Complete Report - University of New South Wales

ARCPHOTOVOLTAICSCENTRE OFEXCELLENCE2010/11ANNUAL REPORT(a) HCSC efficiency as a function of extraction widthof ESCs for different extraction energies ΔE. (b) HCSCefficiency as a function of extraction energy ΔE fordifferent ESCs energy width. Thermalisation time is100 ps, lattice temperature is 300 K. Absorber layerthickness is 50 nm.Figure 4.5.47of wurtzite bulk InN has been considered inperforming computation of carrier densities,pseudo-Fermi potentials and II-AR time constants[4.5.57]. Results have been calculated consideringideal energy selective contacts for the HCSC, whichmeans that contacts have a very high conductivityand a discrete energy transmission level.Recently the limiting efficiency for the hot carrierInN solar cell has been calculated consideringnon-ideal ESCs. In this case the carriers are notextracted on a single energy level, but in a finiteenergy window. Calculations have been performedtaking into account contact resistance and entropygeneration effects.The flux of current travelling through the ESCstowards the cold metal electrodes can be describedusing the following relation.(4.5.5)The current density in this case is proportional tothe occupation probability at the two sides of theESC. Equation (4.5.5) has been derived assuming nocorrelation of energy of electrons in three differentdirections as shown in (4.5.6). This assumption isacceptable if there is a parabolic dispersion relationat minimum energy point along the three differentdirections.(4.5.6)Based on the energy and carrier conservation, Δμand TC at steady state are calculated.(4.5.7)[quantities as defined in Fig. 4.5.45 (a).]The maximum efficiency has been found for a ΔEbetween 1.15 eV and 1.2 eV with a transmissionenergy window δE of 0.02 eV. The value of limitingefficiency is 39.6% compared to 43.6% calculatedin the previous section using ideal ESCs. The dropin efficiency is mostly due to the decrease of opencircuit voltage related to the decreased extractionlevel, equation (4.5.7). This is partially compensatedby an increase in extracted current due to increasedII rate.Figure 4.5.47 (a) shows calculated efficiency as afunction of for several values of extraction energy. Inall the curves two different trends can be identified.If the value of δE is too close to zero, the efficiencyis very low due to low carrier extraction, thus a verysmall value of short circuit current. The conductivityof the contact in this case is indefinitely large.Enlarging δE, the number of carriers available forextraction increases, improving J SC, and so themaximum efficiency. In general the efficiency peakhas been found for values of δE from 0.02 eV to 0.1eV depending on the extraction energy ΔE. For theconfigurations which show higher efficiencies, ΔE< 1.35 eV, the optimum value of δE goes from 0.02eV to 0.05 eV. This optimum value for δE of betweenis very close to kT RT. This represents the variationin energy in the contacts such that approximatelythe kT RTwill inevitably be lost anyway by carriersthermalising within the contacts. Thus it sets alower limit on a reasonable δE. Therefore this resultindicates that the transmission energy range hasto be very small and confirms once again the highselectivity requirements of ESCs for HCSC [4.5.58].In Fig. 4.5.47 (b) the value of maximum efficiency asa function of ΔE is reported for different values ofδE. It can be observed that for small transmissionenergy window the extraction energy which allowsmaximum efficiency is lower compared to the onecalculated using ideal ESCs. This effect is relatedto the higher occupancy at lower energies, whichincreases the value of J SCfor contacts with a smalltransmission window.83