This study is focused on the base region of a polycrystalline back surface field bifacial silicon solar cell (Figure 1) in the quasi-neutral base assumption [5] [6] .

When the bifacial silicon solar cell is illuminated simultaneously on both sides, the solution of excess minority carriers’ continuity equation [7] is:

with

In Equation (1), and are respectively electrons’ diffusion length and diffusion coefficient in the presence of a magnetic field, coefficients a_i and b_i are tabulated values obtained from modelling of the generation rate considered for over all the solar radiation spectrum under Air Mass 1, 5 standard conditions [8] and H is the base thickness.

Constants A₁ and A₂ are determined solving the boundary conditions [5] [7] . Thus, the excess minority carriers’ (electrons) density will be completely determined.

Since the excess minority carriers’ density is known, from Fick’s law applied at the solar cell junction, we can derive the photocurrent density expression as:

Knowing the excess minority carriers’ density, the photovoltage across the solar cell junction is also expressed

using Boltzmann’s relation:

V_T is the thermal voltage, n_i is the intrinsic carriers’ density at thermodynamic equilibrium and N_B is the base doping density.

The photocurrent density and the photo-voltage depend on junction dynamic velocity Sf. While taking the junction dynamic velocity as parameter, we plot in Figure 2 the solar cell Jph-Vph characteristic curves for different values of magnetic field intensity.

The shapes of the different curves in Figure 2 show that the short circuit photocurrent density is a decreasing function of magnetic field while the open circuit photovoltage is an increasing function of the same magnetic field. We note that the short circuit photocurrent density decreases strongly while the open circuit photovoltage increases slightly.

Each curve is characterized by three remarkable points: the short circuit photocurrent density J_sc, the open circuit photovoltage V_oc and a point named “knee” or peak power point [4] which has J_m (or J_p) and V_m (or V_p) as coordinates [1] The peak power (P_p= J_p × V_p) is the maximum electric power (P_m= J_m × V_m) that a solar cell can delivered to an external circuit; so the peak power point is the operating point that permits to obtain the maximum electric power from a solar cell [4] . We note a displacement of the peak power point, towards large values of photovoltage and low values of photocurrent density, when the magnetic field intensity increases and that situation corresponds to a displacement of the solar cell’s operating point and so an increase of the load resistance at the peak power point.

The expression of electric power delivered by the base of the bifacial solar cell to an external circuit is:

with which is the photocurrent density that crosses the external load resistance.

The electric power delivered by the bifacial silicon solar cell to an external circuit depends also on the junction dynamic velocity Sf. While taking the junction dynamic velocity as parameter, we plot in Figure 3 the solar cell P-Vph characteristic curves for different values of magnetic field intensity.

The curves in Figure 3 show that the peak power decreases with magnetic field increase and that corresponds to a displacement of the bifacial solar cell’s operating point towards large values of photovoltage. This means that the increase of magnetic field leads to an increase of the load resistance at the peak power point.

For that, we plot in the same axes system (Figure 4), Jph-Vph and P-Vph characteristics for a given magnetic field intensity.

Using the two characteristics, we determine the values of peak power P_p, peak photovoltage V_p, peak photocurrent density J_p, short circuit photocurrent density J_sc and open circuit photovoltage V_oc according to magnetic field intensity.

Then we calculated the solar cell fill factor (FF) using the formula below:

Knowing the peak photovoltage V_p, and the peak photocurrent density J_p, we calculated the load resistance at ² the peak power point (Maximum Power Point) using Ohm’s law [4] :

The characteristic values of the bifacial solar cell under magnetic field are given in Table 1.

These results show that the peak photocurrent density and the short circuit photocurrent density decrease with magnetic field intensity while the peak photovoltage and the open circuit photovoltage increase with the same magnetic field intensity. These results have been observed on the Jph-Vph characteristics. The peak power decreases with the magnetic field intensity while the fill factor and the load resistance at the maximum power point or peak power point increase. The decrease of peak power with magnetic field increase corresponds to a displacement of the bifacial solar cell’s operating point towards large values of photovoltage, resulting in an increase of charge resistance at the peak power point.

In Table 2, we give the values of maximum electric power delivered by the solar cell to an external circuit and the values of junction dynamic velocity at the maximum power point [5] . We also give the values of the load resistance at the peak power point, determined in this work.

We note that the maximum electric power determined in the previous work [5] is in the same order of size that the peak power determined in this work. One notes also that the junction dynamic velocity at the peak power point and the load resistance at the peak power point evolve in reverse senses. Indeed, when the junction dynamic velocity decreases one evolves towards the open circuit and the load resistance increases. On the other hand, when the junction dynamic velocity increases, one evolves towards the short circuit and the load resistance decreases.