Theoretical and experimental studies of effective carriers lifetime: Magnetic effects

Units of Sciences and Technology, Department of Physics, Laboratory of Heliophysic, Materials and Environment, Nazi Boni University, Bobo Dioulasso, Burkina Faso. Units of Sciences and Technology, Department of physics, Laboratory of Materials and Environment, Joseph Ki-Zerbo University, Ouagadougou, Burkina Faso. Units of Sciences and Technology, University of Ouagadougou, Department of Physics, Laboratory of Thermal and Renewable Energy, Ouagadougou, Burkina Faso


INTRODUCTION
Minority charge carrier effective lifetime is an important parameter to estimate the quality of a PV solar cell. Indeed, the overall energy conversion efficiency of a photovoltaic cell is based on minority charge carrier's effective lifetime of PV solar cell. So, more methods are been developed for effective lifetime measurement (Dhariwal and Vasu, 1981;Mahan et al., 1979). Among these methods, open-circuit voltage decay is a simple and reliable technic to measure the minority charge carrier's effective lifetime in PV solar cell. Since then, both theoretical and experimental investigations on the application of this method to the characterization of  (Sam et al., 2012). photovoltaic devices have been discussed and the technic extended (Jain, 1981;Agarwal et al., 1982).
In this manuscript, we present a technic to measure charge carrier effective lifetime of PV solar cell method. This method mainly used open circuit voltage decay conditions. Firstly, experimental set-up is presented, study assumptions are made and experimental conditions are described. Secondly, in this study, new analytical expressions of excess minority charge carrier density and transient open circuit voltage were determined from mathematical formulation. Thirdly, theoretical and experimental results on charge carrier effective lifetime in a polycrystalline silicon p-n junction under magnetic field are found and analyzed. The effects of magnetic field on effective charge carrier lifetime are then analyzed.

MATERIALS
The list of experimental set-up material is as followed: A monofacial silicon solar cell manufactured by MOTCH INDUSTRY; a pulsed light source MINISTROB PHIWE, a digital oscillo-scope TECKTRONIX model TDS 10013, a computer INTEL 586, a power supply 0-12V DC/ 6V-12V AC , a tesla meter and Helmholtz Coil. The experimental set-up is presented on Figure 1.
The experimental system principle operating is identical than that described by Sam et al. (2012Sam et al. ( , 2016. In addition, the stroboscopic flash used is considered near AM1.5. Also, any external or internal factors which can perturb PV solar cell operating conditions were neglected (Ba and Kane, 1995).
At time t=0, the PV cell is illuminated with the multispectral flash which establishes a steady state characterized by the potential V 2 corresponding to an operating point called 2 (Figure 2). At time t=Te, the flash is abruptly cut off. The voltage V 2 drops from V 2 to V 1 corresponding to a new operating point denoted 1. The decay of voltage from V 2 to V 1 is recorded on a digital scope connected to an external hard drive.
External hard drive permits to save experimental data for the rebuilding of the signal response later. Kaleidagraph software is used to convert complex data obtained during experimentation into transient voltage graphs.

METHODS
A bifacial polycrystaline solar cell operating under a various magnetic field was considered. This PV solar cell, because of its manufacture technic, is constituted of several grains of different sizes and forms separated by grain boundaries that are considerable recombination centers. For the modeling of the processes of generation, diffusion, and recombination, the polycrystalline, PV solar cell was considered as a regular array of many unit cells with dimensions 2a, 2b and H ( Figure 3). This modeling of polycrystalline solar cell structure was described in detail by the authors of references (Ba et al., 1993;Diasso et al., 2020a;Charles et al., 2000;Toure et al., 2012). With this hypothesis, the properties of polycrystalline solar cell can be described by a study of generation, diffusion, and recombination processes only in one grain. Figure 3 shows the theoretical model for a sample grain. The following assumptions for this study to solve diffusion equation are: 1. The emitter and space charge region contributions are neglected to the photocurrent production, so the majority of the current is provided therefore by the base (Diasso et al., 2020d;Dieng and al, 2011;Mohammad, 1987). 2. The grains are under parallelepipedic shape (2a 2b and H) and the joints of the grains are perpendicular to the junction (Mohammad, 1987). 3. The surfaces between two adjacent grains and perpendicular to the junction are characterized by the same carrier recombination process evaluated by a grain boundary recombination velocity (Mohammad, 1987): The magnetic field is oriented according to the direction oy . It is therefore perpendicular to the depth of light penetration in order to observe the effect of the strength of Lorentz on the charge carriers; 4. The solar cell is uniformly. Then, we have a generation rate  In the base, the minority charge carriers are electrons, and charge carriers density expression is given by the resolution of the is the electric field of the crystal lattice and n µ is the mobility of the electrons. Substituting Equation (2) into (1) and taking into account the theory of quasi-neutrality of the base, the diffusion equation of the electrons in the base becomes: The presence of the magnetic field in our model leads to new values of carrier diffusion length L* and carrier diffusion coefficient D* expressions which depend on the magnetic field: Magnetic field intensity is as a function of coefficient θ .
The carriers' generation rate under multispectral light at the depth z in the base can be written by Expression 6: In this equation, coefficients m a and m b are the modeling coefficients of AM1.5 (Ba and Kane, 1995). Equation (1) is solved with the following boundaries conditions: At rear side z = H At surfaces limited by x = ±a and y = ±b x y z t Sgy x y b z t y D δ δ * = ± ∂ = ± = ± ∂ (10) Raguilignaba et al. 191 Sf , Sb and Sg are recombination velocity of minority charge carriers respectively at surfaces z = 0, z = H and x = ± a (or y = ±b). a, b and H are the grain sizes as indicated on Figure 1. A solution of Equation (1) is expressed according to Ba and Kane (1995). Where: β * and j l * are expressed by: The expression (11) can write simply by the following equation: The values of

Effective lifetime of minority charge carriers' measurement
The approach employed in the study is based on the linear approximation of the transient voltage decay because in low injection there are no impedance effects (Muralidharan and Jain, 1982). Figure 4 presents the different regions of transient voltage decay curve.
The linear decay zone of the curve was identified, then, a fit was applied on this zone and a linear regression line was obtained with it equation expression illustrated by Figure 5. In Figure 5, the linear regression equation is established with a good correlation coefficient R. The slope m of this linear regression line is related to the effective lifetime of minority charge carriers by expression 28.

Magnetic effects on effective carriers lifetime
After registration data with the digital scope, the signal of the transient response was remade. Then, the curves of transient voltage decay were gotten for various magnetic field values. Just one example of the transient voltage curves obtained was shown here ( Figure 6). The figure shows two forms of decay: Linear decay and exponential decay. After analysis, it is indicated that the linear region is major than the linear zone (75 against 25%). Ideal types of open circuit transient voltage decay according to Dhariwal and Vasu (1981) and Mahan et al. (1979) was gotten. Additionally, this zone of the curve doesn't present capacitance effects in reference to Dhariwal and Vasu (1981), Mohammad (1987) and Diasso et al. (2020b).

Theoretical results
The theoretical results obtained from a linear fit are given in Table 1. The observation of the precedent table of theoretical results shows the decrease in charge carrier's effective lifetime is a function of magnetic field.

Experimental results
The experimental results of all transient voltage decay  curves linear fitting obtained are given in Table 2.
We remark that the results indicate the decrease of charge carrier's effective lifetime theoretical or experimental values versus magnetic field.
The analysis of the two types of results present a decrease in effective charge carrier's lifetime with the increase in magnetic field.
The increase in magnetic field creates the decrease in diffusion length and diffusion coefficient. This reduction of diffusion length and diffusion coefficient induce fast minority charge carriers' recombination reducing distance and time during recombination when the magnetic field increases. Also, the extension of space charge region width is, an increase in a function of magnetic field  traduces an important disappearance of charge carriers and therefore the strong reduction of effective charge carriers lifetime. The comparison of theoretical results and experimental results show the decay of the charge carries effective lifetime with the increase of magnetic field. So the two types of results are in good agreement qualitatively.

Conclusion
In this paper, theoretical study and experimental study were conducted. For this study, the theoretical approach and the experimental set up are presented. The list of experimental set-up material and experimental conditions are described. Firstly, theoretically, a three dimensional approach of electrons diffusion in the p region of a polycrystalline silicon solar cell is presented when solar cell is front side illuminated by a pulsed light versus external magnetic field. The expressions of charge carriers density and transient voltage decay are established. Secondly, we pointed out a simple and reliable experimental and theoretical technic to measure effective charge carriers' lifetime. Thirdly, the effects of magnetic field on charge carriers' effective lifetime are presented and analyzed.