Perspectives with Hot Carrier solar cell

Transcription

1 In Se Cu AFP PHOTO Perspectives with Hot Carrier solar cell J.F. Guillemoles, G.J. Conibeer,, M.A. Green 24/09/2006, Nice IRDEP Institute of Research and Development of Energy from Photovoltaics UMR CNRS EDF ENSCP (7174)

2 Advanced concepts for solar energy conversion Photons BB 6000K Spectral sorting tandem, up/down conv. Optical materials Optimized Absorption Intermediate band, IPV, Impact ionisation Electronic materials Thermal Systems Hot carriers, thermoelectrics, thermo-ionics Thermal materials 2

3 Thermal approaches Thermoelectrics TE-enhanced PV Thermoionics Hot carriers device: the ultimate TE device? 3

4 Hot Carrier Cell concept Extract carriers before full thermalization Contact n T=T A Absorber T=T H Contact p T=T A Narrow width energy selective contacts V e E g E ds E qv E µ h = J. = J. dt kta kth e- selective energy layer h + selective energy layer (Ross & Nozik 1982; Würfel 1995) 4

5 Motivations Hot carrier cells Simple, 2-terminal device Close to highest efficiency potential AM 1.5 x % a Hot Carrier 65.7% b 86.4% a Tandem ( ) 68.2% a a MA Green, 2003; b Nozik, 82 Are eff. >50% practically achievable? Under which conditions? 5

6 Description Standard HCSC Energy conservation P abs =Q+P em (V i ) +I.(Eg+kT) P abs =Q+P em (V i ) +I. E Particle conservation (radiative limit) J abs =J em (V i ) + I J abs =J em (V i ) + I Boundary conditions (contact) V i = V e ( E- V i )/T i = ( E- V e )/T e Relaxation time approximation: quasi-thermal populations µ, µ H, T, T H 6

7 Current description in the radiative limit ( α ) J = e. Jabs 1+ J 2 2 E. de E. de Jabs = A. f. s + A. ( fem fs ). E E g E E g exp 1 exp 1 kts kta J em = A. f. em E g em 2 E de. E µ h exp 1 kth 7

8 Power exchange in the radiative limit dq J. E = Pabs Pem dt 3 3 E. de E. de Pabs = A. f. s + A. ( fem fs ). E E g E E g exp 1 exp 1 kts kta P em = A. f. em E g. 3 E de E µ h exp 1 kth 8

9 Ideal efficiencies (Q=0) E abs = P abs /J abs E em = P em /J em E is a critical parameter 1. E>E abs : Eg<E em (V) < E 2. E<E abs :Eg< E<E em (V) 3. E=E abs : E=E em (V) Eg I E E = E Eem qv E abs em. J abs 9

10 Extraction eff % E=E abs Eg=1 ev Full conc Delta E E E Eg 10

11 Challenges Carrier thermalization Can it be slow enough for work production? Carrier recombination What happens with non radiative recombination? Carrier extraction Can it be fast enough? Can thermalization be avoided there also? 11

12 Energy loss rate for hot carriers Holes cool faster, but electrons get most of the energy Energy loss by zone center LO phonons (0.1 ps) Build-up of a hot phonon population that slows cooling Hot LO decay via LO-> LA+LA or LO->TO+LA Intervalley Energy Loss acoustic rate (ev/s) quasi elastic e to Acoustic h to Acoustic 3 x LO TO e to Optical h to Optical carrier temperature (K) 1 Deformation potential calculations x

13 Evidence in literature Multiple QW also show reduced cooling InN - some evidence for reduced cooling; Chen & Cartwright, APL 83 ( 03) 4984 Characteristic relaxation time (ps) Injection level Bulk GaAs 1x10 19 cm -3 5x10 18 cm -3 2x10 18 cm -3 InN: 5x10 18 (indirect comparison) GaAs MQW Re-calc. from (Rosenwaks, Phys Rev B, 48 (1993) 14675) Similar data in: Westland et al. SSE, 31 (1988) 431; Snow et al. S/lattices & M/structures, 5 (1989) 595. Carrier temperature, shifted from room temp 13 data (T-300K)

14 Hot carrier cooling in III-V LO phonon generation and decay limit thermalization Q~ n e.e p /τ eff 1E+17 1E+16 Calculated from Rosenwaks 1/Q=1/ Q gen +1/ Q decay Q gen ~ n e.e p /τ LO Q (W/m3) 1E+15 1E+14 1E+13 1E K GaAs lattice Th (K) MQW 5e18 MQW 1e19 BLK 2e18 Blk 5e18 blk 1e19 14 Q decay ~n p.e p /τ LA Carriers at 600K: Bulk: Q decay ~10 16 W/m 3 MQW: Q decay ~10 14 W/m 3

15 Carrier Thermalization in HCSC P inc = W/m² Q gen. ~ (E abs -E g )J abs Q decay > W/m 3 efficiency loss Th=600K Eg=1eV Efficiency loss ~ V/S.Q decay /P inc E Concentration Small generation volume (V/S ~ m) Vanishing efficiency loss with injection level 15

16 Non Ideal computed efficiencies Eg=1 ev Full conc. 60 eff % ? MQW range Relative thermalisation rate 16

17 Concentration ratio Eg=1eV Qr=0.1 E opt > 50% at x2500 eff % SJ Better than ideal single junction (SJ) at x Qr=1 Optimize E concentration ratio 17

18 Non Radiative recombination 75 99% NR with eff. >50% Qr=0 Eg=1 ev x46200 Sensitivity similar to SJ eff % E opt 45 E =Eabs Qr= NR recombination ratio 18

19 Perspectives Phonon dispersion LO TO LA TA L, X Γ L, X Q decay ~n p.e p /τ LA Phononic engineering Increase τ LA Phonon energy (ev) q (1/m) x 10 9

20 DOS for quantum dot array Mini-gaps in all directions DOS - complete gaps energy [ev] ??? Wave vector x DOS 3 4 May also enhance effect, but only for resonant structure 20

21 Interface mismatch Soft Matched x 10 9 Phonon energy (ev) Wavevector (1/m) x 10 9 Gaps can be strongly affected by interface bonds 21

22 Contact width Entropy current/level Excess heat current Efficiency correction E µ H E qv. ds J. = J. = kt kt dt J = Q H J. δ 2.1 δ η = η 0 2V m mu_h T_h E δ/2 E. t h Assumption δ<<kt => max current/contact level < 1µA 22

23 Summary and outlook Thermalization in state of the art nanostructures compatible with efficiencies >50% at x2500 Phononic gaps engineering for lower injection levels Contacts? E~E abs, but optimization needed Width below kt 23

24 Thanks UNSW & EDF support ANR for financial support PhD and Post Doc applications welcome 24

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26 Models Standard diode Hot carrier with Impact ionisation Hot carrier 1-Energy conservation Pabs = Q + Pem (Vi) + I.(Eg+kTA) (not used) Pabs =Q+Pem(T H ) +I. E Q=Q(T H )>0 Pabs=Q+Pem(Vi,T H )+I. E Q=Q(T H )>0 2-Particle conservation 3-Boundary condition Jabs =Jem(Vi) + I Jabs =Jem(T H ) + I Jabs =Jem(Vi,T H ) + I Vi = Ve E/TH = ( E- Ve)/TA ( E-Vi)/TH=( E- Ve)/TA 26

27 Restricting available LA modes Phonon dispersion E LO TO LA TA k L Γ X InN dispersion [Davydov et al, Phys Lett, 75 (1999) 3297] E LO,TO > 2E LA 2LA emission forbidden 27