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Solar cell physics Photovoltaic effect and cell principles Vítezslav Benda Dept. of Electrotechnology, Czech Technical University in Prague Technická 2, 166 27 Praha 6, Czech Republic, e-mail: [email protected] 1. Light absorption in materials and excess carrier generation Photon energy h = hc/ (h is the Planck constant) photon momentum 0 Light is absorbed in the material. (x) is the light intensity d dx = () is the absorption coefficient Absorption is due to interactions with material particles (electrons and nucleus). If particle energy before interaction was W1, after photon absorption is W1+ h • interactions with the lattice – low energy photons, results in an increase of temperature • interactions with free electrons - important when the carrier concentration is high, results also in temperature increase • interactions with bonded electrons- the incident light may generate some excess carriers (electron/hole pairs) Light intensity decreases with the distance x form the surface x ( x) 0 exp(x) 0 exp xL Φ0 = Φin (1 – R) R is the surface reflexivity xL 1 x=xL is the so-called absorption length Φ(xL) = 0.38 Φ0 xL 0 0 ( x)d x 0.68 ( x)dx Photovoltaic Quantum generator This process can be realised in different materials Semiconductors W n0 N c exp F kT Before interaction with photon (in thermodynamic equilibrium) Wg n0 p0 ni BT exp kT 2 photon Si 3 Wg N c N v exp kT bonded electron Si Si free electron Si Si Si hole After interaction with photons h > Wg Si Si Si n = n0 + Δn , p = p0 + Δp np > ni2 Δn, Δp excess carrier concentration (no thermodynamic equilibrium) (Δn = Δp, because electron-hole pairs are generated ) W W Excess carrier generation h Wg W2 Wc Wg Wv 1 h thermalisation Wc bandgap Wg Wv valence band Wc Wg W1 k conduction band 1 h 2 Wv k crystalline W Silicon 1 Wc Wg h 2 Wv k amorphous h (eV) (nm) Carrier generation with respect to solar spectrum dn G(; x) ( ) ( )(; x) dt gen ( ) ( ) 0 ( ) exp ( ) x Total generation 0 0 Gtot ( x) G(; x)d ( ) ( )(; x)d Efficiency of excess carrier generation by solar energy depens on the semiconductor band gap Suitable materials Silicon GaAs CuInSe2 amorphous SiGe CdTe/CdS Carrier recombination n dn dt rec τ is carrier lifetime r irradiative recombination A Auger recombination 1 C An N D2 1 t Ct N t recombination via loca1 centres Resulting carrier lifetime 1 1 r 1 Cr N 1 A 1 t Excess carrier concentration Diffusion current is connected with carrier concentration gradient J ndif qD n dn dx Dn = kTμn/q J pdif qD p dp dx Dp = kTμp/q Continuity equations p p 1 d Gp Jp t p q dx n n 1 d Gn Jn t n q dx usually τn = τp = τ In the dynamic equilibrium n 0 t d 2 p p G ( ; x) 2 2 Dp dx Lp d 2 n n G(; x) 2 2 Dn dx Ln Ln Dn electron diffusion length Lp D p hole diffusion length Excess carrier concentration can be found solving continuity equations under proper boundary conditions Electrical neutrality is in homogeneous semiconductor n p no potencial difference To separate excess carrier generated, an inhomogeneity with a strong internal electric field must be created WFn W WFp Photovoltaic effect and basic solar cell parameters Junction To obtain a potential difference that may be used as a source of electrical energy, an inhomogeneous structure with internal electric field is necessary. Suitable structures may be: • PN junction • heterojunction (contact of different materials). p-type Radiation n-type Wc Wg WF Wv Ln SCL Lp Principles of solar cell function In the illuminated area generated excess carriers diffuse towards the PN junction. The density JFV is created by carriers collected by the junction space charge region J PV ( ) J PVN ( ) J PVP ( ) J OPN ( ) xj • in the N-type region p J PVN ( ) q G ( )dx q 0 • in the P-type region xj J PVP ( ) q H x j d • in the PN junction space charge region G ( )dx q p 0 H xj dx J sr (0) n n d dx J sr ( H ) J OPN ( ) q x j d j G( )dx xj Illuminated PN junction: A supperposition of photo-generated current andPN junction (dark) I-V characteristic I I in dark VOC irradiation V V IPV illuminated ISC Solar cell I-V chacteristic and its importan points Vmp VOC Modelling I-V characteristics of a solar cell qV j J J 01 exp kT PN junction I-V characteristics D 1 Dp 1 J 01 ni2 q n L p L n p n0 n p0 J 02 Rs qVj 1 1 J 02 exp 2kT qni d sc Parallel resistance Rp I Series resistance RS Aill – illuminated cell area IPV D Rp V RL A - total cell area Output cell voltage V = Vj- RsI V Rs I V Rs I V Rs I I Aill J PV I 01 exp q 1 I 02 exp q 1 kT 2kT Rp Influence of parasitic resistances (Rs and Rp) I SC Aill J PV If Rp is high If Rs I SC Rs I SC Rs I SC I 01 exp q 1 I 02 exp q 1 kT 2 kT Rp V0 C 2 2kT I 02 I 02 4 I 01 ( I 02 I 01 Aill J PV ) ln q 2 I 01 VOC Aill J PV I PV I 01 I 02 V kT I PV ln q I 01 V Influence of temperature VOC (A) kT I PV ln q I 01 Wg kT I01 ~ ni 2 BT 3 exp Consequently I VOC 0 T For silicon cells the decrease of VOC is about 0.4%/K Rs increases with increasing temperature V(mV) Pm (W) Rp decreases with increasing temperature Both fill factor and efficiency decrease FF with temperature 0 0 T T At silicon cells 1 0.5% K-1 T temperature (°C) Organic semiconductors orbitales orbitales (a) S S S S S S BC S S S BV (b) BC S S S S + S S S S S BV Hoping mechanism : A1- + A2 -> A1 + e- + A2 -> A1 + A2- P & N materials and cells N N N N Cu N N O N N O N N N N Perylen pigment (n) Cu Phtalocyanin (p) h V - Technological advantages of OSCs : • Wet processing (Ink pad printing) • Soft cells • Large surfaces • Low cost • Molecular materials + + + + + Reflecting Electrode (Al) P type organic semiconductor N type organic semiconductor Transparent Conducting Oxyde Transparent Substrate Photochemical cells glass TCO coating Pt electrolyte dye on TiO2 nanocrystals TCO coating glass light Iodine/iodide redox system 3I- I3- + 2e- To maximise current density JPV it is necessary • maximise generation rate G • minimise losses losses recombination electrical • reflection • emitter region • series resistance • shadowing • base region • parallel resistance •not absorbed radiation • surface optical