REVIEW OF GROUP-V AMORPHOUS SEMICONDUCTORS

(1)

HAL Id: jpa-00220814

https://hal.archives-ouvertes.fr/jpa-00220814

Submitted on 1 Jan 1981

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

REVIEW OF GROUP-V AMORPHOUS SEMICONDUCTORS

E. Davis

To cite this version:

E. Davis. REVIEW OF GROUP-V AMORPHOUS SEMICONDUCTORS. Journal de Physique Col-

loques, 1981, 42 (C4), pp.C4-855-C4-864. �10.1051/jphyscol:19814188�. �jpa-00220814�

(2)

JOURNAL DE PHYSIQUE

CoZZoque C4, suppZ6ment au nOIO, Tome 4 2 , octobre 1981 page C4-855

REVIEW OF GROUP-V AMORPHOUS S E M I C O N D U C T O R S

E.A. Davis

,Physics Department, University of Leicester, Leicester LEI 7RH, U . K .

Abstract

-

The properties of the Group-V amorphous semiconductors, P, As and Sb, are reviewed with particular emphasis on data obtained recently. On the structural side, evidence in favour of CRN models is obtained by consideration of the first sharp diffraction peak at % 12-I and also NQR data which seem to demand a broad distribution of dihedral angles. New results of t i m e resolved luminescence and ODMR for a-P reveal two channels for recombination, one of which is via a triplet exciton state. The effects of chemical modification and alloying on the electrical and optical properties of a-As indi- cate that the Fermi level can be shifted, but not to the extent that it can in a-Si:H; surprisingly hydrogenation makes dopants less effective. Inform- ation from Raman and infrared studies concerning vibrational properties is considered and finally the temperature variations of specific heat and ultrasonic attenuation are presented and discussed.

Structure

-

Continuous random network (CRN) models have been built to simulate the structures of threefold coordinated materials ( 1 , 2 , 3 ) . The radial distribution functions of these models show fairly good agreement with experimental curves for a-As and a-P. Since these models are also quite effective in accounting for the electronic (4,5,6) and vibrational (7,8,9) densities of states, they are prefer~ble to alternative models (10,ll) which have as their basis the short-range order present in the double layers of the rhombohedra1 and orthorhombic crystals and which attach special significance to interlayer separations. Just as for amorphous Group IV materials, the bond lengths and bond angles characteristic of crystalline modi- fications are retained, but the dihedral angle has a broad distribution and interlayer correlations are essentially lost. Figure la shows the dihedral-angle dis- tributions of two hand-built models, one containing only rings comprised of even numbers of atoms and the other constructed without such constraint.

4 5 5 0 a5 60 6 5 70

Y (MHz)

( a ) (b)

Fig.l: (a) Dihedral-angle distribution in the Greaves-Davis (odd/even rings) and Matthews-Davis-Elliott (even rings) threefold coordinated CRNs. (b) Top:

NQR absorption in a-As (solid line and points) and orthorhombic As

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19814188

(3)

JOURNAL DE PHYSIQUE

(dashed peak) at 4.2K. Bottom: Calculated lineshape using the dihedral- angle distribution shown in the inset. ((b) from reference 12).

Figure Ib displays NQR data on a-As by Jellison et al. (44). The broad and asymmetric signal is quite different from that observed in c-As and appears to require the existence of a broad dihedral-angle distribution to explain its form.

It would be interesting to see if the more-structured dihedral-angle of the even- ring model might reproduce the experimental lineshape even more closely.

A prominent feature in scattering data for amorphous Group-V mgterials is a relatively sharp maximum at a value of 41rsin@IX of approximately 1.23 l (see 3, 11 and

3 7 ) . An analogous peak is also observed for amorphous chalcogenides and several

liquids (including Ar) and has been the subject of much discussion. Rather than attempting to identify this with a specific re-occurring real-space distance, we prefer the suggestion of Veprek and Beyeler (12), namely that it arises from the superposition of many terms in the Fourier series representing the pair correlation function. The fact that the height of the peak is rather sensitive to sample preparation conditions or annealing treatments serves to emphasize its dependence on contributions from a rather wide range of real-space distances associated with intermediate-range order. This is not to say that a single contribution cannot dominate; indeed the large sharp peak reported by Daniel and Leadbetter (13) for yellow a-As, prepared by deposition on to substrates at 30K and composed of As4 molecules, has been interpreted in terms of intermolecular atomic se arations of 5-62 with a correlation in molecular orientation over distances % 30E. On warming to room temperature, this metastable material 'polymerizes' to the stable red form and the first diffraction peak is much reduced (figure 2)

n ^-

^yellowa - As deposiled o f 3OK

- - - after heattng to RT (Donael a n d Leadbetler 1981)

Fig.2: X-ray interference functions for vapour-deposited As film (-) and the same sample after warming to room temperature ( - - 3 . (From reference 13).

X-ray (14, 37)and neutron (J. Dore, private comunication) scattering data for a-P have also been obtained. The diffraction curves exhibit a large first peak similar to that in a-As. Its strength and width are sensitive to preparation conditions (37) as will be discussed later.

Optical Properties

-

The optical gaps for a-P and a-As are approximately 2.0eV and 1.2eV respectively. The gap in a-Sb is not known but it is certainly smaller than lev. The optical absorption edges of a-P (15) and a-As (16) have the familiar form for amorphous semiconductor - i.e. an Urbach edge above which the absorption coefficient is proportional to the square of the photon energy (see (17)).

Deposition on to high-temperature substrates or annealing of thin films shifts the

(4)

edge by a few tenths of an eV to higher energy with little change of shape and to- wards that of the bulk materialt, as does incorporation of several percent hydrogen.

The slope of the Urbach tail is a factor of % 1.5 less steep in a-P as compared to a-As

-

an interesting result in view of the identical coordination number (15).

and one which places constraints on models that seek to explain the exponential Urbach behaviour.

Both a-P (18) and a-As (19) luminesce strongly, particularly at low temperatures, when photoexcited near the energy of the optical gap. Eo corresponds to an absorption coefficient %

lo4

cm-1. Figure 3 shows that the emission in the case of P

1 1 1 1 1 1 1 1 1 0 1 1 1

0 4 0.8 1.2 1.6 2.0 2.4 2.8

Photon energy (eV)

Fig.3: Photoluminescence (PL) and excitation (PLE) spectra for bulk a-As and a-P.

Eo denotes the approximate optical gaps (from reference ( 2 0 ) ) .

lies in a broad band centred near 1.4eV and the excitation spectrum is a single peak at 1.9eV, whereas for a-As the emission is around 0.6eV and the excitation spectrum has a unique double-humped structure. The latter has been interpreted (3,201 as arising from transitions across the gap and also from levels in the gap associated with negatively charged twofold-coordinated atoms

-

namely As2. Even when excitation is across the gap it is postulated that the hole is rapidly trapped at As2 centres and therefore,in either event,the defect is converted to a neutral centre which becomes AS: after surrounding structural relaxation. The radiative transition is then electron capture by this centre. AS; centres carry a spin and these have been detected by ESR measurements following photoexcitation at low temperatures (21). A different thermally-generated ESR signal is also found in a-As (21) and it has been suggested (3) that this is associated with AS; centres in thermal equilibrium. Thus it is postulated that, in analogy with chalcogenides, valence alternation pairs of defects AS; and As$ occur, but in addition there exist As9 defects which do not decompose into charged VAPs. An energy level diagram for the defect states has been given in (3) and support for it has been obtained from theoretical calculations (42,43).

The situation in a-P is less clear. Shanabrook et al. report at-this con- ference an equilibrium dark ESR signal corresponding to % 1017 spins cm but, in contrast to that in a-As, it is not temperature dependent, at least from 4.2-100K.

A similar density of photoinduced spins is also reported. The Stokes shift associa ted with the luminescence is see from figure 3 to be about 0.6eV, i.e. about three times greater than in a-As. In spite of this information, it does not seem possible to draw an energy level diagram that is consistent with the known position of the Fermi level (close to gap-centre) in a manner similar to that for a-As.

t Bulk a-P and a-As are available commercially from Mining and Chemical Products, Alperton, Wembley, U.K.

(5)

C4-858 JOURNAL DE PHYSIQUE

Time-resolved luminescence studies at 40K on a-P have been made by Fasol (this volume). The single steady-state band at 1.4eV is present at zero

time delay following photoexcitation. However, the spectrum recorded at a delay time of about 50ns is quite different and peaks at I.leV. With increasing delay time (into the microsecond time regime) this signal is considerably decreased in magnitude and emission at virtually the same energy as the zero-delay-time signal becomes the dominant radiation (figure 4a). This clear temporal separation is indicative of at least two recombination channels.

Ernisston energy (eV)

O *On' 'Gs Delay t t m e Rec" tlrne

Fig.4: (a) Peak energy of the two luminescence bands observed in a-P by time- resolved spectroscopy versus the delay time following photoexcitation.

(b) Possible spectra of recombination times for the -two processes El and E2

If there are only two recombination channels then the observed disappearance of E2 at the expense of El might suggest the spectra of recombination times indicated schematically in figure 4b. However we cannot rule out the possibility that the zero-delay-time signal represents a third distinct recombination mechanism.

Two radiative recombination channels in a-P have also been clearly identi- fied in ODMR studies by Depinna and Cavenett (22). The strengths of the resonance- enhanced luminescence signals have the same spectral dependences as the El and E2 peaks of figure 4a. Depinna and Cavenett also found that the El signal has features unambiguously characteristic of recombination from a triplet exciton state.

Furthermore they demonstrated an important link between the two signals: when the E2 signal is excited, a negative signal is superimposed on that of El i.e. it is selectively quenched, but the converse effect, i.e. a quenching of E2 when El is excited, is not observed. The above authors proppse that recombination in both channels is via neutral defects, the E2 signal arising from recombination of electrons and holes trapped at distant centres and the El signal being due to recombination from the triplet state of an electron-hole

air

trapped at a single centre (figure 5a). They propose that the neutral defect is an IVAP (i.e. a nearest-neighbour P;

~t

^pair). There appear to be two difficulties with this assignment. First, as argued by Street (23) for the chalcogenides, the recombination process involving the conversion of two Do defects to D+ and D- cannot be radiative. As inthe configurational-coordinate diagram of figure 5b, the curves for negative4 defects must cross in order for there to be a positive correlation energy at zero distortion. A similar diagram must be appropriate for the proposed tiripletrecombination process at an IVAP i.e. (~+~-)e+h + (D+D-). A second uiffi-

culty is the absence of any evidence for a coulomb term in the variation of El and E2 with delay time (see figure 4a),as would be expected for neutral centres.

Rather than an IVAP, the present author favours ~ositive-U Pq defects as the recombination centres; although this does not overcome the problem of the absence

(6)

of a coulomb term, it does obviate the difficulty illustrated by figure 5b.

Fig.5: (a) Model proposed in reference 22 for the two recombination paths in a-P (b) Configurational-coordinate diagram for negative-U defects. A positive

value of U must exist at zero distortion.

A final comment on this topic concerns the signal observed at zero delay time (figure 4a). If this is associated with a distinct channel then it could con- ceivably be recombination from the singlet exciton state which should, of course, be much faster than that from the triplet state (B. Cavenett

-

private communication).

If, on the other hand, it is due to the same mechanism as E 2 , then the broad spectrum of recombination times expected from a wide distribution in pair separations must lead to the situation depicted in figure 4b in order to account for the tempor- ary demise of E2 beneath the El signal at intermediate times.

Electrical Properties

-

The temperature dependence of the d.c. conductivity forboth a-P and a-As displays a single activation energy of 1.0-1.2eV for a-P((17) and P.

Extance, private communication) and 0.6-0.7eV for a-As (3).However,in common with other a-semiconductors (doped a-Si:H and a-Ge:H apart) the Fermi level lies close to m

gap. Some variation in those activation energies is observed on annealing. (For a- P it is essential to desorb surface moisture by heating to about 400K to obtain reproducible behaviour). A fairly low density of states at the Fermi level is indicated by the absence of variable-range hopping even at low temperatures. However, a linear variation of log o versus

T - U ~

is observed for a-As when subjected to ion bombardment at low temperatures (R.T.Phillips, private communication) and for both materials when subjected to, or released from,hydrostatic pressure (25,261.

The variations of electrical resistance of a-As and a-P with pressure are shown in figure 6. Following a decrease of many orders of magnitude (partly due to a pressure dependence of the gap, but mainly due to the creation of defects that support variable-range hopping conduction), a-As crystallizes to the rhombohedra1 phase at about 36kbar and a-P to the orthorhombic phase at'about 7Okbar. Interest- ingly a-P prepared by chemical transport in a hydrogen plasma (Veprek material) does not crystallize, at least below 90kbar. This may be associated with the more homo- geneous nature of this material compared to the MCP phosphorus, which is known to have a 5um-diameter-ball-like microstructure (26).

The d.c. conductivity of a-Sb as a function of temperature differs considerably from that of a-P and a-As in that T-'/~ behaviour is observed over approximately six orders of magnitude in conductivity and from 20-300K (27). The density of states at the Fermi level is deduced to be substantial

-

approximately

(7)

Fig.6: Variation of room-temperature resistance for a-As and two samples of a-P. The curves are for a constant load- ing rate. (From references 25 and 26).

lo&

Pressure (k bar)

1019ev eme3. The material is theref ore reminiscent of evaporated (unhydrogenated) Ge and Si in its electrical behaviour and it seems likely that dangling bonds (Sb'$') are responsible for the hopping conduction. A reasonable hypothesis (28) why a-Sb should contain a high density of these centres relative to a-P and a-As is that the average bond angle is 96O (P-10ZO, As-98O) which suggests a small degree of hybridi- zation between s and p states. This mitigates against the transfer of electrons between ~ b q sites to form spin-paired VAPs since the required s -t p promotion energy is large. Evidence in support of this hypothesis is provided by data on As- Sb alloys (29) which still exhibit T - ~ / ~ behaviour but with a larger slope i.e. a lower density of hopping sites.

Detailed Hall effect and thermopower measurements on a-As have been reported (30). These results will not be discussed here except to note the discrepancy in sign between the Hall effect (+ve) and the thermopower (-ve), a feature common to all amorphous semiconductors except for a few that exhibit two-carrier (pseudo- intrinsic) conduction.

Chemical Modification and Alloys

-

The effects of chemical additives on the electrical conductivity and optical absorption edge of a-As have been studied by Mytilineou and Davis (31). Up to several percent of the elements Ni, Ge, S, Se and Te were individually incorporated by co-sputtering in Ar or Ar/H2 mixtures. The results for Ni, Te and Ge are summarized in figure 7. It should be noted that the concentrations were estimated from the corresponding fractional areas on the sputtering targets.

The data indicates readily which additives shift the Fermi level within the gap (doping) and which do not (alloying). For Ni, 2Eo represents the high-temperature activation energy because below room temperature a marked increase in conductivity associated with variable-range hopping (probably in Ni d-states) was evident. Some movement of the Fermi level, particularly with Ni incorporation, is evident for all three additives. However it has not been found possible to dope a-As as effectively as a-Si:H for example. A surprising result is that simultaneous incorporation of hydrogen into the chemically modified As films almost completely nullifies the effects of the dopants.

(8)

Fig.7: Variation of optical gaps (Eopt) and twice the activation energy for electrical conduction

(ZED) versus concentration of Ni, o 0 2 0 4 0 6 0 8 1 0 1 2 % T e or NI

Te and Ge incorporated into a-As.

(Ftom reference 31 and Mytilineou and Davis, to be published).

A study of the electrical roper ties of a-Sb alloyed with Bi, Ga, Ge, Sn and As has been made by Hauser (29). Alloys of Bi-Sb are superconductors at concen-

trations of Sb less than about 70%.

Raman and Infrared Studies

-

IR spectra for bulk a-As (32) and a-P (33,34) are shown together with corresponding Raman data (35,36) in figure 8. In these spectra (from reference (37)) the frequency scales and positions have been chosen to emphasize the correspondence of certain spectral features. The overall picture is that of far less fine structure in the curves for a-As. The Raman spectrum for a-Sb

(not shown, see (35)) exhibits even less structure and in fact consists of two featureless bands. It has been proposed (37) that this reflects an increasing 'molecular' character of the atomic structure in the sequence Sb, As, P, i.e.

stronger interactions within the pseudo-layer structure of the CRN and weaker interlayer or back-bonding interactions. This suggestion is supported by an increasing

Fig.8: Raman and infrared spectra for bulk a-P ((a) and (b)) and a-As ((c) and ( d ) ) (see text for references).

(9)

number of atoms contributing to the second peak of the corresponding RDFs, by an increasing fluctuation in bond angles and by a decreasing size of the first (a161-l) diffraction peak in the sequence P , As, Sb. Of interest is the observation that the Raman spectra of sputtered films of a-As and a-P (35,37) exhibit less structure than that of the bulk material although, for a-P at least, the higher the substrate temperature the closer do the spectra resemble that of the bulk. Again there is a correlation with the size and width of the first diffraction peak, implying a continuous evolution of intermediate-range order (interlayer correlations) with conditions of sample preparation.

Detailed consideration of the fine structure in the Raman and infrared spectra has not led to a unique assignment of the modes responsible. In particular the suggestion (38) that small peaks for a-As at 165cm-I and 280cm-I correspond to undercoordinated and overcoordinated atoms (As; and AS:) has been called into quest- ion by the observation (37) that the corresponding peaks in a-P at 300cm-I and 500 cm-' are either smaller or non-existent in the sputtered films which might be expected to contain a higher density of coordination defects than bulk material.

The overall shapes of the spectra do however suggest a division into optic- like and acoustic-like vibrational modes. Comparison with neutron-scattering data and calculations using the coordinates of CRN models support this division and provide information on the density of vibrational states, the coupling constants and the effective dynamic charge for these materials (see (9) and (37) for references).

Specific Heat and Ultrasonic Attenuation

-

The temperature dependences of specific heat below IK for bulk a-P and a-As are shown in figure 9. The corresponding variation for vitreous silicon is included for comparison. The axes of this plot (which

Fig.9: Variation of specific heat with temperature for a-P, a-As and a-SiOn.

(From reference 39 and W.A. Phillips, private communication).

includes unpublished data of W.A. Phillips) are chosen in order to see easily whether a variation of the form C = AT + B T ~ is appropriate. For a-Si02, and indeed many other glasses, the existence of the linear term, which dominates over the Debye term at lowtemperatures,has been taken to imply the existence of tunnelling states associated wlth, say, a small group of atoms tunnelling from one potential energy minimum to another. This leads to a low-temperature specific heat which is larger than that calculated from measured sound velocities (shown dotted in figure 9). ~ a r l i e r experiments on As (39) have bqen repeated, with the result that the specific heat is now believed to be slightly higher than that previously reported. Neverthe- less, the extrapolated intercept on the CT-I axis is considerably smaller than that for a-Si02. It has been suggested (39,40) that this may reflect the more rigid nature of the threefold coordinated structure (relative to that of Si02 or the

2halcogenides) which inhibits local rearrangements of groups of atoms. However, for

(10)

a-P there does appear to be a large contribution to the specific heat over and above that calculated from the sound velocities, although it will be noticed that the variation is certainly not linear on this plot. The interpretation of low-temperature specific heat measurements on amorphous solids generally, is not made easier by these results,and the nature of the tunnelling states remains a mystery.

Another unexplained result is the variation of ultrasonic attenuation with temperature shown in figure 10a (41). A composite resonator was used at 550kHz

Fig.10: Variation of ultrasonic attenuation and sound velocities for a-P and a-As.

(From reference 41).

to determine these data and those of the sound velocity in figure lob. The peak in the attenuation at about 25K for both a-P and a-As is similar to that observed in a-Si02 at ?. 40K, which has been interpreted again in terms of tunnelling states.

The ultrasonic wave biases the double-well potential and the relative population of the sites is a function of the temperature. The problem with a similar interpretation for threefold coordinated systems is that the density of centres is estimated to be % 1% of the number of atoms and it is difficult to identify what defects might be responsible. The number of undercoordinated atoms estimated from luminescence, ESR and other experiments, which in principle could provide the required centres, is too small. Impurities in these materials, which (apart from hydrogen < 1%) are nominally six-nines pure, also seem unlikely to be responsible. Microstructural defects, such as small pin holes in a-As (39) or the 5u spheres (26,41) in a-P mentioned earlier, should not scatter the lOmm wavelength ultrasound, although the

latter may be responsible for the higher background attenuation in a-P.

In summary, it is clear that, in contrast to some of the other results presented in this paper, the low-temperature phenomena described in this section are poorly understgod and further investigations will be required to interpret them.

Acknowledgements

-

The author is grateful to several authors for providing reprints and/or preprints of their papers.

(11)

JOURNAL DE PHYSIQUE

Ref e

- 1.

2.

'rences

GREAVES G.N. and DAVIS, E.A., Phil. Mag.

29

(1974) 1201.

DAVIS, E.A., ELLIOTT, S.R., GREAVES, G.N. and JONES, D.P., in "Structure of Non-Crystalline Materials" (Taylor and Francis Ltd. 1977) p205.

GREAVES G.N., ELLIOTT, S.R. and DAVIS, E.A., Adv. in Phys.

E

(1979) 49.

KELLY, M.J. and BULLETT D.W., Solid State Commun.

18

(1976) 593; Phil. Mag.

B38 (1978) 423.

POLED,

W.B. and JOANNOPOULOS, J.D., Phys. Rev. B

17

(1978) 1770.

O'REILLY, E.P. and KELLY, M. J., J. Phys. C. (1981 )

-

to be published.

MEEK, P.E., in "Structure of Non-Crystalline Materials" (Taylor and Francis Ltd.

1977) p25.

POLLARD, W.B. and JOANNOPOULOS, J.D., Phys. Rev. B

11

(1978) 1778.

DAVIS, E.A., WRIGHT, H., DORAN, N.J. and NEX C.M.M., J. Non-Crystalline Solids 32 (1979) 257.

SMITH, P.M. LEADBETTER, A.J. and APLING A.J., Phil. Mag.

2

(1975) 57.

BELLISSENT, R. and TOURAND G., J. Physique

37

(1976) 1423.

VEPREK, S. and BEYELER, H.U., Phil. Mag. (1981)

-

to be published.

DANIEL, M.F. and LEADBETTER, A.J., Phil Mag. (1981)

-

to be published.

BEYELER, H.U. and VEPREK, S., Phil. Mag.

41

(1980) 327.

PILIONE, L.J., POMIAN, R.J. and LANNIN, J.S., Solid State Commun. (1981)

-

^to

be published.

GREAVES, G.N., DAVIS, E.A. and BORDAS, J., Phil. Mag.

2

(1976) 265.

MOTT, N.F. and DAVIS, E.A., "Electronic Processes in Non-Crystalline Materials"

2nd edition (Oxford University Press 1979).

KIRBY, P.B. and DAVIS, E.A., J. Non-Crystalline Solids

35, 36

(1980) 945.

KIRBY, P.B. and DAVIS, E.A., in "Proc. 14th Int. Conf. on Physics cf Semi-- conductors" (Institute of Physics 1978) p1309.

DAVIS, E.A., in "Topics in Applied Physics" 36 (Springer-Verlag 1979) p41.

TAYLOR, P.G., FRIEBELE, E.J. and BISHOP,

solid

State Commun.

2

(1978) 247.

DEPINNA, S. and CAVENETT, B.C.,Solid State Commun. (1981)

-

to be published.

STREET, R.A., Phys. Rev. B 17 (1978) 3984.

SPEAR, W.E., LE COMBER, P . G ~ VEPREK, S. and WILD, R., Phil. Mag. B s (I 978) 349 ELLIOTT, S.R., DAVIS, E.A. and PITT. G.D., Solid State Commun.

2

(1977) 481;

ibid. 23 (1977) V.

EXTANCE ~ T a n d ELLIOTT S.R., Phil. Mag. B

42

(1981) 469, 485.

HAUSER, J.J., Phys. Rev. B

2

(1974) 2623.

ELLIOTT, S.R. and DAVIS, E.A., J. Phys. C.

12

(1979) 2577.

HAUSER, J.J., Phys. Rev. B

fi

(1975) 738.

MYTILINEOU, E. and DAVIS, E.A., in "Proc. 7th Int. Conf. on Amorphous and Liquid Semiconductors" (CICL, Edinburgh 1977), p632.

MYTILINEOU, E. and DAVIS, E.A., J. Non-Crystalline Solids 35, 36 (1980) 883.

LUCOVSKY, G. and KNIGHTS, J.C., Phys. Rev. B

10

(1974) 4 3 2 r - LANNIN, J.S. and SHANABROOK, B.V., Solid State Commun.

8

(1978) 497.

SHANABROOK, B.V. and LANNIN, J.S., Solid State Commun.

32

(1979) 1279.

LANNIN, J.S., Phys. Rev. B

5

(1977) 3863.

SHANABROOK, B.V. and LANNIN, J.S., in "Proc. 14th Int. Conf. on Physics of Semiconductors" (Institute of Physics 1978) p713.

SHANABROOK, B.V. and LANNIN, J.S., Phys. Rev. B (1981)

-

to be published.

NEMANICH, R.J., LUCOVSKY, G., POLLARD, W. and JOANNOPOULOS, J.D., Solid State Commun.

6

(1978) 137.

JONES, D.P., THOMAS, N. and PHILLIPS, W.A., Phil. Mag. 38 (1978) 271.

GOLDING, G., J. Non-Crystalline Solids,

2, 36

(1980) 1125.

GILROY, K.S. and PHILLIPS, W.A., J. Non-Crystalline Solids

21, 36

(1980) 1135.

O'REILLY, E.P. Phil. Mag. B

42

(1981) 579; O'REILLY, E.P. and KELLY, M.J.

J. Phys. C (1981)

-

to be published.

POLLARD,-W.B. and JOANNOPOULOS, J.D., Phys. Rev. B E (1979) 4217; Phys. Rev. B 21 (1980) 760.

-

44. JELLISON, G.E., PETERSEN, G.L. and TAYLOR, P.C., Phys. Rev. Lett.

42

(1979) 1413 ; Phys. Rev. B

2

(1980) 3903.