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Dear Label_Name,

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I am writing on behalf of an international publishing house, Science and Education Publishing, USA (http://www.sciepub.com).

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American Journal of Public Health Research
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The Implementation of a Tele-Homecare System with Service Oriented Architecture and HL7 Message Transmission Standard
Ching-Sung Wang

American Journal of Medical and Biological Research
DOI: 10.12691/ajmbr-1-1-2

The Influence of Ethanol on Pyruvate Kinases Activity in Vivo, in Vitro, in Silico
Lelevich Sergey Vladimirovich, Khrustalev Vladislav Victorovich, Barkovsky Eugene Victorovich, Shedogubova Tatyana Aleksandrovna

American Journal of Medical Sciences and Medicine
DOI: 10.12691/ajmsm-1-1-1

Clinical and Histological Features in Wegener Granulomatosis
Li Cavoli Gioacchino, Passantino Rita, Bono Luisa, Tortorici Calogera, Ferrantelli Angelo, Giammarresi Carlo, Rotolo Ugo

American Journal of Infectious Diseases and Microbiology
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The Curse of Lymphatic Filariasis: Would the Continual Use of Diethylcarbamazine Eliminate this Scourge in Papua New Guinea?
Anne Lanham, Lillian Mwanri

We have released issues of some journals on February 2013.
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American Journal of Medical Sciences and Medicine
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American Journal of Cancer Prevention
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Dear Label_Name,

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Welcome to the April, 2013 edition of SciEP newsletter, providing monthly summaries of articles on science & education related topics of interest to scientist and professionals. The mission of our journals is to provide an open access forum for publishing new findings on issues pertinent to scientific and academic field. We also invite you to submit original research papers, review articles, short reports, or case studies are considered for publication in our Multidisciplinary Journals.

American Journal of Public Health Research
DOI: 10.12691/ajphr-1-1-3

The Implementation of a Tele-Homecare System with Service Oriented Architecture and HL7 Message Transmission Standard
Ching-Sung Wang

American Journal of Medical and Biological Research
DOI: 10.12691/ajmbr-1-1-2

The Influence of Ethanol on Pyruvate Kinases Activity in Vivo, in Vitro, in Silico
Lelevich Sergey Vladimirovich, Khrustalev Vladislav Victorovich, Barkovsky Eugene Victorovich, Shedogubova Tatyana Aleksandrovna

American Journal of Medical Sciences and Medicine
DOI: 10.12691/ajmsm-1-1-1

Clinical and Histological Features in Wegener Granulomatosis
Li Cavoli Gioacchino, Passantino Rita, Bono Luisa, Tortorici Calogera, Ferrantelli Angelo, Giammarresi Carlo, Rotolo Ugo

American Journal of Infectious Diseases and Microbiology
DOI: 10.12691/ajidm-1-1-2

The Curse of Lymphatic Filariasis: Would the Continual Use of Diethylcarbamazine Eliminate this Scourge in Papua New Guinea?
Anne Lanham, Lillian Mwanri

We have released issues of some journals on February 2013.
American Journal of Public Health Research
American Journal of Medical Sciences and Medicine
American Journal of Medical and Biological Research
American Journal of Pharmacological Sciences
American Journal of Clinical Medicine Research
American Journal of Nursing Research
American Journal of Cancer Prevention
American Journal of Medicine Studies
American Journal of Infectious Diseases and Microbiology
American Journal of Cardiovascular Disease Research
American Journal of Biomedical Research
American Journal of Mechanical Engineering
American Journal of Microbiological Research
Journal of Preventive Medicine
American Journal of Food and Nutrition
American Journal of Hypertension Research
American Journal of Sports Science and Medicine
Journal of Cancer Research and Treatment
American Journal of Zoological Research
Journal of Biomedical Engineering and Technology
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A Steady-State Spectral Response and Quantum Efficiency Determination of a Bifacial Silicon Solar Cell under Monochromatic Illumination and Constant Magnetic Field Effects by Using the Photoconductivity Method

Amadou Diao*, Adama Ndiaye, Mountaga Boiro, Senghane Mbodji

Department of Physics, Semiconductors and Solar Energy Laboratory, Faculty of Sciences and Techniques, Cheikh Anta Diop University, Dakar, Senegal

Abstract: In this work, a theoretical approach of the effects of wavelength and applied magnetic field on the spectral response and quantum efficiency of a bifacial silicon solar cell, is made. For this, the continuity equation relative to the photogenerated minority carriers in the base of the solar cell, in steady-state, is used. The resolution of this equation allowed us to determine the minority carriers’ density according to the wavelength, the magnetic field and the junction recombination velocity. Based on the expression of minority carriers’ density, we obtained the photoconductivity, the photocurrent density from which the spectral response and the quantum efficiency have been established according to the excitation and phenomenological parameters of the solar cell. We found that, as the magnetic field increases, both the spectral response and quantum efficiency decrease; this situation shows a degradation of the intrinsic properties of the solar cell.

Keywords: bifacial solar cell, photoconductivity, spectral response, quantum efficiency, magnetic field, wavelength

Received September 01, 2023; Revised October 02, 2023; Accepted October 09, 2023

Citation: Amadou Diao, Adama Ndiaye, Mountaga Boiro, Senghane Mbodji, A Steady-State Spectral Response and Quantum Efficiency Determination of a Bifacial Silicon Solar Cell under Monochromatic Illumination and Constant Magnetic Field Effects by Using the Photoconductivity Method. American Journal of Materials Science and Engineering, 11 (2). 29-34. January 2023. doi:10.12691/ajmse-11-2-1

1. Introduction

Photovoltaic energy, a part of renewable energy sources, produced by the solar panels, is a particular interest to overcome environmental problems (greenhouse effects, climate change etc.) and the growing energy demands of the world’s population. However, this solar energy depends on weather conditions, installation technique of PV panels and their energy conversion efficiency, the nature of the solar cells that are used and the manufacturing technology [1]. Therefore, several techniques and methods have been developed for the characterization of solar cells in order to improve the electrical, electronic, phenomenological parameters and the energy conversion efficiency of these cells. Thus, the photoconductivity [2-20], the spectral response [21] and the quantum efficiency [22-33] are widely used as characterization techniques. Furthermore, these authors Andrés Cuevas et al. [34] and Vasiliki Paraskeva et al. [35] have used respectively photoconductivity on the 'emitters' layers of solar cells and the effects of the shunt resistances of germanium multi-junction solar cells to measure their quantum efficiencies. Also, Giorgio Bardizza et al. [36] and Mauro Pravettoni et al. [37] have characterized dye-sensitive solar cells (DSSC) in frequency modulation and concentrated crystalline solar cells using the spectral response technique, respectively. For Baishali Talukdar et al. [38], the shading effect of several cells is shown on spectral response and quantum efficiency.

In this paper, we carry out a theoretical study of the wavelength and applied magnetic field effects on the spectral response and quantum efficiency of a silicon solar cell. We show how some properties of the solar cell, are degraded with the magnetic field.

2. Theory

A bifacial silicon solar cell of a n+-p-p+ type [39-43], is used in a one-dimension following the x-axis that corresponds to the incident illumination. The expression of the photoconductivity is given by [44]:

[picture] | (1)

with:

[picture] | (2)

where: μo is the static mobility of electrons in the base without an applied magnetic field; q, τn and m are respectively the elementary charge, the average lifetime and the effective mass of electrons in the base; δn is the excess minority carriers’ density in the base.

In steady-state, excess minority carriers flow is governed by the continuity equation:

[picture] | (3)

With Dn being the minority carriers diffusion coefficient given by:

[picture] | (4)

Where Do is the minority carriers diffusion coefficient without magnetic field; G is the minority carriers generation rate [45,46] at position x, whose expression is:

[picture] | (5)

Where the parameters α(λ), R(λ) and (λ) are respectively the absorption coefficient, the reflection coefficient and the incident photons flux at wavelength λ.

A solution of equation (3) is given by:

[picture] | (6)

with:

and (7)

Where Ln is the minority carriers diffusion length in the base.

To obtain the complete expression of the minority carriers’ density, we have to determine the coefficients A and C by using the following boundary conditions [46,47]:

- at the junction (x = 0)

[picture] | (8)

- at the back side (x = H)

[picture] | (9)

Where Sf and Sb are respectively junction recombination velocity and back surface recombination velocity. The recombination velocity Sf is the sum of the junction recombination velocity due to the external load that defines the solar cell operating point and the intrinsic junction recombination velocity that materializes an effective recombination velocity of the minority carriers at the emitter-base interface.

For the discussion of the results in this work, we neglect the effective recombinations of the minority carriers at the emitter-base interface by setting the junction recombination velocity Sf = 5.10⁵ cm.s⁻¹ and minimize the minority carriers losses at the rear side, with a back surface recombination velocity Sb = 200 cm.s⁻¹.

3. Expression of the Photocurrent Density

The photocurrent density is determined according to the photoconductivity. Its expression is given by equation (10):

[picture] | (10)

Where γ is a coefficient that depends on geometrical parameters of the solar cell and the nature of the incident illumination; β a coefficient which expression is:

[picture] | (11)

4. Expressions of the Spectral Response and the Quantum Efficiency

The spectral response (SR) is the ratio of photocurrent density Jph to incident power Pi. Its expression is given by [48,49]:

[picture] | (12)

with:

[picture] | (13)

where i is the incident photons flux ((λ)), h is the Planck’s constant and C the light celerity in the vacuum.

Substituting equations (10) and (13) into equation (12), we get:

[picture] | (14)

On the one hand, from the relationship between spectral response and external quantum efficiency (EQE) [50,51,52] in equation (15):

[picture] | (15)

the external quantum and internal quantum (IQE) on the other hand in equation (16):

[picture] | (16)

We deduce the following equation:

[picture] | (17)

Through equations (15), (16) and (17), the quantum efficiency, which can vary with the photoconductivity, also depends on the wavelength and the applied magnetic field.

We present, in the following discussion, some results from these different relationships that are obtained above and consider a constant charge across the solar cell.

5. Results and Discussion

5.1. Profile of the Spectral Response (SR)

In figure 1, we represent the spectral response according to the wavelength for different values of the magnetic field:

Figure 1. Spectral response versus wavelength for different magnetic field values

In figure 1, the spectral response is given according to the wavelength for different values of the magnetic field. We get three curves that have the same behaviour. For a given curve, the spectral response increases with the wavelength until reaching a maximum value SRmax(λL) where λL is a corresponding limit wavelength. From this maximum value, the spectral response decreases with the wavelength. In the interval of wavelength [0.3μm; λL], the increase in spectral response is due to that of photoconductivity [20] which corresponds to a significant absorptivity of the base of the solar cell; what implies a good sensitivity of this cell. However, in the interval of wavelength ]λL; 1.2μm], the spectral response decreases; this leads to a decrease in the sensitivity of the solar cell since the photoconductivity also decreases in the base.

In the table below, we give a few values of SRmax and λL.

From the table, for SRmax = 2.8.10⁻⁵ A.W-1 and SRmax = 2.7.10⁻⁵ A.W⁻¹, we get the same value of λL = 0.7μm when the magnetic field values are respectively B = 0 T and B = 3.10⁻⁴ T. For a magnetic field B = 10⁻³ T, we have SRmax = 2.5.10⁻⁵ A.W⁻¹ and λL = 0.64μm. The variation of Δλl between the values λL = 0.64μm for B = 10⁻³ T and λL = 0.7μm for B = 0 T, and then that of ΔSRmax between the values SRmax = 2.5.10⁻⁵ A.W⁻¹ and SRmax = 2.8.10⁻⁵ A.W⁻¹, give respectively ΔλL = - 0.06μm and ΔSRmax = - 0.3. 10⁻⁵ A.W⁻¹. These negative variations show a wavelength shift towards short wavelength and a decrease of the maximum spectral response; this leads to a narrowing of the solar cell sensitivity range when the magnetic field increases.

Table. A Few values of SRmax and λL for different magnetic fields

5.2. Profiles of the Quantum Efficiencies

In figure 2-a, the external quantum efficiency is represented according to the wavelength for different magnetic field:

Figure 2-a. External quantum efficiency versus wavelength for different magnetic field values

At the figure 2-a above, the three curves of external quantum efficiency according to the wavelength, present the same behaviour for the different magnetic field values. For a given curve, the maximum of the external quantum efficiency is localized in the visible wavelength domain. We obtained three maximum values of the external quantum efficiency: i) the first EQEmax1 = 0.422 corresponds to a wavelength λ1 = 0.34μm for the three magnetic field values; ii) the second EQEmax2 = 0.565 to a wavelength λ2 = 0.52μm for B = 0 T and B = 3.10⁻⁴ T; iii) the third EQEmax3 = 0.555 to a wavelength λ2 = 0.48μm for B = 10⁻³ T. Beyond these maximum values, the external quantum efficiency decreases when the wavelength increases since the absorption of the incident photons becomes feeble in the base depth of the solar cell. From the wavelength λ = 0.455μm, the amplitude of the external quantum efficiency decreases with the increase of the magnetic field.

After studying the external quantum efficiency, we represent, now, in figure 2-b, the internal quantum efficiency according to the wavelength for different magnetic field values:

Figure 2-b. Internal quantum efficiency versus wavelength for different magnetic field values

At the Figure 2-b, the internal quantum efficiency decreases with the wavelength for the three represented curves. For short wavelengths corresponding to high energies of incident photons, the internal quantum efficiency is at its maximum: the photons are strongly absorbed by a certain thickness in the front face of the solar cell. The maximum value IQEmax = 0.978 of the internal quantum efficiency, is obtained at the wavelength λ = 0.30μm. As the wavelength increases, the photon absorption gradually decreases and the base of the solar cell becomes especially transparent of the long wavelengths. The increase of the magnetic field leads to a decrease in the amplitude of the internal quantum efficiency.

The profile of the quantum efficiency (external and internal), according to the wavelength, without an applied magnetic field, is shown in Figure 2-c:

In figure 2-c, we represent both quantum efficiencies curves, without a magnetic field, according to the wavelength. A comparison of these curves, shows a clear difference between the values EQEmax2 = 0.565 and IQEmax = 0.978. From the wavelength λ = 0.30μm to that of up to a slightly higher value than λ = 1μm, the internal quantum efficiency remains higher than the external quantum efficiency. At long wavelengths, the decrease of the quantum efficiency can be linked to a probable recombination of photogenerated minority carriers in the bulk of the base. For wavelengths λ > 1μm, the low quantum efficiency corresponds to a very weak absorption of the incident photons by the base of the solar cell since there is no more photogenerated minority carriers.

Figure 2-c. Quantum efficiency versus wavelength without an applied magnetic field

5.3. Comparative Profiles of the Spectral Response and the External Quantum Efficiency

The spectral response and the external quantum efficiency, according to the wavelength, without an applied magnetic field, are represented in Figure 3:

Figure 3. Spectral response and external quantum efficiency versus wavelength, without an applied magnetic field

In Figure 3, the two curves representing the spectral response and the external quantum efficiency according to the wavelength, have the same behaviour. However, the maximums of the spectral response SRmax = 2.8.10⁻⁵ A.W⁻¹ and the external quantum efficiency EQEmax2 = 0.565, correspond respectively to wavelengths λl and λ2 which all are defined in the visible domain. Thus, we determine the wavelength interval [0.4μm; 0.8μm] where the maximum values of the spectral response and the external quantum efficiency are founded.

6. Conclusion

From the relationships that are established between the studied quantities, we analyzed the effects of the wavelength and the magnetic field on the spectral response and the quantum efficiency. Some specific wavelengths for different magnetic fields, corresponding to the maximum spectral response and quantum efficiency values, were determined. It is noted, from these profiles, that the increase of the magnetic field leads to a narrowing of the sensitivity range of the solar cell and that the specific wavelengths are in the visible domain.

It should be reminded that, in this work, we fixed the junction and the rear side recombination velocities and then neglected the contribution of the solar cell emitter. In addition, for a future work, we will be able to take into account of the influence of junction and the rear side recombination velocities on the spectral response and quantum efficiency in order to determine phenomenological parameters of the solar cell.

We Acknowledge the Semiconductors and Solar Energy Laboratory, the Research Team in Renewable Energies, Materials and Laser and the Dean of the Faculty of Sciences and Techniques for supporting this work.

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