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ELECTRONIC STATES IN AMORPHOUS GERMANIUM CHALCOGENIDES
J. Ma¡ek, B. Velický
To cite this version:
J. Ma¡ek, B. Velický. ELECTRONIC STATES IN AMORPHOUS GERMANIUM CHALCOGENIDES. Journal de Physique Colloques, 1981, 42 (C4), pp.C4-133-C4-136.
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CoZZoque C 4 , suppl6ment au nolO, Tome 42, octobre 1981 page C 4 - 1 3 3
ELECTRONIC STATES IN AMORPHOUS GERMANIUM CHALCOGENIDES
J. ~ a g e k and B . velick?
I n s t i t u t e of Physics, CzechosZovak Academy of Sciences, Prague, CzechosZovakia
Abstract.- We used Bethe lattice to represent the ideal net- work of amorphous GeS, GeSe and GeTe with coordination 4:2 and calculated corresponding densities of electronic states.
Good results were obtained for Harrison Hamiltonian. Further study of a-GeS showed that localized states arise from va- rious bonding defects. On the other hand, the actual arran- gement of the chemically ordered lattice has only little ef- fect on the density of valence states.
Introduction.- Present day theory of amorphous semiconductors has em- phasized the connection between their electronic behaviour and the lo- cal atomic structure: the bonding relations rule over both bulk elec- tronic states and the nature of intrinsic defect centres. This concep- tion gives an explanation of different electronic properties of two important groups of the amorphous semiconductors, i.e. tetrahedral elements and low coordination glasses. The amorphous semiconductors with mean coordination 3 (a-As and germanium chalcogenides) have,
strusturally and chemically, an intermediate position between the two limiting groups. From the theoretical point of view, this should be reflected in the electronic structure. It is also indicated by expe- riment (1,2)
.
Recently, several calculations of the electronic structure of a-As has appeared but the theoretical treatment of amorphous germanium mono- chalcogenides (a-GeCh) is still lacking. In this paper we present the first calculation of the electronic structure of these materials. In addition, our simplified structural model of a-GeCh is utilized to test various Hamiltonian parametrization.
Structure of amorphous germanium cha1cogenides.- In comparison with other amorphous semiconductors, the atomic arrangement in a-GeCh is quite different from the structure of the corresponding crystal. It is understood as a result of enhanced role of covalent forces in absence of long range order. However, the details of the structure still re- main at issue and two competing models are used to interpret. At pre-
sent, the 4:2 model keeping the natural valency of both Ge and Ch atoms is preferred to the 3:3 model (3), isomorphous to a-As, and the structure of a-GeCh is regarded intermediate between Ge, and GeCh .For a-GeS, the 4:2 is supported by the measurement of radial distribugion function (4).
Owing to the bonding balance, the stoichiometric a-GeCh with coordina- tion 4:2 contains a significant number of Ge-Ge bonds, the distribu- tion of which introduces new structural degrees of freedom. That is why several hand-built models of a-GeS (5) and a-GeSe (6) have been constructed. As shown in (5), the statistics of Ge(GenS4-*) tetrahedra is related to the medium range order: the uniform model wlth n = 2
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981425
C4-134 JOURNAL DE PHYSIQUE
has a layered structure, while all structural units are present in the three-dimensional network.
The aim of this work is to obtain a local view of the electronic sta- tes. The complexity of the real structure of a-GeCh (two kinds of atoms and bonds (makes it difficult so that we accept an additional structural approximation and use Bethe lattice to represent the ideal uniform 4:2 structure.
Results.- The object of our calculations is local density of states (LDOS). For small clusters, surrounded by the Bethe lattices, it is easily determined by the Green function technique. We adopt a simple LCAO method: four valence orbitals are attached to each atom and only interactions between bonding neighbours are considered.
The empirical fitting of the interaction parameters in a-GeCh is dif- ficult so that an uniform parametrization procedure is desirable. We tried two ways of Hamiltonian parametrization, the chemical pseudopo- tential method (7) and the method proposed recently by Harrison ( 8 ) . The latter method is for a-GeCh superior to the former, which re- sults in the spectrum without gap. We point out that this is a syste- matical error of the chemical pseudopotential. On the other hand, Harrison parametrization gives good description of the electronic structure of a-GeCh. In the series GeS, GeSe, GeTe, the band gaps, and valence band widths agree well with the experiment.
Resulting densities of states are shown in Fig. 1. The electronic spectrum is generally composed of four main bands. The highest lying band, formed by mixed Ge-Ge and Ge-Ch antibonding states, is separa- ted from the occupied bands by a gap. Bonding states contribute most- ly to the middle part of the broad valence band while its upper part is derived from nonbonding p-states at chalcogens. The lowest lying band contains s-like states at chalcogen atoms.
The reasonable description of the basic electronic structure encoura- ged us to further studies, restricted to a-GeS for simplicity.
Fig. 1. Calculated density of states in amorphous GeS (a), GeSe (b)
,
GeTe (c) and in GeS with coordination 3: 3 (d).
surroundings:
a, the component DOS at Ge in the uniform (full line) and random (dotted) model of a-GeS, b, the component DOS at S, c-f, the defect DOS in the vicinity of the Fermi level (indicated by dots) : c , Ge (S2Gel),
d l S (Gel-), e l S (Gels) f, S (Ge,Ge,S)
First, we investigated how much is the electronic spectrum influenced by the actual atomic arrangement. As the absence of the S-S bonds is preserved also in the random model, we assume the LDOS at chalcogen atoms unchanged by redistribution of the Ge-Ge bonds in the structure but the LDOS at Ge depends on the neighbours. Various configurations were in our calculations modelled by clusters Ge(GenS4-n) surrounded by the uniform Bethe lattice. As a result, the averaged density of valence states was found nearly.equa1 to the LDOS in the uniform lat- tice (Fig. 2a). We explain this result as a consequence of conserved numbers of Ge-Ge and Ge-Ch bonds in the random model.
To complete the comparison of various strcutural models we also cal- culated the LDOS for the Bethe lattice with coordination 3:3 (Fig-ld) The nature of the highest occupied states is remarkably changed, it is now a mixture of nonbonding states at both Ge and S. Also the sha- pe of the total density of states is modified. Elevertheless, even
C4-136 JOURNAL DE PHYSIQUE
small broadening of the DOS makes the 3:3 and the 4:2 models undis- tinguishable.
Defects in a-GeS.- The defect centres in amorphous semiconductors can be viewed as the points where the short range order of the network is disturbed. Also our simplified model of defects consists of atoms with an atypical chemical composition of the nearest neighbour sphe- re, the more distant surroundings is replaced by the Bethe lattice.
The calculated LDOS are for several configurations shown in Fig. 2.
The first class of defects contains atoms with changed valency. The germanium dangling bonds introduce bound states into the gap. The va- lency changes of chalcogens are affected by the presence of their lone electron pairs. A dangling bond leads to a local transfer of states from the bonding and antibonding region into the nonbonding peak at the top of the valence band. On the other hand, this peak is reduced by the third bond.
In contrast to various bonding configuration of Ge the "wrong" bonds S-S break the chemical order of stoichiometric system. The direct in- teraction between two lone pairs then splits the top of the valence band, creating a bound state in the lower part of the gap. Similar effect is observed whenever two chalcogen atoms approach one another.
Summary.
-
The Harrison method gives a reasonable description of the electronic structure of amorphous germanium monochalcogenides. The universality and the separate treatment of geometrical and chemical input data makes the method usable for other disordered compound semi- conductors.The calculation of the LDOS at various atomic configuraions show that the difference in structural models are only weakly reflected in the electronic spectrum of A-GeS, and that localized states originate from various bonding defects. Present calcularions also illustrate the im- portance of the interaction between the defect and an extended system.
Acknowledgement.- The authors would like to thank Dr. V. Drchal for stimulating discussions about the structure of a-GeS.
References
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3 Rowland S.C. et al., J. Appl. Phys.
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(1972) 27414 Cervinka L., Hrubg A., Proc. 5th Int. Conf. Liquid and Amorphous Semicond. (ed. J. Stuke, W. Brenig), Taylor Francis, London (1974) 431
5 Drchal V., Velickg B., Sbornik 6. konf. E s . fyzikb, Ostrava (1979) 05-13, in Czech
6 Popescu M., St6tzel H., Vescan L., Proc. Int. Conf. Amorphous Semi cond-uctors -80, Kishinev (1980) A44
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