Production and characterization of diodes made in thin p-Se layers on top of n-CdSe

Production and characterization of diodes made in thin p-Se layers on top of n-CdSe

91 J. Electroanal. Chem., 280 (1990) 91-103 Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands Production and characterization of diodes ...

829KB Sizes 2 Downloads 8 Views

91

J. Electroanal. Chem., 280 (1990) 91-103 Elsevier Sequoia S.A., Lausanne - Printed

in The Netherlands

Production and characterization of diodes made in thin p-Se layers on top of n-CdSe Andreas Kampmann, Victor Marcu and Hans-Henning Institur f%r Physikalische (F.R.G.) (Received

21 August

Chemie und Elektrochemie,

1989; in revised form 16 October

Heinrich-Heine

Strehblow * Universiiiit,

D-4000

Diisseldorf

I

1989)

ABSTRACT Se layers were grown on top of single crystals of n-CdSe in view of their possible use in a solid-state solar cell. The layers were produced either by electrodeposition from SeO, in a pH 5 buffer at room temperature (298 K) and at 353 K, or by photocorrosion in a partially stabilizing solution containing various amounts of K,[Fe(CN),] and 1 M KCl. The photoelectrochemical behaviour of the CdSe/Se structures was checked in phthalate buffer (pH 5) with and without the redox species (K,[Fe(CN),], K,[Fe(CN),] and SeO,). The difference in the Se and CdSe light absorption coefficient was used to excite charge carriers in either the Se layer or the CdSe substrate (X = 500 or 700 nm monochromatic light, respectively). The behaviour of the layers deposited at 298 and 353 K differs: the higher temperature induces the formation of the trigonal modification of Se, which has a higher photoactivity than that of the amorphous Se deposited at 298 K. It is concluded that Se electrodeposited at 353 K forms p-n heterojunctions in which both Se and CdSe are active. Both photoanodic and photocathodic currents are observed and the i-V curves show the existence of more than one “flat-band potential”. T’he Se layers formed by decomposition are porous and thus no barrier is present.

INTRODUCTION

CdSe/Se diode structures have been used for rectifiers [I] and photosensitive elements [2] for many years. The relatively simple formation of Se and CdSe layers on various substrates raises the question whether thin film diodes may possibly be used as cheap solar cells. This application has already been discussed previously by various authors ([3,4] and refs. cited therein). The photoelectrochemistry of Se was studied in some detail by Gissler [5]. Frese has studied the behaviour of CdSe in the presence of Se formed by photodecomposition [6]. He explained that all the photocurrent was generated in CdSe, not considering Se as an active junction

l

To whom correspondence

0022-0728/90/$03.50

should be addressed.

0 1990 Elsevier Sequoia

S.A.

component. The production of Se was thought to be responsible for the observation of cathodic photoeffects on CdSe in a Na,SO, solution by Tenne and Giriat [7]. Unfortunately, in these solutions, it is not clear whether the Se layer is formed by decomposition or whether it is deposited from Se*- or the seleno-sulphite [8] which may be present at the potentials where the photocathodic effect is observed. In the present paper, we report on the controlled formation of CdSe/Se junctions, in view of the possible application as low-cost solar cells. For this reason we studied the stability of Se and CdSe layers in various electrolytes [9,10]. The CdSe/Se/electrolyte system is well suited for study because it is easily prepared. We proceeded with the formation of the junctions by using two methods: (1) photodecomposition of single crystals of n-CdSe; and (2) electrodeposition in the dark from SeO, solutions. The electrochemical behaviour of such multi-junction structures (transistor-like) is also of theoretical interest. We had the possibility of injecting charge carriers into each junction by causing the adsorption of light in a defined space region, when different wavelengths are used. CdSe itself has been considered a promising material for solar energy conversion, but it is plagued by the problem of photocorrosion. In electrolytes it decomposes to Cd*+ and Se’. The only solutions which are able to stop this process are polysulphides [ll]. Even in these solutions, various processes occur which diminish the quantum yield: absorption of the light by the solution, changes in the composition of the redox species with time and S/Se exchange on the surface [12-141. We have checked the decomposition of CdSe by reducing its products of photocorrosion electrochemically [15]. A conductive, photoactive top layer of Se could protect the CdSe surface, even when no polysulphide is present in the solution. There have been some reports in the past concerning the photoelectrochemistry of junctions involving two semiconductors and the electrolyte [16-181. They were mostly concerned with the possibility of stabilizing low bandgap semiconductors against photocorrosion, by covering them with a larger bandgap material. TiO, was a favourite cover material and both p- and n-type single crystals have been used as substrates. The behaviour of such structures was discussed in terms of the band model of semiconductors, and it was concluded that in most cases the photoresponse is dominated by the top layer and in general, stabilization of the bottom material could not be obtained because the top layer was porous. EXPERIMENTAL

CdSe single crystals with a conductivity of 5 !J cm were purchased from Cleveland Crystals Co. The orientation of the crystals was perpendicular to the c-axis. Ohmic contact was made with In-Ga alloy (Matthey) and with conductive silver epoxy resin (Elecolit-325). The crystals were mounted on a Ni foil and encapsulated in a glass tube. An active area of 0.25 cm* was defined by insulating epoxy resin (Varian, Torr-seal). Prior to the deposition, the crystals were polished to 1 pm with diamond spray (Struers), etched in a K,Cr,O, (4 g) + cont. HNO, (10

93

ml) + H,O (20 ml) solution for 60 s and immersed in a hot (343 K) Na,S + NaOH + S (1 M each) bath to dissolve any Se formed during etching, followed by a final rinse in phthalate buffer (pH 5) and deionized water. Before deposition of the Se, the surface was further cleaned by reduction in the phthalate buffer at - 1.0 V (vs. SHE). In order to deposit Se layers, lo-* M SeO, dissolved in phthalate buffer was added to the nitrogen-purged electrolyte (phthalate buffer) and the potential was changed from - 0.3 to -0.5 V at 353 K, such that a reduction current of 100 /.LA was present in the dark. The deposition temperature Td= 353 K was chosen such that the trigonal modification of Se was formed, as shown by electrochemical deposition under the same conditions on a Ni substrate [lo]. At room temperature amorphous Se is formed [lo], which has a weaker photoactivity. The width of the deposited Se layers was determined both by the deposition charge and by the reduction of Se to Se’-, at -0.7 V. This value was chosen in order to reduce Se slowly, and thus to avoid any mechanical loss of the unreduced part of the layer. The values obtained by both methods were in good agreement. The photocurrent measurements were performed under potentiostatic conditions in phthalate buffer containing K,[Fe(CN),] and K,[Fe(CN),] (lop3 M each). The electrolyte vessel had a front quartz window for illumination and N, purging was used for stirring. The photoresponse current was measured either by chopping the light and measuring the difference directly at the potentiostat output, or through a lock-in amplifier. As the lock-in technique gives only absolute values at output, the sign of the photocurrent is marked in the figures if necessary. The light of a high-pressure XBO 450 W xenon lamp (Osram) was monochromated by a monochromator (AMKO, type Metrospec). All solutions were prepared from analytical grade (pro analysi) reagents and deionized water (Millipore, Milli Q water purification system), without further purification. All potentials given refer to the standard hydrogen electrode (SHE) and are corrected for liquid junction potentials. Hg/HgO/O.l M KOH (E = 0.14 V) and Hg/Hg,SO,/l M Na,SO, (E = 0.68 V) served as reference electrodes. RESULTS

We deposited Se films on top of CdSe at two temperatures, 298 and 353 K, in order to check the influence of the amorphous Se and the trigonal Se modification on the photoresponse of the electrode. The difference in the two corresponding spectra is obvious (Fig. 1). The amorphous Se films deposited at 298 K behave on top of CdSe as mere light filters, while the crystalline Se films contribute appreciably to the photocurrent in the 400-600 nm region. In addition, the amorphous Se films showed a strong decrease of photocurrent with time. Therefore, for our further investigations we applied deposition of the trigonal modification of selenium.

500

600

700 Xfnm

Fig. 1. Anodic phot~u~~t spectrum (quantum efficiency vs. waveleng~) of CdSefSe with Se deposited at Td = 298 and 353 K (thickness d, = 0.12 pm) in phthalate buffer (pH 5). 1O-3 M K3[Fe(CN),]/K4[Fe(CN),]; E = +O.S V (vs. SHE).

Both anodic and cathodic photocurrents (iPh+ and iPh_) were observed, depending on the applied electrode potential. The spectra of both photocurrents for CdSe with Se films up to 50 nm look like that of n-Cd&. but with highly reduced quantum efficiencies with i,, = ca. 5 X / i,_ 1 (Fig. 2). When the thickness of the Se film is increased, they differ more and more from each other. For a 0.4 pm Se layer (Fig. 3) the cathodic photocurrent spectrum at E = -0.3V looks like the pure Se spectrum (dashed line) [lo]. For negative potentials, besides a stationary photocurrent, large positive phototransients are observed for X > 600 nm. In Fig. 3, the cathodic stationary cont~bution of i, is indicated by a dashed line, while the solid line gives

0.060.05 [email protected]

500

600

700 Xlnm

Fig. 2. Photoanodic and photocathodic spectra of CdSe/Se K~[F~CN)~]~~[F~CN)~]. Phthalate buffer (pH 5).

(dss = 0.04

pm)

in

10e3

M

95 transients

-

1 500

I 600

700

hl nm Fig. 3. Photoanodic and photocathodic spectra of CdSe/Se (d, = 0.4 pm) in 1O-3 M Ks[Fe(CN),]/K.,[Fe(CN),1. Large scale corresponds to E = +OS V. Dashed line indicates stationary i,, in the transient region at ca. 700 nm. Phthalate buffer (pH 5).

the total anodic photocurrent in this range. The positively biased electrode, however, shows a large stationary photoacti~ty in the 700 nm region compared to the 400-600 nm region. For these conditions positive transients are very small relative to the stationary values. These results are replotted in Fig. 4 to give the bandgaps of the active layers of the electrode. The calculated values for direct transitions are in

E=-0.30VtSHE)

Fig. 4. Determination of the bandgaps from the data of the photocathodic spectrum in Fig. 3. The part indicated with transients refers to the CdSe response (see text). The values of the bandgaps correspond to the bulk bandgaps of CdSe and Se, respectively.

v

10

20

I

I

30

40

I

50

I

60

I

I

I

70

80

90

QlmC Fig. 5. Cathodic photocurrent during deposition of Se at 353 K in 10m3 M SeO, versus deposition Illumination with light of wavelength A = 500 nm (10 mC =17 nm). Cd/Se, phthalate buffer T = 353 K. E = -0.3 V.

charge. (pH 5),

good agreement with the bandgaps of the bulk materials: E, = 1.7 eV corresponds to CdSe and E, = 1.82 eV to Se. These data are close to the values in the literature: E CdSe= 1.75 eV and Es, = 1.95 eV as reviewed in refs. 19 and 20. Electrodeposited Se layers on Ni show almost the same bandgap, Es, = 1.87 eV [lo]. In Fig. 5 the cathodic photocurrent is presented during Se deposition at 353 K versus the deposition charge. In accordance with Gartner’s equation [21], i,, increases linearly with the layer thickness until a final saturation is reached.

600

700 Xlnm

Fig. 6. Photocathodic K4[Fe(CN),]/Ks[Fe(CN),1 (vs. SHE).

spectrum of CdSe/Se redox couple (low3

(d, = 0.4 pm) with (curve II) and without the M) (curve 1, only phthalate buffer, pH 5). E = -0.3 V

97

The influence of the redox couple on the photoresponse is shown in Fig. 6. For the negatively biased electrode, a large increase of the photocurrent occurs in the 400-600 nm region with increasing concentration of K,[Fe(CN),], owing to higher reduction rates by electrons generated in the outer Se layer which is in direct contact with the electrolyte. The quantum efficiency for sufficiently positive potentials does not increase upon addition of K,[Fe(CN),]; only the photoanodic transients become larger when K,[Fe(CN),] is present.

Flat-band potential According to Gartner’s theory [21], i& vs. E curves give as the abscissa the flat-band potential of a semiconductor-metal or a semiconductor-electrolyte junction. In our case, both anodic and cathodic photocurrents are observed with respect to an n-type semiconductor/p-type semiconductor/electrolyte double junction. If Gartner’s theory is allowed to be extended to such a structure, one should expect at least two values for E,,. The ii,-E plots indeed show more than one flat-band potential (Fig. 7). These E,, values are strongly dependent on the thickness of the Se film and on the applied wavelength. There are two limiting potentials for this

(294) 4\

-B .-

0.

-04 -0L3

-0.3

-02

EISHEII V

-0.1 -0.13

Fig. 7. Determination of the “flat-band” potential. Because of the double junction structure, no single value is obtained from the linear plot. For the significance of the results see Discussion. (b) represents the continuation of (a) at a different scale. CdSe/Se (0.2 pm). phthalate buffer, pH 5, lo-’ M K,[Fe(CN),]/K4[Fe(CN),1, X = 500 nm.

500nm I

-02

-01

0 01 ElSHE)/V

02

Fig. 8. Photocurrent-potential curves as a function of the illumination K4[Fe(CN),]/Ks[Fe(CN),1 solution. The minimum of the curves corresponds the photocurrent. CdSe/Se (0.4 pm), phthalate buffer (pH 5).

wavelength in 10V3 M to the change in sign of

evaluation. At the most negative value of E,,= -0.43V, flat bands are accepted for CdSe. Any applied potential that is more negative will result in a cathodic photocurrent. The most positive flat-band potential at E, = +0.28V corresponds to the flat-band situation at the Se/electrolyte interface. Within this potential range the sign of the photocurrent depends on the absorption depth of the light. For a 0.4 pm Se film, at E = 0 V and h = 500 nm monochromatic light, a cathodic photocurrent is observed. If the absorption depth of the radiation is increased by choosing a longer wavelength (h > 600 nm), the photocurrent becomes anodic (Fig. 8). Apparently, light with X = 500 nm is absorbed in the Se/electrolyte space-charge region and contributes to a cathodic current, while the light which is mainly absorbed in the CdSe/Se space-charge region contributes to an anodic photocurrent. Light of X z 700 nm is absorbed mainly within CdSe. Chopped light of such wavelengths causes large anodic transients in the negative potential range. They are superimposed on the small stationary cathodic current and dominate i,, completely. Therefore, the curve for h = 700 nm shows no change of sign for i,,. The onset of the cathodic photocurrent for the 0.2 pm Se film (Fig. 7) occurs at a more negative potential (E = - 0.4 V) compared to the cathodic onset of the 0.4 pm Se film (E = + 0.1 V) shown in Fig. 8 (for X = 500 nm). Thus, for a given wavelength, the onset potential of the anodic and cathodic photocurrents (i.e. the potential at which

99

the photocurrent changes sign) increases with increasing thickness. Or, for a given thickness of the Se film, the onset potential of the photocurrent increases with decreasing wavelength. Another technique that we have applied to determine flat-band potentials is capacitance measurements of these films. As the donor density in CdSe is about two orders of magnitude lower than the acceptor density in electrodeposited Se, the Schottky-Mott plots will give as the abscissa only the E,, value for the CdSe. These values are in excellent agreement with the more negative flat-band potentials obtained by the i&,/E plots, which correspond to flat-band conditions within CdSe.

We also measured the photovoltages of these junctions. The photovoltage vs. wavelength plots (Fig. 9) look like those of the photocurrent. The open-circuit 1

-v,,I v

1

500

600

700 Xlnm

Fig. 9. Dependence of the open-circuit photovoltage V, on the wavelength. The Se film thickness was 0.4 pm on top of CdSe. Different redox species were used for the three curves. The V, values are not corrected to the spectrum of the lamp. (0) Phthalate buffer (pH 5); (A) 1 X10e3 M K,[Fe(CN),J; (W) 2 x lo- 3 M K,[Fe(CN),].

100

voltage in the 400-600 nm region is about ten times (corrected for light intensity) lower than that in the 700 nm region. The largest value obtained was -0.5 V for 700 nm by adding the K3[Fe(CN),]/K4[Fe(CN),1 redox couple (0.002 M). Without the redox couple we got -0.1 V for the same film and wavelength. In contrast to the photocurrent, which increased upon adding the redox couple only in the ~-6~ nm region, the photovoltage increased in the entire 4~-8~ nm region. DISCUSSION

As in previous studies of multiple layers of semiconductors, we will use the band theory of semiconductors to explain the present results. In Fig. 10 a qualitative diagram for the band shapes of the CdSe/Se/eiectrolyte junction is presented. We may change the band bending according to Figs. lOa-10c with the potential applied to the CdSe/Se electrode. Owing to the different absorption coefficients of CdSe and Se [22,23], light is adsorbed preferentially in the Se top layer or in the CdSe layer, depending on the wavelength of the incident light and on the thickness of the Se layer. A Se layer of 200 run thickness will absorb 90% of the radiation when light of wavelength 500 nm is used, while light of 700 nm will be 90% absorbed in CdSe. Thus, by applying anodic or cathodic polarization to the electrode and by illuminating with light of two different wavelengths, we obtain anodic or cathodic photocurrents depending on the origin of the photocarriers formed. A Se layer on top of C&e reduces the quantum efficiency of the photocurrent drastically. When the Se top layer is thin, most of the light is absorbed in the CdSe and the charge carriers reach the surface by migration, diffusion or tunnelling. The Se layer is too thin to contribute appreciably to the photocurrent by the formation of charge carriers. Both anodic and cathodic photocurrents are observed even in this case, which is an indication of the presence of more than one junction, since no such behaviour is seen on a clean CdSe surface. Even a relatively thick (1 pm) Se layer

CdSe EN -1

I

Se

electrolyte

Eredox

a

Eredox

E redox

b

C

Fig. 10. Schematic energy diagram of the bands as a function of the applied potentid. (a) E = - 0.43 V; (b) E = 0 V; (c) E = +0.28 V. The position of the Se energy bands is fixed with respect to the solution redox potential.

101

formed by photocorrosion does not show photocathodic currents. Se layers formed by photodecomposition are porous [15], thus no additional surface barrier is present. Upon increasing the thickness of the Se film, the quantum efficiency is increased to about 0.05 in the 400-600 nm region and to about 0.5 in the 700 nm region. The presence of Se on CdSe will induce surface states which will act as effective recombination centres. With increasing thickness of the Se overlayer, the charge carriers are separated effectively in the space-charge region of the p-n junction and the positive holes may be transported sufficiently far from the interface, so that the recombination rate is reduced. Thus, the quantum efficiency is regained partially with increasing Se thickness. The anodic and cathodic spectra become more and more different from each other and the cathodic spectrum is that of a pure Se film. At negative potentials (E = - 0.3 V), a vanishingly small stationary current is found for A = 700 nm (Fig. 3). The addition of a redox couple to the solution causes an increasing anodic and cathodic photocurrent only if the charge carriers are generated in the Se layer which is in direct contact with the solution. Consequently, the redox couple influences the sign of the total photocurrent by changing the Se contribution. Charge carriers generated in the CdSe layer, which have to pass the CdSe/Se interface to reach the electrolyte, always produce anodic transients superimposed on a stationary anodic or cathodic photocurrent. The transients should be related to inter-band states at the CdSe/Se junction. When the light is switched on, these states will be charged, leading to an anodic photocurrent peak. In the stationary situation, recombination of the photogenerated charge carriers reduces i,,. When the light is switched off, the opposite processes are effective. The open-circuit photovoltage is increased in the whole spectrum upon the addition of the redox couple because charge carriers do not have to cross the interface. No, or only very small, transients compared to the stationary current are observed when light of X < 500 nm is absorbed in the Se overlayer, because no losses of photogenerated carriers by recombination occur at the inter-band states of the distant CdSe/Se interface. The interpretation of the more negative flat-band potential at -0.43 V refers to the situation in Fig. 10a: the photocurrent is generated in the reversely biased Se top layer. Any change in the potential to more negative values will increase the band bending of the Se/electrolyte junction and therefore the cathodic photocurrent. The most positive flat-band potential should correspond to the situation shown in Fig. 10~: the CdSe is responsible for most of the photoactivity. Any increase of the electrode potential will increase the upwards band bending of the CdSe/Se junction and the corresponding anodic photocurrents. At intermediate potentials (Fig. lob), both anodic and cathodic photocurrents are observed. The sign of the photocurrent depends on the wavelength used and on the thickness of the Se layer (Figs. 7 and 8). The sign of the open-circuit voltage is also dependent on the depth where most of the light is absorbed. When the KJFe(CN),]/KJFe(CN)J redox couple is used,

102

only negative photovoltages are abserved. As the redox couple has an equilibrium potential of +0.4 V, the situation is similar to Fig. lOc, corresponding to the application of a positive potential. Without the redox couple, the dark potential of the phthalate buffer is +O.l V (the band bending is now similar to Fig. lob); thus, for the very thick Se layers (400 nm) we obtain a positive photovoltage (0.05 V) if light of 500 nm wavelength is used. The largest negative photovoltage of 0.48 V was obtained for light of 700 nm wavelength with a concentration of 0.002 M K,[Fe(CN),]. Theoretically, a maximum open-circuit voltage of 0.71 V should be obtained, calculated from the difference of the two flat-band potentials of CdSe and Se (-0.43 and +0.28 V, respectively). CONCLUSIONS

Thin-layer junctions were prepared by the electrodeposition of Se layers on top of single-crystal n-CdSe. The results show that a diode structure is formed between the n-CdSe and the p-Se layers and that a second one exists at the p-Se/solution interface. Each of the layers is photoactive. The spectral behaviour of the diodes depends on the width of the Se top layer. The photoresponse of the pure CdSe is reduced, as the photoactivity of Se is lower than that of a CdSe crystal. Photocurrents originating from light absorbed in the CdSe layer show large superimposed transients, which indicates that the CdSe/Se interface is disturbed by defects which capture the charge carriers passing the interface. The best junction with respect to the photoresponse was obtained by photoetching the CdSe crystal prior to the electrodeposition. The quantum efficiency in the 400-600 nm region was as high as 0.1, compared to 0.05 for cells without the photoetching process. One particular feature of the cell may be added: once a Se layer is present, even without a redox couple in the solution, no further decomposition of the CdSe is seen at positive potentials (i.e. no reduction peaks for Cd2+ and Se0 are observed). Whether the photoreaction is SeO, formation or water splitting is still to be checked. ACKNOWLEDGEMENTS

The financial support of this work by the Ministerium fiir Wissenschaft und Forschung des Landes Nordrhein Westfalen (project IV B 4-10304787) is gratefully acknowledged. One of us (V. Marcu) would like to thank the Minerva GmbH, Mlinchen for a postdoctoral fellowship. REFERENCES 1 S. Poganski, Z. Elektrochem., 56 (1952) 193. 2 J. Stuke in R.A. Zingaro and W.C. Cooper (Eds.), Selenium, Van Nostrand 1974, Ch. 5, pp. 270-286. 3 M.T. Gutierrez and P. Salvador, Sol. Energy Mater., I5 (1987) 99. 4 S. Licht, Nature (London), 330 (1987) 148. 5 W. Gissler, J. Electrochem. Sot., 127 (1980) 1713.

Reinhold,

New York,

103

6 7 8 9 10 11 12 13 14 15 16 17 18 19

20 21 22 23

K.W. Frese, Jr., 3. Electrochem. Sot., 130 (1983) 28. R. Tenne and W. Giriat, J. Electroanal. Chem., 186 (1985) 127. M. Skyllas Kazacos and B. Miller, J. Electrochem. Sot., 127 (1980) 2378. V. Marcu and H.-H. Strehblow, J. Electrochem. Sot., submitted. A. Kampmann and H.-H. Strehblow, to be published. G. Hodes, J. Manassen and D. Cahen, Nature (London), 261 (1976) 403. R.N. Noufi, P.A. Kohl, J.W. Rogers, Jr., J.M. White and A.J. Bard, J. Electrochem. Sot., 126 (1979) 949. A. Heller, G.P. Schwartz, R.G. Vadimsky, S. Menezes and B. Miller, J. Electrochem. Sot., 12.5 (1978) 1156. R.P. Silberstein and M. Tomkiewicz, J. Appt. Phys., 54 (1983) 5428. V Marcu, R. Tenne and I. Rubinstein, J. Electrochem. Sot., 133 (1986) 1143. C.D. Jaeger, F.-R.F. Fan and A.J. Bard, J. Am. Chem. Sot., 102 (1980) 2592. M. Tomkiewicz and J. Woodall, J. Electrochem. Sot., 124 (1979) 1436. P.A. Kohl, S.N. Frank and A.J. Bard, J. Electrochem. Sot., 124 (1977) 225. For CdSe see K.-H. Hellweg (Editor in Chief), Landolt-Bornstein, Numerical Data and Functional Relationships in Science and Technology, New Series, Springer Verlag, Berlin, 1982, Group III, Vol. 17b. For Se see ref. 19, Vols. 17d (1984) and 17e (1983). W.W. G&tner, Phys. Rev., 116 (1959) 84. W. Henrion, Phys. Status Solidi, 12 (1965) K113. J.L. Hartke and P.J. Regensburger, Phys. Rev. A, 139 (1965) 970, as cited in ref. 19.