International Journal of Photoenergy
Volume 2019 (2019), Article ID 7945683, 14 pages
https://doi.org/10.1155/2019/7945683

Research Article

Determination of Technological Features of a Solar Photovoltaic Cell Made of Monocrystalline Silicon P⁺PNN⁺

Cristian-Petre Fluieraru,¹ Gabriel Predușcă,¹ Horia Andrei,¹ Emil Diaconu,¹ Petru Adrian Cotfas,² and Daniel Tudor Cotfas²

¹Department of Electronics, Telecommunications, and Energy Engineering, University Valahia of Târgoviște, Str. Aleea Sinaia, Nr. 13, RO-130004 Târgoviște, Romania
²Department of Electronics and Computer, University Transilvania of Brasov, Str. Universitatii, Nr. 1, Brasov, Romania

Correspondence should be addressed to Cristian-Petre Fluieraru; cristi2006tgv@yahoo.com

Received 6 April 2019; Accepted 26 September 2019; Published 19 November 2019

Academic Editor: Leonardo Palmisano

Copyright © 2019 Cristian-Petre Fluieraru et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

The development in the field of semiconductor materials and electronic devices has a great impact on systems with renewable energy sources. Determination of the functional parameters of photovoltaic solar cells is essential for the subsequent usage of these semiconductor devices. Research was made on type P⁺PNN⁺ monocrystalline silicon wafers. Crystallographic measurements of the photovoltaic solar cell were made by means of FESEM-FIB Auriga Workstation. Initial data were selected from the study of models found in the specialized literature. The experimental results were compared to classical mathematical models. Measurements made on the photovoltaic solar cell were realised in laboratory conditions on the NI-ELVIS platform produced by National Instruments.

1. Introduction

Absorption of photons under certain conditions in a semiconductor plate creates electrical power. The principle of conversion is based on the fact that in a semiconductor the electrons removed from the nucleus can be transformed into free conducting electrons in motion. This creates a positive load and a negative carrier simultaneously.

If there is a potential difference in the semiconductor material due to a p-n junction, then this load carrier can be forced to direct to an external circuit and thus an electric power can be produced. In the case of crystalline silica, the electric charge carriers that have been obtained can only reach this potential barrier due to thermal vibrations. No other force can lead them in this direction. This means that loaded particles will have to survive until they reach the potential barrier. The resulting lifetime is one of the key factors for the efficiency of photovoltaic energy production [1].

The physical effect was first observed by Becquerel in 1839 when he obtained power by exposing silver electrodes to radiation in an electrolyte. The effect was further described by Adams and Day in 1877 [2, 3]. They noticed that the exposure of selenium electrodes to radiation produces electrical voltage thus allowing them to obtain electrical power. Until 1949, when the semiconductor appeared, the photovoltaic effect was not used. Then in 1954, in the US, Chapin developed the first solar cell based on crystalline silicon, which had a 6% efficiency (very good for those times) [4]. In the coming years, efficiency has increased to 10%.

The main reason for the spread of the application of the photovoltaic effect to energy sources was the oil crisis of 1973. Since that time, specific research institutes have emerged around the world. At the beginning of the 1980s, it was recognized that the efficiency of solar cells is very important for reducing the cost of alternative energy systems. From this point on, research and development have been focused on achieving greater efficiency. For the future, it is expected that with the disappearance of fossil fuels, the Sun will be one of the few inexhaustible sources of energy widely used.

The efficiency record is 24-27% and is owned by a monocrystalline silicon solar cell using very complex technology [5, 6].

Cells currently commercially produced have an efficiency of between 14% and 16%. In particular cases, cells that stretch on larger surfaces have an efficiency of between 17% and 19% [7, 8].

In general, the efficiency of photovoltaic energy conversion is very limited of physical causes [9]. Approximately 24% of the solar radiation has a wavelength so large that it cannot be absorbed. In addition, 33% is lost as heat. The following 15-20% losses occur because the cell voltage reaches only 70% of the value corresponding to the energy range [10].

From the recent literatures, it was found that there are no studies on parasitic resistance and characteristics of PV cells made of monocrystalline silicon P⁺PNN⁺.

This study aims to determine the technological characteristics of PV cell monocrystalline silicon P⁺PNN⁺. The present work has five sections. Section 1 covers a review of the literature. Section 2 is based on the experimental setup and methodology of the studied PV cell. Determination and analysis of technological parameters of the studied PV cell are discussed in Section 3. Afterwards, the experimental results are interpreted in Section 4 and compared to theoretical ones. Section 4 provides concluding remarks.

2. Experimental Setup and Methodology

Monocrystalline silicon solar photovoltaic cells are the most stable from the family of photovoltaic cells made of silicon [10–15].

The processing of monocrystalline silicon for obtaining semiconductor devices for solar photovoltaic cells is a complex manufacturing process [16–18]. The studied cells are manufactured at ICPE-Bucharest, and they are type P⁺PNN⁺ solar photovoltaic cells (see Figures 1 and 2). There were type p silicon wafers used for its manufacturing. The production flow chart contains a couple of basic stages, each of it containing a few specific operations with longer or shorter processing times for semiconductor structures, such as photolithography and multiple high-temperature chemical processes. The attributes of semiconductor silicon devices are strongly influenced by temperature [19].

Figure 1: The structure of the analysed photovoltaic cell.

Figure 2: Photovoltaic cell type P⁺PNN⁺.

Semiconductor junctions lay at the foundation of manufacturing and functioning of the majority of semiconductor device categories. Related to conversion efficiency and power output, it is considered that the best results are obtained for the photovoltaic solar cells with p-n junctions [20]. Hence, if two semiconductor materials such as type p and type n are put in contact, they create the p-n junction of the material. Practically, this represents the separation area between the two regions [21], the type p semiconductor being doped with acceptor atoms (for instance, boron) and the type n semiconductor being doped with donor atoms (for instance, phosphorus). Pursuant to the diffusion of majority carriers in the junction area, there appears an area of positive spatial charge in layer n and an area of negative charge in layer p. In this situation, the electric field oriented from layer n to layer p appears [20, 22–24].

Crystallographic measurements of the photovoltaic solar cell were made by means of Auriga FESEM-FIB Workstation equipment. In Figure 3, the SEM analysis in a longitudinal section on a metallic face at a resolution of 100 μm is presented.

Figure 3: SEM analysis in a longitudinal section at a resolution of 100 μm.

X-ray diffraction is an analytic technique which offers structural and chemical information about the crystallography of a range of various materials [25], such as the crystallographic structure of the material, structural analysis of the material, surface analysis of the material, analysis of thin layers, and transformation due to the influence of temperature (see Figures 4 and 5) [25–27]. Graphics data processing was made by the representation of data acquired using a D8 DISCOVER diffractometer, Bruker AXS GmbH.

Figure 4: SEM and EDX for the upper part of the metal-faced layer of a photovoltaic solar cell.

Figure 5: Diffractometry spectrum realised using X-ray on smooth-faced of monocrystalline silicon solar cell.

Silicon is one of the hardest materials to interpret by X-ray diffraction. In order to be subjected to X-ray diffraction, the analysed cell was treated with hydrofluoric acid for 1-3 minutes, because above it is the SiO₂ layer, after which it was ultrasonicated in ionized water and finally dried with a flow of Azote. We identified with Si and the presence of silicon oxide. On one side of the platelet, the silicon oxide was intentionally created. On the other hand, the amount of oxide is small and is due to an accumulation of oxide time on the surface of the single crystalline platelets. From the X-ray diffraction spectra for the solar cell, we observed a shift of the peaks corresponding to the monocrystalline silicon. I noticed not only the additional peaks corresponding to the dopants but also the peaks corresponding to the metal impurities from the metal contacts.

2.1. Data Acquisition of Technological Parameters

The determination of functional parameters of photovoltaic solar cells is essential for the subsequent usage of these semiconductor devices. This is of major interest to manufacturers of such devices, because the parameter’s improvement has as an effect on the growth of photovoltaic cells’ efficiency [13–21]. Measurements made on the photovoltaic solar cell were realised in laboratory conditions on the NI-ELVIS platform produced by National Instruments (see Figure 6) [26, 27].

Figure 6: NI-ELVIS platform.

- characteristics were determined by monitoring the current getting through the photovoltaic solar cell at various temperatures and illumination levels. The values obtained for short-short-circuit current and open circuit voltage were determined using NI-Elvis board and LabView software (see Figure 7).

Figure 7: and study of the solar cell, as a function of temperature using the NI-ELVIS acquisition boards and LabView software.

2.2. Interpretation of - Characteristics of the Studied Photovoltaic Solar Cell

The - characteristics of the measured solar cell were represented and after that fitted using the theoretical model with two exponentials, according to the following relation [28, 29]:

where is the solar cell current, is the saturation current of the diffusion component, is the saturation current of the recombination component, is the parasitic series resistance, is the parasitic parallel (shunt) resistance, is the ideal factor of the diffusion current, and is the ideal factor of the recombination current.

The current in equation (1) contains two components:

(i)A diffusion component representing the contribution of optic-generated carriers which move by diffusion in neutral regions of the p-n junction. For this component, it was considered that the ideal parameter is the theoretical one, namely (ii)The second exponential component of the solar cell’s current is given by the recombination of carriers in the transition region of the p-n junction. It was considered that the recombination process is mainly controlled by the Shockley-Read-Hall recombination from the respective region, being produced by the existence of the contamination of metallic impurities in that area [30, 31]. Because the most profound metallic impurities, namely the ones that have the energetic level close to the forbidden bandwidth of silicon, are the ones that determine the recombination velocities, they were used as an ideal parameter for this current component,

The values of parasitic resistances were determined by means of an experiment, and they have the following values: and .

From measurement analysis, using the equation with 2 currents, considering , , , and and using Mathematica soft for the determination of the parameters by overlapping the curves (see Figures 8 and 9), the following values have been obtained (Table 1):

Figure 8: - diagram of solar cell 1 for (2) and overlapping of curves (1).

Figure 9: - diagram of solar cell 1 for (2) and overlapping of curves (1).

Table 1: Determination of the parameters of a photovoltaic solar cell.

(A)
(A)
(A)
(°C)

0.0291

31.96

0.0357

32.50

0.0430

32.86

0.0512

33.17

0.0604

33.50

0.0705

33.85

0.0817

34.24

0.0941

34.64

0.1077

35.06

0.1225

35.54

0.1384

36.04

2.3. Analysis of Recombination Saturation Current

Recombination saturation current of a photovoltaic solar cell with the p-n junction is given by the following relation:

where is the electron’s charge, is the thickness of the transition region emitter base in direct polarization, is the intrinsic concentration of carriers within silicon, is the junction area emitter base, and is the lifetime of minority carriers from the silicon wafer volume.

The component of current depends on the temperature by the medium of the intrinsic concentration . In the range of the measured temperature , this variation is very weak and can be neglected. Abnormal values, derived from measuring errors or errors of overlapping of the curves, were deleted.

From Table 1, the medium value of recombination saturation current, characteristic of a photovoltaic solar cell, is

This value allows the estimation of a lifetime of the minority carriers within the single-crystal silicon wafers used for manufacturing of the photovoltaic solar cell.

From relation (2) we have

The size of transition region of the p-n junction is computed as follows [30, 31]:

where is the internal voltage of the junction

and is the direct voltage which drops on the solar cell in conditions of a maximum power output.

From the accomplished measurements are obtained,

For the technological case,

which obtains:

Finally, using relation (4), the lifetime results are

Because of the technological conditions of the manufacturing of photovoltaic solar cells, the following range of values is used:

From the interpretation of the measurements for the - characteristics, a first important technological characteristic of photovoltaic solar cells is deducted, namely the value of a lifetime [17].

Hereafter, a qualitative analysis of diffusion saturation current in an ideal p-n junction were made.

For the ideal diode, has the following form [20, 21]:

which becomes, in the case of abrupt junction P⁺N,

or

where and are the length of diffusion and the diffusion coefficient of minority holes from base doped with a concentration of donor atoms.

By contrast with the recombination component , the diffusion current has a variation depending on the temperature which cannot be neglected anymore. It comes from the dependence of temperature of the following terms:

By solving equations (15), (16), and (17) then from (14), results

where and . With a good approximation, the following can be written:

From where

The experimental values obtained for a light source that approach the condition AM 1.5 are presented in Table 2.

Table 2: Values obtained for a photovoltaic solar cell measured in condition AM 1.5.

(A)
(V)
(°C)
(A)

0.122
0.48
35.5

From this table, we have

Below formula (21), the value of the diffusion component at room temperature () was deduced. The following was obtained:

Then the numerical value is ((22)), we have

This value will represent the main checkout key of computer models.

3. Computing Programs for Correlation of Experimental Data with Theoretical Models Using Matlab Simulations

In order to compare the obtained experimental results, the theoretical model of direct current-voltage characteristic was used when . To analyse in Matlab, we used the following material’s features, constants, and calculus formulas, which are available for [17, 31]:

(i)Intrinsic carrier concentration: (ii)Dielectric constant: (iii)Electron charge: (iv)Thermal potential and thermal energy: and (v)Coefficient of diffusion for load carriers:

where electrons are , , , and the holes are , , , and .

The following are the relationships between diffusion coefficient and electric mobility:

(i)Einstein’s relations are

(ii)The Shockley-Read-Hall lifetime recombination is

(iii)The lifetime of radiation recombination is

(iv)The Auger lifetime recombination is

where silicon-n is and silicon-p is (v)Total lifetime is

(vi)The lengths of the diffusion of minority carriers are

(vii)The variation in bandwidth forbidden at high doping levels is

where ; ; ; and (viii)The effective intrinsic concentration of carriers at high levels of doping is

(ix)The effective recombination speed at the P⁺P interface of the emitter is

(x)The density of saturation power at the P⁺P emitter is

(xi)The effective recombination speed on the interface on the base N⁺N is

(xii)The density of saturation power on the base N⁺N is

(xiii)Total saturation power is

(xiv)The open circuit voltage is

(xv)The efficient conversion of solar energy is

(xvi)The solar power in conditions AM 1.5 is

(xvii)The average short-circuit current density value for an AM spectrum 1.5 is

3.1. The Effective Recombination Velocities from an Emitter’s Interface P⁺/P Dependent on Recombination Velocities on the Region’s P⁺ Surface of Emitter

From Figures 10–12, we observe that if at the emitter’s surface, the recombination velocity is 10⁵ cm/s for a doping concentration of the emitter of 10¹⁷ cm⁻³, the recombination velocities decrease to a value of , , and , if an additional diffusion P⁺ is used with a concentration of 10¹⁷ cm⁻³, 10¹⁸ cm⁻³, and 10¹⁹ cm⁻³, respectively. The minimal value for the effective recombination velocities on the interface P⁺/P of emitter is obtained in the case of , , and (see Figure 11), while using a doping concentration of the emitter of , and its value becomes 0.2777  cm/s.

Figure 10: The effective recombination velocities from the emitter’s interface P⁺/P are dependent on recombination velocities on the region’s P⁺ surface of emitter in the following conditions: , , and τSRH = 5 μs.

Figure 11: The effective recombination velocities from the emitter’s interface P⁺/P are dependent on recombination velocities on the region’s P⁺ surface of emitter in the following conditions: , , and .

Figure 12: The effective recombination velocities from the emitter’s interface P⁺/P are dependent on recombination velocities on the region’s P⁺ surface of emitter in the following conditions: , , and .

3.2. The Effective Recombination Velocities from Base’s Interface N/N⁺ Dependent on Base’s Strongly Doped Concentration

A similar effect to the one of the effective recombination velocities from interface P⁺P is obtained at the contact surface of Al base where the recombination velocity is 10⁶ cm/s (see Figures 13–14). If on the back of the wafer an additional layer of diffusion N⁺ is made with a thickness of 5 μm (see Figure 13) and a concentration of 10¹⁹ cm⁻³, then the effective recombination velocities go down to the value of 10 cm/s for a base doped to 10¹⁵ cm⁻³. The minimal value for the effective recombination value from base’s interface N/N⁺ is obtained in the case of and (see Figure 15), using a doping concentration of , this value being of 0.5 cm/s.

Figure 13: The effective recombination velocities from base’s interface N/N⁺ dependent on base’s strongly doped concentration in the case of and .

Figure 14: The effective recombination velocities from base’s interface N/N⁺sp,ef dependent on base’s strongly doped concentration ND⁺ in the case of and .

Figure 15: The effective recombination velocities from base’s interface N/N⁺ dependent on base’s strongly doped concentration in the case of and .

The obtained values are available because they accomplish the following technological conditions:

(i)The average value of phosphorus base doping: (ii)The average value of emitter layer diffusion: (iii)The depth of junction p-n emitter-base:

4. Conclusions

In this study, current-voltage characteristics of a photovoltaic solar cell, measured in various conditions of illumination and temperature, are presented. Also, based on the analysis of these characteristics, the technological characteristics of the studied solar cell are determined.

A mathematical model of the physical processes which leads to the generation of electric currents in a complex photovoltaic solar cell type P⁺PNN⁺ with a finite recombination velocity on the surface is proposed.

Both recombination velocities of charge carriers on the surface and regions N⁺N and P⁺P are essential in photovoltaic solar cell type P⁺PNN⁺ functioning. In a photovoltaic solar cell with a p-n junction, the saturation current is given by the recombination on the two faces of the wafer.

The analysed case was accomplished for for the purpose of the correlation of the experimental data with theoretical models using Matlab.

The initial wafers of silicon are not competitive, but the application of the diffusion process of metallic contamination impurities by doping a phosphorus layer on the back of wafers led to a significant improvement of the lifetime in their volume.

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

The authors would like to thank Dan Sachelarie for his helpful discussion and ICPE Bucharest for measurements of SEM and X-ray diffraction.

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