^{1}

^{1}

^{1}

^{1}

^{1}

^{1}

^{1}

It is well known that temperature acts negatively on practically all the parameters of photovoltaic solar cells. Also, the solar cells which are subjected to particularly very high temperatures are the light concentration solar cells and are used in light concentration photovoltaic systems ( CPV ). In fact, the significant heating of these solar cells is due to the concentration of the solar flux which arrives on them. Light concentration solar cells appear as solar cells under strong influences of heating and temperature. It is therefore necessary to take into account temperature effect on light concentration solar cells performances in order to obtain realistic results. This one-dimensional study of a crystalline silicon solar cell under light concentration takes into account electrons concentration gradient electric field in the determination of the continuity equation of minority carriers in the base. To determine excess minority carrier’s density, the effects of temperature on the diffusion and mobility of electrons and holes, on the intrinsic concentration of electrons, on carrier’s generation rate as well as on width of band gap have also been taken into account. The results show that an increase of temperature improves diffusion parameters and leads to an increase of the short-circuit photocurrent density. However, an increase of temperature leads to a significant decrease in open-circuit photovoltage, maximum electric power and conversion efficiency. The results also show that the operating point and the maximum power point (MPP) moves to the open circuit when the cell temperature increases.

The principle of light concentration photovoltaic systems (CPV) is to concentrate, using parabolic mirrors or Fresnel lenses, the sunlight on a PV cell, to obtain higher conversion efficiency than those classic cells. This process, which is more recent, uses cell technologies which are more expensive but also more efficient than conventional cells [

Among these light concentration solar cells, those which use multispectral conversion technology allow highest efficiency to be obtained [

However, the relatively high cost of these cells makes multispectral conversion a very expensive technology for large-scale adoption of photovoltaic energy [

Several studies have been carried out taking into account the electric field of concentration gradient [

Many authors [

Wang et al. [

In this work, we take into account temperature influence on: mobility and diffusion coefficients of electrons and holes, the intrinsic concentration of carriers, the carrier’s generation rate and the width of band gap. We study temperature effect on diffusion parameters and electrical parameters such as photocurrent density, photovoltage, electrical power and conversion efficiency. We submit a crystalline silicon solar cell to concentrated light (C = 50 Suns) and we take into account electrons concentration gradient electric field.

Our study model is a silicon solar cell illuminated by a concentrated light under temperature influence as shown in ^{+}-p-p^{+}) operating under a concentrated multispectral light (C = 50 Suns) in the quasi-neutral base assumption [

E ( x ) = D p − D n μ n + μ p ⋅ 1 δ ( x ) ⋅ ∂ δ ( x ) ∂ x (1)

The distribution of excess minority carriers in the solar cell’s base along the x axis is given by:

∂ 2 δ ( x , T ) ∂ x 2 − δ ( x , T ) ( L c ( T ) ) 2 = − G n D c ( T ) (2)

with D c ( T ) = μ n ( T ) [ 2 D n ( T ) − D p ( T ) ] + μ p ( T ) D n ( T ) μ n ( T ) + μ p ( T ) (3)

D c ( T ) represents the expression as function of temperature T of diffusion coefficient in the base with the taking into account of the electric field of electrons concentration gradient. The expressions as functions of temperature of the mobility of electrons and holes respectively μ n ( T ) and μ p ( T ) are given by following equations [

μ m ( T ) = μ m min ( T ) + μ m L ( T ) − μ m min ( T ) 1 + ( N m N m r e f ( T ) ) a m ( T ) (4)

μ m L ( T ) = μ m , 300 L ( T 300 ) y 0 , m (5)

μ m min ( T ) = μ m , 300 min ( T 300 ) y 1 , m (6)

N m r e f ( T ) = N m , 300 r e f ( T 300 ) y 3 , m (7)

a m ( T ) = a m , 300 ( T 300 ) y 4 , m (8)

In above equations, m is the type of dopant material (type n or type p). For this work the n-type dopant concentration of N d = 10 18 cm − 3 and p-type of N a = 10 16 cm − 3 ^{ }was determined. We have, for:

· m = n : μ n , 300 L = 5300 cm 2 / V ⋅ s , y 0 , n = − 19 , μ n , 300 min = 1520 cm 2 / V ⋅ s , y 1 , n = − 2 , N d , 300 r e f = 64 × 10 16 cm − 3 , y 3 , n = 37 , a n , 300 = 05 , y 4 , n = 0 .

· m = p : μ p , 300 L = 200 cm 2 / V ⋅ s , y 0 , p = − 1.2 , μ p , 300 min = 24 cm 2 / V ⋅ s , y 1 , p = 1.2 , N a , 300 r e f = 2.5 × 10 17 cm − 3 , y 3 , p = 0.47 , a p , 300 = 1 , y 4 , p = 0 .

Expressions of electrons and holes diffusion coefficient are given by the following equation [

D n , p ( T ) = k T q μ n , p ( T ) (9)

with q the elementary charge, k the Boltzmann constant. The generation rate G n is the sum of two contributions:

· The carrier photo-generation rate G ( x ) at the depth x in the base [

G ( x ) = C ⋅ ∑ i = 1 3 a i e − b i x (10)

C represents light concentration.

· The carrier thermal generation rate which is given by [

G t h = C t h ⋅ n i 2 (11)

C t h is a proportionality coefficient and n i is the intrinsic concentration of minority carriers in the base which expression is given by [

n i = A n ⋅ T 3 2 ⋅ exp ( − E g ( T ) 2 k T ) (12)

A n is a specific constant of the material ( A n = 3.87 × 10 16 for silicon). N_{b} is the base doping concentration in impurity atoms [

E g ( T ) = 1.1557 − 7.021 × 10 − 4 T 2 T + 1108 (13)

G n = G ( x ) + G t h

The excess minority carriers’ density is determined solving continuity Equation (2):

δ ( x , T ) = A c h ( α ( T ) x ) + B s h ( α ( T ) x ) + ∑ i = 1 3 K i ( T ) ⋅ e − b i x + ( L c ( T ) ) 2 D c ( T ) C t h A n 2 T 3 exp ( − E g ( T ) k T ) (14)

with K i ( T ) = C D c ( T ) a i ( L c ( T ) ) 2 [ 1 − ( b i L c ( T ) ) 2 ] and α ( T ) = 1 L c ( T )

Coefficients A and B are determined through the following boundary conditions:

· At the junction (x = 0)

D c ( T ) ⋅ ∂ δ ( x , T ) ∂ x | x = 0 = S f ⋅ δ ( x = 0 , T )

The junction dynamic velocity (Sf) is the sum of two contributions: the intrinsic junction recombination velocity (Sf_{0}) related to carriers losses at the junction and the junction dynamic velocity (Sf_{j}) that defines the operating point of the cell because it is the carriers’ flow imposed by an external load resistance [

S f = S f 0 + S f j

· At the rear side (x = H)

D c ( T ) ⋅ ∂ δ ( x , T ) ∂ x | x = H = − S b ⋅ δ ( x = H , T )

The back surface recombination velocity (S_{b}) quantifies the losses of carriers at the cell’s rear side [

Applying Fick’s law at the junction, we obtained the photocurrent density given by [

J p h ( S f , T ) = q ⋅ D c ( T ) ⋅ ∂ δ ( x , S f , T ) ∂ x | x = 0 (15)

The photovoltage across the solar cell junction derives from the Boltzmann relation [

V p h ( S f , T ) = V ( T ) ⋅ ln [ δ ( x = 0 , S f , T ) n 0 + 1 ] (16)

In this expression V ( T ) represents the thermal voltage and n_{0} is electrons density at thermodynamic equilibrium. We have V ( T ) = k T q and n 0 = n i 2 N B ; n i is intrinsic concentration of electrons.

The electric power delivered by the solar cell base to an external circuit expression is [

P ( S f , T ) = V p h ( S f , T ) ⋅ J p h ( S f , T ) (17)

The solar cell’s conversion efficiency is given by the Equation 18 [

η ( T ) = P m ( S f , T ) P i n c (18)

In this expression, P_{inc} is the power of the incident concentrated light. For a light concentration solar cell and under Air Mass 1.5 standard conditions (1000 W/m^{2}), the proportion of light, which is concentrated, is around 720 W/m^{2}. Thus, for a 50 suns light concentration, P_{inc} is assumed to be [

P i n c = 0.072 W / cm 2 × 50 = 3.6 W / cm 2

We plotted variations of diffusion coefficient and diffusion length, versus temperature as shown respectively in

From 300 K to 314 K,

However from 314 K, the diffusion parameters increase with increasing temperature. This behavior leads to an increase of carriers flow through the junction and therefore an increase of short circuit current density as shown in

The solar cell being under light concentration and therefore operating under high temperatures, in the rest of this work we’ll only take into account the temperatures T ≥ 314 K.

The curves in _{sc}). This increase of short-circuit photocurrent density with increase of temperature is in good agreement with increases of diffusion coefficient and diffusion length observed above for temperatures T ≥ 314 K. This result is in good agreement with Agroui et al. [

The curves in

The curves also show that an increase of temperature leads to a decrease of the value of short circuit junction dynamic velocity Sf_{cc} corresponding to the null values of the photovoltage.

T(K) | 314 | 348 | 382 | 416 | 450 |
---|---|---|---|---|---|

Sf_{cc} (cm/s) | 3.95 × 10^{13} | 4.22 × 10^{11} | 9.00 × 10^{9} | 4.92 × 10^{8} | 2.63 × 10^{7} |

These results confirm that the values of (Sf) from which the photovoltage becomes null decrease when the cell’s temperature increases. This result corresponds to a displacement of the solar cell operating point towards the open-circuit when cell’s temperature increase.

The curves in

of the maximum power. This result is in agreement with increase of photocurrent density and the significant decrease of photovoltage with temperature increase. This result is in agreement with those of Leye et al. [

The curves also show a displacement of the maximum power point towards low values of junction dynamic velocity (open-circuit).This displacement of the maximum power point towards open-circuit can be explained by the displacement of the operating point towards open circuit when temperature increases and which was shown by the study of photovoltage.

We give in _{MPP}) and the solar cell conversion efficiency.

T (K) | 314 | 348 | 382 | 416 | 450 |
---|---|---|---|---|---|

P_{max} (mW/cm^{2}) | 734.46 | 598.79 | 464.06 | 331.20 | 206.89 |

Sf_{MPP}(cm/s) | 4.00 × 10^{4} | 3.10 × 10^{4} | 2.40 × 10^{4} | 1.43 × 10^{4} | 1.11 × 10^{4} |

Efficiency η(%) | 20.40 | 16.63 | 12.89 | 9.20 | 5.74 |

The results confirm a decrease of maximum power and junction dynamic velocity at maximum power point (Sf_{MPP}) when temperature increases.

A one-dimensional study of temperature effect on light-concentrating solar cell was carried out. This study takes into account the electric field of electrons concentration gradient. Temperature effects on diffusion and mobility of electrons and holes, on electrons intrinsic concentration, on carrier’s generation rate as well as on width of band gap have also been taken into account.

Thus, under light concentration with taking into account of electrons concentration gradient electric field, it makes possible to show that an increase of temperature improves the diffusion parameters, thus causing a increase of short-circuit photocurrent density.

However, an increase of temperature adversely affects performances of the solar cell. Thus, there is a significant decrease in open-circuit photovoltage, maximum electric power and conversion efficiency when the temperature increases. These results are in agreement with several authors [

It also appears that an increase of temperature causes a displacement of operating point and maximum power point towards the open circuit. These results confirm the need to use a cooling system for solar cells under intense light concentration.

However in this article, light concentration has been set at C = 50 Suns, while it could vary and therefore influence the temperature values and the results of this work. It would therefore be interesting to vary the concentration, in order to show for different values of light concentration, how the temperature acts on the solar cell.

The ISP, Uppsala University, Sweden is gratefully acknowledged for their support to project BUF01.

The authors declare no conflicts of interest regarding the publication of this paper.

Savadogo, M., Soro, B., Konate, R., Sourabié, I., Zoungrana, M., Zerbo, I. and Bathiebo, D.J. (2020) Temperature Effect on Light Concentration Silicon Solar Cell’s Operating Point and Conversion Efficiency. Smart Grid and Renewable Energy, 11, 61-72. https://doi.org/10.4236/sgre.2020.115005