_{1}

This work was based mainly on the capacitance of a silicon solar cell monofaciale in static conditions under monochromatic illumination and under the influence of temperature. Solving the continuity equation for excess minority carrier’s charge density in the base of the solar cell resulting in the term of the temperature equation in the presence of an optical source. The latter has allowed us to obtain the photocurrent density and photovoltage. Subsequently we studied the capacitance situation of open circuit and short circuit depending on the temperature. Finally with the determination of capacitance under C
_{0} darkness.

Temperature is a very important parameter and cannot be neglected in the behavior of solar cells. Knowing that the total incident energy (100%), a small portion (13%) is reflected by the surface of the sensor and this small portion is extracted as electrical energy, therefore a large portion of energy is dissipated as heat [

The study will be based primarily on the capacitance (open circuit in Short circuit, under dark), after studying the effect of temperature on the density of minority carriers, the photocurrent density, and photo voltage.

This solar cell is n + −p−p + (

In the remainder of this study, the contribution of the issuer as well as the crystalline field that exists within the base has been neglected [

∂ 2 δ ( x ) ∂ x ² − δ ( x ) L 2 = − g ( x ) D (1)

g ( x ) = ϕ ( λ ) α ( λ ) ( 1 − R ( λ ) ) e ( − α ( λ ) x ) (2)

( L ( T ) ) 2 = τ D ( T ) (3)

D ( T ) = μ k b q T (4)

δ ( x ) is denotes the density of electrons generated in the base at position x; (λ) is the flow monochromatic incident light; α ( λ ) is the absorption coefficient of monochromatic to the wavelength of material λ; R ( λ ) is the monochromatic reflectance of the material to the wavelength λ; k b is Boltzmann's constant; q is the elementary charge of an electron; τ is the lifetime of electrons in the base; D the diffusion coefficient of the electrons generated in the base [

Equation (1) is a differential of the second degree with second member whose general solution is:

δ ( x ) = A cosh ( x L ) + B sinh ( x L ) − ϕ ( λ ) α ( λ ) L 2 ( 1 − R ( λ ) ) e ( − α ( λ ) x ) D ( L 2 ( α ( λ ) ) 2 − 1 ) (5)

A and B are constants which are determined by the two following boundary conditions:

At the junction (x = 0) [

∂ δ ( ω , x , T ) ∂ x | x = 0 = S f D ⋅ δ ( ω , 0 , T ) (6)

At the rear side (x = H)

∂ δ ( x ) ∂ x | x = H = − S b D δ ( x ) | x = H (7)

S_{f} [_{b} [

At

the carrier density regresses when the depth x progresses. And also for a low value of the depth (at about the x is lower than 0.015 cm) when the temperature increases, the carrier’s density decreases.

However, for x greater than about 0.015 cm, the temperature of excess minority carrier’s density is increased. The decrease of excess minority carrier’s density versus depth for the two figures is explained by the fact that there recombination volume of excess minority carrier. Regarding temperature has an excitatory function, which explains the behavior of the carrier density.

The photocurrent resulting from the diffusion of the density of minority carriers at the junction and its expression is given by [

J p h ( S b , S f , λ , T ) = q D ∂ δ ( x , S b , S f , λ , T ) ∂ x | x = 0 (8)

We observe that for small values of the recombination velocity at the junction S_{f} (S_{f} less than 2 × 10^{2} cm/s) corresponding to open circuit, the photocurrent density is almost zero because the carriers are stored at the junction. From this value up to almost 5 × 10^{5} cm/s, the photocurrent density increases with that of Sf because some carriers starts passing through the junction. High values S_{f} (S_{f}

greater than 5 × 10^{5} cm/s) corresponds to the short-circuit because the maximum of carriers across the junction. As between 2 × 10^{2} and 5 × 10^{5} cm/s when the temperature increases, the photocurrent density decreases. Therefore 5 × 10^{5} cm/s is the short-circuit increasing the temperature causes one of the photocurrent density. Having made the study of the photocurrent density, are now considering the photo voltage.

The voltage harvested under monochromatic illumination across the solar cell and use the Boltzmann relation, the photo voltage can be expressed by [

V p h ( S b , S f , λ , T ) = V T ln ( N b n i 2 δ ( 0 , S b , S f , λ , T ) + 1 ) (9)

where V_{T} is the thermal voltage, N_{b} doping rate, or the concentration of minority carriers charge.

V T = k b q T (10)

n i 2 = A ⋅ T 3 exp ( − E g k b ⋅ T ) (11)

A is a specific constant of the material; n_{i} is the density of intrinsic carrier temperature.

We note that for low values of the junction recombination velocity corresponds to the open circuit where the carriers are stored at the junction recombination velocity; the photo voltage is at its maximum. Then she starts to decline from certain values of junction recombination velocity, now some carriers are beginning to cross the junction. Photo voltage tends to invalidity for high junction recombination velocity values corresponding to short circuit when the maximum carriers pass the junction. Also when the temperature is increasing, the photo voltage is decreasing.

The diffusion capacitance of the solar cell is known as the resulting ability of the load change during the diffusion process within the solar cell [

C ( S b , S f , λ , T ) = d Q ( S b , S f , λ , T ) d V ( S b , S f , λ , T ) (12)

As

Q = q δ ( x = 0 ) (13)

was as follows:

C = q d δ ( x = 0 ) d V (14)

Equation can be mentioned as follows:

C = q d δ ( x = 0 ) d S f 1 d V d S f (15)

Taking into account the expression of the photo voltage and the excess minority carrier’s density, we obtain the following expression:

C = q ( n 0 ( T ) ) 2 N b V T + q δ ( x = 0 , S b , S f , λ , T ) V T (16)

So

c = c 1 + c 2 (17)

where

c 1 = q ( n 0 ( T ) ) 2 N b V T (18)

is the intrinsic capacitance (ability to darkness) and depends on the nature of the material through the intrinsic concentration is the ability of the solar cell due to the illumination. The following two figures show the ability of the solar cell in open circuit condition and short circuit as a function of junction recombination velocity for different values of the temperature. n_{0}, through doping N_{b} and V_{T} thermal potential.

c 2 = q δ ( x = 0 , S b , S f , λ , T ) V T (19)

where C_{0} is the solar cell capacitance under dark. Equation 19 can be rewritten in the form

C ( S b , S f , λ , T ) = C 0 exp ( V p h V x ) (20)

With the logarithm function, we rewrite equation 20 as:

ln C − ln C 0 = V p h V T (21)

Equation (21) can be expressed as follows:

ln C ( S b , S f , λ , T ) = 1 V T ⋅ V p h ( S b , S f , λ , T ) + ln C 0 (22)

At _{f}_{ }concordant to open circuit, which holders are stored; capacity is at its peak. At this level the capacity remains virtually constant. Also this time the increasing temperature causes a drop in capacity. We note in

recombination velocity is high (

The following figure describes the ability of the solar cell in open-circuit condition in function of temperature for different wavelength values.

We find open circuit at the level of

At _{0} according to the photo voltage for different values of the temperature. The logarithm of the capacitance curves versus photo voltage for various temperature values are given in

From this figure we have determined for each temperature value in its corresponding capacitance C_{0} darkness. The temperature value is a straight line of slop 1/V_{T}.

C_{0} these values are given by

The study of this table shows that when the temperature rises, the darkness under C_{0} capacity also increases.

A theoretical study of a solar cell with monofaciale under static regime under

multispectral illumination is presented. From different studies, we could establish that the temperature favors the presence of photo generated electrons in the base by inhibiting their diffusion and their conduction. The diffusion capacitance of the solar cell increases with the temperature. Finally, the dark capacitance of the solar cell was obtained for any temperature value on the capacitance

T | 200 K | 303 K | 333 K | 400 K |
---|---|---|---|---|

C_{0 } | 8.54 × 10^{−22} F∙cm^{−2} | 1.01 × 10^{−12} F∙cm^{−2} | 5.25 × 10^{−11} F∙cm^{−2} | 5.21 × 10^{−8} F∙cm^{−2} |

(open circuit in Short circuit, under dark). Based on the C-V characteristics, a graphical method has been proposed for the determination of dark capacitances C_{0}.

Sahin, G. (2018) Effect of Temperature on the Capacitance of a Silicon Solar Cell in Static Regime. Energy and Power Engineering, 10, 187-197. https://doi.org/10.4236/epe.2018.105013