**3. Optical losses caused by reflection and absorption**

The optical transmission *T*(*λ*) through the multilayer ZnO/CdS/CIGS structure shown in Fig. 1 can be written as

$$T(\mathcal{X}) = T\_{\rm gr}(1 - R\_{12}) \exp(-a\_2 d\_2)(1 - R\_{23}) \exp(-a\_3 d\_3)(1 - R\_{34}).\tag{3}$$

Here *R*12, *R*23 and *R*34 are the reflection coefficients at the interfaces air/ZnO, ZnO/CdS and CdS/ CIGS respectively, whereas the absorption in ZnO and CdS are represented by exp(–*α*2*d*2) and exp(–*α*3*d*3), where *α*2 and *α*3, *d*2 and *d*3 are the absorption coefficients and thicknesses of the ZnO and CdS layers, respectively.

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 *T*gr is included in Eq. (1) to take care of this effect. In practical modules, the grids are made very narrow and thin such that it shades only about 4–5% of the front area of the ZnO layer. The *T*gr value can be set to 0.95 without introducing much loss [8].

The effect of an antireflection coating is not considered in Eq. (3), which can significantly reduce the reflectance of the front surface *R*12. The commonly used antireflection coating for ZnO is MgF2 which has the refractive index *n*arc close to the theoretical optimal value (*n*2) 1/2, where *n*<sup>2</sup> is the refractive index of ZnO. Fig. 4 compares the refractive indices *n*arc, *n*2 and (*n*2) 1/2 in the wavelength region 300 to 1100 nm.

The reflection coefficient *R*arc of a material with an antireflection coating can be written as [14]:

$$R\_{\rm arc} = \frac{r\_{\rm f}^2 + r\_{\rm b}^2 + 2r\_{\rm f}r\_{\rm b}\cos(2\beta)}{1 + r\_{\rm f}^2r\_{\rm b}^2 + 2r\_{\rm f}r\_{\rm b}\cos(2\beta)},\tag{4}$$

where *r*<sup>f</sup> and *r*b are the Fresnel coefficients, which are the amplitude values of reflectivity from the front and back surfaces of the antireflection material:

$$r\_{\rm f} = \frac{n\_{\rm arc} - n\_{\rm f}}{n\_{\rm arc} + n\_{\rm f}} \,\tag{5}$$

**Figure 4.** Comparison of the spectral dependences of the refractive indices for ZnO (*n*2), MgF2 (*n*arc) and (*n*2) 1/2 [9]

$$
\eta\_{\rm b} = \frac{n\_2 - n\_{\rm arc}}{n\_2 + n\_{\rm arc}} \,\prime\,\tag{6}
$$

and

1/2, where *n*<sup>2</sup>

1/2 in the

(4)

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

The optical transmission *T*(*λ*) through the multilayer ZnO/CdS/CIGS structure shown in Fig.

aa

Here *R*12, *R*23 and *R*34 are the reflection coefficients at the interfaces air/ZnO, ZnO/CdS and CdS/ CIGS respectively, whereas the absorption in ZnO and CdS are represented by exp(–*α*2*d*2) and exp(–*α*3*d*3), where *α*2 and *α*3, *d*2 and *d*3 are the absorption coefficients and thicknesses of the ZnO

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 *T*gr is included in Eq. (1) to take care of this effect. In practical modules, the grids are made very narrow and thin such that it shades only about 4–5% of the front area of the ZnO

The effect of an antireflection coating is not considered in Eq. (3), which can significantly reduce the reflectance of the front surface *R*12. The commonly used antireflection coating for ZnO is

The reflection coefficient *R*arc of a material with an antireflection coating can be written as

b

b

*n n* (5)

and *r*b are the Fresnel coefficients, which are the amplitude values of reflectivity from

=- - - - - gr 12 2 2 23 3 3 34 *TTR d R d R* ( ) (1 )exp( )(1 )exp( )(1 ). (3)

**3. Optical losses caused by reflection and absorption**

layer. The *T*gr value can be set to 0.95 without introducing much loss [8].

MgF2 which has the refractive index *n*arc close to the theoretical optimal value (*n*2)

+ + <sup>=</sup> + + 2 2 f b fb

*r r rr <sup>R</sup>*

f b fb 2 cos(2 ) , 1 2 cos(2 )

*r r rr*


arc 1 , *n n*

f

*r*

arc 2 2

the front and back surfaces of the antireflection material:

is the refractive index of ZnO. Fig. 4 compares the refractive indices *n*arc, *n*2 and (*n*2)

arrows.

1 can be written as

l

6 Solar Cells - New Approaches and Reviews

and CdS layers, respectively.

wavelength region 300 to 1100 nm.

[14]:

where *r*<sup>f</sup>

$$
\beta = \frac{2\pi}{\lambda} n\_{\text{arc}} d\_{\text{arc}}.\tag{7}
$$

Fig. 5a shows a comparison of the reflectance of the bare ZnO surface (curve *1*) and that coated with a 100 nm thick MgF2 (curve *2*). A comparison of the two curves reveals a significant decrease in reflection in the 500-800 nm region due to the antireflection coating. The observed peak in reflectance at *λ* < 500 nm does not produce a significant effect in solar cell performance since the intensity of solar radiation decreases at short wavelength *λ* < 400 nm. In addition, the region below 500 nm is dominated by absorption in the CdS film and the ZnO layer. On the contrary, increase in the reflectance at *λ* > 600 nm affect the solar cell performance significantly.

So, for taking into account antireflective coating, the reflection coefficient *R*12 in Eq. (3) for the transmission should be replaced by the coefficient *R*arc, which is determined by Eq. (4):

$$T(\lambda) = T\_{\rm gr}(1 - R\_{\rm arc}) \exp(-a\_2 d\_2)(1 - R\_{23}) \exp(-a\_3 d\_3)(1 - R\_{34}).\tag{8}$$

Fig. 5b illustrates the impact of antireflective coating on the transmission property of ZnO/CdS layers in CIGS solar cells.

and

6

1 2 cos(2 )

arc 1 arc <sup>1</sup> <sup>f</sup> *<sup>n</sup> <sup>n</sup> <sup>n</sup> <sup>n</sup> <sup>r</sup>*

2 arc <sup>2</sup> arc <sup>b</sup> *<sup>n</sup> <sup>n</sup> <sup>n</sup> <sup>n</sup> <sup>r</sup>*

 

> 600 nm affect the solar cell performance significantly.

arc arc <sup>2</sup> *<sup>n</sup> <sup>d</sup>* 

Fig. 5a shows a comparison of the reflectance of the bare ZnO surface (curve *1*) and that coated with a 100 nm thick MgF2 (curve *2*). A comparison of the two curves reveals a significant decrease in reflection in the 500-800 nm region due to the antireflection coating. The observed peak in reflectance at

< 500 nm does not produce a significant effect in solar cell performance since the intensity of solar

where *r*f and *r*b are the Fresnel coefficients, which are the amplitude values of reflectivity from the

<sup>f</sup> <sup>b</sup> <sup>2</sup>

2 cos(2 ) f b

, (4)

, (5)

, (6)

. (7)

< 400 nm. In addition, the region below 500 nm is dominated

The reflection coefficient *R*arc of a material with an antireflection coating can be written as [14]:

2 b 2 f

*r r r r <sup>r</sup> <sup>r</sup> <sup>r</sup> <sup>r</sup> <sup>R</sup>* 

<sup>b</sup> <sup>2</sup>

<sup>f</sup> arc

front and back surfaces of the antireflection material:

(curve *2*). (b) The optical transmission through the ZnO/CdS layers; curve *1* corresponds to ZnO with MgF2 coating, and curve 2 in the absence of MgF2 [9]. **Figure 5.** (a) Comparison of the reflectivity of bare ZnO surface (curve *1*) and that coated with MgF2 (curve *2*). (b) The optical transmission through the ZnO/CdS layers; curve *1* corresponds to ZnO with MgF2 coating, and curve 2 in the absence of MgF2 [9].

So, for taking into account antireflective coating, the reflection coefficient *R*12 in Eq. (3) for the

Figure 5. (a) Comparison of the reflectivity of bare ZnO surface (curve *1*) and that coated with MgF2

#### **3.1. Reflection and absorptive losses** transmission should be replaced by the coefficient *R*arc, which is determined by Eq. (4):

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 *J*. The value of *J* for the spectral distribution of AM1.5 global solar radiation is calculated using the Table of International Organization for Stand‐ ardization ISO 9845-1:1992 [15]. Taking Φ as the incident spectral radiation power density and *hν* the photon energy, then the spectral density of the incident photon flux is Φ/*hν* and one can write *J* as

$$J = q \sum\_{i} T(\mathcal{A}\_{i}) \frac{\Phi\_{i}(\mathcal{A}\_{i})}{h\nu\_{i}} \Delta \mathcal{A}\_{i} \,\tag{9}$$

where *q* is the electron charge, *∆λ*<sup>i</sup> is the interval between the neighboring values of *λ*<sup>i</sup> in the ISO table.

Assuming that the solar radiation is negligible for *λ* < 300 (> 4.1 eV), the summation in Eq. (9) should be made over the spectral range from *λ*=300 nm to *λ*=*λ*g.=*hc*/*E*g. The corresponding upper limits of the wavelength *λ*g for CIGS solar cell with the bandgap of the absorber *E*g=1.02– 1.04, 1.14–1.16 and 1.36–1.38 eV are ∼ 1200, 1080 and 900 nm respectively.

Analyzing the optical losses, we assume that the QE of the solar cell *η*=1, therefore Eq. (9) does not contain *η*. If the transmission through ZnO/CdS are also taken as 100%, then the photo‐ current density *J* for the CuInSe2, CuIn0.69Ga0.31Se2 and CuIn0.34Ga0.66Se2 solar cells would be equal to *J*o=47.1, 42,0 and 33.7 mA/cm2 , respectively. However, for real situations where there are reflection and absorption losses even with antireflection coating the *J* value becomes equal to 38.4, 33.9 and 27.5 mA/cm2 respectively and if there is no antireflection coating the corre‐ sponding values are 35.0, 30.8 and 24.8 mA/cm2 . It follows that the antireflection coating increases the photocurrent density *J* by 3.4, 3.1 and 2.7 mA/cm2 , respectively for the CIGS absorbers discussed above.

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 *J*o, i.e., to the above values 47.1, 42,0 and 33.7 mA/cm2 for the solar cells with the absorber bandgap 1.02–1.04, 1.14–1.16 and 1.36–1.38 eV, respectively. The calculations show that the antireflection coating increases the photocurrent density *J* by 7.1, 7.4 and 8.0%, for these solar cells, respectively.

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 MgF2 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 *2* depends on the thickness of antireflection coating *d*arc.

**3.1. Reflection and absorptive losses**

200 400 600 800

*2*

(nm)

opposite side.

and

0

absence of MgF2 [9].

5

10

*R* (%)

15

20

8 Solar Cells - New Approaches and Reviews

write *J* as

ISO table.

From a practical point of view, it is important to assess the various types of losses due to

Figure 5. (a) Comparison of the reflectivity of bare ZnO surface (curve *1*) and that coated with MgF2 (curve *2*). (b) The optical transmission through the ZnO/CdS layers; curve *1* corresponds to ZnO with MgF2 coating, and curve 2 in the absence of MgF2 [9].

**Figure 5.** (a) Comparison of the reflectivity of bare ZnO surface (curve *1*) and that coated with MgF2 (curve *2*). (b) The optical transmission through the ZnO/CdS layers; curve *1* corresponds to ZnO with MgF2 coating, and curve 2 in the

So, for taking into account antireflective coating, the reflection coefficient *R*12 in Eq. (3) for the

transmission should be replaced by the coefficient *R*arc, which is determined by Eq. (4):

6

1 2 cos(2 )

arc 1 arc <sup>1</sup> <sup>f</sup> *<sup>n</sup> <sup>n</sup> <sup>n</sup> <sup>n</sup> <sup>r</sup>*

2 arc <sup>2</sup> arc <sup>b</sup> *<sup>n</sup> <sup>n</sup> <sup>n</sup> <sup>n</sup> <sup>r</sup>*

 

> 600 nm affect the solar cell performance significantly.

*1*

arc arc <sup>2</sup> *<sup>n</sup> <sup>d</sup>* 

Fig. 5a shows a comparison of the reflectance of the bare ZnO surface (curve *1*) and that coated with a 100 nm thick MgF2 (curve *2*). A comparison of the two curves reveals a significant decrease in reflection in the 500-800 nm region due to the antireflection coating. The observed peak in reflectance at

< 500 nm does not produce a significant effect in solar cell performance since the intensity of solar

by absorption in the CdS film and the ZnO layer. On the contrary, increase in the reflectance at

(a) (b)

*T* ()

0

0.2

0.4

0.6

0.8

1.0

where *r*f and *r*b are the Fresnel coefficients, which are the amplitude values of reflectivity from the

<sup>f</sup> <sup>b</sup> <sup>2</sup>

2 cos(2 ) f b

, (4)

, (5)

, (6)

. (7)

< 400 nm. In addition, the region below 500 nm is dominated

*1*

1200 

*2*

200 400 600 800

(nm)

The reflection coefficient *R*arc of a material with an antireflection coating can be written as [14]:

2 b 2 f

*r r r r <sup>r</sup> <sup>r</sup> <sup>r</sup> <sup>r</sup> <sup>R</sup>* 

<sup>b</sup> <sup>2</sup>

<sup>f</sup> arc

front and back surfaces of the antireflection material:

radiation decreases at short wavelength

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

An estimate of the decrease in solar cells performance due to the optical losses can be obtained by calculating the photocurrent density *J*. The value of *J* for the spectral distribution of AM1.5 global solar radiation is calculated using the Table of International Organization for Stand‐ ardization ISO 9845-1:1992 [15]. Taking Φ as the incident spectral radiation power density and *hν* the photon energy, then the spectral density of the incident photon flux is Φ/*hν* and one can

> l

n

Assuming that the solar radiation is negligible for *λ* < 300 (> 4.1 eV), the summation in Eq. (9) should be made over the spectral range from *λ*=300 nm to *λ*=*λ*g.=*hc*/*E*g. The corresponding upper limits of the wavelength *λ*g for CIGS solar cell with the bandgap of the absorber *E*g=1.02–

i i i ( ) () ,

 l

*JqT <sup>h</sup>* (9)

in the

l

*i*

1.04, 1.14–1.16 and 1.36–1.38 eV are ∼ 1200, 1080 and 900 nm respectively.

<sup>F</sup> <sup>=</sup> å <sup>D</sup> i i

where *q* is the electron charge, *∆λ*<sup>i</sup> is the interval between the neighboring values of *λ*<sup>i</sup>

reflections from the interfaces and absorption in the ZnO and CdS layers.

1000 1100 1200

It is interesting to see how the photocurrent density *J* (which takes into account the spectral distribution of solar radiation) depends on the thickness of the layer *d*arc. The calculated dependences of decrease in Δ*J/J*o on *d*arc are shown in Fig. 6 for three samples of the studied solar cells. As seen, the losses are minimal when the thickness of the MgF2 film is in the range of 105–115 nm that is close to the thickness commonly used of MgF2 film but the losses become significant when the MgF2 thickness is below or above the 105-115 nm range. Note that the reflection losses reach the range 9.3–12.4% in the absence of antireflection coating while with coating it is only 1.4–1.9%.

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 MgF2 layer in CuInSe2, CuIn0.69Ga0.31Se2 and CuIn0.34Ga0.66Se2 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 CuIn0.33Ga0.67Se2 in the air and in optical contacts with each other. As seen, at the 700 nm region the reflection coefficients at the interfaces (air/MgF2)/ZnO, ZnO/CdS and CdS/CIGS are 10–17 times smaller than those at the interfaces air/ZnO, air/CdS and air/CIGS.

20

15

26

27

*J*

(mA/cm2

)

28

29

10<sup>14</sup> 10<sup>15</sup> 10<sup>17</sup> 10<sup>16</sup>

0 1 2 3 4 5

<sup>n</sup> = 1 ns

*d* (m)

)

<sup>n</sup> = 5 ns

<sup>n</sup> = 20 ns

*N*<sup>a</sup> – *N*<sup>d</sup> (cm–3

20

<sup>n</sup> = 0.5 ns

(a)

2 ns

10 ns 5 ns

20 ns <sup>n</sup> = 1000 ns

*J*

(mA/cm2

)

25

30

22

30

Figure 6. **Figure 6.** Relation between percentage photocurrent loss and thickness of antireflection coating applied on the ZnO surface for CuInGaSe2, CuIn0.69Ga0.31Se2 and CuIn0.34Ga0.66Se2 solar cells.

15

105 cm/s

The sharp increase in reflectance at *λ* < 500 nm for the (air/MgF2)/ZnO interface does not produce a significant effect, which is discussed above. 28 *S*<sup>f</sup> = 0 104 cm/s (a) *S*<sup>f</sup> = 107 cm/s (b)

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 CuInSe2, 2.2 and 5.6% for CuIn0.69Ga0.31Se2 and 1.9 and 7.7% for CuIn0.34Ga0.66Se2 solar cell. The difference in losses for the three types of samples is due to the difference in their bandgaps. 24 26 *S*<sup>f</sup> = 107 cm/s *J* (mA/cm2 ) 106 cm/s 105 cm/s 5 10 *J*/*J* (%) 106 cm/s

)

(b)

10<sup>14</sup> 10<sup>15</sup> 10<sup>17</sup> 10<sup>16</sup>

<sup>n</sup> = 20 ns

> <sup>n</sup> = 10 ns

> > <sup>n</sup> = 5 ns

> > > <sup>n</sup> = 2 ns <sup>n</sup> = 1 ns

0 1 2 3 4 5

*d* (m)

)

(b)

*N*<sup>a</sup> – *N*<sup>d</sup> (cm–3

**Figure 7.** Reflectivity spectra of (MgF2)ZnO, CdS and CuIn0.34Ga0.66Se2 films in contact with air and other materials [9]. 10 ns

0

0

0.5

*J/J* (%)

Figure 16.

1.0

1.5

20 ns

Figure 15.

1000 1200

It seems that reflection losses cannot be reduced by virtue of their nature whereas the absorp‐ tion 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 *d*CdS=40 nm, the loss is about 1-3% when the ZnO layer thickness is in the range of 100-500 nm, and when the layer is thinner (100-200 nm) the loss reduces to ∼ 1%. The loss due to absorption in CdS layer (Fig. 8b) is higher, 4-5%, even at its lowest thickness of 20-30 nm. It seems that by thinning the CdS and ZnO layers the absorption losses may be limited to 2–3%. It seems that reflection losses can not 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 *d*CdS = 40 nm, the loss is about 1-3% when the ZnO layer thickness is in the range of 100-500 nm , and when the layer is thinner (100-200 nm) the loss reduces to 1%. The loss due to absorption in CdS layer (Fig. 8b) is higher, 4-5%, even at its lowest thickness of 20-30 nm. It seems that by thinning the CdS and ZnO layers the absorption losses may be limited to 2–3%.

air/MgF2 /ZnO

ZnO/air

CdS/air

CIGS/air

200 400 600 800

CdS/CIGS ZnO/CdS

0

10

20

*R* (%) 30

40

9

Figure 8. Dependences of the losses caused by absorption in the CdS and ZnO layers on their thicknesses [9]. **Figure 8.** Dependences of the losses caused by absorption in the CdS and ZnO layers on their thicknesses [9].

The sharp increase in reflectance at *λ* < 500 nm for the (air/MgF2)/ZnO interface does not

(a)

Figure 6.

**Figure 6.** Relation between percentage photocurrent loss and thickness of antireflection coating applied on the ZnO

60 80 100 120 140 *d*arc (nm)

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

CuInSe2

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 CuInSe2, 2.2 and 5.6% for CuIn0.69Ga0.31Se2 and 1.9 and 7.7% for CuIn0.34Ga0.66Se2 solar cell. The difference in losses for the

*J*/*J* (%)

200 400 600 800

CdS/CIGS ZnO/CdS

(a)

l(nm)

0

0

0.5

*J/J* (%)

Figure 16.

1.0

1.5

20

*J* /*J*(%)

**Figure 7.** Reflectivity spectra of (MgF2)ZnO, CdS and CuIn0.34Ga0.66Se2 films in contact with air and other materials [9].

Figure 15.

air/MgF2 /ZnO

Figure 14.

ZnO/air

40

1000 1200

2 ns

10 ns 5 ns

20 ns

<sup>n</sup> = 0.5 ns

10<sup>14</sup> 10<sup>15</sup> 10<sup>17</sup> 10<sup>16</sup>

<sup>n</sup> = 20 ns

> <sup>n</sup> = 10 ns

> > <sup>n</sup> = 5 ns

> > > <sup>n</sup> = 2 ns <sup>n</sup> = 1 ns

0 1 2 3 4 5

*d* (m)

)

(b)

*N*<sup>a</sup> – *N*<sup>d</sup> (cm–3

10<sup>14</sup> 10<sup>15</sup> 10<sup>16</sup> 10<sup>17</sup> 10<sup>18</sup>

*N*<sup>a</sup> – *N*<sup>d</sup> (cm–3

)

(b)

(b)

160

CdS/air

60

CIGS/air

0

5

10

15

*S*<sup>f</sup> = 107 cm/s

106 cm/s

105 cm/s

104 cm/s

produce a significant effect, which is discussed above.

surface for CuInGaSe2, CuIn0.69Ga0.31Se2 and CuIn0.34Ga0.66Se2 solar cells.

*S*<sup>f</sup> = 0

0

1

2

*Δ J / Jo (%)* 

3

4

10 Solar Cells - New Approaches and Reviews

0

10<sup>14</sup> 10<sup>15</sup> 10<sup>17</sup> 10<sup>16</sup>

0 1 2 3 4 5

<sup>n</sup> = 1 ns

*d* (m)

)

<sup>n</sup> = 5 ns

<sup>n</sup> = 20 ns

*N*<sup>a</sup> – *N*<sup>d</sup> (cm–3

10

20

*R* (%)

20

15

26

27

*J*

(mA/cm2

)

28

29

20

<sup>n</sup> = 0.5 ns

(a)

2 ns

10 ns 5 ns

20 ns <sup>n</sup> = 1000 ns

*J*

(mA/cm2

)

25

30

22

24

*J*

(mA/cm2

)

26

28

30

30

10<sup>14</sup> 10<sup>15</sup> 10<sup>16</sup> 10<sup>17</sup> 10<sup>18</sup>

*N*<sup>a</sup> – *N*<sup>d</sup> (cm–3

40

*S*<sup>f</sup> = 107 cm/s

106 cm/s

105 cm/s 104 cm/s

three types of samples is due to the difference in their bandgaps.

)

The calculated values of optical losses along with the corresponding decrease in the photo‐ current *J* given in brackets are summarized in Table 1. Note that the calculated data of optical losses are largely in agreement with the results reported in literature, but there are exceptions also. For example, according to our calculations, the reflection losses in CuIn0.69Ga0.31Se2 solar cell (without shading from grid) is equal to 4.0 mA/cm2 and in reference [8] it amount to 3.8 mA/cm2 , indicating similarity. However, the absorption losses in the CdS film for CuIn0.69Ga0.31Se2 and CuIn0.34Ga0.66Se2 solar cells in our calculations are equal to 2.6–2.9 A/cm2 and only 0.8 mA/cm2 in [8]. The losses due to insufficient absorptivity of the CIGS absorber also differ considerably being equal to < 0.1 and 1.9 mA/cm2 , respectively.



**Table 1.** Optical and the corresponding photocurrent losses in CIGS solar cells
