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Forward characteristics and efficiencies of silicon solar cells
Solid-State
Electronics
FORWARD
Pergamon
Press 1962. Vol. 5, pp. l-10.
Printed in Great Britain
CHARACTERISTICS AND EFFICIENCIES OF SILICON SOLAR CELLS* H. J. QUEISSER Shockley
Transistor,
Unit of Clevite Transistor,
(Received 17 July 1961;
Palo Alto, California
in revisedform 10 October 1961)
Abstract-Forward currents in commercial solar cells show an exponential dependence on the forward voltage as exp (qI’/‘iAkT) with A N 3. This factor 3 in the exponent cannot as yet be explained satisfactorily. Experiments indicate that this strange forward characteristic is not an over-all property of the entire cell, but comes from localized regions of the junction area, preferentially at the cell edges. Heat treatments at temperatures low enough to exclude appreciable donor and acceptor diffusion produce significant changes in the characteristics. The results are interpreted in terms of impurities which are either dissolved or precipitated. These experiments show that commercial solar cells contain unnecessary defects which cause their strange characteristics and lower their efficiencies. R&sum&-Les courants directes des cellules solaires commerciales dependent des voltages directes comme exp (qV/AkT) avec A N 3. A l’heure actuelle, le facteur 3 dans l’exponent ne peut pas dtre explique avec satisfaction. Des experiences indiquent que cette &range caracteristique directe n’est pas une propriete de l’entibre cellule, mais vient des regions localisees de la jonction p-n, preferremment au hord de la cellule. Des traitements thermiques a des temperatures assez basses pour ne pas permettre une diffusion appreciable des donneurs et des accepteurs produisent des changements considerables des caracteristiques. Ces resultats sont interpretes en termes d’impuretes qui sont dissoues ou precipitees. Ces experiences demontrent que les cellules solaires commerciales contiennent des defauts qui ne sont pas necessaires et causent leur caracteristiques &ranges et diminuent leur efficacitts. Zusammenfassung-Technische Silizium-Solarzellen zeigen eine Abhangigkeit des Stromes von der Spannung in Flussrichtung gemass exp (qL’/AkT) mit A N 3. Dieser Faktor 3 im Exponenten ist bis jetzt theoretisch noch nicht erklart. Experimente zeigen, dass diese unerklarte Strom-Spannungs-Kennlinie keine Eigenschaft der gesamten Zelle ist, sondern von lokalisierten Bereichen des p-n Uberganges, hesonders an den Kanten, herriihrt. Warmebehandlungen hei Temperaturen, die keine nennenswerte Donatorenund Akzeptoren-Diffusion gestatten, rufen erhebliche Anderungen der Kennlinie hervor. Die Resultate werden mit der Annahme von Verunreinigungen erklart, die entweder gel&t oder als Ausscheidungen vorhanden sind. Diese Experimente zeigen, dass die heutigen technischen Solarzellen unniitige Storungen enthalten, die die eigenartige Kennlinie und einen verminderten Wirkungsgrad hervorrufen.
1. INTRODUCTION
current density, the higher will be the opencircuit voltage developed by the same current density of photon-created carriers reaching the junction. A cell that delivers higher open-circuit voltages for every current density will also have a higher efficiency of energy conversion than another cell with otherwise equal properties. The best possible current-voltage characteristic, and therefore the best efficiency, will be obtained if there is only radiative recombination of the holes and electrons created by the incident
efficiency of a semiconductor photovoltaic energy converter is commonly defined as the ratio of electrical power output into a matched load to the incident power per active area. This efficiency depends highly on the forward current-voltage characteristic of the p-7a junction. The higher the forward voltage necessary to pass a given forward
THE
* Work performed under contract AF 33(616)-7786 with Wright Air Development Division. A
1
H.
2
J. QUEISSER
photons.(l) cnder these conditions the forward characteristic without illumination is given by the ideal rectifier equation: I = la[exp(qV/kT)-
11
(1)
where I is the junction current, 10 the minimum reverse saturation current, as required by detailed balance, V the voltage applied to the junction, q = 191the value of the electronic charge, k the Boltzmann’s constant and 7’ the absolute temperature. The most important photovoltaic energy converters are the silicon solar cells which are produced in great quantities.(s-1) These commercial cells have efficiencies up to 15 per cent at present.(5) Such efficiencies, however, are still considerably below the estimated semi-empirical limit of 22 per cent,(a) or the calculated “detailed balance limit” of 30 per cent.(l) Further gains in efficiency will undoubtedly result from still better contacts, more advantageous structures or better optical properties. It appears that the greatest potential for higher efficiencies lies in materials with higher lifetimes and in the improvement of the junction characteristics. The junctions in today’s solar cells do not exhibit the ideal behavior of equation (1). It has been shown,(l) and this paper gives further evidence, that excessive non-radiative recombinations and/or other unnecessary current paths sharply reduce the voltage and current output, and thus the power delivered by the solar cells. The present status of the theory of solar energy converters is most clearly described by the fact that the forward characteristics of typical commercial cells are not at all understood. The forward behavior is usually described(43697) by a relation of the type of equation (1) with an empirical factor A introduced to account for the experimental data when I = Ii[exp(qV/AkT)where 1; has also only the empirical fitting constant. Values for A between 1 and 2 can on the basis of carrier recombination tion in the space-charge layer.(s) The typically yield A-values of 3 or even values could still be interpreted from recombination centers.(t,s) A
l] meaning
(2) of a
be explained and generaexperiments higher. Such as arising non-uniform
distribution of the centers must then be postulated and certain assumptions must be made about capture and emission of carriers by the centers. It is not yet clear whether these assumptions are physically justified. Other possible explanations have been proposed. Some authors@,la) believe that the high A-values can best be explained with field effects. Junctions with extremely narrow space-charge layers show similar anomalous characteristics which have been interpreted as internal field emission.(ll) Comparable problems of “excess currents” in tunnel diodeso”) have been explained by tunneling together with recombination at levels inside the forbidden gap. It is not obvious that this is also the case in solar cells, which have comparatively much wider space-charge layers. It now appears certain that, in principle, high values of A are undesirable for solar cell operation.“) Although high A-values mean a slower increase of current with voltage, the absolute values of the current for a given voltage are higher than those predicted by the ideal rectifier equation. Empirically it is found(j) that with increasing A the parameter 1; of equation (2) also increases, generally in such a way that higher currents are obtained. Regardless of the specific physical interpretation it can be said that high A-values are an indication of unwanted excess currents in the p-n junction that lower solar cell efficiency. From the foregoing it is evident that there is a potential for improvement of solar cells by improving junction characteristics. An understanding of the high A-values should eventually lead to methods of reducing the forward current, resulting in higher energy conversion efficiences. This paper presents an initial experimental investigation which has developed evidence that there are avoidable current paths in commercial solar cells which are responsible for lowered efficiency. It is shown here that the abnormally high A-values are probably the result of a design compromise dictated by the use of contaminated materials. It appears from the studies reported here that the high A-values are not a necessary consequence of the solar cell design as would be predicted by a simple tunneling hypothesis. 2. EXPERIMENTAL RESULTS Two sets of experiments will be described
which
FORWARD
CHARACTERISTICS
V,
AND
(REVERSE
-5
Vf (FORWARD
EFFICIENCIES
OF SILICON
VOLTAGE)---
_,(-J
SOLAR
(Volts)
VOLTAGE)-
(4
t A
1
0.1 vop
0.2 (OPEN
0.3 CIRCUIT
0.4
_)
(volt s)
VOLTAGE)-
(b)
FIG. 1. (a) Forward and reverse characteristics of a commercial solir cell, measured at 22 “C. (b) Dimensionless fitting parameter A vs. applied forward voltage. (Note suppressed scale for A !).
CELLS
3
4
H.
J.
QUEISSER
lead to the following two conclusions: (a) the strange characteristics with A-values as high as 3 are not an over-all property of the cell, but appear localized; (1~)the characteristic may be changed by heat treatment at temperatures well below those needed for donor- and acceptor-diffusion.
icl-
A. Localized spots with poor characteristics immi Experiments were performed on several cells, with different efficiencies indicated by the supplier.:” All of the cells arc produced by a shallow diffusion of boron into n-type silicon. In each case the value for A was found to be considerably greater than 2. Most cells can be described with A iy_ 3 over a current range of more than two decades. A typical current-voltage characteristic of a solar cell (Hoffman Type 110 C) is given in Fig. 1 (a). By logarithmic differentiation of the “forward” curve, A may be obtained as a function of applied bias. In doing this, the constant term 1; in equation (2) which is justifiable for voltages is neglected, greater than about 120 mV. The resulting function IC A(v) is given in Fig. I(b). It is seen that A is approximately constant = 3. Above 450 mV bias it is the ohmic resistance of the cells that makes the factor A appear larger. The dashed line in Fig. l(a) gives the reverse characteristic. It shows the well-known “softness” of solar cells, which (mm) is especially noticeable for high-efficiency cells.(ra) Equipotential plots(r4) were obtained for the surface of the cell at both a given forward and reverse current by measuring the voltage at the Y surface with respect to a given reference point at the contact. These plots are shown in Fig. 2. They reveal no anomalies except an enhanced potential drop at the lower right edge. This points toward a damaged or shorted portion of the junction, but nothing could be visibly detected.? Information about the current flow may be oh0 tained from the equipotential plots and the sheet resistivity. The current appears to flow rather uniformly with the exception of the lower right FIG. 2. edge. The amount of current flowing through the
I
* Hoffman Electronics Corp., El Monte, California (USA); Solar Systems, Inc., Skokie, Illinois (USA); and International Rectifier Corp., El Segundo, California (USA). t Such anomalies were frequently found at this corner. They may have been introduced by certain peculiarities in the manufacturing process, especially the sawing.
X-
(mm)
Equipotential plots for a commercial solar cell under (a) forward and (b) reverse current flow. Active area of cell = 0.9 X 1 .O cm”. Contact strip is along Y-axis.
junction into the n-type base can be determined hy evaluating the divergence of the corresponding “Four-point probe” measurecurrent field. ments(is) indicated that the sheet resistivitv of the
FORWARD
CHARACTERISTICS
AND
EFFICIENCIES
cell surfaces is fairly uniform. Therefore one can interpret a divergence of grad V as a current sink. Most of these evaluations showed that the forward current flows through the junction in the bulk
OF SILICON
SOLAR
and only small fractions of the current flow across the edges. The potential-probing method is not sensitive enough to detect small differences in the behavior
(b)
,
0.1
0.3
0.2
Vop
(OPEN
CIRCUIT
0.4
'0.5 iv01
VOLTAGE)
~~
*
I
A
0
0.1 V,,
(OPEN
CELLS
0.2 CIRCUIT
0.3
VOLTAGE)
-
0.4 (Volts)
FIG. 3. Behavior of mesas etched out of solar cell. (a) Location and numbering of the mesas on the cell. (b) Open-circuit voltages plotted as a function of illumination level as measured through the reference short-circuit current of a standard cell. Numbers on the curves refer to the mesas in Fig. 3(a); “0” is entire cell. (c) Fitting parameter A vs.open-circuit voltage. Dashed curve is same as Fig. l(b).
5
6
H. J.
QUEISSER
of different regions of the cell. Therefore, the individual characteristics regions of various were measured on mesas etched out of the cell. As indicated by Fig. 3(a), different areas were masked by wax and the rest of the cell surface was etched away. The mesas thus produced did not have contacts on the top layer, but their forward behavior could be measured by the following technique. The etched cell was illuminated. The illumination could be controlled without change in the quality of the radiation (i.e. same color temperature of the light source). The illuminatiorl level was measured through a reference short-circuit current lref of another solar cell serving as a standard. At different levels the open-circuit voltages of the mesas were determined with an infinite impedance voltmeter. When these open-circuit Lroltages l,bI1 arc plotted against the reference current Iref, a current-voltage characteristic is obtained which over a wide voltage range is practically identical to the characteristic measured in the dark using four contacts. The slope of the curve is preserved. The absolute value of the current level may vary because of differences in photon absorption or collection efficiency. The ohmic IR-drop of a cell with high contact resistance R is not measured with the “V,,P vs. Iref” method. Only the series resistance of the standard cell is influential, and it can be kept small if a high efficiency cell with low contact resistance is chosen. In Fig. 3(b), curve 0 gives a “Vor, vs. Iref” curve of the entire unetched solar c-11, which is the same cell as that of Figs. 1 and 2. Comparison with the forward 1--Tcharacteristic measured in the dark (Fig. 3c, dashed curve) shows that the slopes differ by less than 10 per cent up to about 0.3 V. Beyond that voltage the series resistance of the cell results in a higher value for A if the cell is measured with the standard two-contact method. The “\rOPvs. I,,f” method is not hampered by this series resistance. It is seen that A decreases with increasing VoP. The remaining curves on Fig. 3(b) represent the characteristics of different mesas of the etched solar cells. The number of each curve refers to the corresponding mesa as s,hown on Fig. 3(a). Fig. 3(c) gives the A-values for the mesas. These curves have been smoothed, since the differentiation exaggerates the experimental scatter.
Curve 8 typifies the characteristics of all mesas in the center of the cell. The open circuit voltages found are higher than the average voltages as given by curve 0. It is believed that this difference of open-circuit voltages is not caused by different photon absorptions or accidental features. Moreover, the slope of curve X corresponds to considerably lower A-values (see Fig. 3~). Thus the center portions definitely behave less abnormally than the entire cell. The behavior of the lower right corner of the cell, which looked conspicuous in the potential plots of Fig. 2, is given in curve 14. It closel! parallels the over-all behavior with slightly lower open circuit voltages. Still worse behavior is found for mesa no. 9 which is located near the edge. Another edge-mesa is described by curve 5. All of these devices exhibit high A-values and low opencircuit voltages. It is felt that these portions arc chiefly responsible for the poor over-all performance of the cell. hfesas that comprise regions of the former contact show very surprising behavior. This is depicted in curves 3 and 1. Mesa no. 3 shows much higher open-circuit voltages than other center mesas; it gave the largest open-circuit voltage of all mesas measured. Mesa no. 1 is located at a corner but its behavior is superior to all other edge devices. This strange influence of the contact will be further discussed on the basis of a “gettering action” by contact metals. The measurements described here were made on a cell with low conversion efficiency (6-X per cent according to supplier). Highly efficient cells (e.g. Hoffman Type 120~SCG 13, 13 per cent efficiency) showed essentially the same behavior, but with much less spread for different regions of the cell. As is to be expected, allopen-circuit voltages measured for these higher-efficient) cells were larger. No attempt \vas made to set up a four-contact circuit to study the reverse characteristics of the mesas. Two-contact measurements appeared unreliable. Therefore no definite relationship could be established between “softness” and forward characteristics. R. Eflects 4
cells
of heat
treatment
second set of experiments on commercial was performed to find out whether the
FORWARD
CHARACTERISTICS
AND
EFFICIENCIES
OF SILICON
SOLAR
(Amps)
t
IO-*
i-
;r
.05 3
0.2
0.I
V,,
0.3
(OPEN
CIRCUIT
04
VOLTAGE)
J
0.5
~V0175l
0.4
(Volts
--
(4
/
0.1 Vop(OPEN
0.2 CIRCUIT
0.3 VOLTAGE)
-
(b) 4. (a) Forward characteristics of a commercial solar cell after different heat treatments. Curve a before treatment; curve 6 after 0.5 hr at 825 “C and subsequent quenching; c after additional 0.5 hr at 825 “C and very slow cooling; d after 0.5 hr at 845 “C and quenching; e edges of cell etched away. (All measurements at 2.2 “C.) (b) Corresponding A-values vs. open-circuit voltage. FIG.
CELLS
8
H.
J. QUEISSER
characteristics of commercial cells could be influenced by heat treatments at temperatures much lower than those used for diffusion of donors or acceptors. If changes of the characteristics are found, they must then be attributed to the diffusion of other entities, not required in principle for the cells. Such entities could, for instance, be recombination centers of low-activation energy for diffusion. If such centers can be detected it follows that, by removing them, higher efficiencies arc to bc expected. For the experiments, a low-efficiency cell of the same type as before (Hoffman Type 11OC) w-m used. It was etched in aqua regia to dissolve the contacts. The open-circuit voltage was measured and is plotted as curve “a” in Fig. 4(a) against the reference current of the standard ccl1 at the same illumination level. Fig. 4(b) sholvs the corresponding dependence of I-I vs. the opcncircuit voltage 1701,.The cell was heated for 0.5 lx in a hydrogen flow at 825 C. ‘I’he diffusion length l/nt for phosphorus at the same tempcraturc aud time is of the order of 0.01 /L. The dopants most commonly employed in cell production, namely H, As, Sh, have cvcu smaller diffusion lengths, so that donor and acceptor diffusion can be neglected. After heating, the cell was quenched to room temperature with au approximate cooling rate of more than 500 Cimin. The resulting voltage-current curves are labeled b. The quantity .4 is reduced to practically 2. A further heat treatment under the same conditions but with very slow cooling (average rate : 1 C/min) resulted in the characteristic of curve c, with increased .4. Another treatment at the slightly higher temperature of 845 “C with subsequent quenching gave curve d with A-values considerably above .3 aud greatly reduced open-circuit voltages. After tl was measured, the edges of the ccl1 were etched off. Remeasuring resulted in curve e. A partial restoration of the characteristic is observed. ‘rhese substantial changes in the forward currenvoltage dependence are clear evidence that impurities or other defects are determining the anomalies in the characteristics. A brief, speculative discussion of these preliminary measurements will be given in the next section.
From
the
3. DISCUSSION experiments just
described
some
conclusions can be drawn concerning the physical model for the forward characteristics of the solar cells. If field emission or tunneling effects, solely caused by high electric fields in the abrupt junction \vere the reasons for the strange forwwd behavior, one n.ould not expect such lkonuniformities as found in our experiments. Nor do the contacts give rise to the observed anomalies. Our measurements arc practically unaffected by contact resistmces . ‘ .. From a recent publication bp \VOI.F(~‘~J it appears that results related to ours have been observed before. T\‘o details have, honGever, been published and no interpretation is given other than on the basis of a gcneralizcd shunt resistance which affects the open-circuit voltages. 11’01.1; also states a principle of minimum change of powc‘t output nith changes in the characteristics. High d-values result in undesirable shapes of the current -voltage curve, but this is compensated by the higher open-circuit \-oltage in such a \\a) that there is “practically no change in powc~ output from the device”. It is the opinion of the present author that this empirical rule is not the consccluence of some general principle. Unless the physical reasons for the peculiarities in the forIyard characteristics are understood, the “minimum change” rule must be considered as accidental and caused hy limitations of the present fabrication techniques. At the moment, the most attractive hypothesis for the effects described appears to be the follo\viug. Impurities, probably metals, arc present in siguificant quantities in today’s commercial s0la1 cells. l’he starting maierial for these cells is “solar-grade silicon”, \vhich is the normallylowest quality on the mnrkct. If the impurities iu this material merely acted as uuiformly distributed recombination centers in the space-charge layer, oue should find d-values of about 2 fat- a wide rauge of voltages. (X,9) But if silicou samples with sufficiently large impurity coucentrations arc heat treated in a special way, e.g. with slow cooling, precipitates may be formed. From many invcstigations it is well known that such precipitations do occur and are very sensitive to the thermal treatments.(l*,l$-2”) These precipitates might cause the high values of A through a mechanism which is not yet fully understood. For instance, the precipitates may create considerable field
FORWARD
CHARACTERISTICS
AND
EFFICIENCIES
inhomogeneities and may have large enough dimensions practically to short-circuit the spacecharge layer. Although it seems to be generally acceptedc 1~s) that surface phenomena cannot explain the anomalous characteristics of solar cells, it is to be expected that the regions of the exposed junction will be most severely affected by contaminants, especially by those which enter during processing. On the basis of precipitates one may explain the behavior described by Fig. 4. Heating the cell could have dissolved the precipitates because of an increase of solubility with temperature. Quenching did not permit formation of precipitates, so A is reduced (see curves b). Slow cooling restores the precipitates (curves c); possibly a greater number than were observed before, because additional impurities diffused into the cell during the treatments. The A-value is increased again. Curves d should again show lower A-values, because of the quenching. However, nothing definite can be said because the temperature was higher for this run. Apparently this last treatment affected the edges very much, since, by etching them off, lower A-values were obtained (curves e). The crossing of the curves in Fig. 4(a) is an interesting feature, and seems to be the basis for WOLF’s(~~) “minimum-change” rule. Our interpretation follows. Precipitates cause excessive currents at lower voltages until the normal recombination and generation currents dominate. This must finally occur because the latter increase faster, i.e. with A = 2 in the exponent vs. A = 3 or more. Eventually a kink should be observed and A should drop to 2 or below, and then even to 1, according to equation (1). Onset of ohmic behavior will often conceal this kink in normal V-1 characteristics. The kink will occur at higher voltages if the number of recombination centersand hence the recombination current-is made smaller. This seems to be the case for curve c. Most centers are concentrated in the precipitates, whose number is small. On the other hand curve b was interpreted as having many quenched-in centers. These should give more recombination current than was found in case c, but less current at lower voltages because of the absence of precipitates. The data confirm this. Case c (precipitates) seems to be more advantageous than case b (solid solution) for
OF SILICON
SOLAR
CELLS
9
solar-cell operation, for two reasons. Firstly, a higher open-circuit voltage will be delivered, as just discussed. Secondly, it is known(21.22) that precipitation of impurities increases carrier lifetimes because of the reduced number of recombination centers. This should result in higher short-circuit currents because of increased collection efficiency. On the other hand, the precipitates should make the cell “soft” in the reverse direction.* On the basis of this precipitate model, one can understand the relation between “softness”, high efficiency and high A-value. This shows that a compromise has been made because of the impure material. It is clear that no recombination centers would be the best-possible case, and cells with that property should be “hard” under reverse bias. Further evidence for the precipitate model has been found in small-area p-n junctions investigated in this laboratory. The forward characteristics followed the same patterns upon heat treatments. The reverse characteristics were also measurable and showed an additional feature. When precipitates were suspected from the thermal history, and high A-values were found in the forward characteristic, a “double break”? was often found under reverse bias. This means that from a certain voltage below avalanche breakdown, current is passed as if an ohmic resistance were placed across the junction. The reasons for this “double break” are not yet understood, but it is tempting to interpret this ohmic resistance as caused by one or more precipitates. These series resistances should also be noticeable in the forward direction. They might be rather important for the shape of the forward curves. One observation is particularly noteworthycontact areas show the most-favorable behavior [curves 1 and 3 of Fig. 3(b)]. These areas were probably the most exposed to metals and other foreign substances during the formation of the contact. This seeming contradiction could be resolved on the basis of “gettering”. It is possible that the nickel which was used for contacting acted
* “Softness” may, of course, also be introduced by less-careful cleaning and etching procedures than employed for other devices. t Similar diodes.(ss)
observations
have
been made
on GaAs
10
H.
J.
QUEISSER
as getter. Nickel is known to getter effectively and to preserve carrier lifetimes.(14J4-26) The situation is, of course, much more complicated than just described. For example, no mention has been made of the probably important roles of oxygen@O) or dislocations”‘) and their interactions with other impurities.Qs) The possibility of donor or acceptor precipitates or paired donor-acceptor compounds like BP should be considered. Further studies are necessary to prove the relevance, and determine the role of, these defects for silicon solar-cell efficiencies.
4. M. WOLF, Proc. I.R.E. 48, 1246 (1960). 5. WI. WOLF, Energy Conversion .for Space Power (Ed. by N. W. SNYDER) p. 231. Academic Press, New York (1961). 6. I\‘. G. PFANN and
7. 8. 9. 10.
11. 12.
4. CONCLUSIONS
The experiments strongly indicate that some impurities or defects are present in, and lower the efficiency of, commercial solar cells. These defects are probably unnecessary. For their prevention or removal we propose several possible methods. Gettering(l4) should be effective. Material free of oxygen and dislocationsQ9) would probably be more advantageous. The formation of dislocations during diffusion(27) can be avoided by using over- and under-sized dopants in proper proportions so that there is no over-all misfit in the silicon lattice. The edges of the cell should be protected from leakage sources. The knowledge of the junction characteristics is still far from being adequate. It was the purpose of the research described to demonstrate this fact once more and to indicate approaches to the solution of the mysterious forward characteristics which should lead to improvements in solar-cell efficiency.
W. v.4~ RO~SBROECK, J. Appl. Phys. 25, 1422 (1954). P. RAPI’APORT, R.C.A. Rev. 20, 373 (1959). C. T. SAH, R. NOYCE and W. SHOCKLEY, Proc. I.R.E. 45, 1228 (1957). \\‘. QIIOCKLEY and R. Ii. HENLEY, Httll. Amer. Phys. Sot. [II] 6, 106 (1961). X. AZIZOV and G. M. AVAK’IANX. IZO. Akad. Nauk. Uzh.S.S.R., Fiz.-Mat. Nauk. 2, 78 (1960). A. G. CHYNOWETH and K. G. MCKAY, Phys. Rev.. 106, 418 (1957). T. YAJIMA and L. ESAKI, J. Phys. Ser. Japan 13, 1281 (1958).
13. I’or a discussion
14. 15.
16.
17.
18. 19.
concerning the reverse characteristic and a reference to F/I. WOLF and M. B. PHINCE, see Ref. 1, p. 518. A. GOETZBERGERand W. SFIOCKLE~,.]. Appl. Phys. 31, 1821 (1960). L. VALDES, Proc. I.R.E. 42, 420 (1954). M. WOLF, Energy Conversion for Space Power (Ed. by N. W. SNYDER) p. 244. Academic Press, P\JewYork (1961). W. C. DASH, J. Appl. Phys. 27, 1193 (1956). G. H. SCHWUTTKE, J. E/ectrochem. Sot. 108, 163 (1961). H. RIECEH and I<. SEILER, Z. Nuturf. 16a, 220
(1961). 20. A
review on precipitation in semiconductors is given by A. G. TWEET, J. Appl. Phys. 30, 1244 (1959) ; a review on reactions involving oxygen is given by H. REISS and W. KAISER in Properties
of Elemental and Compound Semiconductors (Ed. by H. C. GA~‘os) p. 103. Interscience, New York (1960). G. BEMSKI, Phys. Rev. 103, 567 (1956). 22. A. BAKER and G. BEXKI, I.R.E. Meeting, Denver, Colorado, 1957, as quoted by S. J. SILVERMAN and J. B. SINGLETON, J. Electrochem. Sac. 105, 21.
591 (1958). 23. ‘1’. M. QUIST and H. M. would like to express his gratitude to Dr. W. SHOCKLEY for his encouragement and aid with many suggestions and discussions, and to L. AwwEt and W. HOOPER who carried out most of the experimental work.
Acknowledgements-The
24.
REDIKER, Lincoln Lab. Quart. Rep., January 15, p. 6 (1961). R. A. LOGAN and M. SCHWARTZ, J. Appl. Pkys. 26,
25.
G.
author
1287 (1955).
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Phj,s.
CHAPIN, C. S. FULLER and G. L. PEARSON,
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STRUTHERS, J.
Electrochem.
105, 588 (1958).
J. SHATTES and H. A. R. ~VEGENER,J. Appl. Phys. 29, 866 (1958). 27. H. J. QUEISSER,J. App[. Phys. 32, 1776 (1961). 28. S. G. KALASHNIKOV and A. K. MEDNIKOV, Fiz. Tver. Tela 2, 2058 (1960); (English translation: Sowiet Phys., So/id State 2, 1847 (1961). 29. \V. C. DASH, J. Appl. Phys. 30, 459 (1959); 31, 736 (1960).
26. W.
1. W. SHOCKLEY and H. J. QUEISSER,J. Appl. 32, 510 (1961).
BEM~KI and J. D.
Sot.
Electronics
FORWARD
Pergamon
Press 1962. Vol. 5, pp. l-10.
Printed in Great Britain
CHARACTERISTICS AND EFFICIENCIES OF SILICON SOLAR CELLS* H. J. QUEISSER Shockley
Transistor,
Unit of Clevite Transistor,
(Received 17 July 1961;
Palo Alto, California
in revisedform 10 October 1961)
Abstract-Forward currents in commercial solar cells show an exponential dependence on the forward voltage as exp (qI’/‘iAkT) with A N 3. This factor 3 in the exponent cannot as yet be explained satisfactorily. Experiments indicate that this strange forward characteristic is not an over-all property of the entire cell, but comes from localized regions of the junction area, preferentially at the cell edges. Heat treatments at temperatures low enough to exclude appreciable donor and acceptor diffusion produce significant changes in the characteristics. The results are interpreted in terms of impurities which are either dissolved or precipitated. These experiments show that commercial solar cells contain unnecessary defects which cause their strange characteristics and lower their efficiencies. R&sum&-Les courants directes des cellules solaires commerciales dependent des voltages directes comme exp (qV/AkT) avec A N 3. A l’heure actuelle, le facteur 3 dans l’exponent ne peut pas dtre explique avec satisfaction. Des experiences indiquent que cette &range caracteristique directe n’est pas une propriete de l’entibre cellule, mais vient des regions localisees de la jonction p-n, preferremment au hord de la cellule. Des traitements thermiques a des temperatures assez basses pour ne pas permettre une diffusion appreciable des donneurs et des accepteurs produisent des changements considerables des caracteristiques. Ces resultats sont interpretes en termes d’impuretes qui sont dissoues ou precipitees. Ces experiences demontrent que les cellules solaires commerciales contiennent des defauts qui ne sont pas necessaires et causent leur caracteristiques &ranges et diminuent leur efficacitts. Zusammenfassung-Technische Silizium-Solarzellen zeigen eine Abhangigkeit des Stromes von der Spannung in Flussrichtung gemass exp (qL’/AkT) mit A N 3. Dieser Faktor 3 im Exponenten ist bis jetzt theoretisch noch nicht erklart. Experimente zeigen, dass diese unerklarte Strom-Spannungs-Kennlinie keine Eigenschaft der gesamten Zelle ist, sondern von lokalisierten Bereichen des p-n Uberganges, hesonders an den Kanten, herriihrt. Warmebehandlungen hei Temperaturen, die keine nennenswerte Donatorenund Akzeptoren-Diffusion gestatten, rufen erhebliche Anderungen der Kennlinie hervor. Die Resultate werden mit der Annahme von Verunreinigungen erklart, die entweder gel&t oder als Ausscheidungen vorhanden sind. Diese Experimente zeigen, dass die heutigen technischen Solarzellen unniitige Storungen enthalten, die die eigenartige Kennlinie und einen verminderten Wirkungsgrad hervorrufen.
1. INTRODUCTION
current density, the higher will be the opencircuit voltage developed by the same current density of photon-created carriers reaching the junction. A cell that delivers higher open-circuit voltages for every current density will also have a higher efficiency of energy conversion than another cell with otherwise equal properties. The best possible current-voltage characteristic, and therefore the best efficiency, will be obtained if there is only radiative recombination of the holes and electrons created by the incident
efficiency of a semiconductor photovoltaic energy converter is commonly defined as the ratio of electrical power output into a matched load to the incident power per active area. This efficiency depends highly on the forward current-voltage characteristic of the p-7a junction. The higher the forward voltage necessary to pass a given forward
THE
* Work performed under contract AF 33(616)-7786 with Wright Air Development Division. A
1
H.
2
J. QUEISSER
photons.(l) cnder these conditions the forward characteristic without illumination is given by the ideal rectifier equation: I = la[exp(qV/kT)-
11
(1)
where I is the junction current, 10 the minimum reverse saturation current, as required by detailed balance, V the voltage applied to the junction, q = 191the value of the electronic charge, k the Boltzmann’s constant and 7’ the absolute temperature. The most important photovoltaic energy converters are the silicon solar cells which are produced in great quantities.(s-1) These commercial cells have efficiencies up to 15 per cent at present.(5) Such efficiencies, however, are still considerably below the estimated semi-empirical limit of 22 per cent,(a) or the calculated “detailed balance limit” of 30 per cent.(l) Further gains in efficiency will undoubtedly result from still better contacts, more advantageous structures or better optical properties. It appears that the greatest potential for higher efficiencies lies in materials with higher lifetimes and in the improvement of the junction characteristics. The junctions in today’s solar cells do not exhibit the ideal behavior of equation (1). It has been shown,(l) and this paper gives further evidence, that excessive non-radiative recombinations and/or other unnecessary current paths sharply reduce the voltage and current output, and thus the power delivered by the solar cells. The present status of the theory of solar energy converters is most clearly described by the fact that the forward characteristics of typical commercial cells are not at all understood. The forward behavior is usually described(43697) by a relation of the type of equation (1) with an empirical factor A introduced to account for the experimental data when I = Ii[exp(qV/AkT)where 1; has also only the empirical fitting constant. Values for A between 1 and 2 can on the basis of carrier recombination tion in the space-charge layer.(s) The typically yield A-values of 3 or even values could still be interpreted from recombination centers.(t,s) A
l] meaning
(2) of a
be explained and generaexperiments higher. Such as arising non-uniform
distribution of the centers must then be postulated and certain assumptions must be made about capture and emission of carriers by the centers. It is not yet clear whether these assumptions are physically justified. Other possible explanations have been proposed. Some authors@,la) believe that the high A-values can best be explained with field effects. Junctions with extremely narrow space-charge layers show similar anomalous characteristics which have been interpreted as internal field emission.(ll) Comparable problems of “excess currents” in tunnel diodeso”) have been explained by tunneling together with recombination at levels inside the forbidden gap. It is not obvious that this is also the case in solar cells, which have comparatively much wider space-charge layers. It now appears certain that, in principle, high values of A are undesirable for solar cell operation.“) Although high A-values mean a slower increase of current with voltage, the absolute values of the current for a given voltage are higher than those predicted by the ideal rectifier equation. Empirically it is found(j) that with increasing A the parameter 1; of equation (2) also increases, generally in such a way that higher currents are obtained. Regardless of the specific physical interpretation it can be said that high A-values are an indication of unwanted excess currents in the p-n junction that lower solar cell efficiency. From the foregoing it is evident that there is a potential for improvement of solar cells by improving junction characteristics. An understanding of the high A-values should eventually lead to methods of reducing the forward current, resulting in higher energy conversion efficiences. This paper presents an initial experimental investigation which has developed evidence that there are avoidable current paths in commercial solar cells which are responsible for lowered efficiency. It is shown here that the abnormally high A-values are probably the result of a design compromise dictated by the use of contaminated materials. It appears from the studies reported here that the high A-values are not a necessary consequence of the solar cell design as would be predicted by a simple tunneling hypothesis. 2. EXPERIMENTAL RESULTS Two sets of experiments will be described
which
FORWARD
CHARACTERISTICS
V,
AND
(REVERSE
-5
Vf (FORWARD
EFFICIENCIES
OF SILICON
VOLTAGE)---
_,(-J
SOLAR
(Volts)
VOLTAGE)-
(4
t A
1
0.1 vop
0.2 (OPEN
0.3 CIRCUIT
0.4
_)
(volt s)
VOLTAGE)-
(b)
FIG. 1. (a) Forward and reverse characteristics of a commercial solir cell, measured at 22 “C. (b) Dimensionless fitting parameter A vs. applied forward voltage. (Note suppressed scale for A !).
CELLS
3
4
H.
J.
QUEISSER
lead to the following two conclusions: (a) the strange characteristics with A-values as high as 3 are not an over-all property of the cell, but appear localized; (1~)the characteristic may be changed by heat treatment at temperatures well below those needed for donor- and acceptor-diffusion.
icl-
A. Localized spots with poor characteristics immi Experiments were performed on several cells, with different efficiencies indicated by the supplier.:” All of the cells arc produced by a shallow diffusion of boron into n-type silicon. In each case the value for A was found to be considerably greater than 2. Most cells can be described with A iy_ 3 over a current range of more than two decades. A typical current-voltage characteristic of a solar cell (Hoffman Type 110 C) is given in Fig. 1 (a). By logarithmic differentiation of the “forward” curve, A may be obtained as a function of applied bias. In doing this, the constant term 1; in equation (2) which is justifiable for voltages is neglected, greater than about 120 mV. The resulting function IC A(v) is given in Fig. I(b). It is seen that A is approximately constant = 3. Above 450 mV bias it is the ohmic resistance of the cells that makes the factor A appear larger. The dashed line in Fig. l(a) gives the reverse characteristic. It shows the well-known “softness” of solar cells, which (mm) is especially noticeable for high-efficiency cells.(ra) Equipotential plots(r4) were obtained for the surface of the cell at both a given forward and reverse current by measuring the voltage at the Y surface with respect to a given reference point at the contact. These plots are shown in Fig. 2. They reveal no anomalies except an enhanced potential drop at the lower right edge. This points toward a damaged or shorted portion of the junction, but nothing could be visibly detected.? Information about the current flow may be oh0 tained from the equipotential plots and the sheet resistivity. The current appears to flow rather uniformly with the exception of the lower right FIG. 2. edge. The amount of current flowing through the
I
* Hoffman Electronics Corp., El Monte, California (USA); Solar Systems, Inc., Skokie, Illinois (USA); and International Rectifier Corp., El Segundo, California (USA). t Such anomalies were frequently found at this corner. They may have been introduced by certain peculiarities in the manufacturing process, especially the sawing.
X-
(mm)
Equipotential plots for a commercial solar cell under (a) forward and (b) reverse current flow. Active area of cell = 0.9 X 1 .O cm”. Contact strip is along Y-axis.
junction into the n-type base can be determined hy evaluating the divergence of the corresponding “Four-point probe” measurecurrent field. ments(is) indicated that the sheet resistivitv of the
FORWARD
CHARACTERISTICS
AND
EFFICIENCIES
cell surfaces is fairly uniform. Therefore one can interpret a divergence of grad V as a current sink. Most of these evaluations showed that the forward current flows through the junction in the bulk
OF SILICON
SOLAR
and only small fractions of the current flow across the edges. The potential-probing method is not sensitive enough to detect small differences in the behavior
(b)
,
0.1
0.3
0.2
Vop
(OPEN
CIRCUIT
0.4
'0.5 iv01
VOLTAGE)
~~
*
I
A
0
0.1 V,,
(OPEN
CELLS
0.2 CIRCUIT
0.3
VOLTAGE)
-
0.4 (Volts)
FIG. 3. Behavior of mesas etched out of solar cell. (a) Location and numbering of the mesas on the cell. (b) Open-circuit voltages plotted as a function of illumination level as measured through the reference short-circuit current of a standard cell. Numbers on the curves refer to the mesas in Fig. 3(a); “0” is entire cell. (c) Fitting parameter A vs.open-circuit voltage. Dashed curve is same as Fig. l(b).
5
6
H. J.
QUEISSER
of different regions of the cell. Therefore, the individual characteristics regions of various were measured on mesas etched out of the cell. As indicated by Fig. 3(a), different areas were masked by wax and the rest of the cell surface was etched away. The mesas thus produced did not have contacts on the top layer, but their forward behavior could be measured by the following technique. The etched cell was illuminated. The illumination could be controlled without change in the quality of the radiation (i.e. same color temperature of the light source). The illuminatiorl level was measured through a reference short-circuit current lref of another solar cell serving as a standard. At different levels the open-circuit voltages of the mesas were determined with an infinite impedance voltmeter. When these open-circuit Lroltages l,bI1 arc plotted against the reference current Iref, a current-voltage characteristic is obtained which over a wide voltage range is practically identical to the characteristic measured in the dark using four contacts. The slope of the curve is preserved. The absolute value of the current level may vary because of differences in photon absorption or collection efficiency. The ohmic IR-drop of a cell with high contact resistance R is not measured with the “V,,P vs. Iref” method. Only the series resistance of the standard cell is influential, and it can be kept small if a high efficiency cell with low contact resistance is chosen. In Fig. 3(b), curve 0 gives a “Vor, vs. Iref” curve of the entire unetched solar c-11, which is the same cell as that of Figs. 1 and 2. Comparison with the forward 1--Tcharacteristic measured in the dark (Fig. 3c, dashed curve) shows that the slopes differ by less than 10 per cent up to about 0.3 V. Beyond that voltage the series resistance of the cell results in a higher value for A if the cell is measured with the standard two-contact method. The “\rOPvs. I,,f” method is not hampered by this series resistance. It is seen that A decreases with increasing VoP. The remaining curves on Fig. 3(b) represent the characteristics of different mesas of the etched solar cells. The number of each curve refers to the corresponding mesa as s,hown on Fig. 3(a). Fig. 3(c) gives the A-values for the mesas. These curves have been smoothed, since the differentiation exaggerates the experimental scatter.
Curve 8 typifies the characteristics of all mesas in the center of the cell. The open circuit voltages found are higher than the average voltages as given by curve 0. It is believed that this difference of open-circuit voltages is not caused by different photon absorptions or accidental features. Moreover, the slope of curve X corresponds to considerably lower A-values (see Fig. 3~). Thus the center portions definitely behave less abnormally than the entire cell. The behavior of the lower right corner of the cell, which looked conspicuous in the potential plots of Fig. 2, is given in curve 14. It closel! parallels the over-all behavior with slightly lower open circuit voltages. Still worse behavior is found for mesa no. 9 which is located near the edge. Another edge-mesa is described by curve 5. All of these devices exhibit high A-values and low opencircuit voltages. It is felt that these portions arc chiefly responsible for the poor over-all performance of the cell. hfesas that comprise regions of the former contact show very surprising behavior. This is depicted in curves 3 and 1. Mesa no. 3 shows much higher open-circuit voltages than other center mesas; it gave the largest open-circuit voltage of all mesas measured. Mesa no. 1 is located at a corner but its behavior is superior to all other edge devices. This strange influence of the contact will be further discussed on the basis of a “gettering action” by contact metals. The measurements described here were made on a cell with low conversion efficiency (6-X per cent according to supplier). Highly efficient cells (e.g. Hoffman Type 120~SCG 13, 13 per cent efficiency) showed essentially the same behavior, but with much less spread for different regions of the cell. As is to be expected, allopen-circuit voltages measured for these higher-efficient) cells were larger. No attempt \vas made to set up a four-contact circuit to study the reverse characteristics of the mesas. Two-contact measurements appeared unreliable. Therefore no definite relationship could be established between “softness” and forward characteristics. R. Eflects 4
cells
of heat
treatment
second set of experiments on commercial was performed to find out whether the
FORWARD
CHARACTERISTICS
AND
EFFICIENCIES
OF SILICON
SOLAR
(Amps)
t
IO-*
i-
;r
.05 3
0.2
0.I
V,,
0.3
(OPEN
CIRCUIT
04
VOLTAGE)
J
0.5
~V0175l
0.4
(Volts
--
(4
/
0.1 Vop(OPEN
0.2 CIRCUIT
0.3 VOLTAGE)
-
(b) 4. (a) Forward characteristics of a commercial solar cell after different heat treatments. Curve a before treatment; curve 6 after 0.5 hr at 825 “C and subsequent quenching; c after additional 0.5 hr at 825 “C and very slow cooling; d after 0.5 hr at 845 “C and quenching; e edges of cell etched away. (All measurements at 2.2 “C.) (b) Corresponding A-values vs. open-circuit voltage. FIG.
CELLS
8
H.
J. QUEISSER
characteristics of commercial cells could be influenced by heat treatments at temperatures much lower than those used for diffusion of donors or acceptors. If changes of the characteristics are found, they must then be attributed to the diffusion of other entities, not required in principle for the cells. Such entities could, for instance, be recombination centers of low-activation energy for diffusion. If such centers can be detected it follows that, by removing them, higher efficiencies arc to bc expected. For the experiments, a low-efficiency cell of the same type as before (Hoffman Type 11OC) w-m used. It was etched in aqua regia to dissolve the contacts. The open-circuit voltage was measured and is plotted as curve “a” in Fig. 4(a) against the reference current of the standard ccl1 at the same illumination level. Fig. 4(b) sholvs the corresponding dependence of I-I vs. the opcncircuit voltage 1701,.The cell was heated for 0.5 lx in a hydrogen flow at 825 C. ‘I’he diffusion length l/nt for phosphorus at the same tempcraturc aud time is of the order of 0.01 /L. The dopants most commonly employed in cell production, namely H, As, Sh, have cvcu smaller diffusion lengths, so that donor and acceptor diffusion can be neglected. After heating, the cell was quenched to room temperature with au approximate cooling rate of more than 500 Cimin. The resulting voltage-current curves are labeled b. The quantity .4 is reduced to practically 2. A further heat treatment under the same conditions but with very slow cooling (average rate : 1 C/min) resulted in the characteristic of curve c, with increased .4. Another treatment at the slightly higher temperature of 845 “C with subsequent quenching gave curve d with A-values considerably above .3 aud greatly reduced open-circuit voltages. After tl was measured, the edges of the ccl1 were etched off. Remeasuring resulted in curve e. A partial restoration of the characteristic is observed. ‘rhese substantial changes in the forward currenvoltage dependence are clear evidence that impurities or other defects are determining the anomalies in the characteristics. A brief, speculative discussion of these preliminary measurements will be given in the next section.
From
the
3. DISCUSSION experiments just
described
some
conclusions can be drawn concerning the physical model for the forward characteristics of the solar cells. If field emission or tunneling effects, solely caused by high electric fields in the abrupt junction \vere the reasons for the strange forwwd behavior, one n.ould not expect such lkonuniformities as found in our experiments. Nor do the contacts give rise to the observed anomalies. Our measurements arc practically unaffected by contact resistmces . ‘ .. From a recent publication bp \VOI.F(~‘~J it appears that results related to ours have been observed before. T\‘o details have, honGever, been published and no interpretation is given other than on the basis of a gcneralizcd shunt resistance which affects the open-circuit voltages. 11’01.1; also states a principle of minimum change of powc‘t output nith changes in the characteristics. High d-values result in undesirable shapes of the current -voltage curve, but this is compensated by the higher open-circuit \-oltage in such a \\a) that there is “practically no change in powc~ output from the device”. It is the opinion of the present author that this empirical rule is not the consccluence of some general principle. Unless the physical reasons for the peculiarities in the forIyard characteristics are understood, the “minimum change” rule must be considered as accidental and caused hy limitations of the present fabrication techniques. At the moment, the most attractive hypothesis for the effects described appears to be the follo\viug. Impurities, probably metals, arc present in siguificant quantities in today’s commercial s0la1 cells. l’he starting maierial for these cells is “solar-grade silicon”, \vhich is the normallylowest quality on the mnrkct. If the impurities iu this material merely acted as uuiformly distributed recombination centers in the space-charge layer, oue should find d-values of about 2 fat- a wide rauge of voltages. (X,9) But if silicou samples with sufficiently large impurity coucentrations arc heat treated in a special way, e.g. with slow cooling, precipitates may be formed. From many invcstigations it is well known that such precipitations do occur and are very sensitive to the thermal treatments.(l*,l$-2”) These precipitates might cause the high values of A through a mechanism which is not yet fully understood. For instance, the precipitates may create considerable field
FORWARD
CHARACTERISTICS
AND
EFFICIENCIES
inhomogeneities and may have large enough dimensions practically to short-circuit the spacecharge layer. Although it seems to be generally acceptedc 1~s) that surface phenomena cannot explain the anomalous characteristics of solar cells, it is to be expected that the regions of the exposed junction will be most severely affected by contaminants, especially by those which enter during processing. On the basis of precipitates one may explain the behavior described by Fig. 4. Heating the cell could have dissolved the precipitates because of an increase of solubility with temperature. Quenching did not permit formation of precipitates, so A is reduced (see curves b). Slow cooling restores the precipitates (curves c); possibly a greater number than were observed before, because additional impurities diffused into the cell during the treatments. The A-value is increased again. Curves d should again show lower A-values, because of the quenching. However, nothing definite can be said because the temperature was higher for this run. Apparently this last treatment affected the edges very much, since, by etching them off, lower A-values were obtained (curves e). The crossing of the curves in Fig. 4(a) is an interesting feature, and seems to be the basis for WOLF’s(~~) “minimum-change” rule. Our interpretation follows. Precipitates cause excessive currents at lower voltages until the normal recombination and generation currents dominate. This must finally occur because the latter increase faster, i.e. with A = 2 in the exponent vs. A = 3 or more. Eventually a kink should be observed and A should drop to 2 or below, and then even to 1, according to equation (1). Onset of ohmic behavior will often conceal this kink in normal V-1 characteristics. The kink will occur at higher voltages if the number of recombination centersand hence the recombination current-is made smaller. This seems to be the case for curve c. Most centers are concentrated in the precipitates, whose number is small. On the other hand curve b was interpreted as having many quenched-in centers. These should give more recombination current than was found in case c, but less current at lower voltages because of the absence of precipitates. The data confirm this. Case c (precipitates) seems to be more advantageous than case b (solid solution) for
OF SILICON
SOLAR
CELLS
9
solar-cell operation, for two reasons. Firstly, a higher open-circuit voltage will be delivered, as just discussed. Secondly, it is known(21.22) that precipitation of impurities increases carrier lifetimes because of the reduced number of recombination centers. This should result in higher short-circuit currents because of increased collection efficiency. On the other hand, the precipitates should make the cell “soft” in the reverse direction.* On the basis of this precipitate model, one can understand the relation between “softness”, high efficiency and high A-value. This shows that a compromise has been made because of the impure material. It is clear that no recombination centers would be the best-possible case, and cells with that property should be “hard” under reverse bias. Further evidence for the precipitate model has been found in small-area p-n junctions investigated in this laboratory. The forward characteristics followed the same patterns upon heat treatments. The reverse characteristics were also measurable and showed an additional feature. When precipitates were suspected from the thermal history, and high A-values were found in the forward characteristic, a “double break”? was often found under reverse bias. This means that from a certain voltage below avalanche breakdown, current is passed as if an ohmic resistance were placed across the junction. The reasons for this “double break” are not yet understood, but it is tempting to interpret this ohmic resistance as caused by one or more precipitates. These series resistances should also be noticeable in the forward direction. They might be rather important for the shape of the forward curves. One observation is particularly noteworthycontact areas show the most-favorable behavior [curves 1 and 3 of Fig. 3(b)]. These areas were probably the most exposed to metals and other foreign substances during the formation of the contact. This seeming contradiction could be resolved on the basis of “gettering”. It is possible that the nickel which was used for contacting acted
* “Softness” may, of course, also be introduced by less-careful cleaning and etching procedures than employed for other devices. t Similar diodes.(ss)
observations
have
been made
on GaAs
10
H.
J.
QUEISSER
as getter. Nickel is known to getter effectively and to preserve carrier lifetimes.(14J4-26) The situation is, of course, much more complicated than just described. For example, no mention has been made of the probably important roles of oxygen@O) or dislocations”‘) and their interactions with other impurities.Qs) The possibility of donor or acceptor precipitates or paired donor-acceptor compounds like BP should be considered. Further studies are necessary to prove the relevance, and determine the role of, these defects for silicon solar-cell efficiencies.
4. M. WOLF, Proc. I.R.E. 48, 1246 (1960). 5. WI. WOLF, Energy Conversion .for Space Power (Ed. by N. W. SNYDER) p. 231. Academic Press, New York (1961). 6. I\‘. G. PFANN and
7. 8. 9. 10.
11. 12.
4. CONCLUSIONS
The experiments strongly indicate that some impurities or defects are present in, and lower the efficiency of, commercial solar cells. These defects are probably unnecessary. For their prevention or removal we propose several possible methods. Gettering(l4) should be effective. Material free of oxygen and dislocationsQ9) would probably be more advantageous. The formation of dislocations during diffusion(27) can be avoided by using over- and under-sized dopants in proper proportions so that there is no over-all misfit in the silicon lattice. The edges of the cell should be protected from leakage sources. The knowledge of the junction characteristics is still far from being adequate. It was the purpose of the research described to demonstrate this fact once more and to indicate approaches to the solution of the mysterious forward characteristics which should lead to improvements in solar-cell efficiency.
W. v.4~ RO~SBROECK, J. Appl. Phys. 25, 1422 (1954). P. RAPI’APORT, R.C.A. Rev. 20, 373 (1959). C. T. SAH, R. NOYCE and W. SHOCKLEY, Proc. I.R.E. 45, 1228 (1957). \\‘. QIIOCKLEY and R. Ii. HENLEY, Httll. Amer. Phys. Sot. [II] 6, 106 (1961). X. AZIZOV and G. M. AVAK’IANX. IZO. Akad. Nauk. Uzh.S.S.R., Fiz.-Mat. Nauk. 2, 78 (1960). A. G. CHYNOWETH and K. G. MCKAY, Phys. Rev.. 106, 418 (1957). T. YAJIMA and L. ESAKI, J. Phys. Ser. Japan 13, 1281 (1958).
13. I’or a discussion
14. 15.
16.
17.
18. 19.
concerning the reverse characteristic and a reference to F/I. WOLF and M. B. PHINCE, see Ref. 1, p. 518. A. GOETZBERGERand W. SFIOCKLE~,.]. Appl. Phys. 31, 1821 (1960). L. VALDES, Proc. I.R.E. 42, 420 (1954). M. WOLF, Energy Conversion for Space Power (Ed. by N. W. SNYDER) p. 244. Academic Press, P\JewYork (1961). W. C. DASH, J. Appl. Phys. 27, 1193 (1956). G. H. SCHWUTTKE, J. E/ectrochem. Sot. 108, 163 (1961). H. RIECEH and I<. SEILER, Z. Nuturf. 16a, 220
(1961). 20. A
review on precipitation in semiconductors is given by A. G. TWEET, J. Appl. Phys. 30, 1244 (1959) ; a review on reactions involving oxygen is given by H. REISS and W. KAISER in Properties
of Elemental and Compound Semiconductors (Ed. by H. C. GA~‘os) p. 103. Interscience, New York (1960). G. BEMSKI, Phys. Rev. 103, 567 (1956). 22. A. BAKER and G. BEXKI, I.R.E. Meeting, Denver, Colorado, 1957, as quoted by S. J. SILVERMAN and J. B. SINGLETON, J. Electrochem. Sac. 105, 21.
591 (1958). 23. ‘1’. M. QUIST and H. M. would like to express his gratitude to Dr. W. SHOCKLEY for his encouragement and aid with many suggestions and discussions, and to L. AwwEt and W. HOOPER who carried out most of the experimental work.
Acknowledgements-The
24.
REDIKER, Lincoln Lab. Quart. Rep., January 15, p. 6 (1961). R. A. LOGAN and M. SCHWARTZ, J. Appl. Pkys. 26,
25.
G.
author
1287 (1955).
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Phj,s.
CHAPIN, C. S. FULLER and G. L. PEARSON,
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STRUTHERS, J.
Electrochem.
105, 588 (1958).
J. SHATTES and H. A. R. ~VEGENER,J. Appl. Phys. 29, 866 (1958). 27. H. J. QUEISSER,J. App[. Phys. 32, 1776 (1961). 28. S. G. KALASHNIKOV and A. K. MEDNIKOV, Fiz. Tver. Tela 2, 2058 (1960); (English translation: Sowiet Phys., So/id State 2, 1847 (1961). 29. \V. C. DASH, J. Appl. Phys. 30, 459 (1959); 31, 736 (1960).
26. W.
1. W. SHOCKLEY and H. J. QUEISSER,J. Appl. 32, 510 (1961).
BEM~KI and J. D.
Sot.