- Email: [email protected]
Photovoltaic conversion at reduced dimensions
Physica E 14 (2002) 1 – 10
www.elsevier.com/locate/physe
Photovoltaic conversion at reduced dimensions Hans J. Queisser ∗ Max-Planck-Institute for Solid State Research, Heisenbergstr. 1, D-70506 Stuttgart, Germany
Abstract Reducing the geometric dimensionality in a photovoltaic cell is useful in designing optimal contact geometry, in enhancing the conversion e%ciency by enlarging the concentrations of photogenerated carriers and, generally, by utilizing thin-)lm structures for solar cells. It is not yet obvious whether or not dimensions in the range of nanometers are useful or needed. ? 2002 Elsevier Science B.V. All rights reserved. PACS: 84.60.J Keywords: Nanostructures; Thin )lms; Photovoltaics
1. Introduction Nanostructures and Photovoltaics, what an irresistible combination! Nano, the greek word for dwarf is the novel vocabulary. And: photovoltaics, what great hope this word suggests! To derive our necessary energy from simple cells without moving parts, without noise, without exhaust nor waste. Photovoltaic utilization of the regenerative, vast supply of solar radiation appears to be the ideal solution for our energy crisis. The title of our workshop seems to seriously suggest that nanostructures might improve solar-cell e%ciencies, maybe also even the cost of solar modules. One ought to be cautious, however, not to raise unfounded optimism. Solar-cell technology is complicated and—even today, after decades of research— a rather costly a:air. My contribution to this workshop will be much more modest than directly pertaining to dimensions
∗
Tel.: +49-711-689-1600; fax: +49-711-689-1602. E-mail address: [email protected] (H.J. Queisser).
in the nanometer regime. (I shall, however, use nanometers for quantifying all length dimensions in this paper.) Reductions of geometric scales in semiconductor solar cells have already been proven useful and are thoroughly based on solid-state physics, but really only restricted to the micrometer regime. First, solar cells made with bulk semiconductors are now, generally, regarded as being too expensive. Hence, thin-)lm cells are currently at the center of research and development activities. A thin )lm concentrates the photogenerated electrons and holes more e%ciently than a thick cell, therefore reduces entropy and thus raises the energy conversion e%ciency. Secondly, the conversion is enhanced by using contacts, which no longer cover the entire back surface of a solar cell, but are distributed as optimally reduced small areas. This phenomenon, long overlooked by the engineering community, tends to gainfully preserve the light-generated split into quasi-Fermi levels of electrons and holes. Third, carrier relaxation and recombination processes are reconsidered with the question of whether there might be any chance to utilizing microstructuring in order to inBuence non-radiative
1386-9477/02/$ - see front matter ? 2002 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 6 - 9 4 7 7 ( 0 2 ) 0 0 3 5 3 - 3
2
H.J. Queisser / Physica E 14 (2002) 1 – 10
Fig. 1. Solar-cell e%ciency as function of grain size.
carrier recombination, but no clear pathway is currently visible. That a naive reduction of particle size—as is often useful in nanotechnology—is not bene)cial for conventional semiconductor solar cells is seen in Fig. 1 [1]. This indicates that the grain size reduction tends to reduce e%ciencies, and good single crystals are optimal! 2. Junction basics Contemporary p–n junction semiconductor solar cell are rather primitive devices, when compared to the standards of modern semiconductor technology. This year, the major suppliers of silicon-integrated circuits utilize single-crystalline silicon wafers of 3 × 108 nm diameter to fabricate devices with a design rule of merely 130 nm. The continuous increase of wafer diameter and concomitant decrease of the characteristic device dimensions—together with design cleverness—form the technical basis of the famous law by Gordon Moore [2,3]. 1 Exponentially decreasing cost and sharply rising functionality are the results. Semiconductor devices have been the major new scienti)c invention and the essential new economic force of the second-half of the 20th century. The general public is vaguely aware of this remarkable interplay of science and economics. This awareness is then easily, but erroneously carried over 1
For a simple interpretation, see Ref. [2].
to the economic expectations for solar cells. Why not equally reduce cost for solar energy converter cells? The answer is unfortunately simply evident: size reduction does not apply to solar cells, since we must rely on extensive area for harvesting the sunlight. Solar cells are indeed somewhat primitive. They are not only large-area, non-microstructured devices. They also operate at much, much lower frequencies than the integrated circuits with their GHz capability; cells work at zero frequency, they supply direct current. Solar cells are also primitive in their usage of just one p–n junction, not two as for bipolar transistors. Simulations of device performance thus rely essentially only on the forward portion of the characteristic for the junction current, I , versus voltage, V . The optimal e%ciency results for the recti)er equation [4,5] 2 I=I0 = exp(qV=nkB T ) − 1;
(1)
where I0 is the reverse saturation current, depending on carrier densities, lifetimes, and transport parameters. The electronic charge is conventionally designated by q; kB T is the thermal energy, indicating that the current Bow over the junction is thermally activated. The auxiliary factor n is just an embarrassing )t parameter, forced into Eq. (1) in order to describe non-ideal junctions. This parameter is misleadingly named junction quality factor. Ideal junctions have n = 1; the larger n, the less ideal is the junction current behavior. Lifetime, t, of the charge carriers is of essential importance. The longest possible value of t results only when radiative recombination prevails and is in thermal equilibrium by detailed balance with its surroundings [6]. This principle is the foundation for the thermodynamic theory of solar cell conversion e%ciency [7]. This work was my own personal )rst contact with solar cells, when I joined William Shockley in his laboratory inside an old apricot barn on 391 South San Antonio Road in Mountain View, California in 1959 [3]. In those years, US government research contracts were not easily granted for silicon electronics, but the Sputnik shock forced massive funds into all things for rockets and space. Shockley, however, wanted to understand silicon for his four-layer-diode, a switching device, which would 2
For an outline of junction physics: Ref. [4].
H.J. Queisser / Physica E 14 (2002) 1 – 10
3
Fig. 2. Multijunction solar cell, made in 1959=60 at the Shockley Transistor Corp. in Mountain View, California 9 [10].
only function with silicon junctions [8]. 3 Our little company, Shockley Transistor Corporation, never intended to produce and market solar cells, but we needed the contract money to study and control those irregular and non-ideal p–n junctions in silicon. My other project in 1959 was an experimental task. I fabricated a multijunction silicon cell with many elements in series in an attempt to raise output voltage and not just output current with increasing cell area [9,10]. 4 Shockley optimistically anticipated that large sheets of thin silicon )lms might become available for solar-energy conversion, for example by pulling from a lead–silicon melt. Some technique was, therefore, required to shape these large-area Si )lms into a complete solar-cell module [10]. Fig. 2 shows the principle. I succeeded to fabricate about a dozen of such multicells. These strange devices were actually the )rst integrated silicon circuits. I had to use very thin pieces of Si, of the order of 6 × 104 nm—which demanded steady hands and most delicate handling. Silicon is brittle, tends to break easily, but those thin things turned out to be reasonably Bexible and thus quite forgiving. We were forced to use such thin wafers in order to be able to employ dopant di:usions from both sides, as can be seen in Fig. 2. 3 For a historical and technical perspective of FourLayer-Diodes, see Ref. [8]. 4 The multicell work is reviewed in Ref. [10]. A recent thesis has reconsidered cascaded multijunctions: U. Kerst, Techn. U. Berlin, 2000, also see Ref. [10].
The successful technology for integrated circuits, however, chose another route. Stable silicon wafers of roughly 5 × 105 nm thickness were needed for any viable technology, which in turn invariably led to the contemporary semiconductor methodology of machining circuits only from one side of a silicon wafer. The entire set of electronic functions resides in shallow surface layers, of the order of a few thousand nanometers. The rest of the silicon is just a substrate for handling! Long-time di:usions from both sides, as I had to resort to for my slim little multicells, were totally impractical and unacceptable for mass productions. Contemporary integrated circuits are undeniably top loading appliances! Materials with nanosize dimensions face another serious problem in conventional solar cells. Carrier lifetime is the most sensitive measure of crystalline perfection. Any deviation from an ideal single crystal reduces lifetime and thus lowers conversion e%ciency. Indeed, single-crystalline materials, especially Si and GaAs, provide the cells with highest e%ciencies. Any nanocrystalline material is, therefore, in principle an inopportune choice for a cell material. Grain boundaries and the many other defects sharply curtail cell output. Very small nanoparticles are thus unsuitable, except as speci)c oxides for photoelectrochemical cells, generating chemical output, such as oxygen or hydrogen, instead of electrical power output. Such cells and their relation to nanostructuring [12], are covered elsewhere in this special issue [11].
4
H.J. Queisser / Physica E 14 (2002) 1 – 10
3. Need for thin-lm cells The basic physics of semiconductor solar energy conversion has been adequately understood for quite some time [13,14]. The economic competitiveness of this sort of regenerative energy now hinges entirely on cost of materials, production, assembly, and possibly provisions for energy storage. Solar cells can currently compete with other energies only with massive subsidies or in isolated areas, where satisfactory grid supply is absent. The light weight of the cells, however, makes them ideal energy sources for space applications, where cost is of secondary signi)cance. Terrestrial applications demand a drastic reduction of materials cost [15]. Bulk materials, especially for silicon cells, appear to be uneconomical. Intense development e:orts have therefore recently been exerted towards thin-)lm cells. This problem is not as easy as it seems on )rst sight, since one characteristic length of a solar cells is the 1=e—absorption length for sunlight. Indirect-gap materials, such as silicon, have long mean-free paths of the order of 103 to 104 nm for the impinging photons. Special care has to be taken to compensate for this unfavorable impedance. Light must be trapped by multiple reBections at the boundaries. This trapping is an e:ective method to enhance the optical pathlengths within thin )lms of these indirect materials [16]. Computer programs have been created by Brendel in order to optimize such trapping by cleverly arranging prisms and related structures to maximize internal reBections to curtail all exits for the photons [16]. The second characteristic dimension of a solar cell is the di:usion length LD for the minority carriers, which must be as long as possible such that the charge carriers reach the cell’s external contacts by di:usion. This length typically ranges from about 103 up to about 106 nm and is thus of the same order of magnitudes as the photon mean free path. Nanostructuring is therefore quite far removed from cell technology. Thin )lms can most easily and economically be fabricated by evaporation or sputtering, yet such techniques usually generate imperfect crystals. Modern semiconductor technology thus uses epitaxial crystal growth wherever perfection is required. For solar cells, such epitaxy would become too expensive, unless the single-crystalline substrates are reusable. Such methods are known for quite some time [17] and have been
rediscovered [18] 5 as the cleverly named smart cut, to utilize substrates several times over for solar-cell production. The team of Werner at the University of Stuttgart, for example, is actively engaged in the work of developing novel techniques for economical thin-)lm production [19]. Table 1 reproduces a recent overview [20] for commercial, large-area thin-)lm solar cells. Semiconductors with both direct and indirect optical transitions are listed. Note that cells based on direct-gap semiconductors of the type AII BVI rank very prominently. CIS is the common abbreviation for the compound cadmium–indium diselenide; fabrication procedures for this material were successfully developed by Schock and colleagues [21] at Stuttgart University and are now used in starting large-volume productions in several countries. 6 Reduction of geometric dimensions for photovoltaic solar energy conversion has thus become an important technological topic, but this type of reduction does certainly not at all extend into the nanometer regime. 4. Entropy suppression in thin lms An interesting phenomenon was empirically observed in the study of thin-)lm solar cells. Under otherwise equal conditions of structure, surface recombination, and illumination, cells with thinner active layers indicated higher open-circuit voltages, hence better conversion e%ciencies than those having thicker layers. A variety of interpretations, some being fairly complicated, were o:ered [23]. The reason is, however, very simple and is entirely based on fundamentals of thermodynamics [22,23]. The con)nement within a thinner layer of width W raises the density of carriers (per unit volume), higher density means reduced entropy, thus better conversion e%ciency. The open-circuit voltage, Voc , for I =0 in Eq. (1) is Voc = kB T=q ln(Isc =I0 + 1);
(2)
where Isc is the short-circuit output current for V = 0. The reverse saturation current is Isc = qn0 W= . From 5
The “smart” cut is described in: Ref. [18]. CIS cells are now being produced by WUurth Solar Co. in Marbach, Germany. 6
H.J. Queisser / Physica E 14 (2002) 1 – 10
5
Table 1 Best present large-area thin-)lm solar-cell modules (standard conditions, aperture area) [20]
P ower (W)
Company=date
Device
Size (ft 2 )
91.5 70.8 61.3 59.0 56.0 53.9 44.3 38.0 35.7 31.0
BP Solar 5=00 United Solar, 9=97 First Solar, 6=96 Matsushita 6=00 BP Solar 9=96 BP Solar 4=00 Siemens Solar 3=99 Kaneka 9=00 United Solar 6=97 Golden Photon 4=97
CdS=CdTe a-Si=a-SiGe=a-SiGe=SS CdTe=CdS CdS=CdTe a-Si=a-SiGe CdS=CdTe CdS=CIS-alloy a-Si=c-Si=glass a-Si triple junction CdS=CdTe
9.5 10.2 7.8 6.0 8.2 5.4 4.0 4.1 5.0 3.7
Eqs. (1) and (2) and with Isc I0 , one obtains the derivative dVoc =dW = −kB T=qW . The entropy s per charge carrier particle in a semiconductor with an e:ective density of states Nc in the conduction band, having the electron e:ective mass m∗ ; Nc = 2(2m∗ kB T=h2 )3=2 is s=kB =
5 2
− ln(n=Nc (T )):
(3)
This entropy s is the only physical quantity depending on W , since n(W ) = Isc =qW . Assuming that lifetime remains independent of thickness W and assuming non-degeneracy, we obtain [23] dVoc =dW = (kB T=q)(n−1 dn=dW + p−1 dp=dW ) (4) as the explicit formula for the change of output voltage with change of layer thickness W , based on the consideration of entropy reduction with compression. Since the derivatives of particle densities with respect to thickness, such as dn=dW , are negative, the open-circuit voltage Voc does increase with shrinking W , and so does the e%ciency, since the current remains constant. We have again a direct bearing of geometric dimension upon solar-cell operation, but once more we are far away from the nanometer regime. One might speculate to introduce yet smaller dimensions, such as arrays of quantum wells to more fully bene)t from this e:ect. Practical considerations, such as providing proper contacts for both carrier types or complexity of cell production, seem to argue against this proposal, but future research is advisable. Carrier extraction, as done for example in charge-coupled-devices (CCDs) [24], is a possibility, but probably would
E%ciency (%) 10.6 7.6 (stabilized) 9.1 11.0 7.6 10.8 12.1 10.0 (est. stable) 7.9 9.2
turn out to be by far too complicated and thus too expensive. 5. Early engineering e!orts Solar-cell development in the United States was sharply accelerated during the early days of the reaction to the Soviet Sputnik in the 1960s, which I remember quite well from my apprentice years, working in Mountain View, California, now recognized as the “Cradle of Silicon Valley” [3]. The emphasis then was very much on engineering aspects to quickly obtain modules of energy supply for satellites. The semiconductor junction solar cell was originally invented at Bell Laboratories. Earliest attempts with Si of low perfection were made by Ohl [25], and were not yet convincing. Better silicon materials and more e:ective and controlled ways of doping, such as using di:usion of dopants, were the basis of the successful cell technology by Chapin, Pearson, and Fuller at Bell Labs [26], 7 with Prince providing the )rst theoretical treatise [13,14,27]. Shockley told me that he and colleagues obediently went to the Pentagon in Washington right after the invention of the cell by Chapin, Fuller, and Pearson, but the US government was not at all interested then and allowed free publications. The Bell System then made trials to replace standard batteries in rural telephone networks by solar-cell systems. These tests, done at Americus, 7
Russell Ohl detected by accident junctions in Si crystals via a photovoltage as early as 1939=40; see: Ref. [25].
6
H.J. Queisser / Physica E 14 (2002) 1 – 10
Georgia, failed [28]; the cells were quickly being covered by opaque masses derived from ornithological feces! (Layers of supposedly about 106 nm.) Russian colleagues from the physics community later narrated to me [29] that the Soviet Union immediately recognized the signi)cance for space power sources and began to work at solar cells. In the USA at that time, the proponents of small nuclear power sources for space applications were quite con)dent that their systems would be chosen—and I remember conferences of the American Rocket Society [30], where those Bimsy solar cells were derided as just being toys. 6. Requirements for carrier recombination Engineers took over and made estimates for losses in order to derive maximal e%ciency and to choose optimal materials according to an energy gap Eg to match the solar spectrum. Shockley and I then tried to publish our physics-based thermodynamic theory, which was )rst rejected as being trivial and unnecessary, eventually, however, did get published [7]. We gave talks [31] and tried to tie our e:orts to the glorious work by famous ancestors such as Carnot, whose new science of thermodynamics overcame the purely empirical estimates of steam-engine e%ciency by merely listing all possible energy loss mechanisms, like friction or heat losses, and trying to minimize those. One example of this empirical, pragmatic approach for solar energy conversion is the work by Wolf [32], which served as a convenient engineering guideline for practical developments. Our claim for maximal cell e%ciency was that one should reach the minimal, unavoidable carrier recombination. This case would be attained if only the necessary photon emission, as required from detailed balance [7], were to be present and no non-radiative recombination would take place. I recall a vivid discussion at the American Physical Society March Meeting in Cleveland in 1960, which ensued after my talk [31]. The colleagues from the Princeton RCA Laboratories had just ascertained that recombination in good gallium arsenide crystals was essentially of radiative character, which we now clearly know from the direct band gap structure of this compound semiconductor. Paul Rappaport asked me, if this would not
mean that GaAs should be an excellent solar cell material. Based on our theory, I obviously had to agree. Rappaport then said with a mixture of chagrin and triumph that such was not the case. The band gap of GaAs ought to be most appropriate, but still the cells always showed awfully low e%ciencies. I shrugged my shoulders, feeling embarrassed and helpless at the rostrum. Now, of course, we know especially after the work of Woodall and Hovel [33]—that indeed excellent cells with record conversion e%ciencies (¿ 24%) are made today with GaAs, but one needs to completely suppress the very strong nonradiative surface—recombination processes in GaAs by means of a very thin-surface layer of (Al, Ga) As. Here, truly thin layers of only a few tens of nanometers (typically 30 nm) have proven to be extremely useful! 7. Contact sizes Reduction of Joule losses in the contacts and metallic leads is one of those obvious loss mechanisms. The illuminated front side contacts represent one of the many compromises typical for solar cells. Large-area contact )ngers provide advantageously small ohmic resistance, but they also reduce the area of insolation and cause an e%ciency reduction by about 5% points. The back-side contacts were at that time considered to be much simpler challenges; one just had to cover the entire unilluminated reverse side by a good metallic contact [32]. This seemingly obvious but really naive recipe neglected one decisive fact of basic semiconductor physics. Every contact leads to strong electron–hole recombination and thus forces the two quasi-Fermi levels, n and p , for electrons, n, and holes p, to equalize and reestablish equilibrium conditions of one common Fermi energy EF . A solar cell, however, is by its very principle a device which has to preserve the non-equilibrium, which means to maintain as much and as long as possible this photon-generated split into two separate quasi-Fermi levels. The cell output lives from this non-equilibrium. Present-day solar cells made for very high e%ciencies, such as the high-e%ciency Si cells of Green (For earlier reviews, see Ref. [34].), 8 rely on an opti8
A. Blakers gave a detailed review of solar cell technology as of 1990: High E%ciency Silicon Solar Cells.
H.J. Queisser / Physica E 14 (2002) 1 – 10
7
mized back contact array, where the contact areas are kept as small as possible, and a back-surface )eld is introduced to repel the minority carriers from surface recombination. About 15 years ago, much work was done to establish point contacts on solar cells [35]. Those points, however, had diameters of several thousands of nanometers, being far from zero-dimensional features! [35] To repeat, dimensional control is important and has proven useful, but again not in the regime of nanometers. Contact optimization is usually concerned with geometries in the millimeter or—at most—submillimeter realm. 8. Curtailing relaxation and recombination Entropy must be minimized in solar-cell operation! This imperative, the noble task for the solar-cell physicist, means that one has to courageously—but not too expensively—combat all physical processes that degrade the precious solar input into useless forms of energy, heat obviously being the worst culprit. Most unwanted is the fast relaxation of high-energy electrons, which are generated by photons from the blue spectral emission of the sun. The carriers quickly slide down by intraband transitions via phonon generation to their respective minima of the electronic band structure E(k). Phonon emission is highly probable, thus the carriers cannot supply their nonequilibrium excess energies to the output. Roughly 30% of the solar input is thus wasted in typical silicon cells by such thermal degradation. Materials with higher band gaps would waste less of this energy, but then the losses rise for the unabsorbed red photons of the sunlight, again we encounter one of those necessary compromises of solar cell physics. Figs. 3 and 4 shows the situation after a high-energy, blue photon is absorbed and has created a cold hole at the top of the valence band and a hot electron in the conduction band far above the minimum. Usually, the hot carrier would dribble down to its band extremum, creating heat. One must suppress this entropy generation by providing another pathway (see footnote 12 of Ref. [7]). This situation was studied in detail by Sabine Kolodinski in her doctoral thesis at the Max-Planck-Institute in Stuttgart [36]. Careful spectral studies [37] and even absolute measurements [38] gave evidence of another, highly favorable path for
Fig. 3. Creation of two electron–hole pairs by one blue solar photon. The hot electron e1 donates excess energy and wave vector to another electron in the valence band.
Fig. 4. Maximal conversion e%ciency for a standard cell (lower curve), compared to a cell with optimized multiple-pair production [39].
relaxation. The hot electron e1 imparts its energy and quasi-momentum k to another electron in the valence band, lifting it, electron e2 , up to the conduction band minimum (see arrows in Fig. 2). Two electron–hole pairs are thus created; energies and momenta balance.
8
H.J. Queisser / Physica E 14 (2002) 1 – 10
Considerable impetus was created by Kolodinski’s experiments. If one could utilize this two-pair e:ect and completely suppress heat generation by phonons, one could— theoretically—achieve 44% ef)ciencies [39]. Fig. 3 compares the standard maximal e%ciency—according to detailed balance [7]—with the admittedly rather idealistic idea that all excess energy might be utilized for multiple pair productions. The optimal band gap energy Eg would shift towards lower energies, capturing thus more red sunlight and fully utilizing the enhanced radiation in the blue regime. One can construct optimal band structures and would then be faced with a novel inverse problem of calculating atomic con)gurations from an a priori band structure [40]. Such inverse calculations are di%cult, usually a de)nite solution cannot be found. There might be some possibilities, as cursorily summarized in Ref. [40] in a Helmholtz Memorial meeting and in Ref. [41]. This topic was pursued by Franceschetti and Zunger [42]. We realized, of course, that it would be di%cult to overcome the strong tendencies of recombination via phonons and channel all processes into creation of multiple pairs. We were, however, obedient that one should never say “Never!” and obtained a patent [43] on this idea of multiple pair generation. Brendel and Wolf at Stuttgart [44] worked out the details for one speci)c and easily obtainable—material: alloys of Si and Ge. These crystals ful)ll already the requirement of a band gap Eg smaller than that for Si. The fruits of this labor were disappointing: only very small increases of e%ciency might be expected from this system of a mixed crystal [44]. One Japanese industrial laboratory is apparently continuing along similar lines at the present time, but most unfortunately—no details are being divulged [45]. In the context of this Dresden Workshop the question arises whether there might be any means and ways to support the double-pair generation mechanisms. Nanostructures might be perceived to alter densities of phonon states or even transition matrix elements. Zone folding [46] 9 could, for example, be achieved in multilayer structures of small dimensions. Such folding of states at large values of k towards k = 0 favor direct optical transitions. At )rst 9
For a recent example, see: Ref. [46].
glance, such hopes do not seem to be well founded. Deviations from crystalline perfection and from bulk size have in general a tendency to relax the rules for conservation of k and hence to enlarge phonon generation. Nanostructuring thus appears to be actually a counterproductive proposal. I would nevertheless like to encourage the younger generation to optimistically look at these matters in greater detail. Heavier doping of solar cells is often of advantage, but then, an unavoidable recombination sets in: Auger processes, where an electron–hole pair donates energy and momentum to a third carrier. When Shockley and I looked at all of these unavoidable loss mechanisms, we realized that Auger recombination must be taken into account and asked the expert, Peter Landsberg, for help [7,47]. The Auger recombination involves three particles. One electron–hole pair recombines and imparts energy and momentum to a third particle. The inverse e:ect may be called Auger generation: a hot particle generates a pair, which is exactly what we have suggested to utilize for multiple-pair production from blue photons. Nanometer dimensions do once again not seem to be particularly helpful in harnessing the Auger recombination; probably again dimensional reductions might be playing a deleterious role for energy conversion. Nanostructuring ought nevertheless be investigated for obtaining substantial changes in the energy losses of carriers via relaxation intraband processes as well as by interband or defect-assisted recombination processes. Recombination represents one of the most di%cult and elusive electronic processes in semiconductors, especially in the materials with indirect optical transitions. Hope should not be abandoned that we can learn more about it and even )nd clever new ways to enhance solar cell e%ciencies. One caveat, however, must not be neglected: the cost of solar-cell production should—if anything—be lowered! This same sort of cautious conclusion was expressed already in 1957 by co-inventor Gerald Pearson: the silicon solar battery as such is too expensive to compete with more conventional large package power generators [28]. Here arises our perennial challenge! Acknowledgements I thank the many people with whom I had opportunities to collaborate in studies on solar energy con-
H.J. Queisser / Physica E 14 (2002) 1 – 10
version, starting with William Shockley and Sam Fok in Mountain View in the late-1950s and by interacting with colleagues, such as Gerald Pearson, Calvin Fuller, Peter Landsberg, Paul Rappaport, Joe Loferski, Martin Wolf and others in those early years. I remember with pleasure and respect the cooperation with contract monitors in the US government laboratories in Fort Monmouth, New Jersey and Dayton, Ohio: J. Mandelkorn, G. Hunrath, H. Kittl and, of course, William Cherry. In Stuttgart, I gratefully acknowledge the cooperation with Juergen Werner, Ralf Bergmann, Rolf Brendel, Sabine Kolodinski, Uwe Rau, MichXelle Hirsch, Michael Wolf, Ralf Plieninger and others. The interactions with the Australian colleagues, especially Andrew Blakers and Martin Green, created much enjoyment. Thanks are due to the organizers of this workshop in the city of Dresden, which is literally of vital importance to me since I just barely survived the great air raid there in February of 1945. References [1] R.B. Bergmann, Appl. Phys. A 69 (1999) 187. [2] G. Moore, IEEE spectrum 10 (1979) 301. [3] H.J. Queisser, Kristallene Krisen, Piper, MUunchen, 2nd Edition, 1985; H.J. Queisser, The Conquest of the Microchip, Harvard Press, Cambridge, MA, 1985. [4] W. Shockley, Bell Syst. Tech. J. 28 (1949) 435. [5] S.M. Sze, Physics of Semiconductor Devices, 2nd Edition, Wiley, New York, 1981. (Chapter II); Shockley, Bell Syst. Tech. J. 28 (1949) 435. [6] W. van Roosbroeck, W. Shockley, Phys. Rev. 94 (1954) 1558. [7] W. Shockley, H.J. Queisser, J. Appl. Phys. 32 (1961) 510, reprinted in Ref. [5]. [8] K. Hubner, in: H.R. Hu: et al. (Eds.), Semiconductor Silicon, Electrochemical Society Proceedings 98-1, 1998, Pennington, NJ, 1998, p. 49. [9] H.J. Queisser, Multicell solar energy converters, Contract DA 36 039 SC-85239, US Army Signal Corps, Ft. Monmouth, NJ, 6 August, 1959. [10] H.J. Queisser, in: R.D. Me Connell (Ed.), Photovoltaic Multiplicities, in Future Generation of Photovoltaic Technologies, American Institute of Physics Proceedings 40, AIP, Woodbury, NY, 1997, p. 267; U. Kerst, Thesis, Technical University of Berlin, 2000; U. Kerst et al., Proceedings of the 11th International Conference on Photovoltaics, Nara, 1999. [11] A.M. Eppler, Physica E 14 (2002) 197. [12] K. Kalyanasundaram, M. Graetzel, Coord. Chem. Rev. 77 (1998) 347.
9
[13] M.B. Prince, J. Appl. Phys. 26 (1955) 534. [14] P. WUurfel, Physik der Solarzellen, 2nd Edition, Spektrum, Heidelberg, 2000. [15] R. Bergmann, DGKK Mittlg 59, 155 (1994), reprints through Ralf. [email protected] (Survey). [16] R. Brendel, Progression Report, ZEA, Erlangen, 2001. [17] C. Ascheron, A. Schindler, G. Otto, Phys. Stat. Sol. (A) 92 (1985) 169; C. Ascheron, Phys. Stat. Sol. 124 (1991) 11. [18] M. Bruel, Electron. Lett. 31 (1995) 1201. [19] R.B. Bergmann, J.H. Werner, Thin Solid Films (2002), in press. [20] U.S. Dept. of Energy, Photovoltaic Energy Progression Overview, Feb. 2001, p. 3. [21] U. Rau, H.W. Schock, Appl. Phys. A 69 (1991) 131. J.H. Werner (Ed.), Appl. Phys. A covers Thin )lm solar cells (special issue) [22] H.J. Queisser, Japanese Society of Applied Physics, March meeting, Tokyo, 1993. [23] R. Brendel, H.J. Queisser, Sol. Energy Mater. Sol. Cells 29 (1993) 397. [24] G. Smith, W.S. Boyle, see, for example, S.M. Sze, Ref. [4], p. 407. [25] M. Riordan, L. Hoddeson, Crystal Fire, Norton, New York, 1997. (Chapter 6) [26] D.M. Chapin, C.S. Fuller, G.L. Pearson, J. Appl. Phys. 25 (1954) 676. [27] H. MUuser, Z. Physik 148 (1957) 380. [28] G.L. Pearson, Am. J. Phys. 25 (1957) 591. [29] Victor Vavilov, private communications, 1962, 1966. [30] S Progr. in: N.W. Snyder (Ed.), Astronautics and Rocketry, Energy Conversion for Space Power, Vol. 3, Academic Press, New York, 1961, p. 317. [31] H.J. Queisser, W. Shockley, Bull. Am. Phys. Soc. 5 (1960) 160. [32] M. Wolf, Proc. IRE 48 (1960) 1246. [33] J.M. Woodall, H.J. Hovel, Appl. Phys. Lett. 30 (1977) 492. [34] H. Fischer, FestkUorperprobleme=Adv. Solid State Phys. XIV (1974) 153; A. Blakers, FestkUorperprobleme=Adv. Solid State Phys. 30 (1970) 403. [35] R.A. Sinton, Y. Kwak, J.Y. Gan, R.M. Swanson, Electron Device Lett. 7 (1986) 567; M. Green, in: S.M. Sze (Ed.), Modern Semiconductor Device Physics, Wiley, New York, 1997. [36] S. Kolodinski, Doctoral thesis, University of Stuttgart, 1993. [37] J.H. Werner, S. Kolodinski, H.J. Queisser, Phys. Rev. Lett. 72 (1994) 3851. [38] S. Kolodinski, J.H. Werner, T. Wittchen, H.J. Queisser, Appl. Phys. Lett. 63 (1994) 2405. [39] S. Kolodinski, J.H. Werner, H.J. Queisser, Sol. Energy Mater. Sol. Cells 33 (1994) 275; H. Werner, R. Brendel, H.J. Queisser, Appl. Phys. Lett. 67 (1995) 1028. [40] H.J. Queisser, J.H. Werner, Optimization of high-e%ciency solar cells: an inverse band structure problem, in: H. Lbbig (Ed.), The Inverse Problem, Akademie-Verlag, Berlin, 1995.
10
H.J. Queisser / Physica E 14 (2002) 1 – 10
[41] H.J. Queisser, Proceedings of the 22nd International Conference on Physics Semiconductor, Vancouver, 1994. [42] A. Franceschetti, A. Zunger, Nature 402 (1999) 60. [43] S. Kolodinski, J.H. Werner, H.J. Queisser, German Patent DE 4340221 CL of April 18, 1996. [44] M. Wolf, R. Brendel, J.H. Werner, H.J. Queisser, J. Appl. Phys. 83 (1998) 4213.
[45] Y. Saito, S. Yokoyama, Honda Res. Lab. Wako, Japan, private communication. [46] G. Dehlinger, et al., Science 290 (2000) 2277. [47] P.T. Landsberg, Proc. Inst. Elec. Eng. (London), Part II 106 (Suppl. 17) (1959) 908.
www.elsevier.com/locate/physe
Photovoltaic conversion at reduced dimensions Hans J. Queisser ∗ Max-Planck-Institute for Solid State Research, Heisenbergstr. 1, D-70506 Stuttgart, Germany
Abstract Reducing the geometric dimensionality in a photovoltaic cell is useful in designing optimal contact geometry, in enhancing the conversion e%ciency by enlarging the concentrations of photogenerated carriers and, generally, by utilizing thin-)lm structures for solar cells. It is not yet obvious whether or not dimensions in the range of nanometers are useful or needed. ? 2002 Elsevier Science B.V. All rights reserved. PACS: 84.60.J Keywords: Nanostructures; Thin )lms; Photovoltaics
1. Introduction Nanostructures and Photovoltaics, what an irresistible combination! Nano, the greek word for dwarf is the novel vocabulary. And: photovoltaics, what great hope this word suggests! To derive our necessary energy from simple cells without moving parts, without noise, without exhaust nor waste. Photovoltaic utilization of the regenerative, vast supply of solar radiation appears to be the ideal solution for our energy crisis. The title of our workshop seems to seriously suggest that nanostructures might improve solar-cell e%ciencies, maybe also even the cost of solar modules. One ought to be cautious, however, not to raise unfounded optimism. Solar-cell technology is complicated and—even today, after decades of research— a rather costly a:air. My contribution to this workshop will be much more modest than directly pertaining to dimensions
∗
Tel.: +49-711-689-1600; fax: +49-711-689-1602. E-mail address: [email protected] (H.J. Queisser).
in the nanometer regime. (I shall, however, use nanometers for quantifying all length dimensions in this paper.) Reductions of geometric scales in semiconductor solar cells have already been proven useful and are thoroughly based on solid-state physics, but really only restricted to the micrometer regime. First, solar cells made with bulk semiconductors are now, generally, regarded as being too expensive. Hence, thin-)lm cells are currently at the center of research and development activities. A thin )lm concentrates the photogenerated electrons and holes more e%ciently than a thick cell, therefore reduces entropy and thus raises the energy conversion e%ciency. Secondly, the conversion is enhanced by using contacts, which no longer cover the entire back surface of a solar cell, but are distributed as optimally reduced small areas. This phenomenon, long overlooked by the engineering community, tends to gainfully preserve the light-generated split into quasi-Fermi levels of electrons and holes. Third, carrier relaxation and recombination processes are reconsidered with the question of whether there might be any chance to utilizing microstructuring in order to inBuence non-radiative
1386-9477/02/$ - see front matter ? 2002 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 6 - 9 4 7 7 ( 0 2 ) 0 0 3 5 3 - 3
2
H.J. Queisser / Physica E 14 (2002) 1 – 10
Fig. 1. Solar-cell e%ciency as function of grain size.
carrier recombination, but no clear pathway is currently visible. That a naive reduction of particle size—as is often useful in nanotechnology—is not bene)cial for conventional semiconductor solar cells is seen in Fig. 1 [1]. This indicates that the grain size reduction tends to reduce e%ciencies, and good single crystals are optimal! 2. Junction basics Contemporary p–n junction semiconductor solar cell are rather primitive devices, when compared to the standards of modern semiconductor technology. This year, the major suppliers of silicon-integrated circuits utilize single-crystalline silicon wafers of 3 × 108 nm diameter to fabricate devices with a design rule of merely 130 nm. The continuous increase of wafer diameter and concomitant decrease of the characteristic device dimensions—together with design cleverness—form the technical basis of the famous law by Gordon Moore [2,3]. 1 Exponentially decreasing cost and sharply rising functionality are the results. Semiconductor devices have been the major new scienti)c invention and the essential new economic force of the second-half of the 20th century. The general public is vaguely aware of this remarkable interplay of science and economics. This awareness is then easily, but erroneously carried over 1
For a simple interpretation, see Ref. [2].
to the economic expectations for solar cells. Why not equally reduce cost for solar energy converter cells? The answer is unfortunately simply evident: size reduction does not apply to solar cells, since we must rely on extensive area for harvesting the sunlight. Solar cells are indeed somewhat primitive. They are not only large-area, non-microstructured devices. They also operate at much, much lower frequencies than the integrated circuits with their GHz capability; cells work at zero frequency, they supply direct current. Solar cells are also primitive in their usage of just one p–n junction, not two as for bipolar transistors. Simulations of device performance thus rely essentially only on the forward portion of the characteristic for the junction current, I , versus voltage, V . The optimal e%ciency results for the recti)er equation [4,5] 2 I=I0 = exp(qV=nkB T ) − 1;
(1)
where I0 is the reverse saturation current, depending on carrier densities, lifetimes, and transport parameters. The electronic charge is conventionally designated by q; kB T is the thermal energy, indicating that the current Bow over the junction is thermally activated. The auxiliary factor n is just an embarrassing )t parameter, forced into Eq. (1) in order to describe non-ideal junctions. This parameter is misleadingly named junction quality factor. Ideal junctions have n = 1; the larger n, the less ideal is the junction current behavior. Lifetime, t, of the charge carriers is of essential importance. The longest possible value of t results only when radiative recombination prevails and is in thermal equilibrium by detailed balance with its surroundings [6]. This principle is the foundation for the thermodynamic theory of solar cell conversion e%ciency [7]. This work was my own personal )rst contact with solar cells, when I joined William Shockley in his laboratory inside an old apricot barn on 391 South San Antonio Road in Mountain View, California in 1959 [3]. In those years, US government research contracts were not easily granted for silicon electronics, but the Sputnik shock forced massive funds into all things for rockets and space. Shockley, however, wanted to understand silicon for his four-layer-diode, a switching device, which would 2
For an outline of junction physics: Ref. [4].
H.J. Queisser / Physica E 14 (2002) 1 – 10
3
Fig. 2. Multijunction solar cell, made in 1959=60 at the Shockley Transistor Corp. in Mountain View, California 9 [10].
only function with silicon junctions [8]. 3 Our little company, Shockley Transistor Corporation, never intended to produce and market solar cells, but we needed the contract money to study and control those irregular and non-ideal p–n junctions in silicon. My other project in 1959 was an experimental task. I fabricated a multijunction silicon cell with many elements in series in an attempt to raise output voltage and not just output current with increasing cell area [9,10]. 4 Shockley optimistically anticipated that large sheets of thin silicon )lms might become available for solar-energy conversion, for example by pulling from a lead–silicon melt. Some technique was, therefore, required to shape these large-area Si )lms into a complete solar-cell module [10]. Fig. 2 shows the principle. I succeeded to fabricate about a dozen of such multicells. These strange devices were actually the )rst integrated silicon circuits. I had to use very thin pieces of Si, of the order of 6 × 104 nm—which demanded steady hands and most delicate handling. Silicon is brittle, tends to break easily, but those thin things turned out to be reasonably Bexible and thus quite forgiving. We were forced to use such thin wafers in order to be able to employ dopant di:usions from both sides, as can be seen in Fig. 2. 3 For a historical and technical perspective of FourLayer-Diodes, see Ref. [8]. 4 The multicell work is reviewed in Ref. [10]. A recent thesis has reconsidered cascaded multijunctions: U. Kerst, Techn. U. Berlin, 2000, also see Ref. [10].
The successful technology for integrated circuits, however, chose another route. Stable silicon wafers of roughly 5 × 105 nm thickness were needed for any viable technology, which in turn invariably led to the contemporary semiconductor methodology of machining circuits only from one side of a silicon wafer. The entire set of electronic functions resides in shallow surface layers, of the order of a few thousand nanometers. The rest of the silicon is just a substrate for handling! Long-time di:usions from both sides, as I had to resort to for my slim little multicells, were totally impractical and unacceptable for mass productions. Contemporary integrated circuits are undeniably top loading appliances! Materials with nanosize dimensions face another serious problem in conventional solar cells. Carrier lifetime is the most sensitive measure of crystalline perfection. Any deviation from an ideal single crystal reduces lifetime and thus lowers conversion e%ciency. Indeed, single-crystalline materials, especially Si and GaAs, provide the cells with highest e%ciencies. Any nanocrystalline material is, therefore, in principle an inopportune choice for a cell material. Grain boundaries and the many other defects sharply curtail cell output. Very small nanoparticles are thus unsuitable, except as speci)c oxides for photoelectrochemical cells, generating chemical output, such as oxygen or hydrogen, instead of electrical power output. Such cells and their relation to nanostructuring [12], are covered elsewhere in this special issue [11].
4
H.J. Queisser / Physica E 14 (2002) 1 – 10
3. Need for thin-lm cells The basic physics of semiconductor solar energy conversion has been adequately understood for quite some time [13,14]. The economic competitiveness of this sort of regenerative energy now hinges entirely on cost of materials, production, assembly, and possibly provisions for energy storage. Solar cells can currently compete with other energies only with massive subsidies or in isolated areas, where satisfactory grid supply is absent. The light weight of the cells, however, makes them ideal energy sources for space applications, where cost is of secondary signi)cance. Terrestrial applications demand a drastic reduction of materials cost [15]. Bulk materials, especially for silicon cells, appear to be uneconomical. Intense development e:orts have therefore recently been exerted towards thin-)lm cells. This problem is not as easy as it seems on )rst sight, since one characteristic length of a solar cells is the 1=e—absorption length for sunlight. Indirect-gap materials, such as silicon, have long mean-free paths of the order of 103 to 104 nm for the impinging photons. Special care has to be taken to compensate for this unfavorable impedance. Light must be trapped by multiple reBections at the boundaries. This trapping is an e:ective method to enhance the optical pathlengths within thin )lms of these indirect materials [16]. Computer programs have been created by Brendel in order to optimize such trapping by cleverly arranging prisms and related structures to maximize internal reBections to curtail all exits for the photons [16]. The second characteristic dimension of a solar cell is the di:usion length LD for the minority carriers, which must be as long as possible such that the charge carriers reach the cell’s external contacts by di:usion. This length typically ranges from about 103 up to about 106 nm and is thus of the same order of magnitudes as the photon mean free path. Nanostructuring is therefore quite far removed from cell technology. Thin )lms can most easily and economically be fabricated by evaporation or sputtering, yet such techniques usually generate imperfect crystals. Modern semiconductor technology thus uses epitaxial crystal growth wherever perfection is required. For solar cells, such epitaxy would become too expensive, unless the single-crystalline substrates are reusable. Such methods are known for quite some time [17] and have been
rediscovered [18] 5 as the cleverly named smart cut, to utilize substrates several times over for solar-cell production. The team of Werner at the University of Stuttgart, for example, is actively engaged in the work of developing novel techniques for economical thin-)lm production [19]. Table 1 reproduces a recent overview [20] for commercial, large-area thin-)lm solar cells. Semiconductors with both direct and indirect optical transitions are listed. Note that cells based on direct-gap semiconductors of the type AII BVI rank very prominently. CIS is the common abbreviation for the compound cadmium–indium diselenide; fabrication procedures for this material were successfully developed by Schock and colleagues [21] at Stuttgart University and are now used in starting large-volume productions in several countries. 6 Reduction of geometric dimensions for photovoltaic solar energy conversion has thus become an important technological topic, but this type of reduction does certainly not at all extend into the nanometer regime. 4. Entropy suppression in thin lms An interesting phenomenon was empirically observed in the study of thin-)lm solar cells. Under otherwise equal conditions of structure, surface recombination, and illumination, cells with thinner active layers indicated higher open-circuit voltages, hence better conversion e%ciencies than those having thicker layers. A variety of interpretations, some being fairly complicated, were o:ered [23]. The reason is, however, very simple and is entirely based on fundamentals of thermodynamics [22,23]. The con)nement within a thinner layer of width W raises the density of carriers (per unit volume), higher density means reduced entropy, thus better conversion e%ciency. The open-circuit voltage, Voc , for I =0 in Eq. (1) is Voc = kB T=q ln(Isc =I0 + 1);
(2)
where Isc is the short-circuit output current for V = 0. The reverse saturation current is Isc = qn0 W= . From 5
The “smart” cut is described in: Ref. [18]. CIS cells are now being produced by WUurth Solar Co. in Marbach, Germany. 6
H.J. Queisser / Physica E 14 (2002) 1 – 10
5
Table 1 Best present large-area thin-)lm solar-cell modules (standard conditions, aperture area) [20]
P ower (W)
Company=date
Device
Size (ft 2 )
91.5 70.8 61.3 59.0 56.0 53.9 44.3 38.0 35.7 31.0
BP Solar 5=00 United Solar, 9=97 First Solar, 6=96 Matsushita 6=00 BP Solar 9=96 BP Solar 4=00 Siemens Solar 3=99 Kaneka 9=00 United Solar 6=97 Golden Photon 4=97
CdS=CdTe a-Si=a-SiGe=a-SiGe=SS CdTe=CdS CdS=CdTe a-Si=a-SiGe CdS=CdTe CdS=CIS-alloy a-Si=c-Si=glass a-Si triple junction CdS=CdTe
9.5 10.2 7.8 6.0 8.2 5.4 4.0 4.1 5.0 3.7
Eqs. (1) and (2) and with Isc I0 , one obtains the derivative dVoc =dW = −kB T=qW . The entropy s per charge carrier particle in a semiconductor with an e:ective density of states Nc in the conduction band, having the electron e:ective mass m∗ ; Nc = 2(2m∗ kB T=h2 )3=2 is s=kB =
5 2
− ln(n=Nc (T )):
(3)
This entropy s is the only physical quantity depending on W , since n(W ) = Isc =qW . Assuming that lifetime remains independent of thickness W and assuming non-degeneracy, we obtain [23] dVoc =dW = (kB T=q)(n−1 dn=dW + p−1 dp=dW ) (4) as the explicit formula for the change of output voltage with change of layer thickness W , based on the consideration of entropy reduction with compression. Since the derivatives of particle densities with respect to thickness, such as dn=dW , are negative, the open-circuit voltage Voc does increase with shrinking W , and so does the e%ciency, since the current remains constant. We have again a direct bearing of geometric dimension upon solar-cell operation, but once more we are far away from the nanometer regime. One might speculate to introduce yet smaller dimensions, such as arrays of quantum wells to more fully bene)t from this e:ect. Practical considerations, such as providing proper contacts for both carrier types or complexity of cell production, seem to argue against this proposal, but future research is advisable. Carrier extraction, as done for example in charge-coupled-devices (CCDs) [24], is a possibility, but probably would
E%ciency (%) 10.6 7.6 (stabilized) 9.1 11.0 7.6 10.8 12.1 10.0 (est. stable) 7.9 9.2
turn out to be by far too complicated and thus too expensive. 5. Early engineering e!orts Solar-cell development in the United States was sharply accelerated during the early days of the reaction to the Soviet Sputnik in the 1960s, which I remember quite well from my apprentice years, working in Mountain View, California, now recognized as the “Cradle of Silicon Valley” [3]. The emphasis then was very much on engineering aspects to quickly obtain modules of energy supply for satellites. The semiconductor junction solar cell was originally invented at Bell Laboratories. Earliest attempts with Si of low perfection were made by Ohl [25], and were not yet convincing. Better silicon materials and more e:ective and controlled ways of doping, such as using di:usion of dopants, were the basis of the successful cell technology by Chapin, Pearson, and Fuller at Bell Labs [26], 7 with Prince providing the )rst theoretical treatise [13,14,27]. Shockley told me that he and colleagues obediently went to the Pentagon in Washington right after the invention of the cell by Chapin, Fuller, and Pearson, but the US government was not at all interested then and allowed free publications. The Bell System then made trials to replace standard batteries in rural telephone networks by solar-cell systems. These tests, done at Americus, 7
Russell Ohl detected by accident junctions in Si crystals via a photovoltage as early as 1939=40; see: Ref. [25].
6
H.J. Queisser / Physica E 14 (2002) 1 – 10
Georgia, failed [28]; the cells were quickly being covered by opaque masses derived from ornithological feces! (Layers of supposedly about 106 nm.) Russian colleagues from the physics community later narrated to me [29] that the Soviet Union immediately recognized the signi)cance for space power sources and began to work at solar cells. In the USA at that time, the proponents of small nuclear power sources for space applications were quite con)dent that their systems would be chosen—and I remember conferences of the American Rocket Society [30], where those Bimsy solar cells were derided as just being toys. 6. Requirements for carrier recombination Engineers took over and made estimates for losses in order to derive maximal e%ciency and to choose optimal materials according to an energy gap Eg to match the solar spectrum. Shockley and I then tried to publish our physics-based thermodynamic theory, which was )rst rejected as being trivial and unnecessary, eventually, however, did get published [7]. We gave talks [31] and tried to tie our e:orts to the glorious work by famous ancestors such as Carnot, whose new science of thermodynamics overcame the purely empirical estimates of steam-engine e%ciency by merely listing all possible energy loss mechanisms, like friction or heat losses, and trying to minimize those. One example of this empirical, pragmatic approach for solar energy conversion is the work by Wolf [32], which served as a convenient engineering guideline for practical developments. Our claim for maximal cell e%ciency was that one should reach the minimal, unavoidable carrier recombination. This case would be attained if only the necessary photon emission, as required from detailed balance [7], were to be present and no non-radiative recombination would take place. I recall a vivid discussion at the American Physical Society March Meeting in Cleveland in 1960, which ensued after my talk [31]. The colleagues from the Princeton RCA Laboratories had just ascertained that recombination in good gallium arsenide crystals was essentially of radiative character, which we now clearly know from the direct band gap structure of this compound semiconductor. Paul Rappaport asked me, if this would not
mean that GaAs should be an excellent solar cell material. Based on our theory, I obviously had to agree. Rappaport then said with a mixture of chagrin and triumph that such was not the case. The band gap of GaAs ought to be most appropriate, but still the cells always showed awfully low e%ciencies. I shrugged my shoulders, feeling embarrassed and helpless at the rostrum. Now, of course, we know especially after the work of Woodall and Hovel [33]—that indeed excellent cells with record conversion e%ciencies (¿ 24%) are made today with GaAs, but one needs to completely suppress the very strong nonradiative surface—recombination processes in GaAs by means of a very thin-surface layer of (Al, Ga) As. Here, truly thin layers of only a few tens of nanometers (typically 30 nm) have proven to be extremely useful! 7. Contact sizes Reduction of Joule losses in the contacts and metallic leads is one of those obvious loss mechanisms. The illuminated front side contacts represent one of the many compromises typical for solar cells. Large-area contact )ngers provide advantageously small ohmic resistance, but they also reduce the area of insolation and cause an e%ciency reduction by about 5% points. The back-side contacts were at that time considered to be much simpler challenges; one just had to cover the entire unilluminated reverse side by a good metallic contact [32]. This seemingly obvious but really naive recipe neglected one decisive fact of basic semiconductor physics. Every contact leads to strong electron–hole recombination and thus forces the two quasi-Fermi levels, n and p , for electrons, n, and holes p, to equalize and reestablish equilibrium conditions of one common Fermi energy EF . A solar cell, however, is by its very principle a device which has to preserve the non-equilibrium, which means to maintain as much and as long as possible this photon-generated split into two separate quasi-Fermi levels. The cell output lives from this non-equilibrium. Present-day solar cells made for very high e%ciencies, such as the high-e%ciency Si cells of Green (For earlier reviews, see Ref. [34].), 8 rely on an opti8
A. Blakers gave a detailed review of solar cell technology as of 1990: High E%ciency Silicon Solar Cells.
H.J. Queisser / Physica E 14 (2002) 1 – 10
7
mized back contact array, where the contact areas are kept as small as possible, and a back-surface )eld is introduced to repel the minority carriers from surface recombination. About 15 years ago, much work was done to establish point contacts on solar cells [35]. Those points, however, had diameters of several thousands of nanometers, being far from zero-dimensional features! [35] To repeat, dimensional control is important and has proven useful, but again not in the regime of nanometers. Contact optimization is usually concerned with geometries in the millimeter or—at most—submillimeter realm. 8. Curtailing relaxation and recombination Entropy must be minimized in solar-cell operation! This imperative, the noble task for the solar-cell physicist, means that one has to courageously—but not too expensively—combat all physical processes that degrade the precious solar input into useless forms of energy, heat obviously being the worst culprit. Most unwanted is the fast relaxation of high-energy electrons, which are generated by photons from the blue spectral emission of the sun. The carriers quickly slide down by intraband transitions via phonon generation to their respective minima of the electronic band structure E(k). Phonon emission is highly probable, thus the carriers cannot supply their nonequilibrium excess energies to the output. Roughly 30% of the solar input is thus wasted in typical silicon cells by such thermal degradation. Materials with higher band gaps would waste less of this energy, but then the losses rise for the unabsorbed red photons of the sunlight, again we encounter one of those necessary compromises of solar cell physics. Figs. 3 and 4 shows the situation after a high-energy, blue photon is absorbed and has created a cold hole at the top of the valence band and a hot electron in the conduction band far above the minimum. Usually, the hot carrier would dribble down to its band extremum, creating heat. One must suppress this entropy generation by providing another pathway (see footnote 12 of Ref. [7]). This situation was studied in detail by Sabine Kolodinski in her doctoral thesis at the Max-Planck-Institute in Stuttgart [36]. Careful spectral studies [37] and even absolute measurements [38] gave evidence of another, highly favorable path for
Fig. 3. Creation of two electron–hole pairs by one blue solar photon. The hot electron e1 donates excess energy and wave vector to another electron in the valence band.
Fig. 4. Maximal conversion e%ciency for a standard cell (lower curve), compared to a cell with optimized multiple-pair production [39].
relaxation. The hot electron e1 imparts its energy and quasi-momentum k to another electron in the valence band, lifting it, electron e2 , up to the conduction band minimum (see arrows in Fig. 2). Two electron–hole pairs are thus created; energies and momenta balance.
8
H.J. Queisser / Physica E 14 (2002) 1 – 10
Considerable impetus was created by Kolodinski’s experiments. If one could utilize this two-pair e:ect and completely suppress heat generation by phonons, one could— theoretically—achieve 44% ef)ciencies [39]. Fig. 3 compares the standard maximal e%ciency—according to detailed balance [7]—with the admittedly rather idealistic idea that all excess energy might be utilized for multiple pair productions. The optimal band gap energy Eg would shift towards lower energies, capturing thus more red sunlight and fully utilizing the enhanced radiation in the blue regime. One can construct optimal band structures and would then be faced with a novel inverse problem of calculating atomic con)gurations from an a priori band structure [40]. Such inverse calculations are di%cult, usually a de)nite solution cannot be found. There might be some possibilities, as cursorily summarized in Ref. [40] in a Helmholtz Memorial meeting and in Ref. [41]. This topic was pursued by Franceschetti and Zunger [42]. We realized, of course, that it would be di%cult to overcome the strong tendencies of recombination via phonons and channel all processes into creation of multiple pairs. We were, however, obedient that one should never say “Never!” and obtained a patent [43] on this idea of multiple pair generation. Brendel and Wolf at Stuttgart [44] worked out the details for one speci)c and easily obtainable—material: alloys of Si and Ge. These crystals ful)ll already the requirement of a band gap Eg smaller than that for Si. The fruits of this labor were disappointing: only very small increases of e%ciency might be expected from this system of a mixed crystal [44]. One Japanese industrial laboratory is apparently continuing along similar lines at the present time, but most unfortunately—no details are being divulged [45]. In the context of this Dresden Workshop the question arises whether there might be any means and ways to support the double-pair generation mechanisms. Nanostructures might be perceived to alter densities of phonon states or even transition matrix elements. Zone folding [46] 9 could, for example, be achieved in multilayer structures of small dimensions. Such folding of states at large values of k towards k = 0 favor direct optical transitions. At )rst 9
For a recent example, see: Ref. [46].
glance, such hopes do not seem to be well founded. Deviations from crystalline perfection and from bulk size have in general a tendency to relax the rules for conservation of k and hence to enlarge phonon generation. Nanostructuring thus appears to be actually a counterproductive proposal. I would nevertheless like to encourage the younger generation to optimistically look at these matters in greater detail. Heavier doping of solar cells is often of advantage, but then, an unavoidable recombination sets in: Auger processes, where an electron–hole pair donates energy and momentum to a third carrier. When Shockley and I looked at all of these unavoidable loss mechanisms, we realized that Auger recombination must be taken into account and asked the expert, Peter Landsberg, for help [7,47]. The Auger recombination involves three particles. One electron–hole pair recombines and imparts energy and momentum to a third particle. The inverse e:ect may be called Auger generation: a hot particle generates a pair, which is exactly what we have suggested to utilize for multiple-pair production from blue photons. Nanometer dimensions do once again not seem to be particularly helpful in harnessing the Auger recombination; probably again dimensional reductions might be playing a deleterious role for energy conversion. Nanostructuring ought nevertheless be investigated for obtaining substantial changes in the energy losses of carriers via relaxation intraband processes as well as by interband or defect-assisted recombination processes. Recombination represents one of the most di%cult and elusive electronic processes in semiconductors, especially in the materials with indirect optical transitions. Hope should not be abandoned that we can learn more about it and even )nd clever new ways to enhance solar cell e%ciencies. One caveat, however, must not be neglected: the cost of solar-cell production should—if anything—be lowered! This same sort of cautious conclusion was expressed already in 1957 by co-inventor Gerald Pearson: the silicon solar battery as such is too expensive to compete with more conventional large package power generators [28]. Here arises our perennial challenge! Acknowledgements I thank the many people with whom I had opportunities to collaborate in studies on solar energy con-
H.J. Queisser / Physica E 14 (2002) 1 – 10
version, starting with William Shockley and Sam Fok in Mountain View in the late-1950s and by interacting with colleagues, such as Gerald Pearson, Calvin Fuller, Peter Landsberg, Paul Rappaport, Joe Loferski, Martin Wolf and others in those early years. I remember with pleasure and respect the cooperation with contract monitors in the US government laboratories in Fort Monmouth, New Jersey and Dayton, Ohio: J. Mandelkorn, G. Hunrath, H. Kittl and, of course, William Cherry. In Stuttgart, I gratefully acknowledge the cooperation with Juergen Werner, Ralf Bergmann, Rolf Brendel, Sabine Kolodinski, Uwe Rau, MichXelle Hirsch, Michael Wolf, Ralf Plieninger and others. The interactions with the Australian colleagues, especially Andrew Blakers and Martin Green, created much enjoyment. Thanks are due to the organizers of this workshop in the city of Dresden, which is literally of vital importance to me since I just barely survived the great air raid there in February of 1945. References [1] R.B. Bergmann, Appl. Phys. A 69 (1999) 187. [2] G. Moore, IEEE spectrum 10 (1979) 301. [3] H.J. Queisser, Kristallene Krisen, Piper, MUunchen, 2nd Edition, 1985; H.J. Queisser, The Conquest of the Microchip, Harvard Press, Cambridge, MA, 1985. [4] W. Shockley, Bell Syst. Tech. J. 28 (1949) 435. [5] S.M. Sze, Physics of Semiconductor Devices, 2nd Edition, Wiley, New York, 1981. (Chapter II); Shockley, Bell Syst. Tech. J. 28 (1949) 435. [6] W. van Roosbroeck, W. Shockley, Phys. Rev. 94 (1954) 1558. [7] W. Shockley, H.J. Queisser, J. Appl. Phys. 32 (1961) 510, reprinted in Ref. [5]. [8] K. Hubner, in: H.R. Hu: et al. (Eds.), Semiconductor Silicon, Electrochemical Society Proceedings 98-1, 1998, Pennington, NJ, 1998, p. 49. [9] H.J. Queisser, Multicell solar energy converters, Contract DA 36 039 SC-85239, US Army Signal Corps, Ft. Monmouth, NJ, 6 August, 1959. [10] H.J. Queisser, in: R.D. Me Connell (Ed.), Photovoltaic Multiplicities, in Future Generation of Photovoltaic Technologies, American Institute of Physics Proceedings 40, AIP, Woodbury, NY, 1997, p. 267; U. Kerst, Thesis, Technical University of Berlin, 2000; U. Kerst et al., Proceedings of the 11th International Conference on Photovoltaics, Nara, 1999. [11] A.M. Eppler, Physica E 14 (2002) 197. [12] K. Kalyanasundaram, M. Graetzel, Coord. Chem. Rev. 77 (1998) 347.
9
[13] M.B. Prince, J. Appl. Phys. 26 (1955) 534. [14] P. WUurfel, Physik der Solarzellen, 2nd Edition, Spektrum, Heidelberg, 2000. [15] R. Bergmann, DGKK Mittlg 59, 155 (1994), reprints through Ralf. [email protected] (Survey). [16] R. Brendel, Progression Report, ZEA, Erlangen, 2001. [17] C. Ascheron, A. Schindler, G. Otto, Phys. Stat. Sol. (A) 92 (1985) 169; C. Ascheron, Phys. Stat. Sol. 124 (1991) 11. [18] M. Bruel, Electron. Lett. 31 (1995) 1201. [19] R.B. Bergmann, J.H. Werner, Thin Solid Films (2002), in press. [20] U.S. Dept. of Energy, Photovoltaic Energy Progression Overview, Feb. 2001, p. 3. [21] U. Rau, H.W. Schock, Appl. Phys. A 69 (1991) 131. J.H. Werner (Ed.), Appl. Phys. A covers Thin )lm solar cells (special issue) [22] H.J. Queisser, Japanese Society of Applied Physics, March meeting, Tokyo, 1993. [23] R. Brendel, H.J. Queisser, Sol. Energy Mater. Sol. Cells 29 (1993) 397. [24] G. Smith, W.S. Boyle, see, for example, S.M. Sze, Ref. [4], p. 407. [25] M. Riordan, L. Hoddeson, Crystal Fire, Norton, New York, 1997. (Chapter 6) [26] D.M. Chapin, C.S. Fuller, G.L. Pearson, J. Appl. Phys. 25 (1954) 676. [27] H. MUuser, Z. Physik 148 (1957) 380. [28] G.L. Pearson, Am. J. Phys. 25 (1957) 591. [29] Victor Vavilov, private communications, 1962, 1966. [30] S Progr. in: N.W. Snyder (Ed.), Astronautics and Rocketry, Energy Conversion for Space Power, Vol. 3, Academic Press, New York, 1961, p. 317. [31] H.J. Queisser, W. Shockley, Bull. Am. Phys. Soc. 5 (1960) 160. [32] M. Wolf, Proc. IRE 48 (1960) 1246. [33] J.M. Woodall, H.J. Hovel, Appl. Phys. Lett. 30 (1977) 492. [34] H. Fischer, FestkUorperprobleme=Adv. Solid State Phys. XIV (1974) 153; A. Blakers, FestkUorperprobleme=Adv. Solid State Phys. 30 (1970) 403. [35] R.A. Sinton, Y. Kwak, J.Y. Gan, R.M. Swanson, Electron Device Lett. 7 (1986) 567; M. Green, in: S.M. Sze (Ed.), Modern Semiconductor Device Physics, Wiley, New York, 1997. [36] S. Kolodinski, Doctoral thesis, University of Stuttgart, 1993. [37] J.H. Werner, S. Kolodinski, H.J. Queisser, Phys. Rev. Lett. 72 (1994) 3851. [38] S. Kolodinski, J.H. Werner, T. Wittchen, H.J. Queisser, Appl. Phys. Lett. 63 (1994) 2405. [39] S. Kolodinski, J.H. Werner, H.J. Queisser, Sol. Energy Mater. Sol. Cells 33 (1994) 275; H. Werner, R. Brendel, H.J. Queisser, Appl. Phys. Lett. 67 (1995) 1028. [40] H.J. Queisser, J.H. Werner, Optimization of high-e%ciency solar cells: an inverse band structure problem, in: H. Lbbig (Ed.), The Inverse Problem, Akademie-Verlag, Berlin, 1995.
10
H.J. Queisser / Physica E 14 (2002) 1 – 10
[41] H.J. Queisser, Proceedings of the 22nd International Conference on Physics Semiconductor, Vancouver, 1994. [42] A. Franceschetti, A. Zunger, Nature 402 (1999) 60. [43] S. Kolodinski, J.H. Werner, H.J. Queisser, German Patent DE 4340221 CL of April 18, 1996. [44] M. Wolf, R. Brendel, J.H. Werner, H.J. Queisser, J. Appl. Phys. 83 (1998) 4213.
[45] Y. Saito, S. Yokoyama, Honda Res. Lab. Wako, Japan, private communication. [46] G. Dehlinger, et al., Science 290 (2000) 2277. [47] P.T. Landsberg, Proc. Inst. Elec. Eng. (London), Part II 106 (Suppl. 17) (1959) 908.