III. For thesake of comparison, the window layer without ARC case isalso included in the same figure. One can see that MgFandSiO reproduce the shape of window layer without ARC casegiving the highest transmissivity (0.88 and 0.90, respectively)for a window thickness of about 30 nm. The TaO and Si Nmaterials increase the transmissivity up to 0.91 and 0.92,respectively, but for a lower window thickness (around 10–20nm). The best choice is the MgF/ZnS couple that allows anincrement of transmissivity of 0.04–0.06 with respect to SiNover the whole window thickness range. This AR system

1502 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 44, NO. 9, SEPTEMBER 1997

TABLE IOPTIMUM THICKNESSES OFWINDOW LAYERS AND ANTIREFLECTING COATINGS WITH WHICH MAXIMUM TRANSMISSIVITIES

ARE OBTAINED IN FIGS. 3 AND 4. WHEN THE TABLE SHOWS THAT THE THICKNESS OF A WINDOW LAYER IS 10 nm,THIS INDICATES THAT THE MAXIMUM TRANSMISSIVITY WOULD REALLY REACH WITH A THICKNESS OF 0 nm

Fig. 3. Mean AM1.5D spectrum weighted transmissivity for the 300–900nm wavelength range and for different ARC/WL couplings over a GaAs solarcell versusx = 0:85 constant window layer thickness. In each windowthickness, optimum ARC thicknesses are considered. Increment of meanAM1.5D spectrum weighted transmissivity (%) after deposition of an optimumMgF2/ZnS double layer with respect to the situation without ARC (this isMgF2/ZnS:No ARC), is also shown. In this case the big arrow indicates thereference axis.

reaches its highest transmissivity (0.9673) at the nonpracticalcase of nonexistence of a window layer. TiOand ZnS givethe worst results among the analyzed materials.

We have developed similar calculations for the case ofgraded window layer, as can be seen in Fig. 4 and Table I.Now we can see that all ARC systems reproduce the shapeof window layer without ARC situation. For all materials theoptimum window layer thickness is zero and transmissivitycontinuously decreases with window layer thickness. Since thissituation is not adequate (the presence of a window layer topassive GaAs surface is necessary), it implies that the gradedwindow layer must be as thin as possible, around 10 nmto avoid the tunnel effect that appears at lesser thicknesses.The lesser the window layer thickness, the higher incrementof photocurrent for all ARC materials it is also seen. Thebest single layer material is SiN . Again, the best choice isthe MgF /ZnS couple that implies an increment of 0.05 intransmissivity with respect to SiN case. The effect of best

Fig. 4. Mean AM1.5D spectrum weighted transmissivity in the 300–900 nmwavelength range and for different ARC/WL couplings over a GaAs solar cellversus graded window layer thickness. The aluminum profile in the windowlayer is taken from [6]. In each window thickness, optimum ARC thicknessesare considered. Increment of mean AM1.5D spectrum weighted transmissivity(%) after deposition of an optimum MgF2/ZnS double layer with respect tothe situation without ARC (this is MgF2/ZnS:No ARC), is also shown. In thiscase the arrow indicates the reference axis.

option, this is the double ARC, increases the transmissivity(indicated as MgF/ZnS:No ARC) of graded window layer to agreater extent (52–39%) for thinnest window layer thicknessesand after 80 nm it saturates to a value near 39% (see Fig. 4). Inthe case of constant window layer, the improvement oscillatesand is only slightly higher (40%) than that graded windowlayer (39%) for the 80–140 nm range (see Fig. 3). This fact canbe also seen in Fig. 5 which shows the effect of an optimumMgF /ZnS ARC over a 40 nm thickness both constant andgraded window layer. The ARC applied over graded windowlayer reduces its reflectivity to a greater extent than forconstant window layer. Nevertheless, the transmissivity ishigher for constant window layer than for graded one dueto its lower absorptivity.

For the same conditions of Figs. 3 and 4, we have per-formed calculations for triple ARC. The best combinationsare MgF /ZnS/TiO and MgF /Si N /ZnS, but in both casesthe increment of transmissivity with respect to the MgF/ZnS

ALGORA DEL VALLE AND ALCARAZ: PERFORMANCE OF ANTIREFLECTING COATING 1503

Fig. 5. Spectral transmissivity, reflectivity, and absorptivity of graded andconstant window layers with a thickness of 40 nm over a GaAs solar cell. Thealuminum composition of constant window layer is 0.85 and the aluminumprofile of graded window layer is taken from [6]. Both kind of layers havetheir own optimum MgF2/ZnS ARC.

couple is lower than 0.005. For this reason, they are notincluded in the figures and we think that their use is notjustified from a complexity and economic viewpoint. TheTiO and MgF are not included either in Fig. 4 because theygive worse results than SiOand they complicate this figureconsiderably.

B. Including the Internal Spectral Response

The purposes of this section are a) the determination of thespectral response influence over the ARC optimization andb) the comparison between the constant and graded windowlayers performance when spectral response is considered.

To evaluate the last point, we have measured the externalspectral response of a typical GaAs solar cell grown byILPE in our laboratory endowed with a graded window layer.The GaAs cell does not have ARC and its 60-nm thicknesswindow layer has the graded aluminum content of [6]. Todetermine its internal spectral response we can make twodifferent assumptions, as follows.

1) The Graded Window Layer Does Not Contribute to thePhotogeneration:The transmissivity of this window layer atthe AlGaAs/GaAs interface can be calculated and then theinternal spectral response can be obtained by means of

SRSR

(5)

The spectral response obtained is much higher than unity atthe ultraviolet range [shown in Fig. 6 as SR 60 nm ],which indicates that window layer contributes in some extentto photocurrent.

2) The Graded Window Layer Contributes in Some Extentto the Photogeneration:The for thicknesses thinner

Fig. 6. Spectral responses of different kind of window layers. SRext cor-responds to a GaAs solar cell with a 60-nm thickness graded window layergrown in our lab by ILPE. For determining its internal spectral response, wehave first used (5) to obtain SRint 60 nm (T). A better approach consistsof the supposition that window is an active layer in a part of its thickness,contributing to photocurrent. From the whole spectral responses calculatedin this way, we show the intermediate case, shown as SRint intermediate.Also, the calculated spectral response using the Hovel model of ax = 0:85

constant (ct) window layer with a thickness of 60 nm, SRint ct 60 nm, isshown for comparison.

than the total window layer thickness (from 1 to 59 nm) arecalculated and their corresponding spectral responses, as in theformer point, are calculated. Finally, among all these spectralresponses we have taken the intermediate one (shown in Fig. 6as SR intermediate), as if about half of the window layerthickness would generate and the other half would only absorb.

This is only a qualitative approach and the accurate deter-mination of the total photocurrent generated by window layerneeds specific study. In this sense several authors have claimedthat direct gap sublayers of graded window layer do notremain inactive but contribute effectively to the photocurrent[25]–[27].

We have introduced this intermediate internal spectral re-sponse in (4) to obtain the optimum MgF/ZnS ARC for thegraded layer case. The results are 107.3 nm of MgF, 57.5 nmof ZnS and a transmissivity in comparisonwith the optimum ones obtained from (1), that are 107.3 nmof MgF , 57.3 nm of ZnS and the same .

For the purpose of comparison to the 60-nm graded windowlayer, we have calculated the internal spectral response ofa GaAs solar cell with a constant windowlayer of the same thickness (60 nm). For this thickness,the nonconsideration of the spectral response makes constantwindow layers better than the graded ones, from the pointof view of transmissivity (see Fig. 2). We have used thegeneral accepted model proposed by Hovel [28]. The internalspectral response obtained is (shown in Fig. 6, as SRct 60 nm) introduced in (4) and the optimum MgF/ZnSARC is recalculated. As can be seen in the inset of Fig. 7,the consideration of the SR implies that the optimum

1504 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 44, NO. 9, SEPTEMBER 1997

Fig. 7. Spectral transmissivity, reflectivity and absorptivity of a 60 nmthicknessx = 0:85 constant window layer with an optimum MgF2/ZnS ARC.Two different internal spectral responses (SRint = 1 and SRint = SRint ct60 nm of Fig. 6) are considered. The inset presents the variations of MgF2

and ZnS thicknesses and mean photocurrent weighted transmissivity for bothinternal spectral responses.

thicknesses of the AR system becomes thicker than if it is notconsidered [equivalent to a SR in (1)]. Specifically,the thickness of ZnS goes from 58.9 nm to 62.6 nm and thethickness of MgF goes from 106.4 nm to 111.2 nm. Thismeans an increment of 6.3% and 4.5% in the thickness ofZnS and MgF, respectively. increases from 0.9444 to0.9452.

Therefore, thicknesses obtained in Section IV-A, where wehave not included the spectral response, can be consideredas optimum both for constant and graded window layers.Consequently, the required additional efforts to include thespectral response of each cell in the optimization of its ARsystem thicknesses would be justified only in very specialcases.

Nevertheless, it is useful to accurately know the influenceof the internal spectral response over the ARC optimizationdesign. We can see it in Fig. 7 for the constant windowlayer case. Since the SR of the cell (see Fig. 6) hasthe higher values in the visible-infrared region, its inclusionin the optimization generates new optimum thicknesses thatraise the spectral transmissivity in this region (480–900 nm),though they simultaneously depress it in the ultraviolet region(300–480 nm). Accordingly, reflectivity decreases at highwavelength range and absorptivity decreases in the low range.These slight spectral variations allow the very small increment(0.08%) of . The same behavior is observed in thestudied range (from 0 to 200 nm) of window layer thicknessin which increases fewer than 0.5%.

Concerning comparison between graded and constantwindows layers, we have obtained their photocurrents fromtheir internal spectral responses (SR intermediate andSR ct 60 nm, respectively, in Fig. 6) giving 24.5 and24.3 mA/cm , respectively. These values account for a 12%

Fig. 8. Thicknesses of the WL, oxide, ZnS, and MgF2 layers as a functionof elapsed time after window layer air exposition. Optimum mean AM1.5Dspectrum weighted transmissivities if oxide is considered(Topt) or notT

noxi

are included.

shadowing factor (due to the measured graded window cellis designed for working inside a light confining cavity, andcorrespondingly the same shadowing factor for the calculationof the constant window cell has been assumed). Then, ourqualitative approximation indicates that absorbed light ingraded window layer is used to generate efficiently collectedelectron-hole pairs that increase its internal spectral responsewith respect to constant window layer in such a way that theimprovement in spectral response balances absorption losses.In spite of this balanced situation, at this stage we cannotaccurately determine which of the two window layers, if either,provides a higher photocurrent, so we propose experimentalanalysis (for example, as the based ones in this spectralresponse procedure) as well as theoretical ones to determinethe performance of graded window layers.

C. AlGaAs Window Layer Oxidation

High- Al Ga As layers have propensity to oxidize. Astime goes by the oxide thickness increases, with a sharp onsetof oxidation at about 30 h, saturating it after 100 h [29].Assuming the conditions of [29], that is, a GaAs solar cell witha constant aluminum content window layer of 43.3nm that after 56.3 h becomes a 41.8 nm oxide layer over a 12nm window layer, and taking into account its time evolution,we have performed the ARC optimization. For this purposewe have taken the complex refractive index of oxide [30].

During the elapsed time the oxide thickness is greater thanthe original thickness of consumed AlGaAs, leading to anoverall volume expansion (Fig. 8). ARC optimization showsthat the thickness of both ZnS and MgFmust decrease in sucha way that transmissivity can be maintained more orless constant during the whole process. Nevertheless, if ARCdeposition is performed several days (more than two) after thebeginning of oxidation (for example after the GaAs cap layerremoval), and for calculations of optimum ARC thickness thepresence of the oxide layer is not taken into account and

ALGORA DEL VALLE AND ALCARAZ: PERFORMANCE OF ANTIREFLECTING COATING 1505

consequently, the initial window layer thickness is supposed,the transmissivity that would be obtained in reality ( ,optimum without considering the oxide appearance) woulddecrease with time up to an 83% of its maximum achievablevalue .

Therefore, in the cases that ARC cannot be depositedjust after the air-exposure of the AlGaAs window layer, thethickness determination of both the oxide and window layerjust before the ARC deposition, should be performed prior tocalculating the optimum ARC thickness.

V. SUMMARY AND CONCLUSIONS

We have analyzed the performance of AR systems coupledwith constant and graded aluminum content AlGaAs windowlayers over terrestrial concentrator GaAs solar cells. Thecriterion of maximization photocurrent is used.

In accordance with previous works, the MgF/ZnS doubleARC is better than any other simple or double system. The bestchoice for the AM1.5D solar spectrum is MgF(95.3 nm)/ZnS(48.2 nm)/Al Ga As aluminum constant window layer(10 nm) which gives a mean spectrum weighted transmissivityof 0.9628.

Triple ARC systems have also been analyzed. Best com-binations are MgF/ZnS/TiO and MgF /Si N /ZnS, but inboth cases the increment of transmissivity with respect to theMgF /ZnS couple is lower than 0.005. For this reason, theiruse regarding complexity and economy points of view are notrecommended.

Concerning an accurate optimization of the ARC systems,the internal spectral response of the GaAs solar cells hasbeen considered, but regarding the increase of transmissivitythat produces (less than 0.5%), its use is only justified invery special cases. However, the inclusion of internal spectralresponse in this optimization indicates that the very absorbentgraded window layer generates efficiently collected electron-hole pairs that increase its photocurrent with regard to constantwindow layer, in such a way that the improvement of spectralresponse balances absorption losses. Thus, the graded windowlayer could be even more effective than constant window layerfor GaAs solar cells.

Finally, the propensity to oxidize of AlGaAs appears to bea very important factor for an accurate ARC optimization. Ifit is not considered, mean transmissivities (and consequentlyefficiencies of GaAs solar cells) of only around 83% of thatachievable maximum could be attained.

ACKNOWLEDGMENT

The authors would like to thank C. H. Ambrose for herhelpful comments on the English translation of this paper.

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1506 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 44, NO. 9, SEPTEMBER 1997

Carlos Algora del Valle (M’97) was born inMadrid, Spain, on January 11, 1962. He receivedthe Licenciado en Ciencias F´ısicas degree in 1986and the Doctor en Ciencias Fısicas degree in 1990,both from the Universidad Complutense de Madrid,Spain.

He joined the Instituto de Energıa Solar-Departamento de Electronica Fısica of the Univer-sidad Politecnica de Madrid in 1985. He has beenTitular Professor in the same department since 1991.He has contributed to several European efficiency

records on heteroface AlGaAs/GaAs solar cells. He currently leads the III–VCompounds Technology Group devoted to the physics and technology ofIII–V concentrator photovoltaic cells.

Manuel Felices Alcaraz was born in Almer´ıa,Spain on December 27, 1967. He received theB.S. degree in telecommunication engineering andthe M.S. degree in electronic engineering from theUniversidad Polit´ecnica de Madrid, Spain.

In 1992, he joined the Instituto de Energıa Solar-Departamento de Electronica Fısica of the Universi-dad Politecnica de Madrid, where he was involvedin ARC simulation and optimization. He developedthe computer application used in this research. Heis now with the Carboneras Thermal Power Plant,

Endesa Company, Almer´ıa, Spain.