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Technologies and Materials for Renewable Energy, Environment and Sustainability, TMREES18, Technologies and Materials for Renewable Energy, and Sustainability, TMREES18, 19–21 September 2018,Environment Athens, Greece 19–21 September 2018, Athens, Greece
Temperature Dependence of InGaN / GaN Multiple Quantum Well Solar Cells Multiple Quantum Well Solar Cells Assessing theRabeb feasibility of using the heat demand-outdoor Belghouthia,b,c, Michel Aillerieb,c,* a,b,c b,c, Rabeb for Belghouthi , Michel Aillerieheat * demand forecast temperature function a long-term district Laboratoire d’Electronique et Micro-Electronique, Faculté des Sciences de Monastir, 5019 Tunisia. The 15th International Symposium on District Heating/ and Cooling Temperature Dependence of InGaN GaN
a
a Matériaux Optiques, Photonique et Systèmes, LMOPS, EA 4423, Université de Lorraine, Metz, 57070, France Laboratoire Laboratoire d’Electronique et Micro-Electronique, Faculté des Sciences de Monastir, 5019 Tunisia. a,b,cOptiques, Photonique a aLMOPS, CentraleSupélec, b c c c b Laboratoire Matériaux et Systèmes, Université Paris-Saclay, 57070, France Laboratoire Matériaux Optiques, Photonique et Systèmes, LMOPS, EA 4423, Université de Lorraine, Metz,Metz, 57070, France c Laboratoire Matériaux Optiques, Photonique et Systèmes, LMOPS, CentraleSupélec, Université Paris-Saclay, Metz, 57070, France a IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France Abstract c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France Abstract b
I. Andrić
*, A. Pina , P. Ferrão , J. Fournier ., B. Lacarrière , O. Le Corre
Elements based on nitride family and more specifically, those of the GaN/InGaN family, present a great interest for renewable energy conversion systemsfamily as they potentialities photovoltaic applications, as example for the for realization of Elements based on nitride andoffer morehuge specifically, those in of the GaN/InGaN family, present a great interest renewable concentration solar cells. This is linked the possibility enlarge the applications, part of the solar energeticfor spectrum that a solar energy conversion systems asinterest they offer huge topotentialities in to photovoltaic as example the realization of Abstract cell is able tosolar capture to the possibilities of growing multilayers withofvarious band-gap and thus, with concentration cells.thanks This interest is linked to the possibility to enlargecells the part the solar energetic spectrum that various a solar absorption In thisthanks paper,tothetheperformance multiple quantum wellvarious MQW band-gap solar cellsand withthus, respect the Ncell is ablebands. to capture possibilitiesofofInGaN/GaN growing multilayers cells with withtovarious District heating are commonly inthetheexact literature as quantum one efficiency, of the most solutions the polar orientation. is this investigated orderaddressed to obtain conversion theeffective temperature effectfor asdecreasing well as the absorption bands. networks In paper, the.Inperformance of InGaN/GaN multiple well MQW solar cells with respect to the Ngreenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat spontaneous and piezoelectric polarization effect are taking into consideration in model. The results reveal that the increase of polar orientation. is investigated .In order to obtain the exact conversion efficiency, the temperature effect as well as the sales. Due decreases to the changed climate and building policies, heat demand in reveal the future could decrease, temperature significantly theconditions MQW solarare celltaking efficiency. spontaneous and piezoelectric polarization effect intorenovation consideration in model. The results that the increase of prolonging the investment return period. Our results and discussion would bethe helpful in solar designing and fabricating high efficiency InGaN/GaN solar cell in experiment. temperature decreases significantly MQW cell efficiency. Theresults main scope of this paper is to the heathigh demand – outdoor temperature for heat demand Our and discussion would beassess helpfulthe infeasibility designing of andusing fabricating efficiency InGaN/GaN solarfunction cell in experiment. districtPublished of Alvalade, locatedLtd. in Lisbon (Portugal), was used as a case study. The district is consisted of 665 ©forecast. 2018 TheThe Authors. by Elsevier ©buildings 2019 The Authors. Published by Ltd. that vary in both under construction Three weather scenarios (low, medium, high) and three district This is an open access article the CC period BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) © 2018 The Authors. Published by Elsevier Elsevier Ltd. and typology. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) renovation scenarios were developed (shallow, intermediate, deep). To of estimate the error, values were Selection under responsibility of the scientific Technologies andobtained Materialsheat for demand Renewable Energy, This is an and openpeer-review access article under the CC BY-NC-ND license committee (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of themodel, scientific committee of Technologies and Materials for Renewable Energy, compared with results from a dynamic heat demand previously developed and validated by the authors. Environment Sustainability, TMREES18. Selection andand peer-review under TMREES18. responsibility of the scientific committee of Technologies and Materials for Renewable Energy, Environment and Sustainability, The results showed that when only weather change is considered, the margin of error could be acceptable for some applications Environment and Sustainability, TMREES18. (the error in annualsolar demand lower than 20% forPhotovoltaic all weathereffect; scenarios considered). However, after introducing renovation Keywords:InGaN/GaN cells; was Temperature; Polarization; Conversion efficiency scenarios, the error value increased up to 59.5% (depending on the weather and renovation Keywords:InGaN/GaN solar cells; Temperature; Polarization; Photovoltaic effect; Conversion efficiency scenarios combination considered). The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and improve the accuracy of heat demand estimations. © 2017 The Authors. Published by Elsevier Ltd. * E-mail address:
[email protected] Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and * E-mail address:
[email protected] Cooling. 1876-6102© 2018 The Authors. Published by Elsevier Ltd. Keywords: Heat demand; Forecast; Climate change This is an open access under the CC by BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) 1876-6102© 2018 Thearticle Authors. Published Elsevier Ltd. Selection under responsibility of the scientific of Technologies and Materials for Renewable Energy, Environment This is an and openpeer-review access article under the CC BY-NC-ND licensecommittee (https://creativecommons.org/licenses/by-nc-nd/4.0/) and Sustainability, TMREES18. Selection and peer-review under responsibility of the scientific committee of Technologies and Materials for Renewable Energy, Environment and Sustainability, TMREES18. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of Technologies and Materials for Renewable Energy, Environment and Sustainability, TMREES18. 10.1016/j.egypro.2018.11.245
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Rabeb Belghouthi et al. / Energy Procedia 157 (2019) 793–801 Rabeb Belghouthi and Michel Aillerie / Energy Procedia 00 (2018) 000–000
1. Introduction Currently, the main technology used in solar photovoltaic technology is the Silicon one. The first reasons are the wide availability of silicon all around the word and that silicon is intensively used since the middle of the twenty century in electronic industry assuming a perfect mastering of the various growing, production and fabrication processes based on this technology. Also taking into account the material losses generated by the process itself due to the necessities of thick layers and the important wastes linked to their cutting, for photovoltaic applications, the the narrow and indirect band-gap of silicon devices is definitely one of the main drawback as it limits the quantum efficiency of solar cells. Thus, these drawbacks of silicon cells have invited researchers to study new photovoltaic elements and structures and one of their interest was bring on Solar Photovoltaic Cells (SPC) based on III-N elements. One of the reasons is their controllable band gap allowing promising photovoltaic properties in multi-layer solar cells [1-2]. For example, in InGaN, the modification of the ternary In-Ga-N concentrations allows changes in the energy band gap from 0.77 eV to 3.42 eV related to possible wavelength absorption covering all the energy solar spectrum [3-5]. Nevertheless, due to the scarcity of the constituting elements, only small III-N solar cells with high performance can be produced with III-N elements that dedicate this technology to concentrating solar photovoltaic. It is to be noted, that the high quality and thick InGaN layers with high quantity of indium are required to built efficient SPC. This is relatively difficult to achieve in the growth process due to changes in lattice parameters with the indium incorporation that rapidly induces a high density of dislocations and other structural defects as cracks and lattice mismatches at the interfaces of the various layers [6]. Finally, with direct consequence on the efficiency, the carrier mobility is directly dependent of the crystal or layers quality, on the polarization induced by the intrinsic asymmetry of the bonds in the wurtzite crystal structure, but is also dependent of the working temperature, pointing out the influence of the temperature on the SPC efficiency in actual use. The temperature is thus a fundamental parameter that it is important to consider in the built of optimized efficient InGaN solar photovoltaic cell. Accordingly, in this contribution, the InGaN/GaN MQW solar cell is investigated theoretically and the temperature dependence of photovoltaic properties is obtained. The paper is organized as follows: After a brief introduction, we present in section 2 the basic photovoltaic conversion equations. Numerical results will be discussed in section 3. A summary and conclusions are reported in section 4. 2. Basic equations The schematic of the modeled MQW solar cell is shown in Fig 1.
Figure 1: The InGaN/GaN MQW solar cell with N face configuration
Rabeb Belghouthi et al. / Energy Procedia 157 (2019) 793–801 Rabeb Belghouthi,and Michel Aillerie / Energy Procedia 00 (2018) 000–000
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This kind of structure has been studied by Deng et al.[7]. Our proposed structure is based on sapphire substrate, followed by GaN nucleation layer (LT-GaN) and buffer layer (HT-GaN). The InGaN/GaN MQWs are implanted in the InGaN intrinsic region between the p-type and n-type GaN layers. The current density of MQW solar cell as a function of applied voltage V can be expressed as [8,9]: V J(V) J QW (1 rR )[exp 1] J ph nVth
where
J QW
(1)
is the saturation current density.
is a parameter related to the intrinsic region,
J
rR
denotes the radiative
enhancement, Vth kT / q is the thermal energy and ph is the photocurrent density. The saturation current density taking into account polarization charges is expressed as [8,9]: 2 J QW qn iB
q W 2 4Vth BB exp( p pz ) N 2Vth
(2-a)
where n iB is the equilibrium intrinsic carrier concentration in the barrier epilayer . N is the doping concentration on
the n-and p- sides fixed at 1018 (cm 3 ) , BB is the recombination coefficient and and represents the carrier mobility. ρp is a bulk polarization charge density distributed in a few atomic layers thick layer with a thickness Wpz around 1 nm [9-10] at the InGaN/GaN interfaces. Temperature dependence of the mobility for electron and hole of InGaN is taken into account using the following expression [11]:
T (T) min,i 300
1
max,i
T min,i 300
N 1 3 T N 300
2
T 300
(2-b)
4
i=e,h refer to electron and hole, 𝜇𝜇����� , 𝜇𝜇����� 1 ,2 ,3 , 4 and are Specific parameters depend on the type of semiconductor. The coefficient in the Eq. (1) is dependant on the mobility given by [8-9]: N W (L W L b )
where
qNBB 4kT
(2-c)
LW , Lb are respectively the barrier and well thicknesses. The radiative enhancement can be expressed as [8-
9]: rR 1
where
E (GaN) E g (InGaN) 1 [ 2 exp g 1] kT 2 B DOS
(2-d)
B denotes the oscilator enhancement factor, DOS is density of states enhancement factor denotes the
Rabeb Belghouthi et al. / Energy Procedia 157 (2019) 793–801 Rabeb Belghouthi and Michel Aillerie / Energy Procedia 00 (2018) 000–000
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occupation of the quantum well material in the intrinsic region. The band gaps of the binaries InN and GaN versus temperature are expressed using Varshini’s law [12-14] as: GaN 0.909 10 3 T 2 Eg (T) Eg GaN (T 0K) T 830 3 2 Eg InN (T) Eg InN (T 0K) 0.245 10 T T 624
(3)
with Eg GaN (T 0 K ) 3 . 51 eV and Eg InN (T 0 K ) 0 . 72 eV . Finally For InGaN, the In composition-dependent band gap is defined by: E gInGaN (x,T) xE gInN (T) (1 x)E GaN (T) bx(1 x) g
(4)
where b is the bowing parameter. The InGaN/GaN interfaces induce Psp spontaneous and Ppz piezoelectric polarizations effects, which depend on the indium’s concentration, noted by x, and yielding to a total polarization defined by: P [PInSPGa x
1x N
PInPZGa x
1x N
SP ] PGaN
(5)
The piezoelectric polarization with indium’s content is described by the following Vegard’s law as: PInSPGa x
1x N
PZ PZ xPInN [(x)] (1 x)PGaN [(x)]
(6)
The expressions of Psp and Ppz polarizations: PInSPGa x
1x N
0.042x 0.034(1 x) 0.038x(1 x)
PZ PInN 1.373 7.559 2
(7)
PZ PGaN 0.918 9.541 2
In these equations,ε is the strain induced by the discrepancy between the lattice parameter of the substrate, as and those of the epilayer, ac(x) leading to the expression: a a e (x) (x) s a e (x)
(8)
Finally the discontinuity of P between GaN and InGaN gives rise to polarization charges with a bulk charge density ρpz such as: pz
P Wpz
(9)
The photocurrent density can be defined as [7]: J ph qN W N ph ( n ) exp[ W ( n )L W ] n n
(10)
Rabeb Belghouthi et al. / Energy Procedia 157 (2019) 793–801 Rabeb Belghouthi,and Michel Aillerie / Energy Procedia 00 (2018) 000–000
where N� is the number of quantum wells,
N n
ph
permitted transitions’ wavelengh with line widths,
797 5
( n ) is a parameter related to the solar spectrum , � is the
LW
is the width of the quantum well material and () is the
absorption coefficient. We use the theoretical model proposed by rabeb et al.[9] to describe the absorption coefficient () in the InGaN ternary. The open circuit voltage Voc can be obtained by setting the J in Eq. (1) to be zero: Voc
J kT ln( ph 1) J QW q
(11)
The fill factor (FF) and the power conversion efficiency (PCE) η of a photovoltaic cell are defined as a function of the short circuit current density Jsc and the open circuit voltage Voc: FF
(12)
Pmax J SC VOC
(13)
Pmax V FF J SC OC Pinc Pinc
where Pmax=Vm×Im is the maximum converted power and Pinc is the incident irradiance per area unit. All Details and values of the parameters using in the calculationg of the total current density can be found elsewhere [7-9]. Figure 2 shows the absorption coefficient for different indium and photon energy. It is of the order of 105. It is revealed that the absorption spectrum of InGaN is strongly influenced by the indium content. It should be noted that the absorption spectrum can extend to longer wavelengths with the increasement of indium content which is beneficial for the InGaN solar cell to absorb much enough of low energy photons. Absorption Coefficient ( x105cm-1)
1
3.4
0.9
5.8
4.6
2. 2
0.8
3.4
1
0.7
5
0.6
0.4 0.3 0.2
2. 2 3. 4
2
Photon Energy [eV]
5
7
4
5.8
3
4.6
1 2
1
0
3
2.2
0.1
1
4
6 4.
3.4
2.2
0.5
1
Indium Content
6
6
Fig.2: Absorption coefficient as a function of indium content and photon energy in the InGaN.
1
798 6
Rabeb Belghouthi et al. / Energy Procedia 157 (2019) 793–801 Rabeb Belghouthi and Michel Aillerie / Energy Procedia 00 (2018) 000–000
Indeed, The intrinsic region absorb photons with energy higher than InGaN band gap which explains the strong dependence of the photo-current density Jph on the indium composition as shown in Figure 3. Our result is a good agreement with those obtained by Deng et al.[7].
Fig.3: Dependance of Jph on indium content.
In order to point out the influence of the temperature on the electrical characteristics of the solar photovoltaic, we have plotted in Fig. 4 and 5, in the range 100-600 K, the short-circuit current Jsc and the open-circuit voltage Vocof a InGaN SPC with an indium concentration x=0.2 and with 30 period of quantum well. The width of the well region and the thickness of barrier are fixed to be respectively 4 et 10nm. It should be noted here that with increasing temperature, the short-circuit increases and the open circuit voltage goes down attributed to the band gap narrowing. The decreasing rate of the voltage is more accentuated than the current increasing rate. As a consequence, the conversion efficiency goes down when the temperature increases, since the photo-generated carriers have a larger probability to recombination when the temperature becomes higher. Although the photo-current increases slightly when the temperature gets higher due to the diminution of the InGaN band-gap (Eg), the output voltage drops down significantly. This phenomenon is basically caused by the inverse proportionality of the electrostatic field with the temperature. This is to say, the higher the temperature, the lower the electrostatic field.
Rabeb Belghouthi et al. / Energy Procedia 157 (2019) 793–801 Rabeb Belghouthi,and Michel Aillerie / Energy Procedia 00 (2018) 000–000
799 7
Fig.4: The short circuit current of the In0.2Ga0.8N/GaN MQWs solar cell versus the temperature.
Fig.5: The open circuit voltage of the In0.2Ga0.8N/GaN MQWs solar cell versus the temperature.
Finally, we report in Fig. 8 the evolution of the efficiency, which represents the ratio of maximum converted power and incident irradiance versus temperature for InGaN/GaN MQWsolar cell.
800 8
Rabeb Belghouthi et al. / Energy Procedia 157 (2019) 793–801 Rabeb Belghouthi and Michel Aillerie / Energy Procedia 00 (2018) 000–000
Fig.6: Efficiency dependency of the In0.2Ga0.8N/GaN MQWs solar of the temperature.
It is clear, from Fig. 8. that the increase of temperature decreases significantly the efficiency of the SPCs. In order to achieve high efficiency solar cell based on this kind of structure; Gmilli et al. in Ref. [15] suggested to insert a GaN interlayers in the intrinsic region InGaN (semi-bulk). They proved that the new structure absorbs the excess of indium accumulated at the interface, which contributes to InGaN relaxation and improve the material quality. Belghouthi et al. [9-10] show that the solar cell efficiency of this kind of structure can be enhacing by taking the avantage of polarization. Finally, Biwole et al [16] also prove that the use of phase change material’s (PCM) behind the solar cell can maintain his temperature close of the ambient assuming optimum working conditions for best performance of the solar cell. 3. Conclusion This paper proposes a theoretical calculation based on the ideal diode and ideal quantum well model. The spontaneous and the piezoelectric polarizations as well as the temperature have been included within the developed model. As expected, it has been found that the temperature has a detrimental effect on GaN/InGaN MQWs performance. Accordingly, the obtained results would be accommodating to design and to fabricate a high solar cell performance. References [1] W.El Honi, A. Migan, Z. Djebbour, J.P Salvesrtrini and A. Ougazzaden. "High efficiency indium gallium nitride/Si tandem potovoltaic solar cells modeling using indium gallium nitride semibulk material: monotithic integration versus 4-terminal tandem cells."Progress in Photovoltaics 10.1002 (2016):2807. [2] J.Y. Chang, S.H. Yen, Y.A. Chang, and Y.K. Kuo. "Simulation of High-Efficiency GaN/InGaN p-i-n Solar Cell With Suppressed Polarization and Barrier Effects." IEEE Journal of Quantum Electronics 49 (2013). [3] .Y. Chang, S.H. Yen, Y.A. Chang, and Y.K. Kuo. "Simulation of High-Efficiency GaN/InGaN p-i-n Solar Cell With Suppressed
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Polarization and Barrier Effects." IEEE Journal of Quantum Electronics 49 (2013). [4] J. Y. Chang and Y. K. Kuo."Simulation of N-face InGaN-based p-i-n solar cells." J. Appl. Phys 112 (2012): 033109-1–033109-5. [5] K.H. Lee, P.C. Chang, S.J Chang. "AlGaN/GaN high electron mobility transistors based on InGaN/GaN multi-quantum-well structures with photo-chemical vapor deposition of SiO2 dielectrics."Microelectronic Engineering 104 (2013): 105-109. [6] J.Y. Chang, S.H. Yen, Y.A. Chang, and Y.K. Kuo. "Simulation of High-Efficiency GaN/InGaN p-i-n Solar Cell With Suppressed Polarization and Barrier Effects." IEEE Journal of Quantum Electronics 49 (2013). [7] Q. Deng, X.Wang, H.Xiao , C. Wang, H. Yin, H. Chen, Q.Hou, D. Lin, J. Li, Z. Wang and X. Hou. " An investigation on InGaN/GaN multiple quantum well solar cells. "J. Phys.D:Appl. Phys. 44 (2011) 6. [8] N.G. Anderson. "Ideal theory of quantum well solar cells."J.Appl. Phys. 78 (1195) 3. [9] R. Belghouthi, S. Taamalli, F. Echouchene, H. Mejri, H. Belmabrouk. "Modeling of polarization charge in N-face InGaN/GaN MQW solar cells." Materials Science in semiconductor Processing 40 (2015): 424-428. [10] R. Belghouthi, J.P. Salvestrini, M.H. Gazzeh and C. Chevalier. "Analytical modeling of polarization effects in InGaN double hetero-junction p-i-n solar cells. " Superlattices and Microstructures 100 (2016):168–178. [11] M. Nawaz and A. Ahmad. " A TCAD-based modeling of GaN/InGaN/Si solar cells. "Semiconductor Science and Technology 27 (2012) 9. [12] V. Fiorentini, F. Bernardini, and O. Ambacher. "Evidence for nonlinear macroscopic polarization in III–V nitride alloy heterostructures". Appl. Phys Lett 80 (2002)1204-1206. [13] O. Ambacher, J. Majewski, C. Miskys, A. Link,M. Hermann, M. Eickhoff, M. Stutzmann, F.Bernardini , V.Fiorentini , V.Tilak, B.Schaff, and L.F. Eastman. "Pyroelectric properties of Al(In)GaN/GaN hetero and quantum well structure". J. Phys. Condens.Matter 14 (2002) 33993434. [14] V. Gorge, A.M. Dubois, Z. Djebbour, K. Pantzas, S. Gautier, T. Moudakir, S. Suresh, A.Ougazzaden. " Theoretical analysis of the influence of defect parameters on photovoltaic performance of composition graded InGaN solar cells. " Materials Science and Engineering B 178 (2013) 142-148. [15] Y.El Gmili, G. Orsal, K. Pantzas, T. Moudakir, S. Sundaram, G. Patriache, J. Hester, A. Ahaitouf, J.P. Salvestrini, A. Ougazzaden, Acta Materialia 61 (2013) 6587-6596. [16] P B, Pierre E. F Kuznik "Phase-change materials to improve solar panel’s performance."2014