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Optimization and improvement of a front graded bandgap CuInGaSe2 solar cell
Solar Energy Materials and Solar Cells xxx (xxxx) xxx–xxx
Contents lists available at ScienceDirect
Solar Energy Materials and Solar Cells journal homepage: www.elsevier.com/locate/solmat
Optimization and improvement of a front graded bandgap CuInGaSe2 solar cell ⁎
A. Aissata,b, , H. Arbouza, J.P. Vilcotb a
Laboratory LATSI, Faculty of Technology, University Blida1, 09000 Blida, Algeria Institute of Electronic, Microelectronic and Nanotechnology (IEMN), UMR 8520,University of Lille 1Sciences and Technology, Avenue Poincaré, CS60069, 59652 Villeneuve d′Ascq, France b
A R T I C L E I N F O
A B S T R A C T
Keywords: Semiconductor Gradual bandgap CIGS Thin film Solar cell
This paper reports simulations of gradual bandgap CIGS absorber and its impact on the characteristics of a solar cell. The bandgap of the CIGS absorber varies linearly and drops from Egmax (at the junction limit) to Egmin (in the vicinity of the rear contact).We introduce an effective absorption coefficient based on this variation. We will demonstrate that this gradual profile contributes to an improvement up to 171 mV of the open circuit voltage Voc of the cell that is linked to the modification of the internal electrical field distribution within the absorber. However, a joint reduction of 1.50 mA/cm2 of short circuit current density, Jsc, is observed. Overall, the conversion efficiency increases from 19.2%, for a uniform bandgap absorber structure, to 24.9% in that case of gradual bandgap. Additionally, we investigate the impact of absorber thickness and temperature on cell characteristics.
1. Introduction The quaternary chalcopyrite semiconductor alloy CuIn1−xGaxSe2, commonly noted CIGS, where x represents the ratio Ga/Ga+In, allows thin film solar cells to achieve high efficiency without the environmental concerns of CdTe. It exhibits a direct bandgap which is tunable from 1.02eV to 1.68 eV [1–4] by adjusting x. Then, a high absorption coefficient can be achieved in a wide range of solar spectrum (400–1200 µm) [5,6]. The current record efficiency CIGS solar cell exceeds 21% [6–8] and is obtained for a bandgap energy of 1.15 eV for a material with x = 0.3. While the highest efficiency is theoretically expected to be obtained for a material bandgap of 1.4 eV (x = 0.7) which better matches the absorption of the solar spectrum, the experimental efficiency decreases when increasing the bandgap above 1.2 eV due to material fabrication issues. Improving the efficiency is then achieved using a bandgap grading within the absorber material. It consists on a spatial distribution of the x parameter [9]. This beneficial aspect of bandgap grading appeared first as a side effect of the three stage co-evaporation process and it was then used for optimizing cells performances [10–12]. Several profiles of gradual bandgap structures have been proposed and simulated. What we will hereby call "front grading" represents the gradual increase in Ga concentration from back contact toward the junction interface. It contributes to widen the material bandgap at the front contact allowing the increase of Voc. So,
⁎
"back grading" would have consisted in the gradual decrease of the bandgap toward the back contact, then enhancing carrier collection and reducing recombination rate at the metallurgical contact. Double grading is the combination of those two approaches and is also characterized by the minimum bandgap location within the absorber material depth [10,13,14]. In this work, we focus on the front grading approach. It increases the value of the conduction band level near the CdS/CIGS junction leading to lower recombination level in the space charge region and to increase the open circuit voltage Voc [15]. This study aims to use a simple model of such a gradual bandgap absorber in which the spatial distribution of material absorption that is linked to the variation of the bandgap is converted into a constant effective absorption coefficient all over the absorber depth. The linear gradual profile is then optimized to improve the cell performances. Finally, the behavior of such a gradual absorber structure under temperature fluctuations is investigated on Voc and efficiency values. 2. Theoretical model Optical absorption provides information about the band structure and the bandgap energy of semiconductor materials. The absorption coefficient of a uniform bandgap crystalline semiconductor layer in the high absorption region may be described by the model of Tauc et al.
Corresponding author at: Laboratory LATSI, Faculty of Technology, University Blida1, 09000 Blida, Algeria. E-mail address: [email protected] (A. Aissat).
http://dx.doi.org/10.1016/j.solmat.2017.09.017 Received 30 March 2017; Received in revised form 29 August 2017; Accepted 10 September 2017 0927-0248/ © 2017 Published by Elsevier B.V.
Please cite this article as: Aissat, A., Solar Energy Materials and Solar Cells (2017), http://dx.doi.org/10.1016/j.solmat.2017.09.017
Solar Energy Materials and Solar Cells xxx (xxxx) xxx–xxx
A. Aissat et al.
[16,17] given below.
0hν < Eg ⎧ α= A ⎨ (hν − Eg (x ))mhν > Eg ⎩ hν
α eff =
0
⎨ ⎪ ⎩
α 3 min
(
for
hv − Egmin Egmax − Egmin
)
αmin
for
J0 = J0min (
∆Vg =
3Egmax − Egmin
3Egmax − Egmin 2
−
ξln 2VT
(7)
2VT ) ∆Vg
(8)
∆Eg q
(9)
Where J0 min is the dark current for a material with uniform bandgap energy Egmin. The open circuit voltage Voc is expressed as [24]:
0 < hv < Egmin
for Egmin < hν <
ξln 1+( 2V )2 T
with VT the thermal potential. The dark saturation current density of a variable bandgap material can be approximated by [9]:
(1)
where A is a constant that depends upon the effective masses of both electrons and holes in the semiconductor, ν is the frequency of the incident radiation and m an index depending on the type of optical transitions caused by absorbed photons, m = 1/2 for direct transitions. Fathipour et al. [18] shows that the absorption coefficient, αeff, of a gradual bandgap material can be described the same way as for a uniform bandgap material using the following formulation:
⎧ ⎪2
ln
Lneff =
2
< hv
VOC =
(2)
Where αmin is calculated by Eq. (1) for Eg = Egmin.Egmin is the lowest bandgap value (near the back contact) and Egmax the highest bandgap (near the CdS/CIGS interface). In this study we have assumed that the bandgap variation is due to the change in the conduction band level. The linear bandgap variation from Egmax to Egmin as function of position along the CIGS absorber depth is given by the following formula [18]:
Eg (x ) = Egmax − βx
Jph nkT ln ( +1) q J0
(10)
with q, the electron charge and n the diode ideality factor. The total illumination current density in the case of the gradual bandgap is written as [19]:
Jph =
∫λ
λmax
min
Np (1−R)[1−exp(−α eff d )] d (hv )
(11)
Where Np is the photon density of the incident light at the absorber surface and R the reflection coefficient.
(3) 3. Results and discussion
β=
(Egmax − Egmin ) d
ΔEg = d
(4)
The open circuit voltage Voc, the photo-generated current density Jph, the fill factor FF and the efficiency of cells using gradual and uniform bandgap absorber material have been calculated and compared (all other parameters being identical). The maximum bandgap energy Egmax near the front interface as been varied from 1.15 to 1.6 eV. The minimum bandgap energy Egmin at the back contact was chosen to 1.15 eV. This value corresponds to that used for the cells exhibiting the highest efficiency (uniform bandgap). Fig. 2 shows the effect of Egmax on Jph. The most important point that can be observed is that the photo-generated current density calculated using the effective absorption value (Eq. (2)) in case of a gradual bandgap is higher than for the one obtained for the uniform bandgap case. In addition, the slope of the decrease of photo-current density is smaller in the gradual bandgap case. By comparison with the case of Egmax = 1.2 eV, a photocurrent loss (at Egmax around 1.6 eV) of 1.3 mA/cm2 and 8.06 mA/cm2 is obtained for the gradual and uniform bandgap absorber cases, respectively. This decrease in photocurrent density is linked to the lower probability of photo-generated electrons to be collected due to the electrical field distribution and the increase of the recombination rate at the back contact.
Where d is the thickness of the CIGS absorber layer. The bandgap energy profile is illustrated in the Fig. 1. We used the Varshni relation to describe the temperature dependence of the bandgap energy [20]:
Eg (T ) = Eg (0) −
αT 2 β+T
(5)
Where Eg(0) is the bandgap value at T = 0 K, α and β are constants [21,22]. As compared to the uniform bandgap case, the bandgap variation ΔEg (Eq. (4)) within the absorber modifies the electrical field distribution. It contributes to improve Voc and the collection of generated electron-hole pairs as well as to reduce the bulk recombination. This electrical field modification can be expressed as [23].
ξ=
d∆Eg (6)
dx The electron diffusion length is [9]:
Fig. 2. Variation of photogenerated current density Jph as function of bandgap energy for d = 2 µm.
Fig. 1. Front bandgap energy profile of the CIGS absorber layer.
2
Solar Energy Materials and Solar Cells xxx (xxxx) xxx–xxx
A. Aissat et al.
Fig. 3. Variation of open circuit voltage Voc and efficiency η as function of maximum bandgap energy Egmax.
Fig. 4. Variation of courant density Jsc and fill factor as function of maximum bandgap energy Egmax.
Fig. 3 shows the evolution of open circuit voltage, Voc, and efficiency η, as function of Egmax for an absorber thickness of 3 µm. Voc increases jointly with Egmax, from 0.67 V for Egmax = 1.2 eV to 0.76 for Egmax = 1.6 eV. This can be explained by the fact that the most important part of recombination occurs in the space charge region. When the corresponding bandgap is increased, the barrier height increases and contributes to reduce the recombination processes leading to an increase of Voc. An increase of the efficiency is observed as well from 22.8% for 1.2 eV to 24.7% for 1.4 eV. The efficiency quite saturates close to25% for higher values of Egmax. An optimal value can then be set around 1.5 eV. Fig. 4 shows the variations of the short circuit current density, JSC, and of the fill factor, FF, as function of Egmax for an absorber thickness d = 2 µm. For a bandgap variation from 1.15 to 1.6 eV, the short circuit current density decreases by 1.6 mA/cm2. On the other hand, the fill factor increases by 1.6%. The thickness of the CIGS absorber is an important parameter since, obviously, it will influence the performances of the cell but will also impact the absorber deposition time and its related cost. Fig. 5 shows how CIGS absorber thickness influences Jph, Voc, and η for different values of Egmax. The value of all those parameters quickly saturates with absorber thickness increase due to the diminution of the electrical field within. Slight improvement is obtained for thicknesses higher than 2 µm and their use has to be balanced with material consumption and, in fine, cell cost. Fig. 6 shows the J(V) characteristic for different maximal bandgap energies of gradual bandgap CIGS absorber. As seen on Fig. 3 and 4, the increase of Egmax induces an increase in the open circuit voltage Voc and a decrease of Jsc. When the bandgap energy increases from 1.15 to 1.6 eV, the open circuit voltage increases from 0.54 to 0.76 V, i.e. we obtain an increase of ΔVoc = 0.22 V.These results were compared to those of [25]. The results are reasonably close with slight
Fig. 5. (a) Jph, as CIGS thickness increase, (b) Voc as CIGS thickness increase, (c) efficiency as CIGS thickness increase.
Fig. 6. Variation of J(V) characteristic in accordance as function of the polarization voltage for different maximal bandgap.
differences:0.035 V for Voc and 1.9 mA/cm2 for Jsc. Fig. 7 shows the Pmax(V) for different values of Egmax. When Egmax varies from 1.15 to 1.6 eV, we note that maximum power density increases from 11.8 to 17.5 mW/cm2. There is a relative increase of 32.5%. The electrical field modification versus an uniform bandgap structure is evaluated from Eq. (6) and is around ζ = 1.5× 103 V/cm. The carrier diffusion length is 3
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It is rather difficult to support this theoretical approach by experimental data since (i) front grading is usually jointly included with back grading in devices and their separate effect is then difficult to discern, (ii) bandgap energy is rather difficult to be directly measured on devices and it is commonly assessed by Ga/(Ga+In)or S/(S+Se) ratio measurement within the absorber depth, (iii) Measured cell parameters not only depend on absorber composition. So, to be effective, the comparison shall be made on devices that are identical in every other respect. Under those significant restrictions, some experimental data are consistent with our theoretical results. In [26], the use of an higher Egmax value leads to an increase in Voc(but double grading as well as different front grading profiles are used and Egmax values are outside the range of values that is hereby considered). In [27], it is clear that such a bandgap grading increases the quantum efficiency of the cell (but a particular device structure with backside illumination is used). In [28], the use of a front graded bandgap allows a higher value of Voc as well as its smaller temperature dependence to be obtained (but bandgap grading is assumed to be parabolic rather than linear and temperature behavior has been observed below room temperature).
Fig. 7. Variation of power characteristic P(V) in accordance as function of the polarization voltage for different maximal bandgap.
4. Conclusion In this work, we reported the modeling results about a linear gradual bandgap profile of the absorber layer of a CIGS cell (bandgap grading is high bandgap near the front surface and low bandgap near the backside electrode). The light absorption was modeled using an equivalent absorbing coefficient that is constant all over the absorber depth. The front band gap Egmax at the hetero-junction interface and the thickness of the absorber were varied. Their effects on the induced electrical field modification and on the carrier diffusion length were illustrated via the external characteristics of the cell, i.e. Voc, Jsc and η. The effect of operating temperature on cell characteristics was also investigated. It was shown that the use of such a gradual bandgap structure enhances the open circuit voltage Voc but reduces the short circuit current density. It has been particularly shown that a gradual bandgap energy from 1.5 to 1.15 eV using an absorber thickness of 2 µm allows to improve the overall efficiency of the cell by almost 3% absolute (improvement of 0.172 V in Voc and decrease of Jsc by 1.30 mA/cm2). The electrical field modification versus a uniform bandgap structure led to expand the drift length of 4.5 times. Considering these optimized parameters, an efficiency of 25% has been calculated.
Fig. 8. Variation of the open circuit voltage as function of temperature for d = 2 µm.
References
Fig. 9. Variation of efficiency as function of temperature T of two structures single and graded bandgap for d = 2 µm.
[1] B. Reinhold, M. Schmid, D. Greiner, M. Schüle, D. Kieven, A. Ennaoui, M. Ch. LuxSteiner, Monolithically interconnected lamellar Cu(In,Ga)Se2micro solar cells under full white light concentration, Prog. Photovolt. Res. Appl. 23 (2015) 1929–1939. [2] M. Gloeckler, J.R. Sites, Band-gap grading in Cu(In,Ga)Se2 solar cells, J. Phys. Chem. Solids 66 (2005) 1891–1894. [3] M. Kemell, M. Ritala, M. Leskelä, Thin film deposition methods for CuInSe2 solar cells, Crit. Rev. Solid State Mater. Sci. 30 (2005) 1–31. [4] O. Lundberg, M. Edoff, L. Stolt, The effect of Ga-grading in CIGS thin film solar cells, Thin Solid Films 480–481 (2005) 520–525. [5] S. Ouedraogo, R. Sam, F. Ouedraogo, M.B. Kebre, J.M. Ndjaka, F. Zougmore, Optimization of Copper Indium Gallium Di-Selenide (CIGS) based solar cells by back grading, J. Ovonic Res. 9 (4) (2013) 95–103. [6] N. Bednar, N. Severino, N. Adamovic, Optical simulation of light management in CIGS thin- film solar cells using finite element method, Appl. Sci. 5 (2015) 1735–1744. [7] Y. Hirai, Y. Kurokawa, A. Yamada, Numerical study of Cu(In,Ga)Se2 solar cell performance toward 23% conversion efficiency, Jpn. J. Appl. Phys. 53 (2014) 012301–012306. [8] S. Lee, E. Lee, T. Yeon Kim, J. Sik Cho, Y. JooEo, J. Ho Yun, A. Cho, Effect of annealing treatment on CdS/CIGS thin film solar cells depending on different CdS deposition temperatures, Sol. Energy Mater. Sol. Cells 141 (2015) 299–308. [9] A. Morales-Acevedo, Analytical model for the photocurrent of solar cells based on
then 4.5 times higher that increase notably the collection of electrons at the hetero-junction. Finally, temperature effects on the performance of gradual bandgap CIGS solar cell have been modeled. Fig. 8 illustrates the temperature effect on the open circuit voltage Voc for the two types of bandgap, gradual and uniform. When the temperature varies from 300 to 400 K, Voc decreases by 0.20 V for the uniform bandgap case whereas it decreases by 0.16 V for the gradual bandgap case. Fig. 9 shows the corresponding variation of efficiency as function of the temperature. When the temperature is varied from 300 to 450 K, the efficiency in the case of uniform bandgap decreases by 8.5% whereas it decreases by 7.7% in case of gradual bandgap. For these two parameters, Voc and η, the influence of operating temperature is quite the same but a slightly lower decrease slope is observed for the gradual bandgap material. 4
Solar Energy Materials and Solar Cells xxx (xxxx) xxx–xxx
A. Aissat et al.
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Physica 34 (1) (1967) 149–154. [21] A. Meeder, A. Jäger-Waldau, V. Tezlevan, E. Arushanov, T. Schedel-Niedrigand, M.Ch. Lux-Steiner, Temperature dependence of the exciton gap in monocrystalline CuGaSe2, J. Phys.: Condens. Matter 15 (2003) 6219–6227. [22] M. Troviano, K. Taretto, Urbach energy In CIGS extracted from quantum efficiency analysis of high performance CIGS solar cells, in: Proceedings of the 24th European Photovoltaic Solar Energy Conference, 21-25 September, Hamburg, Germany, 2009, 2933–2937. [23] A. Luqman Sufer, A. Khalid Abdullah, Computer Simulation of the effect of band gap grading of the Cigs absorber layer on the performance of Cds/CIGS thin film solar cell, Al-Rafida Eng. 20 (3) (2012) 44–55. [24] N.J. Carter, C.J. Hages, J.E. Moore, S.M. McLeod, C.K. Miskin, C. Joglekar, M.S. Lundstrom, R. Agrawal, Analysis of Temperature-dependent Current-voltage Characteristics for CIGSSe and CZTSSe Thin Film Solar Cells from Nanocrystal Inks, IEEE, 2013, pp. 3062–3065. [25] T. Dullweber, G. Hanna, U. Rau, H.W. Schock, A new approach to high-efficiency solar cells by band gap grading in Cu(In,Ga)Se2 chalcopyrite semiconductors, Sol. Energy Mater. Sol. Cells 67 (2001) 145–150. [26] R. Knecht, M.S. Hammer, J. Parisi, I. Riedel, Impact of varied sulfur incorporation on the device performance of sequentially processed Cu(In,Ga)(Se,Se,Se,S)2 thin film solar cells, Phys. Status Solidi A 210 (7) (2013) 1392–1399. [27] J. Mattheis, P.J. Rostan, U. Rau, J.H. Werner, Carrier collection in Cu(In,Ga)Se2 solar cells with graded band gaps and transparent ZnO:Al back contacts, Sol. Energy Mater. Sol. Cells 91 (2007) 689–695. [28] A. Chirilӑ, S. Buecheler, F. Pianezzi, P. Bloesch, C. Gretener, A.R. Uhl, C. Fella, L. Kranz, J. Perrenoud, S. Seyrling, R. Verma, S. Nishiwaki, Y.E. Romanyuk, G. Bilger, A.N. Tiwari, Highly efficient Cu(In,Ga)Se2 solar cells grown on flexible polymer films, Nat. Mater. 10 (2011) 857–861.
5
Contents lists available at ScienceDirect
Solar Energy Materials and Solar Cells journal homepage: www.elsevier.com/locate/solmat
Optimization and improvement of a front graded bandgap CuInGaSe2 solar cell ⁎
A. Aissata,b, , H. Arbouza, J.P. Vilcotb a
Laboratory LATSI, Faculty of Technology, University Blida1, 09000 Blida, Algeria Institute of Electronic, Microelectronic and Nanotechnology (IEMN), UMR 8520,University of Lille 1Sciences and Technology, Avenue Poincaré, CS60069, 59652 Villeneuve d′Ascq, France b
A R T I C L E I N F O
A B S T R A C T
Keywords: Semiconductor Gradual bandgap CIGS Thin film Solar cell
This paper reports simulations of gradual bandgap CIGS absorber and its impact on the characteristics of a solar cell. The bandgap of the CIGS absorber varies linearly and drops from Egmax (at the junction limit) to Egmin (in the vicinity of the rear contact).We introduce an effective absorption coefficient based on this variation. We will demonstrate that this gradual profile contributes to an improvement up to 171 mV of the open circuit voltage Voc of the cell that is linked to the modification of the internal electrical field distribution within the absorber. However, a joint reduction of 1.50 mA/cm2 of short circuit current density, Jsc, is observed. Overall, the conversion efficiency increases from 19.2%, for a uniform bandgap absorber structure, to 24.9% in that case of gradual bandgap. Additionally, we investigate the impact of absorber thickness and temperature on cell characteristics.
1. Introduction The quaternary chalcopyrite semiconductor alloy CuIn1−xGaxSe2, commonly noted CIGS, where x represents the ratio Ga/Ga+In, allows thin film solar cells to achieve high efficiency without the environmental concerns of CdTe. It exhibits a direct bandgap which is tunable from 1.02eV to 1.68 eV [1–4] by adjusting x. Then, a high absorption coefficient can be achieved in a wide range of solar spectrum (400–1200 µm) [5,6]. The current record efficiency CIGS solar cell exceeds 21% [6–8] and is obtained for a bandgap energy of 1.15 eV for a material with x = 0.3. While the highest efficiency is theoretically expected to be obtained for a material bandgap of 1.4 eV (x = 0.7) which better matches the absorption of the solar spectrum, the experimental efficiency decreases when increasing the bandgap above 1.2 eV due to material fabrication issues. Improving the efficiency is then achieved using a bandgap grading within the absorber material. It consists on a spatial distribution of the x parameter [9]. This beneficial aspect of bandgap grading appeared first as a side effect of the three stage co-evaporation process and it was then used for optimizing cells performances [10–12]. Several profiles of gradual bandgap structures have been proposed and simulated. What we will hereby call "front grading" represents the gradual increase in Ga concentration from back contact toward the junction interface. It contributes to widen the material bandgap at the front contact allowing the increase of Voc. So,
⁎
"back grading" would have consisted in the gradual decrease of the bandgap toward the back contact, then enhancing carrier collection and reducing recombination rate at the metallurgical contact. Double grading is the combination of those two approaches and is also characterized by the minimum bandgap location within the absorber material depth [10,13,14]. In this work, we focus on the front grading approach. It increases the value of the conduction band level near the CdS/CIGS junction leading to lower recombination level in the space charge region and to increase the open circuit voltage Voc [15]. This study aims to use a simple model of such a gradual bandgap absorber in which the spatial distribution of material absorption that is linked to the variation of the bandgap is converted into a constant effective absorption coefficient all over the absorber depth. The linear gradual profile is then optimized to improve the cell performances. Finally, the behavior of such a gradual absorber structure under temperature fluctuations is investigated on Voc and efficiency values. 2. Theoretical model Optical absorption provides information about the band structure and the bandgap energy of semiconductor materials. The absorption coefficient of a uniform bandgap crystalline semiconductor layer in the high absorption region may be described by the model of Tauc et al.
Corresponding author at: Laboratory LATSI, Faculty of Technology, University Blida1, 09000 Blida, Algeria. E-mail address: [email protected] (A. Aissat).
http://dx.doi.org/10.1016/j.solmat.2017.09.017 Received 30 March 2017; Received in revised form 29 August 2017; Accepted 10 September 2017 0927-0248/ © 2017 Published by Elsevier B.V.
Please cite this article as: Aissat, A., Solar Energy Materials and Solar Cells (2017), http://dx.doi.org/10.1016/j.solmat.2017.09.017
Solar Energy Materials and Solar Cells xxx (xxxx) xxx–xxx
A. Aissat et al.
[16,17] given below.
0hν < Eg ⎧ α= A ⎨ (hν − Eg (x ))mhν > Eg ⎩ hν
α eff =
0
⎨ ⎪ ⎩
α 3 min
(
for
hv − Egmin Egmax − Egmin
)
αmin
for
J0 = J0min (
∆Vg =
3Egmax − Egmin
3Egmax − Egmin 2
−
ξln 2VT
(7)
2VT ) ∆Vg
(8)
∆Eg q
(9)
Where J0 min is the dark current for a material with uniform bandgap energy Egmin. The open circuit voltage Voc is expressed as [24]:
0 < hv < Egmin
for Egmin < hν <
ξln 1+( 2V )2 T
with VT the thermal potential. The dark saturation current density of a variable bandgap material can be approximated by [9]:
(1)
where A is a constant that depends upon the effective masses of both electrons and holes in the semiconductor, ν is the frequency of the incident radiation and m an index depending on the type of optical transitions caused by absorbed photons, m = 1/2 for direct transitions. Fathipour et al. [18] shows that the absorption coefficient, αeff, of a gradual bandgap material can be described the same way as for a uniform bandgap material using the following formulation:
⎧ ⎪2
ln
Lneff =
2
< hv
VOC =
(2)
Where αmin is calculated by Eq. (1) for Eg = Egmin.Egmin is the lowest bandgap value (near the back contact) and Egmax the highest bandgap (near the CdS/CIGS interface). In this study we have assumed that the bandgap variation is due to the change in the conduction band level. The linear bandgap variation from Egmax to Egmin as function of position along the CIGS absorber depth is given by the following formula [18]:
Eg (x ) = Egmax − βx
Jph nkT ln ( +1) q J0
(10)
with q, the electron charge and n the diode ideality factor. The total illumination current density in the case of the gradual bandgap is written as [19]:
Jph =
∫λ
λmax
min
Np (1−R)[1−exp(−α eff d )] d (hv )
(11)
Where Np is the photon density of the incident light at the absorber surface and R the reflection coefficient.
(3) 3. Results and discussion
β=
(Egmax − Egmin ) d
ΔEg = d
(4)
The open circuit voltage Voc, the photo-generated current density Jph, the fill factor FF and the efficiency of cells using gradual and uniform bandgap absorber material have been calculated and compared (all other parameters being identical). The maximum bandgap energy Egmax near the front interface as been varied from 1.15 to 1.6 eV. The minimum bandgap energy Egmin at the back contact was chosen to 1.15 eV. This value corresponds to that used for the cells exhibiting the highest efficiency (uniform bandgap). Fig. 2 shows the effect of Egmax on Jph. The most important point that can be observed is that the photo-generated current density calculated using the effective absorption value (Eq. (2)) in case of a gradual bandgap is higher than for the one obtained for the uniform bandgap case. In addition, the slope of the decrease of photo-current density is smaller in the gradual bandgap case. By comparison with the case of Egmax = 1.2 eV, a photocurrent loss (at Egmax around 1.6 eV) of 1.3 mA/cm2 and 8.06 mA/cm2 is obtained for the gradual and uniform bandgap absorber cases, respectively. This decrease in photocurrent density is linked to the lower probability of photo-generated electrons to be collected due to the electrical field distribution and the increase of the recombination rate at the back contact.
Where d is the thickness of the CIGS absorber layer. The bandgap energy profile is illustrated in the Fig. 1. We used the Varshni relation to describe the temperature dependence of the bandgap energy [20]:
Eg (T ) = Eg (0) −
αT 2 β+T
(5)
Where Eg(0) is the bandgap value at T = 0 K, α and β are constants [21,22]. As compared to the uniform bandgap case, the bandgap variation ΔEg (Eq. (4)) within the absorber modifies the electrical field distribution. It contributes to improve Voc and the collection of generated electron-hole pairs as well as to reduce the bulk recombination. This electrical field modification can be expressed as [23].
ξ=
d∆Eg (6)
dx The electron diffusion length is [9]:
Fig. 2. Variation of photogenerated current density Jph as function of bandgap energy for d = 2 µm.
Fig. 1. Front bandgap energy profile of the CIGS absorber layer.
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Fig. 3. Variation of open circuit voltage Voc and efficiency η as function of maximum bandgap energy Egmax.
Fig. 4. Variation of courant density Jsc and fill factor as function of maximum bandgap energy Egmax.
Fig. 3 shows the evolution of open circuit voltage, Voc, and efficiency η, as function of Egmax for an absorber thickness of 3 µm. Voc increases jointly with Egmax, from 0.67 V for Egmax = 1.2 eV to 0.76 for Egmax = 1.6 eV. This can be explained by the fact that the most important part of recombination occurs in the space charge region. When the corresponding bandgap is increased, the barrier height increases and contributes to reduce the recombination processes leading to an increase of Voc. An increase of the efficiency is observed as well from 22.8% for 1.2 eV to 24.7% for 1.4 eV. The efficiency quite saturates close to25% for higher values of Egmax. An optimal value can then be set around 1.5 eV. Fig. 4 shows the variations of the short circuit current density, JSC, and of the fill factor, FF, as function of Egmax for an absorber thickness d = 2 µm. For a bandgap variation from 1.15 to 1.6 eV, the short circuit current density decreases by 1.6 mA/cm2. On the other hand, the fill factor increases by 1.6%. The thickness of the CIGS absorber is an important parameter since, obviously, it will influence the performances of the cell but will also impact the absorber deposition time and its related cost. Fig. 5 shows how CIGS absorber thickness influences Jph, Voc, and η for different values of Egmax. The value of all those parameters quickly saturates with absorber thickness increase due to the diminution of the electrical field within. Slight improvement is obtained for thicknesses higher than 2 µm and their use has to be balanced with material consumption and, in fine, cell cost. Fig. 6 shows the J(V) characteristic for different maximal bandgap energies of gradual bandgap CIGS absorber. As seen on Fig. 3 and 4, the increase of Egmax induces an increase in the open circuit voltage Voc and a decrease of Jsc. When the bandgap energy increases from 1.15 to 1.6 eV, the open circuit voltage increases from 0.54 to 0.76 V, i.e. we obtain an increase of ΔVoc = 0.22 V.These results were compared to those of [25]. The results are reasonably close with slight
Fig. 5. (a) Jph, as CIGS thickness increase, (b) Voc as CIGS thickness increase, (c) efficiency as CIGS thickness increase.
Fig. 6. Variation of J(V) characteristic in accordance as function of the polarization voltage for different maximal bandgap.
differences:0.035 V for Voc and 1.9 mA/cm2 for Jsc. Fig. 7 shows the Pmax(V) for different values of Egmax. When Egmax varies from 1.15 to 1.6 eV, we note that maximum power density increases from 11.8 to 17.5 mW/cm2. There is a relative increase of 32.5%. The electrical field modification versus an uniform bandgap structure is evaluated from Eq. (6) and is around ζ = 1.5× 103 V/cm. The carrier diffusion length is 3
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It is rather difficult to support this theoretical approach by experimental data since (i) front grading is usually jointly included with back grading in devices and their separate effect is then difficult to discern, (ii) bandgap energy is rather difficult to be directly measured on devices and it is commonly assessed by Ga/(Ga+In)or S/(S+Se) ratio measurement within the absorber depth, (iii) Measured cell parameters not only depend on absorber composition. So, to be effective, the comparison shall be made on devices that are identical in every other respect. Under those significant restrictions, some experimental data are consistent with our theoretical results. In [26], the use of an higher Egmax value leads to an increase in Voc(but double grading as well as different front grading profiles are used and Egmax values are outside the range of values that is hereby considered). In [27], it is clear that such a bandgap grading increases the quantum efficiency of the cell (but a particular device structure with backside illumination is used). In [28], the use of a front graded bandgap allows a higher value of Voc as well as its smaller temperature dependence to be obtained (but bandgap grading is assumed to be parabolic rather than linear and temperature behavior has been observed below room temperature).
Fig. 7. Variation of power characteristic P(V) in accordance as function of the polarization voltage for different maximal bandgap.
4. Conclusion In this work, we reported the modeling results about a linear gradual bandgap profile of the absorber layer of a CIGS cell (bandgap grading is high bandgap near the front surface and low bandgap near the backside electrode). The light absorption was modeled using an equivalent absorbing coefficient that is constant all over the absorber depth. The front band gap Egmax at the hetero-junction interface and the thickness of the absorber were varied. Their effects on the induced electrical field modification and on the carrier diffusion length were illustrated via the external characteristics of the cell, i.e. Voc, Jsc and η. The effect of operating temperature on cell characteristics was also investigated. It was shown that the use of such a gradual bandgap structure enhances the open circuit voltage Voc but reduces the short circuit current density. It has been particularly shown that a gradual bandgap energy from 1.5 to 1.15 eV using an absorber thickness of 2 µm allows to improve the overall efficiency of the cell by almost 3% absolute (improvement of 0.172 V in Voc and decrease of Jsc by 1.30 mA/cm2). The electrical field modification versus a uniform bandgap structure led to expand the drift length of 4.5 times. Considering these optimized parameters, an efficiency of 25% has been calculated.
Fig. 8. Variation of the open circuit voltage as function of temperature for d = 2 µm.
References
Fig. 9. Variation of efficiency as function of temperature T of two structures single and graded bandgap for d = 2 µm.
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