Design and simulation of broadband multi-layered reflection diffraction grating for using in the silicon solar cells

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1 98 K N Toosi Uiversity of Techology Faculty of Electrical Egieerig Ceter of Excellece i Computatio ad Characterizatio of Devices ad Susystems The Secod Iraia Coferece o Egieerig Electromagetics (ICEEM 4), Ja 8-9, 4 Dowloaded from isseemir at : +33 o Suday Novemer 4th 8 Desig ad simulatio of roadad multi-layered reflectio diffractio gratig for usig i the silico solar cells Sh Mohammadejad, M Dehdast *, ad A Salmapour Naoptroics Research Ceter, School of Electrical ad Electroics Egieerig, Ira Uiversity of Sciece ad Techology (IUST), Tehra, Ira * Correspodig author: mahyardehdast@eleciustacir ABSTRACT I this paper, we have performed mathematical aalysis of diffractio gratig To prove diffractio, we have used Fourier method that used for the aalysis of periodic structures The some simulatios have performed for differet value of desig parameters The results showed that this diffractio gratig create a excellet reflectio at a roadad whe it has ee used as the ack layer i a silico solar cell Furthermore, to have the est diffractive structure, we have scaed reflectace accordig to the gratig parameters The results of simulatio show, whe we cosider optimal value for desig parameter ( λ, d), the maximum reflectivity of aout 97% is otaied for the structure KEYWORDS: roadad, diffractio gratig, reflectio, solar cell I INTRODUCTION Diffractio gratigs have played importat roles i the kowledge of optics ad photoics at the atomic ad molecular scale ad large scale Applicatios of these istrumets i sciece ad techology have greatly icreased Amog the ew applicatios, a large part lies o the extraordiary scatterig properties, the so-called diffractio The desire to use ad cotrol photos i a maer aalogous to the cotrol of electros i solids has ispired great iterest i such topics as the localizatio of light, ad light trappig[] Diffractio gratigs geerally have strog variatios of gratig efficiecies or gratig reflectios, geerated y small variatios of icidece or wavelegth[] Reflectio pheomea have led to very iterestig practical applicatios Diffractio gratigs studied i this paper, is similar to what is see i distriuted Bragg reflector(dbr)[3],[4] So, it is a good reflector for waves that are i the desired frequecy ad These coditios have led to strog local ehacemets of the field o the gratig surface O the other had, widead reflectio ca e applied for makig excellet reflector for efficiet photovoltaic cells The commo approach to the desig of a gratig compoet is to use dielectric materials We have employed a ew structure to exploit total iteral reflectio from dielectric iterfaces Cosiderig the maturity of NANO Photoics, various kids of advaced light trappig techiques may e cosidered to achieve this goal[5],[6] I particular, diffractio gratigs preset a great potetial i this field as they ca e used either as advaced ack reflectors to icrease oth the path legth ad the 63 This paper is authetic if it ca e foud i wwwisseemir

2 Dowloaded from isseemir at : +33 o Suday Novemer 4th 8 spectral desity of optical modes at log wavelegths[7] Such gratigs ca e pattered o trasparet ad coductive oxides(tco) For the calculatio of the reflectio ad diffractio waves, we used the Fourier aalysis I this aalysis, it has ee used terms of wave propagatio i dielectric materials that is a result of Maxwell's equatios II THEORETICAL ANALYSIS OF DIFFRACTION STRUCTURES I this sectio, first; we discuss aout the heuristic idea ehid the desig ad the use Fourier aalysis This aalysis also defies the desig Fially, we cosider some gratig profile First we cosider the vacuum space aove the diffractio gratig The electromagetic wave is radiated from this space to gratig profile Electric field y solvig Maxwell's equatios y Fourier aalysis is as Eq () [8]: + jα (x,y) (y)e x E = E () = I Eq () α is the wave umer alog the x- axis ad E (y) is the Fourier coefficiets of field alog the y-axis The value of α is give y Eq (): α π = k siθ + () d Where k = π λ ad θ is agle of icidet light with y-axis d Is period of gratig Fig shows the geeral form of diffractio gratigs If we put E (x, y) i Helmholtz equatio the we arrive to the Eq (3) [8]: + d E (y) jαx + β (y) e E = = dy (3) Where β is equal to β wave umer alog the y-axis = k α It is the Fig Geeral form of diffractio gratigs with d period ad with aritrary material for ody of gratig [] If we sustitute zero i rackets the we will get a secod order differetial equatio This equatio expresses the E (y) Solutio of this differetial equatio is give y Eq (4): j β y jβ y E (y) = I e + R e (4) Where I ad R are icidet ad reflectio coefficiets of diffractio gratig respectively With isertig Eq (4) i Eq () the electrical field ca e achieved as follows: + + ( α β ) ( α + β ) j x y j x y E(x, y) = I e + R e = = (5) Part () ad () imply the compoet of icidet ad reflectio light respectively We wish to have o-damped icidet waves Thus, icidet waves should ot peetrate to the ody of gratig As a result, the value of β must e real ad oly there was exist β for icidet waves Thus, the electrical field ca e achieved as follows: + j x y j x y = + = ( α β ) ( α + β ) E(x,y) I e R e (6) Eq () states that oe compoet of the icidet wave y a diffractio gratig is coverted ito several reflectivity compoets 63

3 Dowloaded from isseemir at : +33 o Suday Novemer 4th 8 I Fig θ is the agle of diffracted th Value of θ is calculated as follows: λ θ = arcsi siθ + d Where for ormal icidet: We have: si ( θ = ) = III DESIGN, SIMULATION AND DISCUSSION eam that is (7) For the aalysis of gratig properties, a electric field formulatio ca e used for the trasverse electric (TE) polarizatio [9] I this research, we have developed a ew diffractio gratig that its Output reflectio is similar to Bragg reflector [], [] I other words, it has the cetral wavelegth ad stop ad adwidth I the first stage, we simulated our scheme the for improvig our structure, desig parameters are scaed Our proposed structure, show i Fig (a) ad () Fig (a) is a cross-sectioal view of our desig ad Fig () is a three-dimesioal of it Values t ad t, show the thickess of the gratig layers t Ad t ca e calculated from Eq (8) ad Eq (9) By simulatig the structure i Fig, we have calculated the reflectio respose that show i Fig 3 t t λ = (8) 4 λ = (9) 4 Where = 46 ad = 35 are refractive idexes of the materials that we have used them ( : SiO, : Si) λ : Bragg wavelegth ad layers thickess set y it For the simulatio, the iitial values of λ ad d have ee regarded 65m ad 5m respectively (a) () Fig (a) Cross sectio of our desiged diffractio gratigs with d period () Three-dimesioal of our diffractio gratigs that is periodic with d Fig 3 Reflectio respose of our diffractio gratigs with λ = 65m ad d = 5m Sulight comprises wavelegths of 3 micros to 3 micros However, silico solar cells ca oly asor the wavelegths lower tha m Our diffractio gratig has the role of ack reflector i silico solar cell Therefore this diffractio gratig should e ale to reflect the wavelegths lower tha m I order to achieve the est reflectio respose, we have scaed the effective parameters i our structure By scaig the d, we otai the optimum value for the period From λ, we use to the thickess of t ad t If we chage d from µ m to 6 µ m the 633

4 reflectio respose will e i Fig 4 The est aswer is related to the value of d = 85µ m that has excellet adwidth with suitale gai Dowloaded from isseemir at : +33 o Suday Novemer 4th 8 Fig 4 Reflectio of diffractio gratigs for differet values of d i the rage of to 6 micros If we cosider the chages to values less tha d = µ m the reflectio respose of the structure will e as Fig 5 There are overlaps i the output The secod parameter is λ that we cosider chages i the rage of 6 m to m By simulatig, we achieve the output show i Fig 6 Accordig to the graphs i Fig 6, the optimal value of λ is equal to 8 m Fig 6 Reflectio respose for values of λ from 6 m to m So y choosig the optimal values for the period of diffractio gratig ad the Bragg wavelegth, we achieve the est possile output for our desig These values are d = 85m ad λ = 8m Accordig to the parameter λ, values thickess, equal to t 37m ad t 57m The fial outputs with values otaied are show i Fig 7 So we desiged the structure which has excellet roadad reflectio ad is very coveiet for usig i a silico solar cells as ack reflector layer [],[3] Fig 5 Reflectio respose for values of d i the rage of m to m All outputs overlap Fig 7 Reflectio respose of diffractio gratigs with Optimized values of λ = 8m ad d = 85m 634

5 Dowloaded from isseemir at : +33 o Suday Novemer 4th 8 IV CONCLUSION I preset ivestigatio, we have desiged a ew diffractio gratig which is composed of several layers Furthermore, we have optimized proposed gratig As a result, we have icreased the stop-ad width I the log ru, the est value for desig parameters are selected These values are d = 85m ad λ = 8m Usig these optimal values, the maximum reflectivity of aout 97% is otaied for the structure The structure is desiged i a adwidth of 5 m, has a reflectivity of more tha 8% (maximum 97%) REFERENCES [] L Martí-Moreo, F J García-Vidal, H J Lezec, K M Pelleri, T Thio, J B Pedry, ad T W Eese, Theory of extraordiary optical trasmissio through suwavelegth hole arrays, Phys Rev Lett, vol 86, o 6, pp 4 7, Fe [] D Maystre, Comptes Redus Physique Diffractio gratigs : A amazig pheomeo Réseaux de diffractio : U curieux phéomèe, Comptes Redus Phys, vol 4, o 4, pp 38 39, 3 [3] K-H Yag ad J-Y Yag, The aalysis of light trappig ad iteral quatum efficiecy of a solar cell with gratig structure, Sol Eergy, vol 85, o 3, pp 49 43, Mar [4] O Isaella, S Dorovolskiy, G Kroo, ad M Zema, Desig ad applicatio of dielectric distriuted Bragg ack reflector i thi-film silico solar cells, J No Cryst Solids, vol 358, o 7, pp 95 98, Sep [5] M Peters, J C Goldschmidt, T Kirchartz, ad B Bläsi, The photoic light trap Improved light trappig i solar cells y agularly selective filters, Sol Eergy Mater Sol Cells, vol 93, o, pp 7 77, Oct 9 [6] O El Daif, E Drouard, G Gomard, A Kamiski, A Fave, M Lemiti, S Ah, S Kim, P Roca I Caarrocas, H Jeo, ad C Seassal, Asorig oedimesioal plaar photoic crystal for amorphous silico solar cell, Opt Express, vol 8 Suppl 3, o Septemer, pp A93 9, Sep [7] X Meg, E Drouard, G Gomard, R Peretti, A Fave, ad C Seassal, Comied frot ad ack diffractio gratigs for road ad light trappig i thi film solar cell, Opt Express, vol Suppl 5, o May, pp A56 7, Sep [8] T Atoakakis, F Baida, ad A Belkhir, Gratigs: Theory ad Numeric Applicatios, [9] K Dossou, M Packirisamy, ad M Fotaie, Aalysis of diffractio gratigs y usig a edge elemet method, JOSA A, vol, o, pp 78 88, 5 [] O Mitrofaov, S Schmult, M J Mafra, T Siegrist, N G Weima, a M Serget, ad R J Molar, Highreflectivity ultraviolet AlGaN AlGaN distriuted Bragg reflectors, Appl Phys Lett, vol 88, o 7, p 7, 6 [] X Sheg, L Z Broderick, ad L C Kimerlig, Photoic crystal structures for light trappig i thi-film Si solar cells: Modelig, process ad optimizatios, Opt Commu, pp 7, Aug 3 [] R Biswas, J Bhattacharya, B Lewis, N Chakravarty, ad V Dalal, Ehaced aocrystallie silico solar cell with a photoic crystal ack-reflector, Sol Eergy Mater Sol Cells, vol 94, o, pp , Dec [3] W Zhag, G-G Zheg, ad X-Y Li, Desig of light trappig structures for light-asorptio ehacemet i thi film solar cells, Opt - It J Light Electro Opt, vol 4, o 6, pp , Aug 3 635