- Email: [email protected]
High efficiency quadruple junction solar cells
Superlattices and Microstructures 91 (2016) 22e30
Contents lists available at ScienceDirect
Superlattices and Microstructures journal homepage: www.elsevier.com/locate/superlattices
High efficiency quadruple junction solar cells R. Bestam a, A. Aissat a, b, *, J.P. Vilcot c a
LATSI Laboratory, Faculty of the Technology, University of Blida 1, BP270, 09.000, Algeria LATSICOM Laboratory, Faculty of Science, University of Blida 1, BP270, 09.000, Algeria Institut d’Electronique, de Micro electronique et de Nanotechnologie, UMR CNRS 8520, Universit e des Sciences et Technologies de Lille1, Avenue Poincar e, CS 60069, 59652 Villeneuve d’Ascq, France
b c
a r t i c l e i n f o
a b s t r a c t
Article history: Received 14 November 2015 Accepted 24 December 2015 Available online 29 December 2015
This work focuses on the modeling and optimization of a structure based on InGaP/InGaAs/ InGaAsN/Ge for photovoltaic. In this study we took into consideration the concentration effect of alloys x (In) and y (N) on the strain, the bandgap, the absorption and structure efficiency. It has been shown that the concentration of indium varies the strain and the bandgap. These two parameters change considerably the yield. Also it optimized the effect of alloys on the total absorption of the structure. For a concentration of indium x ¼ 0.40 and y ¼ 0.03 we had a absorption coefficient which is equal to 2 106 cm1. We have found 50% efficiency for the multi-junction structure based on In0.55Ga0.45P/In0.40Ga0.60As/ In0.30Ga0.70As0.97N0.03/Ge. To achieve a reliable high efficiency multi-junction structure, we just need to optimize the concentrations of different alloys. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Semiconductor New materials Nanostructures Solar cell Optoelectronics
1. Introduction The gallium nitride and its ternary and quaternary alloys in the system Ga (B, In,Al) N have become in recent years the headlights semiconductors in optoelectronics field. Indeed, these materials suffer from lack of agreement mesh substrates for epitaxial growth. They have also a high defect density difficult to achieve p-type doping particularly, the gallium nitride and indium takes a considerable place in photovoltaic field since a decade [1]. These alloys have a bandgap that covers the visible spectrum. They are candidates for the realization of multi-junction solar cells with very high efficiency. The solar cell technology based on triple junction structure GaInP/GaInAs/Ge is performed at 30% conversion efficiency under lighting AM0 [2]. Metamorphic solar junction cells have been studied for terrestrial solar applications and in space. The modeling of components indicates that performance improvements are possible with the splitting of the spectrum still optimized by the use of the disagreement of mesh of semi-conductors IIIeV. However, the terrestrial spectrum conversion efficiency equal to around 40% was considered at the high solar concentration using the triple junction cell [3]. The simple solar cell can absorb a finite interval of wavelength in solar spectrum and thus produce less efficiently. In contrary, the solar cells multi-junctions absorb the maximum of the solar spectrum. Each junction absorbs a portion of the solar spectrum [4].
* Corresponding author. LATSI Laboratory, Faculty of the Technology, University of Blida 1, BP270, 09.000, Algeria. E-mail address: [email protected] (J.P. Vilcot). http://dx.doi.org/10.1016/j.spmi.2015.12.038 0749-6036/© 2015 Elsevier Ltd. All rights reserved.
R. Bestam et al. / Superlattices and Microstructures 91 (2016) 22e30
23
Multi-junction photovoltaic systems of high-efficiency are formed of IIIeV semiconductor alloys with a high optical sensitivity. The perfect combination of the band gap energy increases the absorption coefficient of photons. It creates more electronehole pairs and thus increases the efficiency of the solar cell [4]. Researchers have introduced a new multi-junction photovoltaic cell constituted by GaP/InGaAs/InGaSb structures [4]. Then they compared with simple multi-junction solar cells which already in existence. Several researchers have made the design of solar cells with agreement and disagreement meshes. They tried to reach a theoretical yield of 60% and even more [5,6]. On the other hand, the multi-junction solar cells have evolved to extract energy from a larger energy band of the solar spectrum [7,8]. The multi-junction solar cells can be grouped into two types depends on spectrum splitting up techniques and also the orientation of the intermediate junctions. The two types are, known as vertical multi-junction (VMJ) and as lateral multijunction (LMJ) [9,10]. Generally, VMJ solar cells are more expensive compared to single junction cells because of costly manufacturing steps due to different materials layers [9]. However, the strain and the faults of interface significantly affect the manufacturing efficiency and performance of VMJ solar cells [11]. For IIIeV multi-junctions of high quality the recombination is widely radiative. This effect may have a significant effect on the short-circuit voltage (VOC), and photocurrent densities (JCS) of junctions [12e14]. Therefore, there is a significant work in the literature on experimental extraction and modeling luminescent coupling parameters derived from (JCS) [12e14]. Also our modeling purpose is to study different multi-junctions structures of cells based on semi-conductors with significant importance to exceed conversion efficiency of 50%.It is shown that the use of several layers of different materials mounted in vertical increase the performance and reliability of the solar cell. 2. Theoretical model IIIeV semi-conductors are known for having a very important optical transition and procedures for manufacturing and growth are currently sufficiently well normalized. The properties of the quaternary alloys ABCD are found by the interpolation of the properties of binary Alloys AB or properties of ternary alloys ABC. The properties of the ternary alloys A1exBxC are given by the following relationship:
PABC ðxÞ ¼ x:EBC þ ð1 xÞPAC þ x:ð1 xÞCABC
(1)
CABC is the parameter of Bowing and P represents the parameter of materials. For the calculation of the mesh parameter of the alloys, CABC is zero [15]. From the formulas of empirical interpolation for the ternary alloys A1exBxC, the properties of the quaternary alloys AxB1exCy D1ey are interpreted by:
Pðx; yÞ ¼
x:ð1 xÞ½y:TABC ðxÞ þ ð1 yÞ:TABD ðxÞ þ yð1 yÞ½x:TACD ðyÞ þ ð1 xÞ:TBCD ðyÞ x:ð1 xÞ þ yð1 yÞ
(2)
The approach of eq (2) tends to give better agreement with experiment than an alternative treatment of Moon et al. [16] which is known to overestimate the quaternary bowing [17,18] Krijn [19] gives polynomial expansions of Q(x,y) derived from eq (2) for the energy gaps and spineorbit splitting of several IIIeV quaternaries. The quaternary may then be represented as a combination of two lattice-matched constituents, one of which must be a ternary while the other may be either a binary or a ternary. The semiconductor materials in the hetero-structures do not necessarily have the same mesh parameters a. These internal deformations have important consequences for the electronic and optoelectronic properties, and can be exploited to achieve high performance structures. Some semiconductors are not necessarily in agreement to mesh with the available substrates. A solution is to make them grow without agreement of mesh. In this case, the dislocations will be formed and possibly the high layer may be used as 'pseudo-substrate'. This procedure of growth, allows in principle to have an improved flexibility in the technology of semiconductors [20]. To perform the growth of a semiconductor (1) for parameter of mesh a1 on a semiconductor (2) with a mesh parameter a2. The strain between the two materials is defined as:
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R. Bestam et al. / Superlattices and Microstructures 91 (2016) 22e30
ε¼
a2 a1 a1
(3)
The interface layer will be under strain and the system produces an elastic energy. This energy increases with the increase of the thickness of the layer distorted. For a small disagreement of mesh ε ¼ 1%, the initial growth of the upper layer occurs with a small deformation of mesh parameters. When the thickness of the layer increases, dislocations will eventually be generated in this layer [21]. The dislocations are beginning to appear from a critical thickness LC. 3. Absorption The absorption of photon energy larger than the band gap will excite an electron from the valence band to the conduction band. The electron will leave an empty state in the valence band, called a hole, with a charge þ q and an effective mass mh. The electron has a charge -q and an effective weight me. There are other absorption mechanisms such as the absorption assisted by phonons, absorption by free carriers, or absorption by impurities. The absorption step is followed by a relaxation step wherein the electron returns to the valence band by electronehole recombination. Relaxation can be of several types, a radiative recombination, a non-radiative recombination as Auger recombination. For a direct gap semiconductor, excited by a photon of energy close to that of the bandgap, the absorption band and the radiative recombination are the two dominant phenomena. The coulomb interaction between the electronehole pair formed a state called exciton [22,23]. The energy of the exciton resonance is weaker than unbound electronehole pair and excitonic states are located just below the bandgap energy. For solar cells, the absorption coefficient is a very important parameter since it will determine the amount of photons absorbed by the material and thus the amount of carriers that can be produced. The absorption through a layer of semiconductor of thickness L is given by the following equation:
Itrn ðlÞ ¼ Iinc ðlÞ:eaðlÞ:L
(4)
with Itrn Transmitted intensity of light Iinc Incident intensity of light a(l) Absorption coefficient l Wavelength For the absorption coefficient we used the model proposed by Wu et al. [23,24].
aðEÞ ¼ a0
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E ESt g E
(5)
a0 Adjustment parameter ESt g strained bandgap energy E light energy 4. Electrical characteristic Under illumination, the incident photons will generate electronehole pairs whose behavior will differ depending on the absorption area: In the space charge zone (SCZ) generated by the pen junction, the electronehole pairs created are separated by the electric field. The electrons are accelerated and then injected into the n region (emitter) and holes in the p region (base). A generation of photocurrent is created. In base and emitter areas, the generated minority carriers (holes and electrons in the transmitter in the base) will diffuse to the (SCZ). If they reach the latter before recombining, they are injected into the n region for electrons and the p-zone for holes and become majority. A photo-current distribution is created. Both contributions are added to give the resulting photocurrent from minority carriers Iph. It is proportional to the light intensity [25]. The current delivered to a load by an illuminated photovoltaic cell is then written:
IðVÞ ¼ Iph IobsðVÞ With Iobs is the dark current. The photon-current (Iph) is given by the following expression:
(6)
R. Bestam et al. / Superlattices and Microstructures 91 (2016) 22e30
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ZlMax Jph ¼ q
FðlÞ:EQEðlÞdl
(7)
lMin
q: elementary charge 4.1. F (l): solar spectrum l: wavelength EQE(l) the external quantum efficiency is given by:
EQE ¼
Jemetter ðlÞ þ Jsc ðlÞ þ Jbase ðlÞ q:FðlÞ
(8)
Jemetter (l): photon-current of the transmitter. J sc(l): photon-current of the depletion region. 4.2. Jbase (l): base photon current
!
Jemetter ðlÞ ¼
qFð1 RÞa:Lp ½ a2 Lp2 1
Sp Lp Dp
x x S L eaxj ð Dp pp cosh Lpj þ sinh Lpj aLp eaxj xj xj Sp Lp þ sinh cosh Dp Lp Lp
þ aLp
Jsc ðlÞ ¼ qFð1 RÞeaxj 1 eawdep
(9)
(10)
Fig. 1. Structure of a multijunction solar cell.
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R. Bestam et al. / Superlattices and Microstructures 91 (2016) 22e30
Fig. 2. Variation of the strain of different layers depending on the indium concentration with y ¼ 0.03.
Jbase ðlÞ ¼
Sn L n !2 H * eaH* þ sinh H* þ aL eaH * 3 cosh n Dn Ln Ln qFð1 RÞaLn 4 5eaðxj þwdep Þ aL n a2 L2n 1 * * Sn Ln H H Dn sinh Ln þ cosh Ln
(11)
R: reflection coefficient. a: absorption coefficient of the sub-cell. Ln: electron diffusion length. Lp: diffusion length of holes. Dn: diffusion constant of electrons. Dp: diffusion constant of holes. Sn: surface recombination velocity of electrons. Sp: surface recombination velocity of holes. xj: width of the N-type region. wdep: depletion width. 5. Results and discussion Fig. 2 illustrates the variation of the constraint of the different layers of the solar cell as a function of the concentration of indium. For InGaP/InGaAs layers it has a compressive and extensive strain. If x ¼ 0.49 we have a mesh matching. If x > 0.49 the strain is compressive and for x < 0.49 the strain become extensive with maximum deformation of 4%. For InGaAsN/Ge layers we have a mesh match at x ¼ 0.09 and for greater than 0.09 the constraint is compressive with a maximum value of 6%.We have an extensive strain when x < 0.09. Finally for the InGaAs/InGaAsN layer we have a purely
Fig. 3. Variation of the critical thickness of the structure as a function of the indium concentration for y ¼ 0.03.
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27
Fig. 4. Evolution of the bandgap as a function of the indium concentration and the temperature with y ¼ 0.03.
constraint compressive with a maximum deformation of 6.6%.This study allowed us to optimize the concentrations of the different layers of alloys. Fig. 3 represents the variation in the critical thickness between the different layers of the InGaP/InGaAs/InGaAsN/Ge cell depending on the concentration of indium. We must find an optimal critical thickness for a definite concentration of indium. For example for a concentration of indium of 0.20 the critical thickness of the InGaP layer must not exceed the110Ᾰ.By contrast to the other two layers InGaAsN and InGaAs the critical thickness must not exceed 448 Ᾰ and 219Ᾰ for the same concentration x ¼ 0.20. Fig. 4 shows the evolution of the bandgap energy of each material according to the indium concentration. It is found that the bandgap of the lower layer of the cell is more reliable than the bandgap of the other layers. For x ¼ 0.20 the bandgap of layers are EInGaP ¼ 2.89 eV, EInGaAs ¼ 1.17 eV and EInGaAsN ¼ 0.91 eV with a strain that does not exceed 2%. We can decrease the gap of different layers, but the strain will increase. If we take x ¼ 0.40, the gaps become EInGaP ¼ 2.11 eV, EInGaAs ¼ 0.94 eV and EInGaAsN ¼ 0.76 eV but the strain believes for the two layers InGaAsN and InGaAs. The strain ε exceeds 2%.
Fig. 5. a. variation of the absorption coefficient of different layers depending on the wavelength and the indium concentration. b. variation of the total absorption coefficient as a function of the wavelength and the indium concentration with y ¼ 0.03.
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R. Bestam et al. / Superlattices and Microstructures 91 (2016) 22e30
Fig. 6. Variation of EQE as a function of the wavelength of the different layers.
Fig. 5a shows the variation of the absorption coefficient as a function of the wavelength and the concentration of indium in different layers of the structure of InGaP/InGaAs/InGaAsN. We note that each material absorbs some of the solar spectrum. In fig. 5b we have trace the evolution of the coefficient of total absorption atot ¼ aInGaP þ aInGaAs þ aInGaAsN as a function of wavelength and the concentration of indium. For example for In ¼ 0.10 and l ¼ 0.6 mm the absorption coefficient is worth 1.38 106 cm1, if we increase the concentration of indium at 0.40 with wavelength the absorption coefficient reaches the value 1.99 106 cm1. So we have an increase of the absorption coefficient of Da ¼ 0.71 106 cm1 that is to say there is an increase of 35.67%, but with a 2.5% strain. This study allowed us to optimize the multi-junction structure for photovoltaic by varying compositions of the alloys. Fig. 6 shows the variation of the external quantum efficiency (EQE) of the solar cell based on InGaP/InGaAs/InGaAsN/Ge depending on the wavelength of the solar spectrum. It is noted that each layer absorbs a part of the solar spectrum. The absorption of the different layers of the structures gives the total absorption. From these layers we cover the range of the solar spectrum from 0.330 to 1.86 mm with amplitude of EQE which varies from 90 to 96%.In Fig. 1 we also illustrates the variation of total EQE of different layers. With the use of four layers we reached EQE amplitude of 96%. Fig. 7 shows the variation of the IeV curve as a function of the bias voltage. We studied the characteristics of currentevoltage for the different layers of the cell of multi-junction cells based on In0.60Ga0.40P/In0.17Ga0.83As/ In0.20Ga0.60As0.97N0.03/Ge. Then we determined the total currentevoltage characteristic. We obtained a minimum density current Jcc which is equal to 14.84 mA/cm2. The open voltage is equal to 3.36 V. We compared with the results of other authors who have worked on double junction GaInP/GaAs [26] and triple-junction GaInP/GaInAs/Ge structures [2]. We note that the current density Jcs of the three structures is very close. The current density of the structure to double junction is equal to 12 mA/cm2 and that of the triple junction is worth 16.4 mA/cm2. In contrary to our structure InGaP/InGaAs array InGaAsN/Ge it is worth 14.84 mA/cm2. The current densities of the three structures are close. For open circuit voltage VOCe3 of our structure is larger than the other two junctions. It reached 3.357 V. It was noted that the voltage of the junction studied worth: VOCe3 ¼ 1.05 VOCe2 and VOCe3 ¼ 1.35 VOCe1.
Fig. 7. JeV variation of each layer and the total cell-based InGaP/InGaAs/InGaAsN/Ge.
R. Bestam et al. / Superlattices and Microstructures 91 (2016) 22e30
29
Fig. 8. PeV variation of different layers and total cell-based InGaP/InGaAs/InGaAsN/Ge.
Fig. 8 illustrates changes in PeV depending on the bias voltage of each layer of the multi-junction structure. Also we calculated the power according to the voltage of the total structure. The maximum power reaches the value of 52 mW.We can optimize the maximum power of the multi-junction solar cell by varying the alloys of the different materials of the layers. Also we made the comparison between the three junctions. The maximum power dual and triple junction structures are equal to 26.56 and 42.43 mW/cm2, respectively. If we compare with the maximum power of our structure which is equal to 52 mW/ cm2 it was found that the maximum power of our structure is equivalent to: Pmaxe3 ¼ 1.22 Pmaxe2 and Pmaxe3 ¼ 1.96 Pmaxe1. Fig. 9 shows the variation in efficiency as a function of the bandgap energy of the two layers InGaP and InGaAs by setting the bandgap energy InGaAsN layer at 0.89 eV. We note that the maximum efficiency reached 40%.Then we can optimize the maximum efficiency by changing the alloys of the three layers. This study allows the manufacturer the right choice of structures in order to achieve reliable multi-junction solar cells. For example for the In0.55Ga0.45P/In0.35Ga0.65As/ In0.30Ga0.70As0.97N0.03/Ge structures the multi-junction cell efficiency reaches 45% and more. Then to make the maximum efficiency we varies the concentrations and y of the different layers of the cells multi-junction structure.
Fig. 9. Variation in efficiency depending on the bandgap energy.
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R. Bestam et al. / Superlattices and Microstructures 91 (2016) 22e30
6. Conclusion In this work we modeled and simulated a multilayer structure based InGaP/InGaAs/InGaAs/Ge, for photovoltaic. In our study we optimize the multi-junction structure taking into account the effect of different alloys on the optical and electrical properties. We were able to optimize and improve the absorption coefficient of the structure. We also have shown that we have the possibility of increasing the efficiency of the structure around 50%.This work allowed us to vary the alloy layers of different materials to achieve maximum efficiency of the solar cell with an acceptable strain that does not exceed 2%. References [1] J. Wu, W. Walukiewicz, K.M. Yu, W. Shan, J.W. Ager III, E.E. Haller, H. Lu, W.J. Schaff, W.K. Metzger, Sarah Kurtz, Superior radiation resistance of In1exGaxN alloys: full-solar-spectrum photovoltaic material system, J. Appl. Phys. 94 (10) (2003) 6477e6482. [2] M. Stan, D. Aiken, B. Cho, A. Cornfeld, J. Diaz, V. Ley, A. Korosty shev sky, P. Pate, P. Sharps, T. Varghese, Very high efficiency triplejunction solar cells grown by MOVPE, J. Cryst. Growth 310 (2008) 5204e5208. [3] R.R. King, D.C. Law, K.M. Edmondson, C.M. Fetzer, G.S. Kinsey, H. Yoon, R.A. Sherif, N.H. Karm, Appl. Phys. Lett. 90 (2007) 183516. [4] Indranil Bhattacharya and Simon Y. Foo, Effects of Gallium-Phosphide and Indium-Gallium-Antimonide Semic Materials on Photon Absorption of Multijunction Solar Cells, IEEE 978-1-(2010) 4244e5853. [5] R.R. King, A. Boca, W. Hong, D. Law, G. Kinsey, C. Fetzer, M. Haddad, K. Edmondson, H. Yoon, P. Pien, N. Karem, High-Efficiency Multijunction Photovoltaics for Low-Cost Solar Electricity, IEEE Lasers Electro-Optics Soc. (2008) 2e3. [6] R. McConnell, M. Symko-Davies, Multijunction Photovoltaic Technologies for High-Performance Concentrators, IEEE Photovoltaic Energy Conversion, in: 4th World Conf., 2006. [7] M.K. Alam, F.H. Khan, A.M. Imtiaz, Interconnection and optimization issues of multijunction solar cells-A new mitigation approach using switching power converters, in: Proc. IEEE Applied Power Electronics Conf. (APEC), 2012, pp. 583e589. [8] X. Wang, A. Barnett, One lateral spectrum splitting concentrator photovoltaic architecture: measurements of current assemblies and analysis of pathways to 40% efficient modules, in: Proc.35th IEEE Photovoltaic Specialists Conf. (PVSC), 2010, pp. 2745e2750. [9] M. Khorshed Alam, F. Khan, A.M. Imtiaz, optimization of subcell interconnection for multijunction solar cells using switching power converters, IEEE Trans. Sustain. Energy 4 (2) (2013). [10] A.G. Imenes, D.R. Mills, Spectral beam splitting technology for Increased conversion efficiency in solar concentrating systems: Are- view, Sol. Energy Mat. Sol. Cells 84 (1e4) (2004) 19e69. [11] J.H. Karp, J.E. Ford, Multiband solar concentrator using trans-missive dichroic beam splitting, in: Proc. SPIE, vol. 7043, 2008, 70430Fe70430F-8. [12] D.J. Friedman, J.F. Geisz, M.A. Steiner, Effect of Luminescent Coupling on the Optimal Design of Multijunction Solar Cells, IEEE, J. Photovoltaics 4 (3) (2014) 986e990. [13] D. Derkacs, D.T. Bilir, V.A. Sabnis, Luminescent coupling in GaAs/GaInNAsSb multijunction solar cells, IEEE J. Photovoltaics 3 (1) (2013) 520e527. [14] C. Baur, M. Hermie, F. Dimroth, A.W. Bett, Effects of optical coupling in III-V multilayer systems, Appl. Phys. Lett. 90 (2007), 192109e192109-3. [15] J. Piprek, Semiconductor Optoelectronic Devices: Introduction to Physics and Simulation, Academic Press, California, 2003. [16] R.L. Moon, G.A. Antypas, L.W. James, J. Electron. Mater. 3 (1974) 635. [17] T.H. Glisson, J.R. Hauser, M.A. Littlejohn, C.K. Williams, Energy bandgap and lattice constant contours of IIIeV quaternary alloys, J. Electron. Mater. 7 (1) (1978) 1e16. [18] P.A. Houston, Growth and characterization of InGaAsP lattice-matched to InP, J. Mater. Sci. 16 (11) (1981) 2935e2961. [19] M.P.C.M. Krijn, Heterojunction band offsets and effective masses in III-V quaternary alloys, Semicond. Sci. Technol. 6 (1991) 27e31. [20] J. Singh, Electronic and Optoelectronic Properties of Semiconductor Structures, Cambridge University Press, 2003. [21] J.E. Ayers, Compliant Substrates for Heteroepitaxial Semiconductor Devices: theory, Experiment, and Current Directions, J. Electron. Mater. 37 (10) (2008) 1511e1523. [22] W.W. Chow, S.W. Koch, Semiconductor-Laser Fundamentals Physics of the Gain Materials Berlin Springer-Verlag, 1999. ves a 1,55mm en laser a cavite verticale externe pour application a l'e chantillonnage optique line aire, the se de [23] K. Aghiad, Source d'impulsions bre Doctorat de l’Ecole Polytechnique, 2009. [24] J. Wu, W. Walukiewicz, K.M. Yu, J.W. Ager III, E.E. Haller, H. Lu, W.J. Schaff, Small bandgap bowing in In1-xGaxN alloys, Appl. Phys. Lett. 80 (25) (2002) 4741e4743. basse temperature pour applications photovoltaïques,These, Institut [25] F. ABDO, Croissance de couches minces de silicium par epitaxie en phase liquide a es de Lyon, 2007. National des Sciences Applique [26] D.J. Friedman, J.F. Geisz, M.A. Steiner, Analysis of Multijunction Solar Cell CurrenteVoltage Characteristics in the Presence of Luminescent Coupling, IEEE J. Photovoltaics 3 (4) (2013) 1429e1436.
Contents lists available at ScienceDirect
Superlattices and Microstructures journal homepage: www.elsevier.com/locate/superlattices
High efficiency quadruple junction solar cells R. Bestam a, A. Aissat a, b, *, J.P. Vilcot c a
LATSI Laboratory, Faculty of the Technology, University of Blida 1, BP270, 09.000, Algeria LATSICOM Laboratory, Faculty of Science, University of Blida 1, BP270, 09.000, Algeria Institut d’Electronique, de Micro electronique et de Nanotechnologie, UMR CNRS 8520, Universit e des Sciences et Technologies de Lille1, Avenue Poincar e, CS 60069, 59652 Villeneuve d’Ascq, France
b c
a r t i c l e i n f o
a b s t r a c t
Article history: Received 14 November 2015 Accepted 24 December 2015 Available online 29 December 2015
This work focuses on the modeling and optimization of a structure based on InGaP/InGaAs/ InGaAsN/Ge for photovoltaic. In this study we took into consideration the concentration effect of alloys x (In) and y (N) on the strain, the bandgap, the absorption and structure efficiency. It has been shown that the concentration of indium varies the strain and the bandgap. These two parameters change considerably the yield. Also it optimized the effect of alloys on the total absorption of the structure. For a concentration of indium x ¼ 0.40 and y ¼ 0.03 we had a absorption coefficient which is equal to 2 106 cm1. We have found 50% efficiency for the multi-junction structure based on In0.55Ga0.45P/In0.40Ga0.60As/ In0.30Ga0.70As0.97N0.03/Ge. To achieve a reliable high efficiency multi-junction structure, we just need to optimize the concentrations of different alloys. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Semiconductor New materials Nanostructures Solar cell Optoelectronics
1. Introduction The gallium nitride and its ternary and quaternary alloys in the system Ga (B, In,Al) N have become in recent years the headlights semiconductors in optoelectronics field. Indeed, these materials suffer from lack of agreement mesh substrates for epitaxial growth. They have also a high defect density difficult to achieve p-type doping particularly, the gallium nitride and indium takes a considerable place in photovoltaic field since a decade [1]. These alloys have a bandgap that covers the visible spectrum. They are candidates for the realization of multi-junction solar cells with very high efficiency. The solar cell technology based on triple junction structure GaInP/GaInAs/Ge is performed at 30% conversion efficiency under lighting AM0 [2]. Metamorphic solar junction cells have been studied for terrestrial solar applications and in space. The modeling of components indicates that performance improvements are possible with the splitting of the spectrum still optimized by the use of the disagreement of mesh of semi-conductors IIIeV. However, the terrestrial spectrum conversion efficiency equal to around 40% was considered at the high solar concentration using the triple junction cell [3]. The simple solar cell can absorb a finite interval of wavelength in solar spectrum and thus produce less efficiently. In contrary, the solar cells multi-junctions absorb the maximum of the solar spectrum. Each junction absorbs a portion of the solar spectrum [4].
* Corresponding author. LATSI Laboratory, Faculty of the Technology, University of Blida 1, BP270, 09.000, Algeria. E-mail address: [email protected] (J.P. Vilcot). http://dx.doi.org/10.1016/j.spmi.2015.12.038 0749-6036/© 2015 Elsevier Ltd. All rights reserved.
R. Bestam et al. / Superlattices and Microstructures 91 (2016) 22e30
23
Multi-junction photovoltaic systems of high-efficiency are formed of IIIeV semiconductor alloys with a high optical sensitivity. The perfect combination of the band gap energy increases the absorption coefficient of photons. It creates more electronehole pairs and thus increases the efficiency of the solar cell [4]. Researchers have introduced a new multi-junction photovoltaic cell constituted by GaP/InGaAs/InGaSb structures [4]. Then they compared with simple multi-junction solar cells which already in existence. Several researchers have made the design of solar cells with agreement and disagreement meshes. They tried to reach a theoretical yield of 60% and even more [5,6]. On the other hand, the multi-junction solar cells have evolved to extract energy from a larger energy band of the solar spectrum [7,8]. The multi-junction solar cells can be grouped into two types depends on spectrum splitting up techniques and also the orientation of the intermediate junctions. The two types are, known as vertical multi-junction (VMJ) and as lateral multijunction (LMJ) [9,10]. Generally, VMJ solar cells are more expensive compared to single junction cells because of costly manufacturing steps due to different materials layers [9]. However, the strain and the faults of interface significantly affect the manufacturing efficiency and performance of VMJ solar cells [11]. For IIIeV multi-junctions of high quality the recombination is widely radiative. This effect may have a significant effect on the short-circuit voltage (VOC), and photocurrent densities (JCS) of junctions [12e14]. Therefore, there is a significant work in the literature on experimental extraction and modeling luminescent coupling parameters derived from (JCS) [12e14]. Also our modeling purpose is to study different multi-junctions structures of cells based on semi-conductors with significant importance to exceed conversion efficiency of 50%.It is shown that the use of several layers of different materials mounted in vertical increase the performance and reliability of the solar cell. 2. Theoretical model IIIeV semi-conductors are known for having a very important optical transition and procedures for manufacturing and growth are currently sufficiently well normalized. The properties of the quaternary alloys ABCD are found by the interpolation of the properties of binary Alloys AB or properties of ternary alloys ABC. The properties of the ternary alloys A1exBxC are given by the following relationship:
PABC ðxÞ ¼ x:EBC þ ð1 xÞPAC þ x:ð1 xÞCABC
(1)
CABC is the parameter of Bowing and P represents the parameter of materials. For the calculation of the mesh parameter of the alloys, CABC is zero [15]. From the formulas of empirical interpolation for the ternary alloys A1exBxC, the properties of the quaternary alloys AxB1exCy D1ey are interpreted by:
Pðx; yÞ ¼
x:ð1 xÞ½y:TABC ðxÞ þ ð1 yÞ:TABD ðxÞ þ yð1 yÞ½x:TACD ðyÞ þ ð1 xÞ:TBCD ðyÞ x:ð1 xÞ þ yð1 yÞ
(2)
The approach of eq (2) tends to give better agreement with experiment than an alternative treatment of Moon et al. [16] which is known to overestimate the quaternary bowing [17,18] Krijn [19] gives polynomial expansions of Q(x,y) derived from eq (2) for the energy gaps and spineorbit splitting of several IIIeV quaternaries. The quaternary may then be represented as a combination of two lattice-matched constituents, one of which must be a ternary while the other may be either a binary or a ternary. The semiconductor materials in the hetero-structures do not necessarily have the same mesh parameters a. These internal deformations have important consequences for the electronic and optoelectronic properties, and can be exploited to achieve high performance structures. Some semiconductors are not necessarily in agreement to mesh with the available substrates. A solution is to make them grow without agreement of mesh. In this case, the dislocations will be formed and possibly the high layer may be used as 'pseudo-substrate'. This procedure of growth, allows in principle to have an improved flexibility in the technology of semiconductors [20]. To perform the growth of a semiconductor (1) for parameter of mesh a1 on a semiconductor (2) with a mesh parameter a2. The strain between the two materials is defined as:
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ε¼
a2 a1 a1
(3)
The interface layer will be under strain and the system produces an elastic energy. This energy increases with the increase of the thickness of the layer distorted. For a small disagreement of mesh ε ¼ 1%, the initial growth of the upper layer occurs with a small deformation of mesh parameters. When the thickness of the layer increases, dislocations will eventually be generated in this layer [21]. The dislocations are beginning to appear from a critical thickness LC. 3. Absorption The absorption of photon energy larger than the band gap will excite an electron from the valence band to the conduction band. The electron will leave an empty state in the valence band, called a hole, with a charge þ q and an effective mass mh. The electron has a charge -q and an effective weight me. There are other absorption mechanisms such as the absorption assisted by phonons, absorption by free carriers, or absorption by impurities. The absorption step is followed by a relaxation step wherein the electron returns to the valence band by electronehole recombination. Relaxation can be of several types, a radiative recombination, a non-radiative recombination as Auger recombination. For a direct gap semiconductor, excited by a photon of energy close to that of the bandgap, the absorption band and the radiative recombination are the two dominant phenomena. The coulomb interaction between the electronehole pair formed a state called exciton [22,23]. The energy of the exciton resonance is weaker than unbound electronehole pair and excitonic states are located just below the bandgap energy. For solar cells, the absorption coefficient is a very important parameter since it will determine the amount of photons absorbed by the material and thus the amount of carriers that can be produced. The absorption through a layer of semiconductor of thickness L is given by the following equation:
Itrn ðlÞ ¼ Iinc ðlÞ:eaðlÞ:L
(4)
with Itrn Transmitted intensity of light Iinc Incident intensity of light a(l) Absorption coefficient l Wavelength For the absorption coefficient we used the model proposed by Wu et al. [23,24].
aðEÞ ¼ a0
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E ESt g E
(5)
a0 Adjustment parameter ESt g strained bandgap energy E light energy 4. Electrical characteristic Under illumination, the incident photons will generate electronehole pairs whose behavior will differ depending on the absorption area: In the space charge zone (SCZ) generated by the pen junction, the electronehole pairs created are separated by the electric field. The electrons are accelerated and then injected into the n region (emitter) and holes in the p region (base). A generation of photocurrent is created. In base and emitter areas, the generated minority carriers (holes and electrons in the transmitter in the base) will diffuse to the (SCZ). If they reach the latter before recombining, they are injected into the n region for electrons and the p-zone for holes and become majority. A photo-current distribution is created. Both contributions are added to give the resulting photocurrent from minority carriers Iph. It is proportional to the light intensity [25]. The current delivered to a load by an illuminated photovoltaic cell is then written:
IðVÞ ¼ Iph IobsðVÞ With Iobs is the dark current. The photon-current (Iph) is given by the following expression:
(6)
R. Bestam et al. / Superlattices and Microstructures 91 (2016) 22e30
25
ZlMax Jph ¼ q
FðlÞ:EQEðlÞdl
(7)
lMin
q: elementary charge 4.1. F (l): solar spectrum l: wavelength EQE(l) the external quantum efficiency is given by:
EQE ¼
Jemetter ðlÞ þ Jsc ðlÞ þ Jbase ðlÞ q:FðlÞ
(8)
Jemetter (l): photon-current of the transmitter. J sc(l): photon-current of the depletion region. 4.2. Jbase (l): base photon current
!
Jemetter ðlÞ ¼
qFð1 RÞa:Lp ½ a2 Lp2 1
Sp Lp Dp
x x S L eaxj ð Dp pp cosh Lpj þ sinh Lpj aLp eaxj xj xj Sp Lp þ sinh cosh Dp Lp Lp
þ aLp
Jsc ðlÞ ¼ qFð1 RÞeaxj 1 eawdep
(9)
(10)
Fig. 1. Structure of a multijunction solar cell.
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R. Bestam et al. / Superlattices and Microstructures 91 (2016) 22e30
Fig. 2. Variation of the strain of different layers depending on the indium concentration with y ¼ 0.03.
Jbase ðlÞ ¼
Sn L n !2 H * eaH* þ sinh H* þ aL eaH * 3 cosh n Dn Ln Ln qFð1 RÞaLn 4 5eaðxj þwdep Þ aL n a2 L2n 1 * * Sn Ln H H Dn sinh Ln þ cosh Ln
(11)
R: reflection coefficient. a: absorption coefficient of the sub-cell. Ln: electron diffusion length. Lp: diffusion length of holes. Dn: diffusion constant of electrons. Dp: diffusion constant of holes. Sn: surface recombination velocity of electrons. Sp: surface recombination velocity of holes. xj: width of the N-type region. wdep: depletion width. 5. Results and discussion Fig. 2 illustrates the variation of the constraint of the different layers of the solar cell as a function of the concentration of indium. For InGaP/InGaAs layers it has a compressive and extensive strain. If x ¼ 0.49 we have a mesh matching. If x > 0.49 the strain is compressive and for x < 0.49 the strain become extensive with maximum deformation of 4%. For InGaAsN/Ge layers we have a mesh match at x ¼ 0.09 and for greater than 0.09 the constraint is compressive with a maximum value of 6%.We have an extensive strain when x < 0.09. Finally for the InGaAs/InGaAsN layer we have a purely
Fig. 3. Variation of the critical thickness of the structure as a function of the indium concentration for y ¼ 0.03.
R. Bestam et al. / Superlattices and Microstructures 91 (2016) 22e30
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Fig. 4. Evolution of the bandgap as a function of the indium concentration and the temperature with y ¼ 0.03.
constraint compressive with a maximum deformation of 6.6%.This study allowed us to optimize the concentrations of the different layers of alloys. Fig. 3 represents the variation in the critical thickness between the different layers of the InGaP/InGaAs/InGaAsN/Ge cell depending on the concentration of indium. We must find an optimal critical thickness for a definite concentration of indium. For example for a concentration of indium of 0.20 the critical thickness of the InGaP layer must not exceed the110Ᾰ.By contrast to the other two layers InGaAsN and InGaAs the critical thickness must not exceed 448 Ᾰ and 219Ᾰ for the same concentration x ¼ 0.20. Fig. 4 shows the evolution of the bandgap energy of each material according to the indium concentration. It is found that the bandgap of the lower layer of the cell is more reliable than the bandgap of the other layers. For x ¼ 0.20 the bandgap of layers are EInGaP ¼ 2.89 eV, EInGaAs ¼ 1.17 eV and EInGaAsN ¼ 0.91 eV with a strain that does not exceed 2%. We can decrease the gap of different layers, but the strain will increase. If we take x ¼ 0.40, the gaps become EInGaP ¼ 2.11 eV, EInGaAs ¼ 0.94 eV and EInGaAsN ¼ 0.76 eV but the strain believes for the two layers InGaAsN and InGaAs. The strain ε exceeds 2%.
Fig. 5. a. variation of the absorption coefficient of different layers depending on the wavelength and the indium concentration. b. variation of the total absorption coefficient as a function of the wavelength and the indium concentration with y ¼ 0.03.
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Fig. 6. Variation of EQE as a function of the wavelength of the different layers.
Fig. 5a shows the variation of the absorption coefficient as a function of the wavelength and the concentration of indium in different layers of the structure of InGaP/InGaAs/InGaAsN. We note that each material absorbs some of the solar spectrum. In fig. 5b we have trace the evolution of the coefficient of total absorption atot ¼ aInGaP þ aInGaAs þ aInGaAsN as a function of wavelength and the concentration of indium. For example for In ¼ 0.10 and l ¼ 0.6 mm the absorption coefficient is worth 1.38 106 cm1, if we increase the concentration of indium at 0.40 with wavelength the absorption coefficient reaches the value 1.99 106 cm1. So we have an increase of the absorption coefficient of Da ¼ 0.71 106 cm1 that is to say there is an increase of 35.67%, but with a 2.5% strain. This study allowed us to optimize the multi-junction structure for photovoltaic by varying compositions of the alloys. Fig. 6 shows the variation of the external quantum efficiency (EQE) of the solar cell based on InGaP/InGaAs/InGaAsN/Ge depending on the wavelength of the solar spectrum. It is noted that each layer absorbs a part of the solar spectrum. The absorption of the different layers of the structures gives the total absorption. From these layers we cover the range of the solar spectrum from 0.330 to 1.86 mm with amplitude of EQE which varies from 90 to 96%.In Fig. 1 we also illustrates the variation of total EQE of different layers. With the use of four layers we reached EQE amplitude of 96%. Fig. 7 shows the variation of the IeV curve as a function of the bias voltage. We studied the characteristics of currentevoltage for the different layers of the cell of multi-junction cells based on In0.60Ga0.40P/In0.17Ga0.83As/ In0.20Ga0.60As0.97N0.03/Ge. Then we determined the total currentevoltage characteristic. We obtained a minimum density current Jcc which is equal to 14.84 mA/cm2. The open voltage is equal to 3.36 V. We compared with the results of other authors who have worked on double junction GaInP/GaAs [26] and triple-junction GaInP/GaInAs/Ge structures [2]. We note that the current density Jcs of the three structures is very close. The current density of the structure to double junction is equal to 12 mA/cm2 and that of the triple junction is worth 16.4 mA/cm2. In contrary to our structure InGaP/InGaAs array InGaAsN/Ge it is worth 14.84 mA/cm2. The current densities of the three structures are close. For open circuit voltage VOCe3 of our structure is larger than the other two junctions. It reached 3.357 V. It was noted that the voltage of the junction studied worth: VOCe3 ¼ 1.05 VOCe2 and VOCe3 ¼ 1.35 VOCe1.
Fig. 7. JeV variation of each layer and the total cell-based InGaP/InGaAs/InGaAsN/Ge.
R. Bestam et al. / Superlattices and Microstructures 91 (2016) 22e30
29
Fig. 8. PeV variation of different layers and total cell-based InGaP/InGaAs/InGaAsN/Ge.
Fig. 8 illustrates changes in PeV depending on the bias voltage of each layer of the multi-junction structure. Also we calculated the power according to the voltage of the total structure. The maximum power reaches the value of 52 mW.We can optimize the maximum power of the multi-junction solar cell by varying the alloys of the different materials of the layers. Also we made the comparison between the three junctions. The maximum power dual and triple junction structures are equal to 26.56 and 42.43 mW/cm2, respectively. If we compare with the maximum power of our structure which is equal to 52 mW/ cm2 it was found that the maximum power of our structure is equivalent to: Pmaxe3 ¼ 1.22 Pmaxe2 and Pmaxe3 ¼ 1.96 Pmaxe1. Fig. 9 shows the variation in efficiency as a function of the bandgap energy of the two layers InGaP and InGaAs by setting the bandgap energy InGaAsN layer at 0.89 eV. We note that the maximum efficiency reached 40%.Then we can optimize the maximum efficiency by changing the alloys of the three layers. This study allows the manufacturer the right choice of structures in order to achieve reliable multi-junction solar cells. For example for the In0.55Ga0.45P/In0.35Ga0.65As/ In0.30Ga0.70As0.97N0.03/Ge structures the multi-junction cell efficiency reaches 45% and more. Then to make the maximum efficiency we varies the concentrations and y of the different layers of the cells multi-junction structure.
Fig. 9. Variation in efficiency depending on the bandgap energy.
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6. Conclusion In this work we modeled and simulated a multilayer structure based InGaP/InGaAs/InGaAs/Ge, for photovoltaic. In our study we optimize the multi-junction structure taking into account the effect of different alloys on the optical and electrical properties. We were able to optimize and improve the absorption coefficient of the structure. We also have shown that we have the possibility of increasing the efficiency of the structure around 50%.This work allowed us to vary the alloy layers of different materials to achieve maximum efficiency of the solar cell with an acceptable strain that does not exceed 2%. References [1] J. Wu, W. Walukiewicz, K.M. Yu, W. Shan, J.W. Ager III, E.E. Haller, H. Lu, W.J. Schaff, W.K. Metzger, Sarah Kurtz, Superior radiation resistance of In1exGaxN alloys: full-solar-spectrum photovoltaic material system, J. Appl. Phys. 94 (10) (2003) 6477e6482. [2] M. Stan, D. Aiken, B. Cho, A. Cornfeld, J. Diaz, V. Ley, A. Korosty shev sky, P. Pate, P. 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