Physical model of back line-contact front-junction solar cells

The analysis of advanced front-junction solar cells where the metal contact to the base region is locally formed on the back surface in the shape of lines usually requires numerical simulations. Here, we describe an approach based on a geometric formulation of carrier crowding towards the localized contact, in conjunction with a partition of the device in two distinct regions. This permits a one dimensional analysis of carrier flow, both in the region immediately adjacent to the contact and in the peripheral region surrounding it. The resulting model is simple enough to provide insight into the physics of device operation and reasonably accurate in cases of practical interest. By applying it to different cases, we identify unexpected anomalies and explain them in terms of the peculiar interplay between carrier transport and recombination that takes place in this type of solar cell

Capture cross sections of the acceptor level of iron-boron pairs in p-type silicon by injection-level dependent lifetime measurements

Injection-level dependent recombination lifetime measurements of iron-diffused, boron-doped silicon wafers of different resistivities are used to determine the electron and hole capture crosssections of the acceptor level of iron-boron pairs in silicon. The relative populations of iron-boron pairs and interstitial iron were varied by exposing the samples to different levels of illumination prior to lifetime measurements. The components of the effective lifetime due to interstitial iron and iron-boron pairs were then modeled with Shockley-Read-Hall statistics. By forcing the sum of the modeled iron-boron and interstitial iron concentrations to equal the implanted iron dose, in conjunction with the strong dependence of the shape of the lifetime curves on dopant density, the electron and hole capture cross-sections of the acceptor level of iron-boron pairs have been determined as (3±2)×10-14cm-2 and (2±1)×10-15cm-2

Geometrical Analysis of Solar Cells With Partial Rear Contacts

The analysis of solar cells where the posterior metal contact is formed only on part of the rear surface, which is mostly covered by a nonconductive, passivating layer, is both important and complex. A possible approach, based on a geometrical representation of the device structure, is examined here. As minority carriers flow toward the localized rear contact, they crowd inside a diminishing cross-sectional area, resulting in a high current density. The latter demands a strong gradient in their concentration, which leads to an increase of the open-circuit voltage Voc. Similarly, the crowding of majority carriers requires a strong gradient of the electrostatic potential, which leads to an increased series resistance Rs. These effects of carrier crowding are described here with simple mathematical expressions that permit an approximate evaluation of Voc and Rs for partial rear contact solar cells

Electrons and holes in solar cells with partial rear contacts

When the metal contact of a silicon solar cell is restricted to a fraction of the rear surface, the flow of electrons and holes towards that contact is constricted, which is beneficial for minority charge carriers but detrimental for majority carriers. It is possible to describe their 2D/3D transport and determine their concentration in the vertical and transversal dimensions of the solar cell by separately studying the central region near the contact and the peripheral region surrounding it. A virtue of such geometric approach is that it establishes a link between analytical models and computer simulations, providing both physical insight and sufficient accuracy to optimise partial rear contact devices. In this paper, we extend a previous version of the geometric model to solar cells having a full-area, locally contacted dopant diffusion on the rear surface. The case for n-type versus p-type wafers is considered, point contacts are compared with line contacts, including the impact of the metal/semiconductor resistance and bulk recombination is evaluated

Empirical determination of the energy band gap narrowing in p+ silicon heavily doped with boron

In the analysis of highly doped silicon, energy band gap narrowing (BGN) and degeneracy effects may be accounted for separately, as a net BGN in conjunction with Fermi-Dirac statistics, or lumped together in an apparent BGN used with Boltzmann statistics. This paper presents an experimental study of silicon highly doped with boron, with the aim of evaluating the applicability of previously reported BGN models. Different boron diffusions covering a broad range of dopant densities were prepared, and their characteristic recombination current parameters J0 were measured using a contactless photoconductance technique. The BGN was subsequently extracted by matching theoretical simulations of carrier transport and recombination in each of the boron diffused regions and the measured J0 values. An evaluation of two different minority carrier mobility models indicates that their impact on the extraction of the BGN is relatively small. After considering possible uncertainties, it can be concluded that the BGN is slightly larger in p⁺ silicon than in n⁺ silicon, in qualitative agreement with theoretical predictions by Schenk. Nevertheless, in quantitative terms that theoretical model is found to slightly underestimate the BGN in p⁺ silicon. With the two different parameterizations derived in this paper for the BGN in p⁺ silicon, both statistical approaches, Boltzmann and Fermi-Dirac, provide a good agreement with the experimental data

Comment on "Mechanisms for the anomalous dependence of carrier lifetime on injection level and photoconductance on light intensity" [J. Appl. Phys. 89, 332 (2001)]

In a recent article [J. Appl. Phys. 89, 332 (2001)], Karazhanov proposed a single-level recombination model as an explanation for the anomalous dependence of the carrier lifetime on injection-level observed in cast multicrystalline silicon. This approach contrasts with previous models which involved the use of two distinct levels, one causing recombination and the other only trapping. The purpose of this comment is to outline some critical considerations which suggest that only a two-level (or indeed a multi-level) model can satisfactorily explain the experimental observations

Capacitive effects in quasi-steady-state voltage and lifetime measurements of silicon devices

When measuring I-V characteristics and carrier lifetimes in quasi-steady-state QSS conditions, it is important to consider the time dependence of the charge due to excess carriers within the device. This paper shows that the space-charge region present in pn-junction devices and in many lifetime test structures can produce a significant capacitive effect when measuring the low voltage and low carrier density range of QSS I-V curves. Both computer modeling and experiments show that the junction capacitance is particularly significant in the case of low-resistivity silicon wafers, but it can also be noticeable in intermediate and high-resistivity samples. The paper demonstrates that the static I-V characteristics can be accurately reconstructed using a simple analytical model for the space-charge region. It thus fills a gap in the understanding of the low injection range of QSS voltage and lifetime measurements

Empirical determination of the energy band gap narrowing in highly doped n+ silicon

Highly doped regions in silicon devices should be analyzed using Fermi-Dirac statistics, taking into account energy band gap narrowing (BGN). An empirical expression for the BGN as a function of dopant concentration is derived here by matching the modeled and measured thermal recombination current densities J0 of a broad range of n+ dopant concentration profiles prepared by phosphorus diffusion. The analysis is repeated with Boltzmann statistics in order to determine a second empirical expression for the apparent energy band gap narrowing, which is found to be in good agreement with previous work