Summary of the reported records [14] and the calculated limits of Si and GaAs solar cells performances under the global AM1.5 spectrum.
\\n\\n
More than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\\n\\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\\n\\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\\n\\nAdditionally, each book published by IntechOpen contains original content and research findings.
\\n\\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\\n\\n\\n\\n
\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'
Simba Information has released its Open Access Book Publishing 2020 - 2024 report and has again identified IntechOpen as the world’s largest Open Access book publisher by title count.
\n\nSimba Information is a leading provider for market intelligence and forecasts in the media and publishing industry. The report, published every year, provides an overview and financial outlook for the global professional e-book publishing market.
\n\nIntechOpen, De Gruyter, and Frontiers are the largest OA book publishers by title count, with IntechOpen coming in at first place with 5,101 OA books published, a good 1,782 titles ahead of the nearest competitor.
\n\nSince the first Open Access Book Publishing report published in 2016, IntechOpen has held the top stop each year.
\n\n\n\nMore than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\n\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\n\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\n\nAdditionally, each book published by IntechOpen contains original content and research findings.
\n\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\n\n\n\n
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To be familiar with metrology requires choosing the best combination of techniques, standards, and tools to control a project from advanced simulations to final performance measurements and periodic inspections. This book contains a cluster of chapters from international academic authors who provide a meticulous way to discover the impacts of metrology in both theoretical and application fields. The approach is to discuss the key aspects of a selection of untraditional metrological topics, covering the analysis procedures and set of solutions obtained from experimental studies.",isbn:"978-1-78984-463-4",printIsbn:"978-1-78984-462-7",pdfIsbn:"978-1-83962-256-4",doi:"10.5772/intechopen.77475",price:119,priceEur:129,priceUsd:155,slug:"standards-methods-and-solutions-of-metrology",numberOfPages:106,isOpenForSubmission:!1,hash:"29d82c2091fb9ca1c49620000d170f2c",bookSignature:"Luigi Cocco",publishedDate:"October 2nd 2019",coverURL:"https://cdn.intechopen.com/books/images_new/7669.jpg",keywords:null,numberOfDownloads:2253,numberOfWosCitations:1,numberOfCrossrefCitations:3,numberOfDimensionsCitations:4,numberOfTotalCitations:8,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"October 24th 2018",dateEndSecondStepPublish:"December 6th 2018",dateEndThirdStepPublish:"February 4th 2019",dateEndFourthStepPublish:"April 25th 2019",dateEndFifthStepPublish:"June 24th 2019",remainingDaysToSecondStep:"2 years",secondStepPassed:!0,currentStepOfPublishingProcess:5,editedByType:"Edited by",kuFlag:!1,biosketch:null,coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"112023",title:"Dr.",name:"Luigi",middleName:null,surname:"Cocco",slug:"luigi-cocco",fullName:"Luigi Cocco",profilePictureURL:"https://mts.intechopen.com/storage/users/112023/images/system/112023.jpg",biography:'Dr. Luigi Cocco has received his master\'s degree in Telecommunication Engineering and his Ph.D. in Information Engineering before to join the automotive industry. Since 2005, From the Ferrari F1 Team to Automobili Lamborghini, he has worked on Electrical/Electronics systems; he has expertise in Research & Design, Supply Quality and Product Development. Currently, he is System Responsible for Passive Safety & ADAS of Maserati vehicles. His research interests include electronic measurements and digital signal processing, he has published several papers and three books with InTech: "Modern Metrology Concerns” (2012), "New Trends and Developments in Metrology” (2016) and "Standards, methods, and solutions of Metrology” (2018).',institutionString:"Maserati S.p.A.",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"0",totalChapterViews:"0",totalEditedBooks:"3",institution:null}],coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"1417",title:"Metrology",slug:"technology-metrology"}],chapters:[{id:"66092",title:"Metrological Traceability at Different Measurement Levels",slug:"metrological-traceability-at-different-measurement-levels",totalDownloads:502,totalCrossrefCites:2,authors:[{id:"94982",title:"Dr.",name:"Tetyana",surname:"Gordiyenko",slug:"tetyana-gordiyenko",fullName:"Tetyana Gordiyenko"},{id:"223340",title:"Prof.",name:"Oleh",surname:"Velychko",slug:"oleh-velychko",fullName:"Oleh Velychko"}]},{id:"66673",title:"Self-Calibration of Precision XYθz Metrology Stages",slug:"self-calibration-of-precision-xy-em-sub-z-sub-em-metrology-stages",totalDownloads:413,totalCrossrefCites:0,authors:[{id:"178057",title:"Prof.",name:"Chuxiong",surname:"Hu",slug:"chuxiong-hu",fullName:"Chuxiong Hu"}]},{id:"65687",title:"Third-Order Nonlinear Optical Properties of Quantum Dots",slug:"third-order-nonlinear-optical-properties-of-quantum-dots",totalDownloads:772,totalCrossrefCites:1,authors:[{id:"36065",title:"Dr.",name:"Khalil",surname:"Jasim",slug:"khalil-jasim",fullName:"Khalil Jasim"}]},{id:"67358",title:"Analysis of Pulsating White Dwarf Star Light Curves",slug:"analysis-of-pulsating-white-dwarf-star-light-curves",totalDownloads:261,totalCrossrefCites:0,authors:[{id:"265224",title:"Dr.",name:"Denis",surname:"Sullivan",slug:"denis-sullivan",fullName:"Denis Sullivan"}]},{id:"67258",title:"Biotoxicological Monitoring of Organic Solvents in the Tunisian Footwear Industry",slug:"biotoxicological-monitoring-of-organic-solvents-in-the-tunisian-footwear-industry",totalDownloads:307,totalCrossrefCites:0,authors:[{id:"186371",title:"Associate Prof.",name:"Imed",surname:"Gargouri",slug:"imed-gargouri",fullName:"Imed Gargouri"},{id:"188100",title:"Dr.",name:"Moncef",surname:"Khadhraoui",slug:"moncef-khadhraoui",fullName:"Moncef Khadhraoui"},{id:"294793",title:"Dr.",name:"Fatma",surname:"Omrane",slug:"fatma-omrane",fullName:"Fatma Omrane"}]}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"278926",firstName:"Ivana",lastName:"Barac",middleName:null,title:"Ms.",imageUrl:"https://mts.intechopen.com/storage/users/278926/images/8058_n.jpg",email:"ivana.b@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. 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Venkateswarlu",coverURL:"https://cdn.intechopen.com/books/images_new/371.jpg",editedByType:"Edited by",editors:[{id:"58592",title:"Dr.",name:"Arun",surname:"Shanker",slug:"arun-shanker",fullName:"Arun Shanker"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"47490",title:"Theoretical Calculation of the Efficiency Limit for Solar Cells",doi:"10.5772/58914",slug:"theoretical-calculation-of-the-efficiency-limit-for-solar-cells",body:'
In recent years there has been intense research work into the development of high efficiency solar cells relying on emerging novel materials and structures. All this has lead to a continuous record breaking of highest achievable efficiencies using different technologies. Since the first photovoltaic devices were developed the most prevalent concern is to hem in all sorts of efficiency losses preventing from reaching the physical limits [1-3]. To overcome this impediment, thorough investigations have been carried out to control and unearth their origins in order to identify potential efficiency advantages. Numerous thermodynamic approaches were employed to calculate solar cell efficiency limit, starting from the ideal Carnot engine to the latest detailed balance with its improved approach.
The aim of this chapter is to present a review of the techniques used to calculate the energy conversion efficiency limit for solar cells with detailed calculation using a number of numerical techniques. The study consists of analyzing the solar cell intrinsic losses; it is these intrinsic losses that set the limit of the efficiency for a solar energy converter. Several theoretical approaches were used in order to obtain the thermodynamic limit for energy conversion.
In the first place a solar cell could be considered as a simple energy converter (engine) able to produce an electrical work after the absorption of heat from the sun. In this fundamental vision the solar cell is represented by an ideally reversible Carnot heat engine in perfect contact with high temperature reservoir (the sun) and low temperature reservoir representing the ambient atmosphere. If the sun is at a temperature of 6000K and the ambient temperature is 300K, the maximum Carnot efficiency is about 95% this value constitutes an upper limit for all kind of solar converters.
When the solar cell is supposed a blackbody converter absorbing radiation from the sun itself a blackbody, without creating entropy, we obtain an efficiency of about 93 % known as the Landsberg efficiency limit, which is slightly lower than Carnot efficiency.
Whilst a solar cell is assumed as an endoreversible system [4], the energy conversion efficiency is limited to 85.7% this figure is obtained where the sun is assumed fully surrounding the cell (maximum concentration). If we bear in mind that in a real situation the solar cell does not operate always in maximum concentration and the solid angle under which the cell sees the sun is in fact only a minute fraction of a hemisphere, the maximum efficiency is not larger than 12.79%, which is actually lower than most recently fabricated solar cells. However, we can conclude that solar cell is a quantum converter and cannot be treated as a simple solar radiation converter [5].
Semiconductor pn junction solar cell is a quantum converter where the energy band-gap of semiconductor material is the most important and critical factor controlling efficiency. Incident photons with energy higher than the energy gap can be absorbed, creating electron-hole pairs, while those with lower energy are not absorbed, either reflected or transmitted.
In the ideal model of a monochromatic cell incident photons are within a narrow interval of energy, while the cell luminescence outside this range is prevented. The overall resulting efficiency upper limit for an infinite number of monochromatic cells is 86.81% for fully concentrated sun radiation.
The ultimate efficiency of a single band gap pn junction for an AM1.5 G solar spectrum gives a value of 49%, this maximum efficiency, if compared to Carnot efficiency limit, is substantially lower. Therefore in quantum converters it is obvious that more than 50% of the solar radiation is lost because of spectral mismatch.
To represent a more realistic picture of a solar cell, three other fundamental factors should be taken into account, namely; the view factor of the sun seen from the solar cell position, the background radiation which could be represented as a blackbody at ambient temperature, and losses due to recombination, radiative and non-radiative.
In the detailed balance efficiency limit calculation first suggested in 1961 by Shockley and Queisser (SQ) in their seminal paper [6]. It is assumed that illumination of semiconductor pn junction by a blackbody source creates electron-hole pairs due to the fundamental absorption of photons with energies greater than the band-gap. These pairs either recombine locally if they are not separated and extracted along different paths to perform work in an external circuit. They assumed that recombination in the semiconductor is partly radiative and the maximum efficiency is attained when radiative recombination in dominant. The Shockley-Queisser model has been extended and completed to account for more physical phenomena [7-13]. For instance, the generalised Planck radiation law introduced by Würfel [7], the effect of background radiation has been included and elaborate numerical techniques has been used in order avoid mathematical approximations which would yield erroneous results.
The currently achieved short-circuit current densities for some solar cells are very close to predicted limits [14]. Nevertheless, further gain in short-circuit current can therefore still be obtained, mainly by minimising the cell surface reflectivity, while increasing the thickness, so as to maximize the photons absorption. For thin film solar cells gain in photocurrent can be obtained by improving light trapping techniques to enhance the cell absorption.
Radiative recombination and the external fluorescence efficiency have a critical role to play, if the created photons are re-emitted out of the cell efficiently, which corresponds to low optical losses, the open circuit voltage and consequently the cell efficiency approach their limits [15]. Concentrating solar radiation onto a solar cell improves remarkably its performance. Comparable effect could be obtained if the solar cell emission and acceptance angles were made equal.
Thermodynamics has widely been used to estimate the efficiency limit of energy conversion process. The performance limit of solar cell is calculated either by thermodynamics or by detailed balance approaches. Regardless of the conversion mechanism in solar cells, an upper efficiency limit has been evaluated by considering only the balances for energy and entropy flux rates. As a first step the solar cell was represented by an ideally reversible Carnot heat engine in perfect contact with high temperature Ts reservoir (the sun) and low temperature Ta reservoir representing the ambient atmosphere. In accordance with the first law of thermodynamics the extracted work, the cell electrical power output, is represented as the difference between the net energy input from the sun and the energy dissipated to the surrounding environment. The model is illustrated in figure 1. Where Q1 is the incident solar energy impinging on the cell, Q2 is the amount of energy flowing from the converter to the heat sink and W is the work delivered to a load in the form of electrical energy (W=Q1\n\t\t\t\t\t– Q2). The efficiency of this system is defined using the first thermodynamic law as:
for a reversible engine the total entropy is conserved,
Hence the Carnot efficiency could be represented by:
This efficiency depends simply on the ratio of the converter temperature, which is equal to that of the surrounding heat sink, to the sun temperature. This efficiency is maximum (ηc=1) if the converter temperature is 0\n\t\t\t\t\tK and the solar energy is totally converted into electrical work, while ηc=0 if the converter temperature is identical to that of the sun Ts the system is in thermal equilibrium so there is no energy exchange. If the sun is at a temperature of 6000K and the ambient temperature is 300K, the Carnot efficiency is 95% this value constitutes an upper limit for all solar converters.
A schematic diagram of a solar converter represented as ideal Carnot engine.
Another way of calculating the efficiency of a reversible heat engine where the solar cell is assumed as a blackbody converter at a temperature Tc, absorbing radiation from the sun itself a blackbody at temperature Ts, without creating entropy, this efficiency is called the Landsberg efficiency[16].
Under the reversibility condition the absorbed entropy from the sun Sabs is given off in two ways one is emitted back to the sun Semit and the second part goes to the ambient thermal sink Sa. Under this condition, the solar cell is called reversible if:
In accordance with the Stefan–Boltzmann law of black body, the absorbed heat flow from the sun is:
For a blackbody radiation, the absorbed density of entropy flow is:
The energy flow emitted by the converter at a temperature Tc is:
And the emitted entropy flow is:
In this model the blackbody source (sun) surrounds entirely the converter at Tc which is assumed in a contact with a thermal sink at Ta then Tc=Ta. Therefore the entropy transferred to the thermal sink is:
And the transferred heat flow is:
The entropy-free, utilizable work flow is then:
Therefore the Landsberg efficiency can be deduced as:
The actual temperature of the converter Tc depends on the operating point of the converter and is different from the ambient temperature Ta, (Tc ≠ Ta). To maintain the same assumption as the Landsberg efficiency calculation, the entropy transferred to the ambient thermal sink is rewritten as:
We arrive to a more general form of the Landsberg efficiency η’:
Both forms of Landsberg efficiency (ηL and η’L) are plotted in Figure 2, Carnot efficiency curve is added for comparison. At 300K\n\t\t\t\t\tηL and η’L coincide at 93.33 % which is slightly lower than Carnot efficiency. When the temperature of the converter is greater than the ambient temperature (Tc > Ta) there is less heat flow from the converter to the sun (in accordance with Landsberg model). This means that much work could be extracted from the converter leading to a higher efficiency. As Tc approaches the sun temperature, the net energy exchange between the sun and the converter drops, therefore the efficiency is reduced and finally goes to zero for Tc=Ts.
Landsberg and Carnot Efficiency limits of a solar converter versus ambient temperature.
In the Landsberg model the blackbody radiation law for the sun and the solar cell has been included, unlike the previous Carnot engine.
This figure represents an upper bound on solar energy conversion efficiency, particularly for solar cells which are primarily quantum converters absorbing only photons with energies higher or equal to their energy bandgap. On the other hand in the calculation of the absorbed solar radiation the converter was assumed fully surrounded by the source, corresponding to a solid angle of 4π.
Using the same approach it is possible to split the system into two subsystems each with its own efficiency; the Carnot engine that include the heat pump of the converter at Tc and the ambient heat sink at Ta, with an efficiency ηc (ideal Carnot engine).
The ambient temperature is assumed equal to 300 K, therefore high efficiency is obtained when the converter temperature is higher then the ambient temperature.
The second part is composed of the sun as an isotropic blackbody at Ts and the converter reservoir assumed as a blackbody at a temperature Tc. The energy flow falling upon Qabs and emitted by the solar converter Qemit are given by:
In which f is a geometrical factor taking into account the limited solid angle from which the solar energy falls upon the converter. In accordance with the schematic representation of figure 3, where the solar cell is represented as a planar device irradiated by hemisphere surrounding area and the sun subtending a solid angle ωs at angle of incidence θ,\n\t\t\t\t\tf is defined as the ratio of the area subtended by sun to the apparent area of the hemisphere:
ωs being the solid angle subtended by the sun, where ωs=6.85×10-5 sr. The concentration factor C (C > 1) is a measure of the enhancement of the energy current density by optical means (lens, mirrors…).The maximum concentration factor is obtained if we take Ts=6000°K:
Then
The case of maximum concentration also corresponds to the schematic case where the sun is assumed surrounding entirely the converter as assumed in previous calculations.
Similar situation can be obtained if the solid angle through which the photons are escaping from the cell (emission angle) is limited to a narrow range around the sun. This can be achieved by hosing the cell in a cavity that limits the angle of the escaping photons.
A schematic representation of a solar converter as a planar cell irradiated by the sun subtending a solid angle ωs at angle of incidence θ.
The efficiency of this part of the system (isolated) is given by:
the resulting efficiency is simply the product:
This figure represents an overall efficiency of the entropy-free energy conversion by blackbody emitter-absorber combined with a Carnot engine. The temperature of the surrounding ambient Ta is assumed equal to 300K. When f is taken equal to ωs/π=2.18×10-5 and without concentration (C=1) we obtain a very low efficiency value (about 6.78%), as shown in figure 4. The efficiency for concentrations of 10, 100 and full concentration (46200) is found respectively 31.36, 53.48 and 85.38%. In this model the solar cell is not in thermal equilibrium with its surrounding (Tc ≠ Ta), then it exchanges radiation not only with the sun but also with the ambient heat sink. Therefore, energy can be produced or absorbed from the surrounding acting as a secondary source. Neglecting this contribution naturally decreases the efficiency of the converter, particularly at C=1. The second explanation of the low efficiency value is the under estimation of the re-emitted radiation from the cell, at operating conditions the solar cell re-emits radiation efficiently especially at open circuit point.
Efficiency ηac for different concentration rates (C=1, 10, 100 and Cmax) with Landsberg and Carnot Efficiency limits of a solar converter as a function of ambient temperature.
A more realistic model has been introduced by De Vos et al. [8] in which only a part of the converter system is reversible, endoreversible system. An intermediate heat reservoir is inserted at the temperature of the converter Tc, this source is heated by the sun at Ts (blackbody radiation) and acting as a new high temperature pump in a reversible Carnot engine. In this system the entropy is generated between the Ts reservoir and the converter, the temperature Tc is fictitious and is different from the ambient temperature Ta. The effective temperature Tc depends on the rate of work production. In this model the solar converter is assumed to behave like the Müser engine, itself a particular case of the Curzon-Ahlborn engine, as shown in Fig.5, the sun is represented by blackbody source at temperature T1=Ts the solar cell includes a heat reservoir assumed as blackbody at T3=Tc (the converter temperature) and an ideal Carnot engine capable of producing utilizable work (electrical power), however Tc is related to the converter working condition. This engine is in contact with an ambient heat sink at T2 representing the ambient temperature T2=Ta. In addition to the absorbed energy from the sun, the converter absorbs radiation from ambient reservoir assumed as a blackbody at Ta.
A schematic diagram of a solar converter represented as an endoreversible system.
The net energy flow input to the converter, including the incident solar energy flow
The Müser engine efficiency (Carnot engine):
The converter temperature can be extracted from ηM:
And the solar efficiency is defined as ratio of the delivered work to the incident solar energy flux:
hence
The maximum solar efficiency is then a function of two parameters; the Müser efficiency and the surrounding ambient temperature. From the 3d representation at figure 6 of the solar efficiency (ηs) against Müser efficiency ηM and the surrounding temperature Ta, the efficiency is high as the temperature is very low and vanishes for very high temperature (as Ta approaches the sun temperature). For Ta=289.23K the efficiency is 12.79% if the sun’s temperature is 6000°K.
The solar efficiency surface ηs (ηM, Ta), the sun as a blackbody at Ts=6000°K.
A general expression of solar efficiency of the Müser engine is obtained when the solar radiation concentration factor C is introduced:
Compared to Carnot efficiency engine the Müser engine efficiency, even when C is maximal, remains low.
If the ratio
Hence, the corresponding ηS becomes:
In the assumption of Ta=289.23K the maximum efficiency without concentration, i.e. the solar cell sees the sun through a solid angle ωs is 12.79% which is better than the predicted value of Würfel [7] but still very low, as shown in figure 8. For concentration equal to 10, 100 and CMAX, the efficiency reaches 33.9, 54.71 and 85.7% respectively.
The maximum solar efficiency using Müser engine for different concentration rates (C=1, 10, 100 and Cmax) with Carnot Efficiency limit as a function of ambient temperature.
The solar efficiency using Müser engine for different concentration rates (C=1, 10, 100 and Cmax) as a function of Müser efficiency.
In a quantum converter the semiconductor energy band-gap, of which the cell is made, is the most important and critical factor controlling efficiency losses. Although what seems to be fundamental in a solar cell is the existence of two distinct levels and two selective contacts allowing the collection of photo-generated carriers [2].
Incident photons with energy higher than the energy gap can be absorbed, creating electron-hole pairs, while those with lower energy are not absorbed, either reflected or transmitted. The excess energy of the absorbed energy greater than the energy gap is dissipated in the process of electrons thermalisation, resulting in further loss of the absorbed energy. Besides, only the free energy (the Helmholtz potential) that is not associated with entropy can be extracted from the device, which is determined by the second law of thermodynamics.
It is interesting to examine first an ideal monochromatic converter illuminated by photons within a narrow interval of energy around the bandgap
The number of created electron-hole pairs, in the assumption that each absorbed photon yields an electron-hole pair, could be simply represented by:
Where μeh is the emitted photon chemical potential, with μeh=Fn-Fp, (Fn, Fp are the quasi Fermi levels of electrons and holes respectively). The cell is assumed in thermal equilibrium with its surrounding ambient, then Tc=Ta.
This expression describes both the thermal radiation (for μeh=0) and emission of luminescence radiation (for μeh ≠ 0). The number of emitted photons from the cell is then:
This equation allows the definition of an equivalent cell temperature Teq from:
When a solar cell formed by a juxtaposition of two semiconductors p- and n-types is illuminated, an electrical voltage V between its terminals is created. This voltage is simply the difference in the quasi Fermi levels of majority carriers at Ohmic contacts for constant quasi Fermi levels and ideal Ohmic contacts, this voltage is equal to the chemical potential: qV=μeh=Fn-Fp.
At open circuit condition, the voltage Voc is given by a simple expression (deduced from (31)):
The density of work delivered to an external circuit (density of extracted electrical power) dW is:
The incoming energy flow from the sun can be written as:
The emitted energy density from the solar cell in a radiation form (radiative recombination) is:
The efficiency of this system is:
The work extracted from a monochromatic cell is similar to that extracted from a Carnot engine. The equivalent temperature of this converter is directly related to the operating voltage. At short-circuit condition it corresponds to the ambient temperature (μeh=0 then Teq,sc=Tc=Ta) whereas at open circuit condition and for fully concentrated solar radiation, the equivalent temperature is that of the sun, (dJ=0 then Teq,oc=Ts). For non-concentrated radiation (C ≠ CMax) at open circuit voltage Teq,oc is obtained by solving the equation
It is therefore possible to consider a monochromatic solar cell as reversible thermal engine (Carnot engine) operating between Teq,oc and Ta.
We can see that an ideal monochromatic cell, which only allows radiative recombination, represents an ideal converter of heat into electrical energy.
In order to find the maximum efficiency of such a cell as a function of the monochromatic photon energy (hνg), the dW=dJ×V versus V characteristic is used. We search for the point (dJmp, Vmp) corresponding to the maximum extracted power. The maximum chemical energy density (dWmp=dJmp× Vmp) is divided by the absorbed monochromatic energy gives the efficiency ηmono(Eg) as a function of the bandgap.
The monochromatic efficiency is considerable, particularly in the case of fully concentrated radiation (C=CMax), and rises with the energy bandgap, as shown in figure 9. In theory the connection of a large number of ideal monochromatic absorbers will produce the best solar cell for the total solar spectrum. To calculate the overall efficiency numerically, a fine discretization of the frequency domain is made; the sum of the maximum power density over the solar spectrum divided by the total absorbed energy density. The efficiencies resulting from this calculation are respectively 67.45% and 86.81% for non-concentrated and fully concentrated radiation.
To cover the whole solar energy spectrum an infinite number of monochromatic absorbers, each for a different photon energy interval, are needed. Each absorber would have its own Carnot engine and operate at its own optimal temperature, since for a given voltage the cell equivalent temperature depends on the photon energy (hνg). Finally this model can not be directly used to describe semiconductor solar cells where the electron-hole pairs are generated in bands and not discrete levels, besides if the cell is considered as a cascade of tow-level converters; the notion of effective or equivalent temperature is no longer valid, since for each set of levels a different equivalent temperature is defined.
The monochromatic efficiency against the photon energy corresponding to the energy band-gap of the cell for non-concentrated (C=1) and fully concentrated (C=Cmax) solar spectrum.
The total number of photons of frequency greater than νg (Eg=hνg) impinging from the sun, assumed as a blackbody at temperature Ts, in unit time and falling upon the solar cell per unit area Ns is given by:
This integral could be evaluated numerically.
In the assumption that each absorbed photon will produce a pair of electron-hole, the maximum output power density that could be delivered by a solar converter will be:
The solar cell is assumed entirely surrounded by the sun and maintained at Tc=0K as a first approximation and to get the maximum energy transfer from the sun. The total incident energy density coming from the sun at Ts and falling upon the solar cell, Pin is given by
In accordance with the definition of the ultimate efficiency [6, 17], as the rate of the generated photon energy to the input energy density, its expression can be evaluated as a function of Eg as follows:
This expression is plotted in figure 10, so the maximum efficiency is approximately 43.87% corresponding to Eg=1.12 eV, this energy band-gap is approximately that of crystalline silicon. Similar calculation of the ultimate efficiency taking the solar spectrum AM1.5 G (The standard global spectral irradiance, ASTM G173-03, is used [18]) is shown in figure 10 gives a slightly higher value of 49%. If one compares this efficiency to the aforementioned thermodynamic efficiency limits, most of them approach the Carnot limit for the special case where the converter’s temperature is absolute zero, this ultimate efficiency limit is substantially lower (44% or 49%) than the Carnot limit (95%). In quantum converters it is obvious that more than 50% of the solar radiation is lost because of the spectral mismatch. Therefore, non-absorption of photons with less energy than the semiconductor band-gap and the excess energy of photons, larger than the band-gap, are the two main losses.
The ultimate efficiency against the energy band-gap of the solar cell, using the AM1.5G spectrum with the blackbody spectrum at Ts=6000°K.
The detailed balance limit efficiency for an ideal solar cell, consisting of single semiconducting absorber with energy band-gap Eg, has been first calculated by Shockley and Queisser (SQ) [6]. The illumination of a pn junction solar cell creates electron-hole pairs by electronic transition due to the fundamental absorption of photons with hν > Eg, which is basically a quantum process. The photogenerated pairs either recombine locally or circulate in an external circuit and can transfer their energy. Their approach reposes on the following main assumptions; the probability that a photon with energy hν > Eg incident on the surface of the cell will produce a hole-electron pair is equal to unity, while photons of lower energy will produce no effect, all photogenerated electrons and holes thermalize to the band edges (photons with energy greater than Eg produce the same effect), all the photogenerated charge carriers are collected at short-circuit condition and the upper detailed balance efficiency limit is obtained if radiative recombination is the only allowed recombination mechanism.
The model initially introduced by SQ [6] has been improved by a number of researchers, by first introducing a more exact form of radiative recombination. The radiative recombination rate is described using the generalised Planck radiation law introduced by Würfel [7], where the energy carried by emitted photons turn out to be the difference of electron-hole quasi Fermi levels. While for non-radiative recombination the released energy is recovered by other electrons, holes or phonons.
In the following sub-section the maximum achievable conversion efficiency of a single band-gap absorber material is determined.
Now we consider a more realistic situation of a solar cell, depicted in figure 3. Three factors will be taken into account, namely; the view factor of the sun seen from the solar cell, the background radiation is represented as a blackbody at ambient temperature Ta, and losses due to recombination (radiative and non-radiative).
In steady state condition the current density J(V) flowing through an external circuit is the algebraic sum of the rates of increase of electron-hole pairs corresponding to the absorption of incoming photons from the sun and the surrounding background, in addition to recombination (radiative and non-radiative). This leads to a general current voltage characteristic formula:
with reference to the solar cell configuration shown in figure 3, Ts, Ta and Tc are the respective temperatures of sun, ambient background and solar cell. As defined previously, C and f are the concentration factor and the sun geometrical factor, while fRR represents the fraction of the radiative recombination rate or radiative recombination efficiency. If UNR and URR are the non-radiative and radiative recombination rates respectively, fRR is defined by:
The current density formula (43) can be rewritten in a more compact form as follows:
With:
Under dark condition and zero bias the current density must be null, then:
Therefore the current density expression becomes:
From the above J (V) expression we can obtain the short-circuit current density (Jsc=J(V=0)) as follows:
In the ideal case the short-circuit current density depends only on the flux of impinging photons from the sun and the product Cf, recombination has no effect. The term φa in Jsc, representing the radiation from the surrounding ambient is negligible. The total photogenerated carriers are swept away and do not recombine before reaching the external circuit where they give away their electrochemical energy. Figure 11 illustrates the maximum short-circuit current density to be harvested against band-gap energy according to (49) for a blackbody spectrum at Ts=6000°K normalised to a power density of 1000W/m2 and a spectral photon flux corresponding to the terrestrial AM1.5G spectrum. Narrow band-gap semiconductors exhibit higher photocurrents because the threshold of absorption is very low, therefore most of the solar spectrum can be absorbed. For power extraction this is not enough, the voltage is equally important and more precisely, the open circuit voltage.
The currently achieved short-circuit current densities for some solar cells are very close to predicted limits. Nevertheless, further gain in short-circuit current can therefore still be obtained, mainly by minimising the cell surface reflectivity, while increasing its thickness, so as to maximize the photon absorption. For thin film solar cells the gain in Jsc can be obtained by improving light trapping techniques to enhance the cell absorption.
For instance crystalline silicon solar cells with an energy band-gap of 1.12 eV at 300K has already achieved a Jsc of 42.7 mA/cm2 compared to a predicted maximum value of 43.85 mA/cm2 for an AM1.5 global spectrum (only 39.52 mA/cm2 for a normalised blackbody spectrum at 6000°K), while for GaAs with Eg=1.43eV a reported maximum Jsc of 29.68 mA/cm2 compared to 31.76 mA/cm2 (only 29.52 mA/cm2 for a normalised blackbody spectrum at 6000°K) [14].
\n\t\t\t | \n\t\t\t\t\n\t\t\t\t\tJsc(mA/cm2)\n\t\t\t\t\n\t\t\t | \n\t\t\t\n\t\t\t\t\n\t\t\t\t\tVoc(V)\n\t\t\t\t\n\t\t\t | \n\t\t\t\n\t\t\t\t\n\t\t\t\t\tη (%)\n\t\t\t\t\n\t\t\t | \n\t\t|||
Limit | \n\t\t\trecord | \n\t\t\tlimit | \n\t\t\trecord | \n\t\t\tlimit | \n\t\t\trecord | \n\t\t|
Si | \n\t\t\t43.85 | \n\t\t\t42.7 | \n\t\t\t0.893 | \n\t\t\t0.706 | \n\t\t\t34.37 | \n\t\t\t25.0 | \n\t\t
GaAs | \n\t\t\t31.76 | \n\t\t\t29.68 | \n\t\t\t1.170 | \n\t\t\t1.122 | \n\t\t\t33.72 | \n\t\t\t28.8 | \n\t\t
Summary of the reported records [14] and the calculated limits of Si and GaAs solar cells performances under the global AM1.5 spectrum.
The maximum short-circuit current density against the energy band-gap of the solar cell, using the AM1.5G spectrum with the blackbody spectrum at Ts=6000°K.
At open circuit condition electron-hole pairs are continually created as a result of the photon flux absorption, the only mechanism to counter balance this non-equilibrium condition is recombination. Non-radiative recombination could be eliminated, whereas radiative recombination has a direct impact on the cell efficiency and particularly on the open circuit voltage. The radiative current as the rate of radiative emission increases exponentially with the bias subtracts from the current delivered to the load by the cell. At open circuit condition, external photon emission is part of a necessary and unavoidable equilibration process [15]. The maximum attainable Voc corresponds to the condition where the cell emits as many photons as it absorbs. The open circuit voltage of a solar cell can be found by taking the band gap energy and accounting for the losses associated with various sources of entropy increase. Often, the largest of these energy losses is due to the entropy associated with radiative recombination.
In the case where qV is several kT smaller than
The current density expression becomes then:
The open circuit voltage can be deduced directly from this expression as:
The open circuit voltage is determined entirely by two factors; the concentration rate of solar radiation C (C ≥1) and radiative recombination rate fRR (fRR ≤1).
Radiative recombination has a critical role to play, if the created photons are re-emitted out of the cell, which corresponds to low optical losses, the open circuit voltage and consequently the cell efficiency approach the SQ limit. Therefore the limiting factor for high Voc (efficiency) is the external fluorescence efficiency of the cell as far as radiative recombination is concerned. Since the escape cone is in general low, efficient external emission involves repeated escape attempts and this is ensured by perfect light trapping techniques. In this case the created photons are allowed to be reabsorbed and reemitted again until they coincide with the escape cone, reaching high external fluorescence efficiency [15, 18-19].
So dominant radiative recombination is required to reach high Voc and this is not sufficient to reach the SQ limit, the other barrier is to get the generated photons out of the cell and this is limited by the external fluorescence efficiency ηfex. Hence, the external fluorescence efficiencyηfex, is introduced in the expression of Voc and fRR is multiplied by ηfex, (ηfex ≤ 1) then:
If we define a maximum ideal open circuit voltage value Voc,max for fully concentrated solar radiation (C=Cmax=1/f) and when the radiative recombination is the only loss mechanism with maximum external fluorescence efficiency (i.e, fRRηfex=1), then:
It is worth mentioning that (56) is not an exact evaluation of Voc. As shown in figure 12.b equation (56) for narrow band-gap semiconductors yields wrong values of Voc,max (above Eg/q line), acceptable values are obtained only for Eg greater than 2 eV, where it coincides with the result obtained when solving numerically (45) for J(V)=0.
From this figure one can say that taking Voc,max=Eg/q is a much better approximation; thus, instead of (56) we can use the following approximation:
A more accurate value of Voc is obtained after numerical resolution of equation (45) for J(V)=0, the results are plotted in figure12a and 12.b.
The other type of entropy loss degrading the open-circuit voltage is the photon entropy increase due to isotropic emission under direct sunlight. This entropy increase occurs because solar cells generally emit into 2π steradian, while the solid angle subtended by the sun is only 6.85×10−5 steradian.
The most common approach to addressing photon entropy is a concentrator system. If the concentration factor C of sun radiation is increased, this is generally achieved by optical means, a significant increase of Voc is obtained (as shown in figure 12.b). The calculation is carried out assuming a dominant radiative recombination and with maximum external fluorescence efficiency (fRRηfex=1). In this case we can notice that as C is increased Voc approaches its ultimate value Eg/q, for example GaAs (Eg=1.43 eV) for C=CMax we get Voc=0.99×Eg/q=1.41 V, which corresponds to an efficiency limit of approximately 38.5% (blackbody spectrum at 6000K). This theoretical limit shows the importance of dealing with entropy losses associated with angle of acceptance of photons from the sun and emission of photons from the cell efficiently. This value is well above the predicted SQ limit, where the concentration factor was considered.
The Voc/Eg against energy band-gap of the solar cell, using a blackbody spectrum at Ts=6000°K; a)-for different radiative recombination rates, b)-for different solar concentrations and a plot of (56) for C=Cmax.
With reference to table 1 we can clearly see that the record open circuit voltage under one-sun condition (C=1) of gallium arsenide solar cell (1.12 V) is already close to the SQ limit (1.17 V) while silicon solar cell is still behind with a record Voc of 0.706 V compared to a limit of 0.893 V, this difference is due to the fact that GaAs has a direct band gap, which means that it can be used to absorb and emit light efficiently, whereas Silicon has an indirect band gap and so is relatively poor at emitting light. Although Silicon makes an excellent solar cell, its internal fluorescence yield is less than 20%, which prevents Silicon from approaching the SQ limit [20]. On the other hand It has been demonstrated that efficiency in Si solar cells is limited by Auger recombination, rather than by radiative recombination [20-22].
Energy conversion efficiency η is usually known as the most relevant figure for solar cell performance. Solar cell efficiency is calculated by dividing a cell\'s electrical power output at its maximum power point by the input solar radiation and the surface area of the solar cell. The maximum power output from the solar cell is obtained by choosing the voltage V so that the product current-voltage (IV) is a maximum. This point corresponds to the situation where a maximum power is extracted from the cell. Using equation 45 we can define the power delivered by a cell as:
The maximum power
For AM1.5G solar spectrum Pin is replaced by 1000.
Figure 13 illustrates efficiency against energy band-gap of a solar cell, using the AM1.5G spectrum and the blackbody spectrum at Ts=6000°K for one sun and full concentration (C=CMax), the only recombination mechanism is radiative and 100% external fluorescence efficiency, which means that all emitted photons from the cell (issue from radiative recombination) are allowed to escape. The maximum efficiency is 34.42% for AM1.5G corresponding to a gap of 1.34 eV, for a blackbody spectrum normalized to 1000 W/m2 the maximum efficiency is 31.22% at 1.29 eV, while for a full solar concentration the maximum is 40.60% at 1.11 eV, this confirms the fact that the optimal band gaps decrease as the solar concentration increases.
In figure 14 the product of radiative recombination rate and the external fluorescence efficiency (
The maximum efficiency against the energy band-gap of the solar cell, using the AM1.5G spectrum with the blackbody spectrum at Ts=6000°K for one sun and full concentration (C=CMax).
The maximum efficiency against the energy band-gap of the solar cell, using the AM1.5G spectrum with the blackbody spectrum at Ts=6000°K for one sun and full concentration (C=CMax)
Since the power output of the cell is determined by the product of the current and voltage, it is therefore imperative to understand what material properties (and solar cell geometries) boost these two parameters. Certainly, the short-circuit current in the solar cell is determined entirely by both the material absorption property and the effectiveness of photo-generated carriers collection at contacts. As previously mentioned (section 2.4.1), the manufactured solar cells with present technologies and materials have already achieved short-circuit currents close to predicted limits. Therefore the shortfall in efficiency could be attributed to the voltage. We show here that the key to reaching the highest possible voltages is first to have a recombination predominantly radiative with a maximal external emission of photons from the surface of the solar cell. Secondly we need a maximum solar concentration. The second condition could be achieved either by using sun concentrators, there are concentrators with concentration factor from ×2 to over ×1000 [23] or by non-concentrating techniques with emission and acceptance angle limited to a narrow range around the sun [24-26].
At this level we can conclude that the efficiency limit of a single energy gap solar cell is bound by two intrinsic limitations; the first is the spectral mismatch with the solar spectrum which retains at least 50% of the available solar energy. The best known example of how to surmount such efficiency restraint is the use of tandem or stacked cells. This alternative will become increasingly feasible with the likely evolution of materials technology over the decades to 2020 [27].
The second intrinsic loss is due to the entropy associated with spontaneous emission. To overcame this limitation three conditions should be satisfied, that is: a) – prevailing radiative recombination (to eliminate the non-collected electro-hole pairs), b)-efficient external fluorescence (to maximise the external emission of photons from the solar cell) and c)-using concentrated sun light or restricting the emission and acceptance angle of the luminescent photons to a narrow range around the sun.
For single junction cell the record at present is 28.8% (GaAs) [14] compared to the SQ limit of 33.7% which is a significant accomplishment and little room has been left for improvement. Immense experimental research is now directed towards maximizing the external emission of photons from the solar cell. One way of getting beyond the SQ limit for a single junction is the use of concentrated radiation, the current record for concentrator cell is only 29.1% (GaAs) under 117 suns [14], this technology has a number of challenging problems (such as tracking and cooling systems) and there is still a long way to go. The same goal is accomplished by matching the angles under which light impinges from the sun and into which light is emitted from the solar cell. Recently it has been demonstrated that light trapping GaAs solar cell with limited emission angle efficiencies above 38% may be achievable with a single junction solar cell [25].
To overcome the restrictions of a single junction solar cell several directions were investigated during the last decades (i.e. hot carrier cells, carrier multiplication and down-conversion, impurity photovoltaic and multiband cells, thermophotovoltac and thermophotonic conversion…).
The most widely explored path has been tandem or stacked cells; they provide the best known example of how such high efficiency might be achieved. The present efficiency record for a triple junctions cell (InGaP/GaAs/InGaAs) is 37.9% compared to a predicted value of over 51% for an optimised set of three stacked cells [28, 29]. The major technological challenge with tandem solar cells is to find materials with the desired band gaps and right physical properties (i.e. lattice constant and thermal parameters). The ultimate efficiency target for this kind of configuration is 86.81% (for a set of an infinite number of stacked monochromatic cells under maximum solar concentration) which constitutes an arduous target, corresponding to an infinite number of stacked junctions radiated by a maximum solar concentration. The best performance that the present technology can offer is 44.4% using a triple junction GaInP/GaAs/GaInAs cell under 302 suns [14].
The author would like to thank Professor Helmaoui A. for his valuable and helpful discussions throughout the preparation of this work.
About 10 years ago, a duration of 300 min was the upper limit for a physiological parturition [1]. Since then, litter size and farrowing duration increased steadily [1]. Nowadays, sows are hyperprolific (average litter size > 16) with an average farrowing duration of longer than 300 min [1, 2, 3, 4, 5, 6, 7]. This means that more than half of all parturitions are longer than physiologically. This rapid increase is concerning and leads to a high incidence of dystocia with subsequent negative consequences on piglet survival and sows’ fertility and longevity [1, 2, 3, 4, 5, 6, 7]. An older survey showed that dystocia was mostly of maternal origin [8], whereas a newer survey identified that dystocia is nowadays almost exclusively due to maternal causes; with uterine inertia being the most common cause [9]. Primary uterine inertia, which is the reduction or complete absence of contractility of the myometrium already at the beginning of parturition, is due to hormonal abnormalities such as increased progesterone, and/or deficiencies of oxytocin and prostaglandin secretion and/or the presence of their receptors. Stress, e.g., caused by the inability of sows to express normal nest-building behavior, is an important cause of primary uterine inertia [10]. Other causes are nutritional factors, e.g., diets low in fiber and high in energy leading to constipation and obesity [11]. Secondary uterine inertia is more common than primary inertia, usually occurring because of a prolonged farrowing particularly associated with a large litter size [12]. Idiopathic dystocia may occur because of the use of prostaglandin F2α and oxytocin to induce or control parturition [12].
\nThus, in order to prevent birth complications, the needs of the sow must be fulfilled, stress must be avoided, and nutrition must be optimized. If not, hormonal imbalance will result into weak uterine contraction and subsequently dystocia. Therefore, active birth management starts before birth in order to prevent this and continues during birth when proper response to hormonal imbalance is needed.
\nSufficient mammary gland development is important for optimal colostrum production and therefore prevention of piglet mortality [13]. Pre-weaning piglet mortality rate was 7.1% (reference value: <11%), when piglets ingested more than 200 g of colostrum, and increased to 43.4% when intake was less than 200 g [14]. Thus, piglets need at least 200 g of good quality (>50 mg IgG/ml) colostrum. Unfortunately, colostrum yield is highly variable, averaging 3.5 kg and ranging between 1.5 and 6.0 kg [15, 16]. This means that some sows will not produce enough colostrum for their piglets. Further, even though the average yield might be enough for a litter of average size (about 17–18 piglets), it can be difficult for many sows to adequately nurse more than 10–11 piglets without human assistance (such as assisted suckling, cross fostering, movement to a nurse sow, split or suckling assistance) [17]. Thus, factors affecting mammary gland development and colostrum production need to be identified and optimized [13]. One of these factors is the hormonal status of the sow, which can be because of stress, suboptimal feeding, and husbandry during the week(s) before parturition.
\nBesides the production of a sufficient amount of good quality colostrum, there are further challenges. One of them is the length of the colostral phase. Colostrum is produced only during the first day after the start of parturition. Already after the first 6 h, the IgG content in colostrum is halved [18]. Since large litters can easily extend farrowing beyond 6 h [1], many piglet are born too late in order to get an appropriate amount of good quality colostrum. Therefore, the goal at each parturition is not only to optimize colostrum production by the sow but also the colostrum uptake by neonate piglets. Neonate piglets must acquire a sufficient amount of immunoglobulins from ingested colostrum for energy and passive immune protection [19]. The concentration of immunoglobulins in the plasma of piglets shortly after birth correlates positively with their survival rate [20]. Thus, it is necessary to assess colostrum quality and colostrum intake by piglets throughout parturition in order to reduce piglet pre-weaning mortality. This is especially important if mammary gland development is low and/or parturition is prolonged.
\nPDS is the most important puerperal disease and is characterized by insufficient colostrum and milk production by the sow during the first days of lactation [21]. As consequence, colostrum and milk intake by piglets is reduced, and therefore their mortality increased [21]. Further, PDS negatively affects subsequent reproductive health of the sow [4]. Unspecific symptoms for PDS include fever (>40°C), loss of appetite, and lethargy [21]. Specific symptoms are dysgalactia and vulvar discharge syndrome [21]. Causes of the vulvar discharge syndrome are vaginitis, endometritis, and cystitis [22].
\nAn increasing incidence for PDS of up to 34% was recently reported [23], which is connected with the increase in litter size and farrowing duration [3]. In one study, the percentage of sows with fever during the first 24 h postpartum increased from 40 to 100%, when the farrowing duration increased from less than 2 to more than 4 h [24]. Furthermore, until the third day postpartum, the percentage of sows with reduced appetite was higher in sows with a farrowing duration of more than 4 h than in sows with less than 4 h [24]. In another study, 85.9% of sows with puerperal disease had farrowing durations of more than 6 h, whereas 78.8% of healthy sows completed parturition in less than 3 h [25].
\nBoth prolonged farrowing and PDS share mutual risk factors [11, 21]. Further, both are connected with a decrease in subsequent fertility [4, 5, 26]. Thus, prevention of birth complications and proper birth management will also prevent postpartum disease and therefore optimize subsequent reproductive performance.
\nProper management of hyperprolific sows in order to optimize piglet survival and sow’s reproductive health starts before parturition. The aim is to improve mammary gland development and colostrum production as well as to prevent birth complications and puerperal diseases. In order to do so, optimizing environment, management, and nutrition is highly important. Table 1 provides a checklist for preventive measures.
\nChecklist for prevention of birth complications and puerperal diseases as well as for improving mammary gland development and colostrum production.
Modern housing and production systems have promoted the confinement of sows in crates during farrowing. In crates, the sow’s movement is severely restricted, and bedding and rooting material is often limited. Consequently, nest-building behavior is reduced or does not occur at all. The lack of space and absence of nest-building materials and behavior are important stressors in sows [27]. This promotes the release of opioids and results into decreased oxytocin secretion and reduced uterine contractility [10, 28]. Thus, the lack of space and bedding material can prolong parturition due to uterine inertia. Considering that a large litter itself can prolong parturition [1, 12], hyperprolific sows need access to space and rooting material in order to prevent birth complications. Allowing the sow to move freely before and during farrowing reduces the duration of farrowing by an average of 100 min, thereby reducing the risk of stillborn piglets and birth of piglets with low vitality [12].
\nBesides an increase in oxytocin secretion, proper nest-building behavior increases prolactin [29], which is essential for colostrum production. The prepartum decrease in progesterone leads to an increase in prolactin [30]. Delays in progesterone decrease and in prolactin increase relative to the onset of parturition were associated with a strongly reduced yield of colostrum [31]. Thus, as with farrowing duration and prevention of birth complications, studies have found a positive effect of provision of space and nest-building material on oxytocin and prolactin release and therefore colostrum production and maternal nursing behavior [32].
\nProper management, especially hygiene, is highly important for the prevention of PDS and therefore piglet mortality and decreased fertility in sows [21]. The current hypothesis is that interactions between endotoxins produced by Gram-negative bacteria in the gut, mammary gland, and/or urogenital tract and alterations in the immune and endocrine functions play a central role in the development of PDS [21]. This is supported by a study where periparturient sows were challenged with lipopolysaccharide (LPS) endotoxin of E. coli, in which sows generated symptoms similar to PDS [33]. E. coli originates from the environment or can already be present in the urogenital tract of prepartum sows or enter during or after parturition. Predominantly, E. coli followed by Staphylococcus spp. and Streptococcus spp. are isolated from the urogenital tract in case of cystitis, endometritis, and mastitis [34, 35]. Considering that these are unspecific bacteria originating from feces and environment, it is important to keep hygiene before and during parturition at a high level [36]. Risk factors for PDS are the use of unslatted floor, no washing of sows and no use of disinfectants in the farrowing rooms [36].
\nBesides hygiene, alterations in the immune and endocrine functions play a central role in the development of PDS [21]. Considering that parturition itself decreases immunity and causes significant inflammatory changes [23], all other factors affecting immunity and endocrinology need to be kept at a minimum level. The most important factor is stress, as described above. Stress needs to be reduced as much as possible. Stress due to restricted space in farrowing crates and lack of nest-building material is discussed above [21]. Other stressors are high ambient temperature and abrupt change from group housing during gestation to restraint in crates a few days before farrowing [37, 38].
\nNutrition and body condition are important to prepare the sow for farrowing and the production of colostrum and milk. The sow should have an optimal body condition around parturition. Obesity needs to be avoided [11]. The fatter the sow, the longer the duration of parturition. It is possible that the fat deposition stores lipid-soluble steroids such as progesterone. In this case, the prepartum decline in progesterone may be delayed which in turn affects oxytocin receptor activation [10, 12]. Low concentration of oxytocin receptors will result in weak uterine contractions and colostrum let-down. Higher backfat and progesterone lead also to lower colostrum quality and production [39, 40]. If possible, backfat should be between 16 and 20 mm [11].
\nBesides body condition, there is a negative correlation between constipation and farrowing duration [11]. The more constipated the sow, the longer the duration of parturition. One reason may be that constipation can cause a physical obstruction to the passage of the piglets [12]. Another reason may be that constipation may result in higher concentrations of LPS. LPS can be absorbed from the gut and affect normal endocrine changes associated with farrowing [41]. A third explanation may be that the discomfort and pain associated with constipation affect hormonal changes associated with parturition [12]. Studies have found that pain releases opioids, which inhibit oxytocin secretion during parturition [28, 42]. Therefore, pain due to prolonged constipation, or any other source of pain, can reduce myometrial contractions and therefore cause birth complications. Constipation can be evaluated using a constipation index [43]. Constipation index should be two or higher, i.e., feces should be present, pellet-shaped, and not dry [11].
\nIn order to prevent constipation and obesity, ad libitum feeding in the last third, especially in the last week, of gestation should be avoided. Restricted feeding supports the birth process, mammary gland development, and colostrum production [44]. There were positive associations between colostrum yield and plasma concentrations of urea, creatinine, and free fatty acids [45]. Further, there was a positive association between backfat loss in the last third of gestation and colostrum yield [46]. These results show that feed restriction with protein and fat mobilization for metabolism has positive effects on colostrum production [30]. Nevertheless, this can probably only be recommended for sows that have reached a good body condition (>18 mm) at the end of gestation. Unfortunately, sows usually receive high-energy concentrated diet low in fiber during late gestation [47]. Such diets can promote obesity and constipation, leading to poor mammary gland development [30], low colostrum quality [48], birth complication [11], and PDS [21, 49]. Late pregnancy diets should contain at least up to 7–10% fiber [43]. A good fiber source can also be provided by offering different types of roughage, e.g., straw or hay, or adding any other feedstuffs with high levels of fiber such as sugar beet pulp [50].
\nBesides amount and composition of feed, the feeding intervals are important. A short time-lapse between the last meal prior to the onset of the expulsion stage and the onset considerably shortens the duration of farrowing [51]. Farrowing duration, odds for farrowing assistance, and odds for stillbirth were low, intermediate, and high when the time between the last meal and onset of parturition was less than 3, 3–6, and more than 6 h, respectively [51].
\nIn addition to improving mammary gland development by means of management, environment, and nutrition, the mammary gland needs to be evaluated before each parturition. It is important to assess the number and morphology of functional teats and the degree of edema. The number of functional teats available per piglet is positively associated with piglet survival [52]. If piglets had access to less than one functional teat, mortality increased to more than 14% [52]. If more than one teat was available, mortality was reduced to below 8% [52]. Besides the number of functional teats, also the morphology is important. Piglets tend to suck first from teats that are close to the abdominal midline and have longer inter-teat distances [53]. Thus, a functional teat with short inter-teat distance and/or long distance between teat base and abdominal midline may be unusable for the piglet [54].
\nFurthermore, severe edema of the mammary gland before parturition will have a negative impact on teat accessibility, reduce colostrum quality, and increase the risk of PDS [48, 49]. The degree of mammary gland edema can be graded visually or via ultrasound [48, 49, 55]. At visual inspection, sows with severe udder edema have dimpled skin with persistent marks of the floor (Figure 1A). Further, teats are swollen and mammary glands are indistinct (Figure 1A) [48, 49]. Ultrasound of the mammary glands shows thickened dermal and subdermal tissues, hyperechoic lobuloalveolar tissue with enlarged blood vessels, and severe shadowing (Figure 1B) [48, 49, 55]. Also at the end of lactation, the assessment of the mammary gland, as described above, is crucial and should be used for the decision of removing the sow from the herd.
\nSevere prepartum edema of the mammary gland. Visual inspection (A) reveals dimpled skin with persistent marks of the floor, swollen teats, and indistinguishable gland complexes. Ultrasonographic image (B) shows shadowing, thickened dermal tissue, hyperechoic lobuloalveolar tissue, and enlarged blood vessels, lymphatic ducts, and milk ducts. Images taken by Stefan Björkman.
During parturition, it is important to recognize birth complications and treat accordingly. Further, evaluation of colostrum quality is necessary in order to know whether the sow has good quality colostrum or if piglets need additional colostrum from another sow. Also, the vitality and colostrum uptake of the piglets need to be assessed. Piglets with low vitality and low colostrum uptake are at risk of starving and hypothermia. Both increase piglet mortality, especially due to crushing by the sow. Tables 2 and 3 provide protocols for diagnosis and treatment of birth complications. Tables 4 and 5 provide guidelines for the assessment of colostrum quality and piglet vitality.
\nRisk factors for birth complications. Farrowing supervision should occur every 30 min when sow is at risk. Otherwise, farrowing supervision once an hour.
Guideline for evaluating colostrum quality (colostrum collected from several anterior teats within 0–3 h from the start of farrowing) using Brix refractometer [70].
Behavioral and physiological indicators of low colostrum intake and neonatal mortality.
Appropriate and prompt treatment of a sow with birth complications is important to avoid still- or weak-born piglets and to increase piglets’ health and survival. This can be achieved through continuous farrowing supervision [56]. Farrowing supervision is also necessary for reducing the risk of puerperal disease [38]. Already before parturition, it is important to spot those sows that may be at risk of dystocia. These sows are usually gilts or old sows (≥6 parity), thin (≤14 mm) or fat (≥23 mm) sows, constipated sows (<2), and sows with history of birth complications and birth of still and weak piglets [11, 57]. These sows need an obstetrical examination if more than 30 min have passed since the last piglet was expelled (Table 2) [12]. This applies also to sows that are restless and have strong abdominal contractions during parturition or to sows with prolonged parturition (>300 min) [12]. Obstetric intervention is usually not indicated before 1–15 h has passed since the last piglet was born in sows without risk for dystocia, which are at the beginning of parturition (<300 min since the expulsion of the first piglet) and show no signs of strong abdominal straining or restlessness [11, 12, 57]. Restlessness can occur if stress and pain are present [58]. For instance, increased stress induces higher frequency of postural changes and longer duration of standing position of sows during the expulsion stage of parturition [58].
\nWhenever the abovementioned criteria are fulfilled, an obstetrical examination needs to be performed. An obstetric examination includes palpation and ultrasonography of the birth canal [12, 59]. Palpation of the birth canal should always occur through the rectum and not through the vagina. Vaginal palpation can lead to an increased risk of subsequent dystocia, stillborn piglets, and PDS [3, 7, 12, 57]. Rectal palpation is necessary to determine the exact cause of dystocia before any intervention is undertaken. When no piglet is felt within the birth canal, then the cause of dystocia is uterine inertia [8, 9, 12]. Other causes are, e.g., obstruction of the birth canal due to ventral deviation of the uterine horns or fetal malposition [8, 9, 12]. After these obstructive causes are ruled out, treatment for uterine inertia can be applied [12].
\nUltrasonography can be used to determine whether farrowing is over or if the sow has retained piglets [59] or placentae [60] (Figure 2).
\nTransabdominal ultrasonographic image of a non-expelled piglet (A; arrows indicate vertical and horizontal dimension) and placentae (B; arrows indicate placentae). Scale bars on right margins in 1 cm steps. Images taken by Alexander Grahofer (A) and Stefan Björkman (B).
Oxytocin, an uterotonic agent, is used during farrowing to treat dystocia by provoking uterine contractions [61]. If primary uterine inertia occurs, before administration of any exogenous oxytocin, we recommend trying means of releasing endogenous oxytocin, e.g., manual induction of the Ferguson reflex and massaging the udder of the sow [8]. Furthermore, movement and physical exercise of the sow have positive effects on the farrowing duration, especially if the sow is still at the beginning of the second phase [12]. If that does not help, we recommend waiting for at least 30 min. Often progesterone has not fully declined and oxytocin receptors are not fully expressed [62], which makes oxytocin administration contraindicated. In this case, possible stressors and sources of pain should be investigated, and provision of nest-building material or application of pain medication may be indicated. If the sow is constipated, removing feces from the rectum by hand is beneficial.
\nImmediate application of exogenous oxytocin is indicated if secondary uterine inertia is diagnosed towards the end of the second phase of parturition [12]. Several studies were conducted to prove the effect of oxytocin on the birth process and piglet survivability and to evaluate the proper dosage of oxytocin in dystotic sows [63, 64, 65]. An intramuscular administration of 10 IU of oxytocin did not cause any side effects. However, higher dosages led to an increase in stillborn piglets, changes in the umbilical cord, and higher meconium scoring [63, 64, 65]. Furthermore, the improper use of oxytocin can lead to unwanted side effects. These side effects are increased uterine inertia and manual assistance [66, 67] as well as ruptured or damaged umbilical cord [68] and decreased placental blood flow [69]. Hence, we recommend administering oxytocin only restrictively, e.g., 5–10 IU one to two times during parturition [12].
\nIt is possible to easily collect colostrum during parturition due to the almost continuous (every 5–40 min) milk ejections [29]. A brix refractometer can be used for quality assessment. Brix refractometer can be an inexpensive, rapid, and satisfactorily accurate method for estimating IgG concentration on farm [70, 71]. We recommend collecting a colostrum from several anterior teats within 0–3 h from the start of farrowing when the IgG level peaks [70]. If this is done early during parturition, sows with low-quality colostrum can be spotted and more support to her litter, e.g., assisted nursing and split suckling, can be provided. Nevertheless, it is possible to determine colostrum quality at any stage of parturition. This may be indicated if piglets are born late (farrowing duration > 12 h). Differentiation between good and poor IgG content of colostrum is possible interpreting the results with the categories proposed in Table 3. Colostrum with an IgG level of 50 mg IgG/ml is considered of good quality [14]. When Brix values are <20%, they reflect very low levels of IgG, while values from 25% upwards are considered to correspond to good or very good concentration of IgG in colostrum. Results between 20 and 24% are defined as borderline [70]. With borderline results, we suggest taking another sample within 1–2 h to determine whether the development of the estimated IgG content is stable, increasing, or decreasing from the initial value.
\nColostrum can also be stored and used later for piglets with low colostrum intake or for litters of sows with low colostrum quality. Colostrum can be stored in a fridge for 1–2 days or in the freezer for 3–6 months. Only sows with high colostrum quantity and quality should be selected. The collected colostrum can be administered to piglets using a feeding bottle with a suitable nipple or using a syringe.
\nCertain behavioral and physiological indicators can be used to identify piglets with low vitality and low colostrum uptake [72]. Piglets with low vitality may need assistance with colostrum uptake in order to prevent starvation, hypothermia, and crushing by the sow [2]. Table 5 provides an overview of these indicators. Besides birth weight and crown-rump length, piglet’s survival chance correlates with body temperature, vitality score, rooting response, and latency to teat and suckle [72]. Whenever the following criteria are met, the piglet needs assistance with colostrum uptake: vitality score of less than two (no movements within 15 s of birth), latency to teat and therefore to suckle of more than 30 min, and a body temperature of less than 37oC during the first hour after birth. In order to spot these piglets in time, we suggest looking at them every 30 min during parturition.
\nHowever, this may be difficult to implement into practice. It may be helpful to make use of thermal images to overcome these difficulties [53]. Similar to body temperature, skin temperature is linked to birth weight, vitality, and colostrum ingestion and can be used to see whether a piglet has reached the teat and suckled and ingested colostrum within 30 min of birth [73, 74]. As a piglet begins to suck and ingest colostrum, energy and warmth are produced, increasing body and therefore skin temperature [53]. If skin temperature drops below 30oC, the piglet has not been successful [53] and needs to be assisted to suckle and ingest colostrum.
\nIt is important to ensure that each piglet in the whole litter has a sufficient intake of good quality colostrum (more than 200 g) within 12–16 h from the beginning of parturition [14, 75]. When possible, piglets with low colostrum uptake should be assisted to suckle, by helping them to attach to the smallest functioning teats. This procedure should be repeated three to four times within the first few hours. Additionally, weakly piglets can be hand-fed with colostrum collected from their own mother or other sows.
\nAssisted suckling and hand-feeding are appropriate in small or normal size litters where only one or two piglets require help. In large litters or when more piglets require assistance, split suckling is more effective. In order to minimize the sibling competition for colostrum intake, the litter is split into two groups. The heavier and stronger piglets are kept in the creep area or in a separate box, allowing the smaller piglets to suckle for 60–90 min, and then the groups are switched. When separating the piglets, both groups should always have free access to a warm creep area. This can be easily achieved by using a box with an additional heat lamp for the separated group, which leaves the creep area accessible for the remaining group to suckle. Assisted suckling should be combined with split suckling if some small piglets are still unable to successfully suckle.
\nAnother strategy is to prolong the colostral phase. Piglets ingest colostrum usually until 24 h after the onset of parturition [75]. The composition of colostrum is affected by the status of tight junctions between mammary epithelial cells, and the ability to manipulate mammary tight junctions in the late colostral phase could allow Ig concentrations to be maintained at higher levels for a longer period. Injecting a supraphysiological dose of oxytocin to sows on day 2 of lactation (i.e., between 12 and 20 h after birth of the last piglet) increased the concentrations of IGF-I, IgG, and IgA in milk collected 8h after the injection [76]. The injection of oxytocin in the early postpartum period therefore delayed the occurrence of tightening of mammary tight junctions and prolonged the colostral phase, thereby having beneficial effects on the composition of early milk.
\nAfter parturition, it is important to investigate whether the sow is at risk or suffers from puerperal disease. Sows at risk are, e.g., sows that had constipation or stress, are obese, had a prolonged parturition, experienced birth help, and gave birth to more than one stillborn piglets (Table 6) [3, 21, 35]. These sows need to be checked within 3 days after parturition whether the animals shows general symptoms or other clinical signs of PDS [77, 78]. Underlying causes for PDS can be constipation, endometritis/metritis, cystitis, and mastitis [12, 62]. The underlying cause needs to be diagnosed and immediately treated.
\nIndicators, based on clinical history and clinical symptoms, for postpartum dysgalactia syndrome.
General symptoms include fever, reduced appetite, lethargy, and vaginal discharge [41]. Body temperature is the most frequently used to evaluate the health status of a sow in the puerperal period [78]. Reference values range from 39 [24] to 40°C [38]. Though body temperature is a sign of inflammation, it can also be affected by several other parameters such as the circadian rhythm [79], parity [79], variation in repeated measurements [80], and positioning of the thermometer in the rectum [81]. Vulvar discharge occurs also in healthy and diseased animals [82, 83] with the highest incidence between days 2 and 4 postpartum [78, 84]. Further, the color, consistency, and quantity of vaginal discharge vary regardless of whether the vaginal discharge is physiological or pathological [85]. The color can vary from clear, whitish, yellowish to reddish (Figure 3). The consistency varies from watery to creamy with lumps, and the amount can be up to 500 ml [85, 86]. Increased volumes of vaginal discharge are associated with endometritis, but otherwise there does not seem to be strong correlations between other characteristics of vaginal discharge and PDS [86].
\nPuerperal vaginal discharge with different colors. 0 = clear, 1 = reddish, 2 = yellowish, and 3 = whitish. The color of vaginal discharge varies regardless of whether the vaginal discharge is physiological or pathological [85]. Increased volumes of vaginal discharge are associated with endometritis. Images taken by Alexander Grahofer.
In conclusion, body temperature, especially under 40.0°C; appetite; and vaginal discharge cannot be used alone and as the single criterion for PDS. Still, body temperature of more than 40.0°C together with other clinical symptoms such as general behavior and feed intake are associated with PDS and require further diagnostics [78, 79]. These symptoms can be normal or associated with an infection of the urogenital tract or the mammary gland and constipation.
\nBesides prolonged parturition, obstetrical intervention, and the birth of more than one dead piglet, also retained placentae is a risk factor for endometritis [3]. For both, endometritis and retained placentae, ultrasonography is considered the best tool for diagnosis [3, 59, 78, 87]. Examination of uterine structures currently utilizes three criteria: fluid echogenicity, echotexture, and size [59, 87]. Changes in echotexture are a reflection of changes in the endometrial edema. Increased echotexture and any fluid echogenicity must be considered abnormal and indicative of an exudative inflammation of an acute or acute-chronic type [59, 87]. Fluid echogenicity is often associated with uterine edema and therefore increased echotexture and size of uterine cross-sections [3]. Thus, all criteria, enlarged uterine size, hyperechoic fluid accumulation, and heterogeneous uterine wall, are interconnected and can be used as ultrasonographic parameters to ascertain uterine disorders (Figure 4) [3, 87, 88].
\nTransabdominal ultrasonographic images of uterine cross-sections (X, Y) of sows assessed 3 days after parturition with enlarged and heterogeneous uterine wall (A) and hyperechoic fluid accumulation (B). Uterine vessels are prominently enlarged (examples marked with arrows). Scale bars on right margins in 1 cm steps. Images taken by Stefan Björkman.
In contrast, chronic endometritis, representing the most common type of uterine inflammation in pigs and most common cause of reproductive failure, cannot be definitively diagnosed by ultrasonography or by any other tool [59, 87]. Therefore, it is essential to recognize acute endometritis in time. This can be done based on the criteria mentioned above, but it must be considered that fluid echogenicity, uterine edema, and increased uterine size during the first few days after parturition may be normal [3, 78, 88]. Furthermore, when interpreting uterine size, the age and parity of the sow as well as the number of postpartum days need to be considered [3, 59, 87].
\nUltrasonography can also be used for the diagnosis of cystitis [89, 90]. Still, it is not as reliable as in the diagnosis of acute endometritis. Clear changes in the wall thickness and regularity and the mucosal wall surface are volume dependent [89, 90]. Overall, these measurements seem to be unreliable for diagnosis of cystitis. On the other hand, animals with cystitis have moderate to high amounts of sediment [89, 90]. Unfortunately, half of the sows without cystitis also show moderate to high amounts of sediment, which is mainly caused by the diet [89, 90]. Nevertheless, when none to mild amounts is present, the probability that the sow is suffering from no cystitis is high. When moderate to high amounts of sediment are present, other diagnostic tests need to be applied.
\nAnother diagnostic test is urinalysis. It is preferred to collect spontaneous midstream urine in a transparent tube. The best time for collection is in the morning before feeding. On-farm urinalysis includes macroscopic urine evaluation and urine stix testing. During the macroscopic urine evaluation, the color, odor, and turbidity are evaluated [91, 92]. The color can vary between light yellow and dark yellow, depending on urinary concentration. The color should not be red or brown which indicates hematuria or myoglobinuria. The turbidity of the urine should be clear. Cloudy or turbid appearance indicates the presence of bacteria. The presence of bacteria can also increase ammonia in the urine and cause a putrid odor. Urine turbidity has a sensitivity of 0.74–0.80 and a specificity of 0.50–0.92 and 0.50 [93, 94]. Nevertheless, if urine is physiological, the probability that the sow is suffering from no cystitis is 0.85 [95]. Thus, because of low sensitivities of certain single markers, several markers need to be evaluated together. A macroscopic evaluation should always be combined with urine sticks testing. Urine sticks allow testing for protein, pH, nitrite, blood, and leukocytes. Parameters with low sensitivity are leukocytes, pH, and nitrite [93, 94]. Parameters with good sensitivity are blood and protein [95]. The normal pH is between 5.5 and 8, and an increase above 8 is indicative for the presence of bacteria. On the other hand, many other factors can increase the pH such as feeding, other diseases, and medication. Whenever the majority of these markers indicate cystitis, a urine sample should be sent for bacterial investigation.
\nMammary gland, unlike the urogenital tract, is located outside the body and therefore easily accessible by hand. Thus, the diagnosis of mastitis can be done by palpation of the mammary gland. Mammary glands may appear swollen, firm, and warm [35]. In addition, skin color may be changed.
\nOther rapid mastitis tests as applied to cows are not available for sows. Diagnosis via cell count is not common and data on thresholds are rare [96]. A threshold of >107 cells per mL was proposed [35]. Further, a milk pH of more than 6.7 was reported [96]. If needed, ultrasonography can be used in the diagnosis. Affected mammary glands provide heterogeneous and hyperechoic images [97].
\nHyper-prolificacy challenges the performance of the sow in terms of parturition, colostrum production, neonatal survival, and fertility. Birth complications, piglet mortality, and puerperal disease need to be prevented. Before parturition, we recommend that sows are allowed to move freely and that nest-building materials, e.g., straw, hay, sawdust, or paper sheets, are provided. Modifying the sow’s late gestation diet in order to prevent constipation and high body condition will also have beneficial effects. During parturition, timely application of birth assistance is highly important. The exact cause of dystocia must be diagnosed and treated. Hyper-stimulation of the uterus with excessive oxytocin must be avoided. Close attention and assistance needs to be given to weak-born piglets, small piglets, and piglets without teats. New technologies, such as the use of Brix refractometer and infrared cameras, can help in the assessment of the status of colostrum and the newborn. After parturition, sows at risk of PDS need to be identified and checked within the first 3 days postpartum. Hungry and noisy piglets making vigorous nursing efforts indicates PDS. The exact cause of PDS should be determined for proper treatment. Acute endometritis is indicated by large amounts of vaginal discharge and diagnosed best using ultrasonography. Inspection and palpation of the mammary gland and evaluation of the sow’s behavior best diagnose mastitis. Cystitis can be diagnosed by performing a macroscopic evaluation of urine and urine stix testing. If needed, samples of urine and vaginal discharge can be sent for bacteriological examination. If no signs of mastitis, cystitis, and endometritis around, the cause may be constipation.
\nThe authors would like to thank Claudio Oliviero and Olli Peltoniemi from the Faculty of Veterinary Medicine of the University of Helsinki and Kati Kastinen from the ProAgria Meat Competence Center for contributing to the conception of this work. Further, the authors would like to thank the Finnish Ministry of Agriculture and Forestry for the financial support of this work and publication.
\nThe authors declare no conflict of interest.
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