DOI: http://dx.doi.org/1.4314/gjpas.v2i2.9 GLOBAL JOURNAL OF PURE AND APPLIED SCIENCES VOL. 2, 214: 139-148 COPYRIGHT BACHUDO SCIENCE CO. LTD PRINTED IN NIGERIA ISSN 1118-579 www.globaljouralseries.com, Email: ifo@globaljouralseries.com INFLUENCE OF ELECTROMAGNETIC WAVES PRODUCED BY AN AMPLITUDE MODULATION RADIO ANTENNA ON THE ELECTRIC POWER DELIVERED BY A SILICON SOLAR CELL I. ZERBO, M. ZOUNGRANA, A. OUEDRAOGO, B. KORGO, B. ZOUMA AND D. J. BATHIEBO 139 (Received 14 July 214; Revisio Accepted 5 September 214) ABSTRACT This article presets a oe dimesioal modelig of the ifluece of electromagetic waves o the electric power delivered by a silico solar cell uder moochromatic illumiatio i steady state. The electromagetic waves are produced by a amplitude modulatio radio atea of 2MW power of radiatio ad located at a variable distace of the solar cell [ 1 m,+ [. The magetotrasport ad cotiuity equatios of excess miority carriers are solved with boudary coditios ad led to ew aalytical expressios of miority carrier s desity, photocurret desity, photovoltage ad electric power depedig o electromagetic field itesity ad wavelegth λ. The depedece of the electromagetic field ad the icidet light wavelegth o photocurret desity, photovoltage ad electric power is studied. The itesity of the electromagetic field depeds o the distace betwee the solar cell ad the amplitude modulatio radio atea. We determie the peak power ad the operatig poit of the solar cell accordig to distace or electromagetic field itesity ad also accordig to the wavelegth of the moochromatic light. KEYWORDS: 1- Amplitude modulatio, 2- Radio atea, 3- Electromagetic waves, 4- Moochromatic illumiatio, 5- Solar cell INTRODUCTION The efficiecy of a solar cell is closely boud to its electroic properties but some exteral factors as magetic field (Dieg et al., 211; Zougraa et al.,211; Zougraa et al.,212),ad exteral electric field (Zougraa et al.,212), ca ifluece the solar cell quality. The magetic field ca have various origis: terrestrial magetic field, magetic compoet of the electromagetic waves comig from radio trasmitters, televisio trasmitters ad telecommuicatio trasmitters, magetic field comig from high voltage/ low voltage trasformer, etc. Also, we are iterested i the effect of electromagetic waves comig from radio trasmitters ad other telecommuicatio sources o silico solar cell because whatever is their istallatio place, the silico solar cells of photovoltaic paels by their priciple of fuctioig (movemet of electros) ca be iflueced by the magetic field as well as the electric field of the electromagetic waves of the differet telecommuicatio sources that exist close to their istallatio place. I previous works we studied the ifluece of electromagetic waves produced by AM ad FM radio ateas o silico solar cell electroics ad electrical parameters (Zerbo et al., 211; Zerbo et al., 212; Sow et al., 212). I these works, the solar cell was illumiated by a multispectral light i steady state. I the preset article, we study the effect of electromagetic waves produced by a amplitude modulatio radio atea o the electric power delivered by a silico solar cell illumiated by a moochromatic light. The AM radio atea is the source of productio of progressive moochromatic plae electromagetic waves liearly polarized whose electric field itesity measured at a distace r from the atea is depedat of the power radiated by the atea ad the distace r. Therefore we will study the ifluece of electromagetic field ad wavelegth o photocurret desity, photo voltage ad electric power. I. Zerbo, Laboratoire d Eergies Thermiques et Reouvelables (L.E.T.RE), Départemet de Physique, U.F.R-S.E.A, Uiversité de Ouagadougou, BURKINA FASO M. Zougraa, Laboratoire d Eergies Thermiques et Reouvelables (L.E.T.RE), Départemet de Physique, U.F.R- S.E.A, Uiversité de Ouagadougou, BURKINA FASO A. Ouedraogo, Laboratoire d Eergies Thermiques et Reouvelables (L.E.T.RE), Départemet de Physique, U.F.R- S.E.A, Uiversité de Ouagadougou, BURKINA FASO B. Korgo, Laboratoire d Eergies Thermiques et Reouvelables (L.E.T.RE), Départemet de Physique, U.F.R-S.E.A, Uiversité de Ouagadougou, BURKINA FASO B. Zouma, Laboratoire d Eergies Thermiques et Reouvelables (L.E.T.RE), Départemet de Physique, U.F.R- S.E.A, Uiversité de Ouagadougou, BURKINA FASO D. J. Bathiebo, Laboratoire d Eergies Thermiques et Reouvelables (L.E.T.RE), Départemet de Physique, U.F.R- S.E.A, Uiversité de Ouagadougou, BURKINA FASO
14 I. ZERBO, M. ZOUNGRANA, A. OUEDRAOGO, B. KORGO, B. ZOUMA AND D. J. BATHIEBO 2. Theory 2.1. Excess miority carriers desity Polycrystallie back surface field silico solar cell with + -p-p + structure is studied uder moochromatic illumiatio ad uder electromagetic waves (figure 1) Figure 1: Silico solar cell illumiated by moochromatic light ad uder electromagetic waves ifluece Whe the solar cell is illumiated with a moochromatic light ad submitted to the actio of a electromagetic field, the cotiuity equatio relative to excess miority carriers (electros) desity photo geerated i the base regio ca be writte as (Zerbo et al., 212; Sow et al., 212) 2 δ ( x) LE δ( x) δ ( x) G( x) + + = ----------------------------------------------- (1) 2 2 2 x x L L D I equatio (1), 2 E L E= µ is a coefficiet that characterizes migratio pheomea i solar cell base. I this D L expressio, µ is the electro mobility, E is the electric field itesity, L ad diffusio coefficiet, L ad D are the electro diffusio legth ad D are the electro diffusio legth ad diffusio coefficiet i the presece of magetic field. δ(x) ad G(x) are respectively carriers desity ad optic geeratio rate. LE δ( x) The term of equatio (1) beig a first derivative i relatio with positio x, is similar to a term of dampig. 2 L x The electros-holes pair s optic geeratio rate for a moochromatic icidet light is give by α( λ)x Gx ( ) = α( λ) Φ [ 1 R( λ) ] e ----------------------- (2) α(λ) ad R(λ) are respectively absorptio ad reflectio coefficiet at the wavelegth λ ad Φ is the icidet photo flux. The excess miority carriers (electros) desity, solutio of equatio (1) is completely determied usig the two boudary coditios below: - At the juctio emitter-base (x = ) δ( x ) δ( ) = Sf --------------------------------------------- (3) x x= D - At the rear side of the solar cell (x = H) δ( x) δ( H) = Sb ---------------------------------------------- (4) x x= H D Sf is the sum of two cotributios: Sf which is the itrisic juctio recombiatio velocity related to the losses of carriers at the juctio iterface ad Sf j which is the juctio recombiatio velocity imposed by a exteral circuit ad defies the operatig poit of the cell (Zerbo et al., 212; Sow et al., 212): Sf = Sf + Sf ----------------------------------------------- (5) j Sb is the effective back surface recombiatio velocity For a isotropic atea radiatig a power P r (W) i free space, the electric field itesity E (V /m) depedig o the distace r (m) is give by the formula (Freyer et al., 1994):
INFLUENCE OF ELECTROMAGNETIC WAVES PRODUCED BY AN AMPLITUDE MODULATION RADIO 141 1 Pr Z E= ---------------------------------------- (6) 2 r π r beig the distace that separates the source of radiatio from the measuremet poit of electric field itesity E ad Z is the characteristic impedace i free space. Table 1: Iformatio cocerig electric ad magetic field itesities calculated for a AM radio atea radiatig power, Pr= 2 MW i free space, for differet values of distace betwee the solar cell ad the atea usig equatio (6). Alphabetic letter Distace r (m) E (V/m) B (T) A 1 774.3 2.581X1-6 B 5 154.9 5.162 X1-7 C 1 77.4 2.581 X1-7 D 5 15.5 5.162 X1-8 E 1 7.7 2.581 X1-8 F r = +oo 2.2. Photocurret desity Applyig Fick s law at the solar cell juctio, we get photocurret desity expressio i the presece of electromagetic field (Zerbo et al., 212; Sow et al., 212) as: δ( x) Jph( Sf) = q D + µ E δ( ) ------------------------------- (7) x x= D with D = ad 1 ( B ) µ + µ 2 µ = which are respectively electros diffusio coefficiet i the magetic field 1+ ( µ B ) 2 ad electros mobility i the magetic field 2.2-1 Effect of electromagetic field or distace o photo-curret desity The photo-curret desity versus juctio recombiatio velocity curves are plotted o figure 2 for differet values of electromagetic field itesity or for differet values of the distace betwee the AM radio atea ad the solar cell. Figure 2: Photo-curret desity versus juctio recombiatio velocity for differet values of electromagetic field or distace (L=.2cm; H=.3cm;D=26cm 2 /s;µ =1cm 2 /V.s, λ=.68µm)
142 I. ZERBO, M. ZOUNGRANA, A. OUEDRAOGO, B. KORGO, B. ZOUMA AND D. J. BATHIEBO Curves of figure 2 show that the ope circuit photo-curret is ull i the absece of electromagetic field but ot ull i the presece of electromagetic field. The ope circuit photo-curret or leakage curret is proportioal to the electromagetic field itesity ad stretches toward the value of short circuit photo-curret for large values of electromagetic field itesity. The short circuit photo-curret ad the leakage photo-curret are icreasig fuctios of electromagetic field itesity. The presece of photocurret i the eighborhood of the ope circuit explais the presece of leakage curret at the solar cell juctio. Ideed, while applyig the boudary coditio give by equatio (3), equatio (7) gives: Jph( Sf) = q [ Sf+ µ E] δ( ) ----------------------------------------- (8) Rewritig equatio (8) ad takig equatio (5) ito accout, oe gets: Jph( Sf) = q [ Sf+ Sf + µ ] j E δ( ) ----------------------------------------- (9) The photocurret ca be divided i two compoets: a compoet that depeds o the itrisic juctio recombiatio velocity Sf ad the electromagetic field applied at the solar cell ( Sf) F that depeds o the impedace of he exteral circuit ad also the applied electromagetic field Jph ( Sf) = q [ Sf + µ E ] ( ) F δ ad Jph( Sf) T q Sfj δ( ) Jph(Sf) T is the photocurret that crosses the exteral circuit ad iterface pheomea ad therefore - I ope circuit Sf ( Sf + µ E) leakage curret. - I short circuit Sf ( + ) j Jph ad a secod compoet Jph ( Sf) T. = ----------------------- (1) ( Sf) F Jph ( Sf) T is a leakage photocurret. ad ( ) F Jph is the photocurret that is lost because of Jph Sf JphSf ( ), which meas that the photocurret is reduced to the Jph Sf JphSf ( ). I this fuctioig mode, the photocurret is almost µ ad ( ) T j Sf E etirely delivered to a exteral circuit, the losses of curret to the iterfaces beig weak. - I a itermediate fuctioig mode, the recombiatio boud to iterface effects ad to the impedace of the exteral circuit are to be take ito accout. 2.2-1 Effect of icidet moochromatic light wavelegth o photo-curret desity The photo-curret desity curves versus juctio recombiatio velocity are plotted o figure 3 for differet wavelegth of the icidet moochromatic light ad for a give electromagetic field itesity or a fixed distace betwee the AM radio atea ad the solar cell. Figure 3: Photo-curret desity versus juctio recombiatio velocity for differet values of icidet moochromatic light wavelegth (L=.2 cm; H=.3 cm; D=26 cm 2 /s; µ =1 cm 2 /V.s, r=1m )
INFLUENCE OF ELECTROMAGNETIC WAVES PRODUCED BY AN AMPLITUDE MODULATION RADIO 143 The ope circuit curret is firstly weak ad it icreases with the icrease of the wavelegth. The ope circuit curret reaches a maximum for the wavelegth λ =.68 µm. The it becomes weaker if the wavelegth cotiues to icrease: it appears the iversio pheomeo. The leakage curret ad the short circuit curret icrease with the wavelegth to reach a maximum at the wave legth λ =.68 µm. 2.3. Effect of electromagetic field or distace o photo-voltage Usig Boltzma s relatio (Zerbo et al., 212; Sow et al., 212) we ca determie the solar cell juctio photovoltage as: δ ( ) ( ) k ( ) B T δ VphSf =V l 1 = l + 1 T + ---------------------------- (11) q Where = 2 i NB a VT =kb T / q ; i is the itrisic carrier s desity at thermal equilibrium; N B the dopig desity of the base ad V T is the thermal voltage. 2.3-1 Effect of electromagetic field or distace o photo-voltage We plot o figure 4 below, photo-voltage versus juctio recombiatio velocity curves for differet values of electromagetic field itesity or for differet values of the distace betwee the AM radio atea ad the solar cell. Figure 4: Photo-voltage versus juctio recombiatio velocity for differet values of electromagetic field or distace (L=.2 cm; H=.3 cm; D=26 cm 2 /s; µ =1 cm 2 /V.s, λ=.68 µm) It appears o the curves of figure 4 that for large value of juctio recombiatio velocity (Sf 1 1 cm.s - 1 ), the photo voltage is ull while for low value of juctio recombiatio velocity (Sf 1 2 cm.s -1 ) the ope circuit voltage is maximal ad depeds of electromagetic field itesity. The ope circuit voltage decreases while the electromagetic field itesity icreases. Ideed, we have observed o the curves of figure 2 the existece of a curret i ope circuit amed leakage curret due to the passage of some carriers through the solar cell juctio i ope circuit. Thus, a
144 I. ZERBO, M. ZOUNGRANA, A. OUEDRAOGO, B. KORGO, B. ZOUMA AND D. J. BATHIEBO decrease of the ope circuit voltage meas a reductio of the quatity of carriers stocked at the juctio. I fact, some carriers will cross the juctio ad produce a leakage curret that will be quatified from a microscopic view poit, by the itrisic juctio recombiatio velocity. A decrease of the ope circuit voltage traslates to a icrease i the losses of carriers at the juctio or eve a icrease of the itrisic juctio recombiatio velocity at the solar cell juctio. 2.3-2 Effect of icidet moochromatic light wavelegth o photo-voltage The photo-voltage curves versus juctio recombiatio velocity are plotted o figure 5 for differet wavelegth of the icidet light ad for a give electromagetic field itesity or a fixed distace betwee the AM radio atea ad the solar cell Figure 5: Photo-voltage versus juctio recombiatio velocity for differet values of icidet moochromatic light wavelegth (L=.2cm; H=.3cm; D=26 cm 2 /s; µ =1 cm 2 /V.s, r=1m) The pheomeo of iversio observed o the curves of figure 3 appears also here. Ideed, the theoretical ope circuit voltage icreases while the wavelegth, λ; icrease ad reach a maximum at λ=.68µm. Beyod λ=.68µm, the ope circuit voltage decreases while the wavelegth cotiues to icrease. 2.4. Solar cell electric power The electric power delivered by the solar cell base to a exteral load circuit is expressed usig the equatio (12) below: P( Sf) =Vph( Sf) Jph( Sf) T ----------------------------------------------------------------- (12) I this expressio, Jph ( Sf) T is the photo-curret that crosses the exteral load resistace ( Jph( Sf) =q Sf δ( ) ). T j
INFLUENCE OF ELECTROMAGNETIC WAVES PRODUCED BY AN AMPLITUDE MODULATION RADIO 145 2.4-1 Effect of electromagetic field or distace o electric power Electric power variatios versus juctio recombiatio velocity for differet values of electromagetic field itesity or for differet values of the distace betwee the AM radio atea ad the solar cell are plotted o figure 6. Figure 6: Electric power delivered by the solar cell versus juctio recombiatio velocity for differet values of electromagetic field or distace (L=.2cm; H=.3cm; D=26cm 2 /s; µ =1 cm 2 /V.s, λ=.68 µm) The aalysis of the differet curves shows that the electric power delivered by the solar cell base is ull ear the ope circuit ad the short circuit. It passes by a maximum that is located at a itermediate operatig poit. This operatig poit for which the electric power is maximal moves toward the short circuit (large values of Sf) whe the distace betwee solar cell ad electromagetic source reduces (electromagetic field itesity icreases). We observe also o this figure that the maximum electric power is obtaied i absece of electromagetic field (large distace betwee the AM radio atea ad the solar cell) because from.4µm to.8µm, carriers are geerated ear the juctio ad the electromagetic field has o effect o them. Coversely, from.8µm to 1µm, excess miority carriers are geerated iside the base (far from the juctio) ad the electromagetic field has a great effect o their mobility. We determied the values of maximum electric power delivered by the solar cell to a exteral circuit ad the values of correspodig juctio recombiatio velocity, for differet values of electromagetic field itesity ad for a icidet moochromatic light wavelegth, λ=.68µm. These results are cosiged i table 2 below. Table 2: Maximum electric power ad correspodig juctio recombiatio velocity for differet values of electromagetic field itesity for icidet moochromatic light wavelegth λ=.68µm. Distace 1 5 1 5 1 absece of (m) atea E (V/m) 774.3 154.9 77.4 15.5 7.7 B (T) 2.581X1-6 5.162 X1-7 2.581 X1-7 5.162 X1-8 2.581 X1-8 P max (W/cm 2 ).25582.2731.27224.27229.27358.27358 Sf (1 4 cm/s) 19.546 5.12861 3.9817 3.71535 3.1995 3.199517
146 I. ZERBO, M. ZOUNGRANA, A. OUEDRAOGO, B. KORGO, B. ZOUMA AND D. J. BATHIEBO The results cosiged i table 2 cofirm the above oes of figure 6. Ideed, it appears that the maximum electric power delivered by the solar cell base to a exteral circuit icreases while electromagetic field itesity decreases. We also ote that the itese values of electromagetic field itesity leads to weak values of maximum electric power for large values of juctio recombiatio velocity. This pheomeo ca be iterpreted as a icrease of carriers losses at solar cell juctio (itrisic juctio recombiatio velocity icrease). 2.4-2 Effect of icidet light wavelegth o electric power Electric power variatios versus juctio recombiatio velocity for differet wavelegth of the icidet moochromatic light ad for a give electromagetic field itesity or distace betwee the AM radio atea ad the solar cell are plotted o figure 7. Figure 7: Electric power delivered by the solar cell versus juctio recombiatio velocity for differet values of icidet light wavelegth (L=.2 cm; H=.3 cm; D=26 cm 2 /s; µ =1 cm 2 /V.s, r=1m ) It appears from this figure that for each curve, the electric power passes by a maximum that is located i a itermediate operatig poit. We observe also that the maximum electric power icreases with the icrease i wavelegth util λ=.68µm. Beyod λ=.68 µm, the pheomeo of iversio observed while studyig photocurret desity ad photo voltage appears also. I table 3 below, we give the maximum electric power delivered by the solar cell to a exteral circuit ad the correspodig juctio recombiatio velocity value for differet wavelegths ad for a give electromagetic field itesity.
INFLUENCE OF ELECTROMAGNETIC WAVES PRODUCED BY AN AMPLITUDE MODULATION RADIO 147 Table 3: Maximum electric power ad correspodig juctio recombiatio velocity for differet wavelegth ad for a give electromagetic field itesity Wavelegth λ (µm) P max (W/cm 2 ) Sf (1 4 cm/s).4.96398 3.6378.5.2573 3.9817.6.24926 3.8945.68.27224 3.9817.7.25695 3.9817.8.2433 3.8945.9.17581 3.9817 1..138 3.71535 The results of table 3 cofirm the above oes of figure 7. We also ote that the maximum electric power is obtaied almost at the same itermediate operatig poit for all wavelegths (Sf = 3.9x1 4 cm.s -1 ). CONCLUSION A theoretical study of amplitude modulatio radio waves effects o silico solar cell electric power is preseted. The study of photo curret desity shows that for a give wavelegth, the short circuit photocurret ad the ope circuit photo-curret or leakage curret are icreasig fuctios of electromagetic field itesity. The, for a give electromagetic field itesity, the leakage curret ad the short circuit curret icrease with the wavelegth to reach a maximum at the wavelegth λ =.68 µm; ad they decrease, while the wavelegth cotiues to icrease: this is the pheomeo of iversio. As for the photo voltage, for a give wavelegth, the ope circuit voltage is a decreasig fuctio of electromagetic field itesity. We also ote that, for a give electromagetic field itesity, the ope circuit voltage icreases with the wavelegth to reach a maximum at the wavelegth λ=.68 µm ad decreases while the wavelegth cotiues to icrease. The umeric calculatios, deduced from the aalysis of electric power curves, show icrease i the maximum electric power delivered by the solar cell, with decrease i electromagetic field itesity at a itermediate operatig poit for a give wavelegth. For a give electromagetic field itesity, the electric power maifests the pheomeo of iversio, after the wavelegth, λ =.68 µm, where it is maximal. This iversio presets a similarity with the spectral iversio of solar radiatio with a wavelegth gap of a few hudred aometers betwee the maximum poits. I fact, the poit of maximum power for the cell is ot achieved for the equivalet wavelegth of maximum solar radiatio, as it is kow that this value is reached for wavelegth, ragig from 475 to 5m (Beicher et al., 2). For all wavelegths, the electric power is almost maximal at the same itermediate operatig poit (Sf = 3.9x1 4 cm.s -1 ). It appears i this study that solar cells are iflueced oe the less by the electromagetic waves produced by AM ad FM radio ateas but also by light of high wave legths. So it cofirms that it would be judicious to take ito accout these parameters whe istallig silico solar cells photovoltaic paels to optimize their efficiecies. REFERENCES Beicher, R., Serway, R., 2. Physics for Scietists ad Egieers with Moder Physics Fifth Editio. Orlado, FL: Sauders College Publishig Dieg, A., Zerbo, I., Wade, M., Maiga, A. S. ad Sissoko, G., 211. Three-dimesioal study of a polycrystallie silico solar cell: the ifluece of the applied magetic field o the electrical parameters. Semicod. Sci. Techol. 26 9523 Freyer, U., 1994. Nachrichte-Uebertragugstechik, Carl Haser Sow, O., Zerbo, I., Mbodji, S., Ngom, M. I., Diouf, M. S. ad Sissoko, G., 212. Silico solar cell uder electromagetic waves i steady state: electrical parameters determiatio usig the I-V ad P-V characteristics. Iteratioal Joural of Sciece, Eviromet ad Techology, 1, (4): 23 246. Zerbo, I., Zougraa, M., Seré, A. D., Ouedraogo,F., Sam,R., Zouma, B. ad Zougmoré, F., 211. Ifluece d ue ode électromagétique sur ue photopile au silicium sous éclairemet multispectral e régime statique. Revue des Eergies Reouvelables, 14, (3): 517 532. Zerbo, I., Zougraa, M., Seré, A. D. ad Zougmoré, F., 212. Silico solar cell uder electromagetic wave i steady state: effect of the telecommuicatio source s power of radiatio. 212 IOP Cof. Ser.: Mater. Sci. Eg. 29 1219 Zougraa, M., Dieg, B., Lemrabott, O. H., Toure, F., Ould El Moujtaba, M. A. Sow, M. L. ad Sissoko, G., 212. Exteral Electric Field Ifluece o Charge Carriers ad electrical Parameters of Polycrystallie Silico Solar Cell. Research Joural of Applied Scieces, Egieerig ad Techology, 4, (17): 2967-2972. Zougraa, M., Zerbo, I., Ouédraogo, F., Zouma, B. ad Zougmoré, F., 212. 3D modellig of magetic field ad ligth cocetratio effects o a bifacial silico solar cell illumiated by its rear side. 212 IOP Cof. Ser.: Mater. Sci. Eg. 29 122
148 I. ZERBO, M. ZOUNGRANA, A. OUEDRAOGO, B. KORGO, B. ZOUMA AND D. J. BATHIEBO Zougraa, M., Zerbo, I., Sere, A., Zouma, B. ad Zougmoré, F., 211. 3D Study of Bifacial Silico Solar Cell Uder Itese Light Cocetratio ad Uder Exteral Costat Magetic Field: Effect of magetic field o carriers mobility ad carriers desity. Global Joural of Egieerig Research, 1, (1&2): 113-124.