Kevin B Cohen
email: kevin.cohen@gmail.com

Margot Mieskes
email: margot.mieskes@h-da.de

Aurélie Névéol
email: neveol@limsi.fr

Reviewing Natural Language Processing Research

This tutorial will cover the goals, processes, and evaluation of reviewing research in natural language processing. As has been pointed out for years by leading figures in our community [START_REF] Webber | Breaking news: Changing attitudes and practices[END_REF], researchers in the ACL community face a heavy-and growing-reviewing burden. Simultaneously, notable "false negatives"rejection by our conferences of work that was later shown to be tremendously important after acceptance by other conferences [START_REF] Church | Last words: Reviewing the reviewers[END_REF]-have raised awareness of the fact that our reviewing practices leave something to be desired. . . and we do not often talk about "false positives" with respect to conference papers, but conversations in the hallways at *ACL meetings suggest that we have a publication bias towards papers that report high performance, with perhaps not much else of interest in them [START_REF] Christopher | Computational linguistics and deep learning[END_REF].

It need not be this way. Reviewing is a learnable skill [START_REF] Basford | How to... review an article[END_REF][START_REF] Paice | How to write a peer review[END_REF][START_REF] Dale J Benos | How to review a paper[END_REF][START_REF] Koike | WJES: how to review a clinical paper[END_REF][START_REF] Satish | How to review an article[END_REF][START_REF] Tandon | How to review a scientific paper[END_REF][START_REF] Spyns | Scientific Peer Reviewing: Practical Hints and Best Practices[END_REF][START_REF] Philip | How to review a surgical paper: a guide for junior referees[END_REF][START_REF] Kohnen | How to write a good peer review[END_REF][START_REF] Mcfadden | How to review a paper: Suggestions from the editors of surgery and the journal of surgical research[END_REF][START_REF] Michael | How to review a clinical research paper[END_REF]. Kevin Bretonnel Cohen has written, overseen, and received hundreds of reviews. Karën Fort is an associate professor at Sorbonne Université. Besides being a reviewer for most major NLP conferences, she has been editor in chief for a Traitement automatique des langues journal special issue on ethics and acted as Area Chair for ACL in 2017 and 2018 (as senior AC). She coauthored the report on the EMNLP reviewer survey [START_REF] Névéol | Report on EMNLP Reviewer Survey[END_REF]. Margot Mieskes is a professor at the Darmstadt University of Applied Sciences. She has written and received reviews for numerous conferences and journals. She is a member of the ACL Professional Conduct Committee and an active member of the Widening NLP efforts. She co-authored the report on EMNLP reviewer survey [START_REF] Névéol | Report on EMNLP Reviewer Survey[END_REF].

Type: Introductory


Laurent Lescop

Bruno Suner

Designing Intradiegetic and Extradiegetic Spaces for Virtual Reality

Keywords: 360°cinema, Virtual Reality, Methodology and pedagogy, narrative grammar, Set construction, Isovist 3D

Fictions for virtual reality are mostly conceived either in an entirely virtual environment or in a real environment with very little transformation. It is infinitely rare to find examples of sets designed and built specifically for a 360°e xperience. Building, rather than remaining purely virtual, raises complex questions about the organization of a ``space to play'' and therefore how to produce a narrative for immersion and create a 360°film grammar.We thus have created a first 360°set for the famous director Marc Caro, for whom the question of off-screen raised a very complex technical problem regarding lighting, visual effects, staging, blocking and acting. In this contribution we will show how this was solved and why the definition of a 360°narrative grammar is crucial. These are important intricacies that place the user-spectator in the optimal conditions to appreciate the experience.

INTRODUCTION

Announced several years ago, the generalization of Virtual Reality and 360°films in our image consumption habits is only being realized very gradually. The constraint of owning specific equipment coupled with a still uncomfortable practice hinders the massive adoption of 360°content in the leisure field. However, the year 2020 may be the year of the longawaited breakthrough if the consequences of the pandemic allow it. The availability of user-friendly equipment such as the Oculus Quest or the HTC Cosmos and the multiplication of camera models, some at very attractive prices, could boost the market. Nonetheless, the production of content is abundant and the many festivals around the world are distinguishing works of exceptional quality that radically renew our relationship with filmed narrative. The creation of 360°content infuses the field of research, but little in schools, be it cinema, art or architecture. Like a little more than a century ago, when cinema established itself in the landscape of artistic production, know-how precedes theoretical knowledge, action produces reflection, example guides theoretical construction, the multiplication of propositions allows us to discern constants.

For us, who introduced 360°narration at the Ecole Nationale Supérieure d'Architecture in Nantes 20 years ago through interactive 3D universes designed in WRML, the technical stakes of immersive tools have been confronted with almost ethical issues of redefining prerogatives for architects. The resistance of the professional world, reflected in the Figure 1 360 view from the set. Sets for 360°fi lms are extremely rare. The construction of a real set helps to understand issues and solutions for a virtual reality experience. Photo M. Kolchesky pedagogy of schools and more generally in schools of architecture, has paradoxically given our studio an avant-garde and innovative aura that pushes us to an even deeper exploration of a 360°narrative grammar.

We made the bet very early on that animated and then interactive digital images would become essential tools for architects. We anticipated software developments and monitored what was going on in the world of video games in order to catch a glimpse of the graphical improvements of the rendering engines. Cinema is also a constant reference. Although our students are big consumers of film images, whether from a movie or a series, few of them know the fundamentals of writing for the screen and how one can, without talking, depict a situation, portray a character, anchor a story in a space and time. The construction of a pedagogy based on narrative design has, over the years, made possible the development of two fields of research, the first one concerning the writing of content intended for immersion and the other one the design of devices hosting immersive experiments (LESCOP&Al. 2018).

In the set that we have created, the "grand salon" is thus raised, it gives this part of the set the feeling that it is a place of power and decisions, it is a land-mark when it comes to knowing when history will take an important turn. The spaces of the pods, on the sides, like rotating barrels that are embedded in the main set, are like insert shots, they draw attention as if actors were developing a parallel action. We also have a control console located close to the camera which provides the equivalent of close-ups on the actors and insert shots and details of hands and buttons as they are viewed.

CURRENT UNDERSTANDING: ISSUES

360-degree sets are quite rare (Figure 1). The exploration of filmed productions shows either purely digital productions or films shot in real environments. Browsing through the catalogues on offer easily proves this. In the design of this first set, which we launched in 2018, the aim was to design and build in the same way as we would do in the film industry, but with the constraints of 360°filming in mind. This particularly concerns the issue of the technical off-screen, which must be designed to hide elements that do not have to be seen in the image. The creation of a 360°set for a filming for virtual reality headsets implies a large number of precautions to be taken if we do not want to be harassed by a large Figure 2 A real set for a 360°v irtual reality film. Photo P. Lescure amount of post-production work. First of all, the acting space should not be too large. We have noted that beyond 3 meters from the camera, the details are not really discernible anymore, both because of the resolution of the cameras and, for the moment, the main obstacle, the resolution of the screens in the headset. This gives, for a fixed camera, a diameter of 5 to 6 meters in which it is possible to install a set of actors. However, it is possible to create background spaces or very large backgrounds, which gives a real feeling of openness, but one cannot place narrative elements that would not be well discriminated by the spectator. It should also not be to the detriment of the need and willingness to understand and empathize with the actors' acting (Figure 2). Unlike what one would generally imagine, 360 degree film for a virtual experience is not an extension of the classic film. With a 360°camera, it is indeed not possible to frame in close-up or medium or overall. It is up to the filmed character to adjust these shot values by getting up more or less close to the camera. With care, however, the short focal lengths of the cameras soon produce grotesque effects. Similarly, high angle or tilt shot will not easily be possible. If it is feasible to move the camera (slowly) to reframe the scene, it will be preferable, as in the theater, to build in parts of the set that allow a view from above or the opposite angle. The staging will position the characters in the right place at the right time to achieve the desired visual effect (Figure 3).

Figure 3

Section of the set: the camera is in a central position. To create a tilt shot, the ground is raised while the camera itself can be lowered a bit.

Model Archirep Studio, rendering L.Lescop

Panoramic framing also implies that the lighting system should be integrated as much as possible into the diegetic space. This requires imagining solu-tions to dim the light and to avoid hot spots that are unattractive by burning part of the image.The other challenge is to properly distribute the lights sources.

A scene where the light would be concentrated in one point would complicate the stitching, that is to say the assembly of the various filmed views to compose a 360°image. This is one of the problems encountered when filming outdoors in natural light and when the sun is very bright. It is also what distinguishes the qualities of cameras on the market.

RESEARCH QUESTION: WHAT KIND OF NARRATIVE GRAMMAR FOR A 360°VIR-TUAL EXPERIENCE

The testing of the construction materializes theoretical questions about narrative grammar for virtual reality (Figure 4). The first set of questions concerns the transposition of the composition of a frame from a plane image to a 360°image. We have seen that it is obviously not possible to change the framing of a shot with a panoramic camera, but it is possible to organize the space and the movements in this space to suggest close-ups, inserts, wide area shots and even camera movements such as panning or traveling. There is another element of film grammar that concerns editing. Kulechov and his pupil Eisenstein showed very early in the history of cinema how to give meaning and symbolism through editing.In immersion, as we mentioned, direct transposition is not possible. A succession of sequences can be considered, but transposing the art of editing is against the very nature of the medium. In fact, the search for an equivalence with cinema wears itself out rather quickly. On the other hand, analogies with the theater are much more fertile. In the same way as in the theater, the playing space is entirely delivered to the spectator and as in the theater, pace, which could be compared to the editing process, the dynamics are given by the actors' performance (Pavis 2013). Intense, stirring, voluble, it induces haste and forward running, calm and soothed, it will transmit feelings of dullness or serenity. And as in the theater, overframing can be done by set elements or by light. Narrative implies the appropriation of a point of view. This point of view facilitates empathy with the characters and gives the story its tone. In 360°virtual reality, the point of view requires an intra-diegetic viewpoint. The spectator is physically in the story and for this reason asks for his position to be clarified. There are three kinds of points of view. In the first, the spectator is a ghost and his presence, invisible, does not disturb the course of the story. In the second, the spectator is present in the story as an inactive witness and in the third, he is a participating spectator-actor, which, consequently, requires a decision on whether or not to show a visible body. Many examples illustrate all these solutions, resulting in works ranging from passive contemplation to active participation.

The actors' acting is also to be compared to that of the theater. The movements must be fairly clearly expressed and the gestural dynamics must be legible. During the shooting of the film Dans la Lune with Marc Caro, we saw a clear difference in the cultural background between the actors from the theater and those from television and cinema. Staging of the actors did not follow the same standards as in cinema, but rather those of the theater staging. Filming at 360°requires that the director cannot be physically present on the set, he has to be at a distance, which confuses film actors (Figure 5). Before clapping, all the indications must be incorporated and the adjustments are marginally made during the play.

The question is therefore to understand how the extra-diegetic space will shape an efficient intradiegetic experience, according to two criteria: a space to play and create when the design process is carried out and a space of astonishment and fascination when the experiment is made. We believe that these questions lead to the definition of a narrative grammar for a 360°virtual experience. It is quite obvious to think that in a 360°space the off-screen no longer exists. In fact, it's more complicated than that, and the off-screen still exists, it's just defined differently. Traditionally, the off-screen is that space that is not seen outside of the stage frame in a theater or the camera frame in a movie.

FINDINGS: DESIGNING THE OFF-SCREEN

The off-screen therefore has two main functions: it extends the diegetic space into the spectator's imagination (the spectator imagines continuities in what is hidden from him), and the off-screen offers opportunities for the technicians to install equipment that helps in creating the image: usually, we will find off-screen projectors, microphones, and many other things (Figure 6). So there are two kinds of off-screen depending on whether you are a spectator or a director, for the first it is the projection of the imaginary, for the second, the technique.

This frame that defines the off-screen is moving in RV, it means that nothing can escape the view, which can greatly hinder the shooting process. Céline Tricart has well described the constraints of shooting at 360°. For her film Marriage Equality VR shot in 2015, the great difficulty was to hide the technical team, who in the bushes, who in the trees, who behind street furniture (Tricart 2017). The off-screen should therefore no longer be defined as being outside the filming frame, but rather outside the field of vision. It is no longer to be considered laterally, but in depth. This means that the off-screen becomes what is out of the field of vision. For the construction of our set, it was consequently necessary to determine this out-of-field of vision, which was done with the help of the Isovist. From a given point, it is possible to fire rays in all directions and thus visualize the portions of space seen and the portions of space hidden. In this way, we were able to determine, by making the point of the ray shooting coincide with the camera's point, the volumes of space invisible to the eye, our famous deep off-field. These volumes can therefore be occupied by technique or by accessories, we are certain that they will not be visible to the camera.

The decor being a confined space, the problem was relatively simple, it mainly concerned the placement of the background visible through the bays of the spacecraft. As the background was painted on a constructed support, the distance and surface had to be very precisely adjusted to match the physical constraints of the studio. To do so, we used the T4SU tools developed by [START_REF] Hartwell | T4SU : analyses et représentations des vues du ciel , du soleil et des saillances paysagères dans le contexte d'un outil de CAO[END_REF] dedicated to sunlight, but with a very good Isovist module (Figures 7,8). T4SU is a free plugin, developed for Sketchup. It calculates cones of visibility from a given point and thus gives the volumes of vision. It is also possible to have the area of intersection between the volume of vision and the affected surfaces, which allowed us to determine very precisely the areas to be worked on for the set. Grasshopper definitions were also tested, but T4SU's ease of use made it the preferred tool (Figure 9). However, for future developments, we know that a Grasshopper definition will allow us to obtain the unseen volumes, which will be very useful for more complex sets. The isovists used to determine the off-field of the 360°camera set have also been tested to understand the resolution issues of the 360°camera. Indeed, quite logically, a single pixel will cover a larger area as the distance increases. We can therefore establish a relationship between the distance of the surfaces of the set and the resolution of the details to be built or painted. It is useless to put a poster at a distance if it will be barely visible or readable. And, once again, the additional constraint doubles with the definition of the media to see the film, quality headphones or telephone. To meet the standard of the market's systems today, we have opted for a definition of 3840x1920. It is an equirectangular image that will then be mapped onto a virtual sphere. So there are 7,372,800 pixels to be distributed, with each pixel describing a projected surface area that can be determined. We do not really need a very complex calculation to guide us in the creation of the scenery, on the other hand, knowing that at a certain distance the resolution will already be half as high makes it possible to greatly anticipate the way in which visual information will be processed. It is the orders of magnitude that are interesting.

A fairly simple definition has been put together. The set modeled in Sketchup is imported with the Trimmed Planes option in order to have some Breps. In Sketchup, each object has been grouped and put on a different layer for an easier management afterwards. In Grasshopper, a point is placed which indicates the position of the camera. A UV sphere is used to visualize the resolution of the image. A vector follows the normal of each face of the sphere. A collision test is performed between this vector and the set and the background. This creates a volume which is then tested in Boolean operation with the elements of the set. It is the footprint of the tiling of the sphere that gives a grid printed on the decor and thus gives an idea of the resolution of the image as a function of distance (Figures 10,11).

At the moment, Grasshopper's tests show errors if the resolution of the sphere is too high. This question will be the subject of further tests.

CONTRIBUTION: WRITING FOR A 360°R EAL-VIRTUAL SPACE

One of the first conceptual obstacles concerning 360°w riting or more globally for immersion is the relation to temporality and more specifically to what is called "real time".Immersion, lived as an embodied experience, may imply that temporal continuity is made identically or at least according to the same rules.

However, the very nature of the concept of narrative implies the mastering of the temporality with which it will be played out. The creation of a narrative rests on the choices made in the organization of time, which can be accelerated, slowed down, cut or shifted at will. It is this very reorganization of temporality that makes a narrative; without it we are only in a voyeuristic posture waiting for an uncertain event.

In the world of cinema, Robert McKee's book "Story" serves as a reference to describe the stakes of the filmic narrative (McKee 1997).

Writing for 360°therefore requires controlling a space and a time that are not necessarily the equivalent of reality, but rather perceived rhythms that match the beats of the narrative. To put it another way, the narrative does not take place in a continuous space-time but in a discrete space-time. An illustration of this transformation of a contained space into a discrete space can be found in the world of video games. The game GTA (Grand Theft Auto) faithfully reproduces the city of Los Angeles in its opus V, which can be travelled in all directions at will. The game is part of a narrative logic, however, and for this reason the stakes must be renewed to maintain interest. Two different temporalities coexist, that of the diegetic space and that of the player. While one has Figure 12 Dans la Lune, during the shooting. Above on set, bellow outside the set in the control area. Photo M. Kolchesky, montage L. Lescop the feeling of living everything "in real time", a whole day lasts only 8 minutes while a full hour passes in 2 minutes without having the feeling of being in an accelerated time.The space that is supposed to be embedded in reality also has ellipses and finds shortcuts to go from one point of interest to another. This narrative ellipse, which in a cinema montage would have been a cut, is in GTA the juxtaposition of two distant spaces, which made us say that there has been a conversion from time to space. [START_REF] Lescop | Topologies de l'immersion[END_REF] The complexity clearly comes from the medium itself. Immersed in an experience of virtual reality, the time it takes to install oneself in the diegetic narrative is relatively long, one has to find one's markers and find one's bearings, whereas events can arise from any place (Figures 12,13).This therefore implies the use of sequences of relatively long duration, or even the use of a single shot and a play for the actors close to that of the theater or the first films at the cinema. One of the most important issues that authors and directors writing on the subject try to understand is how to focus the spectator's interest on a particular point of virtual space (Nielsen&al.2016), (Elmezeny&al. 2018), (Pillai&Verma 2019). Jessica Brillhart (Brillhart 2016) was one of the first to theorize about the creation of points of interest that will, like spatio-narrative beacons, refocus the viewer's attention where the director wants the action to be observed, what she called: probabilistic editing theory. This focusing, motivated by a sound signal or by a form of visual appeal, only partially resolves the management of the narrative space. There are three different attitudes to the development of a narrative: the spectator can be synchronous with the unfolding of the events, he discovers the events at the same time as the protagonists, and the narrative follows the rhythm of these discoveries. Second option, the spectator is late relative to the protagonist(s) in the unfolding of the events. The narrative progresses by the succession of revelations that make the spectator catch up on the data of the events. Third option, the spectator is in advance and has better information than the protagonist(s).This is a bit like the "Punch and Judy" effect where we know that the gendarme is hidden behind the curtain. Abundantly used by director Alfred Hitchcock, this process works on the spectator's anticipation of the course of events and on the screenwriter's ability to work on time or to produce false leads [START_REF] Snyder | Save The Cat! The Last Book on Screenwriting You'll Ever Need[END_REF]

FURTHER DEVELOPMENTS

Offering a space in which a maximum number of constraints can be anticipated, a constructed set invites us to develop formal answers to theoretical questions (Figure 14). This exercise, combining research and pedagogy, in which we are involved while observing an emergent process that will radically disrupt our approaches. As mentioned at the beginning of this article, two headsets making a radical breakthrough appeared during the second half of 2019: the Oculus Quest and the Vive Cosmos. These headsets, especially the Quest, have been characterized by their ability to offer a free experience, without any physical connection, over an extremely wide area of action. This means that we enter a new universe in which the spectator is really a spectator-actor interacting with what is happening around him. Entirely new paradigms are thus being put in place, paradigms that shall be on the agenda of our forthcoming teachings.

Figure 4

 4 Figure 4 3D model of the set.

  Figure 5 Film director Marc Caro staging at distance. Photo P.Lescure

  Figure 6 Off-screen visible outside the set. It is where extra-diegetic light are installed. Photo P. Lescure

  Figure 7 One of the key issue is to only construct what is going to be seen in the image whatever the format is. Isovist helped defining the available surface for the background, and then the built result. Illustrations L.Lescop

  Figure 9 Except of the Grasshopper definition. Ill. Lescop

  Figure 13 Preparing the shot. Photo P.Lescure

D2.T9.S2. CULTURE / SHIFT THROUGH UBIQUITOUS COMPUTING/ SCRIPTING AND LINGUA FRANCA -Volume 2 -eCAADe 38 |

| eCAADe 38 -D2.T9.S2. CULTURE / SHIFT THROUGH UBIQUITOUS COMPUTING/ SCRIPTING AND LINGUA FRANCA -Volume 2

| eCAADe 38 -D2.T9.S2. CULTURE / SHIFT THROUGH UBIQUITOUS COMPUTING/ SCRIPTING AND LINGUA FRANCA -Volume 2

| eCAADe 38 -D2.T9.S2. CULTURE / SHIFT THROUGH UBIQUITOUS COMPUTING/ SCRIPTING AND LINGUA FRANCA -Volume 2

| eCAADe 38 -D2.T9.S2. CULTURE / SHIFT THROUGH UBIQUITOUS COMPUTING/ SCRIPTING AND LINGUA FRANCA -Volume 2

| eCAADe 38 -D2.T9.S2. CULTURE / SHIFT THROUGH UBIQUITOUS COMPUTING/ SCRIPTING AND LINGUA FRANCA -Volume 2

ACKNOWLEDGEMENTS

We would like to thank the director Marc Caro for the inspiration he has given us, the teaching colleagues who have been with us for many years now and above all the students of the "Archirep" option who have inspired us all these years with their talent and involvement.


A Ioannides

T N D Tibbits

J P Connolly

D B Bushnell

K W J Barnham

C Calder

G Hill

J S Roberts

G Smekens

Strain Balanced Quantum Well Monolithic Tandem Solar Cells

HAL is

INTRODUCTION

The best InGaP/GaAs monolithic tandem solar cell today has an AM1.5g efficiency of 30.2% [START_REF] Green | Solar Cell Efficiency Tables (Version 27)[END_REF]. However, as with most InGaP/GaAs tandem solar cells, it is current limited by the bottom GaAs junction [START_REF] Friedman | 30.2% Efficient GaInP/GaAs Monolithic Two-Terminal Tandem Concentrator Cell[END_REF]. Incorporating strain balanced multi-quantum well solar cell (SB-QWSC) structures in GaAs cells has been shown to extend the absorption of the cell to the longer wavelengths [START_REF] Ekins-Daukes | Strain-balanced quantum well solar cells[END_REF]. The increase in photocurrent due to the SB-QWSC structure over-compensates the drop in open circuit voltage thus enhancing the efficiency compared to a bulk GaAs cell [START_REF] Barnham | Quantum Well Solar Cells[END_REF]. Modelling shows that the ability of the SB-QWSC to optimize the band-gap of the current-limiting GaAs cell in a InGaP/GaAs tandem without influencing the band-gap of the InGaP top cell can significantly enhance tandem efficiencies [START_REF] Tibbits | The Potential for Strain Balanced Quantum Well Solar Cells in Terrestrial Concentrator Applications[END_REF].

Currently there are no ternary alloys with lower bandgap that are lattice matched to GaAs or Ge (see Fig. 1). The SB-QWSC is lattice matched to GaAs and we have also successfully grown them on Ge substrates. InGaP/InGaAs tandem cells have achieved efficiencies above 30% on relaxed or virtual substrates [START_REF] Green | Solar Cell Efficiency Tables (Version 27)[END_REF] but there is always a residual dislocation density which is completely absent in the SB-QWSC [START_REF] Ekins-Daukes | Strain-balanced quantum well solar cells[END_REF]. Furthermore, as can be seen from Fig. 1, as the InGaAs band-gap reduces with increasing lattice constant under relaxation, the band-gap of the InGaP top-cell also reduces.

The use of strained InGaAs quantum wells has been suggested for enhancing tandems [START_REF] Freundlich | Multi-Quantum Well Tandem Solar Cells with Efficiencies Exceeding 30% AM0[END_REF] but we have shown that it is not possible to grow sufficient strained wells before relaxation occurs, dramatically reducing the voltage performance [START_REF] Ekins-Daukes | Strain-balanced quantum well solar cells[END_REF]. Other possible materials, such as GaInNAs dilute nitrides, have not yet achieved the required photocurrent densities to be considered suitable candidates [START_REF] Ptak | Enhanced-Depletion-Width GaInNas Solar Cells Grown by Molecular-Beam Epitaxy[END_REF].

In this paper results are presented for InGaP/GaAs dual junction monolithic solar cells featuring a SB-QWSC in the GaAs junction which show efficiency enhancement in a tandem SB-QWSC for the first time.

SB-QWSC TANDEMS

A contour plot of AM1.5d tandem cell efficiencies as a function of top and bottom cell band-gaps at 300x concentration is shown in Fig. 2 [START_REF] Tibbits | The Potential for Strain Balanced Quantum Well Solar Cells in Terrestrial Concentrator Applications[END_REF]. The band-gap of the InGaP/GaAs tandem corresponds to the intersection of the two lines. Lowering the band-gap of the GaAs cell without changing the InGaP band-gap, as with a SB-QWSC, moves the intersection along the horizontal line directly to the 38% contour. In an InGaP/InGaAs tandem cell, grown on a relaxed substrate, the movement is diagonal, parallel to the contours in this region. In addition the GaAs cell band-gap reduction by means of a SB-QWSC is achieved without introducing any misfit dislocations [START_REF] Ekins-Daukes | Strain-balanced quantum well solar cells[END_REF]. Fig. 3 depicts the band structure diagram of a SB-QWSC. The strain balancing technique seeks to balance the compressive stress developed by the InGaAs wells. This is achieved with the insertion of GaAsP barriers on either side of each InGaAs well. By appropriate choice of layer compositions and widths, the smaller lattice constant GaAsP barriers provide tensile stress. On average the barrier-well-barrier structure has zero residual stress in the bulk GaAs cell (see Fig. 4). This technique produces no misfit dislocations even for large numbers of quantum wells [START_REF] Ekins-Daukes | Strain-balanced quantum well solar cells[END_REF]. Two different SB-QWSC designs will be presented here and compared to a control InGaP/GaAs tandem cell. The bottom cells of the SB-QWSC tandem cells are identical with the exception of the multi-quantum well (MQW) structure. The MQW structures in the top limited (TL) and current matched (CM) cells were grown with exciton peaks at 918nm and 922nm respectively. The SB-QWSC bottom cells were grown at the EPSRC National Centre for III-V Technologies using Metal Organic Vapour-Phase Epitaxy (MOVPE) on GaAs substrates. The tunnel junctions and InGaP top cells were overgrown at Energies Nouvelles et Environment in Belgium. The final processing stage was again performed at the EPSRC National Centre in Sheffield. The tandem cell structures are depicted in Fig. 5. Table 1 shows the layer widths for the i-and nregions of TL and CM SB-QWSC.

Quantum Efficiency Measurements and Modelling

Measuring the quantum efficiency (QE) of a multijunction cell in a monolithic, series connected tandem configuration is more challenging than for single junction solar cells. The current through the tandem cell is limited by the lowest current producing junction. During characterization, the junction not being characterized will not pass any current unless illuminated. In order to overcome this, dc light-bias was applied on the junction not being characterized without affecting the junction under test. Using an infra-red LED and a blue LED, the bottom and top junctions respectively can be light biased during the measurement. The amount of light biasing is adjusted to match the maximum current output of the junction under test. Over-light biasing can forward bias the light-biased junction and in turn the junction under test becomes reversed biased since the tandem cell is held at zero volts bias by an active bias control. In this case the QE measured will not reflect the actual QE at zero volts bias. The junction under test is illuminated by a chopped light source monochromator and measured by a lock-in amplifier to minimize noise. The QE of the junction is obtained after comparison to a reference scan of a calibrated silicon cell with a known QE. This technique produces QE measurements accurate to within 5%.

The measured QE's of the Control and CM cells are depicted in Fig. 3. The exciton peak, centred at 922nm, of the SB-QWSC can be clearly seen. The presence of the SB-QWSC extends the QE of GaAs in the 900 to 925nm range. This in conjunction with an improved InGaP top cell The experimental QE measurements are modelled using SOL, a 1-d drift diffusion model developed at Imperial College London. Fig. 7 depicts the measured and modelled QE for the TL tandem cell. As seen the modelling accuracy is high with 1% agreement for the top cell and 5% agreement for the SB-QWSC, both within the experimental error. The accuracy of the model enables prediction of current matched tandem cell configurations to be made by integrating the QE over a particular spectrum. The TL tandem cell was fabricated prior to the development of the current matched CM tandem cell. This cell demonstrated a high quality SB-QWSC bottom junction with a projected short-circuit current density of 148.4 A/m 2 in Am1.5g spectrum. The choice of top cell iregion and n-region width for the current matched tandem in Table 1 were optimized based on the SOL fit to the TL tandem in Fig. 7. The CM tandem top cell and tunnel junction were then overgrown on a second SB-QWSC.

LIGHT I-V EFFICIENCY MEASUREMENTS

Monolithic multi-junction solar cells are very susceptible to spectral variations due to the fact that the spectrum determines the current limiting junction. For example a dual junction tandem cell under a blue rich spectrum will be limited by the current in the bottom cell. Therefore small variations in the spectrum can affect the total efficiency of the cell greatly. In the absence of an AM1.5g light source a different method needs to be employed to determine the I-V characteristics of a multijunction solar cell.

A 3000°K black body light source was utilized to perform the light I-V characterization. This method is not optimal as the output efficiency of the tandem cells would not reflect the expected output efficiency under AM1.5g spectrum, for which the tandem cells were optimized. However this method is adequate for demonstrating the principle of efficiency enhancement with a SB-QWSC.

Another method employed was simulated AM1.5g illumination conditions using two monochromatic laser sources that illuminated each junction separately. This method demonstrated higher efficiencies; however the narrow band-width of the laser sources meant that the SB-QWSC did not exhibit its full potential. Also the high experimental uncertainty in this method of determining the illumination intensity of each laser source restricted the accuracy of the efficiency estimate Table 2. Calculated short-circuit current densities under AM1.5g spectrum

The expected short circuit current densities of the three tandem cells were calculated using the measured QE's and the standard AM1.5g spectrum (see Table 2). In order to perform the I-V curve Fig. 8. Light I-V curves for the three cells under 3000°K black body spectrum at 1000 W/m 2 measurement the intensity of the 3000°K light source was adjusted so that the output short circuit current density of the tandem cell matched the lowest short-circuit current density from the constituent junctions. The I-V curves are shown in Fig. 8 and the cell parameters in Table 3. As expected the TL tandem cell exhibits a poor fill factor which can be attributed to the large mismatch between the bottom and top cell current densities. The error in determining the efficiency by this method is estimated to be 3.5%. Therefore the efficiency of the current matched CM cell under a 3000°K black body spectrum of total irradiance of 1000W/m 2 is determined as (23.4±0.8)%.

Cell

CONCLUSIONS

We have demonstrated that incorporation of a SB-QWSC in an InGaP/GaAs monolithic tandem cell increases the bottom cell photocurrent. Thus the bottom cell current limiting constraint can be lifted. Based on measurements and QE fits on a top cell limited SB-QWSC tandem a current-matched top cell has been designed using SOL our cell simulator. The corresponding current matched SB-QWSC tandem has been grown and a significant increase in efficiency of 2.3% absolute demonstrated compared to a control cell in a 3000K black-body spectrum. This is the first experimental observation of tandem efficiency enhancement with a quantum well cell. Further optimization of the top and bottom cell for the AM1.5d spectrum could lead to a new dual junction record tandem cell for concentrator applications.

Fig. 1 .

 1 Fig. 1. Band-gap energy variation with lattice constant for GaInAsP and AlGaAsSb alloys [8].

Fig. 2 .

 2 Fig. 2. Optimum bandgap combinations contour plot for AM1.5d spectrum (300x concentration). Intersecting lines depict the InGaP/GaAs tandem cell [5].

Fig. 3 .

 3 Fig. 3. Band structure diagram of a SB-QWSC.

Fig. 4 .

 4 Fig. 4. Stress balancing technique incorporated in MQW structures.

Fig. 5 .

 5 Fig. 5. (a) Control and (b) SB-QWSC tandem structures.

Fig. 6 .

 6 Fig. 6. Quantum efficiencies of CM and control tandem cells.

Fig. 7 .

 7 Fig. 7. The measured and modelled QE of the top cell limited tandem.

Table 1 .

 1 InGaP top cell i-region and n-region layer widths

	Cell	i-region width	n-region width
		x µm	y µm
	TL	0.13	0.52
	CM	0.34	0.57

Table 3 .

 3 Experimental tandem cell efficiencies in a 3000°K black-body spectrum at intensity of 1000W/m

		Fill Factor (%)	Efficiency (%)
	CM	87.1	23.4
	TL	81.2	21.0
	Control	86.1	21.1

2

.


K W J Barnham
email: k.barnham@ic.ac.uk

Ian Ballard

J P Connolly

N J Ekins-Daukes

B G Kluftinger

J Nelson

Carsten Rohr

Quantum well solar cells

HAL is

Introduction

This paper will review the development over the past decade of the quantum well solar cell (QWSC). The study of quantum wells (QW) and, more recently, quantum dots (QD) have dominated opto-electronic research and development for the past two decades. QWs have been very extensively studied in reverse bias where they are used in photodetectors and optical modulators. In forward bias at forward current, QWs are already employed in lasers and LEDs. However, for forward bias and reverse current, the quadrant of the IV plot where photovoltaic (PV) power can be extracted, QWs have been much less extensively studied. The physics of this quadrant is, however, interesting in itself as well as having important potential applications in PV. The people who have worked in this area could be assembled in one room. In fact many of them were at the workshop and their work is represented in these proceedings.

The Quantum Photovoltaic (QPV) group at Imperial College has pioneered this area. I will be concentrating on their work as I know it best. I will try to give due credit to others who have contributed, particularly those present at the meeting! I apologise in advance that I will not have the space to do justice to everyone's work.

In this review I will introduce the advantages of QWs for solar cells and discuss some of the fundamental aspects that have caused some controversy. I will discuss work by ourselves and other authors on modelling dark-currents and results on the temperature, radiation and field dependence of QWSCs.

I will not have space to cover three important areas of our current work. The use of strain-balanced quantum wells for tandem and thermophotovoltaic (TPV) applications are discussed by Ned Ekins-Daukes [1] and Carsten Rohr [2], respectively, in other papers in these proceedings. Details of our novel use of quantum dots, as the replacement for the dyes in a luminescent concentrator, can be found in Ref. [START_REF] Chatten | th IEEE PVSC[END_REF].

Quantum Well Solar Cells

Fig. 1 shows a schematic of a QWSC. An intrinsic region is inserted into a conventional p-n solar cell to extend the field-bearing region. The importance of maintaining the built-in field across the i-region will be discussed in Sec. 5. The quantum wells (QWs) extend the absorption below the bulk band-gap E g to threshold E a . If the field is maintained across the i-region, the carriers produced by the extra photons absorbed in the well escape to the bulk cell and contribute extra current with high quantum efficiency (QE) at room temperature [START_REF] Barnham | [END_REF]. There is some voltage loss to which we will discuss. However, we have demonstrated, in three latticematched QW material systems, that the current enhancement of the QWs is sufficient to overcome the voltage loss. Hence, in lattice-matched systems, the wells can enhance efficiency compared with conventional cells with the bulk-band-gap E g . The extra current comes for the extended absorption at longer wavelengths and also from the increased absorption in the i-region above the quantum well. This can be seen in Fig. 2 where the spectral response (SR-quantum efficiency at zero bias) is shown for a 30 QW AlGaAs/GaAs QWSC and a homostructure AlGaAs control made entirely with the barrier material of the QWSC. The i-region has the same thickness in both cells. We have developed a programme SOL which can fit the SR of QWSC and control cells in a number of III-V systems [5,6].

The question of what output voltage the QWSC will achieve in the ideal limit has been a matter of some controversy as will be discussed in Sec. 3. However, we have demonstrated in three lattice-matched multi-quantum well (MQW) systems that the open-circuit voltage of the QWSC is greater than the control sample made from well material [7]. The enhancement is greater that that expected from the increase in absorption threshold E a due to the effect of quantum confinement. The effect results from the dark-current being lower than expected for bulk cells at comparable E g [7]. This will be discussed further in Sec. 3 & 4. Fig. 2. Spectral response (heavy dots) for a 30-well AlGaAs/GaAs QWSC and a homostructure AlGaAs control cell. The i-region has the same thickness in both cases. Thin lines are fits with the programme SOL.

Fundamental Efficiency Limits

It was relatively straightforward to show that QWs enhance solar cell current, but some authors claim [START_REF] Araujo | Proc. 12th European Photovoltaic Solar Energy Conf[END_REF] that, in the radiative limit, the voltage would be determined by the lowest band-gap in the system (E a ). Fundamentally, the output voltage is determined by the variations in the quasi-Fermi levels for the electrons and holes across the cell. However, the way these behave in a QW system was not known. In 1994 Antonio Marti and co-workers produced a detailed balance model for quantum well cells which assumed that [START_REF] Araujo | Proc. 12th European Photovoltaic Solar Energy Conf[END_REF]:

1) Cells are in the ideal limit when all recombination is radiative.

2) Absorption is 100% for photon energies greater than the effective band-gap E a .

3) In the ideal situation the quasi-Fermi level separation (!E F ) is equal to the applied bias at all points. Under these assumptions situation an ideal QWSC cannot have higher efficiency than the conventional homostructure cell with the band-gap corresponding to maximum efficiency.

In order to investigate if this model holds, we have developed a method for determining the quasi-Fermi level separations [START_REF] Tsui | [END_REF]10] that we have demonstrated on single (SQW) and asymmetric double (DQW) quantum well samples [10,11]. The method involves studying radiative recombination by extracting the electroluminescence (EL) signal at room temperature in absolute units. The EL is calibrated by comparison with the photoluminescence (PL) signal when illuminating in the QW with a certain generation rate G. The PL is calibrated by comparing the forward bias PL signal with reverse bias photo-conductivity (PC) at low temperatures (e.g. 40 K) where non-radiative recombination is small. In this case the large field across the well in reverse bias will extract all the carriers. In reverse bias therefore, the PC measures the rate of carrier escape from the well and hence the generation rate G. In forward bias at low temperatures all the carriers recombine to give the PL signal. Hence the maximum integrated luminescence rate is equal to G and the device is calibrated for all further luminescence by that sample.

We use a generalised, detailed balance approach to fit the absolute EL spectrum

L(E,F)dE as a function of photon energy and field F in the wells as below

The fit is made in terms of !E F and the absorption coefficient !(E,F), which we calculate from first principles [START_REF] Tsui | [END_REF]10] using the same approach as in the programme SOL which fits the SR of the QWs. Confidence in our method is provided by the voltage dependence of the integrated radiative currents which we extract. These should have unit ideality factor if they result from radiative recombination. In Fig. 3 we show room temperature results for our AlGaAs/GaAs asymmetric DQW samples [11]. We have also managed to extract the much smaller radiative signal from the narrower of the two wells. Both radiative components have slopes consistent with unit ideality factor over a large number of decades. In contrast, the darkcurrents of the cells, dominated by non-radiative recombination, have ideality near 2. We have shown that, at room temperature in SQW samples and the dominant wider well of DQW samples, the quasi-Fermi level separation ("E F ) is less than the applied bias i.e. recombination is less than predicted on the assumptions of the detailed balance arguments in Ref. [START_REF] Araujo | Proc. 12th European Photovoltaic Solar Energy Conf[END_REF].

In the case of GaAs/InGaAs SQW samples we have been able to observe the radiative recombination signal from the bulk GaAs in addition to the SQW [10]. As shown in Fig. 4, we can fit the bulk GaAs-cell signal assuming that the quasi-Fermi level separation is equal to the bias. However, the well signal, in the same sample, can only be fitted if the quasi-Fermi level (and hence the radiative recombination) is reduced significantly.

dE e E F E c h L n dE F E L T k E E W B F 1 ) , ( 2 ) , ( / ) ( 2 2 3 2 ! ≪ ! ! ! ≺
Our DQW results show that the quasi-Fermi level separation is different in wide and narrow wells. The temperature dependence suggests that the quasi-Fermi level of the wide-well approaches the bias as the temperature is reduced and carrier escape becomes less likely [11]. This observation adds strength to our conjecture that the reduced radiative recombination in the QW results from the escape of the carriers from the well to the wider band-gap region at room temperature.

These results clearly demonstrate that radiative recombination in QW systems cannot be described by the assumption that the chemical potential is equal to the bias. Martin Green pointed out that that a feature of "Third Generation" cells is that the chemical potential is not equal to the bias [START_REF] Green | Abstract No[END_REF]. We therefore believe that our results clearly demonstrate that the QWSC is a "Third Generation" device.

The observation that if the QW and barrier are radiatively coupled then the system should be described by more that one quasi-Fermi level was first made by Stefan Ketteman and Jean-Francois Guillimoles [START_REF] Kettemann | 13th EU PVSEC[END_REF]. This idea has been taken further recently by Stephen Bremner, Richard Corkish and Christiana Honsberg [START_REF] Stephen | [END_REF]. They have modelled the situation represented in Fig. 5. The transitions they assume to be radiative are indicated by arrows. They conclude that, in the radiative recombination limit, if the well to barrier transition is also radiatively coupled, quantum well cells are capable of achieving 63.2% efficiency. Further details of this model are given in the paper of Christiana Honsberg [15].

Modelling Quantum Well Solar Cells

A little before the detailed-balance model of Ref. 8 appeared, Richard Corkish and Martin Green modelled MQW cells by introducing the idea that the QW contribution could be added as an incremental cell in parallel with a host homostructure cell corresponding to the barrier [START_REF] Corkish | Proc. 23rd IEEE PVSC[END_REF]. In contrast with the model of Ref. 8, their model predicts a small amount of efficiency enhancement for small well widths in the ideal limit.

The next model, due to Mohaidat et al., involved a detailed calculation of the resonant tunnelling contribution to electron transport in MQW systems [START_REF] Mohaidat | [END_REF]. Their calculations emphasised that carrier escape would be enhanced compared to recombination if the resonant tunnelling condition was optimised. This model has been tested in a series of measurements on GaInAsP/InP based systems [18]. This data is discussed further in Sec. 5.

Neal Anderson modelled the QWSC as a baseline, realistic p-n junction with an ideal iregion and MQW [19]. This model was successful in reproducing the V oc performance of some InGaAs/InP QWSCs and their controls [20]. Neal has gone further in comparing differing QWSC models in his review paper in these proceedings [21].

The model of Argyrios Varonides [START_REF] Varonides | 2nd WCPVSEC[END_REF] is notable for its comprehensive treatment of the tunnelling and thermionic emission contributions to carrier collection. This model has recently been compared with experimental data, on the temperature dependence of AlGaAs/GaAs QWSCs as will be discussed in the next section. He has also developed his model further as discussed in his own paper [START_REF] Varonides | [END_REF].

Apart from the extension of our spectral response fitting programme, discussed in Sec. 2, to different materials, our main modelling effort at Imperial College has been in the fundamental studies (Sec. 4), and attempting to explain experimental data on the dark-current behaviour of QWSCs [START_REF] Nelson | [END_REF][START_REF] Connolly | th IEEE PVSC[END_REF]. As in the case of the PL and EL studies discussed in Sec. 4, we have built on the success of SOL. This means that we are able to calculate from our knowledge of the electron and hole eigenstates in the QW the density of states of the carriers as a function of energy and field. Because of differences in effective mass, the conduction and valence band density of states differ, and this asymmetry changes as one moves from barrier to well. Given that in equilibrium the Fermi-level E F is constant across interface, the intrinsic Fermi energy level E i must be discontinuous between well and barrier. We therefore introduce shifts in the intrinsic level ! n , ! p , defined as in Fig. 6, which can be calculated from the QW eigenstate energies. It should be noted that the ! parameters depend in a known way on the QW parameters. The electron density in the well are then related to the quasi-Fermi levels by: A similar expression holds for the hole density. We have investigated two approaches to solving for the n(x) and p(x) variation throughout the i-region, either assuming the depletion approximation or a fully self-consistent calculation including the constraints of Poisson's equation. We have shown that the two approaches are equivalent at least up to voltages of the order of V oc . Once we have the carrier densities then we can calculate a recombination rate assuming the Shockley-Hall-Read approach, as long as we can estimate the recombination lifetimes, which depend on material quality. We find the results are not particularly sensitive to differences between the electron and hole carrier lifetimes, so we can equate them and are left with two material quality parameters to determine, the carrier lifetime in the barrier and the well, # B and # W respectively.

We determine these two parameters by fitting homostructure or double heterostructure controls which have i-regions formed from the material of the barrier or the well respectively. The procedure can be illustrated by considering the example of the AlGaAs/GaAs system. Fig. 7a shows the fits made with this model in the depletion approximation to GaAs and AlGaAs p-in homostructure devices. It can be seen that the slope of the data is consistent with an ideality factor ~2 and hence with the dominance of the Shockley -Hall -Read recombination over ideal behaviour. The fits give lifetimes # B ~1ns and # W ~10ns consistent with the superior material quality of the binary compound.

Fig. 7b shows how the recombination rate varies with position in the i-region of a 30well MQW at different forward biases including the bias at which the i-region is not fully depleted using the lifetimes determined from the heterostructures. Integrating this recombination profile gives the prediction (light-dotted line) for the dark-current compared with experiment (heavy dotted line) in Fig. 8a. The same lifetimes give the prediction in Fig. 8b for a 50-well MQW grown with similar material quality. In both cases the predictions using the lifetimes determined from the homostructure controls falls significantly above the experiment. Agreement with the data can be achieved (as in the dashed lines in Fig. 8) if one assumes that, as we have demonstrated in the SQW and DQW (see Sec. 3), the quasi-Fermi level separation is reduced in the wells compared to the barrier. Our fits to double-heterostructures and MQWs in the GaInAsP/InP system show a similar effect. These results give further support to our view that recombination in quantum wells is reduced compared to that in homostructures. However, we still need to understand why the quasi-Fermi level reductions in MQWs, which we observe in this way, are considerably larger than we observe in the radiative signal in SQW and DQWs.

Temperature, Radiation and Field Dependence

We have demonstrated that Al x Ga 1-x As/GaAs MQW cells have better T-dependence of efficiency than comparable control heterostructure cells made from the barrier materials (Al x Ga 1- x As with Al fraction x = 0.2 and x = 0.3) as shown in Fig. 9 [START_REF] Ballard | 2nd WCPVSEC[END_REF]. The Al = 0.3 MQW cell also has better temperature coefficient of efficiency than a control cell made from the well material (GaAs).

The improved efficiency does not come from an increase in the level of the spectral response. This is consistent with the observation in Sec. 2 that the QE for carrier escape from the wells saturates at a value close to unity at room temperature. The improvement in efficiency appears to come from a relative improvement in the dark-current with increasing temperature.

Improved temperature dependence of AlGaAs/GaAs QWSCs has also been seen by Aperathitis et al. [START_REF] Aperathitis | [END_REF]. The data have been explained by the model of Varonides discussed in Sec. 4 in terms of differing contributions from thermionic and tunnelling currents [START_REF] Aperathitis | th IEEE PVSC[END_REF].

Evidence that InP/InAsP strained MQW cells demonstrate an improved radiation tolerance compared to homostructure controls is discussed by Alex Freundlich in another paper at this meeting [START_REF] Aperathitis | th IEEE PVSC[END_REF]. The most likely reason for the improved performance is that in a MQW cell a large proportion of the carrier collection occurs in the i-region where the collection is by drift rather than in the base where collection is by diffusion.

The importance of the built-in field to the operation of QWSC is the final topic to be reviewed in this section. The first report of efficiency enhancement in QWSCs showed that background doping must be low to preserve field across i-region and keep the QE and collection efficiency high [START_REF] Barnham | [END_REF]. The importance of a critical built-in field has also been demonstrated in strained InAsP/InP QWSCs [START_REF] Serdiukova | [END_REF]. Our extensive studies of carrier escape from SQW and DQWs show that the holes dominate with the mechanism being thermally assisted tunnelling which is strongly field dependent [30]. Studies of the temperature and bias dependence of photoluminescence in addition to photoconductivity, show that the electron and hole escape is linked by the influence of space-charge on the field [31]. Similarly, the photoluminescence signal from GaInAsP/InP QWSCs shows field screening [32]. The latter group has recently demonstrated sequential resonant tunnelling effects in QWSCs at critical field values [33]. In the original proposal for the QWSC [34] it was pointed out that resonant tunnelling might reduce recombination effects and that variable well-widths could enhance this. The authors of Ref. 33 have demonstrated a sequential tunnelling enhancement in bias dependence of the darkcurrent and photocurrent in a GaInAsP/InP QWSC with 16 equally spaced wells. Most interestingly, in view of the discussion in Sec. 3, they observed a that the photoluminesence signal was reduced at the resonant bias which they interpreted as a reduction in the radiative recombination rate at the resonant field. Some unpublished work of our group is relevant to question of field dependence [34]. We have had a sample grown with 14 strained InGaAs/GaAs QWs in the neutral n-region of a pn cell. The measured spectral response of this cell is compared in Fig. 10 with a similar cell with 15 strained InGaAs QWs in the i-region and with the comparable p-n homostucture control cell. One sees that the quantum wells in the n-region contribute about one fifth as strongly as the iregion wells, i.e. only approximately 3 wells are contributing to the absorption. Confirmatory information comes from the QE just above the bulk GaAs band-gap. The main contribution to absorption here is the n-region base layer, which has a considerably reduced QE. Our spectral response fitting programme suggests this reduction results from a reduction of the hole minority carrier diffusion length due to the presence of the wells in the n-region to around 2 barrier widths. This is therefore consistent with saying that only the three wells within a (reduced) minority carrier diffusion length contribute carries that are collected by the built-in field. This is a warning for those designing quantum dot solar cells which rely on diffusion alone, without drift. From this last discussion we can see that there are problems with incorporating wells and quantum dots in field free regions. We have also looked at the performance of self-assembled quantum dots in a p-n structure and found their absorption to be rather low and the non-radiative recombination very high. As an alternative, we are studying what quantum dots can contribute to one old, but potentially very useful idea, the luminescent (or fluorescent) concentrator. This idea originally proposed in Ref. 36, is discussed in Ref. [START_REF] Chatten | th IEEE PVSC[END_REF].

Conclusions

The efforts of a number of researchers, from our own and other groups, have clearly demonstrated that quantum wells enhance current and efficiency relative to conventional cells with the barrier band-gap in lattice matched systems. They also enhance voltage compared to conventional cells with the well band-gap. QWSCs have advantages in terms of temperature dependence of efficiency, which is important in concentrator and TPV applications, and in radiation tolerance.

Our own studies of the radiative recombination contribution to the dark-current have shown that single and double QW systems in a built-in field have reduced radiative recombination and have quasi-Fermi level separation which is less than the external bias. These results demonstrate that quantum well cells can already claim to belong to the "Third Generation" of solar cells in Martin Green's definition.

All our experiments on "E F have been conducted on the dark-current. We appreciate that these should be extended to light bias conditions where the results might well be different but the experiments are not simple. An extension of this type of experiment would look for direct evidence for photonic coupling between well and barrier to test the Bremner, Corkish and Honsberg model. We also need to extend these studies from SQW and DQW cells to MQWs. Here the experimental problem is that we cannot use the calibration method described in Sec. 3 as it is not possible to turn off the photo-current at low temperature. Carrier escape in MQWs is too efficient.

On the theoretical side, our own dark-current modeling of practical MQW cells supports the observation of reduced "E F in the wells but more work is required to understand why the suppression appears to be larger in these non-radiative currents than in the radiative currents of SQWs and DQWs. There is a difficulty in extending this model to the interesting situation of the strain-balanced QWSCs as in this case it is not possible to determine the carrier lifetimes which depend on material quality as there are no appropriate bulk homostructures or heterostructures. It is the great advantage of the strain-balanced QWSC that it can produce effective band-gaps that cannot be achieved in bulk material.

For the reasons discussed in Sec. 5 we believe that the built-in field is important for the operation of the QWSC. We believe that the theories for the limiting efficiency should be modified to incorporate the effects of the field. This could be the key to understanding the quasi-Fermi level variation. The experimental studies of radiative recombination in MQW systems will also require a treatment of photon recycling effects.

There is still much to be done for a full understanding of this Third Generation PV cell, particularly in the radiative limit. However, this will not inhibit the development of the applications discussed in Refs. 1 and 2. These deal with practical, non-radiative-dominated material. It could turn out that the most important property of the QWSC is the variety of bandgaps that can be achieved with the strain-balanced version.

Fig. 1 .

 1 Fig. 1. Schematic energy band diagram of a quantum well solar cell.

Fig. 3 .

 3 Fig. 3. Radiative currents extracted from the wide and narrow wells of double quantum well devices compared with the dark currents of the devices.

Fig. 4 .

 4 Fig. 4. Calibrated EL from a GaAs/InGaAs SQW device at room temperature. The signal at 1.42 eV from the barrier can be modelled with "E F equal to the bias (V app ). The well signal requires a reduced "E F .

Fig. 5 .

 5 Fig. 5. Schematic representation of the radiative transitions in the model of Ref. 14.

Fig. 6 .

 6 Fig. 6. Definition of the parameters ! n , ! p which shift the intrinsic Fermi energy between barrier and well.

Fig. 7 .

 7 Fig. 7. a) Fits with model described to AlGaAs and GaAs heterostruture p-i-n controls. b) Recombination as a function of position in i-region for 30 MQW cell.

Fig. 8 .

 8 Fig. 8. Experimental dark currents (heavy dots) for AlGaAs/GaAs QWSCs with a) 30 wells and b) 50 wells compared with model using homostructure control lifetimes (light dots) and with reduced "E F (broken lines).

Fig. 9 .

 9 Fig. 9. Normalised efficiency of 30 well Al x Ga 1-x As/GaAs MQWs (Al fraction x = 0.2 and 0.3) measured in a 3000K blackbody spectrum and corrected using QE measured as function of temperature to AM1.5 conditions. Comparison is with control, homostructure AlGaAs p-i-n cells with comparable x values.

Fig. 10 .

 10 Fig. 10. Spectral response of a strained InGaAs/GaAs p-n MQW device with the 14 wells in the neutral n-region compared with its p-n control and a p-i-n cell with 15 wells in the i-region.

Acknowledgements

I would like to that Richard Corkish, Stefan Ketteman and Jenny Nelson for their very efficient organisation of a very stimulating conference.

The QPV group has been supported by the Greenpeace Trust, The Mark Leonard Trust, the European Union, Training and Mobility of Researchers programme and the U.K. Engineering and Physical Sciences Research Council (EPSRC). We are grateful for the material and device fabrication of our collaborators in the EPSRC III-V Facility, University of Sheffield.

We are also grateful for the material supplied by Tom Foxon and Tin Chen at the University of Nottingham, Christine Roberts of the Centre for Electronic Materials and Devices at Imperial College. We are particularly grateful for the advice Massimo Masser of the CNR-IME, University of Lecce, Italy on strain-balance material problems.


C I Cabrera

J C Rimada

L Hernandez

James P Connolly

A Enciso

D A Contreras-Solorio

Anisotropic emission and photon-recycling in

Keywords: Quantum well, Strain in solids, Solar cell, Conversion efficiency, Modelling

published or not. The documents may come

I. Introduction

The strain-balanced quantum well solar cell (SB-QWSC) is a GaAs p-i-n solar cell with quantum well (QW) layers incorporated into the i-region with InGaAs as well material and GaAsP as barrier material. The compressive strain in the InGaAs QW is matched by tensile strain in GaAsP barriers, overcoming the lattice-mismatch limitation. Using this strain-balancing technique, more than 65 quantum well layers have been grown without dislocations [START_REF] Johnson | Proceedings of the 4th World Conference on Photovoltaic Energy Conversion[END_REF][START_REF] Ekins-Daukes | [END_REF]. The purpose of this design is to improve the spectral response of the cell in the energy region below the absorption edge of host material, in order to gain an extra photocurrent and therefore an increment in the short-circuit current. Under solar radiation, a drop in open circuit voltage (V oc ) of a SB-QWSC is avoided, due to the inclusion of GaAsP with a higher bandgap than GaAs. This way the addition of short-circuit current (J sc ) from the quantum wells leads to an increase of the solar cell conversion efficiency. Photo-generated carriers can escape from the quantum wells with near unity efficiency via a thermallyassisted tunneling process due to the presence of the built-in electric field in the intrinsic region. SB-QWSC can achieve optimal band-gaps for the highest single-junction efficiencies due to the tunability of the quantum well thickness and composition. The GaAsP and InGaAs layer widths were chosen to ensure the average lattice parameter across the i-region was equal to that of GaAs. Elastic constants were considered to evaluate the tensile and compressive strain in GaAsP and InGaAs layers. Thus, if L B is the barrier thickness, L W is the well thickness,

Biaxial strain can only be achieved on the nano-scale, giving nano-structured solar cells a fundamental advantage over bulk semiconductor solar cells. The changes in the band structure of the layer under strain have significant effects on the SB-QWSC. The growth of strained GaAsP and InGaAs layers allows a wider choice of P and In compositions to fit the energy levels in the quantum wells. Thus, the balanced strain between GaAsP and InGaAs layers is also designed as an extra parameter to tailor the layer materials and the SB-QWSC performance.

The total strain in the layer may be resolved into a hydrostatic component and an axial component.

For unstrained bulk material, the heavy hole (hh) and light hole (lh) bands at the top of the valence band are degenerated at the Brillouin zone centre. The hydrostatic component of strain acts on the band edges, thereby changing the band gaps. However, it is the axial strain component, acting on degenerate bands such as in the valence bands, in which the axial component lifts the degeneracy that exists for the heavy-hole and light-hole bands at the band edge ( Γ point). Under compressive strain, bottom energy of the conduction band is displaced to higher energy and the valence band splits, with the lh band moving further from the conduction. On the contrary, under tensile strain the GaAsP band gap is reduced and the highest valence band is the light hole band. Consequently, when the In an P compositions are varied, the strains in the barrier and well layers modify absorption threshold in both layers. This behavior was demonstrated in previous work [3].

Therefore, compressive strain results in lower thermal occupancy of the lh band relative to the hh band, and radiative transitions from the conduction to the hh band are favored over those to the lh band. If the splitting becomes greater than a few ~kB T, lh transitions could be suppressed almost entirely [START_REF] Adams | Recent results for single junction and tandem quantum well solar cells[END_REF][START_REF] Adams | Experimental measurement of restricted radiative emission in quantum well solar cells[END_REF]. In order to examine this behavior, the anisotropic radiative recombination and gain, as consequence of the strain in the quantum wells, is investigated in this paper in order to determinate their influence in the SB-QWSC performance.

As a result of the dislocation-free material, the radiative recombination dominates in SB-QWSCs at high current levels. This makes possible the exploitation of radiative recycling by mean of the growth of distributed Bragg reflectors between the active region and the substrate of the cell which it has been possible to enhance SB-QWSC [START_REF] Johnson | Observation of photon recycling in strain-balanced quantum well solar cells[END_REF].

The observed rise in solar cell efficiency due to distributed Bragg reflectors (DBRs) is product of the reflection of photons back into the cell of photons (which would otherwise have been absorbed in the substrate) leading to photon recycling, that results when photons emitted by carrier recombination are reabsorbed in the same device. The photon recycling effect can be observed as an increase in the quantum well absorption.

We will discuss the theoretical background to radiative recombination, gain, photon recycling and then present the results of simulations of the SB-QWSC that it takes account of DBR and anisotropic effects. We calculated quantum and conversion efficiencies and observed an increment in the SB-QWSC performance, particularly under solar concentration.

II. Anisotropic radiative emission and gain

In previous paper [3], it was shown that high SB-QWSC performance was achieved for 3% In composition. Moreover, for SB-QWSC with deeper quantum wells (higher indium fraction) the efficiency falls. However, the radiative recombination current could be suppressed in SB-QWSC devices with deep QWs relative to the prediction of the generalized Planck formula assuming isotropic emission. This effect was not considered in reference [3] but it will be taken into account in the present work.

Following reference [START_REF] Adams | Recent results for single junction and tandem quantum well solar cells[END_REF][START_REF] Adams | Experimental measurement of restricted radiative emission in quantum well solar cells[END_REF], emission can be defined as TE, which is polarized in the plane of the QWs, and TM, which is polarized perpendicular to the plane of the QWs. It is therefore possible for TEpolarized light to be emitted either out of the face or the edge of the QWs, whereas TM-polarized light can only be emitted out of the edge of the QWs, as shown in Fig. 1. The hh transition couples solely to TE-polarized emission, and the lh band couples predominantly to TM-polarized emission with a minor TE-polarized contribution.

The spontaneous emission rates, R spon , were calculated by ab-initio methods [START_REF] Singh | Electronic and Optoelectronic Properties of Semiconductor Structures[END_REF], where the transition from bulk to quantum wells structures was carried out by converting the 3D density of states to the 2D density states. To compute TE and TM emissions out of the faces and edges of a quantum well, it was considered that when the In and P compositions and their layer widths are varied, such that the condition given by Eq. ( 1) is satisfied, the generated strain modifies the spontaneous emission rate.

The emission spectrum from a solar cell depends on the absorption coefficient and the carrier density through the quasi-Fermi-level separation, ∆E f . To model the emission from either sample at a given generated strain we first calculated the absorption coefficient using a quantum-mechanical model. We solved for the energy levels of the strain-balanced QW within the envelope function approximation and then calculated the absorption coefficient using Fermi's golden rule. In order to determine the QW energy levels in the hh and lh bands under varying compressive strain a 4x4 k•p Kohn-Luttinger Hamiltonian was used [3]. Furthermore, valence band structure for holes in the quantum well was calculated using a 4x4 k.p Hamiltonian model. The f E Δ values for the AM1.5 solar spectrum [START_REF]Standard Tables for Reference Solar Spectral Irradiances: Direct Normal and Hemispherical on 37 C Tilted Surface[END_REF] were computed for a more general method to the one reported by Tsiu et al [START_REF] Tsui | [END_REF].

We assumed that the number of photogenerated carrier pairs is equal to the total emitted photo flux. In the absence of any photon density, the emission rate is the spontaneous emission rate, provided an electron is present in the state k r and a hole is present in the same state k r in the valence band. The rate depends on the occupation probability functions for electrons, e f , and holes, h f , with the same k-value. The occupation probability function for electrons and holes depends on the corresponded quasi-Fermi level. The spontaneous emission rate expression for quantum well structures is obtained be integration over all possible electronic state:

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 , 2 e h if n m spon n m e h e n h m d k a p E k E k R d f E k f E k δ ω π ω ω ⎡ ⎤ ⋅ - - × ⎢ ⎥ ⎢ ⎥ = Α ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ∫ ∑ ∫ r r r h h h r r (2)
The integral over ( )

d ω
h is to find the rate for all photon emitted and the integration over 2 d k is to get the rate for all the occupied electron and hole subband state.

Equation ( 2) summarizes the discrete energy states of the electrons (index n) and the heavy holes (index m) in the well.

( )

e
2 2 3 2 0 2 r q n m c Α =
h is a material dependent constant, where h is the reduced Planck constant, r n is the refractive index of the well material, 0 m is the free electron mass, q is the electron charge and c is the speed of light. The first term inside the element ˆif a p ⋅ r represents the polarization unit vector, â , while the second term represents the momentum matrix element, if p r .The spontaneous emission rate of the QWs was calculated using the above formula.

In a semiconductor in nonequilibrium condition, the total electron concentration n and the total hole concentration p are described to be the respectively electron and hole quasi-Fermi levels. If detailed balance is applied when each photons produce one electron-hole pair and all recombination events produce one photon, the electrons and hole quasi-Fermi levels in the quantum well structure were calculated by solving the following equation systems:

( ) ( ) e h e h F F f F F n E p E E E E = Δ = - (3)
where

f E Δ is the quasi-Fermi level separation.
Determining f E Δ is essentially a matter of normalizing the emission spectrum to the generation rate.

If detailed balance applies, the number of photogenerated carrier pairs is equal to the total emitted photon flux, and the gain (G) is defined as the number of photogenerated carrier pairs per unit area and time:

( ) ( ) ( ) 0 0 , G G z dzd L d λ λ ω ω ∞ ∞ = = ∫ ∫ ∫ h h ( 4
)
where ( )

, G z
λ is the electron-hole pair generation rate at a z depth from the surface in the grown direction and is given be the expression:

( ) ( ) ( ) ( ) ( ) 0 , 1 , exp , z G z R z F z dz λ λ α λ λ α λ ⎡ ⎤ ′ ′ = - - ⎡ ⎤ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ ∫ (5)
where ( ) R λ is the surface reflectivity spectrum of the antireflection layer (ARC), ( ) F λ is the AM1.5 solar spectrum and ( )

, z α λ is the absorption coefficient to a z depth from the surface. The exponential factor is due to the attenuation of light in the layers between the surface of the cell and the depletion layer. The layers considered in our calculus are antireflection layer, emitter layer, and space-charge region from to the emitter layer (see figure 2).

The emitted flux density ( )

L ω h , of photons of energy ω h , is given by: ( ) ( )( )

2 2 3 2 2 1 f B r E k T n L h c e ω α ω ω ω -Δ = - h h h h (6)
At low enough carrier density, where f E Δ is much smaller than the effective band gap, the Boltzmann approximation is used, and Eq. ( 6) is simplified, then the dependence on f E Δ is an explicit function. From Eq. ( 4) and Eq. ( 6), we found:

( ) ( )( ) ( ) 2 2 3 2 0 2 1 ln 2 B k T r f B n E k T e d G c ω α ω ω ω π ∞ - ⎡ ⎤ Δ = - ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ∫ h h h h h (7)
The total electron concentration is calculated by: E are the conduction valence band edge energy for quantum well and barrier material respectively, QW e g is the electron quantum well density of states and Bulk e g is the electron bulk density of states. To calculate the total hole concentration we proceed in a similar way. Then the equation system (3) may be solved and the quasi-Fermi level is determined. To compute the spontaneous emission rate from QW region, the expression (2) was used.

( ) ( ) ( ) ( )
Figure 3 shows TE and TM spontaneous emission rates and its relation as a function of In fraction. The broken lines are due to the emergence of QW energy levels, e 2 -hh 2 and e 2 -lh 2 transitions, when the well depth increases. It can be seen that increasing In fraction, the QWs are under higher compressive strain, resulting in that radiative transitions from the conduction band to hh band (TE) are favored over those to lh band (TM). However, both polarized emissions increase with well depth, showing that biaxial compressive strain does not suppresses a mode of radiative recombination in the plane of the QWs, although certainly the TM/TE relation diminishes. So that, increasing the In composition leads to larger radiative recombination that increases the recombination dark current. In figure 4, spontaneous emission rates and gain are plotted as a function of In fraction. The spontaneous emission rates in QWs have already been displayed in a previous figure but are repeated here together to G to emphasize the huge difference between their values. From these results it follows that the generation of electron-hole pairs in the QWs is much higher than the radiative recombination, and if to these is added the existence of transverse electric field in the depletion region, which favors thermally assisted tunneling, then the carriers escape from the QWs with unity efficiency.

III. Photon-recycling

A DBR is a region consisting of layers of alternating refractive indices optimized for a specific wavelength such that each layer is a quarter wavelength thick. As a result, partial reflections from each interface interfere constructively and the reflectivity is high over a narrow wavelength band. Photon-recycling is the generation of an electron-hole pair via the absorption of a photon emitted elsewhere in the cell. The increased absorption is due to the reflection of incident solar radiation which has not been absorbed on its first pass through the cell and may then be reabsorbed on its second pass. It is equivalent to say that a DBR doubles the optical path length of a SB-QWSC without altering the length over which minority carriers must travel. The photons emitted by recombination into quantum wells were also considered. The net solar incident radiation flow on front surface of a solar cell was modeled as a Fabry-Perot cavity. We calculated the contribution of the multiple internal reflections inside the device and, so that the new AM1.5 solar spectrum F net (λ) is given by:

( ) ( ) ( ) ( ) * * 2 * 1 T T B A net B A T j j j r r e F F e r r l α α λ λ α α λ ⎡ ⎤ + ⎢ ⎥ = + ⎢ ⎥ - ⎣ ⎦ = ∑ (9)
Where ( ) j α λ are the absorption coefficients of each layer of Fabry-Perot cavity structure, where it was taken into account the exciton effect in the quantum well, j l are their widths and A r , B r are the internal reflectivity from the front and back surface of the cell, respectively. The photocurrent J PH is calculated from the total quantum efficiency (QE TOTAL ) of the cell:

( ) ( ) ( ) * 2 * 1 2 1 T T B A PH TOTAL B A r r e J q F QE d e r r α λ α λ λ λ λ ⎡ ⎤ + ⎢ ⎥ = + ⎢ ⎥ - ⎣ ⎦ ∫ (10)
where 1 λ = 400nm and 2 λ is the effective absorption threshold determined by the fundamental electron and hole confinement states. The p-region and n-region contribution to QE TOTAL was classically evaluated solving the carrier transport equations at room temperature within the minority carrier and depletion approximations [START_REF] Hovel | Semiconductors and Semimetals, Solar Cells[END_REF]. The contribution of photo-generated carriers in the intrinsic region to QE TOTAL values is calculated by the expression [START_REF] Rimada | [END_REF]:

( ) ( ) ( ) 3 * 1 1 exp 1 exp i j j B W W j QE R z W N λ λ α α α = ⎧ ⎫ ⎡ ⎤ = - - × - - - ⎡ ⎤ ⎨ ⎬ ⎣ ⎦ ⎣ ⎦ ⎩ ⎭ ∑ (11)
where ( ) R λ is again the surface reflectivity spectrum of ARC. The first exponential factor is due to the attenuation of light in the layers between the surface of the cell and the depletion layer (see figure 1). On the other hand, j α and j z are the absorption coefficient and the width of these precedent layers, respectively, B α is the absorption coefficient of the bulk barrier material, and * W α is the dimensionless quantum well absorption coefficient, used for energies below the barrier band gap. Following Bastard [START_REF] Bastard | Wave Mechanics Applied to Semiconductor Heterostructures[END_REF], we calculate the density of states for the single quantum well within the envelope function approximation. The dimensionless quantum well absorption coefficient can be calculated as follows:

* W W α α = Λ (12) ( ) ( ) , , (
)

n m n m W eh h el h n m n m E E E α α α - - = + ∑ ∑ (13)
where W α is the well absorption coefficient and Λ is the ''quantum thickness of the heterostructure'' which represents the width of the region containing the QW system, ( )

.

m E E E E E E E E E E E E a α ψ ψ δ - ⎡ ⎤ Θ - - - ⎢ ⎥ Β ⎢ ⎥ = Λ ⎢ ⎥ + - - - + ⎢ ⎥ ⎣ ⎦ h ( 14
)
The formula summarizes the discrete energy states of the electrons (index n) and the heavy holes (index m) in the well. m -is the reduced mass of the e-hh system, and the second term the additional absorption peak contributed by the excitons. Here ex a denotes the effective Bohr radius of the exciton. For e-lh transition a similar expression is obtained with hh replaced by lh and p E by 3 p E . The absorption of the QWs was calculated using the above formula. The other parameters have been previously stated. On the other hand, the exciton binding energies were analytically evaluated in the framework of fractionaldimensional space [START_REF] Mathieu | [END_REF].

Figure 5 shows modeled and experimental quantum efficiency (QE) versus wavelength for qt1897b sample from the Quantum photovoltaics Group of Imperial College. The cell is a p-i-n diode with an i-region containing five QWs that are 9.6 nm wide of compressively strained In 0.16 Ga 0.84 As inserted into tensile-strained GaAs 0.91 P 0.09 barriers at strain-balance condition. The extra absorption is displayed in the inset of figure 4, at wavelengths in excess of the GaAs band gap where the increase in quantum efficiency in the 880 nm-1µm is readily apparent. The figure also shows the computed QE spectrum with DBR, using r A = 0.1 and r B = 0.95. The main feature of this plot is that for a highly reflecting mirror, nearly all photons absorbed contribute to the QE.

  denote the QW subbands of the electrons and heavy holes andδ denotes the Dirac delta function. The factor ( )

  well states n and m, which numbers depend on the quantum wells width and depth, coefficients due to electron-heavy hole and electronlight hole transitions to conduction band, respectively, which considered the exciton absorption to match accurately with experimental data in the long wavelength region. The quantum well absorption coefficients

E

  denotes the QW energies of the electrons and heavy holes as difference from the conduction or valence band, respectively, binding energy and ( ) E Θ is the step function. For the simulation model, the δ -distribution, was modified by a Gaussian broadening term to represent the inhomogeneous broadening caused by thermal effects as well as the deviation from ideality of the QW due to the limitations of the growth. The factor is a material dependent constant. The matrix element contains the electron wave function n e ψ for the nth electron level and the heavy hole wave function m hh ψ of the mth heavy hole level and p E is the Kane matrix element (~23eV). The first term inside square bracket represents the occupation probability and determines the absorption edge of a bound state where * e hh

Figure 1 Figure 2

 12 Figure 1

Figure 3

 3 Figure 3

Figure 4

 4 Figure 4

Figure 5

 5 Figure 5

Figure 6

 6 Figure 6

Figure 7 Figure

 7 Figure 7

Fig. 1 .

 1 Fig.1. The polarization of the emission out of the faces and edges of a quantum well. Light polarized in the TM mode can only be emitted out of the edge. Light polarized in the TE mode can be emitted out of the face or the edge [4, 5].

Fig. 2

 2 Fig.2The schematic band-structure of the SB-QWSC. The QW stack is embedded within the depletion zone of the GaAs cell and extends the absorption edge of the cell beyond that of a classical GaAs solar cell.

Fig. 3 .

 3 Fig. 3. Modeled spontaneous emission rate for TE and TM modes and TM/TE ratio versus In composition for 10 well embedded within i-region of the SB-QWSC. Well width, L W =15 nm and P composition, y =0.05. The TE mode is favored over TM mode, but both polarized emissions increase with well depth.

Fig. 4 .

 4 Fig. 4. Spontaneous emission rate and gain versus In composition for 10 well embedded within intrinsic region of the SB-QWSC. Well width, L W =15 nm and P composition, y =0.05. Gain is several orders greater than radiative recombination.

Fig. 5 .

 5 Fig. 5. Modelled and experimental quantum efficiency versus wavelength for 5 well qt1897b sample from the Quantum photovoltaics Group of Imperial College. The inset shows the wavelength range dominated by the QW absorption with and without influence of Bragg reflector.

Fig. 6 .

 6 Fig.6. Contour plot for conversion efficiency as a function of Bragg reflectivity and quantum well number. P composition, y = 0.09. In composition, x=0.17 and L W =9.6 nm.

Fig. 7 .

 7 Fig. 7. Conversion efficiency as a function of solar concentration for several GaAs 0.96 P 0.04 /In 0.03 Ga 0.97 As/GaAs SB-QWSC which differ in the number of QW embedded within the i-region with and without influence of Bragg reflector.

We have also demonstrated that photon recycling effect have a substantial impact on the overall performance of a SB-QWSC. DBR reflectivity values depend on the number of quantum wells in the i-region. We have optimized SB-QWSC design to achieve single junction efficiencies above 30%. These results on DBR SB-QWSC's show that they hold much promise for use in both single junction and multi-junction space solar cells or terrestrial concentrator solar cells.

This is clearly a desirable feature as it implies that carrier collection from the MQW is very efficient allowing the increase in short circuit current. It is a good indicator that the QE of an MQW cell could well approach that of a bulk cell with a similar band-gap if the light could be confined inside the cell until it was completely absorbed.

IV. Influence of anisotropic radiative emission and photon recycling on the SB-QWSC performance

The conventional current-voltage characteristic for a p-i-n solar cell can be written as a function of applied voltage (V) by the well-known Shockley equation for ideal diode to which the generation and recombination currents in the intrinsic region of photogenerated carriers are added. To calculate the recombination current density and photocurrent, anisotropic radiative emission and photon recycling were taken into account. Once the expressions for the effective density of states, the absorption coefficient, the radiative recombination current density, and photocurrent were found for SB-QWSC, then it is possibly to compute the J-V characteristic, and conversion efficiency (η) can be evaluated [3,14].

The dependence of conversion efficiency on back mirror reflectivity and quantum well number (N w ) is examined in figure 6. This plot suggests that with the addition of a distributed Bragg reflector in the device, fewer quantum wells are required to grow in the i-region in order to achieve high performance. In fact, low energy photons from the radiative recombination in the QWs can be reflected back into i-region and reabsorbed, lowering the radiative recombination current and improving the open-circuit voltage. On the other hand, with increasing N w it is necessary to use DBR with high reflectivity to overcome the recombination losses.

It can be expected that SB QWSC under concentration will be operating in a regime where recombination is dominated by radiative processes. Therefore, photon recycling effect is favored under solar concentration when photons emitted from radiative recombination are subsequently reabsorbed by the solar cell. This outcome can be observed as an increase in minority carrier lifetime or reduction in dark-current [15].This behavior is shown in Figure 7, where we have examined the conversion efficiency as a function of solar concentration for optimized GaAs 0.96 P 0.04 /In 0.03 Ga 0.97 As/GaAs solar cell with 20 nm quantum well width [3]. We used r A = 0.1, r B = 0.95 and resistive effects were neglected. It can be observed how the conversion efficiency should increase with solar concentration up to 1000 suns. In any concentration range, the DBR cell efficiency improvement over the non-DBR cell which is explained by the fact of the lower dark current in the DBR cell. This effect also causes that the net increase in conversion efficiency is lower with increasing N w , as it can be noted in figure 7.

Summary

We have studied the emission light polarized in the plane perpendicular to the quantum well, which is related to the light hole transition and, the emission polarized in the plane of the quantum wells. It was found that the spontaneous emission rates TM and TE increase when the quantum wells are deeper. We have demonstrated that biaxial compressive strain does not suppresses a mode of radiative recombination in the plane of the QWs. The assumption that the photogenerated carriers can escape from the QWs with near unity efficiency, via a thermally-assisted tunneling process, is strongly supported by the several orders difference between gain and radiative recombination. For the modeled SB-QWSC with deeper QWs, both conversion efficiency and open-circuit voltage always fall because the radiative recombination increases.