1. Introduction
The exponential increase in the demand of green energy is one of the environmental challenges which are currently faced in the energy sector. One of the most reliable sources of green energy is the generation of electricity from the sun, a field in which different technologies compete for the lowest energy production cost. Cu (In, Ga) Se
2 (CIGS)-based thin-film solar cells are one of the most promising technologies due to their rapid efficiency improvement. Some of the latest breakthroughs, such as the record efficiency over 23% achieved in a laboratory [
1] or an 18% efficiency on a large area module [
2], put this material at the same level as crystalline silicon devices in terms of photovoltaic potential.
The attractiveness of CIGS as a thin-film technology can be explained by the small amount of materials required to produce a solar panel, because the thickness of the device layers is typically in the range of a few microns. The layers that are normally present in thin-film solar cells are as follows: (i) a transparent front contact (TCO), which in CIGS devices is usually an n-type doped zinc oxide (ZnO) film of around 0.3 µm [
3], although other alternatives are possible; (ii) a buffer layer as an interface between the front contact and the absorber—in CIGS, a thin cadmium sulfide (CdS) layer of 20 to 50 nm is used [
4], although there is ongoing research to replace this toxic material with a more environmentally friendly one [
1,
5,
6]; (iii) the absorber, in this case, is a Cu (In, Ga) (S, Se)
2 compound semiconductor with a thickness between 1–3 µm, and in some cases even lower thicknesses are reported, such as in [
7,
8]; (iv) the absorber is deposited on top of the back contact, which is usually a molybdenum (Mo) layer of 0.2 to 1 µm [
9]; (v) all these materials are deposited on a soda-lime glass substrate that supplies sodium (Na) to the sample to enhance its performance [
10,
11]. However, excess Na was reported to degrade the performance of the solar cell [
12]. Na was also found to play an important role in the degradation of CIGS solar cells when exposed to detrimental operation conditions, such as high temperatures, high humidity or externally applied biases, which lead to one of the most damaging mechanisms for CIGS solar cells, referred to as potential-induced degradation (PID) [
13,
14].
Improving CIGS solar cells over the current efficiency record requires a better understanding of loss mechanisms and the underlying physical principles [
15]. A barrier at the back contact interface (Mo/CIGS) is known to be a potential loss mechanism due to the formation of a second junction, but with opposite polarity. The effect of this barrier can be seen in low-temperature current–voltage (I–V) measurements as blocking behavior of the current under forward bias, also named as the roll-over effect [
16,
17,
18,
19,
20]. Moreover, it affects other parameters of the solar cell, such as the fill factor and the open-circuit voltage (Voc) of the device, and thereby, the efficiency. Other barriers, induced by bandgap gradients or a band offset at the CIGS/CdS interface, are a plausible source of performance losses in CIGS solar cells, although they typically present their own unique signatures in low-temperature I–V measurements, such as the S-kink [
21,
22] or a complete blocking of the current under forward bias [
23].
The impact of these barriers on the electronic transport can be diminished or enhanced in CIGS solar cells as a consequence of a metastable behavior that is typical for this technology. In [
24], for instance, CIGS samples with different buffer layers are treated with light soaking and reverse bias at room temperature. The results of [
24] show that a reverse-bias treatment induces a distortion, or roll-over, of the I–V curve that is more pronounced at low temperatures, where the metastable changes are not reversible. When the samples were left to relax at room temperatures, the distortion of the I–V curve was not found. The barrier was correlated in [
24] with the N1 defect that is found in CIGS solar cells with admittance spectroscopy as a step in the capacitance–frequency curve.
The fill factor of the cell is also affected depending on the treatment; for instance, in [
25,
26] a reverse-bias treatment was found to induce a shunt in the I–V curve that resembles the S-kink previously mentioned. At low temperatures of 120 K, this metastable behavior is frozen, which means that it does not relax to the initial state. Light soaking, on the other hand, increases the fill factor and decreases the shunts in the I–V curves [
25]. These two effects are correlated in [
26,
27] with redistributions of charges in the absorber; the reverse-bias treatment, for instance is suggested to enhance an already existing barrier in the form of a p
+ -type “defected” layer that is found at the ZnO/CdS/CIGS heterointerface on the absorber’s side. Light soaking and forward-bias treatments reduce the amount of accumulated charges in this layer according to [
25,
28]. Both treatments are also known to increase the apparent carrier concentration that is found in capacitance–voltage (C–V) measurements calculated from the Mott–Schottky equation [
28]. Redistribution of charges is explained in [
26] and [
29] as a change of the configuration of V
Se–V
Cu complexes. Reverse-bias treatments, for instance, convert those complexes near the heterointerface from the donor into the acceptor configuration, while in the bulk, the opposite happens. With light soaking and forward bias [
29], the situation is reversed. These changes could explain the variations in the net-doping level extracted from the C–V profile using the Mott–Schottky equation, and the shunts induced in the I–V curve by means of the p
+ type “defect” layer previously mentioned. However, the effects of the changes induced by these treatments should also be considered regarding the Schottky back contact interface, as in [
30].
The origin of the Schottky barrier is still up for debate because of the existence of a thin MoSe
2 layer between the Mo/CIGS layers. Although the Mo/MoSe
2 interface behaves as a Schottky barrier for holes, the Mo/CIGS junction is quasi-ohmic when a thin MoSe
2 layer exists [
17]. The thickness and other physical properties of this thin MoSe
2 layer depend primarily on the fabrication process. In [
17], two deposition processes for CIGS are compared, namely the two-step selenization after sulfurization (SAS), and the sequential sputtering/selenization process [
31]. The latter process was found in [
17] to create no MoSe
2, and a Schottky barrier appeared at the Mo/CIGS interface reducing the performance of the cell. In the SAS process, on the other hand, a thin MoSe
2 layer was formed according to [
17], and the negative effect of the barrier on the performance was diminished.
The simplest model that considers this blocking behavior at low temperatures in thin-film solar cells is based on the five-parameter model [
32], which includes an additional diode with a polarity that opposes that of the pn junction [
33]. Notwithstanding, this model with two opposing diodes presents some limitations, such as its inability to reproduce the dependence of the saturated forward current on the illumination level, a side effect of the back contact barrier that is also visible in experimental results. A phototransistor model was proposed in [
19,
34,
35] to account for this effect; in this model, the solar cell is presented in a similar manner as an npn bipolar phototransistor, in which the absorber is the equivalent of the (very thick) base, while ZnO/CdS represents the emitter, and Mo is the collector. With a forward bias applied to the solar cell, the ZnO/CdS/CIGS pn junction is polarized in the forward direction, while the Mo/CIGS junction is polarized in the reverse direction, which means that the photogenerated carriers are separated by the latter junction. The current extracted in the forward bias is modulated by the illumination level, and the relation between both is represented by a gain factor in the same manner as in a normal transistor [
34].
Other issues related to the phototransistor model can be also seen in the I–V curves of CIGS solar cells, such as the Early effect or the punch-through effect. The first consists of a linear increase in the emitter–collector current when the bias between both terminals increases, instead of a perfect saturation because of the proximity between both space charge regions (SCR) that reduces the carrier recombination. It can be found in the I–V curves of CIGS solar cells under certain conditions, for instance, in very thin absorbers or in a low-doping absorber concentration [
36]. The punch-through is the extreme case of the Early effect; when both SCRs overlap, the current increases exponentially with the applied bias, and a significant decrease in Voc is also found in solar cells when this effect takes place under normal conditions [
37]. The punch (or reach)-through effect was first reported in cadmium telluride (CdTe) solar cells [
38] but is also known to occur in CIGS devices [
37].
The phototransistor effect is mostly visible in the I–V curves measured at low temperatures in the range from 100 to 200 K. However, it was also reported that accelerated ageing tests might induce this effect even at room temperature [
30] because of the oxidation of the Mo back contact, and a decrease in the apparent doping due to the metastable redistribution of charges that was previously mentioned. According to [
39], this decrease in doping level is responsible for an increase in non-radiative recombination at the heterointerface on the absorbers side.
This article discusses the effect of the back contact barrier on the performance of CIGS solar cells from the perspective of the phototransistor model introduced in [
34]. The results hereby presented provide strong evidence in support of this phototransistor model. Moreover, the effect of the back contact barrier is considered in the broader context of metastable changes typical for CIGS solar cells, induced by certain operation conditions dependent on the temperatures or electrical biases. The gain factor in the phototransistor model was also found to be affected depending on the applied treatment, and, in some cases, the treatment could induce the phototransistor behavior even at high temperatures (350 K). A barrier-lowering effect was proposed for the simulation model presented in this paper to explain a slight exponential increase in the current under forward bias that appears in the experimental I–V measurements on some of the samples. The punch-through effect is described in this paper as a side effect of the phototransistor model that could influence the performance of CIGS solar cells detrimentally, especially in very thin absorbers where the SCRs of both junctions are very close each other.
In summary, the effect of the back contact barrier on the phototransistor behavior was discussed in detail in this contribution. Furthermore, a relation between metastabilities and the phototransistor effect is established and supported by numerical modelling. Finally, barrier lowering as a consequence of high electric fields is proposed within the phototransistor model in order to account for experimental findings.
The article is divided into five parts. The introduction provides the reader with a concise context of the paper and a comprehensive literature review of the topic. The third chapter describes the results and is divided into two sections. The first section demonstrates the experimental results obtained from the characterization of CIGS solar cells, in particular the I–V curves of samples that were treated under different operation conditions (high temperatures and electrical biases), and other parameters extracted from the aforementioned samples, such as activation energies and barrier heights. The second section of part three discusses the I–V curves obtained from the simulation cases corresponding to the experiments, and also provides the calculated values of the activation energies and barrier heights mentioned above; the effect of the barrier-lowering in the model and the punch-through effect are also discussed with respect to the corresponding I–V curves. The fourth part discusses the results presented in chapter three in the framework of the phototransistor model. Finally, the conclusions summarize the findings of this paper and discuss the applications and research questions that are still open.
2. Materials and Methods
Both numerical simulations and experimental characterization were used in the development of this work, and their findings are in good agreement.
All the experimental results involve the electrical characterization of the samples in a wide range of temperatures, mainly because the phototransistor behavior is visible only in low-temperature regimes. From temperature-dependent current–voltage (I–V) characterization, it is possible to extract the activation energy and the height of the potential barrier at the back contact [
40]. Both parameters are calculated from the extrapolation of the Voc (T) values to 0 K in the low- and high-temperature regimes, as the results will show.
Three CIGS samples from the same batch grown by a three-stage co-evaporation process, with similar behavior of the I–V curves, were characterized in this work. An accelerated ageing test consisting of a high temperature treatment and different biases was applied to two of the samples (+0.4 V to one of the treated samples and −0.4 V to the other) over a period of 16 h at 100 °C to assess how these detrimental conditions alter the effect of the back contact barrier and the phototransistor behavior. These treatments were performed by placing two of the samples in a WKL 34/40 climate chamber [
41] (Weiss Umwelttechnik, Stuttgart, Germany) with an external connection to a Keithley 4200-SCS Semiconductor Analyzer [
42] (Tektronix, Beaverton, OR, USA) that was applied to the sample the appropriate bias and monitored the I–V curve every hour. The third sample was only kept at room temperature.
After these treatments, each sample was characterized in the temperature range from 100 K to 400 K in steps of 25 K. This was achieved by placing the samples in an OptistatDN-V model cryostat (Oxford Instruments-Nanoscience [
43], Oxford, UK) cooled with liquid nitrogen. The cryostat includes an external connector to perform the electrical measurements. The I–V curves were measured with a 4155 C Semiconductor Analyzer [
44] (Keysight, Santa Rosa, CA, USA). The cryostat also has a small glass aperture in the measurement chamber to illuminate the sample when needed. In this case, the external illumination for light I–V measurements was provided by a LOT-Oriel LSE 340 solar simulator (Quantum Design GmbH, Darmstadt, Germany), and a set of transmission filters was used to regulate the illumination level. The effective doping concentration was calculated based on the Mott–Schottky equation [
28] from the capacitance–voltage profiles measured at 300 K with 4192 LF Impedance Analyzer [
45] (Keysight, Santa Rosa, CA, USA) with a frequency and magnitude of alternating current (AC) signal of 100 kHz and 50 mV, respectively. A parallel circuit model consisting of a resistor and a capacitor was selected in the instrument for the extraction of the capacitance from the solar cell.
The simulations were performed by means of the Sentaurus TCAD suite [
46] (Synopsys, Palo Alto, CA, USA). The simulation model consists of a vertical stack of ZnO/CdS/CIGS/Mo, each material with the properties presented in
Table 1, including the physical dimensions of each layer, doping levels, bandgap energies and electron affinities where appropriate and other parameters that are relevant for the simulations in the scope of this work.
Apart from these layers, the Mo/CIGS interface is defined as a Schottky interface with a barrier that is adjusted through the work function of Mo and a surface recombination velocity of 1 × 10
7 cm
2/s for electrons and holes. The interface model also includes a barrier-lowering effect [
36] to represent another minor effect found in the experimental results presented in this work. In this model, the height of the barrier decreases when the component of the electric field that is perpendicular to the Mo/CIGS interface increases. Barrier lowering is a known property of Schottky barriers that could be attributed to tunneling or to a force exerted by image charges at the Mo/CIGS interface according to [
36]. The equation in [
36] that describes the barrier-lowering mechanism is presented in Equation (1).
In this equation, ∆ΦB is the barrier lowering in eV, q is the elementary electric charge, Enorm is the component of the electric field that is normal to the metal–semiconductor interface and εs is the dielectric permittivity of CIGS at the Mo/CIGS interface; a value of 10 was selected for the relative permittivity of CIGS. However, when tunneling is considered instead, the equation might be slightly different. In the presented simulations, the empirical model provided by Synopsys TCAD was used. This model includes a multiplicative factor of 2.2 × 10−4 eV and an exponential factor of 0.5, both of which are applied to the component of the electric field that is normal to the Mo/CIGS interface.
The model of the solar cell stack used for the simulation is presented in
Figure 1 with a horizontal orientation and an absorber thickness of 2.0 µm. Simulations are performed in the range of temperatures between 100 K to 400 K with steps of 50 K.
Finally, the punch-through effect that was mentioned in the introduction will be discussed in the context of simulations by adjusting the thickness of the absorber and its doping concentration in order to increase the proximity between the SCRs of the main pn junction and the metal–semiconductor junction of the Mo/CIGS interface. A lower thickness of the absorber and two different p-type doping levels are considered, one of 1 × 1016 cm−3 and the other of 7 × 1014 cm−3 for CIGS.
The simulation cases were designed based on the experimental results relative to the changes of two electronic parameters, namely the p-type doping concentration of the absorber and the height of the back contact barrier. Therefore, three simulation cases have been identified: (i) low doping (7 × 1014 cm−3) and a high barrier (460 meV); (ii) intermediate doping and barrier (1 × 1015 cm−3 and 300 meV); and (iii) high doping (1 × 1016 cm−3) and a low barrier (200 meV). These cases correspond to the experimental results of (i) the reverse bias-treated sample (with −0.4 V at 100 °C); (ii) the untreated sample; and (iii) the sample treated with a forward bias (+0.4 V at 100 °C), respectively. Experimental and simulated I–V curves for the three mentioned cases are presented for low (100 K) and high temperature (350 K). The curves that represent the temperature dependence of Voc are also provided for each experimental and simulation case; the activation energies and barrier heights calculated from these curves are also compared. Two additional simulated I–V curves at 100 K based on the high-doping (1 × 1016 cm−3) and low-barrier (200 meV) case are presented to study the barrier-lowering effect in more detail. The first corresponds to the simulation model without the barrier-lowering effect included, and the second I–V curve corresponds to the simulation model that considers the barrier-lowering effect. Finally, two more simulation results based on the low-doping (7 × 1014 cm−3) high-barrier case (460 meV) and the high-doping (1 × 1016 cm−3) low-barrier (200 meV) case, but with a thinner absorber (1.5 µm instead of 2 µm), are included to discuss the punch-through effect in CIGS solar cells associated with the phototransistor model.
4. Discussion
These results provide further evidence of the phototransistor behavior in CIGS solar cells. As previously discussed in [
34,
35], this behavior depends on the doping level in the absorber and the height of the barrier at the Mo/CIGS interface. These premises are also verified here with the experimental results presented in
Figure 2 and the simulations of
Figure 6. For instance, the sample treated in reverse bias, which corresponds to the low-doping high-barrier simulation case presented in
Figure 2a and
Figure 6a, respectively, shows a strong dependence of the current in the forward-bias regime on the illumination level. The gain factor that represents this dependence increases when the doping level of the absorber decreases with respect to that of ZnO/CdS, when the barrier height of the Mo/CIGS junction increases or when the width of the absorber decreases. When a normal transistor is considered, the gain depends on the doping levels of the emitter and the base, on the width of both quasi-neutral regions and on the diffusion lengths of holes and electrons in the emitter and the base, respectively [
36]. In CIGS solar cells, the doping level of the absorber was found to decrease when a reverse-bias treatment was applied, and the width of the SCR in CIGS increased at the same time, according to
Figure 5; thus, the width of the absorbers quasi-neutral region decreased, which leads to the higher gain factor in the phototransistor model.
Non-idealities of BJT transistors were also found in CIGS solar cells under certain conditions as a side effect of the phototransistor behavior. For instance, the Early effect is clearly visible in
Figure 2a,b for experimental results, and also in
Figure 6a,b in simulations. An extreme Early effect was found in
Figure 10a where the current increases exponentially; this increase can be explained by an almost non-existent quasi-neutral region in the absorber as shown in
Figure 11a. This extreme case of the Early effect is known as punch-through, and it implies a very high current flowing between the emitter and collector. In
Figure 10a, the current flowing when a bias of 1.5 V is applied in the simulation is around 500 mA/cm
2, but with a thinner absorber, it could reach values of 1 × 10
4 mA/cm
2 (not shown), which is an extremely high value.
The phototransistor model in CIGS solar cells presented in [
34] considers the Mo/CIGS junction as the collector/base junction, which is a Schottky junction instead of a normal pn junction. The polarity of this junction opposes that of the main pn junction, which leads to a decrease in Voc of the solar cell. This explains the saturation of the Voc curve over temperature found in
Figure 3 and
Figure 7, because the effect of this Schottky barrier increases when temperature decreases. At low temperatures, depending on the treatment applied to the sample or the parameters considered for the simulation, Voc was found to be independent of the illumination level, which is another indicator of the phototransistor effect [
34]. In
Figure 3a, for the sample treated in reverse bias, this independence of the illumination level is present over a wide range of temperatures, in contrast with the sample treated in forward bias, where Voc behaves as in a normal pn junction solar cell at temperatures as low as 200 K. The metastable nature of the phototransistor behavior, as a redistribution of charges in the absorber, is also shown in
Figure 5. The change in the effective doping also explains the differences in the forward current presented by each sample. A lower net doping level in the absorber, as in the reverse-treated sample case in
Figure 5, means a smaller effective base width in the phototransistor model, which, in turn, leads to a higher gain. Moreover, as the net doping level near the Mo/CIGS interface is smaller, the blocking of the current by this junction will be lower. Therefore, the current density in the forward bias under illumination will be higher, as shown in
Figure 2a. The opposite situation occurs in the forward-treated sample with a forward bias, as shown in
Figure 2c.
However, the simulated Voc curves shown in
Figure 8 diverge somewhat from the experimental ones of
Figure 4. For instance, the Voc curve of the sample treated in reverse bias in
Figure 3a has a smaller slope in the high-temperature regime, which leads to an extrapolated value of 0.8 eV instead of 1.2 eV because the phototransistor behavior was still present in the high-temperature regime. On the other hand, the simulation of the low-doping high-barrier case does not display this saturation of Voc in the high-temperature regime, which leads to an extrapolated value at 0 K slightly higher than 1.2 eV in
Figure 8a. The curve of the untreated sample in
Figure 4b is in good agreement with the simulation of the intermediate case presented in
Figure 8b. Finally, the simulation of the high-doping low-barrier case shows a diminished saturation of Voc in the low-temperature regime in contrast with the results of the sample treated in forward bias, which yields a calculated barrier height that is lower than the defined value (150 meV instead of 200 meV). This could be explained by the barrier-lowering model that was used in the simulations. The extrapolation of the activation energies from the high-temperature regime in the simulations of the intermediate case and the high-doping low-barrier case lead to a value that is around 1.3 eV, which is higher than the defined value of the bandgap (1.2 eV). The temperature dependence of the effective density of states N
c and N
v, according to [
48], could explain the difference between both values.
It was already mentioned that a barrier-lowering model for the Mo/CIGS interface was considered to explain some details of the experimental results. An example of this is seen in
Figure 2c, with the sample treated in forward bias. This treatment increases the effective doping according to C–V profiles, as shown in
Figure 5, through a metastable redistribution of charges, and the apparent barrier height that is calculated from I–V–T measurements is decreased at the same time. These two changes also lead to a higher effective width of the base, and the result is a lower gain of the phototransistor in the model, but also a lower current in forward bias. However, a less pronounced Early effect and a more saturated forward current density are expected as a result of the lower gain and the higher doping, which
Figure 2c seems to contradict. Instead, these curves present a slight exponential increase in the current density with a forward bias. The need for a mechanism that reconciles both findings in the experimental J–V curves can be solved with the barrier lowering, because this mechanism is independent of the base width of the phototransistor, and also explains the non-linear increase in the forward current density with the applied bias, as shown in
Figure 9. The J–V curves of the untreated sample in
Figure 2b exhibit more pronounced phototransistor behavior, but also a non-linear increase in the forward current density with the applied bias; the reason behind this increase could be attributed to a non-linear Early effect, but also to the barrier lowering at the Mo/CIGS interface. In this case, the barrier-lowering mechanism seems a better explanation regarding this non-linear increase in the forward current in the untreated sample, because the sample treated with reverse bias only shows a linear Early effect with a lower effective doping and a higher calculated apparent barrier height. The simulated I–V curve of the intermediate case in
Figure 6b only exhibits a linear Early effect in contrast with the experimental results of the untreated samples in
Figure 2b. In this case, the doping concentration used in the simulations for the absorber is not sufficiently high for the barrier lowering to be significant, but it is high enough to prevent a non-linear Early effect due to a reduced effective width of the base.