INFLUENCE OF CORRELATION EFFECTS ON THE ELECTRONIC PROPERTIES OF AMORPHOUS SILICON

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INFLUENCE OF CORRELATION EFFECTS ON THE ELECTRONIC PROPERTIES OF AMORPHOUS

SILICON

L. Schweitzer, M. Grünewald, H. Dersch

To cite this version:

L. Schweitzer, M. Grünewald, H. Dersch. INFLUENCE OF CORRELATION EFFECTS ON THE

ELECTRONIC PROPERTIES OF AMORPHOUS SILICON. Journal de Physique Colloques, 1981,

42 (C4), pp.C4-827-C4-830. �10.1051/jphyscol:19814182�. �jpa-00220808�

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ColLoque C4, supple'ment au nO1O, Tome 4 2 , octobre 1981 page c4-827

INFLUENCE OF CORRELATION EFFECTS ON THE ELECTRONIC PROPERTIES OF AMORPHOUS SILICON

L. Schweitzer, M. Grfinewald and H. Dersch

Fachbereich Physik, U n i v e r s i t a t Marburg, Renthof 5, F. R. G.

Abstract.- The influence of correlation effects on the density of states deduced from field-effe6t and capacitance-voltage measurements are considered. A positive Hubbard U is required to account for the observed Curie-law behaviour of the magnetic suszeptibility. Hence, statistics of correlated electrons have to be used rather than Fermi-statistics to cal- culate the density of states distribution function g(E) from the measured charge density. Within this model g(E) 'differs appreciably from previously published "field effect" densities.

Introduction.- The knowledge of the distribution of localized states in amorphous semiconductors is of fundamental importance for understanding the electronical properties of these materials. The most detailed information about the density of states distribution in amorphous silicon has been obtained hy means of the field effect technique1 1 * I 3 : 4 . This method, however, is rather indirect since the procedure of extracting N(E) from the measured change of the conductance G with field voltage V is not straight-forward5. Furthermore, the density of states N ( E ) deduced from such experiments will, as we shall show below, essentially depend on the physical model on which the evaluation scheme is based. Up to now, the "field effect" density of states N(E) has been obtained by deconvoluting6

where f (E) is the Fermi distribution function, f (E) = (eB(E-E~) + l)-l,

B

= l/kT, and Ne(V) is the surplus density of charge carriers which can be calculated directly from experiment6. The result generally deduced is the well known picture which exhibits besides the valence- and conduction band-tail states two additional features, the Ex and Ey peaks2.

So far, no satisfactory model has been proposed to explain the origin of these states. Neither the divacancy analogy suggested by spear7 nor the defect model of ~ o t t * can account for the observed asymmetry of the gap states, since these models require equal densities of Ex and Ey states.

The aim of this paper is to show that inclusion of electron-correlation into the evaluation scheme will drastically change the density of states distribution function calculated from field effect and capacitance-voltage measurements for amorphous Si:H.

Correlation effects in a-Silicon.- The main evidence for correlation effects in a-Silicon is supplied by numerous electron spin resonance (ESR) experiments, which show that the spin density of dangling bond type defects with the well known g-value 2.0055 does not depend on temperature9. This Curie-law susceptibility of the para-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19814182

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C4-828 JOURNAL DE PHYSIQUE

Fig. 1: Spin density of Boron doped a-Si:H as a function of temperature

magnetic centers can be explained by a positive correlation energy U associated with the possible double occupancy of these states. Recent ESR experiments on doped a-Si:H1° yield the same behaviour at low temperatures for another resonance line g = 2.013, with spin densities Ns up to 10'~cm-~ (fig. 1). This line, as well as the resonance at g = 2.0043 are intrin- sic and clearly not the result of the phosphorus and boron doping as demon- strated convincingly by light induced ESR experiments1 l l 2 . Therefore, one abso- lutely has to take electron correlation into account since in thermal equilibrium a one-electron model cannot explain a Curie-law susceptibility1 3.

The decrease of Ns in boron doped samples at higher temperatures instead of an expected increase for k T % U is pro- bably due to the fact that

I E ~ - E ~ - u ~

^{% k ~ ,}

i.e. the mobility edge E,, limits the reservoir of possible localized spins, since electrons in delocalized states do contribute to the neutrality condition but not to the spin signal.

Thus having realized the importance of correlation effects one must not use simple fermi statistics in evaluating the field effect data. The density of states g(E) is now obtained by deconvoluting

and no+nl +n2'1

Since the correlation energy U must vanish at E,, and E,, i.e. when the states become delocalized, U must depend on energy. Please notethat we distinguish between the band edges Ev, Ec and the mobility edges E,, and EV. The "density of states" N(E) extracted from field-effect measurements and published so far is related to the true density of states g(E) by

g(E!)

where the Ei are the roots of

and

w

= (1 -e-BU(E'))1/2 (8)

In contrast to the true density of states g(E), the field effect density N(E) depends on temperature and on the correlation energy U.

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N (E) we have calculated N (El using eq. 6 for a given model density g(E), which is shown together with N(E) in fig. 2 for comparison. The assumed energy dependence cf U is drawn below.

The different U values for the localized valence band-tail states

( % 0.3 eV) and the defect states near

midgap ( % 0.5 eV) reflect the stronger localization of the deep gap states.

Our model density of states g(E) was assumed to consist simply of a valence band-tail, a conduction band-tail and a peak of localized defects near midgap. As we can see from fig. 2, if correlation effects are neglected in the evaluation scheme, a distribution

" function N(E) is obtained, which is

E - E,

^(eV) ^Ecquite similar to the well known density of states distributions published previouslylf 2 l 3, 4. This surprising Fig. 2: Density of states g(E) and the corres- can be as

ponding "field effect density" N(E). The so called Ey peak arises from the doubly occupied valence band-tail states which are shifted to higher energies by the amount of the Coulomb repulsion U.

The small minimum above E,, arises from the energy dependence of U. The rise of U(E) = O at El, to its maximum value Uo also causes the band-tail to flatten. The Ex peak, on the other hand, if not due to surfaces or interface states, originates from the doubly occupied defect states, shifted to higher energies by U. The conduction band-tail is hardly altered by correlation effects. In addition, the experimentally observed small U values reflect the weaker localization of these states. The alloca- tion of the three ESR resonance lines observed in a-Silicon to energy states within the gap is in accordance with the suggestions of Street and ~iegelsenl~: The defect states, somewhat below midgap are due to the well known dangling bond line with g=2.0055 and a correlation energy of about 0.5 eV. The two lines with g=2.0043 and 2.013 are due to localized electrons in conduction band-tail and holes in valence band-tail states, with correlation energies of approximately 0.01 eV and 0.25 eV, respectively.

At the moment it seems not necessary to introduce further states into the gap of a-Si:H since the present model accounts very well for the observed features and details in the distribution of localized gap states. The corresponding spin densities as a function of the position of the Fermi level can be calculated from g(E)

E v Ec

Fig. 3: Calculated spin density Ns as a and are shown in fig. 3. One could functi-on of the position of the compare this result with the experi- Fermi level EF mental data of doped a-si:~", a

close agreement, however, would be

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C4-830 JOURNAL DE PHYSIQUE

somewhat artifical since at least three problems remain unsolved. First, doping does not only shift the Fermi level as assumed in our calculation, but it introduces new defects too, thus changes g(E). Second, in general the activation energy E,, of the conductivity must not be equal Eu -EF and therefore does only indirectly reflect the position of the Fermi level, hence the relation to our energy scale is not obvious.

The third and main problem, however, is the unsatisfactory knowledge of the energy dependence of U. This detailed information is the crucial point in the quantitative understanding of the density of states as wellas the spin densities in a-Si:H. The U values used in our calculation have been estimated from the temperature dependence of the spin density1'. In principle, the position of the mobility edges could be deter- mined experimentally from the saturation of the spin density by shifting the Fermi level to the band edges (fig. 3).

The influence of correlation effects on the electrical conductivity depends essentially on the type of transport considered. If transport takes place in delocalized states above a mobility edge EV, the correlation U only enters the calculation of the statistical shift of the Fermi level, as long as the doubly occupied states appear energetically below EV. For hopping-transport, one has to distinguish between hops to either empty or singly occupied states, since transitions to the latter involve an additional U. In this case the use of an effective density of states15, p (E), which includes the correlation effects seems to simplify the calcu- lations.

In conclusion, we have suggested that correlation effects have to be considered for extracting the density of states from the measured charge density, for calculating the spin densities from g(E) and to describe hopping transport.

We thank E. Kurras for calculating the spin densities.

1. SPEAR W.E., LeCOMBER P.G., J. Non-Cryst. Solids

8-10

(1972) 727

2. MADAN A., LeCOMBER P.G., SPEAR W.E., J. Non-Cryst. Solids

0

(1976) 239 3. GOODMAN N.B., FRITZSCHE H., OZAKI H., J. NOn-Cryst. Solids 358.36 (1980) 599 4. GRUNEWALD M., WEBER K., FUHS W., THOMAS P., this conference

5. GOODMAN N.B., FRITZSCHE H., Phil. Mag. B

42

(1980) 149

6. GRUNEWALD M., THOMAS P.,

WRTZ

D., phys.stat.so1. (b)

100

(1980) K 139 7. SPEAR W.E., Proc. 5th Int. Conf. on Amorphous and Liquid Semiconductors, ed.

by J. Stuke and W. Brenig, London, Taylor & Francis (1974) p. 1 8. MOTT N.F., Phil..Mag.

6

(1972) 505

9. BRODSKY M.H., TITLE R.S., AIP Conf. Proc.

31

^{(1976) 97}

10. DERSCH H., STUKE J., BEICHLER J., phys.stat.So1. (b) (1981) in press 11. KNIGHTS J.C., BIEGELSEN D.K., SOLOMON I., Solid State Comm.

22

(1977) 133 12. STREET R.A., BIEGELSEN D.K., J. Non-Cryst. Solids 35&36 (1980) 651 13. KAPLAN T.A., MAHANTI S.D., HARTMANN W.M., Phys.Rev.Lett.

27

(1971) 1796 14. STREET R.A., BIEGELSEN D.K., Solid State Comm.

2

(1980) 1159

19. SCHWEITZER L., GRUNEWALD M., DERSCH H., Solid State Comm. (1981) in press