Optical and the corresponding photocurrent losses in CIGS solar cells
1. Introduction
For a long time, solar cells based on CuIn_{1x}Ga_{x}Se_{2} (Cu(In,Ga)Se_{2}, CIGS), similar to CdTebased devices, keep a stable position in thinfilm photovoltaics as an alternative to solar modules based on mono and polysilicon wafers. The IIIIVI CIGS alloy is a solid solution of copper indium diselenide (CIS) and copper gallium diselenide (CGS). This alloy is tolerant in terms of material stability and miscibility in a wide range of
To date, mass production of costeffective thinfilm polycrystalline and monolithically interconnected CIGSbased modules has been achieved by many companies worldwide. Since 2007, one Japanese company Solar Frontier, alone for example, delivered over 1 GW CIGS modules. The CIGS devices demonstrate excellent longterm stability; can be fabricated on lightweight and flexible substrates that are desirable for portable, buildingintegrated photovoltaics and many other applications when solar panels are used to replace conventional building materials in parts of the roof or facades. It should also be noted that the CIGS modules, in addition to their longterm stability, have shown higher resistance to ionizing radiation compared to crystalline Si and IIIV solar cells, i.e., such devices are promising for space application [1].
The energy conversion efficiency of CIGS modules is in the range of 1215%, but for small area laboratory cells, the efficiency milestone of > 20% was achieved in 2010 [2]. In 2014, Solar Frontier has achieved 20.8% energy conversion efficiency for small area CIGS cells and Zentrum für Sonnenenergieund WasserstoffForschung BadenWürttemberg (ZSW) shortly improved the cell efficiency to 20.9% [3,4]. Since the efficiency of CIGS modules lie in the 1215% range (except for a 16.6 % world record [5]), which is about half of the theoretical limit 2830%, there are plenty of opportunities to contribute towards the scientific and technological advancement of CIGS PV technology.
The device architecture of CIGS and CdTe solar cells are alike, similar to other pn heterojuctions. In both cases, the CdS/absorber heterostructure is the key element in determining the electrical and photoelecnric characteristics of the device. In CIGS solar cells, the heterojunction is formed between the pCIGS and nCdS. The conductivity of CIGS is determined to a large degree by intrinsic defects, while the nCdS is doped to a much larger extent by donors. This asymmetric doping causes the space charge region (SCR) to extend much further into the CIGS. As in CdTe solar cell, a thin layer of CdS serves as “window”, through which radiation penetrates into the absorber.
The difference between these devices lays in their popular superstrate (CdTe) and substrate (CIGS) configurations. In superstrate configuration devices, the sunlight enters the absorber through the glass substrate and transparent conductive oxide layer (TCO, usually SnO_{2}:F) while only through the TCO layer (usually ZnO:Al) in substrate configuration. These design features are not of fundamental importance from the point of view of the physical processes taking place, but demand different device fabrication technologies. The physical models used for the interpretation of the CdTe solar cell characteristics has been successfully applied with some modifications to the CIGS devices [6,7].
Based on the above reasoning, in this chapter a detailed analysis of the optical and recombination losses in CIGS devices are presented, which are important causes of poor quantum efficiency (QE), leading to low solartoelectric energy conversion efficiency in solar cells. A quantitative determination of the losses is presented and some possible pathways to reduce them are identified. Calculations of the optical losses are carried out using the optical constants, refractive indices and extinction coefficients, of the materials used. Equally important are the recombination losses, which are determined using the continuity equation considering the drift and diffusion components of the photocurrent and all possible recombination losses. In order to discuss the influence of the electrical parameters of the heterojunction on the photoelectric conversion efficiency of the device, an analysis of the currentvoltage characteristics recorded in dark and under illumination is also included in this chapter. It seems that the analysis of the physical process involved in the photoelectric conversion is useful from a practical point of view since undoubted successes in the development of efficient CIGS solar cells have been achieved mainly empirically [8].
2. Optical constants and related material parameters
Three typical cases, with distinct bandgaps for the CIGS absorber
Fig. 1 shows the schematic representation of a typical CIGS solar cell architecture, where the notations corresponding to the optical constants
Photoelectric conversion in these solar cells occurs in the CIGS absorber with a thickness of about 2 μm, while a thin ntype CdS buffer layer (20–50 nm) serves as the heterojunction partner and the window through which the radiation penetrates into the absorber. The Al doped ZnO layer serves as TCO with a thickness of 100–500 nm. Application of an undoped highresistivity iZnO layer with thickness in the range 20–50 nm between TCO and CdS is very common in both substrate and superstrate configuration devices. In efficiency solar cells, an antireflection layer MgF_{2}, generally of ∼ 100 nm thick is also deposited onto the front surface of ZnO.
In the QE calculations of CdS/CIGS cell, one needs to know the optical transmission of the ZnO/CdS structure
where
Fig. 2 shows the spectral dependences of
It is worth to note the fact that for CIGS, the extinction coefficient in the photon energy range
This extended QE response can be explained by the presence of socalled ‘tails’ of the density of states in the bandgap of the semiconductor with strong doping or/and disordered crystal structure. In this case, the electron wave functions and force fields of impurity atoms overlap, whereby the discrete impurity levels are broadened and transformed into an impurity band. At a certain critical impurity (defect) concentration, this band joins with the conduction (valence) band, i.e., the tails of the density of states appear. The absorption coefficient in the range of tail depends exponentially on the photon energy, i.e.,
Based on the above comments, it is valid to use the
In the range
The above correction of the spectral curves (Fig. 2b) does not exclude the possibility of determining the bandgaps of the samples by using Eq. (2) and the experimental values of
The intercept of the extrapolated straight line portions on the photon energy
3. Optical losses caused by reflection and absorption
The optical transmission
Here
In order to minimize current losses in PV module, thin metal grids are deposited onto the front surface of ZnO, which serve as lateral current collectors. But these grids cause shadowing and a factor
The effect of an antireflection coating is not considered in Eq. (3), which can significantly reduce the reflectance of the front surface
The reflection coefficient
where
and
Fig. 5a shows a comparison of the reflectance of the bare ZnO surface (curve
So, for taking into account antireflective coating, the reflection coefficient
Fig. 5b illustrates the impact of antireflective coating on the transmission property of ZnO/CdS layers in CIGS solar cells.
3.1. Reflection and absorptive losses
From a practical point of view, it is important to assess the various types of losses due to reflections from the interfaces and absorption in the ZnO and CdS layers.
Reflection loss at an interface can be determined using Eq. (8) as the difference between the photon flux that incident on the interface and that passed through it. Absorptive losses can be found from the difference between the photon flux entered the layer and that reached the opposite side.
An estimate of the decrease in solar cells performance due to the optical losses can be obtained by calculating the photocurrent density
where
Assuming that the solar radiation is negligible for
Analyzing the optical losses, we assume that the QE of the solar cell
It is convenient to report the optical and other types of losses in percentage. Below, all the losses in percentage we will determine relatively to the photocurrent generated by the photon flux incident on the solar cell
Fig. 5a shows that the zero reflectance of ZnO with an antireflection coating takes place at the wavelength of 570 nm for a 100 nm thick layer of MgF_{2} that corresponds approximately to the maximum of the solar radiation under the AM1.5 conditions. According to Eq. (4) and (7), the position of the reflectance minimum of the curve
It is interesting to see how the photocurrent density
Next the results of calculations of the reflection losses at all interfaces and the absorptive losses in the ZnO and CdS layers are given for solar cells under study.
The losses due to reflection from the front surface of ZnO with an antireflection coating of a 100 nm thick MgF_{2} layer in CuInSe_{2}, CuIn_{0.69}Ga_{0.31}Se_{2} and CuIn_{0.34}Ga_{0.66}Se_{2} solar cells are equal to 1.9, 1.5 and 1.4%, respectively. Using Eqs. (8) and (9) the calculated values of the reflection loss at the ZnO/CdS interface are 0.9, 0.9 and 1.0% respectively for these solar cells, whereas for the CdS/CIGS interfaces in the three cases the corresponding losses are 1.3, 1.2 and 1.1%, respectively.
Low reflection losses at the interfaces are due to the close values of the optical constants of different layers. This is illustrated in Fig. 7 by plotting the calculated values of the reflectance for ZnO, CdS and CuIn_{0.33}Ga_{0.67}Se_{2} in the air and in optical contacts with each other. As seen, at the 700 nm region the reflection coefficients at the interfaces (air/MgF_{2})/ZnO, ZnO/CdS and CdS/CIGS are 10–17 times smaller than those at the interfaces air/ZnO, air/CdS and air/CIGS. The sharp increase in reflectance at
Absorption losses in the 300 nm thick ZnO and 40 nm thick CdS layers are larger as compared to reflection losses and equal respectively to 2.9 and 5.2% for CuInSe_{2}, 2.2 and 5.6% for CuIn_{0.69}Ga_{0.31}Se_{2} and 1.9 and 7.7% for CuIn_{0.34}Ga_{0.66}Se_{2} solar cell. The difference in losses for the three types of samples is due to the difference in their bandgaps.
It seems that reflection losses cannot be reduced by virtue of their nature whereas the absorption losses can be reduced by thinning the CdS and ZnO layers. The data in Fig. 8 give some indication of a possible way of lowering these absorption losses. As seen, for
The calculated values of optical losses along with the corresponding decrease in the photocurrent









Air/ZnO interface with ARC ZnO/CdS interface CdS/CIGS interface Total reflection losses 
2.5% (0.8 mA/cm^{2}) 0.9% (0.4 mA/cm^{2}) 1.3% (0.7 mA/cm^{2}) 4.7% (1.9 mA/cm^{2}) 
1.9% (0.6 mA/cm^{2}) 0.9% (0.4 mA/cm^{2}) 1.2% (0.6 mA/cm^{2}) 4.0% (1.6 mA/cm^{2}) 
1.4% (0.5 mA/cm^{2}) 1.0% (0.4 mA/cm^{2}) 1.1% (0.4 mA/cm^{2}) 3.5% (1.3 mA/cm^{2}) 


Absorption in ZnO Absorption in CdS Insufficient absorptivity Total absorption losses 
2.9% (1.5 mA/cm^{2}) 5.2% (2.7 mA/cm^{2}) 0.6% (0.1 mA/cm^{2}) 8.1% (4.3 mA/cm^{2}) 
2.2% (1.1 mA/cm^{2}) 5.6% (2.9 mA/cm^{2}) 0.2% (0.1 mA/cm^{2}) 7.8% (4.1 mA/cm^{2}) 
1.9% (0.7 mA/cm^{2}) 7.7% (2.6 mA/cm^{2}) 0.4% (0.1 mA/cm^{2}) 9.6% (3.4 mA/cm^{2}) 

17.4% (9.4 mA/cm^{2})  16.0% (9.0 mA/cm^{2})  17.5% (7.3 mA/cm^{2}) 
3.2. Effect of multiple reflection in ZnO and CdS layers
In the calculations outlined in Section 3.1, we omitted the multiple reflections and interference effects in the ZnO and CdS layers, although they occur like those in antireflection coating (oscillations in CIGS are suppressed by strong absorption of the material). It should be noted that the periodic oscillations in the quantum efficiency spectra of the CIGS solar cells, originating from the interference effects, in many cases are not observed. To explain this fact, we calculated the optical transmission of the ZnO/CdS layered structure taking into consideration multiple reflections [9] and using the formula for the doublelayer antireflection coatings [16]:
where
Considering a grid contact at the front surface of the ZnO layer and using Eq. (10), one can write the expression for the transmission of the ZnO and CdS layers:
where
The curve labeled
Eq. (10) describes the oscillations in the reflection spectra due to interference effects in the ZnO and CdS layers, however it does not take into account absorption in these layers. When extinction coefficient
The results of calculations using Eq. (17) are shown in Fig. 9 as curve
The spectrum
It should also be borne in mind that the Eq. (17) has been deduced for flat, perfect and parallel interfaces air/ZnO, ZnO/CdS and CdS/CIGS. But real interfaces will be far away from the ideal conditions; hence the oscillations in the transmission spectra can be less than 0.5% or even not visible. In contrast, if the interfaces are perfect as mentioned above, the periodic variations in the transmission and photoresponse spectra of the devices will be clear [17].
3.3. Absorptive capacity of the CIGS absorber layer
In the previous sections while discussing the photocurrent, we assumed 100% lighttoelectric conversion in the CIGS layer. However, there are losses related to the incomplete absorption of light in this layer. Considering this fact, while estimating the exact values of
It should be noted that in the photon energy range from
The
Here summation is for the spectral range starting from
According to Eq. (18) for CuInSe_{2}, CuIn_{0.69}Ga_{0.31}Se_{2} and CuIn_{0.34}Ga_{0.66}Se_{2} solar cells, 99.4, 99.6 and 99.8% photon absorption happens for a layer thickness of 2 μm. But with a layer thickness of 1 μm the photon absorptivity values for these solar cells are equal to 97.0, 98.3 and 97.7% respectively, i.e., optical losses become noticeable. On the other hand, in another directgap semiconductor CdTe the photon absorptivity of 99.4–99.8% takes place at a thickness of about 30 μm [18].
It should also be borne in mind that CIGS solar cell is a substrate configuration device having metallic substrate as one of the electrodes. This implies that long wavelength radiation with low absorption coefficient can reflect back from the rear surface. In the event of 100% reflectance from the back surface, the absorptivity is the same as for the double thickness of the absorber layer, i.e., the
4. Recombination losses
Electrons and holes (electronhole pairs) created as a result of photon absorption in the space charge region (SCR) of CdS/CIGS heterostructure move apart under the influence of the junction builtin voltage. The electrons move towards to CdS side and reach the front metal grid contact after passing through the ZnO layer, while holes move to the neutral part of the CIGS layer and reach the Mo back contact. Not all the photogenerated carriers contribute to the current; some of the carriers recombine in the SCR before reaching the contacts. Recombination can also occur at the front surface of the absorber contacting with the CdS film. Minority carriers (electrons), which are generated outside the SCR, also take part in the formation of the photocurrent, when electrons reach the SCR as a result of diffusion. This process competes with the recombination of electrons with the majority carriers (holes) in the neutral part of the absorber. Finally, recombination of electrons can occur on the back surface of the absorber, i.e., at the CIGS/metal interface.
For a given thickness of the absorber, the recombination losses depend mostly on the carrier lifetime and the width of the SCR, which in the case of a semiconductor containing both acceptor and donor type impurities are determined by the concentration of uncompensated acceptors
Consideration of the statistics in a nonequilibrium state leads to the conclusion that the lifetimes of electrons
The recombination losses can be judged by the value of photocurrent density
where
The CdS/CIGS solar cell is generally treated as an abrupt asymmetric pn heterostructure, in which the SCR (depletion layer) is practically located in the pCIGS and the photoelectric conversion takes place almost in this layer (see [8] and references therein). The potential and field distributions in abrupt asymmetric pn junction are practically the same as in a Schottky diode, therefore, further consideration of the processes in CdS/CIGS solar cells can be studied on the basis of the concepts developed for Schottky diodes.
The exact expression for the photovoltaic quantum efficiency of a ptype semiconductor Schottky photodiode obtained from the continuity equation taking into account the recombination at the front surface has the form [21]:
where
In Eqs. (20) and (21)
and the following notations are used:
where the
In a CIS or CIGS with both acceptor and donor impurities, the SCR width
where
For the convenience in analyzing the dependence of
In a solar cell, CIS or CIGS, with the barrier height from the semiconductor side φ_{bi} is of the order of 1 eV and the width of the SCR is about 1 μm, i.e., the electric field is close to 10^{4} V/cm. At the boundary between the depletion layer and the neutral region (
The integrand
Thus, we can find the value of
which is reduced to the quadratic equation
with the solution
Since the second term under the square root is much less than unity,
Similarly, by replacing the integration in Eq. (23), we can obtain the expression for
So, considering all the simplifications made for the photoelectric quantum yield it is possible to substitute Eq. (20) with the following expression:
As an example comparison of the curves
In the calculations we used the absorption curve
It should be bear in mind that Eq. (34) takes into consideration both the drift and diffusion components of the quantum efficiency but does not take into account recombination at the back surface of the absorber layer [21] which can result in significant losses in the case of a thinfilm solar cell. In the case of CdS/CdTe cell, for example, it is possible to neglect the recombination at the back surface if the thickness of the absorber exceeds 4–5 μm. However, solar cells with thinner layers are also of considerable interest. In this case, Eq. (34) is not valid, and the drift and diffusion components of the quantum efficiency should be separated.
To find an expression for the drift component of the photoelectric quantum yield one can use Eq. (34). Indeed, the absence of recombination at the front surface (
The above equation also ignores recombination at the back surface of the absorbed layer. Eq. (34) does not take into account recombination inside the SCR, therefore, subtracting the absorptive capacity of the SCR layer 1 – exp(–
For the diffusion component of the photoelectric quantum efficiency taking into account surface recombination at the back surface of the absorber layer, one can use the exact expression obtained for the player in a solar cell with pn junction [22]:
where
The internal quantum efficiency of photoelectric conversion in the absorber layer is the sum of the two components:
whereas the external quantum efficiency can be written in the form
where
Fig. 11 shows a comparison of the measured quantum efficiency spectra of CuInSe_{2}, CuIn_{0.69}Ga_{0.31}Se_{2} and CuIn_{0.34}Ga_{0.66}Se_{2} solar cells taken from [8] with the results of calculations using Eq. (39). Note that the data on the extinction coefficients (and hence the absorption coefficient
According to the data in the above reference [8], in the calculations, the thicknesses of the CIGS, ZnO, CdS and MgF_{2} layers were assumed to be 2000, 300, 20–50 and 100 nm, respectively. The parameters of the absorber layer were varied within the limits reported in the literature. It should be noted that for polycrystalline CIGS, there is a large spread in mobility values of electrons and holes. At room temperature, the values of the hole mobility are most often indicated in the range from 1–5 to 30–50 cm^{2}/(Vs) and from 1 to 100 cm^{2}/(Vs) for the electron mobility [23–25]. Unlike this, it was found in [26] that the electron and hole mobilities in Cu(In,Ga)Se_{2} are much lower than 1 cm^{2}/(Vs). As mentioned in Section 2, we believe that such low mobilities refer to the charge transport in the subband joined with the conduction band (valence band) due to high doping or/and disorder in the crystal lattice. In contrast, electrons and holes arising as a result of absorption of photons with the energy
The lifetime of minority carriers (electrons), determining their diffusion length
Yet another important parameter determining the quantum efficiency spectra of solar cells is the concentration of uncompensated acceptors
The velocity of recombination at the front surface
Our calculations in section 4.3 show that recombination at the rear surface of 2 μm thick absorber layers of CuInSe_{2}, CuIn_{0.76}Ga_{0.24}Se_{2} and CuIn_{0.39}Ga_{0.61}Se_{2} manifests itself very weakly and only for long lifetimes of electrons.
It follows that the main parameters of the absorber layer affect the QE spectrum of the solar cell
As can be seen, a deviation upward or downward from the optimum value of the minority carrier lifetime (
The concentration of uncompensated acceptors
Finally, the variation of the CdS layer thickness manifests itself only in the range of the fundamental absorption of this semiconductor, i.e., when
Parameters giving best match for the spectral distribution of calculated and experimental QE of the studied cells are summarized in Table 2. Notice that in the investigated solar cells, the SCR width (0.4–0.6 μm) amounts to a small part of the thickness of the absorber layer and the recombination velocity
Back in the late 1980s, it was shown that the CIGS solar cells are insensitive to defects caused by a lattice mismatch or impurities at the CdS/CIGS interface. In fact, the lattice mismatch is rather small for CdS and CuInSe_{2} (∼ 1%) and weakly increases with the Ga content. In addition, the deposition of CdS on the treated and cleaned surface of the CIGS layer is characterized by pseudoepitaxial growth, and the intermixing of the heterojunction constituents is observed even at relatively lowtemperature processes [30, 31].






CuInSe_{2}  1.04  0.60  5  2×10^{15}  1×10^{5}  45 
CuIn_{0.3}Ga_{0.7}Se  1.14  0.75  20  9×10^{15}  5×10^{5}  50 
CuIn_{0.67}Ga_{0.3}Se  1.36  0.95  2  5×10^{15}  2×10^{5}  40 
A comparison of measured and calculated results presented in Fig. 11 shows that the theoretical model describes in detail the spectral distribution of the quantum efficiency of CIGS solar cells, which is important for further analysis of recombination losses. But the question arises, how this model can be applicable in polycrystalline material, with its inhomogeneity, recombination at the grain boundaries, etc. A possible explanation for the applicability of the model in question to efficient solar cells based on polycrystalline CIGS is that during the growth of the absorber layer and postgrowth processing, recrystallization leading to grain growth and their coalescence occur. Also no less important is the fact that a structure in the form of ordered columns oriented perpendicular to the electrodes is created in the CIGS layer (see reviews [32] and references therein). One can assume that in a layer of columnar structure, collection of photogenerated charge occurs without crossing the grain boundaries. In addition, the scattering and recombination on the lateral surfaces of the columns also have no significant effect due to the strong electric field in the barrier region.
Indeed, the width of the SCR in the studied solar cell is about 0.5 μm, and the electric field at a barrier height φ_{bi} of about 1 eV is higher than 10^{4} V/cm. Under such conditions, the drift length of charge carriers with the mobility of 2030 cm^{2}/(Vs), and lifetimes 10^{–9} s is several microns which is significantly greater than the width of SCR and makes recombination improbable. Outside the SCR, where the diffusion component of photocurrent is formed, the electric field does not exist, but due to the high absorption capacity of CIGS the vast majority of solar radiation is absorbed in the SCR. This is illustrated in Fig. 13 with the example of CuIn_{0.39}Ga_{0.61}Se_{2} (
Calculation given by Eq. (39) shows that for the parameters listed in Table 2, the contributions of the diffusion component in the photocurrent of CuInSe_{2}, CuIn_{0.76}Ga_{0.24}Se_{2} and CuIn_{0.39}Ga_{0.61}Se solar cells is about 2, 4 and 8%, which are far inferior to the drift component. This significantly weakens the role of recombination at the grain boundaries.
4.1. Recombination losses at the absorber front surface
To determine the recombination losses, we will calculate the photocurrent density by varying the parameters of solar cells such as the recombination velocity at the absorber surface, concentration of uncompensated acceptors and carrier lifetimes in the material, as well as the thickness of the absorber. Photocurrent density will be calculated by Eq. (19) using for
Until now, the internal quantum efficiency was calculated under zero bias, since it was necessary for comparison with the spectra measured at
Consider how the photocurrent density
As seen in Fig. 14a, if the concentration of uncompensated acceptors exceeds 10^{17} cm^{–3}, surface recombination does not reveals itself, but at lowering the
4.2. Recombination losses in the SCR
Recombination of photogenerated charge carriers in the SCR can be taken into account, using the wellknown Hecht equation [33]:
where
In CdS/CIGS heterostructure, the electric field is not uniform, but the problem of the nonuniformity is simplified, since the field strength
Evidently, charge collection efficiency in the
Fig. 15 shows the photocurrent density
As can be seen in Fig. 15a, when
Fig. 15b shows the reduction in
4.3. Recombination losses at back surface and neutral part of absorber
Useful information about the effect of recombination at the back surface of the solar cell and the neutral part of the absorber on the photocurrent
Subtracting the currents calculated for the recombination velocity
Fig. 16a shows the dependences of photocurrent
As can be seen from Fig. 16b, the decrease in photocurrent does not exceed 1.5% even with lifetimes of electrons 20 ns. With such low recombination losses, the creation of a heavily doped layer adjacent to the back contact as it is proposed in CdS/CdTe solar cells [7] or to form a bandgap gradient outside the SCR in the CIGS absorber [8] to reduce the negative impact of recombination at the rear surface of the absorber seems to be unreasonable. As previously mentioned, a very small fraction of carriers taking part in the photocurrent formation (2–8%) falls on the neutral part of the studied CIGS solar cells that also should be borne in mind.
Of course, recombination of photogenerated carriers happens not only at the back surface of the absorber, but also in whole neutral part (outside the SCR). The losses due to such recombination can be found as the difference between photocurrent at: (i) real electron lifetime and recombination velocity at the rear surface and (ii) large value of the electron lifetime when recombination can be ignored (
The calculated values of
The total recombination losses in CuInSe_{2}, CuIn_{0.76}Ga_{0.24}Se_{2} and CuIn_{0.39}Ga_{0.61}Se_{2} solar cells amount to 5.4, 7.0 and 4.1%, respectively. It can be assumed that the charge collection efficiency of the photogenerated charge in the absorber is 94.6, 93.0 and 95.9%, respectively. Having these data, it is worth to analyze the possibility of reducing the recombination losses and improving the charge collection efficiency that we will make with an example of CuIn_{0.76}Ga_{0.24}Se_{2} solar cell.







Front surface Spacecharge region Neutral part of absorber and back surface Only back surface 
2.2% (0.9 mA/cm^{2}) 0.7% (0.4 mA/cm^{2}) 2.5% (1.0 mA/cm^{2}) 0.2% (< 0.1 mA/cm^{2}) 
1.9% (0.7 mA/cm^{2}) 0.1% (< 0.1 mA/cm^{2}) 5.0% (1.8 mA/cm^{2}) 1.0% (0.4 mA/cm^{2}) 
0.2% (< 0.1 mA/cm^{2}) 1.0% (0.3 mA/cm^{2}) 2.9% (1.0 mA/cm^{2}) 0.1% (< 0.1 mA/cm^{2}) 
Total recombination losses  5.4% (2.3 mA/cm^{2})  7.0% (2.5 mA/cm^{2})  4.1% (1.4 mA/cm^{2}) 
According to Eq. (36), the recombination losses at the front surface can be lowered by increasing the hole diffusion coefficient
Significant improvement of the charge collection efficiency can be achieved by increasing the lifetime of electrons, which is equivalent to an increase of electron mobility since the diffusion length
The recombination losses in the SCR 0.1% at large electron and holes mobilities approach to zero since the drift lengths of carries are proportional to the their mobilities. Thus, due to a real increase of the mobility of electrons and holes by one order of magnitude the charge collection efficiency improves from 93.0 to 98.6%.
An even greater improvement of the charge collection efficiency can be achieved by extending the SCR, which leads to absorption of a greater part of the radiation in the SCR and hence the better collection of the photogenerated charge. However, one should keep in mind that when the electron lifetime and mobility increase, the diffusion length becomes longer than the absorber thickness. This weakens the desired effect and in fact the charge collection efficiency for
There is also a positive impact for a higher carrier lifetime and expanded SCR since it leads to a decrease in the forward recombination current. Analyzing the electrical characteristics of the solar cell, it is not difficult to show that this causes enhancing the open circuit voltage (see the next sections).
Some useful information can be obtained from the spectral distribution of the reflection, absorption and recombination losses. Fig. 17 shows the distribution of these losses over the whole spectrum for CuIn_{0.76}Ga_{0.24}Se_{2} solar cell obtained from the results given above.
As clearly seen, the recombination losses are considerably less than those caused by reflection and absorption in the ZnO layer and especially in the CdS layer. The radiation in the range
5. Electrical characteristics of CIGS solar cells
The electrical properties of CIGS solar cells are presented in many publications, but their
In this section we analyze the dark
5.1. Experimental results and discussion
The
As seen in Fig. 18b, the dark current in solar cell with the bandgap of the absorber 1.04 eV follows quite well the voltage dependence
Useful information about the electrical properties of the diode can be obtained from the analysis of the voltage dependence of the differential resistance
One can assume that shunting in the studied solar cells is caused by pinholes and defects associated with a thin film of CdS (20–30 nm) used in the layered structure. In high efficiency CIGS solar cells, a thin intrinsic iZnO layer is applied which is capped by a thicker Aldoped ZnO layer. It is believed that the iZnO layer reduces the shunt paths by forming a thin high resistive transparent film (HRT), thin enough to promote tunneling, which is proven to enhance the device performance. However, ZnO is usually deposited by sputtering which is known as a damaging process [35]. Seemingly the damages at the CdS/CIGS interface produced by iZnO sputtering leads also to the occurrence of shunts. However, in the case of iZnO, the value of the shunt resistance is much larger compared to ZnO:Al due to high resistivity of iZnO and the shunting reveals itself only at relatively low voltages.
The voltageindependent differential resistance at
As seen in Fig. 18b,
The obtained results can create the impression that the occurrence of shunt is due to the introduction of Ga into the CuInSe_{2} crystal lattice in order to widen the semiconductor bandgap for increasing the efficiency of solar cells. However, some results reported in the literature indicate that the shunting in solar cells with wide bandgap can be avoided by modifying the fabrication technology, in particular by increasing the temperature of CIGS deposition and postgrowth processing [36].
Sodalime glass is a common substrate material used in CIGS solar cells due to its low cost and good thermal expansion match to CuInSe_{2}. In addition, the sodalime glass supplies sodium to the growing CIGS layer by diffusion through the Mo back contact, leading to enhanced grain growth with a higher degree of preferred orientation.
It is known that the CIGS deposition requires a substrate temperature at least 350°C and efficient cells have been fabricated at the maximum temperature ∼ 550°C, which the glass substrate can withstand without softening. In these temperature ranges, CIGS solar cells are typically made with low Ga content (
It was shown in [36] that the growth and postgrowth processing at temperature higher than 550°C leads to significant improvements of the performance of CIGS solar cells with bandgaps up to 1.4–1.5 eV. For this purpose, borosilicate glasses have been used in CIGS research even though it has nonoptimum thermal coefficient of expansion and no sodium in it. Nevertheless the solar cells with a wide bandgap for CIGS absorber, fabricated on borosilicate glass at the substrate temperatures in the range of 600 to 650°C had a rather high efficiency.
In addition to improving efficiency, the shunting of heterostructure in the device fabricated at an elevated temperature can be eliminated. This is illustrated by Fig. 20 where the data obtained for solar cells with the absorber bandgap 1.5 eV fabricated using standard technology
As can be seen in Fig. 20a, for solar cells fabricated using standard technology, the
The
As seen in Fig. 20a, the data obtained for solar cells fabricated at elevated temperature of 650°C is in good agreement with the expression
5.2. Generation–recombination in space–charge region theory
As mentioned previously, the theory of generation–recombination of charge carriers in the spacecharge region (SCR) was developed for the linearly graded silicon pn junction by Sah et al. [19] and modified and adapted to a Schottky diode taking into account the distribution of the potential and free carrier concentrations in the SCR [37,38].
The generation–recombination rate through a single level trap for nonequilibrium but steadystate conditions in the cross section
where
The expressions for the electron and hole concentrations in the SCR of Schottky diode involved in Eq. (47) in the chosen reference system take the form [39]
where ∆
φ_{bi} is the height of the potential barrier in equilibrium for holes from the CIGS side related to the builtin (diffusion) voltage
The recombination current density under forward bias and the generation current under reverse bias are found by the integration of
From the above equations one can obtain the exponential voltage dependence of the recombination current under forward bias.
Substitution of Eqs. (48)–(50) into Eq. (47) and simple manipulation yield the following expression for the generation–recombination rate:
where
We assume that CIGS contains a lot of shallow and deep impurities (defects) of donor and acceptor types. According to the ShockleyReadHall statistics the most effective generation–recombination centers are those whose levels are located near the middle of bandgap. Taking into account this, one can neglect the first term in the denominator of Eq. (52) and obtain the following expression for the current density using Eq. (51):
where
The function
So Eq. (53) in the integral form yields the exponential dependence of the recombination current on the applied voltage (sinh(
Fig. 21 shows a comparison of the voltage dependence of the recombination currents in CIGS solar cell, for example, with
As seen in Fig. 21, the
In addition to the results shown in Fig. 21, it is appropriate to draw attention to the rather important fact. If we express the voltage dependence of the recombination current as
The difference of
5.3. Finding the photoelectric characteristics of solar cells
First consider an applicability of the above theory of generation–recombination in the SCR to the experimental data discussed in Section 5.2.
The dark
As seen in Fig. 22, the calculated results agree well with the experimental data for all solar cells. One point to be mentioned is that in order to obtain a fit with the experimental data of solar cell with
Knowing the dark
Fig. 23b shows the dependences of the electrical power in the solar cell circuit
As seen in Fig. 23a, the calculated curve for sample with the bandgap 1.04 eV practically coincides with experimental curve, but in the cases of the absorbers with bandgaps 1.14 and 1.36 eV the calculations give overestimated values of the current. However, if the shunts are taken into account, the calculated and experimental curves for all samples practically coincide. It follows that a comparison of the theory and experiment gives the
As seen in Fig. 23, the calculated results agree well with the experimental data and indicate a noticeable negative effect of shunting in the studied cells. The effect of shunting is higher when the bandgap of the CIGS absorber is large (shunting does not reveal itself in CIS solar cell). As expected, the shunting does not practically vary the open circuit voltage but reduces the fill factor and the energy conversion efficiency. For the cell with absorber bandgap 1.14 eV, shunting leads to decreasing the fill factor from 0.73 to 0.70 and the efficiency from 13.3 to 12.7%. For cell with the absorber bandgap 1.36 eV, these values are 0.77 to 0.70 and 14.3 to 13.0%, respectively. The fill factor and efficiency of CuInSe_{2} solar cell are equal to 0.67 and 11.3%, respectively.
Note that the efficiency of studied CIGS solar cells is in the range of 1114% which is comparable with the efficiency of the modules produced in large volume, but much inferior to record efficiency of small area CIGS solar cells achieved so far.
6. Conclusions
The optical losses in Cu(In,Ga)Se_{2} solar cells caused by reflections from the interfaces and absorption in the ZnO and CdS layers have been calculated using the optical constants of the materials. When calculating the integral photoelectric characteristics of a solar cell, ignoring the multiple reflections and interference effects in the ZnO and CdS layers cannot cause remarkable errors. (i) The losses due to reflection (reducing the shortcircuit current density) from the front surface of ZnO with an antireflection coating in CuInSe_{2}, CuIn_{0.69}Ga_{0.31}Se_{2} and CuIn_{0.34}Ga_{0.66}Se_{2} solar cells are equal to 2.5, 1.9 and 1.4%, respectively (antireflection coating increases the photocurrent by 7.1%, 7.4% and 8.0%). The reflection losses at the ZnO/CdS interface are equal to 1.0, 0.9 and 0.9% for these cells, respectively, whereas for the CdS/CIGS interface the losses are 1.3, 1.2 and 1.1%, respectively. The total reflection losses for typical parameters of these solar cells are equal to 4.7, 4.0 and 3.5%, respectively (excluding shading by grid). (ii) The losses caused by absorption in the ZnO and CdS layers amount to 8.1, 7.8 and 9.6% for these solar cells, respectively. The losses due to insufficient absorptivity of the CIGS absorber are 0.6, 0.2 and 0.4%, respectively. The
The recombination losses in the studied solar cells have been determined by comparing the measured quantum efficiency spectra with the calculation results. This approach allowed determining the real main parameters of the devices such as: lifetimes of charge carriers, concentration of uncompensated acceptors in the absorber, recombination velocity at the front and back surfaces, the thickness of the CdS film. (i) Recombination at the front surface of the absorber reduces the shortcircuit current density by 2.2, 1.9 and 0.2% in solar cells with the CIGS bandgap 1.04, 1.14 and 1.36 eV, respectively. (ii) Recombination in the spacecharge region causes a reduction of the shortcircuit current density by 0.7, 0.1% and 1.0% for these devices, respectively. (iii) The losses in the neutral part of the absorber and the back surface amount to 2.5, 5.0 and 2.9%, respectively. (iv) Recombination only at the back surface of solar cells cause a decrease in the shortcircuit current by no more than 0.2, 1.0 and 0.1%, respectively.
Knowing the shortcircuit current density and the dark
Acknowledgments
Author would like to thank Xavier Mathew (Instituto de Energias Renovables, UNAM, Mexico) for his valuable suggestions and support in compiling this chapter.
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