Winter College on Optics and Energy February Photophysics for photovoltaics. G. Lanzani CNST of Milano Italy

Transcription

1 13-4 Winter College on Optics and Energy 8-19 February 010 Photophysics for photovoltaics G. Lanzani CNST of Milano Italy

2 Winter College on Optics and Energy Guglielmo Lanzani CNST of Milan Italy The Abdus Salam International Centre for Theoretical Physics Trieste, Italy

3 Safe, Cheap(?) Nuclear Energy movie Core (15 million K), Photosphere (visible surface, 5800 K)

4 Is it enough?

5 The sun as a black body J eω σt 4 /π (W/Sr m ) ρ E I e σt 4 A (W) total power emitted J eω (ρ E /4π) xc (W/Sr m )

6 Thermodynamic limit I sun σ 4 T π Ω L A I em Ω L σ 4 T π A A Ω L A T T T 0 S A 300 K 5800 K 478K η abs η TL I η sun I abs I sun η C em 1 T T 4 A 4 S η 4 T A T TS T A C 1 T 0 T 85 % A

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8 The PV lay out Light Harvesting Light Absorption Charge Generation Charge Transport Charge Collection Electrical Work

9 Absorption The electro magnetic field interacting with a material can deposit energy at the characteristic frequency which defines the absorption spectrum. E P power volume E y dpy ( t) 1 ( t) Re P dt [ * E( iω ) ] time - average ~ A y ( t ) Re [ i ω A ( t ) e t ] y

10 PP(E) ) ( ) ( ) ( (1) 0 (1) ω ω χ ε ω E P (3) () (1) P P P P ) ( Im ) ( Re ) ( (1) (1) (1) ω χ ω χ ω χ i (1) 0 Im 1 E volume power χ ωε

11 The Lambert-Beer approximation I t I 0 e α ( ω) z T I t I o A log10 T di dz power dissipated unit volume 1 ωε0 Im χ (1) E I ε ε 0 cε n E n α ω Im χ ( 1) σ ( ω) ΔN cn Cross-section POPULATION

12 The concept of cross-section [σ]cm F number of photons per unit area and unit time N number of target per unit volume σn effective total area per unit volume [L -1 ] σnf number of transition per unit time, i.e. transition rate movie

13 Absorption and population j α ij ( ω ) σ ( ω )( N N ij i j ) i α σ (ω)( N i, j ij i N j )

14 Cross-section for the two level model ( ) ω μ σ ω g( ω ) c ε n 0 T 1 T 1 g( ω) Δω T ( ω ω ) 0 Δω Δω + ~ 1 1 μ μ μ * 1

15 Optical Bloch Equation Δn N e N g P T 1 T Nμge g e Δn t + Δn Δn T 1 0 E ω P t P P ω μ + + ω P t T t 3 ΔnE

16 Impulsive response function of the material T 1 T g e G eg i ϑ( t) exp ω eg T ( i t t / ) G ee i ϑ( t)exp T ( t / ) 1 P(t) ΔN(t)

17 Adibatic Approximation and Frank-Condon Overlap m e /M N << 1 or ΔΕ e /ΔE N >> 1 Ψ ψ ( q, Q) φ( Q) ~ μ ψ ( q, Q) φ ( Q) μ ( q) ψ ( q, Q) φ ( Q ) e en eg g gl Electronic contribution ψ ( q, Q) μ e eg ( q) ψ ( q, Q) g ~ ' μ + μ Q eg eg +... Condon approximation: α ψ ( q, Q) μ ( q) ψ ( q, Q) φ ( Q) φ ( Q) e eg g en gl α ~ μ ω eg ( ω ) FC ( n, l) g en / gl

18 I S FC: Displaced Harmonic Oscillators (T0) ~ μ e S S n! g( ω ω n0 eg en/ g 0 Δ Δ n FC m ω 1 / δq ) I 01 I 00 S Δ 1.4 e e1 e0 g g1 g0 Δ Q

19 Molecular absorption cross-section Adiabatic approximation Dipole allowed transition Condon approximation σ A ω c μ φ φ Γ 0 f i B 1 i ε π ω 0 i Ψ ψ ( q, Q) φ( Q) μ ψ ˆ μ ψ e g 0 μ ( Q) μ0 f ( E E ) F i + Γ B i Boltzman factor

20 Jablonski diagram unimolecular photophysical processes A IC ISC S T S 1 A IC Internal Conversion ISC Inter System Crossing VR Vibrational Relaxation A F A P T 1 A Absorption F Fluorescence S 0 P Phosphorescence

21 Dynamics comes in For a given process i a monomolecular rate k i is defined, k i 1/τ i (s -1 ) The total rate is k k0 + T k i i, efficiency η i k k i T k VR s -1 k IC s -1 (S n S 1 ) k IC s -1 (S 1 S 0 ) k ST s -1 (S 1 T 1 ) k TS s -1 (T 1 S 0 )

22 CHARGE PHOTO GENERATION (CPG)

23 Band-like semiconductor: CPG K e E K h K e K h K + K h e 0 K E + E hυ > e h E g

24 Charge photo-generation η n. ( e h) n. photons CB-VB Xtal, Inorganic η 1 hν + h e Localized state Amorphous, Organic η Φ Ω << 1 0 Φ hν S 0 Ω nd (E,T) + n CT -

25 The multi-step process: (1) Abs () AI (3) Thermalization (4) Dissociation Vac 0 0 ()+(3) r th Δr Δr S X (1) (4) CB S n E g S 1 E CT S 0

26 Auto Ionization S n k AI + - k n S 1 Inorganic Amorphous Semicond Φ 0 1 Organic Semicond Φ 0 <<1 Φ 0 k AI k AI + k n

27 Critical Parameters ΔΕ hν E CT Excess energy r τ th th Dτ th Thermalization distance ΔΕ D r hν th hν p p ΔΕ Activation Energy: Ε A e 4πε r th Coulomb radius: r C e 4πε KT

28 ONSAGER model Random Walk under mutual Coulomb attraction and External field n( r, t) kt μ ( U KT ( U KT ) e ne t e U e ( r) eer 4πεr cos ϑ n density of diffusing particles Boundary condition: r0 is a sink (RECOMBINATION) n(r,0) g(r th ) Initial condition

29 3D ONSAGER solution η Φ 0 Ω 3 / Ω D r r e r E th e 1 + c KT! Ωescape probability +... Weak Field: Ω 3D A T r / th ( ) e r Ω0 Strong Field: Ω 3D E 1 E

30 Onsager behavior r th r th (hν): r th < r C Ω 3D Ω 3D (F) r th > r C Ω 3D ~ 1 Dimensionality Ω 1D erthe r KT C e r / rth E Ω 1 3D 1D E

31 r m ΔΕ 0 Poole-Frenkel model Thermal activation above Coulomb barrier e εe e 3 E πε E E CT U(r) r m ΔE0 r E K b PF E CT ΔE E βf 0 CT 1 E β PF CT F PF ν exp( )exp( ) KPF + KGPR KT KT 1 Ω K

32 How to measure η(e,t,hν) 1) Photoconductivity I PC AΦ ΩE 0 Photon Fluence Low impedance current detector ) Pump-probe 3) m-wave/thz A Electrode width ew 4) Field assisted PL quenching μτ I ν mobility ( D ) 1 e α ( ν ) Carrier lifetime

33 Action spectra α PC Energy In organics the optical gap and the electrical gap are different

34 Organic Photoconductors: when α(ω)pc(ω) S X S n K F 1 1 θ 1 β cosθ K E d O KFdΩθ K O e 1 Field (Thermal) Assisted Tunneling K F K 0 senh(β E) βe ( cosθ ) S 1 S 0 K 1 K F Ω PF + Ω 1 CT 1 Ω 1 -Ω PF - Z.D. Popovic Chem. Phys. 86, 311(1984)

35 Comparison Field assisted Field assisted

36 Zero Field? S 1 K CT Ω E + - S 1 S 1 - CT S 0 + S 0 Disorder induced charge separation (H. Baessler)

37 r D e - ν exp The Marcus model A ( E K T ) λ Reorganization Energy a B Energy D / A λ + D / A E A E a ( ε ) λ 4λ ε Reaction path ε (ev) movie

38 A bright evidence for the inverted region R Safety light * P * P P Reaction path The phenomenon is an example of chemiluminescence. Safety lights of this kind, which are non-flammable and waterproof are used by seamen and divers in emergency.

39 Examples of Charge Transfer reactions

40 To be continued.