Iterative Optimization of Spatial Solar Cell: Performance and Technology

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1 Sold State Pheoea Vols (4) pp (4) Tas Tech Publcatos, Swtzelad oual do:1.48/ Ctato (to be seted by the publshe) Copyght by Tas Tech Publcatos Iteatve Optzato of Spatal Sola Cell: Pefoace ad Techology uas Ulbkas, Kaols Požela 1, ava Ulbke 1 1 Secoducto Physcs Isttute, A. Goštauto 11, LT 6 Vlus, Lthuaa Isttute of Lthuaa Scetfc Socety, A. Goštauto , LT 6 Vlus, Lthuaa Keywods: spatal sola cells, popetes of sola cells. Abstact. Cosdeg optzato of the techology ad poducto of Sola Cells a oveall goal s to lowe the poducto costs pe Watt though optzato of the paaetes of Sola Cell. The doat ateal up to ow fo the aoty of coecally poduced sola cells s cystalle slco (c-s). A lot of effots has bee udetake to cease the electcal effcecy of S based sola cells above % [3-5]. Ufotuately, effcecy poveets ae ofte eached oly wth the help of costly pocess steps ad as esult wthout possblty to use such poveets dustal poducts. Oe of the teds achevg hghe effcecy oocstalle S based Sola Cells s toducto of coplcated spatal stuctue o absobg suface of SC. Repots dcates expectatos of effceces as hgh as 4% laboatoy saples but wth sgfcat ase costs fo Spatal SC poducto (Fg. 1). It s clea that optzato of techologcal steps ad paaetes ust be cosdeed thkg about toducto of Spatal SC. Optzato the case of Spatal SC ust be povded by two steps: fst of all we eed to evaluate pact of spatal stuctue to physcal popetes of the SSC ad the ext step evaluate techologcal possbltes fo poducto of the SSC wth optzed physcal chaactestcs. Backgoud fo the Calculatos of the Sola Cell Photocuet Fg. 1. Exaples of Spatal Sola Cells. Let us cosde the Spatal Sola Cell (SSC) wth the followg cofguato (Fg. ). The photocuet geeated by the lght caes s collected at the segets 4, 5. The photocuet desty s: Fg.. Seget fo photocuet evaluato. The p- ucto segets 4, 5 wth Ohc cotacts ae the actve pat of SC. The seget s the p + -p uctos. d = q (1) d x whee x s the pepedcula to the p- ucto suface, q s the electo chage ad s electo dffuso coeffcet. The dstbuto of geeated by lght photoelectos s foud fo the electo cotuty All ghts eseved. No pat of cotets of ths pape ay be epoduced o tastted ay fo o by ay eas wthout the wtte pesso of TTP, (I: , Pesylvaa State Uvesty, Uvesty Pak, Uted States of Aeca-5/6/14,:45:8)

2 11 Self-Foato Theoy ad Applcatos Ttle of Publcato (to be seted by the publshe) equato the pesece of exteal geeato ate g ( x,, fo two desoal case d d x d + + G = d y L () whee L s the dffuso legth, G = g( x, /. To solve the Eq. () the Gee fucto was used. That fucto, whch satsfes the Eq. () at the pots x, y, s the Modfed Bessel fucto K [6], whee ( x x ) + ( y y ) L =. The bouday codtos ae: d =, at segets 4, 5; ad Sb =, at aothe segets, whee Sb s the suface d x ecobato ate at the segets. The electo cocetato at pots x, y s: ( x, y ) ( x, y ) ( x y ) = + (3) whee ad 1, ( y ) = g ( x, K d x d y, (4) L y x 1 1, ( ) x = y K L l, µ d l (5) whee l s the seget s legth. The ages of tegato cludes the eghbos cells utl K becoes eglgble. The weght facto µ the Eq. (5) s deteed fo the bouday L codtos: ( x, y ) = o ( x, y ) = 1( x, y ). (6) 5 µ K ( x, y ) dl + K ( x, y ) dl + K ( x, y ) dl + K( x, y ) dl +... = = 1 l l + ly l ly l + ly = G ( x, K ( x, y ) dxdy wth = 4,5. (7) y x The bouday codtos at the seget ae:

3 Sold State Pheoea Vols Ttle of Publcato (to be seted by the publshe) 3 d Sb x + d Sb d Sb = o x 1 + = + x dx dx 1 (8) dx whee x s the ut vecto ad x s the coodate pepedcula to the suface l. Ths gves 5 Sb x µ K ( x, y ) dl K( x, y ) dl K( x, y ) dl... µ K( x, y ) dl... = = 1 l l + ly l ly l Sb = x g( x, K ( x, y ) + K ( x, y ) dx dy wth =. (9) y x Hee dk K. (1) = dx x y The esolvg of the syste Eq. (7) ad Eq. (9) allows us to fd facto ( x, y ) (Eq. (5)) ad ( x, y ) (Eq. (4) at segets 4, 5). 1 The geeated by lght electos cuet though the p- ucto s equal to: µ ad, cosequetly, ( x, y ) = q lh wth =4,5 (11) dx x whee h s the thckess of the SC. The dak cuet though the p- ucto s: qv = exp 1lh wth =4,5 (1) 1 kt whee p = + 1 q. (13) N d Lp N ALN Hee N d ad N A s the cocetato of ozed doos ad acceptos, espectvely. It s assued that the equlbu cocetato -S laye = N d, ad cosequetly, p p = N A. Fo S at oo tepeatue p = c -3. The total cuet fo the p ucto of segets 4, 5 s =. (14) The axal value of the powe geeated by the SC P = I V (15) s uecally deteed fo the equato:

4 11 Self-Foato Theoy ad Applcatos 4 Ttle of Publcato (to be seted by the publshe) I qv = 1 exp lh at = 4, 5. (16) kt 1 The SC fll facto s FF I = (17) SC V V C whee shot cuet SC = ad C the sulght coveso to electcal powe s I V P V s ope ccut voltage at =. The sola cell effcecy of = (18) p whee P s desty of the cdet lght powe. The Ifluece of the SSC Stuctues o the SSC Effcecy Let us assued that testy of the electo geeato the SC s deteate as d( x) = Aexp dt x g( x) (19) whee s lght absopto coeffcet. Assug that P s fully absobed, the SC body s geeated P electos pe secod h! P h! lx = Ae x A dx = e lx x " A, ad P A =. () h! I Fg. 3 I(U) chaactestc fo SSC faget used fo sulato s peseted. It s close to theoetcal fo ()S SC ad t s clea that odel ca be used fo evaluato of chaactestcs of SSC. Fg. 3. I(U) chaactestc fo SSC faget used fo sulato. Optal paaetes: U =.59 V, I =.47 A.

5 Sold State Pheoea Vols Ttle of Publcato (to be seted by the publshe) 5 I few pctues below (Fgs. 4-6) ae peseted soe esults of SSC optzato ad depedeces of SSC effcecy o geoety of SSC. It ca be oted that SSC effcecy s flueced by soe geoetcal paaetes to lage degee whle t s alost sestve to the vaato of the othes. Theefoe t ca be stated that physcal popetes of the SSC wll stogly deped o poposed SSC stuctue ad geoety. As t s clea fo the fgues bellow toducto of spatal stuctue fo Sola Cells ca esult obtag cosdeably hghe pefoace chaactestcs. Fg. 4. epedeces of Spatal Sola Cell effcecy o thckess of seget d fo dffeet lght absopto coeffcet values: (1) =.5 1/µ, () =.1 1/µ, (3) =.5 1/µ. Othe paaetes: thckess = 3 µ, a = 1 µ, b = 6 µ, c = 1 µ, dffuso legth L = 1 µ, dffuso coeffcet = 5 c /s, ecobato ate S = µ/s, ecobato ate S_A = µ/s, photo eegy hv = 1.6 ev. Fg. 5. epedeces of Spatal Sola Cell effcecy o thckess of seget b fo dffeet values of seget a: (1) a = µ, () a = 1 µ, (3) a = 1µ. Othe paaetes: lght absopto coeffcet =.1 1/µ, thckess = 3 µ, c = 1 µ, d = 1 µ, dffuso legth L = 1 µ, dffuso coeffcet = 5 c /s, ecobato ate S = µ/s, ecobato ate S_A = µ/s, photo eegy hv = 1.6 ev. Fg. 6. epedeces of Spatal Sola Cell effcecy o thckess of seget d fo dffeet values of seget b: (1) b = 6 µ, () b = 1 µ. Othe paaetes: lght absopto coeffcet =.1 1/µ, thckess = 3 µ, a = 1 µ, c = 1 µ, dffuso legth L = 1 µ, dffuso coeffcet = 5 c /s, ecobato ate S = µ/s, ecobato ate S_A = µ/s, photo eegy hv = 1.6 ev.

6 114 Self-Foato Theoy ad Applcatos 6 Ttle of Publcato (to be seted by the publshe) Coclusos Wth ecet toducto of Spatal Sola Cell cocept as oe of pospectve ways to ase effcecy of Sola Cells poble of optzato of physcal popetes of Sola Cell a vew of geoetcal stuctue s becoe potat. I ths pape sulato esults of depedeces of SSC popetes takg to accout geoety of SSC ae peseted. Obtaed esults dcate coplcated behavo of effcecy of SSC wth the chage of geoetcal stuctue of SSC. Idcatos coceg ateal popetes sutable fo SSC poducto also ae peseted. It s clea fo peseted esults that optzato of SSC paaetes ae coplcated task volvg ot oly geoetcal but also ateal popetes as well. I addto t ust be oted that optzato of physcal popetes s oly fst step to the optzed SSC techology. I addto to the peseted hee esults, optzato of techologcal pocesses of SSC poducto ust be volved. Peseted hee odel fo sulato of SSC popetes based o self-foato techology applcato ca becoe useful tool fo optzg poposed stuctues of ovel SC ad also seachg ad pedctg ew SC stuctues. O the othe had the use of sulato fo optzato of SSC techology dustal applcatos ca lead to the sgfcat educto of costs of techology fo SSC developet. Refeeces [1] B. Hezel ad W. Hoffa: Poc. 3d Wold Cofeece o Photovoltac Eegy Coveso, Osaka, apa, 3. [] S. aušos: Self-Foato Mcoelectocs Vol. 14, Issue 3 (Cabdge Uvesty Pess, USA ), p [3] S. Noo Mohaad:. Appl. Phys. Vol. 61() (1987), p [4] M.. Che, C.-Y. Wu: Sold State Electo. Vol. 8, No. 8 (1985), p [5] F.. Bsschop, L.A. Vehoef ad W.C. Ske: IEEE T. Electo ev. Vol. 17, No. (199), p [6] E.W. Wesste: CRC Cocse Ecyclopeda of Matheatcs (Chapa & Hall, Lodo, New Yok 1999).

7 Self-Foato Theoy ad Applcatos 1.48/ Iteatve Optzato of Spatal Sola Cell: Pefoace ad Techology 1.48/ OI Refeeces [5] F.. Bsschop, L.A. Vehoef ad W.C. Ske: IEEE T. Electo ev. Vol. 17, No. (199), p do:1.119/