**5.1. Experimental results and discussion**

The *J–V* characteristics of CIGS solar cells having bandgaps of the absorber *E*g=1.04, 1.14 and 1.36 eV under standard AM1.5 illumination taken from [8] are shown in Fig. 18a. The voltage dependences of the dark current derived from the difference between the short-circuit current density *J*sc and the current density under illumination *J*IL at each voltage are shown in Fig. 18b by solid (closed) circles, squares and triangles. At *V* < 0.2 V, the values of *J*IL and *J*sc are very close to each other, therefore the dark current cannot be determined with a proper accuracy. 28 the dark current derived from the difference between the short-circuit current density *J*sc and the current density under illumination *J*IL at each voltage are shown in Fig. 18b by solid (closed) circles, squares and triangles. At *V* < 0.1 V, the values of *J*IL and *J*sc are very close to each other, therefore the dark current cannot be determined with a proper accuracy.

Dark currents (solid circles, squares, triangles) and currents obtained by subtracting the current through the shunt from the dark current in the absorber bandgaps 1.14 and 1.36 eV (open circles, squares). **Figure 18.** a) Voltage dependences of the current density in CIGS solar cells under illumination [8], (b) Dark currents (solid circles, squares, triangles) and currents obtained by subtracting the current through the shunt from the dark cur‐ rent in the absorber bandgaps 1.14 and 1.36 eV (open circles, squares).

Figure 18. (a) Voltage dependences of the current density in CIGS solar cells under illumination [8], (b)

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 *J* exp(*qV*/2*kT*) (dashed lines) in the range of almost four order of magnitude that confirms the recombination mechanism of charge transport suggested in [8, 34]. However, for the absorbers with the bandgap of 1.14 and 1.36 eV the *J–V* curves have a complicated form. As seen, the dependences *J* exp(*qV*/2*kT*) are observed only at *V* > 0.5 and 0.7 V for the samples with *E*g = 1.14 (solid squares) and 1.36 eV (solid circles), respectively. At lower voltage the *J–V* relationship deviates from such dependence for some reason. Note that, despite the significant difference of currents at higher voltages, the dark currents in these two cells at low voltages 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 *J* ∝ exp(*qV*/2*kT*) (dashed lines) in the range of almost four order of magnitude that confirms the recombination mechanism of charge transport suggested in [8, 34]. However, for the absorbers with the bandgap of 1.14 and 1.36 eV the *J– V* curves have a complicated form. As seen, the dependences *J* ∝ exp(*qV*/2*kT*) are observed only at *V* > 0.5 and 0.7 V for the samples with *E*g=1.14 (solid squares) and 1.36 eV (solid circles),

practically coincide and the *J–V* relationship can be interpolated by the expression *J* exp(*qV*/*AkT*)

Useful information about the electrical properties of the diode can be obtained from the analysis of the voltage dependence of the differential resistance *R*dif = *dV*/*dI* [22]. These dependences for three samples are shown in Fig. 19. It is known that the differential resistance of a semiconductor diode decreases exponentially with increasing forward voltage in a wide range including the lowest voltage as shown in Fig. 19 by dashed oblique straight lines. Such behavior of the differential resistance is observed only for CuInSe2 diode (*E*g = 1.04 eV). For other two diodes, when a low forward voltage is applied, the dependence of *R*dif on *V* deviates downward from the exponent and

realistic to assume that at low voltages, the current through the shunt rather than through the diode is dominant and only when bias is above 0.4 and 0.6 V respectively for devices with CIGS bandgaps *E*g = 1.14 and 1.36 eV, the diode currents are higher than that through the shunts (for CIS

. It is quite

an invariance of *R*dif takes place at the level of 0.3-0.4 for diode area of 0.4 cm<sup>2</sup>

with enormous large value of the ideality factor *A* = 6.7.

cell with bandgap *E*g = 1.04 the shunt is absent).

respectively. At lower voltage the *J–V* relationship deviates from such dependence for some reason. Note that, despite the significant difference of currents at higher voltages, the dark currents in these two cells at low voltages practically coincide and the *J–V* relationship can be interpolated by the expression *J* ∝ exp(*qV*/*AkT*) with enormous large value of the ideality factor *A*=6.7.

developed for the linearly graded silicon p-n junction in [19] and modified and adapted to a thin-film CdS/CdTe heterostructure taking into account peculiarities of the distribution of the electric potential and the concentrations of free electrons and holes in the SCR [29]. This is valid for CIGS solar cells taking into account the effect of the shunts at low forward voltages and the voltage drop across the series resistance at high forward currents. It is also shown that knowing the short–circuit current density (which can be obtained from spectra of the quantum efficiency and solar radiation), it is possible to calculate the *J–V* curves under illumination and find the open–circuit voltage, the fill factor and eventually the energy conversion efficiency. The electric losses caused by the presence of the shunts and series resistances of the bulk part

The *J–V* characteristics of CIGS solar cells having bandgaps of the absorber *E*g=1.04, 1.14 and 1.36 eV under standard AM1.5 illumination taken from [8] are shown in Fig. 18a. The voltage dependences of the dark current derived from the difference between the short-circuit current density *J*sc and the current density under illumination *J*IL at each voltage are shown in Fig. 18b by solid (closed) circles, squares and triangles. At *V* < 0.2 V, the values of *J*IL and *J*sc are very close to each other, therefore the dark current cannot be determined with a proper accuracy.

the dark current derived from the difference between the short-circuit current density *J*sc and the current density under illumination *J*IL at each voltage are shown in Fig. 18b by solid (closed) circles, squares and triangles. At *V* < 0.1 V, the values of *J*IL and *J*sc are very close to each other, therefore the

*V* (V)

10–4

10–2

*J* (mA/cm2

Figure 18. (a) Voltage dependences of the current density in CIGS solar cells under illumination [8], (b) Dark currents (solid circles, squares, triangles) and currents obtained by subtracting the current through the shunt from the dark current in the absorber bandgaps 1.14 and 1.36 eV (open circles, squares).

**Figure 18.** a) Voltage dependences of the current density in CIGS solar cells under illumination [8], (b) Dark currents (solid circles, squares, triangles) and currents obtained by subtracting the current through the shunt from the dark cur‐

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 *J* exp(*qV*/2*kT*) (dashed lines) in the range of almost four order of magnitude that confirms the recombination mechanism of charge transport suggested in [8, 34]. However, for the absorbers with the bandgap of 1.14 and 1.36 eV the *J–V* curves have a complicated form. As seen, the dependences *J* exp(*qV*/2*kT*) are observed only at *V* > 0.5 and 0.7 V for the samples with *E*g = 1.14 (solid squares) and 1.36 eV (solid circles), respectively. At lower voltage the *J–V* relationship deviates from such dependence for some reason. Note that, despite the significant difference of currents at higher voltages, the dark currents in these two cells at low voltages practically coincide and the *J–V* relationship can be interpolated by the expression *J* exp(*qV*/*AkT*)

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 *J* ∝ exp(*qV*/2*kT*) (dashed lines) in the range of almost four order of magnitude that confirms the recombination mechanism of charge transport suggested in [8, 34]. However, for the absorbers with the bandgap of 1.14 and 1.36 eV the *J– V* curves have a complicated form. As seen, the dependences *J* ∝ exp(*qV*/2*kT*) are observed only at *V* > 0.5 and 0.7 V for the samples with *E*g=1.14 (solid squares) and 1.36 eV (solid circles),

Useful information about the electrical properties of the diode can be obtained from the analysis of the voltage dependence of the differential resistance *R*dif = *dV*/*dI* [22]. These dependences for three samples are shown in Fig. 19. It is known that the differential resistance of a semiconductor diode decreases exponentially with increasing forward voltage in a wide range including the lowest voltage as shown in Fig. 19 by dashed oblique straight lines. Such behavior of the differential resistance is observed only for CuInSe2 diode (*E*g = 1.04 eV). For other two diodes, when a low forward voltage is applied, the dependence of *R*dif on *V* deviates downward from the exponent and

realistic to assume that at low voltages, the current through the shunt rather than through the diode is dominant and only when bias is above 0.4 and 0.6 V respectively for devices with CIGS bandgaps *E*g = 1.14 and 1.36 eV, the diode currents are higher than that through the shunts (for CIS

an invariance of *R*dif takes place at the level of 0.3-0.4 for diode area of 0.4 cm<sup>2</sup>

)

1.0

102

(b)

0 0.2 0.4 0.6 0.8

*E*<sup>g</sup> = 1.04 eV

*V* (V)

*J* exp(*qV*/2*kT*) *J*exp(*qV*/6.7*kT*)

*E*<sup>g</sup> = 1.36 eV

*E*g= 1.14 eV

. It is quite

28

of the CIGS absorber are also determined.

32 Solar Cells - New Approaches and Reviews

**5.1. Experimental results and discussion**

0

*J*IL (mA/cm2

)

10

20

30

(a)

–30

–20

–10

dark current cannot be determined with a proper accuracy.

*E*<sup>g</sup> = 1.36 eV

*E*g=1.14 eV

*E*g= 1.04 eV

0.2 0.4 0.6 0.8

with enormous large value of the ideality factor *A* = 6.7.

rent in the absorber bandgaps 1.14 and 1.36 eV (open circles, squares).

cell with bandgap *E*g = 1.04 the shunt is absent).

Useful information about the electrical properties of the diode can be obtained from the analysis of the voltage dependence of the differential resistance *R*dif=*dV*/*dI* [22]. These depend‐ ences for three samples are shown in Fig. 19. It is known that the differential resistance of a semiconductor diode decreases exponentially with increasing forward voltage in a wide range including the lowest voltage as shown in Fig. 19 by dashed oblique straight lines. Such behavior of the differential resistance is observed only for CuInSe2 diode (*E*g=1.04 eV). For other two diodes, when a low forward voltage is applied, the dependence of *R*dif on *V* deviates downward from the exponent and an invariance of *R*dif takes place at the level of 0.3-0.4 Ω for diode area of 0.4 cm2 . It is quite realistic to assume that at low voltages, the current through the shunt rather than through the diode is dominant and only when bias is above 0.4 and 0.6 V respec‐ tively for devices with CIGS bandgaps *E*g=1.14 and 1.36 eV, the diode currents are higher than that through the shunts (for CIS cell with bandgap *E*g=1.04 the shunt is absent).

**Figure 19.** Voltage dependences of the differential resistance of the studied CIGS solar cells.

One can assume that shunting in the studied solar cells is caused by pin-holes 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 i-ZnO layer is applied which is capped by a thicker Al-doped ZnO layer. It is believed that the i-ZnO 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 pro‐ duced by i-ZnO sputtering leads also to the occurrence of shunts. However, in the case of i-ZnO, the value of the shunt resistance is much larger compared to ZnO:Al due to high resistivity of i-ZnO and the shunting reveals itself only at relatively low voltages.

The voltage-independent differential resistance at *V* < 0.2 and 0.4 V for the two samples (Fig. 19) means that the shunt is a *linear* element of the electric circuit. Therefore, the effect of the shunt can be taken into account by subtracting the current through the shunt *V*/*R*sh from the measured current *J*. The results of such manipulations for cells with the absorber bandgaps 1.14 and 1.36 eV are shown in Fig. 18b by open squares and circles, respectively, whereas the *J–V* curves without accounting for the shunt and series resistances are shown by solid circles and squares.

As seen in Fig. 18b, *qualitative* changes in the forward *J–V* characteristic of cells with the absorber bandgaps 1.14 and 1.36 eV occur after subtracting the current through the shunt resistance. In the range *V* < 0.45 V for the first cell (*E*g=1.14 eV) and *V* < 0.65 V for the second cell (*E*g=1.36 eV), the forward current rapidly decreases with decreasing the voltage by three and five orders of magnitude, respectively, continuing the same trend of the curves *J*(*V*) as at the higher voltages. It is important to note that after subtracting the current through the shunt the current in the cells with the absorber bandgaps 1.14 and 1.36 eV as well as the measured current in a cell with the bandgap 1.04 eV (CuInSe2) without shunting are proportional to exp(*qV/AkT*) at *A*≈2.

The obtained results can create the impression that the occurrence of shunt is due to the introduction of Ga into the CuInSe2 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 post-growth processing [36].

Soda-lime glass is a common substrate material used in CIGS solar cells due to its low cost and good thermal expansion match to CuInSe2. In addition, the soda-lime 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 (*x* ≤ 0.3) resulting in an absorber bandgap value of 1.1-1.2 eV. However as suggested by the theory, for optimum conversion efficiency it is desirable to open the bandgap up to *Eg*=1.4-1.5 eV.

It was shown in [36] that the growth and post-growth 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 non-optimum 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 *T* < 550°C (sample #1) and at elevated temperature 600–650°C (sample #2) are shown by solid and open circles, respectively. The *J–V* curves for recombination current *J*=*J*o[exp(*qV*/2*kT*) – 1] are also shown in Fig. 20a by solid lines *2* and *6*. optimum 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 650C 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 *T* < 550C (sample #1) and at elevated temperature 600–650C (sample #2) are shown by solid and open circles, respectively. The *J–V* curves for recombination current *J* = *J*o[exp(*qV*/2*kT*) – 1] are also

For this purpose, borosilicate glasses have been used in CIGS research even though it has non-

30

solar cells with wide bandgap can be avoided by modifying the fabrication technology, in particular

Soda-lime glass is a common substrate material used in CIGS solar cells due to its low cost and good thermal expansion match to CuInSe2. In addition, the soda-lime glass supplies sodium to the growing CIGS layer by diffusion through the Mo back contact, leading to enhanced grain growth with a higher

It is known that the CIGS deposition requires a substrate temperature at least 350C and efficient cells have been fabricated at the maximum temperature 550C, which the glass substrate can withstand without softening. In these temperature ranges, CIGS solar cells are typically made with low Ga content (*x* ≤ 0.3) resulting in an absorber bandgap value of 1.1-1.2 eV. However as suggested by the

by increasing the temperature of CIGS deposition and post-growth processing [36].

degree of preferred orientation.

shown in Fig. 20a by solid lines *2* and *6*.

duced by i-ZnO sputtering leads also to the occurrence of shunts. However, in the case of i-ZnO, the value of the shunt resistance is much larger compared to ZnO:Al due to high

The voltage-independent differential resistance at *V* < 0.2 and 0.4 V for the two samples (Fig. 19) means that the shunt is a *linear* element of the electric circuit. Therefore, the effect of the shunt can be taken into account by subtracting the current through the shunt *V*/*R*sh from the measured current *J*. The results of such manipulations for cells with the absorber bandgaps 1.14 and 1.36 eV are shown in Fig. 18b by open squares and circles, respectively, whereas the *J–V* curves without accounting for the shunt and series resistances are shown by solid circles

As seen in Fig. 18b, *qualitative* changes in the forward *J–V* characteristic of cells with the absorber bandgaps 1.14 and 1.36 eV occur after subtracting the current through the shunt resistance. In the range *V* < 0.45 V for the first cell (*E*g=1.14 eV) and *V* < 0.65 V for the second cell (*E*g=1.36 eV), the forward current rapidly decreases with decreasing the voltage by three and five orders of magnitude, respectively, continuing the same trend of the curves *J*(*V*) as at the higher voltages. It is important to note that after subtracting the current through the shunt the current in the cells with the absorber bandgaps 1.14 and 1.36 eV as well as the measured current in a cell with the bandgap 1.04 eV (CuInSe2) without shunting are proportional to

The obtained results can create the impression that the occurrence of shunt is due to the introduction of Ga into the CuInSe2 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

Soda-lime glass is a common substrate material used in CIGS solar cells due to its low cost and good thermal expansion match to CuInSe2. In addition, the soda-lime glass supplies sodium to the growing CIGS layer by diffusion through the Mo back contact, leading to enhanced grain

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 (*x* ≤ 0.3) resulting in an absorber bandgap value of 1.1-1.2 eV. However as suggested by the theory, for optimum conversion efficiency it is desirable to

It was shown in [36] that the growth and post-growth 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 non-optimum 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.

resistivity of i-ZnO and the shunting reveals itself only at relatively low voltages.

and squares.

34 Solar Cells - New Approaches and Reviews

exp(*qV/AkT*) at *A*≈2.

post-growth processing [36].

open the bandgap up to *Eg*=1.4-1.5 eV.

growth with a higher degree of preferred orientation.

Figure 20. Voltage dependence of dark current density [36] (a) and differential resistance (b) of CIGS solar cells with absorber bandgap ~ 1.5 eV fabricated at standard temperature 550C (sample #1) and elevated temperature 650C (sample #2). **Figure 20.** Voltage dependence of dark current density [36] (a) and differential resistance (b) of CIGS solar cells with absorber bandgap ~ 1.5 eV fabricated at standard temperature ≤ 550°C (sample #1) and elevated temperature 650°C (sample #2).

As can be seen in Fig. 20a, for solar cells fabricated using standard technology, the *J–V* relationship at *V* < 0.4 V deviates from the expression *J* [exp(*qV*/2*kT*) – 1] (curve #*1*) that is caused by the effect of shunting. This observation is confirmed by the dependence of the differential resistance *R*dif of this As can be seen in Fig. 20a, for solar cells fabricated using standard technology, the *J–V* relationship at *V* < 0.4 V deviates from the expression *J* ∝ [exp(*qV*/2*kT*) – 1] (curve #*1*) that is caused by the effect of shunting. This observation is confirmed by the dependence of the differential resistance *R*dif of this sample shown in Fig. 20b. As expected, the *R*dif(*V*) relationship deviates from the exponential decrease at low voltages in the range *V* < 0.4 V. However, the *R*dif value does not become constant when the voltage approaches zero as it is observed in samples with the absorber bandgaps 1.14 and 1.36 eV in Fig. 19. Therefore, the shape of a measured curve cannot be accurately calculated by adding the current through the shunt *V*/*R*sh to the recombination current. An approximate description of the measured curve is possible by taking the average value of the shunt resistance *R*sh=1.3×105 Ω. (line *3* in Fig. 20a).

The *J–V* relationship shown in Fig. 20a for sample #1 (solid circle) also deviates downward from the exponential increase at *V* > 0.6 V due to voltage drop across the series resistance *R*<sup>s</sup> of the neutral part of the absorber layer. If this voltage drop is subtracted from *V*, a good agreement of theory with experiment can be achieved (curve *3* at *V* > 0.6 V).

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 *J*=*J*o[exp(*qV*/2*kT*) – 1] over the whole voltage range. Thus, by growth and post-growth processing of the film at higher temperatures, CIGS solar cells with wide bandgap for the absorber (up to 1.5 eV) can be fabricated without shunting at low voltages and the voltage drop across the series resistance at high currents.
