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This work deals with minority carrier diffusion coefficient study in silicon solar cell, under both temperature and applied magnetic field. New expressions of diffusion coefficient are pointed out, which gives attention to thermal behavior of minority carrier that is better understood with Umklapp process. This study allowed to determine an optimum temperature which led to maximum diffusion coefficient value while magnetic field remained constant.

The photovoltaic conversion efficiency depends on the nature and structure of the semiconductor, its manufacturing processes and the operating conditions. In order to improve solar cell performance, several characterization techniques of semiconductor material have been proposed. Among the most important parameters in the different characterization techniques, it can be noted the diffusion coefficient [

The applied magnetic field (B) [

The base doping rate (Nb) [

Modulated frequency (ω) [

The damage coefficient (Kl) and the irradiation flux (Φp) [

The minority carrier recombination velocity at the grain boundaries (Sg) and the grain size (g) [

Many of previous parameters can be combined to produce new expressions of diffusion coefficient [

It then affects the determination of the recombination parameters in the bulk i.e. lifetime (τ) and on the surfaces, specially, the back surface recombination velocity (Sb) and junction surface recombination velocity (Sf)) [

In static regime, the photocurrent Iph is studied versus absorption coefficient wavelength dependent (λ) and leads to spectral response [

In frequency regime, we note the studies of both Sb and Sf, excess minority carrier recombination velocity respectively at the junction and at the back side surfaces, by the help of Bode and Nyquist diagrams, leading to electrical equivalent models, with effect of both external (B, E, Φ, kl) and internal (g, Sg, (λ)) parameters [

In this article, the study focuses on the minority carriers diffusion coefficient in silicon solar cell under both temperature and applied magnetic field.

We consider a back surface field (B.S.F) silicon solar cell (n^{+}-p-p^{+} type) under influence of temperature and applied magnetic field (

When the solar cell is illuminated, the phenomena of generation, diffusion and recombination of the minority carriers in the solar cell base are considered.

The minority carrier diffusion coefficient D × (B) in the base under the influence of applied magnetic field B [

where D_{0}(T) is the diffusion coefficient versus temperature T, in the solar cell without magnetic field. It is given by the Einstein-Smoluchowski relation [

With μ(T) is the minority carriers mobility temperature [

q is the electron elementary charge and kb is Boltzmann’s constant given as kb = 1.38 × 10^{−23} m^{2}・kgs^{−2}・K^{−1}.

For a given temperature, the diffusion coefficient is maximum and almost constant when the magnetic field is weak. Indeed, for low magnetic field values, the carrier mobility is not strongly influenced by magnetic field variation and this explains the bearing observed. On the other hand, when the magnetic field is

greater than 10^{−3} T, mobility and minority carrier diffusion decrease with the magnetic field [^{−3} T, where the diffusion coefficient increases with temperature.

For lower magnetic field values (<10^{−3} T), the diffusion coefficient increases with temperature and reaches a maximum value corresponding to a temperature called optimum temperature Topt (B) then decreases. Indeed, when the temperature is below Topt (B), the Umklapp process [

On the other hand, when the magnetic field is greater than 10^{−3} T, the diffusion coefficient increases with temperature.

Moreover, it may be noted that the optimum temperature increases according to the magnetic field intensity

The optimum temperature Topt (B) for maximum diffusion is determined using two methods:

・ Graphical method

From the curves in

From

Considering the average right, the following relationship is obtained:

The constants a and b are determined from the curve, the following equations is obtained:

The resolution of the equations constituted by relations (6) and (7) gives:

a = −1.58 (cm^{2}/s・T) et b = 12.26 (cm^{2}/s)

Hence the relationship Topt:

・ Analytical method

The diffusion coefficient is maximum when the temperature is equal to Topt for a given magnetic value B which remained constant. Thus, by annulling its derivative versus temperature, we can determine Topt while keeping B constant value.

Magnetic field B (T) | 0.0003 | 0.0004 | 0.0005 | 0.0006 | 0.0007 | 0.0008 | 0.0009 | 0.001 |
---|---|---|---|---|---|---|---|---|

Optimum temperature T (K) | 255 | 285 | 308 | 335 | 355 | 380 | 400 | 410 |

Diffusion coefficient D (cm^{2}/s) | 33.364 | 28.178 | 24.694 | 22.206 | 20.276 | 18.763 | 17.571 | 16.642 |

The derivative of the diffusion coefficient at T = Topt is given by the relation as:

We then deduce the relationship:

Using the relation (10), the optimum temperature can be calculated for different magnetic field values. Results are presented in

For a comparative study of the two methods, we represent in

Magnetic field B (T) | 0.0003 | 0.0004 | 0,0005 | 0.0006 | 0.0007 | 0.0008 | 0.0009 | 0.001 |
---|---|---|---|---|---|---|---|---|

Optimum temperature (K) | 254.7 | 286.6 | 313 | 336.5 | 361.4 | 381.9 | 401.0 | 418.8 |

Diffusion coefficient (cm^{2}/s) | 33.368 | 28.173 | 24.66 | 22.202 | 20.259 | 18.757 | 17.561 | 16.548 |

The minority carrier diffusion coefficient

Otherwise, the diffusion coefficient increases with temperature, reaches a maximum value corresponding to a temperature called optimum temperature. For a fixed magnetic field value, the diffusion coefficient decreases with the optimum temperature. The relation obtained between the maximum value of the diffusion coefficient and the optimum temperature allows justifying the selection of the temperature values for the study of the solar cell parameters.

Mane, R., Ly, I., Wade, M., Datta, I., Douf, M.S., Traore, Y., Ndiaye, M., Tamba, S. and Sissoko, G. (2017) Minority Carrier Diffusion Coefficient D*(B, T): Study in Temperature on a Silicon Solar Cell under Magnetic Field. Energy and Power Engineering, 9, 1-10. http://dx.doi.org/10.4236/epe.2017.91001