Introduction

In recent years, a lot of research focus has been shifted to producing a new generation of cheaper solar cells, consisting of thin films fabricated using more affordable methods compared to the first generation of the wafer-based photovoltaic (PV) cells. Many methods have been used for thin-film PV cell fabrication on a range of substrates, including flexible substrates, such as evaporation, sol–gel, electroplating, and chemical vapor deposition. The properties of the materials fabricated using these techniques are highly dependent on many deposition parameters and material compositions, which can impact the thin films physical, optical, and electrical properties. Some of the well-established thin-film systems which have been extensively studied and are commercially available include hydrogenated amorphous silicon (a-Si:H), gallium arsenide (GaAs), copper indium gallium diselenide Cu (InxGa1−x) (Se)2 (CIGS), cadmium telluride (CdTe), and organic solar cells [1,2,3,4,5,6]. Thin-film PV cells are expected to become cheaper, but they continue to lack efficiency and stability compared to the first-generation crystalline silicon solar cells. As new mature materials continue to emerge, thin films continue to be in high demand [7]. In particular, CIGS and GaAs thin-film systems are of great interest due to their reasonable power conversion efficiency associated with their flexibility, high absorption coefficients, and tunable bandgaps [8, 9].

To improve the energy conversion efficiency in today’s solar cells, it became essential to have a clear understanding of the main loss mechanisms that focuses on reducing the amount of incident light energy converted into usable electrical energy. Although many factors hinder the energy conversion efficiency, two main loss mechanisms are attributed to strongly reducing the energy conversion efficiency of solar cells. The first loss mechanism is contributed by the spectral mismatch between the incident light and the energy bandgap of the semiconductor material used in the solar cell. The second mechanism is contributed by the electronic and optical properties of the different layers of the solar cells, such as poor contact formation. In particular, poor contacts forming during the deposition of the cathode electrode will ultimately create a small ohmic contact with the active semiconductor layer called the series resistance. In this work, we focus on studying the second loss mechanism using two different approaches. The first approach explores the impact of the series resistance on the short-circuit current, fill factor, efficiency, and open-circuit voltage of the solar cell. The second approach explores the variation of doping levels’ effect on the energy conversion efficiency due to charge recombination. The studied structures are simulated using SCAPS version 3.3.10, a solar cell simulation program that is affirmed for studying thin-film solar cells such as CIGS and CdTe-based solar cells. The University of Gent developed the simulator with the description of the simulator program, and the algorithms it uses are available in the literature [10,11,12,13].

Solar cell simulation model

A solar cell can be modeled as a semiconductor diode without illumination, which has the characteristics of the PN junction. Hence, the solar cell dark current, Id, can be given as

$${I}_{\mathrm{d}}={I}_{0}\left({\mathrm{e}}^{\left(\frac{{V}_{\mathrm{d}}}{n{V}_{t}}\right)}-1\right),$$
(1)

where I0 is the saturation current, Vd is the voltage applied across the PN junction, n is the ideality factor, and Vt is the thermal voltage. The minority carriers will flow across the junction during illumination, producing a photocurrent Iph. The flow of this photocurrent to an external electrical load will produce a forward voltage across the solar cell terminals. Figure 1a shows the solar cell model with the consideration of the effect of the series resistance Rs and shunt resistance Rsh effects [14].

Fig. 1
figure 1

a Solar cell model. b Typical J–V characteristics of a solar cell showing the main parameters

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The series resistance of a solar cell Rs represents the sum of all resistance elements distributed in the semiconductor, the ohmic contacts, and the semiconductor contacts. The value of the series resistance Rs can range from a few tenths of an ohm to a few ohms. While the shunt resistance Rsh represents the bulk resistance of the base, which can be very high with values ranging from a few tens of an ohm to a few hundred-kilo ohms. The main parameters that are used to characterize the performance of solar cells are the maximum power Pmax, the short-circuit current density Jsc, and the open-circuit voltage Voc. These parameters are determined from the illuminated J–V characteristic curve, as illustrated in Fig. 1b. Other important parameters are the power conversion efficiency η and the fill factor FF, which are dependent on the previous parameters [15]. The maximum power, Pmax, is the product of maximum output voltage \({V}_{\mathrm{mp}}\) and maximum current \({J}_{\mathrm{mp}}\) and is expressed as

$${P}_{\mathrm{max}}={J}_{\mathrm{mp}}\times {V}_{\mathrm{mp}}.$$
(2)

The short-circuit current density Jsc is the maximum current that flows through the external circuit when the electrodes of the solar cell are shorted together. The short-circuit current depends on the collected minority carriers generated within the solar cell and the fraction of minorities that diffuse to the PN junction. Theoretically, the short-circuit current is equal to the photocurrent, which assumes that every photon generates only one electron–hole pair. The photocurrent density Jph can be written as

$${J}_{\mathrm{ph}}=q\times {G}_{\mathrm{L}}\left({L}_{\mathrm{n}}+W+{L}_{\mathrm{p}}\right),$$
(3)

where q is the electron charge, GL is the photogeneration rate, Ln is the minority-carrier-diffusion length for electrons, Lp is the minority-carrier-diffusion length for holes, and W is the width of the depletion region. The photogenerated current density and the short-circuit density increase as the generation rate increases and the photon flux density. The open-circuit voltage Voc is the voltage at which no current flows through the external circuit, the maximum voltage a solar cell can generate. It can be expressed in terms of the generation rate GL, the lifetime τo of the minority charge carriers, and the intrinsic density of the charge carriers ni in the semiconductor material as follows:

$${V}_{\mathrm{oc}}=n\times {V}_{\mathrm{t}}\mathrm{ln}\left({G}_{\mathrm{L}}\times \frac{{\tau }_{\mathrm{o}}}{{n}_{\mathrm{i}}}\right).$$
(4)

The open-circuit voltage Voc increases with the increase of the illumination or the generation rate of charge carriers. Furthermore, the open-circuit voltage Voc increases as the lifetime of the minority charge carrier becomes more extended, which is determined by the recombination rate and the doping levels.

Finally, the fill factor FF is essentially a measure of the quality of the solar cell, which plays an essential role in controlling the efficiency of the cell; at the same time, it represents how well the photogenerated carriers are extracted from the cell. It has been claimed that FF depends on the interface quality between the active layer and the negative electrode. FF is expressed as the ratio between the maximum power, Pmax, generated by the solar cell and the product of Voc and Jsc shown as follows:

$$\mathrm{FF}=\frac{{J}_{\mathrm{mp}}{V}_{\mathrm{mp}}}{{V}_{\mathrm{oc}}{J}_{\mathrm{sc}}}.$$
(5)

The power conversion efficiency η is the ratio between the maximum generated powers Pmax and the incident power Pin as shown as follows:

$$\eta =\frac{{P}_{\mathrm{max}}}{{P}_{\mathrm{in}}}=\frac{{J}_{\mathrm{mp}}{V}_{\mathrm{mp}}}{{P}_{\mathrm{in}}}=\frac{{V}_{\mathrm{oc}}{J}_{\mathrm{sc}}\mathrm{FF}}{{P}_{\mathrm{in}}}$$
(6)

Figure 2 shows three-layer CIGS baseline solar cells. The cell structure can be deposited on a 3 mm soda-lime glass substrate with a 100 nm sputtered molybdenum layer as a back contact. The thicknesses of the (InxGa1−x) (Se)2 absorber layer and CdS windows layer are varied for the experiment. A grid top contact is created by depositing a 40 nm thin layer of Indium.

Fig. 2
figure 2

The schematic cross-section of a typical (InxGa1−x) (Se)2 solar cell

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It is proved that Ga content x equals 0.3, which resides approximately at Eg = 1.48 eV. According to the Shockley–Queisser model, this value is near optimum for a solar spectrum. For this simulation, a maximum efficiency of 24.34% is achieved [16]. The simulation is performed under global AM1.5 solar spectrum conditions at an ambient temperature of 25 °C. The measurements of the photovoltaic parameters are performed under the condition of variable series resistances and an infinite shunt resistance. The used electronic parameters were extracted from the literature [17,18,19] and provided in Ref. [16].

Results and discussion

The effect of series resistance

The photocurrent density Jph can be expressed in terms of the flux density of incident photons Φ and the spectral power density associated with the solar radiation. Under the assumption of zero reflection in Eq. (4) and incident photons with energies greater than the bandgap energy Eg, the photocurrent density Jph can be expressed as

$${J}_{\mathrm{ph}}=q\times A\times \Phi \times \beta \left(1-{\mathrm{e}}^{-\alpha x}\right)=q\times \left(\frac{P\lambda }{hc}\right)\times \beta \left(1-{\mathrm{e}}^{-\alpha x}\right),$$
(7)

where q is the electronic charge, A is the cell area, α is the absorption coefficient, x is the thickness of the solar cell, β is the collection efficiency, λ is the wavelength, h is plank constant, and c is the light velocity. Furthermore, a more complete equation expressing the photocurrent density in terms of light intensity irradiance would be

$${J}_{\mathrm{ph}}=q\times A\times {\int }_{\lambda }P\left(\lambda \right)\bullet \left(\frac{\lambda }{hc}\right)\left(1-{\mathrm{e}}^{-\alpha \left(\lambda \right)x}\right)\beta (\lambda )\mathrm{d}\lambda .$$
(8)

From Fig. 3a, the current I provided to the load in the solar cell model can be written as

$$I={I}_{\mathrm{ph}}-{I}_{\mathrm{d}}-{I}_{\mathrm{sh}},$$
(9)

where Iph is the photocurrent generated by the solar cell, Id is the dark current, and Ish is the current flowing through the shunt resistance. The shunt resistance can be written as follows:

$${I}_{\mathrm{sh}}=\frac{{V}_{\mathrm{d}}}{{R}_{\mathrm{sh}}}=\frac{V+{R}_{\mathrm{s}}I}{{R}_{\mathrm{sh}}},$$
(10)

where V is the voltage across the load RL. Substituting for Id from Eq. (1), Iph from Eq. (7), and Ish from Eq. (10), Eq. (9) can be rewritten as

Fig. 3
figure 3

a Short-circuit current Ish, b open-circuit voltage Voc, c power conversion efficiency η, and d fill factor FF, as a function of light intensities for different values of series resistance Rs

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$$I=q\times \left(\frac{P\lambda }{hc}\right)\times \beta \left(1-{\mathrm{e}}^{-\alpha x}\right)-{I}_{0}\left({\mathrm{e}}^{\left(\frac{V+{R}_{\mathrm{s}}I}{n{V}_{t}}\right)}-1\right)-\frac{V+{R}_{\mathrm{s}}I}{{R}_{\mathrm{sh}}}.$$
(11)

For the short-circuit current, the voltage V across the load resistance RL becomes zero such that Eq. (11) can be expressed as

$${I}_{\mathrm{sc}}=q\times \left(\frac{P\lambda }{hc}\right)\times \beta \left(1-{\mathrm{e}}^{-\alpha x}\right)-{I}_{0}\left({\mathrm{e}}^{\left(\frac{{R}_{\mathrm{s}}{I}_{\mathrm{sc}}}{n{V}_{t}}\right)}-1\right)-\frac{{R}_{\mathrm{s}}{I}_{\mathrm{sc}}}{{R}_{\mathrm{sh}}}.$$
(12)

The SCAPS simulator is used to investigate the solar cell model shown in Fig. 1 under low and high light intensities, focusing on the series resistance effect on the short-circuit current. For this, various circuit parameters are determined while keeping the series resistance a variable under investigation. The shunt resistance value is 20 kΩ, and the ideality factor n equals one. Considering the energy bandgap of Cu (InxGa1−x) (Se)2 at 1.48 eV, the limits of integration used in Eq. (8) are determined to be from 0.45 to 1.2 μm, corresponding to the cutoff wavelength where the absorption process can be ignored above these values. For this material, the absorption coefficient decreases with the increase in the light wavelength, and it has a sharp absorption edge. Figure 3 shows the simulation results for the short-circuit current Ish, open-circuit voltage Voc, power conversion efficiency η, and the fill factor FF as a function of light intensities for a range of series resistances Rs values.

Figure 3a shows two distinct regions for each series resistance value. The first region at low light intensity values has an approximately constant high slope. In contrast, the second region at high light intensity values consists of a slightly variable, smaller slope. During the high light intensity region, the short-circuit current variations depend on the series resistance, where the slope of the curve decreases as the series resistance increases. At the same time, the interval between one curve and the other is reduced as the series resistance increases due to the saturation of the photocurrent. To explain these observations, Eq. (12) can be mathematically manipulated to extract an expression for dIsc/dp as follows:

$$\frac{\mathrm{d}{I}_{\mathrm{sc}}}{\mathrm{d}p}=\frac{1}{q\times \left(\frac{\lambda }{hc}\right)\times \beta \left(1-{\mathrm{e}}^{-\alpha x}\right)+{I}_{0}\left(\frac{{R}_{\mathrm{s}}}{n{V}_{\mathrm{t}}}\right){\mathrm{e}}^{\left(\frac{{R}_{\mathrm{s}}{I}_{\mathrm{sc}}}{n{V}_{\mathrm{t}}}\right)}+\frac{{R}_{\mathrm{s}}}{{R}_{\mathrm{sh}}}}.$$
(13)

There are two distinctly dominant terms in the denominator of Eq. (13), a constant term that does not depend on the short-circuit current Isc and a varying term that does depend on the short-circuit current Isc. At low Isc values, the constant term becomes more significant than the varying term. At large Isc values, the variable term becomes significantly greater than the constant term where the slope can be approximated as follows:

$$\frac{\mathrm{d}{I}_{\mathrm{sc}}}{\mathrm{d}p}=\frac{1}{{I}_{0}\left(\frac{{R}_{\mathrm{s}}}{n{V}_{\mathrm{t}}}\right){\mathrm{e}}^{\left(\frac{{R}_{\mathrm{s}}{I}_{\mathrm{sc}}}{n{V}_{\mathrm{t}}}\right)}}.$$
(14)

It is evident from Eq. (14) and Fig. 3 that the variation of Isc will be less significant as the light intensity increases due to the high effect of Rs. This effect can be explained by the internal resistance hindering the drift transport of free charge carriers towards the electrodes under the influence of an internal electric field [20]. Figure 3b shows the change of Voc as a light intensity function for different Rs values. Voc increases with the light intensity before reaching saturation at light intensities exceeding 2000 W/m2 while being independent of Rs. The behavior is based on the single diode model, which can be explained by rewriting Eq. (11) under open-circuit voltage conditions where I is equal to zero as follows:

$${I}_{0}{\mathrm{e}}^{\left(\frac{{V}_{\mathrm{oc}}}{n{V}_{t}}\right)}+\frac{{V}_{\mathrm{oc}}}{{R}_{\mathrm{sh}}}={I}_{\mathrm{ph},\mathrm{oc}}+{I}_{0},$$
(15)

where Iph,oc is the photogenerated current at open-circuit condition. For large values of Rsh, the second term on the left side of Eq. (15) can be neglected while solving for the open-circuit voltage Voc yields

$${V}_{\mathrm{oc}}=n{V}_{\mathrm{t}}\mathrm{ln}\left(\frac{{I}_{\mathrm{ph},\mathrm{oc}}}{{I}_{0}}+1\right).$$
(16)

Equation 16 agrees with the results of Fig. 3b. The open-circuit voltage Voc increases linearly with the photogenerated current until reaching saturation due to the significant effect of Rs earlier discussed, where Voc becomes independent of both Rsh and Rs.

Figure 3c shows the simulation results of Rs and their impact on the power conversion efficiency of the solar cells under different light intensities. At Rs equal to zero, the efficiency increases with the increase of light intensity at around 500 W/m2 before reaching saturation at greater light intensities exceeding 2000 W/m2. At high concentrated sunlight, the saturated efficiency is attributed to Auger recombination, which significantly limits solar efficiency due to the decrease in the lifetime of carriers. As Rs value is increased from zero, an exponential decrease in efficiency occurs with a strong detrimental impact on the device at low light intensities. Furthermore, the efficiency significantly drops as the series resistance increases due to the limited amount of photocurrent generated by the solar cell. Figure 3d shows the simulation results of Rs and their impact on the fill factor FF of the solar cells under different light intensities. The non-linear decrease of FF with the increase of Rs can be expressed by the following empirical equation [21]:

$$\mathrm{FF}={\mathrm{FF}}_{\mathrm{ref}}\left(1-\frac{{R}_{s}{I}_{\mathrm{sc}}}{{V}_{\mathrm{oc}}}\right),$$
(17)

where FFref is the reference fill factor at specific Rs values for the solar cell. Comparably, Eq. (17) and Fig. 3d clearly illustrate the pronounced decrease rate of FF as light intensity increases for larger Rs values.

The effect of doping levels of the absorber layer

Considering the Molybdenum back contact and the high carrier recombination near the junction, in this case, the solar cell will have a noticeable reduction in electrical performance, influencing its overall power conversion efficiency. To reduce the overall effect of the Molybdenum back contact, an increased level of acceptor doping concentration NA must be applied to the absorber CIGS layer. Figure 4 shows the simulation results for the short-circuit current Ish, open-circuit voltage Voc, power conversion efficiency η, and the fill factor FF as a function of acceptor doping concentration for a range of light intensities values while fixing the donor doping concentration ND at \(2\times {10}^{17}{\mathrm{cm}}^{-3}\).

Fig. 4
figure 4

a Short-circuit current Ish, b open-circuit voltage Voc, c power conversion efficiency η, and d fill factor FF, as a function of acceptor doping concentration for a range of light intensities

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Figure 4a shows the short-circuit current Isc decreasing as the doping concentration increases due to an increase in the carrier recombination rate near the space charge region. This issue can be resolved by depositing a thin Al2O3 layer over the Molybdenum back contact to improve the optical confinement and increase the short-circuit current density [22]. Parisi et al. introduced an alternative approach by testing the use of high-energy gap absorbers. However, this would cause an increase in the defect density due to increasing the Ga content [23]. The problem with this approach is that it creates a variable absorber composition with an increased energy bandgap in the area near the Molybdenum back contact only. Therefore, the doping concentration in the absorber should linearly increase to the maximum value of NA in the layer near the absorber–Molybdenum interface. This is true only if NA near the junction is less than or equal to ND concentration. Otherwise, the efficiency will noticeably decrease due to the previously mentioned carrier recombination effect near the junction.

Interestingly, the intervals between the curves in Fig. 4a decrease as the light intensity decreases. At high light intensity, the short-circuit current decline as the doping concentration increases due to a shorter carrier's lifetime, which limits the photocurrent generated by the solar cell. Figure 4b shows an exponential increase in Voc as the acceptor doping concentration increases. This behavior is evident in Eq. (16), as the emitter saturation current density decreases at the expense of a constant photogenerated current for high doping levels. Therefore, the maximum value of Voc occurs at moderate light intensities such as 1500 W/cm2 rather than at greater light intensities. The conversion efficiency and fill factor at different light intensities as a function of NA doping concentration is shown in Fig. 4c and d, respectively. The maximum efficiency is obtained at approximately NA equal to ND as it slowly increases with the doping concentration up to 1016 cm−3 and then drops quickly beyond this value.

Furthermore, a similar trend has been obtained for a range of ND values ranging from 1014 to 1019 cm−3 as shown in Fig. 5. The maximum efficiency and the edge of droop efficiency increase as the donor level ND increases. As the doping level of ND increase by more than 1018 cm−3, the efficiency and droop edge increase which makes this doping level a level of interest for researchers and provides an efficiency of around 18% and drops efficiency of around \(5\times {10}^{17}\) cm−3.

Fig. 5
figure 5

The variation of power conversion efficiency as a function of acceptor doping concentrations for a range of donor concentrations

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The effect of the doping level of the buffer layer

The CdS buffer layer, having direct bandgap energy of 2.4 eV, improves the overall performance of the solar cell. The CdS buffer layer has a refractive index that falls between those of ZnO and CIGS, which reduces reflection losses at the cell surface, provides a low interface carrier recombination rate, and prevents undesirable shunt paths to the absorber layer. The buffer layer can improve the blue wavelength response until 0.45 µm at the frontal side of the solar cell with a low surface concentration and shallow junction depth [24]. Figure 6 shows the simulation results for the short-circuit current Ish, open-circuit voltage Voc, power conversion efficiency η, and the fill factor FF as a function of donor doping concentration for a range of light intensities values while fixing the acceptor doping concentration NA at 1016 cm−3. Figure 6a shows the short-circuit current Ish dominantly constant with the doping concentration. At the same time, the open-circuit voltage Voc constantly starts before declining as the concentration level exceeds 1016 cm−3 which is more evident at larger light intensities. The behavior of the open-circuit voltage Voc is consistent with the limitation of the photocurrent generated in the solar cell due to the reduced lifetime of the carriers. In contrast to the short-circuit current and open-circuit voltage, the conversion efficiency and fill factor increase with the doping concentration before reaching saturation when ND exceeds 1018 cm−3. This phenomenon is apparent from Eqs. (5) and (6) as the product of Voc and Ish decreases, the fill factor FF and the conversion efficiency η increase.

Fig. 6
figure 6

a Short-circuit current Ish, b open-circuit voltage Voc, c power conversion efficiency η, and d fill factor FF, as a function of donor doping concentration for a range of light intensities

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Conclusions

The composition in the layers of a thin-film solar cell is of great importance to improve the cell’s overall performance due to the enhanced sheet and series resistances of the structure. The increase in series resistance results in the decrease of the short-circuit current while causing a slight increase in the open-circuit voltage. As a result, the power conversion efficiency is reduced with a more pronounced effect at greater light intensities limiting the benefits of light concentrators that typically improve the short-circuit current. In general, doping the absorber layer with a large acceptor concentration will reduce the short-circuit current while increasing the open-circuit voltage. As a result, the power conversion efficiency and fill factor show a slow increase while the absorber layer’s doping level is smaller than the buffer layer’s doping level. It was observed that the power conversion efficiency and fill factor are drastically reduced when the absorber layer’s doping level exceeds the buffer layer’s doping level. Thus, the maximum values are obtained when absorber and buffer layers are doped with the same concentration levels. A minimal effect has been observed when the doping level of the buffer layer is increased on the solar cell performance. However, it was previously claimed that the increase would improve the blue response at the frontal side of the solar cell.