**2. Optical constants and related material parameters**

Three typical cases, with distinct bandgaps for the CIGS absorber *E*g=1.02–1.04 eV (*x*=0), *E*g=1.14–1.16 eV (*x* ≈ 0.3) and *E*g=1.36–1.38 eV (*x*=0.6 – 0.65) are considered for the analysis. The absorber with bandgap in the range 1.14-1.16 eV is widely utilized in the industry for the mass production of solar modules, however, material with bandgap in the range 1.36 – 1.38 eV is promising to achieve the theoretically optimal value for maximum efficiency 28–30%.

improved the cell efficiency to 20.9% [3,4]. Since the efficiency of CIGS modules lie in the 12-15% range (except for a 16.6 % world record [5]), which is about half of the theoretical limit 28-30%, there are plenty of opportunities to contribute towards the scientific and technological

The device architecture of CIGS and CdTe solar cells are alike, similar to other p-n heterojuc‐ tions. 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 p-CIGS and n-CdS. The conductivity of CIGS is determined to a large degree by intrinsic defects, while the n-CdS 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

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 SnO2: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

Based on the above reasoning, in this chapter a detailed analysis of the optical and recombi‐ nation losses in CIGS devices are presented, which are important causes of poor quantum efficiency (QE), leading to low solar-to-electric 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 photo‐ electric conversion efficiency of the device, an analysis of the current-voltage 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

Three typical cases, with distinct bandgaps for the CIGS absorber *E*g=1.02–1.04 eV (*x*=0), *E*g=1.14–1.16 eV (*x* ≈ 0.3) and *E*g=1.36–1.38 eV (*x*=0.6 – 0.65) are considered for the analysis. The absorber with bandgap in the range 1.14-1.16 eV is widely utilized in the industry for the mass

advancement of CIGS PV technology.

2 Solar Cells - New Approaches and Reviews

penetrates into the absorber.

some modifications to the CIGS devices [6,7].

cells have been achieved mainly empirically [8].

**2. Optical constants and related material parameters**

Fig. 1 shows the schematic representation of a typical CIGS solar cell architecture, where the notations corresponding to the optical constants *n*<sup>i</sup> and *κ*<sup>i</sup> and the reflection coefficients *R*ij at the interfaces used in the calculations are indicated.

Photoelectric conversion in these solar cells occurs in the CIGS absorber with a thickness of about 2 μm, while a thin n-type 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 high-resistivity i-ZnO 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 MgF2, 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 *T*(*λ*), which is determined by reflections from the interfaces air/ZnO, ZnO/ CdS and CdS/CIGS and absorption in the ZnO and CdS layers. For estimating the transmission *T*(*λ*), it is necessary to know the refractive indices *n*<sup>i</sup> and extinction coefficients *κ*<sup>i</sup> of ZnO, CdS and CIGS. According to the Fresnel equations, when the light is at near-normal incidence, the reflection coefficients (reflectances) from three interfaces *R*12, *R*23 and *R*34 (see Fig. 1) can be calculated as

$$R\_{\rm ij} = \frac{\left|{n\_{\rm i}^{\*} - n\_{\rm j}^{\*}}\right|^2}{\left|{n\_{\rm i}^{\*} + n\_{\rm j}^{\*}}\right|^2} = \frac{\left(n\_{\rm i} - n\_{\rm j}\right)^2 + \left(\kappa\_{\rm i} - \kappa\_{\rm j}\right)^2}{\left(n\_{\rm i} + n\_{\rm j}\right)^2 + \left(\kappa\_{\rm i} + \kappa\_{\rm j}\right)^2} \tag{1}$$

where *n*<sup>i</sup> <sup>∗</sup> and *n*<sup>j</sup> <sup>∗</sup> are the refractive indices of the materials, which account for light absorption containing imaginary parts and are written as *n*<sup>i</sup> <sup>∗</sup> =*n*<sup>i</sup> – *iκ*<sup>i</sup> and *n*<sup>j</sup> <sup>∗</sup> =*n*<sup>j</sup> – *iκ*<sup>j</sup> .

Fig. 2 shows the spectral dependences of *n* and *κ* for ZnO taken from [8] and [10], CdS from [11] and CIGS from [12] (in some cases the extinction coefficient was determined using the relation *κ=αλ*/4*π*, where *α* is the absorption coefficient).

It is worth to note the fact that for CIGS, the extinction coefficient in the photon energy range *hν* < *E*g (*λ* > *λ*g) has a value of 0.04-0.05, which corresponds to an absorption coefficient *α=*4*π κ*/*λ*=(4-5)×103 cm–1 [12]. With such values of *α*, a fairly high efficiency should be obtained for the solar cell, but, in fact, this is not observed. At *λ* > *λ*g=*hс*/*E*g, the quantum efficiency decreases quite rapidly with wavelength up to zero within a range about 120-150 nm above *λ*g.

This extended QE response can be explained by the presence of so-called '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, where <sup>i</sup>

Fig. 2 shows the spectral dependences of *n* and *κ* for ZnO taken from [8] and [10], CdS from [11] and

/4,

3

Radiation

**Figure 1.** Schematic representation of a typical CIGS solar cell [9]. CIGS from [12] (in some cases the extinction coefficient was determined using the relation *κ =α*where *α* is the absorption coefficient).

Figure 2. Wavelength dependences of the refractive indices (a) and extinction coefficients (b) of ZnO, CdS, CuInSe2, CuIn0.69Ga0.31Se2 and CuIn0.34Ga0.66Se2. It is worth to note the fact that for CIGS, the extinction coefficient in the photon energy range **Figure 2.** Wavelength dependences of the refractive indices (a) and extinction coefficients (b) of ZnO, CdS, CuInSe2, CuIn0.69Ga0.31Se2 and CuIn0.34Ga0.66Se2.

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., *α*(*hν*) ∝ exp[– (*E*g – *hν*)/*E*o), where *E*o is a spectral independent value. Such spectral dependence is sometime called the Urbach rule (*E*<sup>o</sup> can be proportional to *kT* at sufficiently high *T*). In this case, in order for the electron to make an interband transition and take part in the formation of the photocurrent, the electron must get the energy, which is equal to or greater than *E*g. In the case of the tail *hv* < *E*g ( > g) has a value of 0.04-0.05, which corresponds to an absorption coefficient *α =* 4 *κ*/ = (4-5)10<sup>3</sup> cm–1 [12]. With such values of *α*, a fairly high efficiency should be obtained

absorption at *hν* < *E*g this transition occurs because part of the energy, equal to *hν*, electron gets from photon, while the deficit (*E*g – *hυ*) is covered by phonons (the so-called multiphonon transitions). The probability of the multiphonon process decreases exponentially with lowering the *hν,* reproducing the spectral curve of photocurrent but with a stronger depend‐ ence on *hν* compared with the density of states and the absorption curve (in the tails of state density some of the transitions occur without phonon participation) [13]. It is important to mention that an electron excited due to the absorption of a photon with energy *hν* < *E*g takes part in the photocurrent formation just as in the case of absorption of a photon with energy *hν* ≥ *E*g.

Based on the above comments, it is valid to use the *κ*(*λ*) curves of CIGS corrected in the longwavelength region as shown in Fig. 2b by dashed lines. Anticipating the tail effect, it can be noted that the spectrum at *hν* < *E*<sup>g</sup> makes a relatively small contribution to the photocurrent in solar cells: 1.0 % (0.5 mA/cm2 ), 1.1% (0.4 mA/cm2 ) and 1.9% (0.6 mA/cm2 ) respectively for the absorber bandgaps 1.04, 1.16 and 1.38 eV.

In the range *hν* ≥ *E*g, the absorption coefficient follows the law for a direct-gap semiconductor:

$$
\alpha = \alpha\_\text{o} \text{(}\hbar \nu - \text{E}\_\text{g}\text{)}^{1/2} \text{ /} \hbar \nu \text{ .} \tag{2}
$$

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 *α* as illustrated in Fig. 3.

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., *α*(*hν*) ∝ exp[– (*E*g – *hν*)/*E*o), where *E*o is a spectral independent value. Such spectral dependence is sometime called the Urbach rule (*E*<sup>o</sup> can be proportional to *kT* at sufficiently high *T*). In this case, in order for the electron to make an interband transition and take part in the formation of the photocurrent, the electron must get the energy, which is equal to or greater than *E*g. In the case of the tail

It is worth to note the fact that for CIGS, the extinction coefficient in the photon energy range

Figure 2. Wavelength dependences of the refractive indices (a) and extinction coefficients (b) of ZnO,

**Figure 2.** Wavelength dependences of the refractive indices (a) and extinction coefficients (b) of ZnO, CdS, CuInSe2,

1000 1200 1400

ZnO:Al (*n*2, *κ*2)

Cu(In,Ga)Se2 (*n*4, *κ*4)

Air (*n*1, *κ*1)

ZnO:Al (*n*2, *κ*2) CdS (*n*3, *κ*3)

Air (*n*1, *κ*1)

Radiation

Radiation

3

*R*<sup>12</sup>

Metal grid

*R*<sup>12</sup>

Metal grid

*R*<sup>23</sup> *R*<sup>34</sup>

Metal

*R*<sup>23</sup> *R*<sup>34</sup>

Metal

*E*g= 1.16 eV

*E*g= 1 eV

/4,

CdS (*n*3, *κ*3)

High-resistive ZnO

**Figure 1.** Schematic representation of a typical CIGS solar cell [9].

200 400 600 800

(nm)

CdS, CuInSe2, CuIn0.69Ga0.31Se2 and CuIn0.34Ga0.66Se2.

ZnO

CdS

Cu(In,Ga)Se2 *E*g= 1.01 eV

*E*g= 1.38 eV *E*g=1.16 eV

where *α* is the absorption coefficient).

(a)

containing imaginary parts and are written as i

where <sup>i</sup>

*n* ()

*hv* < *E*g (

*α =* 4 *κ*/

1.5

 > 

CuIn0.69Ga0.31Se2 and CuIn0.34Ga0.66Se2.

= (4-5)10<sup>3</sup>

2.0

2.5

3.0

3.5

*<sup>n</sup>* and j

4 Solar Cells - New Approaches and Reviews

Anti-reflection coating

High-resistive ZnO

Anti-reflection coating

Cu(In,Ga)Se2 (*n*4, *κ*4)

Substrate (glass, polyimide, metal foil)

Figure 1. Schematic representation of a typical CIGS solar cell [9].

Fig. 2 shows the spectral dependences of *n* and *κ* for ZnO taken from [8] and [10], CdS from [11] and CIGS from [12] (in some cases the extinction coefficient was determined using the relation *κ =α*

()

1.0

10

(b)

0.1

10–2

10–3

10–4

g) has a value of 0.04-0.05, which corresponds to an absorption coefficient

cm–1 [12]. With such values of *α*, a fairly high efficiency should be obtained

Substrate (glass, polyimide, metal foil)

*<sup>n</sup>* <sup>=</sup> *<sup>n</sup>*i – *iκ*i and j

*n* are the refractive indices of the materials, which account for light absorption

*n* = *n*j – *iκ*j.

CdS

(nm)

ZnO

*E*g= 1.38 eV

Cu(In,Ga)Se2

200 400 600 800 1000 1200 1400

**Figure 3.** Dependence of the absorption coefficient *α* of CuIn1–xGaxSe2 on the photon energy *hν* in accordance with Eq. (2).

The intercept of the extrapolated straight line portions on the photon energy *hυ* axis corre‐ sponds to the bandgaps of the discussed materials. The estimated bandgaps are 1.02, 1.16 and 1.38 eV for CuInSe2, CuIn0.69Ga0.31Se2 and CuIn0.34Ga0.66Se2, respectively. The wavelengths corresponding to these bandgaps are indicated on the extinction coefficient data in Fig. 2b by arrows.
