Simulations of the irradiation and temperature dependence of the efficiency of tandem photoelectrochemical water-splitting systems

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SUPPORTING INFORMATION FOR Simultions of the irrdition nd temperture dependence of the efficiency of tndem photoelectrochemicl wter-splitting systems Sophi Hussener, Shu Hu, Chengxing Xing, Adm Z.

1 SUPPORTING INFORMATION FOR Simultions of the irrdition nd temperture dependence of the efficiency of tndem photoelectrochemicl wter-splitting systems Sophi Hussener, Shu Hu, Chengxing Xing, Adm Z. Weber, nd Nthn S. Lewis Sptil nd temporl vrition in solr irrdition Figure S1 depicts the sptil, hourly nd sesonl vrition in solr irrdition. ) b) Figure S1. Annul men of hourly solr irrdition (), nd hourly resolved irrdition for four chrcteristic sesonl dys in Brstow, Cliforni (b). Mterils properties Tble S1 presents the properties of the mterils chosen for the system s well s their temperture dependence between 300 K nd 353 K. The increse in solution conductivity with temperture ws pproximted by l l, T =293K T, (S1) 1

2 where κ l,t=293k nd α were fitted to experimentl dt vilble for 1 M sulfuric cid 1. The temperture dependence of the conductivity of non-permeble polymeric membrne, i.e. Nfion, ws given by mem 0,mem exp E RT, (S2) where E represents the ctivtion energy 2. The decrese in the equilibrium potentil for the one-step wter-electrolysis rection with incresing temperture is given by U U T, (S3) 3 where U θ is the equilibrium potentil ssuming hydrogen reference electrode, nd α 3 is given by the temperture-dependence of the Gibbs free energy (ΔG=-nFU).The electrochemicl rections were described by Butler-Volmer expressions, i R,OER/HER red ox red,oer/her c F op c ox c,oer/her F op i0,oer/her exp exp, (S4) c red,0 RT c ox RT 0 with i i 0,OER/HER 0,OER/HER, T exp ref E RT. (S5) The kinetic prmeters used in the study re for stte-of-the-rt ctlysts, i.e. Pt-bsed electrodes for the HER rection nd RuO 2 -bsed electrodes for the OER rection. For the HER, trnsfer coefficients between 1 nd 2 hve been reported 3, nd vlues of α,her = α c,her = 1 were ssumed. For the OER, α,her = 1.7 nd α c,her = 0.1 were used, which is consistent with the reported 35 mv per decde Tfel slope 4 s well s n ssumed negligible bck rection t the potentil of interest. The temperture dependences were extrcted from vrious experimentl studies 5-8. The temperture-dependent conductivity of trnsprent conducting oxide (TCO) lyer ws given by 2

3 TCO A0 E exp R t kt, (S6) s,0 where R s is the sheet resistnce of the TCO mteril of thickness t, nd ΔE is the ctivtion energy in ev 9. The temperture dependence of the bnd gp ws described using the Vrshi model 10-12, E T 2 2 g E g,0 T (S7) with the constnts α 2 nd β fitted to experimentl dt for Si nd GAs 12. Tble S1. Prmeters used for the vrious mterils nd components in the system, s function of temperture. Prmeter Vlue Prm. Vlue Prm. Vlue Ref. i 0,OER,Tref 4.62 A cm -2 E,OER 48.6 kj mol i 0,HER,Tref A cm -2 E,HER 28.9 kj mol κ 0,mem S m -1 E,mem 2 kj mol κ l,t=293k 40 S m -1 α K R s,0 10 Ω/ A ΔE ev E g,0,si ev α 2,Si ev K -1 β Si 1108 K E g,0,gas ev α 2,GAs ev K -1 β GAs 572 K A H B H C H A O B O C O , 6, 13 7, 8 2, , 12 10, Tble S1 lso presents the set of prmeters used in this study. The supporting informtion shows detiled current-voltge behvior nd chrcteristics (i sc, V oc, FF) of dul- 3

4 bsorber tndem cells for hourly, sesonl, nd locl vritions in the solr irrdition nd for vrious isotherml system tempertures. The temperture-dependence of the sturtion concentrtions of H 2 (g) nd O 2 (g) were given by 2 c exp A B / ( T /100K) C ln( T /100K) / M 1000, (S8) st, k k k k in the units mol/m 3. H O Semiconductor performnce nd chrcteriztion Figure S2 depicts the chnge in current-voltge chrcteristics of dul-bsorber tndem cell (mde of 1.7/1.1 ev bndgp mterils) during typicl summer dy t Brstow. Figure S2. Current vs. voltge performnce nd its vrition during the dy of dul-bsorber tndem cell composed of 1.7/1.1 ev bndgp mterils for typicl July dy. Figure S3 depicts the short-circuit current density, open-circuit voltge, nd fill fctor (FF) of two chrcteristic types of dul-bsorber tndem cells, i.e. (i) current-mtched cell composed of 1.7/1.1 ev bnd gp mterils (i.e. GAsP/Si), nd (ii) non-current mtched 4

5 cell composed of 1.43/1.1 ev bnd gp mterils (i.e. GAs/Si). The short-circuit current density is proportionl to the solr irrdition. ) b) c) Figure S3. Vrition in short-circuit current density (), open-circuit potentil difference (b), nd form fctor (c), of the current mtching (1.7/1.1 ev) nd non-current mtching (1.43/1.1 ev) dul-cells during four typicl dys in winter, spring, summer, nd fll. Figure S4 depicts the short-circuit current density, open-circuit voltge, nd fill fctor (FF) of two dul-bsorber tndem cells, for vritions in the isotherml system temperture (between 300 K nd 353 K). The short-circuit current density decreses for dul-bsorber tndem cell 5

6 becuse the current-mtching bnd gp combintion evolves into less fvorble current combintion ( non-current mtching) s the temperture is chnged. The results re in ccord with reported dt 12. ) b) c) d) Figure S4. Temperture-dependent short-circuit current density (), open-circuit voltge (b), fill fctor (c), nd i-v-performnce for I=1kWm -2, for the dul cell composed of 1.43/1.1 ev bnd gps (t room temperture). An rtificil series resistnce within the semiconductor model ws used to more ccurtely ccount for non-idelities. Figure S5 depicts the current density vs. voltge performnce of dul-bsorber tndem cell. 6

Figure S6 depicts the chnges in short-circuit current density, open-circuit voltge, nd fill fctor for

voltge performnce nd its chnge with incresing series resistnce, i.e. decresing fill fctor, for 1.6/1.

The dotted line depicts the detiled blnce limit. ) b) c) Figure S6.

7 Figure S6 depicts the chnges in short-circuit current density, open-circuit voltge, nd fill fctor for vrious combintions of bnd gps t 1kW/m 2, 1.5 AM solr irrdition. Figure S5. Current density vs. voltge performnce nd its chnge with incresing series resistnce, i.e. decresing fill fctor, for 1.6/1.0 ev bnd gp dul-bsorber tndem cell for 1 sun nd 1.5 AM solr irrdition. The dotted line depicts the detiled blnce limit. ) b) c) Figure S6. () Short-circuit current density (ma/cm 2 ), (b) open-circuit voltge (V), nd (c) fill fctor for vrious combintions of top nd bottom bndgp energies t 1 kw/m 2, 1.5 AM solr irrdition. 7

8 Relistic dul bsorbed tndem cell The performnce of relistic dul bsorber tndem cell composed of currently vilble Si nd GAs cells hs lso been predicted vi the mesured performnce of individul single cells, s given in Tble S2. Tble S2. Mesured short-current density, open-circuit voltge, fill fctor, nd temperture coefficients of commercil GAs (Alt devices * ) or Si (Schott,16 ) solr cells. GAs cell Si cell i sc, ma cm ma cm -2 V oc, V V FF α bs % K % K -1 γ bs or β bs % K -1 2 mv K -1 The intensity dependence nd temperture dependence of the performnce cn be pproximted s: I isc isc,0 1 bs T 298, (S9) I sc sc,0 bs 0 V V 1 T 298, (S10) oc oc,0 bs 298 V V T, (S11) with the mesured temperture coefficients α bs, γ bs, nd β bs. The performnce of the tndem configurtion ws clculted by using the Si nd GAs cells in series, with the irrdition of the bottom cell (Si) reduced by the frction of light bsorbed by the top cell (GAs), s given by its temperture-dependent bnd gp energy clculted using eqution (S7). * 8

9 ) b) c) d) Figure S7. () η of conventionl stnd-lone PV system with Si/GAs dul bsorber tndem structure bsed on the mesured individul cell performnce, with the tndem cell electriclly connected to stnd-lone electrolyzer, for four typicl sesonl dys t three isotherml conditions (T = 300, 333, 353 K), nd (b,c) η of PEC device with Si/GAs dul bsorber tndem-cell bsed on mesured individul cell performnce for four typicl sesonl dys t three isotherml conditions (T = 300, 333, 353 K) for design B with η pc = 1, (b) l el = 50 mm, nd t e = 1 mm, nd (c) l el = 10 mm, nd t e = 10 mm, nd (d) the normlized nnully integrted fuel production for the conventionl system nd for the integrted system with m tot,h 2,T0 = 6.6, 5.9, nd 8.3 kg m -2 yer -1 for the PV+electrolyzer, the integrted system, nd the optimized integrted system, respectively, for detiled blnce limit (solid line) nd the relistic cse (dotted line). 9

10 The resulting performnce of the integrted system nd stnd-lone tndem PV plus stndlone electrolyzer system (electrolyzer efficiency of 75% nd DC-DC-converter efficiency of 85%) using Si/GAs-bsed dul bsorber tndem-cell bsed on mesured single cell performnce re depicted in Figure S7. As observed for systems tht were ssumed to operte in the Shockley-Quiesser limit, unlike the integrted solr fuels genertor system, the relistic stnd-lone PV plus stnd-lone electrolyzer system displyed its highest η during mid-dy nd its highest d t mid-yer. Increses in the temperture from 300 K to 353 K of the light bsorber components of the discrete system decresed of the stnd-lone system combintion from 11.2% to 8.7%, with slight increse in σ (from 0.24% to 0.27%). The integrted system for design B with η pc = 1, l el = 50 mm, nd t e = 1 mm, showed = 11.3% nd 6.4% for T = 300 K nd 353 K, respectively, with slight increse in σ (from 0.02% to 0.03%). Chnging the dimensions of the system to l el = 10 mm, nd t e = 10 mm resulted in n increse in to vlues of 14.3% nd 10.6% for T = 300 K nd 353 K, respectively, with decrese in σ (from 0.34% to 0.28%). Figure S7d shows the normlized, nnully integrted fuel production for the stnd-lone PV nd stnd-lone electrolyzer combintion, s well s for two cses of the integrted solr fuels genertor system: i) with l el = 50 mm nd t e = 1 mm nd lrge totl overpotentil, nd ii) the optimized cse for l el = 10 mm nd t e = 10 mm with smll, non-limiting totl overpotentil. The mss of H 2 produced nnully, m tot,h 2,T, ws 6.6, 5.9, nd 8.3 kg m -2 yer -1 0 for the stnd-lone PV nd stnd-lone electrolyzer combintion, the integrted system, nd the optimized integrted system, respectively t n bsorber operting temperture of 300 K in ll cses. 10

11 Integrted vs. stnd-lone PV plus stnd-lone electrolyzer system η, d,, σ, nd the yerly mount of fuel produced by n integrted solr fuels genertor system were compred to the behvior of system insted comprised of conventionl photovoltic (PV) module-bsed stnd-lone system coupled electriclly to stnd-lone electrolysis unit. The efficiency of the system comprised of the discrete components cn be described by eqution (11). An electrolyzer efficiency of 75% nd DC- DC-converter efficiency of 85% were used in the clcultions. Figure S8 shows the performnce of the stnd-lone PV system in combintion with the stnd-lone electrolyzer system. The dul bsorber tndem-cell of the PV system ws tken to consist of 1.0/1.6 ev bnd-gps t ll tempertures, which showed to led to the best tndem-cell PV performnce. Unlike the integrted solr fuels genertor system, the stndlone PV plus stnd-lone electrolyzer system displyed its highest η during mid-dy nd its highest d t mid-yer. Increses in the temperture, from 300 K to 353 K, of the light bsorber components of the discrete system decresed of the stnd-lone system combintion from 24.2% to 21.9%, with slight increse in σ (from 0.97% to 1.13%). The bnd-gp of the light bsorber usully decreses by to ev K nd therefore this stright-forwrd comprison neglects the penlty due to reduced current mtching, i.e. lower i sc, of such dul bsorber tndem-cell t higher tempertures. 11

12 ) b) c) Figure S8. () η of conventionl stnd-lone PV system with its optiml bnd-gp combintion for the dul bsorber tndem-cell (1.0/1.6 ev t ll tempertures), electriclly connected to stnd-lone electrolyzer, for four typicl sesonl dys t three isotherml conditions (T = 300, 333, 353 K), nd (b) the instntneous efficiency normlized by for the stnd-lone PV plus stnd-lone electrolyzer system compred to the instntneous efficiency of n integrted solr fuels genertor system with l el = 10 mm, t e = 10 mm, nd η pc = 1, t its optiml bnd-gp combintion (0.8/1.6 ev t ll tempertures) nd (c) the normlized nnully integrted fuel production for the conventionl system nd for the integrted system with m tot,h 2,T0 integrted system, respectively. = 14.0, nd 17.4 kg m -2 yer -1 for the PV+electrolyze nd 12

13 References 1 H. E. Drling, Journl of Chemicl & Engineering Dt, 1964, 9, Y. Sone, P. Ekdunge nd D. Simonsson, Journl of The Electrochemicl Society, 1996, 143, J. O. M. Bockris, I. A. Ammr nd A. K. M. S. Huq, The Journl of Physicl Chemistry, 1957, 61, G. Lodi, E. Sivieri, A. Bttisti nd S. Trstti, Journl of Applied Electrochemistry, 1978, 8, K. Kinoshit, Electrochemicl Oxygen Technology, John Wiley nd Sons, Inc.,, L. Kriksunov, L. Bunkov, S. Zbusov nd L. Krishtlik, Electrochimic Act, 1994, 39, N. M. Mrkovic, B. N. Grgur nd P. N. Ross, The Journl of Physicl Chemistry B, 1997, 101, W. Sheng, H. A. Gsteiger nd Y. Sho-Horn, Journl of The Electrochemicl Society, 2010, 157, B1529 B J. George nd C. Menon, Surfce nd Cotings Technology, 2000, 132, Y. Vrshni, Physic, 1967, 34, R. Pässler, physic sttus solidi (b), 2003, 236, P. Singh nd N. Rvindr, Solr Energy Mterils nd Solr Cells, 2012, 101, A. Dmjnovic, A. Dey nd J. O. Bockris, Journl of The Electrochemicl Society, 1966, 113, H. Ito, T. Med, A. Nkno nd H. Tkenk, Interntionl Journl of Hydrogen Energy, 2011, 36, W. Hynes, CRC Hndbook of Chemistry nd Physics, Tylor & Frncis, M. A. Green, K. Emery, Y. Hishikw, W. Wrt nd E. D. Dunlop, Progress in Photovoltics: Reserch nd Applictions, 2013, 21,

Simulations of the Irradiation and Temperature Dependence of the Efficiency of Tandem Photoelectrochemical Water-splitting Systems

Simulations of the Irradiation and Temperature Dependence of the Efficiency of Tandem Photoelectrochemical Water-splitting Systems Simultions of the Irrdition nd Temperture Dependence of the Efficiency of Tndem Photoelectrochemicl Wter-splitting Systems Sophi Hussener 1,, Shu Hu 2, Chengxing Xing 2 Adm Z. Weber 3, nd Nthn S. Lewis