The electronic properties of dangling bonds in silicon

Physiea 116B (1983) 79-84 North-Holland Publishing Company

Paper presented at ICDS-12 Amsterdam, August 31 - September 3, 1982

THE ELECTRONIC PROPERTIES OF DANGLING BONDS IN SILICON

MJ. KIRTON, M. JAROS and S. BRAND

Department of Theoretical Physics, The University Newcastle upon Tyne, NEI 7RU, U.K. We have used our direct-matrix self-consistent pseudopotential method to calculate the electronic structure of dangling bonds at line defects and at the reconstructed vacancy in silicon. We find that the width and form of the dangling-bond bands obtained in our calculations are incompatible with the conventional interpretation of the DLTS peaks observed in plastically deformed crystals. We also show that the omission of the effects of electron-electron interaction, temperature dependence, and the Franck-Condon effect in the analysis of standard electrical measurements - e.g. Hall effect and photoconductivity - lead to misleading conclusions concerning the overall character of line-defect phenomena.

I.

INTRODUCTION

Even though substantial progress has recently been made in the study of plastically deformed silicon by means of electron microscopy llI, the microscopic structure of the core regions of dislocations remains poorly understood. In spite of this fact, a great deal of effort has been made to establish a link between electrical and spectroscopic measurements and theoretical models of the dislocation structure. Most theoretical studies 12,3,4,51 have used the 60 ° Hornstra dislocation as a starting point, and the idea that such a core topology should give rise to a narrow (<0.2 eV) dangling-bond band has been generally accepted by workers in the field. In addition, a number of experimental studies have appeared in the literature which purport to be able to lend some support to the existence of narrow dislocation bands le.g. 6,7 I. More recently, studies on partial dislocations have become more prominent since it is now widely recognised that perfect dislocations are dissociated into partials over considerable portions of their length. The main purpose of this paper is not to enter into the debate over the detailed structure of glide-set or shuffle-set dislocations; rather, in the light of our own recent pseudopotential calculations 181 we wish to re-examine some very general features relating to the nature of dangling-bond phenomena at line defects in crystalline silicon. In order to strengthen the validity of our arguments based on the insight provided by our quantitative studies, we have applied our method to the case of the ideal and reconstructed (i.e. JahnTeller distorted) vacancy in silicon. We will show that our new direct-matrix technique is comparable with the self-consistent Greenfunction schemes 19,111. Our results - including those presented in our earlier publications complete our picture of the dangling bonds in silicon, and provide a link between point, line and planar defects. In this present context, the significance of these results lies in the fact that they enable us - in our examination of

0 378-4363/83/0000-0000/$03.00 © 1983 North-Holland

the experimental evidence - to draw upon the achievements in the physics of point defects and surfaces where the link between theory and experiment is more advanced. We find that our prediction of broad dislocation bands is compatible with the results obtained by studies on point and planar defects and that the existing experimental evidence - if correctly processed - does not contradict this prediction.

2.

THEORETICAL RESULTS

In Figure I, we present the density of states in the band gap for a silicon crystal containing one unreconstructed 60 ° dislocation. It is quite

5.0

4,0

3.0

"6 2.0

121

1.0

0

I

1.0 Energy (eV)

I

2.0

Figure I : The density of states of a localised band at a model 60 ° dislocation.

M.J. Kirton et al. / Electronic properties o f dangling bonds in Si

80

02

Figure 2 :

Charge-density contour plot of the t2"state of the silicon vacancy. Contours 0.2 to 2.0, A = 0.2. Units are electrons per unit-cell and the three-fold degenerate state is populated with two electrons.

02

Figure 3 :

Charge-density contour plot of the b 2 state of the tetragonally distorted vacancy. Contours 0.2 to 2.0, A = 0.2. Units are electrons per unit-cell and the state contains two electrons,

M.J. Kirton et al. / Electronic properties o f dangling bonds in Si

VTOrAL

0 ~ -10

--~

"

0!6

CONSENT

r UNITS OF A

LATTfOE

~ 4c -5(

.-TG -Be

Figure 4 : Spherical average of the components of the self-consistent silicon vacancy potential.

clear that this dangling-bond band is somewhat wider than the 0.2 eV predicted by workers employing empirical tight-binding methods. Moreover, our band lies higher above the valence band edge than do the tight-binding bands. These differences are not accidental. This is best demonstrated by comparing the corresponding results for a single vacancy: the tight-binding method yields a t 2 level which lies about ~ eV below our result; also, the charge density in our state is less well localised. The essential results of our vacancy calculations are shown in Figures 2, 3 and 4. If we compare 1121 our charge-density contour plots for the t 2 and b 2 levels with those of the Green-function methods (e.g. Figure 5 of reference [9 I and Figure 17 of reference IIO1), then not only do we find excellent overall agreement but we also obtain - if our earlier line-defect work 181 and the results of surface calculations are included - a clear and coherent picture of dangling bonds at point, line and planar defects in crystalline silicon. In addition, the self-consistent vacancy potential depicted in Figure 4 is identical to that shown in references 191 and Illl. This means that the convergence of our calculation is up to the highest standards of the present state-of-the-art. Although we have studied several models of the dislocation core, the general picture of the electronic structure (e.g. band width, spatial distribution and localisation of charge density) appears to be relatively insensitive to the details of the atomic co-ordinates in the neighbourbood of the core. A most striking piece of

81

evidence supporting our conclusion emerged from the study of Northrup et al 1131: these workers carried out a pseudopotential calculation concerning the unreconstructed 30 ° partial dislocation, with the core geometry determined by a detailed fit to the data recovered from highresolution electron microscopy. The band of dangling bonds is very similar to that obtained in our calculations and its most important properties can be very simply linked to the nearestneighbour distance defining the line defect and to the relative orientation of adjacent dangling bonds. However, the results are expected to be sensitive to reconstruction affecting the translational symmetry of the line. We have already seen that the unreconstructed dangling bonds at line defects can be regarded as analogous to those at semiconductor surfaces. Since the main point of interest here is the band width and electron correlation, we can exploit the link between the line and planar defects in an attempt to assess the effects of reconstruction upon these parameters. In the absence of any experimental information concerning the possible reconstruction process along the line defect, such a strategy seems the most profitable one. Probably the most intensively studied reconstruction process is that which takes place at the (iii) surface of silicon. Although we still do not have a very clear picture (theoretical or experimental) of the details of the electronic structure, it has been shown experimentally and theoretically that the dangling-bond bands are substantially broader than 0.2 eV I14,15,16,171; this is either a direct result of the reconstruction geometry itself or a combination of geometrical and correlation effects which tend to broaden these bands. Thus the existing theory of the electronic structure of extended defects predicts that the observable width of the dislocation band - if such a band exists - should be of order ~0.4 eV, irrespective of the details of the system in question.

3.

COMPARISON OF THEORY WITH EXPERIMENT

Reports of experimental results concerning the electronic structure of line defects are based on observations of electron-spin-resonance (ESR), transient capacitance (DLTS), optical excitations and on standard electrical measurements (e.g. C-V characteristics and the Hall effect). The format of this paper does not allow us to give a comprehensive assessment of all existing data. We will, therefore, focus on a few representative examples to demonstrate that the existing experimental evidence does not in fact contradict our theoretical predictions. We also suggest that it might be more useful to regard the localised phenomena as a dominant part of the problem, with the effect of broadening due to the extended character of the defect being demoted to a secondary role. Let us begin by considering the DLTS spectrum I191 normally associated with line defects

M.J. Kirton et aL / Electronic properties o f dangling bonds in Si

82

Q) DLTS SPECTRUM OF IRRADIATED n-GoAs

150

200

250

300

I 350

Temperofure ( K )

b) DLTS SPECTRUM OF DEFORMED SILICON

100

150

200

250

Temperoture ( K ) Figure 5 : (a) DLTS spectrum of irradiated nGallium Arsenide (after Lang 1201); (b) DLTS spectrum of plastically deformed silicon (after Kimerling et al I191).

(Figure 5b). Although a number of sharp features usually appear in DLTS spectra of n-type deformed silicon, these spectra can be removed by annealing and only the peak in Figure 5b survives in the 800 - 900 ° range. It is this thermal stability and the fact that the peak is broad that led to the suggestion that it might represent the narrow dislocation band of dangling bonds calculated by Marklund and others. It is, first of all, worth noticing that peaks of similar width have been observed in irradiated crystals (Figure 5a) where they were associated with localised defects 120,211 - the width of the peaks was related to the damage due to exposure to irradiation, without invoking the existence of extended defects with well-defined translational symmetry. Peaks of such width have also been seen in amorphous Si:H, and it has been shown that in systems

with state densities as small as iO 15 cm -3 eV -I the relationship between the density of states in the gap and DLTS spectra requires careful processing 122[. Even if we adopt a simplified interpretation of DLTS spectra as a superposition of unresolved individual peaks (small signal/low frequency/high temperature approximation) corrected for line width (AT ~ T) and assume a narrow band of ~O.2 eV of the type obtained in reconstructed one-electron surface calculations (e.g. reference I231), we do not obtain a "triangular" peak like that shown in Figure 5b but instead a broader peak with a flat top. It would be, therefore, more appropriate to regard the spectrum in Figure 5b as a means of dispensing with the theory of narrow bands. Nor is the position of the peak comparable with "levels" obtained in electrical measurements. Only rarely does the activation energy obtained from the conventional Arrhenius plot correspond to the level depth! (For details, see Chapter 8 of reference 1241.) This brings us to the evidence obtained by standard electrical measurements. These, unlike DLTS, measure a sum of all contributions from states in this gap. Consequently, in systems involving many states in the gap, the characteristic level energy normally deduced from, say, Hall data is unlikely to be related to any single one-electron state predicted from theoretical models. Furthermore, in Hall measurements the transition is often that of an electron between the top of the dangling-bond band and the host crystal conduction band. Since the danglingbond band is pinned to the top of the valence band and the band gap of Si decreases with increasing temperature, the difference between free energy and enthalpy in the relevant temperature range (~O.i eV) should be accounted for in the assessment of the level depth. To the best of our knowledge there is no mention of such corrections in the Hall-data reports on deformed silicon. In their assessment of the width of the dislocation band, Mantovani et al 17J also invoke the assessment of the effective Fermi level obtained from C-V measurements. However, in their fit of the experimental data they assume, among other approximations, that the dangling-bond concentration is given by the ideal (average) distance between dangling bonds (3.67 ~). DLTS data, however, shows that only about I/lOOth of the dangling-bond electrons contribute to the signal attributed to the dislocation bands J191~ The fact that only a small fraction of dangling electrons normally associated with the line defect appear to be "active" strongly supports our theoretical prediction that the relevant peaks are linked to some localised phenomena associated with the presence of dislocations rather than to the extended nature of the defect. This is also the view originally suggested on intuitive grounds by Kimerling and Patel [25 I. Finally, we must consider the evidence provided by optical experiments. Indeed, since we are mainly concerned here with the question of band width, optical experiments are the only direct

M.J. Kirton et al. / Electronic properties o f dangling bonds in Si

n)

b)

83

c)

2

g a=

123 K ///////

EC / / / ' / / >,

>-

_p_.._L/°.52 E0

...._ ~ ~--tl

0.39 . . . . . I

0.3 0.5 0.7 0.9 1.1

Ev

I I I I .

\0.26

ua

/////// LATTICE COORDINATE

Phofon energy (eV)

Figure 6 :

(a) Photoconductivity spectrum of plastically deformed silicon (after Kos and Neubert 161); (b) The model of Kos and Neubert used to explain their data; (c) The usual configuration-coordinate diagram for the absorption and emission of a particle at a deep level.

means of providing the relevant evidence. The photoconductivity of plastically deformed silicon was studied by Kos and Neubert J6J. Their results are summarised in Figures 6a,b. They proposed that the curves in Figure 6a correspond to two transitions: one with a threshold at 0.52 eV corresponding to a jump from the valence band to the top of the dislocation band; and the other with a threshold of ~O.80 eV corresponding to a jump from the bottom of the dislocation band to the conduction band. Firstly, it is difficult to explain with this model why the photoconductivity should in fact be reduced above the photon energy of 0.80 eV and why the first threshold should mark the top and not the midpoint of the dislocation band, which is assumed by the authors to be half-filled. Secondly, if the overlap between the adjacent dangling bonds is very small then we must expect the electron-electron interaction to be large enough for the experiment to detect it. As in the case of point defects we might also expect the coupling of the dangllng-bond states to the lattice to be significant and the lattice coordinate of the core atoms to change with charge state. These effects are not taken into account in the model of Kos and Neubert shown in Figure 6b. In the analysis of deep-level phenomena it is customary to picture complementary transitions such as those of Figures 6a,b in a configurationcoordinate diagram (Figure 6c). Clearly the threshold energies of complementary transitions involving systems strongly coupled to the lattice do not have to add up to the band-gap energy and the spectrum shows a characteristic broadening with temperature. Consequently, the effect reported in Figure 6a might be associated with the presence of a single deep state in the gap. The form of the photoconductivity signal at higher energies is a result of competition between the transitions involving the valence and

conduction bands and the effect of temperature (examples of the relationships involving the lineshape and the above parameters have been discussed in Jaros 1261).

ACKNOWLEDGEMENTS M.J. Kirton would like to thank the University of Newcastle upon Tyne for the award of an IBM (UK) Limited Fellowship.

REFERENCES Iii

Cullis, A.G. and Joy, D.C. (eds), Microscopy of Semiconducting Materials, 1981 (Institute of Physics Conf. Ser. 60, Bristol, 1981).

J2J

Marklund, S., Electron states associated with the core region of the 60 ° dislocation in silicon and germanium, Phys. Status Solidi b85 (1978) 673-681.

[31

Marklund, S., Electron states associated with partial dislocations in silicon, Phys. Status Solidi b92 (1979) 83-89.

141

Jones, R., Electronic states associated with the 60 ° edge dislocation in silicon, Phil. Mag. 35 (1977) 57-64.

151

Jones, R., Theoretical calculations of electron states associated with dislocations, J. Physique Coil. C6 (1979) 33-38.

J6J

Kos, H.J. and Neubert, D., Two-step photoconductivity in dislocations in silicon, Phys. Status Solidi a44 (1977) 259-264.

84

M.J. Kirton et al. / Electronic properties o f dangling bonds in Si

17L

Mantovani, S., del Penino, U., and Valeri, S., Energy band associated with dangling bonds in silicon, Phys. Rev. B22 (1980) 1926-1932.

181

Kirton, M.J. and Jaros, M., The nature of dangling bonds at line defects in covalent semiconductors, J. Phys. C: Solid St. Phys. 14 (1981) 2099-2115.

191

Baraff, G.A. and Schl~ter, M., New selfconsistent approach to the electronic structure of localised defects in solids, Phys. Rev. BI9 (1979) 4965-4979.

II01

Baraff, G.A., Kane, E.O. and Schl~ter, M., Theory of the silicon vacancy: an Anderson negative-U system, Phys. Rev. B21 (1980) 5662-5686.

Iiii

Bernholc, J., Lipari, N.O. and Pantelides, S.T., Scattering-theoretic method for defects in semiconductors II, Phys. Rev. B21 (1980) 3545-3562.

1121

Kirton, M.J., The Electronic Structure of Point and Line Defects in Covalent Semiconductors, Ph.D. Thesis, University of Newcastle upon Tyne (1982).

If31

Northrup, J.E., Cohen, M.L., Chelikowsky, J.R., Spence, J. and Olsen. A., The electronic structure of the unreconstructed 30 ° partial dislocation in silicon, Phys. Rev. B24 (1981) 4623-4628.

1141

1151

1161

Uhrberg, R.I.G., Hansson, G.V., Nicholls, I, J.M. and Flodstrom, S.A., Experimental evidence for one highly dispersive danglingbond band on Si (Iii) 2×1, Phys. Rev. Lett. 48 (1982) 1032-1035. Parke, K.C., McKinley, A., Williams, R.H. and Srivastava, G.P., The electronic structure of cleaved silicon (III) surfaces following adsorption of aluminium, J. Phys. C: Solid St. Phys. 13 (1980) L369-374. Northrup, J.E., Ihm, J. and Cohen, M.L., Spin polarization and atomic geometry of the Si (iii) surface, Phys. Rev. Lett. 47 (1981) 1910-1913.

I171

Pandey, K.C., New ~-bonded chain model for Si (iii) 2xl surface, Phys. Rev. Lett. 47 (1981) 1913-1917.

1181

Del Sole, R. and Chadi, D.J., Correlation effects on the electronic structure of Ixl and 2xl reconstructed Si (iii) surfaces, Phys. Rev. B24 (1981) 7431-7434.

1191

Kimerling, L.C., Patel, J.R., Benton, J.L. and Freeland, P.E., Dislocations in silicon, in Hasiguti, R.R. (ed), Defects and Radiation Effects in Semiconductors, 1980 (Institute of Physics Conf. Ser. 59, Bristol, 1981).

1201

Lang, D.V., Deep-level transient spectroscopy: a new method to characterise traps in semiconductors, J. Appl. Phys. 45 (1974) 3023-3032.

1211

Lang, D.V. and Kimerling, L.C., Observations of athermal defect annealing in GaP, Appl. Phys. Lett. 28 (1976) 248-250.

1221

Lang, D.V., Cohen, J.D. and Harbison, J.P., Measurement of the density of gap states in hydrogenated amorphous silicon by spacecharge spectroscopy, Phys. Rev. B25 (1982) 5285-5320.

1231

Schl~ter, M., Chelikowsky, J.R., Louie, S.G. and Cohen, M.L., Self-consistent pseudopotential calculations for Si (iii) surfaces, Phys. Rev. BI2 (1975) 4200-4214.

E241

Jaros, M., Deep Levels in Semiconductors (Adam Hilger/Institute of Physics, Bristol, 1982).

1251

Kimerling, L.C. and Patel, J.R., Defect states associated with dislocations in silicon, Appl. Phys. Lett. 34 (1979) 73-75.

1261

Jaros, M., Wave functions and optical cross sections associated with deep centres in semiconductors, Phys. Rev. BI6 (1977) 3694.