how to understand spectral luminescence from thin film absorbers, absorber layer sequences and complete solar cells

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1 how to understand spectral luminescence from thin film absorbers, absorber layer sequences and complete solar cells G.H. Bauer Institute of Physics, Carl von Ossietzky University Oldenburg, D Oldenburg, F.R. Germany basics of steady state luminescence (Planck s generalized law) application to experimental results and requirements for evaluation o influence of temperature, spectral absorption, quasi-fermi levels o lateral inhomogeneous absorbers o carrier depth profiles and depth dependent parameters numerical modeling of spectral pl interpretation of results (including multilayer optics) with re-absorption of luminescence photons, excess carrier depth profiles, lateral inhomogeneities no summary

2 how to understand spectral luminescence from thin film absorbers, absorber layer sequences and complete solar cells method applied to a-si:h/c-si heterodiodes (-> optimization of interface) c-si absorbers (-> passivation) c-si reference absorbers in 3rd generation approaches polycrystalline semiconductors / diodes (CdTe, Cu(Ga,In)Se 2, Cu(Ga,In)S 2.. ) thin polycristalline injection diodes diodes of anorganic matrices with organic dyes

3 cross section of a Cu(In 0.7 Ga 0.3 )Se 2 thin film on Mo coated glass substrate ZnO CdS CIGS glass sketch by A.K., TU Darmstadt Mo SEM by ZSW Stuttgart

4 photoluminescence for determination of effects of manipulation of coupling solar light into absorbers up-conversion detector excitation (IR) up-convert. profile excitation (IR)

5 photoluminescence for determination of effects of manipulation of coupling solar light into absorbers α photonic stop-gaps excitation α detector angle dependence excitation detection pl emission pl emission detector excitation

6 photoluminescence for determination of effects of manipulation of coupling solar light into absorbers metallic nano particles IR excitation (ħω<e g ) E g detector

7 splitting of quasi-fermi levels (ε Fn - ε Fp ) via Planck s generalized law photon flux from matter Γ(ω) = ε(ω) ω 2 {exp [(ħω µ phot )/ kt ] 1} -1 T, µ phot dω ε(ω ) - spectral emissivity µ phot - chemical potential of the photon field Γ(ω) coupling of Bosons (µ phot ) and Fermions (µ n,p ) via rate equations of absorption and emission (spont. & stim.) in an electronic 2-level/band system µ phot = µ n,p = (ε Fn - ε Fp ) v oc (necessary condition in thermal non-equilibrium: τ intraband (momentum and energy relax.) < < τ interband (recomb.) (maximum entropy distribution function -> temperature) integration over entire volume of matter Γ(ω) dω including wave optics (propagation, scattering, absorption, reflexion, photon recycling,..)

8 steady state conditions and fast intraband relaxation solar photons reflect sun surface temperature 6000 K provide for hot carriers E = ħω E kt S fast relaxation of energy (τ e ) and wave vector (τ k ) absorption/ excitation slow relaxation to ground state (τ recomb ) solar photon flux Γ(ω) k τ e, τ k << τ recomb max. entropy distribution (T)

9 maximum achieavable chemical potential of electron hole-ensemble steady state balance of photon fluxes from sun (T sun ) absorbed by system at (T rec ) with chemical potential of electron hole ensemble µ n,p T S any excitation e.g. solar light absorption emission spont. stimul.

10 maximum achieavable chemical potential of electron hole-ensemble steady state balance of photon fluxes from sun (T sun ) absorbed by system at (T rec ) with chemical potential of electron hole ensemble µ n,p T S any excitation e.g. solar light absorption emission spont. stimul. non-radiative further decrease in excess carrier densities drop in chemical potential µ np (ε Fn ε Fp )

11 chemical potential of photon field and of electron hole-ensemble electrons/holes (fermions) photon field (bosons) ε 2 absorption ε 1 spont. & stimul. emission coupling of fermions with bosons by rate equations for transitions between ε 1 and ε 2

12 COUPLING of BOSONS (PHOTONS) and FERMIONS (ELECTRONS-HOLES) in an ELECTRONIC TWO-LEVEL/BAND SYSTEM o optical transitions ħω= ε 2 ε 1 = ε g absorption, stimulated & spontaneous emission B 12 n(ε 1 ) p(ε 2 ) u phot (ħω) 4π = B 21 n(ε 2 ) p(ε 1 ) u phot (ħω) 4π + A 21 n(ε 2 ) p(ε 1 ) (B 12 = B 21 ) o level occupation by Fermi-/quasi-Fermi-statistics: n(ε 2 ) = D(ε 2 ) f n* (ε 2 ) = D(ε 2 ) {exp[(ε 2 - ε Fn )/kt] +1} -1 (conduction band) p(ε 1 ) = D(ε 1 ) f p* (ε 1 ) = D(ε 1 ) {exp[ε Fp - ε 1 )/kt] +1} -1 (valence band) and via charge neutrality n(ε 1 ) = D(ε 1 )[1-f p* (ε 1 )] (valence band) p(ε 2 ) = D(ε 2 )[1-f n* (ε 2 )] (conduction band)

13 maximum achieavable chemical potential of electron hole-ensemble with rate equations µ phot = µ n,p Ω inc steady state balance: photon flux from sun (T sun ) absorbed by system at (T rec ) vs. photon flux emitted by system at (T rec ) with chemical potential µ n,p 2 2 Α( ω ) ω dω Ε( ω ) ω dω = Ω emiss ω µ 0 ω 0 n, p exp 1 exp 1 kt sun kt rec + rate + rate Α ( ω) =Ε( ω) luminescence non radiative _ recomb. carrier injection / extration access to actual chemical potential of electron hole ensemble (E Fn -E Fp )

14 messages included in the spectral pl-yield (Planck s generalized law) Γ(ω) = C α(ω) ω 2 {exp [(ħω µ phot )/ kt ] 1} -1 α(ω) = ε(ω) ; µ phot = µ n,p slope in log-plot kt amplitude chemical potential µ 1- exp[-αd] 1 (complete absorption) ~ αd (weak absorption)

15 chemical potential of the electron-hole-ensemble µ np via Bose-Term of Planck s Generalized Law Bose-term {exp[(ħω-µ phot )/kt]-1 } -1 steady state µ phot = µ np = (ε Fn ε Fp ) = v oc,max Log [Bose-term] (a.u.) µ phot photon energy [(ħω)/kt] slope represents kt

16 contribution to photon flux from many volume elements T, µ phot dω Γ i (ω) detector Γ tot (ω) by integration of over entire volume dω Γ tot (ω) = Γ i (ω) dω including wave optics (propagation, scattering, absorption, reflection, photon recycling,..) multilayer optics for the formulation of total photon flux to detector

17 formalization of luminescence photon propagation (plane wave approach) incoherent scattering / reflection at glass/air interface glass 2 mm CIGSe Γ rhs detector ( ) 0 z d r10 exp( 2 αz)exp[ i2 kz] + ( r10 ) exp( 4 αz) 12 α α Φrhs ( z) ΦB t exp( 2 ( d z)) 1 2 r r exp( 2 d )exp[ i 2 kd ] ( r r ) exp( 4 αd ) 1 ω µ Φ = Γ 4 kt 2 np, B εω ( ) phot ( z) ω exp[ ] ( t12t01) exp( 2 αd) ( r12 ) exp( 2 αd)exp[ ikd] 01 ( 10 ) exp(2 α ) α ( ) r t z ( ) ( r12 )2exp( 2 α( d z))exp( ik( d z)) + ( r12 ) exp( 4 α( d z))) 1+ 2( r r ) exp( 4 d) ( r r )2exp( ikd)exp( 2 αd) no photon recycling considered since in CIGSe (300 K) r non-rad >> r rad

18 calibrated room temperature photoluminescence at AM1-equivalent excitation from optimally passivated monoc-si and thin film Cu(In 0.7 Ga 0.3 )Se 2 excess carrier depth profile most flat V oc -equivalent Y PL (photons m -2 ev -1 s -1 sr -1 ) c-si 761 mev / 314 K CIGSe 648 mev / 336 K CIGSe- pl shows interference pattern photon enery E ph (ev)

comparison of experimental and calculated pl-yields 10 14 pl-yield (arb. un.

19 comparison of experimental and calculated pl-yields pl-yield (arb. un.) nd excess carrier depth profile almost flat (S 0 =S d = 10 4 cm/s) photon energy E ph (ev) nd nd nd

20 calibrated luminescence from CuInGaSe 2 with interference pattern interfrerence peaks with refractive index n = n(ħω)

21 laterally resolved photoluminescence from Cu(In 0.7 Ga 0.3 )Se 2 40 µm 40 µm yield of confocally recorded photo-luminescence of CuInGaSe 2 (L. Gütay et al., 2004)

22 spectral pl-yields and histogram of quasi-fermi level splitting from confocally recorded room temperature luminescence of Cu(In 0.7 Ga 0.3 )Se 2 absorbers local variation of E Fn -E Fp 18 mev

23 calibrated room temperature luminescence (AM1 equivalent excitation) versus confocally resolved luminescence 1 mm mev 1 µm mev

24 problems by averaging photon fluxes lateral pattern of photon fluxes with different chemical potentials avereging of photon individual fluxes Y pl,i extraction of quasi Fermi level splitting E Fn -E Fp ~ kt ln ( Y pl,i ) ) averaging of individual chemical potentials E Fn -E Fp ~ kt ln (Y pl,i ) )

25 problems by averaging photon fluxes lateral pattern of photon fluxes with different chemical potentials analyze distribution function (FWHM)

26 problems by averaging photon fluxes lateral pattern of photon fluxes with different chemical potentials δ = kt Ypl 0+ Ypl 0 Ypl 0+ ln (( Ypl) ( f ( Ypl )) dypl ln ( Ypl) f ( Ypl) dypl Ypl0 Ypl 0+ Ypl 0 ( ) ln[( Ypl) f ( Ypl ] dypl avereging of photon individual fluxes overestimation of (E Fn -E Fp ) by non-locally resolved experiments Y pl,i extraction of quasi Fermi level splitting E Fn -E Fp ~ kt ln( Y pl,i ) ) avereging of individual chemical potentials E Fn -E Fp ~ kt ln (Y pl,i ) )

27 problems by averaging photon fluxes lateral pattern of photon fluxes with different chemical potentials avereging of photon individual fluxes Y pl,i extraction of quasi Fermi level splitting E Fn -E Fp ~ kt ln( Y pl,i ) ) actual values for CIGSe avereging of individual chemical potentials E Fn -E Fp ~ kt ln (Y pl,i ) )

28 spectral absorption coefficient of Cu(In 0.7 Ga 0.3 )Se 2 extracted from laterally highly resolved (1 µm) white light transmission lateral pattern of white light transmitted A ( ) ( 1 exp[ ]) photons (variation of (αd)) average ω = α idi i 1 ln 1 ( ) d average absorption coefficient?? αaverage ( ω ) = ( Aaverage ω )

29 critical / inappropriate averaging of relevant magnitudes lateral pattern of white light transmitted photons (variation of (αd)) ( i( ω ) i ) < A( ω) >= A ( ω) = 1 exp[ α d ] average ( ) ( ( ) ) ln 1 < α ω d >= α ω d = average 1 1 exp ( ) i average absorption coefficient?? i [ αi ω d i] lateral pattern of photon fluxes with different chemical potentials average chemical potential < Y E E > kt ln Y Fn Fp pl, i i 2 ω, αω i( ) ω ( EFn EFp) exp 1 kt pl i

30 avoid inappropriate averaging of magnitudes that superimpose non-linearly

31 dependence of spectral luminescence signal on carrier depth profile excess carrier depth profiles for numerical calculation of pl signal at the detector excess carrier density (arb. un.) excitation from l.h.s. r.h.s. pl depth position x/d detector photoluminescence yield (arb. un.) excitation from l.h.s. r.h.s. Bose-Term kt photon energy ħω (ev)

32 numerical modelling for examination of influence of carrier depth profile on spectral pl d 0.05 d 0.1 d 0.2 d 2.5 d absorption lengths pl detector excess carrier depth profiles and according spectral pl-yields (plane wave approach)

33 excess carrier depth profiles and according spectral pl-yields (plane wave approach) pl detector excess carrier depth profiles and according spectral pl-yields (plane wave approach)

34 excess carrier depth profiles and according spectral pl-yields (plane wave approach) pl detector

35 carrier depth profiles and according spectral luminescence yields

36 determination of quasi-fermi level splitting excess carrier depth profiles (E Fn -E Fp ) calculated from carrier profiles versus (E Fn -E Fp ) from pl-evaluation maxima front surface for surface recombination velocities S 3x10 3 cm/s departure of (E Fn -E Fp ) by pl-evaluation from exact value < 1 mev

37 excess carrier depth profiles and according spectral pl-yields plane wave approach spherical wave approach confocal setup (?) / SNOM

38 interference pattern from luminescence (centers distributed across depth) and from spectral transmission

39 interference patterns from spectral luminescence versus those from spectral transmission pl emission centers

40 lateral, inhomogeneous with percolative transmission (low concentration of absorbing centers (dyes)) lateral distribution of absorption centers

41 NO summary calibrated spectral luminescence yields information on relevant parameters for quantum solar energy conversion (pv) (E Fn -E Fp ), α(ω), T don t mix magnitudes (luminescence, absorption, etc.) that superimpose non-linearly!! front side / light entrance = position of hetero junction, for decent front layer passivation (E Fn -E Fp ) e Voc; departure of high energy pl-photon fluxes from ideal Bose-behavior indicates by positive curvature shift of maximum carrier concentration deep in the absorber by negative curvature depth dependent optoelectronic properties of absorber (gradient in band gap, life time etc.)

42 luminescence as tool for analyses of quality of photo excited states in matter persons involved in pl-studies R. Brüggemann J. Behrends ( HMI) D. Berkhahn K. Bothe ( ISFH) S. Burdorf R. Fuhrmann H. Graaf ( TU Chemnitz) F. Heidemann L. Gütay ( Uni Luxb) M. Langenmeyer S. Knabe S. Meier M. Meesen M. Suhlmann P. Pargmann K.-Ch. Schersich S. Tardon ( Q-Cells) T. Unold ( HMI) F. Voigt S. Vignoli (UCB Lyon) S. Wilken R.B. Wehrspohn ( U/MPI Halle-Witt.) GHB thanx funds over the years BMBF BMU HBFG (DFG/ State Nds) VW PROCOPE / DAAD

Photonic Devices. Light absorption and emission. Transitions between discrete states

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