Simulation of the real efficiencies of high-efficiency silicon solar cells

The temperature dependences of the efficiency η of high-efficiency solar cells based on silicon are calculated. It is shown that the temperature coefficient of decreasing η with increasing temperature decreases as the surface recombination rate decreases. The photoconversion efficiency of high-efficiency silicon-based solar cells operating under natural (field) conditions is simulated. Their operating temperature is determined self-consistently by simultaneously solving the photocurrent, photovoltage, and energy-balance equations. Radiative and convective cooling mechanisms are taken into account. It is shown that the operating temperature of solar cells is higher than the ambient temperature even at very high convection coefficients (~300 W/m² K). Accordingly, the photoconversion efficiency in this case is lower than when the temperature of the solar cells is equal to the ambient temperature. The calculated dependences for the open-circuit voltage and the photoconversion efficiency of high-quality silicon solar cells under concentrated illumination are discussed taking into account the actual temperature of the solar cells.     

Recombination in the space-charge region of Schottky barrier solar cells

The expression for the recombination rate as a function of voltage, of illumination level, and of position in the space-charge region of the semiconductor is derived analytically. The recombination current density is derived by numerical integration of the above expression. The results show good agreement with experiment for the typical Au-n-type Si near-ideal Schottky barrier solar cells, and the comparison provides information on the uncovering of deep recombination centers by the hole quasi-Fermi level under increasing illumination. It is found that the principal effect of recombination under illumination is the reduction of the photocurrent. A rather surprising but gratifying result is that, once the above effect is taken into account by using short-circuit currents rather than photocurrents, the remaining (voltage dependent) effect of recombination is extremely close to the one in the dark, provided the increase in “uncovered” recombination centers with illumination is taken into account.     

Comparative analysis of limiting photoconversion efficiency of usual solar cells and solar cells with quantum wells

An analytical approach to calculation of limiting photoconversion efficiency η in solar cells with quantum wells is suggested and the value of η is compared with the limiting photoconversion efficiency of usual solar cells. In the described approach, along with bulk recombination, surface recombination at the barrier semiconductor-quantum well interfaces is taken into account. Features of formation of open-circuit voltage in Si-based p-i-n structures with long lifetimes of nonequilibrium charge carriers and in GaAs-based structures with short lifetimes of nonequilibrium carriers are compared.     

Quantum efficiency and formation of the emission line in light-emitting diodes based on InGaN/GaN quantum well structures

The spectra of electroluminescence, photoluminescence, and photocurrent for the In_0.2Ga_0.8N/GaN quantum-well structures are studied to clarify the causes for the reduction in quantum efficiency with increasing forward current. It is established that the quantum efficiency decreases as the emitting photon energy approaches the mobility edge in the In_0.2Ga_0.8N layer. The mobility edge determined from the photocurrent spectra is E _me = 2.89 eV. At the photon energies hv > 2.69 eV, the charge carriers can tunnel to nonradiative recombination centers with a certain probability, and therefore, the quantum efficiency decreases. The tunnel injection into deep localized states provides the maximum electroluminescence efficiency. This effect is responsible for the origin of the characteristic maximum in the quantum efficiency of the emitting diodes at current densities much lower than the operating densities. Occupation of the deep localized states in the density-of-states “tails” in InGaN plays a crucial role in the formation of the emission line as well. It is shown that the increase in the quantum efficiency and the “red” shift of the photoluminescence spectra with the voltage correlate with the changes in the photocurrent and occur due to suppression of the separation of photogenerated carriers in the field of the space charge region and to their thermalization to deep local states.     

Quantitative analysis of optical and recombination losses in Cu(In,Ga)Se<Subscript>2</Subscript> thin-film solar cells

Optical and recombination losses in a Cu(In,Ga)Se₂ thin-film solar cell with a band gap of 1.36–1.38 eV are theoretically analyzed. The optical transmittance of the ZnO and CdS layers through which the radiation penetrates into the absorbing layer is determined. Using optical constants, the optical loss caused by reflection at the interfaces (7.5%) and absorption in the ZnO and CdS layers (10.2%) are found. To calculate the recombination loss, the spectral distribution of the quantum efficiency of CdS/CuIn_1–xGa_xSe₂ is investigated. It is demonstrated that, taking the drift and diffusion components of recombination at the front and rear surfaces of the absorber into account, the quantum efficiency spectra of the investigated solar cell can be analytically described in detail. The real parameters of the solar cell are determined by comparing the calculated results and experimental data. In addition, the losses caused by the recombination of photogenerated carriers at the front and rear surfaces of the absorbing layer (1.8% and <0.1%, respectively), at its neutral part (7.6%), and in the space-charge region of the p–n heterojunction (1.0%) are determined. A correction to the parameters of Cu(In,Ga)Se₂ is proposed, which enhances the charge-accumulation efficiency.     

Voltage dependence of the differential capacitance of a p +-n junction

The dependences of the differential capacitance and current of a p ⁺-n junction with a uniformly doped n region on the voltage in the junction region are calculated. The p ⁺-n junction capacitance controls the charge change in the junction region taking into account a change in the electric field of the quasi-neutral n region and a change in its bipolar drift mobility with increasing excess charge-carrier concentration. It is shown that the change in the sign of the p ⁺-n junction capacitance with increasing injection level is caused by a decrease in the bipolar drift mobility as the electron-hole pair concentration in the n region increases. It is shown that the p ⁺-n junction capacitance decreases with increasing reverse voltage and tends to a constant positive value.     

Operating limits of Al-alloyed high-low junctions for BSF solar cells

Experimental estimations of the effective surface recombination velocity of the high-low junction (S_eff) and of the base diffusion length are carried out for Al-alloyed n⁺pp⁺ bifacial cells and the results are presented in form of histograms. These results agree with calculated values of S_eff when the characteristics of the recrystallized Si layer and heavy doping effects are taken into account. It is concluded that thick Al layers and high alloying temperatures (over 800°C) are necessary to obtain low values of S_eff. This conclusion agrees with experimental results of other authors. Recomendations to avoid diffusion length degradation are given and the operating limits of the Al alloying technology are discussed.     

Efficiency droop in GaN LEDs at high current densities: Tunneling leakage currents and incomplete lateral carrier localization in InGaN/GaN quantum wells

The phenomenon of the emission efficiency droop of InGaN/GaN quantum wells (QWs) in light-emitting diode p-n structures is studied. The influence exerted by two basic processes on the emission efficiency is considered: tunnel injection into a QW and incomplete lateral carrier localization in compositional fluctuations of the band-gap width in InGaN. The sharp efficiency peak at low currents and the rapid efficiency droop with increasing current are due to tunneling leakage currents along extended defects, which appear as a result of a local increase in the electron hopping conductivity via the depletion n region and a corresponding local decrease in the height of the injection p barrier. A less sharp efficiency peak and a weak, nearly linear, decrease in efficiency with increasing current are caused by incomplete lateral carrier localization in the QW due to slowing-down of the carrier energy-relaxation rate and to the nonradiative recombination of mobile carriers.     

Radiative recombination channels in Si/Si<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Ge<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> nanostructures

Using the solution of the 2D Schrödinger equation, systematic features of distribution of charge carriers in the Si/Si_{1 ? x} Ge _x nanostructures and variations in the efficiency of radiative recombination when pyramidal 2D clusters are transformed into 3D dome clusters with increasing thickness of nanolayers are established. The effect of the composition of the layers on the efficiency of the elastic stress in the structure and, as a consequence, the variation in conduction bands and valence band of the Si_{1 ? x} Ge _x nanostructures is taken into account. On realization of the suggested kinetics model, which describes recombination processes in crystalline structures, saturation of radiation intensity with increasing the pump intensity caused by an increase in the contribution of the Auger recombination is observed. A decrease in the contribution of the nonradiative Auger recombination is attained by decreasing the injection rate of carriers into the clusters, and more precisely, by an increase in the cluster concentration and an increase in the rate of radiative recombination.     

Photophysics of Molecular‐Weight‐Induced Losses in Indacenodithienothiophene‐Based Solar Cells

The photovoltaic performance and optoelectronic properties of a donor–acceptor copolymer are reported based on indacenodithienothiophene (IDTT) and 2,3‐bis(3‐(octyloxy)phenyl)quinoxaline moieties (PIDTTQ) as a function of the number‐average molecular weight (M_n). Current–voltage measurements and photoinduced charge carrier extraction by linear increasing voltage (photo‐CELIV) reveal improved charge generation and charge transport properties in these high band gap systems with increasing M_n, while polymers with low molecular weight suffer from diminished charge carrier extraction because of low mobility–lifetime (μτ) product. By combining Fourier‐transform photocurrent spectroscopy (FTPS) with electroluminscence spectroscopy, it is demonstrate that increasing M_n reduces the nonradiative recombination losses. Solar cells based on PIDTTQ with M_n = 58 kD feature a power conversion efficiency of 6.0% and a charge carrier mobility of 2.1 × 10^?4 cm² V^?1 s^?1 when doctor bladed in air, without the need for thermal treatment. This study exhibits the strong correlations between polymer fractionation and its optoelectronics characteristics, which informs the polymer design rules toward highly efficient organic solar cells.     

Effect of molecular weight on morphology and photovoltaic properties in P3HT:PCBM solar cells

The molecular weight of poly(3-hexylthiophene) is an important factor influencing the photovoltaic properties of bulk heterojunction organic solar cells based on this material. However, since different synthetic processes or repetitive soxhlet extractions – generally applied to obtain the different molecular weight batches under study – result in samples with simultaneously varying regioregularity (RR) and polydispersity index (PDI), it has not been possible yet to find an unambiguous correlation between the molecular weight and the photovoltaic performance. In the present work preparative gel permeation chromatography is introduced as a versatile technique to fractionate the donor polymer and thereby obtain a systematic variation of the number average molecular weight (M_n = 11–91 kg mol⁻¹) with an almost constant PDI and RR. Polymer crystallinity and conjugation length are evaluated by UV–Vis spectroscopy, rapid heat-cool calorimetry and selected area electron diffraction, and are found to be deeply affected by M_n. This in turn influences the behavior of the charge transfer state energy, measured via Fourier transform photocurrent spectroscopy, and therefore the open-circuit voltage. The short-circuit current is also affected by M_n, but mainly due to a change in absorption coefficient. The apparent recombination order is shown to be linked to the morphology of the polymer:fullerene blend and is determined using transient photovoltage and photocurrent techniques. Finally, a correlation between recombination and fill factor is also suggested.     

Recombination of point defects and their interaction with the surface in the course of the clusterization of these defects in Si

The growth kinetics of the {113} interstitial defects in n-and p-Si under in situ electron irradiation in a JEOL-1250 high-voltage electron microscope was analyzed in detail. The competing effects of the recombination of point defects and their interaction with the surface on the point-defect clusterization were considered. It is shown that the prevailing interaction of vacancies with the crystal surface is a consequence of the emergence of an energy barrier for the recombination of point defects in lightly doped Si crystals. Under these conditions, the drain of vacancies to the surface compensates for an increase in the crystal energy caused by the separation of the Frenkel pairs. It is assumed that a large difference between the growth rates of the {113} defects in n-Si and p-Si observed experimentally under the conditions when recombination is dominant is caused by a difference in the energy barriers for recombination. The barrier heights obtained correlate with the lattice-relaxation energy of a vacancy in various charge states.     

Optimization of the parameters of power sources excited by β-radiation

The experimental results and calculations of the efficiency of the energy conversion of Ni-63 β-radiation sources to electricity using silicon p–i–n diodes are presented. All calculations are performed taking into account the energy distribution of β-electrons. An expression for the converter open-circuit voltage is derived taking into account the distribution of high-energy electrons in the space-charge region of the p–i–n diode. Ways of optimizing the converter parameters by improving the technology of diodes and optimizing the emitter active layer and i-region thicknesses of the semiconductor converter are shown. The distribution of the conversion losses to the source and radiation detector and the losses to high-energy electron entry into the semiconductor is calculated. Experimental values of the conversion efficiency of 0.4–0.7% are in good agreement with the calculated parameters.     

The radiative recombination coefficient and the internal quantum yield of electroluminescence in silicon

The results of the analysis of variations in the radiative recombination coefficient with varying doping level and concentration of excess electron-hole pairs are reported. It is shown that, along with the effect of narrowing of the band gap calculated in the many-electron approximation, the effect of screening of the Coulomb interaction responsible for the decrease in the excition binding energy should be taken into account. Both effects produce similar trends and decrease the radiative recombination coefficient with increasing levels of doping or injection. The contributions of excitonic radiative recombination and band-to-band radiative recombination to the total radiative recombination coefficient are separated from each other. It is shown that, in the region of room temperature, both contributions are comparable, while at liquid-nitrogen temperature, the excitonic component dominates over the band-to-band component. The results obtained by refined calculations of the limiting value of the internal quantum yield of electroluminescence for the silicon diodes and p-i-n structures are presented. It is shown that the internal quantum yield of electroluminescence can be as high as 14%. However, this values sharply decreases with increasing surface recombination rate and decreasing lifetime of excess charge carriers in the bulk.     

On the ohmicity of Schottky contacts

The conditions under which Schottky contacts become ohmic are analyzed. Proceeding from classical concepts of the mechanisms of current flow, a generalized Schottky contact model is investigated. This model takes into account the thermionic current of majority charge carriers and the recombination current of minority carriers in Schottky contacts with a dielectric gap. Based on an analysis of the predictions of this model, ohmicity criteria are obtained for Schottky contacts and the conditions for a low injection level and the ohmicity of Si-based Schottky contacts are compared. It is shown that the conditions for Schottky-contact ohmicity do not coincide with those for p–n junctions.     

Volterra series analysis of the photocurrent in an Al/6T/ITO photovoltaic device

Using Volterra series we resolve analytically the non-linear rate equations describing the time evolution of the charge carrier concentration in an Al/6T/ITO cell when the device is illuminated and charge carriers are uniformally generated in the bulk at a known rate. We present the analytic expressions of the charge carrier densities in the bulk as a function of time and the expression for the photocurrent across the device. We show that the response contains a transient part and a permanent one. Using the first and the second order permanent response the photocurrent action spectrum of the device is obtained. We use these analytic results to suggest a method to evaluate experimentally the carrier lifetimes τ_n and τ_p and the Langevin bimolecular recombination rate. The system of rate equations has also been resolved numerically, using the Runge–Kutta method. Finally we compare successfully the measured photocurrent action spectrum with those obtained numerically and analytically.     

Analysis of silicon solar cells with stripe geometry junctions

Silicon solar cells with stripe geometry junctions are analyzed. The base region collection efficiency is found to be insensitive to the transmissivity of the electrode and/or the diffused layer but quite sensitive to the width and separation of the stripe junctions. The additional losses of carriers are mainly due to the increased bulk recombination rather than the surface recombination. In one case analyzed the collection efficiency decreases by 22% when the junctions are separated by about one sixth of the diffusion length with the surface recombination velocity at 300 cm/sec. Possible uses of the stripe-junction design in p-n junction cells and Schottky barrier cells are re-examined in the light of the new calculation and found to be less attractive than previously suggested.     

Some investigations on secondary breakdown in p-n junctions considering the effect of thermally generated carriers

The V-I characteristic of a p-n junction under breakdown is calculated taking the thermally generated carriers into account. The current density distributions computed under different conditions have been given. The light emission and other characteristics reported by Chiang and Lauritzen and others have been explained.     

Photosensitivity of Pb<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Sn<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Te:In films in the region of intrinsic absorption

The steady-state photocurrent in the fundamental absorption region of Pb_{1 ? x} Sn _x Te:In films is calculated with the field injection of electrons from the contact and their capture by traps in the bulk taken into account. The calculated and experimental current-voltage characteristics are compared at liquid-helium temperature. The represented experimental data on the dependence of the Hall effect on the injection level agree well with the considered model.