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

Authors: Cristian-Petre Fluieraru; Gabriel Predușcă; Horia Andrei; Emil Diaconu; Petru Adrian Cotfas; Daniel Tudor Cotfas
Journal: International Journal of Photoenergy
 (2019)

---

## 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.


---

## Body

## 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 Figure3, 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 100μm.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.I-V 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 Isc and open circuit voltage Voc were determined using NI-Elvis board and LabView software (see Figure 7).Figure 7
Isc and Voc study of the solar cell, as a function of temperature using the NI-ELVIS acquisition boards and LabView software.


### 2.2. Interpretation ofI-V Characteristics of the Studied Photovoltaic Solar Cell

TheI-V 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]:
(1)I=I01⋅expV−Rs⋅IkT/q⋅n1+I02⋅expV−Rs⋅IkT/q⋅n2+VRp,where I is the solar cell current, I01 is the saturation current of the diffusion component, I02 is the saturation current of the recombination component, Rs is the parasitic series resistance, Rp is the parasitic parallel (shunt) resistance, n1 is the ideal factor of the diffusion current, and n2 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 parametern is the theoretical one, namely n1=1
(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, n2=2The values of parasitic resistances were determined by means of an experiment, and they have the following values:Rs=0.750Ω and Rp=379Ω.From measurement analysis, using the equation with 2 currents, consideringn1=1, n2=2, Rs=0.75Ω, and Rp=379Ω 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
I-V diagram of solar cell 1 for Iph=0.0291A (2) and overlapping of curves (1).Figure 9
I-V diagram of solar cell 1 for Iph=0.1225A (2) and overlapping of curves (1).Table 1
Determination of the parameters of a photovoltaic solar cell.
Iph (A)
I01 (A)
I02 (A)
T (°C)
0.0291
9.76×10−10
4.37×10−9
31.96
0.0357
1.38×10−9
1.49×10−9
32.50
0.0430
2.31×10−9
2.05×10−9
32.86
0.0512
2.1×10−9
2.13×10−9
33.17
0.0604
1.52×10−9
1.58×10−9
33.50
0.0705
1.71×10−9
1.73×10−9
33.85
0.0817
3.01×10−9
3.09×10−9
34.24
0.0941
1.62×10−9
1.63×10−9
34.64
0.1077
2.34×10−9
2.35×10−9
35.06
0.1225
1.98×10−9
1.17×10−9
35.54
0.1384
2.13×10−9
1.61×10−9
36.04


### 2.3. Analysis of Recombination Saturation CurrentI02

Recombination saturation current of a photovoltaic solar cell with the p-n junction is given by the following relation:(2)I02=qwni2τAwhere q is the electron’s charge, w is the thickness of the transition region emitter base in direct polarization, ni is the intrinsic concentration of carriers within silicon, A is the junction area emitter base, and τ is the lifetime of minority carriers from the silicon wafer volume.The component of currentI02 depends on the temperature by the medium of the intrinsic concentration ni. In the range of the measured temperature T=32−37°C, 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 Table1, the medium value of recombination saturation current, characteristic of a photovoltaic solar cell, is
(3)I02≈2×10−9A.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.Fromrelation (2) we have
(4)τmedium=qwniA2I02,medium.The size of transition regionw of the p-n junction is computed as follows [30, 31]:
(5)w=2εq⋅NA+NDNA⋅ND⋅V0−V,where V0 is the internal voltage of the junction
(6)V0=kTq⋅lnNANDni2,and V is the direct voltage which drops on the solar cell in conditions of a maximum power output.From the accomplished measurements are obtained,(7)V=0.35V.For the technological case,(8)ND=1016cm−3,NA=1017cm−3,which obtains:(9)V0=26×10−3V×ln1033cm−61020cm−6=60×13×10−3V=0.78V,w=2×10−12F/cm1.6×10−19C×11016cm−3×0.43V=0.23×10−4cm=0.23μm.Finally, using relation (4), the lifetime results are
(10)τmedium=1.6×10−19C×2.3×10−5cm×1010cm−3×4cm22×2×10−9A=3.7×10−5s≅40μs.Because of the technological conditions of the manufacturing of photovoltaic solar cells, the following range of values is used:(11)τSRH=1÷100μs.From the interpretation of the measurements for theI-V 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,I01 has the following form [20, 21]:
(12)I01=qADpLp⋅ni2ND+DnLn⋅ni2NA,which becomes, in the case of abrupt junction P+N,
(13)I01=qA⋅DpLp⋅ni2ND,or
(14)I01=qA⋅Dpτp⋅ni2ND, where Lp and Dp are the length of diffusion and the diffusion coefficient of minority holes from base n doped with a concentrationND of donor atoms.By contrast with the recombination componentI02, the diffusion current I01 has a variation depending on the temperature which cannot be neglected anymore. It comes from the dependence of temperature of the following terms:
(15)D=kTq⋅μ≈T1,(16)τ=1c⋅NT=1σ⋅V⋅NT≈1V≈1T1/2,(17)ni≈T3/2⋅exp−EG2kT.By solving equations (15), (16), and (17) then from (14), results
(18)I01≈T1/2⋅T1/4⋅T3⋅exp−EGkT,where qA≈T1/2 and Dp/τp=T1/4. With a good approximation, the following can be written:
(19)I01≈T4⋅exp−EGkT.From where
(20)I01T1I02T2=T1T24⋅expEGk⋅1T2−1T1.The experimental values obtained for a light source that approach the condition AM 1.5 are presented in Table2.Table 2
Values obtained for a photovoltaic solar cell measured in condition AM 1.5.
Isc (A)
Voc (V)
T (°C)
I01 (A)
0.122
0.48
35.5
2×10−9From this table, we have(21)I01=2×10−9A,laT=309K.Below formula (21), the value of the diffusion component at room temperature (T=300K) was deduced. The following was obtained:
(22)I01300K=I01309K⋅3003094⋅exp1.1×10326⋅300309−1.Then the numerical value is ((22)), we have
(23)I01300K=5×10−10A.This value will represent the main checkout key of computer models.


## 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.I-V 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 Isc and open circuit voltage Voc were determined using NI-Elvis board and LabView software (see Figure 7).Figure 7
Isc and Voc study of the solar cell, as a function of temperature using the NI-ELVIS acquisition boards and LabView software.


## 2.2. Interpretation ofI-V Characteristics of the Studied Photovoltaic Solar Cell

TheI-V 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]:
(1)I=I01⋅expV−Rs⋅IkT/q⋅n1+I02⋅expV−Rs⋅IkT/q⋅n2+VRp,where I is the solar cell current, I01 is the saturation current of the diffusion component, I02 is the saturation current of the recombination component, Rs is the parasitic series resistance, Rp is the parasitic parallel (shunt) resistance, n1 is the ideal factor of the diffusion current, and n2 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 parametern is the theoretical one, namely n1=1
(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, n2=2The values of parasitic resistances were determined by means of an experiment, and they have the following values:Rs=0.750Ω and Rp=379Ω.From measurement analysis, using the equation with 2 currents, consideringn1=1, n2=2, Rs=0.75Ω, and Rp=379Ω 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
I-V diagram of solar cell 1 for Iph=0.0291A (2) and overlapping of curves (1).Figure 9
I-V diagram of solar cell 1 for Iph=0.1225A (2) and overlapping of curves (1).Table 1
Determination of the parameters of a photovoltaic solar cell.
Iph (A)
I01 (A)
I02 (A)
T (°C)
0.0291
9.76×10−10
4.37×10−9
31.96
0.0357
1.38×10−9
1.49×10−9
32.50
0.0430
2.31×10−9
2.05×10−9
32.86
0.0512
2.1×10−9
2.13×10−9
33.17
0.0604
1.52×10−9
1.58×10−9
33.50
0.0705
1.71×10−9
1.73×10−9
33.85
0.0817
3.01×10−9
3.09×10−9
34.24
0.0941
1.62×10−9
1.63×10−9
34.64
0.1077
2.34×10−9
2.35×10−9
35.06
0.1225
1.98×10−9
1.17×10−9
35.54
0.1384
2.13×10−9
1.61×10−9
36.04


## 2.3. Analysis of Recombination Saturation CurrentI02

Recombination saturation current of a photovoltaic solar cell with the p-n junction is given by the following relation:(2)I02=qwni2τAwhere q is the electron’s charge, w is the thickness of the transition region emitter base in direct polarization, ni is the intrinsic concentration of carriers within silicon, A is the junction area emitter base, and τ is the lifetime of minority carriers from the silicon wafer volume.The component of currentI02 depends on the temperature by the medium of the intrinsic concentration ni. In the range of the measured temperature T=32−37°C, 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 Table1, the medium value of recombination saturation current, characteristic of a photovoltaic solar cell, is
(3)I02≈2×10−9A.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.Fromrelation (2) we have
(4)τmedium=qwniA2I02,medium.The size of transition regionw of the p-n junction is computed as follows [30, 31]:
(5)w=2εq⋅NA+NDNA⋅ND⋅V0−V,where V0 is the internal voltage of the junction
(6)V0=kTq⋅lnNANDni2,and V is the direct voltage which drops on the solar cell in conditions of a maximum power output.From the accomplished measurements are obtained,(7)V=0.35V.For the technological case,(8)ND=1016cm−3,NA=1017cm−3,which obtains:(9)V0=26×10−3V×ln1033cm−61020cm−6=60×13×10−3V=0.78V,w=2×10−12F/cm1.6×10−19C×11016cm−3×0.43V=0.23×10−4cm=0.23μm.Finally, using relation (4), the lifetime results are
(10)τmedium=1.6×10−19C×2.3×10−5cm×1010cm−3×4cm22×2×10−9A=3.7×10−5s≅40μs.Because of the technological conditions of the manufacturing of photovoltaic solar cells, the following range of values is used:(11)τSRH=1÷100μs.From the interpretation of the measurements for theI-V 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,I01 has the following form [20, 21]:
(12)I01=qADpLp⋅ni2ND+DnLn⋅ni2NA,which becomes, in the case of abrupt junction P+N,
(13)I01=qA⋅DpLp⋅ni2ND,or
(14)I01=qA⋅Dpτp⋅ni2ND, where Lp and Dp are the length of diffusion and the diffusion coefficient of minority holes from base n doped with a concentrationND of donor atoms.By contrast with the recombination componentI02, the diffusion current I01 has a variation depending on the temperature which cannot be neglected anymore. It comes from the dependence of temperature of the following terms:
(15)D=kTq⋅μ≈T1,(16)τ=1c⋅NT=1σ⋅V⋅NT≈1V≈1T1/2,(17)ni≈T3/2⋅exp−EG2kT.By solving equations (15), (16), and (17) then from (14), results
(18)I01≈T1/2⋅T1/4⋅T3⋅exp−EGkT,where qA≈T1/2 and Dp/τp=T1/4. With a good approximation, the following can be written:
(19)I01≈T4⋅exp−EGkT.From where
(20)I01T1I02T2=T1T24⋅expEGk⋅1T2−1T1.The experimental values obtained for a light source that approach the condition AM 1.5 are presented in Table2.Table 2
Values obtained for a photovoltaic solar cell measured in condition AM 1.5.
Isc (A)
Voc (V)
T (°C)
I01 (A)
0.122
0.48
35.5
2×10−9From this table, we have(21)I01=2×10−9A,laT=309K.Below formula (21), the value of the diffusion component at room temperature (T=300K) was deduced. The following was obtained:
(22)I01300K=I01309K⋅3003094⋅exp1.1×10326⋅300309−1.Then the numerical value is ((22)), we have
(23)I01300K=5×10−10A.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 whenτSRH=5μs. To analyse in Matlab, we used the following material’s features, constants, and calculus formulas, which are available for T=300K [17, 31]:
(i)
Intrinsic carrier concentration:ni=1010cm−3
(ii)
Dielectric constant:ε=10−12F/cm
(iii)
Electron charge:q=1.6∙10−19C
(iv)
Thermal potential and thermal energy:T/q=25.9mV and kT/q=25.9mV
(v)
Coefficient of diffusion for load carriers:(24)D=D01+N/N0dD1, where electrons are D0n=35cm2/s, D1n=1.8cm2/s, N0=1017cm−3, d=0.6 and the holes are D0p=12.5cm2/s, D1p=1cm2/s, N0=1017cm−3, and d=0.6.The following are the relationships between diffusion coefficient and electric mobility:(i)
Einstein’s relations are(25)Dn=kTqμn,Dp=kTqμp.
(ii)
The Shockley-Read-Hall lifetime recombination is(26)τSRH=τ01+N/K,K=7×1015cm−3
(iii)
The lifetime of radiation recombination is(27)τrad=1BN,B=2×10−14cm3/s
(iv)
The Auger lifetime recombination is(28)τAug=1CN2where silicon-n is Cn=10−31cm6/s and silicon-p is Cp=2.8×10−31cm6/s
(v)
Total lifetime is(29)1τ=1τSRH+1τrad+1τAug
(vi)
The lengths of the diffusion of minority carriers are(30)Electrons:Ln=Dnτn1/2Holes:Lp=Dpτp1/2
(vii)
The variation in bandwidth forbidden at high doping levels is(31)ΔEG=aN∗Nb+1−cwhere a=0.231eV; b=3/4; c=2/3; and N∗=1020cm−3
(viii)
The effective intrinsic concentration of carriers at high levels of doping is(32)ni,ef2=ni2expΔEGkT
(ix)
The effective recombination speed at the P+P interface of the emitter is
(33)sp,ef=DP+Lp+ni+2ni2NDND+sP+Lp+/Dp++thwB+/Lp+1+sp+Lp+/Dp+thwB+/Lp+
(x)
The density of saturation power at the P+P emitter is
(34)Jb0+=qDpni2LpNDsp,efLp/Dp+thwB/Lp1+sp,efLp/DpthwB/Lp
(xi)
The effective recombination speed on the interface on the base N+N is
(35)sn,ef=Dn+Ln+ni+2ni2NANA+sn+Ln+/Dn++thwB+/Ln+1+sn+Ln+/Dn+thwB+/Ln+
(xii)
The density of saturation power on the base N+N is
(36)Jb0+=qDnni2LnNAsn,efLn/Dn+thwB/Ln1+sn,efLn/DnthwB/Ln
(xiii)
Total saturation power is(37)I0=Je0AE+Jb0AB,pas+Jb0+AB,metAB,pas+AB,met=AcelJ0=I0Acel
(xiv)
The open circuit voltage is(38)VOC=kTq⋅lnJSCJ0
(xv)
The efficient conversion of solar energy is(39)η=JSC⋅VOC⋅fPsolara
(xvi)
The solar power in conditions AM 1.5 is(40)Psolara=100mW/cm2
(xvii)
The average short-circuit current density value for an AM spectrum 1.5 is(41)JSC=35mA/cm2


### 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 sn+

From Figures10–12, 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 sn,ef=103cm/s, sn,ef=102cm/s, and sn,ef=1cm/s, 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 sn,ef is obtained in the case of NA+=1018cm−3, wE+=0.5×10−4cm, and τSRH=5μs (see Figure 11), while using a doping concentration of the emitter of NA+=1015cm−3, and its value becomes 0.2777  cm/s.Figure 10
The effective recombination velocities from the emitter’s interface P+/P sn,ef are dependent on recombination velocities on the region’s P+ surface of emitter sn+ in the following conditions: NA+=1017cm−3, wE+=0.5×10−4cm, and τSRH = 5 μs.Figure 11
The effective recombination velocities from the emitter’s interface P+/P sn,ef are dependent on recombination velocities on the region’s P+ surface of emitter sn+ in the following conditions: NA+=1018cm−3, wE+=0.5×10−4cm, and τSRH=5μs.Figure 12
The effective recombination velocities from the emitter’s interface P+/P sn,ef are dependent on recombination velocities on the region’s P+ surface of emitter sn+ in the following conditions: NA+=1019cm−3, wE+=0.5×10−4cm, and τSRH=5μs.


### 3.2. The Effective Recombination Velocities from Base’s Interface N/N+sp,ef Dependent on Base’s Strongly Doped Concentration ND+

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+sp,ef is obtained in the case of wB+=20×10−4cm and sp+=106cm/s (see Figure 15), using a doping concentration of ND=1014cm−3, this value being of 0.5 cm/s.Figure 13
The effective recombination velocities from base’s interface N/N+sp,ef dependent on base’s strongly doped concentration ND+ in the case of wB+=5×10−4cm and sp+=106cm/s.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 wB+=10×10−4cm and sp+=106cm/s.Figure 15
The effective recombination velocities from base’s interface N/N+sp,ef dependent on base’s strongly doped concentration ND+ in the case of wB+=20×10−4cm and sp+=106cm/s.The obtained values are available because they accomplish the following technological conditions:(i)
The average value of phosphorus base doping:ND=1.5∙1014cm−3
(ii)
The average value of emitter layer diffusion:NA=1017cm−3
(iii)
The depth of junction p-n emitter-base:wE=5μm


## 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 sn+

From Figures10–12, 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 sn,ef=103cm/s, sn,ef=102cm/s, and sn,ef=1cm/s, 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 sn,ef is obtained in the case of NA+=1018cm−3, wE+=0.5×10−4cm, and τSRH=5μs (see Figure 11), while using a doping concentration of the emitter of NA+=1015cm−3, and its value becomes 0.2777  cm/s.Figure 10
The effective recombination velocities from the emitter’s interface P+/P sn,ef are dependent on recombination velocities on the region’s P+ surface of emitter sn+ in the following conditions: NA+=1017cm−3, wE+=0.5×10−4cm, and τSRH = 5 μs.Figure 11
The effective recombination velocities from the emitter’s interface P+/P sn,ef are dependent on recombination velocities on the region’s P+ surface of emitter sn+ in the following conditions: NA+=1018cm−3, wE+=0.5×10−4cm, and τSRH=5μs.Figure 12
The effective recombination velocities from the emitter’s interface P+/P sn,ef are dependent on recombination velocities on the region’s P+ surface of emitter sn+ in the following conditions: NA+=1019cm−3, wE+=0.5×10−4cm, and τSRH=5μs.


## 3.2. The Effective Recombination Velocities from Base’s Interface N/N+sp,ef Dependent on Base’s Strongly Doped Concentration ND+

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+sp,ef is obtained in the case of wB+=20×10−4cm and sp+=106cm/s (see Figure 15), using a doping concentration of ND=1014cm−3, this value being of 0.5 cm/s.Figure 13
The effective recombination velocities from base’s interface N/N+sp,ef dependent on base’s strongly doped concentration ND+ in the case of wB+=5×10−4cm and sp+=106cm/s.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 wB+=10×10−4cm and sp+=106cm/s.Figure 15
The effective recombination velocities from base’s interface N/N+sp,ef dependent on base’s strongly doped concentration ND+ in the case of wB+=20×10−4cm and sp+=106cm/s.The obtained values are available because they accomplish the following technological conditions:(i)
The average value of phosphorus base doping:ND=1.5∙1014cm−3
(ii)
The average value of emitter layer diffusion:NA=1017cm−3
(iii)
The depth of junction p-n emitter-base:wE=5μm


## 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 forτSRH=5μs 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.



---

*Source: 7945683-2019-11-19.xml*