Solar cells operation
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1 Solar cells operation photovoltaic effect light and dark V characteristics effect of intensity effect of temperature efficiency efficency losses reflection recombination carrier collection and quantum efficiency resistive losses 1
2 Generation and recombination of electron-hole pairs generation recombination Free electrons and holes are created either thermally or optically Optical generation: valence electron is excited to the conduction band leaving behind a hole after absorption of photon of energy hv>eg. Electron can combine with hole, e-h pair disappears giving away their energy to the lattice by emitting a photon. generation Electric field separates electron-hole pair preventing recombination 2
3 Photovoltaic effect in pn junction - e E c 1. absorption 2. thermalisation 3. diffusion 4. drift E F E g h + 1 o o o o -e o o o o o o o o o o o o + o o o o o o o p space-charge E v o o o o o o o o o o o o o o o o o o o o o o o o n important parameters: o band gap E g o doping level o absorption coefficient α o lifetime of carriers τ o diffusion length L d o mobility µ 3
4 Current-voltage characteristics under illumination J dark o -V in the dark J J oo o ev (exp 1) AkBT Ea exp k BT -V under illumination superposition principle: ill ill dark o ev exp 1 AkBT for pn junction A1 EaEg A ideality factor, 1<A<2 Ea activation energy depending on transport mechanism 4
5 η Efficiency mp P V in mp V P oc in FF maximum power mp V mp short circuit current: more absorbed photons - larger V oc open circuit voltage larger bandgap - higher V oc FF fill factor FF mp V V mp oc cu urrent dark voltage illuminated 5
6 Photogeneration and thermalisation Thermalisation, transmission and radiative recombination limit efficiency to 31% Queisser-Shockley limit 6
7 Maximum efficiency if: 7
8 Efficiency dependence on E g Maximum efficiency solar spectrum AM1,5 (1 kw/m 2 ) E g 1,4-1,5 ev E g 1,9 ev E g 1,4 ev irradian nce E g 0,95 ev wavelength (nm) max. possible efficiency for single junction (only radiative recombination, only thermalization losses, no other losses) 8
9 Maximum efficiency when Eg Voc when Eg η max : E g 1.5 ev 9
10 V oc Effect of light intensity Ak BT ln e o + 1 Ak BT ln e ~ Φ (photon flux) V oc ~ln Φ intensity o Effect of temperature V o V oc oc oo AkBT ln e Ea exp kbt AEa AkBT ln e e ~ const o oo for pn junction E a E g, A1, temperature 10
11 Resistive losses A] current [m R sh current [ma A] R s voltage [V] voltage [V] shunt resistance grains, edges, junction breakdown etc series resistance bulk absorber, contacts, electrical connections, etc 11
12 Effect of series and shunt resistance effect on fill factor: FFFF 0 (1-r s ), r s R s /(V oc / ) FFFF 0 (1-1/r sh ) r sh R sh /(V oc / ) effect on illuminated current-voltage characteristics: ill e(v R exp ) s o 1 AkBT + V R R sh s 12
13 Recombination losses contra collection real cell ideal cell Type of recombination bulk recombination surface recombination recombination at metal semi conductor contact Remedy high purity of bulk material surface passivation (SiN, SiO) heavy doping of the contact region (BSF) front surface recombination bulk recombination back surface recombination bulk recombination diffusion length of minority carriers L d front and back surface recombination surface recombination velocity of minority carriers S e, S h 13
14 Energy losses in the cell (1) thermalisation loss; (2) junction loss; (3) contact loss; (4) recombination loss. 14
15 Collection probability of photogenerated carriers W - thickness of the device; α(λ) - absorption coefficient; H 0 - number of photons at each wavelength generation rate collection probability depends on bulk and surface recombination 15
16 Quantum efficiency QE number of electrons per one incident photon deal case:qe1 external QE includes optical losses (reflection, transmission) internal QE includes only loss after absorption of a photon CdS/CdTe cell 16
17 Equations for solar cell operation distribution of electric field current transport -R n -R np continuity equations generation R n R p recombination bulk (Auger, radiative, SRH) and surface 17
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