Light is an electromagnetic wave

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David Toledo Lucero
hace 6 años
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1 Generación y recombinación. Absorción de la luz. Foto-generación

2 Light is an electromagnetic wave An electromagnetic wave is a traveling wave that has time-varying electric and magnetic Fields that are perpendicular to each other and the direction of propagation z.

3 Energy E / ev 3,0 2,5 2,2 2,05 1,7 UV IR Wavelength λ / nm 1 ev = 1, J 1 kt = 0,025 ev (T = 300 K) 1 nm = 10-9 m = 10 Å

4 Out-put of a solar cell The output of a solar cell (photocurrent) is determined by a balance between photogeneration, charge recombination and current generation.

5 Electrons and holes in intrinsic semiconductor

6 Generation and Recombination Generation: An electronic excitation event increasing the number of free carrier available to carry charge. Requires an input of energy provided by the vibrational energy of the lattice (phonons), light (photons) or the kinetic energy of another carrier. For solar cell, the most important generation is photogeneration, i.e. by the absorption of a photon. Recombination: An electronic relaxation event reducing the number of free carrier. Releases energy taken by the same mechanisms to those of generation. For every generation process there is an equivalent recombination process.

7 Light Absorption Para describir las propiedades ópticas de los sólidos se introduce el índice de refracción complejo: n * = n ik n(w): índice de refracción; k(w): coeficiente de extinción.

9 Ecuación de una onda electromagnética que se propaga en una substancia cuyo índice de refracción es n* en la dirección x: E = E o e ωn* x i ( ωt c ) E = E o e ωnxω k ω x i ( ωt ) c c e i)nos muestra una onda plana de frecuencia ω que se propaga con la velocidad c/n y cuya amplitud se amortigua exponencialmente a lo largo de la dirección de propagación. ii) Fase afectada por parte real de n*.

10 En la práctica se mide la intensidad I de la luz: I E 2 I e 2kωx c 2kω c ω = α I = I(0) e αxx α α: coeficiente de absorción. Probabilidad de la absorción de un fotón por una muestra de espesor unidad. α -1 puede considerarse como la longitud media del recorrido libre del fotón en la substancia (profundidad de penetración).

12 Absorción de la luz. La absorción de la fundamentalmente a la mecanismos siguientes: Intrínseca o fundamental. Excitónica. Por portadores de carga libre. Por impurezas. Fonónica. luz se acción debe de los

14 El espectro de absorción completo del sólido se compone de los espectros de absorción relacionados con la acción de los distintos mecanismos. = i α( λ) α λ ( ) i

15 Absorción intrínseca o fundamental

16 Optical absorption generates electron hole pairs. Energetic electrons must loose their excess energy to lattice vibrations until their average energy is (3/2)kT in the conduction band.

17 Absorción en semiconductores con band-gap directo.

The absorption coefficient α depends on the photon energy hυ and hence on the wavelength. Density of states increases from band edges and usually exhibits peaks and troughs.

18 The absorption coefficient α depends on the photon energy hυ and hence on the wavelength. Density of states increases from band edges and usually exhibits peaks and troughs. Generally α increases with the photon energy greater than Eg because more energetic photons can excite electrons from populated regions of the VB to numerous available states deep in the CB.

We also needed available CB states into which the electrons can be excited, otherwise the electrons cannot find empty states to fill.

19 g(e): number of states per unit energy per unit volume. We assume that the VB states are filled and that the CB states are empty (n<<n c ). The photon absorption process increases when there are more VB states available as more electrons can be excited. We also needed available CB states into which the electrons can be excited, otherwise the electrons cannot find empty states to fill. The probability of photon absorption depends on both the density of VB states and the density of CB states. For photons of energy hν A =E g, the absorption can only occur from E V to E C where the VB and CB densities of states are low and thus the absorption coefficient is small.

20 Esperamos algo así:

22 Coeficiente de absorción para semiconductores con band-gap directo. α( hν ) A( hν Eg 1/ ) 2 A=cte.=2x10 4 [cm -1.eV -1/2 ]

23 Absorción en semiconductores con band-gap indirecto.

25 Dependencia espectral del Dependencia espectral del α para para las transiciones indirectas. las transiciones indirectas. 2 ) ( ) ( Ω ± h E h B h g r r r ω ω α ) ( ) ( Ω ± h E h B h g ω ω α

26 Direct vs. indirect semiconductors The indirect bandgap of Si makes optical absorption inefficient due to the requirement of phonon emission/scattering with photons in order to conserve crystal momentum.

27 Photon flux. The photon flux is a quantity useful in solar cell calculations: it is defined as the number of photons crossing a unit area perpendicular to the light beam per second. If we let I(E) denote the intensity of the light in W/cm 2 then we have: I( E) = b( E) E = b( E) hc λ av Where b(e) is the number of photons carrying the energy.

28 Photon flux calculation

29 Photogeneration rate If we can assume that all photons are absorbed to generate free carriers, then the rate of carrier generation, per unit volume, at a depth x below the surface is given by: ω ω α ω g( h, x) = I( h, x) ( h, x) Where I is the photon flux at x. Notice that is the number and not the energy of photons which determines the photogeneration rate.

30 Photogeneration rate To relate g to incident flux we need to allow for reflection of photons at the surface and attenuation within the material. [ R ω ] α ω I ω e αx g( hω, x) = 1 ( h ) ( h ) ( h ) 0

31 Photogeneration rate The integral should be extended only over energies where photon absorption primarily results in free carrier generation. G( x) = hω g g( h ω, x) d( hω)

32 FIN

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