2p Photoabsorption in amorphous, trigonal and monoclinic selenium

Journal of Non-Crystalline Solids 27 (1978) 119-125 © North-Holland Publishing Company

2p PHOTOABSORPTION IN AMORPHOUS, TRIGONAL AND MONOCLINIC SELENIUM E. BELIN, C. SENEMAUD and C. BONNELLE Laboratoire de Chimte Physique *, Universitd Paris V1, 11 rue Pierre et Marie Curie, 75005 Paris, France

Recewed 16 December 1976 The 2p photoabsorption spectra of amorphous and polycrystalline trigonal and c~-monoclinic selenium have been studied. Our experimental results, accounting for the transition probabilities and inner level broadening, are in qualitative agreement with Kramer's pseudo-potential formalism calculations of the density of unoccupied states. The amorphous selenium spectrum seems intermediate between the two crystalline form spectra and we deduce that both trigonal chains and monoclinic rings are randomly distributed m the amorphous phase.

I. Introduction Variations in the optical and electronic properties of solid selenium have been observed between its different allotropes. There are two crystalline forms, monoclinic (ix or/3) and trigonal, and one amorphous form. They are characterized by different structural arrangement o f the atoms, in particular by various bond lengths and angles. Eight-membered, puckered rings, Se8, constitute the basic structural unit of the a-monoclinic phase, while in the ~3-monoclinic, one bond of the ring is broken and an eight-membered chain is formed [1]. The trigonal phase is composed by infinite helical chains whose axes are parallel to the c-axis, arranged on a twodimensional hexagonal lattice. It is generally admitted that both chains and Sea rings are randomly distributed in the amorphous phase of selenium. Lattice parameters for the different allotropes are summarized in a recent paper [2]. Band structure calculations have been performed recently for trigonal and amorphous selenium [ 3 - 5 ] and compared to experimental results obtained by UV photoemission spectroscopy (LIPS) [6]. These transitions involve both valence and conduction bands. The same holds for the optical spectra. On the contrary, with a higher photon energy, it is possible by soft X-ray spectroscopy (SXS) separately to study the valence and conduction bands by analysing emission or absorption transitions involving an inner level. The relative position of the valence and conduction * Associ6 au CNRS. 119

120

E Behn et al. / 2p photoabsorptton tn selenium

bands can be obtained directly by this method; its resolving power is limited by the lifetime of the inner level which corresponds in most practical cases to an energy width of 0.5-1.0 eV. Compared to this one-electron effect, the perturbation due to the many-body interactions are generally small and can be neglected [7], particularly for the semiconductors. The soft X-ray spectra depend also on the transition probabilities and, as a consequence, data on the different characters of the outer distributions can be obtained by choosing a suitable inner level symmetry. Moreover, the charge effects which depend on the electronic properties of the sample may be large in UPS, but they do not intervene in SXS; as for the surface effects they are much more critical in UPS than m SXS. We have undertaken a comparative study of the different allotropic forms of selenium by this method and in this paper we present the results for the Ln. m absorption spectra. They correspond to the transition of a 2p electron towards the first empty states of the conduction band and reflect principally the s or d character of the conduction band. For selenium, the analysis of the M spectra would be less convenient as the 3pal2 level is about twice as broad as the 2p3/2 [8].

2. Experimental The Se L spectra, situated near 8 A, were studied with a 250 mm radius cylindrically bent crystal spectrograph. A mica crystal (reflecting system 002) was used. The photoabsorption coefficient was measured as described previously [7]. The fourth-order Pd La [9] and second-order A1 Kal, 2 [10] lines were chosen as reference lines for the absolute wavelength measurements. The selenium layers, about 6000 A thick, were deposited on a plastic (makrofol 2/a) or an aluminium foil (0.5 tz). The amorphous sample was prepared by thermal evaporation of powdered trigonal Se (99.99%), the layer exhibiting a red transparency. The trigonal screen was obtained by heating an amorphous screen to 110°C in air for a few hours. The a-monoclinic screen was prepared by deposition of powdered a-monoclinic selenium (99.999%) of 1000 A mean grain size, mixed with alcohol and sprayed on to the foil. We did not try to prepare the/3-monoclinic form which is rather unstable. The crystalline form of the samples was checked by X-ray diffraction before use.

3. Results

The photoabsorption curves of trigonal, a-monoclinic and amorphous selenium, near the absorption LIU edge are plotted in fig. 1. In all cases the photoabsorption coefficient presents a first maximum (A) followed by an abrupt variation (B), conventionaUy called the absorption edge or discontinuity. Line A has a total width of about 4 eV, towards high energies there is a slight shoulder, and the inflexion point

E Behn et al. / 2p photoabsorptton in selemum

121

b A

B

triganaL

~ '~~ /, / ~ '1- , ~

amorphous

mONOCNlICI

leV Ftg. 1. Experimental photoabsorption curves of trigonal, amorphous and c~-monoclinic selenium compared with theoretical density of states curves (Kramer et al.) and with convolution products of theoretical curves with lorentzlan distribution of the LII I level (dashed lines). o f the d i s c o n t i n u i t y is situated at a b o u t 5 eV from the m a x i u m u m o f A. In the trigonal selenium spectrum, this d i s c o n t i n u i t y has two slightly different slopes, 1 and 2. On the a m o r p h o u s spectrum a shoulder s appears at the b o t t o m o f the disc o n t i n u i t y whose position coincides with the d i s c o n t i n u i t y (2) o f the trigonal Table 1 Wavelengths in Xu. Present work

Sandstrom

KLII

8358.8 -+ 1.9 Xu

8355.7 Xu

hLllI

trigonal (1) (2) c~-monoclinic amorphous

8597.9 8593.9 8592.9 8593.9

+- 1,0 Xu -+ 1,0 Xu ± 1,0 Xu ± 1,0 Xu

8593.8 Xu

122

E Belin et al. / 2p photoabsorptton in selenium

Table 2 Energy positions m eV

maximum A shoulder minimum

Trlgonal

Amorphous

a-monochnic

0 l4 3.2 (1) 4.3

0 35 1.7 30 (s) 3.6

03 1.3 3.8

4.95 7.0 8.1

5.1 6.0 8.2

edge. first maximum second maximum

(2) 4.95 6.1 7.7

phase. Beyond the edge, the positions of the absorption structures differ from one allotrope to another. The Lu absorption spectra differ much less, and we have only observed the discontinuity. The wavelengths of the LII and LIII discontinuities of selenium (~LII and ~LIII) were measured by Sandstr/Sm [l 1] (table 1), but the crystalline form of the sample used was not specified. For each allotrope we have measured ~LI1 and ~LIII. The corresponding values are given in table 1. No observable differences have been found for ~'Lu for the three allotropes and our value is rather higher than Sandstrom's. For ~'LuI' the value given by Sandstr6m seems in good agreement with our values for amorphous and trigonal (2) phases, within the experimental precision. In table 2 we compare for the three allotropes, the energy positons of the different structures of the Lm spectra. The distances are referred to the maximum (A) of the trigonal curve. Slight differences exist between the three allotropes.

4. Discussion We shall discuss these results by comparison with the theoretical density of states calculations of Kramer [5] made in the pseudo-potential formalism. From these calculations the conduction states of trigonal and amorphous selenium consist of a first band with a p character, about 4 eV wide, separated from an s-character second conduction band by a 1.5 eV gap. To obtain the density of s-character states from the Lm photoabsorption curve, it is necessary to take into account the resolving power of the experimental curve which is mainly determined by the inner level distribution. To our knowledge, the width of the Lm level of selenium has not been measured. Values have only been given for neighbouring elements [12]. From these data, we have deduced by inter-

E. Belin et al. / 2 p photoabsorption tn selenium

123

polation an approximate width of 1.0 eV for Se Lni. The deconvolution of the experimental curve is rather difficult and this mathematical treatment can introduce some deformations of the density of states distribution. It seemed more convenient to compare, as is usually done, the experimental curve with the curve calculated by convolution of the theoretical density of states with a lorentzian curve having a total width at half maximum of 1.0 eV. These calculated convolution products are plotted in fig. 1 (dashed lines) and compared with Kramer's theoretical density of states curves. The adjustment in energy with the experimental curves is made by taking into account the total width of line A. 4.1. Trigonal selenium

The sharp structures of the first theoretical band A are smoothed out by the convolution, there remains only a slight asymmetry on the high-energy side which seems to correspond to the shoulder of the experimental curve. Owing to this asymmetry, the maximum of the convoluted and experimental curves do not exactly coincide. The calculated curve has a broadened maximum and a shoulder which correspond to the two sharp features (b) and (c), respectively, which appear in the second part B of the theoretical band. The position of (b) is in agreement with part 1 of the experimental curve. Part 2 may be considered to correspond to the shoulder on the convoluted curve. The differences between the shapes of the curves in this energy range can be interpreted by the fact that the calculation covers a range of only 8 eV from the bottom of the conduction band. The relative intensity of A and B found experimentally indicates that the first band has principally a p character with a slight s hybridization, while the second has an s character. 4.2. A m o r p h o u s selenium

The density of states calculated for the amorphous form is roughly the same as for the trigonal form. The width of the first conduction band A and the relative positions of A and B are approximately the same, but the sharp structures are smeared out in the amorphous form. On the calculated curve, the first band (A) is nearly symmetrical, which is in agreement with tile experimental result. The limit of the second band corresponds to the shoulder (s) situated at the bottom of the discontinuity. This suggests that p states could still be present in this region, while the limit of the s states should correspond to the position of the edge of the experimental curve. The disappearance of the strong peak (b) is confirmed by the fact that at its energy position, the variation of the photoabsorption coefficient is small for amorphous selenium. 4.3. a-monoclinic selenium

There is no calculation of the density of unoccupied states for this phase. From our experiments, the position of the first conduction band is nearly the same as in

124

E. Behn et a L / 2p photoabsorptton tn selemum

the trigonal phase. The limit of the second conduction band presents no shoulder and the discontinuity has a constant slope. It is slightly shifted towards high energy relative to those of the trigonal (2) and of the amorphous curves. (The shift is at the lmalt of experimental precision.) As in the amorphous case, the curve has a slow variation of the photoabsorptlon coefficient at the position of the peak b, and there is a better agreement for this part of the curve of the c~-monoclinic phase with the amorphous than with the trigonal curve. Beyond the discontinuity, the structures are more marked than in the amorphous phase and even in the trigonal phase. The agreement observed between the shape of the first conduction band in the three allotropic forms suggests that this part of the density of unoccupied states depends principally on the short-range order. The first band is separated from a second band by a gap whose width is approximately the same for the three allotropes. The shape of the limit of the second band vanes from one allotrope to another. The total energy range of the limit observed for the amorphous form overlaps the whole energy range covered by trigonal and c~-monoclinic limits: this result confirms that both rings and chains are present in the amorphous phase. The photoabsorption structures beyond the discontinuity are, as already known [7], different for the three forms; they are mainly determined by long-range order effects.

5. Conclusion Our results are in agreement with the shape of the conduction band found theoretically for trigonal and amorphous selenium. They confirm the existence of a first conduction band with a predominant p character, slightly sp hybridized and distinctly separated from a second conduction band having principally an s character. For the amorphous form, our results suggest the presence of p states at the bottom of the second conduction band. Although the sharp peaks of the trigonal theoretical curve are smoothed and overlap when folded with the Ltn distribution, a clear difference is observed between the trigonal and amorphous experimental curves at the position of the sharp peak b. At this energy, no difference is seen between the ct-monoclinic and amorphous Se. Thus peak b is characteristic of the periodic chain arrangement. In order to discuss the structures beyond b, it will be necessary to obtain calculations over a more extended range of energy. Complementary data on the valence band of each allotropic form of selenium, and also on the band gap, can be obtained from their L emission spectra and by comparison with the L photoabsorption. But phase transformations of the samples may be induced by electron bombardment [13] so that observation of the spectra by secondary excitation must be carried out. This study is in progress.

E Belin et al / 2 p photoabsorption in selenium

125

References [ 1] [2] [3] [41 [51 [6] [7] [8]

[9] [10] [11] [12] [13]

R.B Burb.'ink, Acta Cryst. 5 (1952) 236. R.M. Martin, G. Lucovsky and K. Helliwell, Phys. Rev. B13 (1976) 1383. I. Chen, Phys. Rev. B7 (1973) 3672. R. Sandrock, Phys. Rev. 169 (1968) 642. L D. Laude, B. lqtton, B. Kramer and K. Maschke, Phys. Rev. Letters 27 (1971) 1053. B Kramer, K. Maschke and L D. Laude, Phys. Rev. B8 (1973) 5781. L.D. Laude, B. Kramer and K. Maschke, Phys. Rev. B8 (1973) 5794. C. Senemaud, M.T. Costa Lima, J. Phys. Chem. Solids 37 (1976) 83. J. Riga, private communication, to the published. J A. Bearden, X-ray Wavelengths, (US Atomic Energy Commission, Dwision of Technical Information Extension, Oak Ridge Tennessee, 1964). C. Senemaud, C.R. Acad, Sci. Pads 265 (1967) 403. A Sandstrom, Nova Acta Reg. Soc. Sci. Upsal. 9 (11) (1935). K.D. Sevier, Low Energy Electron Spectrometry (Wiley-Interscience, New York, 1972). E. Belm, Th~se de Doctorat d'Etat, Paris 1974. E Belin, C. Bonnelle and D Delafosse, J. Appl. Cryst. 4 (1971) 383.