Luigi Abenante

Optical Path Length Factor at Near-Bandgap Wavelengths in Si Solar Cells

By using the Rand and Basore (R&B) physical model for light trapping, a particular analytical expression for near-bandgap optical path length factor Zo is derived for the case where back surface reflectivity RBACK is equal to unity (RBACK = 1). This expression shows that according to the R&B physical model, at RBACK = 1, Zo has a finite value. At RBACK = 1, the R&B expression for Zo is shown to diverge. By using the original R&B derivation procedure, a new expression for Zo is obtained, which at RBACK = 1, reduces to the aforementioned particular expression for ideal back surface reflectance. The new expression is immune from the physical incongruity and tendency to overestimate Zo that affect the R&B expression. By using the new expression, a relationship between Zo and the Yablonovitch and Cody (Y&C) absorption-enhancement factor is derived for devices where parasitic absorption predominantly occurs at backside reflector. This relationship is shown to be in agreement with the literature. In the derivation, a connection between the approaches to light trapping of R&B and Y&C is exploited. This connection allows obtaining a new method to evaluate RBACK at near-bandgap wavelengths in most Si solar cells. The new method is checked on two real Si solar cells and found to provide plausible results. Compared to the method used by R&B, the method presented in this paper is shown to be more reliable

Modeling the performance of solar cells with and without the depletion approximation

Abstract The measured internal spectral response and open-circuit voltage of two silicon solar cells were modeled with the simulation program PC1D version 4.4 by both applying and not applying the depletion approximation (DA). A comparison between the results from the two modeling approaches shows that dividing the device under exam into regions according to the DA is preferable in order to get both modeling reliability and physical insight into the device operation. Not using the DA leads in fact to both overestimate the bulk lifetime and neglect the optical properties of highly doped regions.

Apparent band-gap narrowing doping functions for silicon in the Dhariwal and Ojha's form facilitating solar cell modeling

It is shown that reported doping functions for apparent band-gap narrowing (ABGN) in silicon that are written in the Slotboom and De Graaffs form (Slotboom, De Graaff, Solid-State Electron. 19 (1976) 857) can be set in the Dhariwal and Ojhas form (Dhariwal, Ojha, Solid-State Electron. 25 (1982) 909) at all dopings without any significant deviation in their capability of fitting the experimental data. The use of the Dhariwal and Ojhas form is preferable because it allows for a straightforward application of the depletion approximation in the non-uniformly doped regions of silicon devices like ion-implanted and diffused solar cells, facilitating the device performance modeling and analysis. This is demonstrated by an application to the internal spectral responses of two ion-implanted silicon solar cells and a comparison with a modeling method which does not use the depletion approximation.

Comments on “20.8% PERC Solar Cell on 156 mm × 156 mm p-Type Multicrystalline Silicon Substrate”

In the commented paper, the optical path length factor Z₀ is evaluated in a high-performance Si solar cell by using a reported procedure, which requires a previous determination of the slope 1/W_{IQ E} and theyintercept 1/η c of the linear fit to inverse internal quantum efficiency 1/IQE versus absorption depth 1/α, where α is the absorption coefficient. The authors of the commented paper calculate values of WIQE and η_c that are inconsistent with their data and graphs. In this comment, self-consistent values of W_IQE and η_c are derived that are congruent with the data.

Transparent and quasi-transparent regional solutions to minority-carrier transport in arbitrarily doped semiconductors

The exact analytical regional solution to minority-carrier transport is derived in arbitrarily doped transparent semiconductor regions. By using this solution, new regional quasi-transparent solutions for emitter light-generated current density are derived in both the Cuevas and Balbuena approach (Cuevas and Balbuena, IEEE Trans. Electron Devices, vol. 36, pp. 553-560, 1989) and the Hamel approach (Hamel, IEEE Trans. Electron Devices, vol. 46, pp. 104-109, 1996) . Either of the new third-order quasi-transparent expressions is shown to be more accurate than both the local second-order quasi-transparent expression of Cuevas and Balbuena and the third-order regional expression of Bisschop et al (IEEE Trans. Electron Devices, vol. 37, pp. 358-364, 1990). In particular, while the new expression derived according to Hamel is more accurate at passivated surfaces, the new expression derived according to Cuevas and Balbuena is always more accurate, except for the case of a negligible surface recombination, where it is as accurate as the third-order regional expression of Bisschop et al.

Modeling of array performance degradation including single-module failure

A model for the performance degradation of a series-parallel array is presented, which includes single-module failure as an independent parameter. The model is checked by using data relevant to two arrays located at the ENEA Casaccia research center near Rome (Italy). By using the model, a first assessing of the influence of single-module failure on array degradation is performed. As a result, it is found that module replacement is not always necessary.

Indoor I-V swept technique : model and experimental results

Abstract The theoretical basis of the indoor I-V swept technique is investigated. A simple analytical model which provides the value of the optimal capacitor to be used and an estimate of the time of measurement, is developed. Temporal fluctuations of the solar simulator light are taken into account with respect to their effect on device parameter computation. Various photovoltaic devices, fabricated with different semiconductor materials, are considered and their I-V characteristics, obtained by means of both the indoor swept technique and the more conventional power supply method, are compared. Excellent agreement is found for all the tested devices.

Applications of the green's expression for saturation current vs. bandgap in Si and CIGS solar cells

Two applications of the Greens expression for saturation current vs. bandgap are proposed. The first one aims at assessing the energy bandgap, Eg, in the quasi-neutral regions (QNR) of Si and CIGS solar cells, which is associated to the saturation current in those regions, J0,QNR. Values for J0,QNR are obtained from both fits to pseudo-dark I-V curves and the textbook expression for open-circuit voltage. The second application deals with detecting the recombination mechanism prevailing in the QNR of CIGS solar cells from the order of magnitude of the value that must be assigned to a parameter of the Greens expression to fit measured curves of performance data vs. Eg. The data utilized in the two applications are both original and taken from the literature.

A simplified expression for optical absorbance in Si solar cells

An expression for optical absorbance in Si is derived, which is a simplification of the expression for the same quantity given by Basore. Unlike the Basore expression, the simplified expression does not require the determination of the front-surface external and internal reflectance prior to be used. For textured solar cells it is equivalent to the Basore expression, if the average ray-path angle with respect to the surface normal is equal at all passes of light across a cell. Unlike the Basore expression, it allows fitting the measured quantum efficiency of planar solar cells with diffuse rear surface. The simplified expression can be easily implemented in the numerical simulation program PC1d. The measured quantum efficiency of a textured solar cell is fitted with both the new and Basore expressions. Overlapping fit-curves are obtained. The measured quantum efficiency of a planar solar cell with not-polished rear surface is fitted by using the new expression. Finally, with the new expression, the maximum absorbance for weakly absorbed light is estimated in solar cells with textured back surface at both flat and textured front surfaces.

Simple analytical model for 2kT current in forward-biased p-n junctions

The junction space-charge region (JSCR) is modeled as a separate region with carrier recombination at the surface and in the bulk. Bulk recombination is modeled according to the idealized model of C. T. Sah, R. N. Noyce, and W. Shockley [Proc. IRE45, 1228 (1957)]. JSCR surface recombination is modeled by combining at high biases the approaches of A. S. Grove [Physics and Technology of Semiconductor Devices (Wiley, New York, 1967), pp. 301–302] and of C. H. Henry, R. A. Logan, and F. R. Merrit [J. Appl. Phys. 49, 3530 (1978)]. In the treatment, it is assumed that the densities of states in the bulk and at the surface are related to each other. The transport equations are solved in JSCR at high biases and an expression for the JSCR recombination current is obtained. The model is adjusted for Si emitters and diodes, in such a way that it agrees with the numerical simulation program PC1D at all voltages.