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We report the study of the temperature dependance of the performance electronic parameters of an N-P solar cell by considering as model, the columnar cylindrical orientation associated to the dynamic junction velocity (SF) concept. We presented the photocurrent-photovoltage (I-V) and Power-photovoltage (P-V) characteristic curves. The short-circuit photocurrent (
*I _{sc}*), the open circuit photovoltage (

*U*), the fill factor (FF) and the efficiency (

_{oc}*η*) are linearly dependent on the temperature. The temperature coefficients (T-coefficient) relative to the short-circuit, open-circuit photovoltage and efficiency are calculated and the comparison with data from the literature showed the accuracy of the considered model.

The photovoltaic effect was first discovered in 1839 by Edmond Becquerel [^{2}) at 25˚C [

However, there are some limitations to increasing the efficiency of solar cells and photovoltaics modules. These limitations are mainly due to the recombination phenomena [

Many authors, using different methods, have studied the temperature effect on the solar cell due to sunlight exposure and the effect of absorption [

One can note Priyanka et al.’s work [

Using the Performance Ratio as a grading technic, the temperature influence on the roof-top photovoltaic system which is set up on the library roof-top in Indian Institute of Science, Bangalore, India, is studied [

Ultimately, we have noted through the literature that temperature plays an important role in the performance of photovoltaic systems but works which consider the temperature effects of the solar cell constituted of cylindrical columnar grains were not produced yet [

The solar cell is assumed to have three zones [

When the solar cell is illuminated, there is creation of electron-hole pairs in the base [

∂ 2 δ ( r , θ , z ) ∂ r 2 + ∂ 2 δ ( r , θ , z ) ∂ z 2 + 1 r 2 ⋅ ∂ 2 δ ( r , θ , z ) ∂ θ 2 + 1 r ⋅ ∂ δ ( r , θ , z ) ∂ r − δ ( r , θ , z ) L 2 ( T ) = − G ( z ) D ( T ) (1)

We assume that in our model, the intragrain material is homogeneous and the doping level in each region is assumed to be uniform, hence no electric field in the top or the base region. This leads to azimuthal symmetry and the number of independent coordinates reduces to two, namely, rand z, using the conventional cylindrical coordinate system. Therefore the continuity equation becomes:

∂ 2 δ ( r , z ) ∂ r 2 + ∂ 2 δ ( r , z ) ∂ z 2 + 1 r ⋅ ∂ δ ( r , z ) ∂ r − δ ( r , z ) L 2 ( T ) = − G ( z ) D ( T ) (2)

with:

δ ( r , z ) : excess minority carrier’s density;

L ( T ) is the electron diffusion length in the base;

D ( T ) is the electron diffusion coefficient in the base. Its specifications are given in [

L 2 ( T ) = τ ⋅ D ( T ) (3)

τ is the lifetime;

and

D ( T ) = μ ( T ) ⋅ k b q ⋅ T (4)

μ ( T ) is the coefficient mobility [

μ ( T ) = 1.43 × 10 9 ⋅ T − 2.42 c m 2 ⋅ V − 1 ⋅ S − 1 (5)

k b is the Boltzmann constant;

q is the elementary charge of an electron;

G ( z ) is the electron-hole pairs generation expressed as [

G ( z ) = α ⋅ I 0 ⋅ ( 1 − R ) ⋅ exp ( − α ⋅ z ) (6)

The coeﬃcient α denotes the absorption of light for wavelength λ ; and I 0 is the incident photon ﬂux [

While proceeding by the separation method of the variables used by [

δ ( r , z ) = ∑ k ≥ 1 ∞ f k ( r ) ⋅ sin ( c k ⋅ z ) + K k (7)

The general solution of the excess minority carriers density is then given by:

Coefficients A k and K k are obtained from the boundaries conditions of the solar cell:

・ at the junction (z = 0) [

∂ δ ( r , z , T ) ∂ z | z = 0 = S f D ( T ) ⋅ δ ( r , T , z = 0 ) (9)

・ at the back side of the solar cell [

∂ δ ( r , z , T ) ∂ z | z = H = − S b D ( T ) ⋅ δ ( r , T , z = H ) (10)

・ at the grain boundary (r = R) [

∂ f ( r , T ) ∂ r | z = R = − S g b D ( T ) ⋅ f ( R , T ) (11)

In Equation (9), as shown by [

Sb, in Equation (10), is the back-side surface recombination velocity. It quantiﬁes the rate at which excess minority carriers are lost at the back-side surface of the cell [

In ^{5} cm・s^{−1}.

^{5} cm・s^{−1} and then decreases very slightly.

A part the open circuit operating area, the behavior of the power-SF curve matches fairly with works presented in [^{3} cm・s^{−1}. The result states the series resistance (R_{s}) determination which is calculated considering the solar cell in open circuit operating condition as a voltage generator. On the other hand, our model could be used to determine the shunt (R_{sh}) of the solar cell. It can be also applied using characterization methods to determine the real back-side surface recombination (Sb) [_{eff}) [

The current-voltage (I-V) and power-voltage (P-V) characteristic curve are presented in

It is noted in _{sc}) and the photo voltage (V_{oc}) increases and decreases, respectively as shown in [

The temperature dependence of the performance parameters of polycrystalline silicon solar cell is considered. We presented the open circuit photovoltage (V_{oc}), the fill factor (FF) and the short circuit photocurrent (I_{cc}) variations with the cell temperature in Figures 5-7, respectively.

In _{oc}-T, I_{cc}-T and FF-T for various grain boundary recombination velocity (Sgb) and various radius (R), respectively.

We notice in Figures 5-7, that the open circuit voltage is observed to decrease slightly with cell temperature and Sgb. But fill factor decreases very softly with cell temperature and increases when the radius (R) increases while the short-circuit current is found to increase with cell temperature [

It is obvious that the solar cell temperature plays a key role in the solar cell performance as shown in [_{g}), the reverse saturation current (I_{0}), the ideality factor (n), the parasitic resistance which are the shunt (R_{sh}) and the series resistance (R_{s}). Indeed, it is shown that [_{0}),

which corresponds to recombination in neutral regions, increases with increasing temperature whereas it decreases with increasing bandgap. I_{0} is the most heavily affected parameter when the temperature varies [

The decrease in bandgap with increasing temperature, observed on several semi-conductors, results in an increase of the reverse saturation current. These decrease due to additional thermally generated electrons in the conductivity band and the holes in the valence band; which leads to lower open-circuit operating point (V_{oc}).

Some authors have also shown that, increasing the solar cell temperature increases the intrinsic concentration, n_{i} and decreases the contact potential difference (ddp). As, the open circuit voltage (V_{oc}) is proportional to the ddp, it decreases as shown in [

The short-circuit current (I_{sc}) is proportional to the number of generated charge carriers and mobility as well as it depends strongly on the generation rate and the diffusion length. The diffusion length depends on the product of the carrier lifetime and excess minority carrier mobility which is more sensitive to the temperature variation. The excess minority carrier mobility which determines diffusion length evolution with the temperature is linked to the lattice scattering, ionized acceptor and donor impurities scattering and electron-hole scattering. Hence the total excess minority carriers mobility is determined considering the minority electron mobility limited by lattice, acceptor, donor and hole. But it is shown [_{L}) decreases very sharply with temperature leading both increase of photons and the short-circuit current. Moreover, it is also noted that the rate of generation of charge carrier increases with cell temperature leading to an increment of the short circuit current as shown in [

A similar behavior of our result is also observed in earlier reported work of other researchers for silicon solar cells [

By plotting the FF-T and η-T curves, we remarked that the Fill Factor (FF) and efficiency (η) decrease with the increase of the temperature as shown in [_{oc} and the increase of the I_{sc}. The increase of I_{sc} with solar cell temperature does not affect much to FF and η due to high variation of I_{0} with temperature with over 270% increase from T = 25˚C to 70˚C as shown by [_{i}(STC) with η the efficiency of the SPV and STC, the standard test condition.

We plotted in Figures 9-11 the temperature coefficient (T-coefficients) of short circuit photocurrent, open circuit photovoltage and efficiency versus temperature, respectively. Indeed,

whereas in _{oc}, which will decrease the temperature sensitivity of the solar cell. This means that decreasing the recombination currents in the bulk and on the surfaces of the cell greatly improves the temperature coefficient of open circuit photovoltage [

In summary, we have investigated the impact of temperature on the performance of an N-P solar cell considering the columnar cylindrical grain. Findings showed that with the temperature increasing, the short circuit increases slightly, and the open-circuit decreases sharply. The short-circuit photo current density, the open circuit photovoltage, the fill factor, the efficiency and the T-coefficients are linearly dependent on the temperature. The increase of the temperature entails a reduction of tension and a light growth of the current and thereafter, a relative decrease of the maximal power. Therefore, temperature influences negatively on the output of production of the solar cells.

Leye, S.N., Fall, I., Mbodji, S., Sow, P.L.T. and Sissoko, G. (2018) Analysis of T-Coefficients Using the Columnar Cylindrical Orientation of Solar Cell Grain. Smart Grid and Renewable Energy, 9, 43-56. https://doi.org/10.4236/sgre.2018.93004