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Are odd-membered rings responsible for differences between the valence bands of crystalline and amorphous silicon?
Journal of Non-Crystalline Solids 77 & 78 (1985) 57-58 North-Holland, Amsterdam
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ARE ODD-MEMBERED RINGS RESPONSIBLE FOR DIFFERENCES BETWEEN THE VALENCE BANDS OF CRYSTALLINE AND AMORPHOUS SILICON? T.M. HAYESand J.W. ALLEN Xerox Palo Alto Research Center, Palo Alto, California 94304, USA J.L. BEEBY Department of Physics, University of Leicester, Leicester LE1 7RH, UK S.-J. OH Department of Physics, Seoul National University, Seou1151, Korea Our understanding of amorphous silicon (a-Si) rests on knowledge of the structural differences between crystalline (c-) and a-Si, and of the relationship between these and the electronic properties.
The important structural differences entail correlations involving
more than three atoms, the simplest of which are the dihedral.angle distribution and the relative populations of short N-bond "rings" where N differs from the crystalline value of 6. It is widely agreed that there must be a broad, if not yet precisely quantified, distribution of dihedral angles, but the a priori importance of five- and seven-member rings is much less certain because they are not required in generating a continuous random network. The effects of ring statistics in the radial distribution function are very subtle, so that the only direct evidence for odd-membered rings comes from differences between the x+ray photoemission (xPS) valence-band spectra of c- and a-Si measured by Ley et al. 1 We find the conclusions 1-4 drawn from these spectra to be wrong. The density of valence-band states of c-Si has peaks at approximately - 9.5, - 6.8, and - 2 . 5 eV from the top of the valence band, which we will label A, B, and C, respectively. The differences between the c- and a-Si spectra of Ley et al. were characterized 1,2 by saying that peaks A and B in the crystal have merged to form a single broad feature in the amorphous sample.
This characterization led to an explanation for the differences by
analogy with differences in the calculated densities of valence-band states for two crystalline forms of silicon, diamond cubic and ST-12, where it was believed that the crucial differentiating feature of the ST.12 atomic structure is the occurrence of odd-membered rings. 3 Subsequent theoretical studies4 concluded that no structural element other than odd-membered rings is likely to add spectral weight between peaks A and B. Thus the reported observation of such added weight by Ley et al. 1 was taken to be direct evidence for the existence of odd-membered rings in a.Si. We have obtained new xPs data which show that those differences previously attributed to odd-membered rings do not actually occur. Our c-Si spectrum differs from that of Ley et 0022-3093/85/$03.30 © Elsevier Science Publishers B.V. (North-HoUand Physics Publishing Division)
T.M. Hayes et aL/ Odd-membered rings
58
al. 1 in that the height of peak B is significantly smaller and the height of peak C is greater. Recent oxidation experiments show that both differences are due to oxygen contamination of the c-Si sample of Ref. 1, which was cleaved out of vacuum. The oxygen-induced shifts in spectral weight distorted profoundly the original comparison with the a-Si spectrum. If one compares instead our spectrum of un-oxidized c-Si with that of a-Si:H, the principal difference is clearly that weight is shifted from peaks B and C in the crystal to fill the valley between them in the a-Si spectrum.
Our new xPs data on c- and a-Ge show similar
behavior. Odd-membered rings are not uniquely able to account for these shifts of spectral weight. We explain the differences between the xPs valence-band spectra of c- and a-Si using a new theoretical technique5 which uniquely enables isolation of the effects of specific structural elements on the density of electronic states n(E). The atomic arrangements are modeled as ideal tetrahedra joined together as specified by a distribution of dihedral angles, which is taken as (a) uniform for a.Si and (b) discrete values for c-Si.
n(E) is
calculated for s-wave scattering and mapped onto the lower half of the s-p valence band of silicon in analogy with the transformation of Thorpe and Weaire. 6 The principal effect of the dihedral-angle disorder incorporated in case (a) is to build a peak at - 5 eV at the expense of peaks at - 6 . 5 and -2.5 eV in case (b). These differences correspond quite closely with the observed differences between our xPS spectra. The xPs valence-band spectra of c-Si and a-Si:H differ principally in that intensity in peaks B and C for the crystal is reduced in the amorphous sample while the intensity between them is increased. A similar shift in weight is seen to result in the theoretical density of valence-band states from dihedral-angle disorder. While this does not preclude the existence of odd-membered rings in the amorphous sample, we point out that there are no longer any properties of. a-Si which provide direct evidence for the existence of such rings. We are indebted to C.C. Tsai for preparing our a.Si:H sample. REFERENCES 1) L. Ley, S. Kowalczyk, R. Pollak, and D.A. Shirley, Phys. Rev. Lett. 29, 1088 (1972). 2) L. Ley, Photoemission and optical properties, in: The Physics of Hydrogenated Amorphous Silicon II, eds. J.D. Joannopoulos and G. Lucovsky (Springer-Verlag, Berlin, 1984) pp. 61-168.
3) J.D. Joannopoulos and M.L. Cohen, Phys. Rev. B 7, 2644 (1973). 4) For a review, see J.D. Joannopoulos and M.L. Cohen, Theory of short-range order and disorder in tetrahedrally bonded semiconductors, in: Solid State Physics, Vol. 31, eds. H. Ehrenreich, F. Seitz, and D. Turnbull (Academic Press, New York, 1976) pp. 71-148.
5) J.L. Beeby and T.M. Hayes (to be published); T.M. Hayes and J.L Beeby (in this volume). 6) M.F. Thorpe and D. Weaire, Phys. Rev. B 4, 3518 (1971 ).
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ARE ODD-MEMBERED RINGS RESPONSIBLE FOR DIFFERENCES BETWEEN THE VALENCE BANDS OF CRYSTALLINE AND AMORPHOUS SILICON? T.M. HAYESand J.W. ALLEN Xerox Palo Alto Research Center, Palo Alto, California 94304, USA J.L. BEEBY Department of Physics, University of Leicester, Leicester LE1 7RH, UK S.-J. OH Department of Physics, Seoul National University, Seou1151, Korea Our understanding of amorphous silicon (a-Si) rests on knowledge of the structural differences between crystalline (c-) and a-Si, and of the relationship between these and the electronic properties.
The important structural differences entail correlations involving
more than three atoms, the simplest of which are the dihedral.angle distribution and the relative populations of short N-bond "rings" where N differs from the crystalline value of 6. It is widely agreed that there must be a broad, if not yet precisely quantified, distribution of dihedral angles, but the a priori importance of five- and seven-member rings is much less certain because they are not required in generating a continuous random network. The effects of ring statistics in the radial distribution function are very subtle, so that the only direct evidence for odd-membered rings comes from differences between the x+ray photoemission (xPS) valence-band spectra of c- and a-Si measured by Ley et al. 1 We find the conclusions 1-4 drawn from these spectra to be wrong. The density of valence-band states of c-Si has peaks at approximately - 9.5, - 6.8, and - 2 . 5 eV from the top of the valence band, which we will label A, B, and C, respectively. The differences between the c- and a-Si spectra of Ley et al. were characterized 1,2 by saying that peaks A and B in the crystal have merged to form a single broad feature in the amorphous sample.
This characterization led to an explanation for the differences by
analogy with differences in the calculated densities of valence-band states for two crystalline forms of silicon, diamond cubic and ST-12, where it was believed that the crucial differentiating feature of the ST.12 atomic structure is the occurrence of odd-membered rings. 3 Subsequent theoretical studies4 concluded that no structural element other than odd-membered rings is likely to add spectral weight between peaks A and B. Thus the reported observation of such added weight by Ley et al. 1 was taken to be direct evidence for the existence of odd-membered rings in a.Si. We have obtained new xPs data which show that those differences previously attributed to odd-membered rings do not actually occur. Our c-Si spectrum differs from that of Ley et 0022-3093/85/$03.30 © Elsevier Science Publishers B.V. (North-HoUand Physics Publishing Division)
T.M. Hayes et aL/ Odd-membered rings
58
al. 1 in that the height of peak B is significantly smaller and the height of peak C is greater. Recent oxidation experiments show that both differences are due to oxygen contamination of the c-Si sample of Ref. 1, which was cleaved out of vacuum. The oxygen-induced shifts in spectral weight distorted profoundly the original comparison with the a-Si spectrum. If one compares instead our spectrum of un-oxidized c-Si with that of a-Si:H, the principal difference is clearly that weight is shifted from peaks B and C in the crystal to fill the valley between them in the a-Si spectrum.
Our new xPs data on c- and a-Ge show similar
behavior. Odd-membered rings are not uniquely able to account for these shifts of spectral weight. We explain the differences between the xPs valence-band spectra of c- and a-Si using a new theoretical technique5 which uniquely enables isolation of the effects of specific structural elements on the density of electronic states n(E). The atomic arrangements are modeled as ideal tetrahedra joined together as specified by a distribution of dihedral angles, which is taken as (a) uniform for a.Si and (b) discrete values for c-Si.
n(E) is
calculated for s-wave scattering and mapped onto the lower half of the s-p valence band of silicon in analogy with the transformation of Thorpe and Weaire. 6 The principal effect of the dihedral-angle disorder incorporated in case (a) is to build a peak at - 5 eV at the expense of peaks at - 6 . 5 and -2.5 eV in case (b). These differences correspond quite closely with the observed differences between our xPS spectra. The xPs valence-band spectra of c-Si and a-Si:H differ principally in that intensity in peaks B and C for the crystal is reduced in the amorphous sample while the intensity between them is increased. A similar shift in weight is seen to result in the theoretical density of valence-band states from dihedral-angle disorder. While this does not preclude the existence of odd-membered rings in the amorphous sample, we point out that there are no longer any properties of. a-Si which provide direct evidence for the existence of such rings. We are indebted to C.C. Tsai for preparing our a.Si:H sample. REFERENCES 1) L. Ley, S. Kowalczyk, R. Pollak, and D.A. Shirley, Phys. Rev. Lett. 29, 1088 (1972). 2) L. Ley, Photoemission and optical properties, in: The Physics of Hydrogenated Amorphous Silicon II, eds. J.D. Joannopoulos and G. Lucovsky (Springer-Verlag, Berlin, 1984) pp. 61-168.
3) J.D. Joannopoulos and M.L. Cohen, Phys. Rev. B 7, 2644 (1973). 4) For a review, see J.D. Joannopoulos and M.L. Cohen, Theory of short-range order and disorder in tetrahedrally bonded semiconductors, in: Solid State Physics, Vol. 31, eds. H. Ehrenreich, F. Seitz, and D. Turnbull (Academic Press, New York, 1976) pp. 71-148.
5) J.L. Beeby and T.M. Hayes (to be published); T.M. Hayes and J.L Beeby (in this volume). 6) M.F. Thorpe and D. Weaire, Phys. Rev. B 4, 3518 (1971 ).