Manganese luminescence in GaAs/GaAlAs superlattices

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Manganese luminescence in GaAs/GaAlAs superlattices

This article has been downloaded from IOPscience. Please scroll down to see the full text article. 1986 J. Phys. C: Solid State Phys. 19 4279 (http://iopscience.iop.org/0022-3719/19/22/014) View the table of contents for this issue, or go to the journal homepage for more

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J . Phys. C: Solid State Phys. 19 (1986) 42794289. Printed in Great Britain

Manganese luminescence in GaAs /GaAlAs superlattices B Plot, B Deveaud, B Lambert, A Chomette, A Regreny Centre National d’Etudes des Telecommunications (LAB/ICM), 22301 Lannion, France

Received 2 December 1985, in final form 21 January 1986

Abstract. Luminescence transitions associated with manganese have been studiedin GaAlAs layers and GaAs-GaAIAs superlattices. In GaAIAs. manganese shows a behaviour characteristic of a centre that is partly deep and partly hydrogenic. In a superlattice, the ionisation energy of manganese increases as a function of the well width: it is 110 meV in GaAs. 132 meV in a 67 A well and 192 meV in a 13 8,well. The change in ionisation energy can be explained by taking into account both the ‘deep’and the hydrogenic character of manganese. Changes in ionisation energies are compared with theoretical calculations of the heavy hole confinement energy.

1. Introduction

A large number of studies have been devoted in the last fifteen years to deep level impurities in semiconductors. Among important deep levels, the transition metal ion centres have received a lot of attention because of their importance in device technology both as useful centres (e.g. chromium in GaAs or iron in InP) and as detrimental centres (nickel in Gap, Mn in GaAs), for a recent review, see for example [l].The description of the main properties of transition metal impurities in bulk III-V materials has now started to be very well documented. Theoretical descriptions are much less complete but the trends in experimental results are quite well reproduced by different models P-41.

Manganese is a widely occurring inadvertent doping species in III-V : Mn luminescence is very often observed in undoped InP showing a persistent contamination with Mn at a level close to 10’’ ~ 1 1 [75 ]~.In~ InP, Mn is a deep acceptor at 220 meV above the valence band. Mn related luminescence is also very often observed after heat treatments in GaAs. Two explanations have been proposed for the occurrence of manganese: redistribution from a low residual doping or pollution due to the manganese emission f r o q stainless steel, for further references see [6]. It happens that, in the same way, Mn can be a contaminating impurity in GaAsGaAlAs superlattices. In our case, this was due to some pollution of the gallium source so that we have grown a series of samples with a rather large doping concentration of ) . GaAs, Mn doping gives rise to a well known D-A pair manganese (-10’’ ~ m - ~In transition (or e-Ao transition depending on temperature and excitation density) [7]. This transition results in a sharp line at 1.409 eV with phonon replica (TA and LO) at lower energies. 0022-3719/86/224279

+ 11$02.50 @ 1986 The Institute of Physics

4279

4280

B Plot, B Deveaud, B Lambert, A Chomette and A Regreny

Apart from being an easily observed centre (the detection limit of the luminescence in GaAs is of the order of 1013~ m - and ~ ) from being an often occurring residual dopant, Mn has the very interesting property of showing both a deep lave1 characteristic and a quasi-hydrogenic behaviour. The deep level behaviour is characterised by the fact that, when referred to the vacuum level [8] the acceptor level (Mn2+/Mn3+)of manganese remains constant when changing the host from InP to GaAs or to GaP [9]. Also characteristic of a deep level behaviour is the shape of the infrared absorption. On the other hand the Mn centres in GaAs and InP show a set of sharp lines (either in the infrared absorption [9, 101 or in the selective luminescence [ l l ] ) corresponding to hydrogeniclike excited states. This shows that, outside the central core, the wavefunctions of a hole around a manganese centre almost look like hydrogenic wavefunctions. It has been recently suggested by Langer and Heinrich [12] that transition metal (TM) impurities might help to predict the band offsets between two compounds. This method does not require the study of a real superlattice (SL) or multiple quantum well (MQW) but only uses the study of the energy states of one particular TM (Fe in this case) in GaAs and in various GaAlAs alloys. This makes the study rather easy, but it needs the rather large assumption that the level to which the TM ions are fixed is the same as the level that governs the equilibrium at the interface between two different compounds. This is a very interesting proposition but it has to be checked by other experiments. However, the behaviour of a deep TM impurity inside a SL or a MQW shows that the active TM impurities will locate in the GaAs layer. Then as one deals with a deep level, and thus with a centre which gives rise to a highly localised potential one may at first assume that the deep level does not experience the existence of GaAlAs barriers unless it lies very close to the interface. In that case the band offset can be estimated from the distance of the unmodified deep level to the modified electron or hole level. If Langer's and Heinrich's statement [12] is true, the position of the level inside the well will be fixed. since the deep level will not be influenced by the proximity of the barrier. In this paper, we take the opportunity of the occurrence of an unwanted Mn pollution in our growth chamber to study the behaviour of manganese in MQW and SL over a large range of well widths (100 8, down to 13 A). In 9 2 we present the luminescence results that have been obtained on thick Mn doped GaAlAs layers. In 0 3 we describe the luminescence results obtained on our MQW samples, the binding energy will be shown to increase from 110 meV in bulk GaAs up to 192 meV in the case of a 13 8, large well. Section 4 is devoted to the discussion of the variation of the binding energy and to the comparison of this variation with different theoretical calculations. 2. Manganese luminescence in GaAs and in GaAlAs layers Mn gives rise in GaAs to a deep acceptor level 110 meV above the valence band. A lot of experimental studies have been devoted to that centre, in particular a strong luminescence band with a zero-phonon line at about 1.409 meV has been observed [7]. This luminescence band is shown in figure 1, it corresponds to a mixing of a D-A pair transition ( A being the manganese acceptor) and electron-acceptor transition. This centre has also been studied by infrared absorption [lo]. The photo-ionisation transition shows quite strong sharp lines demonstrating the quasi-hydrogenic behaviour of Mn although its binding energy is four times larger than the hydrogenic acceptor binding energy. + 6Al) is observed around 1.4 eV with In Gap, an internal transition of Mn2+(4T1

Manganese luminescence in GaAslGaAlAs superlattices

4281

Wavelength Ipmi

0.90

95

135

0.85

140

145

150

Energy l e v )

Figure 1. Luminescence spectrum of manganese in GaAs. The zero-phonon line at about 1.409 eV mixes D-A pair transitions and e-acceptor transitions. TA and LO phonon replica are evidenced.

a zero-phonon line at 1.55 eV [13]. The corresponding transition is not observed in GaAs, as expected, due to the fact that the 4T1excited state of Mn2+lies above the conduction band edge. This forbids the internal transition just as happens in the case of chromium [14]. One might expect that increasing the band gap by going to Gal-,A1,As layers with increasing aluminium content, will allow the observation of the internal transition of Mn*+above a given x . With that idea in mind, we have diffused a series of LPE GaAlAs layers of varying x with manganese. Diffusion is performed for 1h at 700 "C. A thin layer of Mn is flashed on the sample surface and then this sample is coated on both faces with sputtered Si3N4. Diffusion is then carried out in an open furnace with hydrogen flow. Two different luminescence structures are observed after diffusion (see figure 2) that are related to the manganese diffusion. A D-A-type, rather strong transition is observed close to the band edge. A very weak and very broad band, corresponding to an internal transition of Mn2+,is observed around 1.5eV. No zero-phonon line is observed contrary to what occurs in GaP [13]; this might be due either to a larger coupling to phonons or to alloy broadening effects. The zero-phonon energy would be larger than 1.6 eV. As the acceptor binding energy of Mn in GaAlAs with x 35% is about 160 meV, we only expect to observe the Mn2+internal luminescence when the alloy band gap is larger than 1.76 eV. In such a case the 4T1excited state of Mn is below the conduction band and the 4T1+. 6A, internal luminescence can be observed. As a matter of fact, we only observe the Mn2+internal transition in samples having an aluminium concentration larger than 34%.

-

4282

B Plot, B Deveaud, B Lambert, A Chomette and A Regreny Wavelength ipm)

1

0.70

0.75

0.80

0.65

I GaAs

15

LlO-AO

1.6

17

1.8

19

2.0

Energy (eV)

Figure 2. Luminescence spectrum of a manganese diffused GaAlAs layer ( x = 38%). Two structures are induced by manganese diffusion: a DA (or e-A) transition involving a manganese acceptor having a binding energy of 187 meV. A broad band beginning at 1.6 eV, due to the 7 ,+ 6A1internal transition of Mn2+is also observed.

As mentioned above, the D-A pair transition allows us to determine the Mn acceptor binding energy in the alloy. As an example, we obtain EM”= 167 meV for x = 34%. This shows that Mn cannot be considered as a hydrogenic acceptor: the effective mass for holes is typically changed by -10% whereas the binding energy of manganese is shifted by more than 50%. Such a behaviour can be understood if we recall that the transition metal ion acceptor binding energies are not related to the valence band edge, as usual acceptors are, but rather to what might be defined as some ‘internal vacuum level’ [8, 12, 131. This kind of behaviour is now quite well documented [8,3,9,12,15,16,17]and has allowed Langer and Heinrich [12] to propose the determination of the band offsets at the GaAs/GaAlAs interface by using a deep transition metal acceptor level (iron in that case) as a reference level. They obtained in this way a value which is now often proposed [18, 191:

AQ, = 66% - AQv = 34% where AQ, and AQv are the percentages of the energy gap difference giving rise to the potential barrier in the conduction bands and the valence bands respectively. As for other transition metal ions, the acceptor level of manganese seems to be pinned to the same ‘internal vacuum reference level’; in GaAs the binding energy is 110 meV, it is 220 meV in InP and 450 meV in Gap. This is true even if some of the properties of Mn in 111-V are ‘hydrogenic-like’. If we use the position of the manganese acceptor level in order to predict the band offsets at the interface between GaAs and GaAlAs, in exactly the same way as proposed by Langer and Heinrich [12], we find a very different result: the offsets would be

Manganese luminescence in GaAslGaAlAs superlattices

4283

predicted to amount to: AQ,

- 88%

AQ,

- 12%

This result is very different from the one obtained on Fe in GaAlAs. To our knowledge, Mn is the only transition metal ion whose level is not found to be fixed by the VRBE rule. Our results are in agreement with what has been found by Shantharama et a1 [20] in the GaInAsP alloys. This behaviour might perhaps be explained by larger hydrogenic effects, in the case of manganese, than for any other transition metal ion. As a summary of our results on manganese in GaAlAs, we have found the expected behaviour: the appearing of the 4T1+ 6A1Mn2+ internal transition for large enough aluminum contents. A large variation of the manganese binding energy is observed. However, this variation is not large enough to be accounted for by the 'internal vacuum level' to which transition metal impurities might be fixed. It seems that a certain amount of hydrogenic character has to be taken into account. 3. Experiments

Our samples are grown by molecular beam epitaxy (MBE) in optimised conditions. The high quality of our samples has been demonstrated in luminescence [21. 221. Pollution of the gallium oven by manganese occurred once so that a series of samples have been grown with a doping level of manganese above 10'' ~ m - The ~ . characteristics of these samples are displayed in table 1,the exact parameters Lz (well width), L , (barrier width) and x (aluminum content of the barrier) of each sample are determined using x-ray diffraction [23, 241. The manganese concentration is homogeneous over the whole structure due to the high diffusion coefficient of manganese at the growth temperature. The presence of manganese has been checked by SIMS measurements. Table 1. First hypothesis: the position of manganese inside the well is the same as in bulk GaAs. The increase between the binding energy in the bulk ( E R , = 110meV) and in superlattices (Eh,")is simply the confinement energy of holes (AEHHI).Comparison is made with EMA theoretical calculations.

AEHHltheory SampleNo

L;

LB(A)

x

,EMn

AEHH exp.

328 294 330 297 278 361 362

67 50 40 30 26 20 13

133 50 40 30 26 67 63

0.25 0.28 0.24 0.27 0.30 0.23 0.25

132 139 145 154 164 177 192

22 29 35 44 54 61 82

60-40

80-20

12 18 24 35 43 53 77

10 15 18 24 28 34 45

The luminescence of our samples is very intense and dominated by free exciton recombination (see the spectrum of sample No 297 (30-30 SL) in figure 3). Indirect excitation of the buffer layer by the SL emission is also observed. A very strong manganese related luminescence is observed coming from the buffer layer. On the contrary, luminescence from manganese in the superlattice is not observed in usual conditions. In

4284

ynU-[; B Plot, B Deveaud, B Lambert, A Chomette and A Regreny Waveiength lpm)

Buffer layer

-c

-

SL

I

)r

t c W + c -

1 14

17

16

15 Energy lev)

Figure 3. Luminescence spectrum of sample No 297 ( L ; = 30 A. LB = 30 A, see table l ) , under usual excitation conditions 100 mW cm-’) The spectrum is dominated by excitonic transitions of the superlattice structure Luminescence of the GaAs buffer layer. including Mn luminescence. is also observed This luminescence is excited by reabsorption of superlattice luminescence (2

090

Wavelength lpm) 0,85 080

la) e-Mn

075

I

l b ) e-Mn-sL

1

GaAs Buffer

14

15

16

Energy ieVl

Figure 4. Luminescence of a 40 A-40 8, superlattice ( a ) (Sample No 363) at very low power density (10 UWcm-2). Extrinsic luminescences are now favoured, see the transitions associated with shallow acceptors around 1.6 eV. The band edge transitions of the buffer layer are no longer observed and the e-Mn transition in the superlattice is evidenced. For comparison, ( b )shows the same luminescence in a 26 8,well (sample No 278). Luminescence from manganese in the buffer is still observed. ( c ) If the power density is lowered again Mn luminescence in the buffer is no longer observed.

Manganese luminescence in GaAsf GaAlAs superlattices

4285

order to observe extrinsic luminescences in superlattices it is necessary to lower the incident power [25];in the present case we had to use a power density of 10 to 100 pW cm-*. At these very low densities, the extrinsic transitions (e-Mn') are not saturated and can be observed (Mn' is the semiconductor notation, Mn3+would be the spectroscopic notation). At higher power densities, they are masked by excitonic and D-A transitions involving carbon atoms in the buffer layer. A typical luminescence spectrum at very low excitation power is shown in figure 4. This spectrum is obtained in a 40-40 SL (No 363), two manganese related structures are observed with almost the same intensity. Between 1.32 and 1.410 eV the e-Mno transition appears in the buffer layer and between 1.410 and 1S20 eV the e-Mno transition appears in the superlattice. Even for this very narrow well width, the two transitions look very similar and it is worth noticing that the linewidth is not much increased in the SL when compared to the buffer layer. On the same figure is shown the manganese luminescence in a 26-26 superlattice (No 278). Ionisation energy of Mn in the SL can then be deduced if we assume that we indeed deal with an e-Ao transition and if we know the binding energy of the exciton (we shall take the theoretical values given by different authors [25]). It is now admitted that D-A pair transitions disappear at low well width [26-281 so that the observed transition is indeed e-Mno rather than D-Mn'. Ionisation energies obtained in that way are reported in table 1.

E,,

= h v ( X ) - hv(Mn)

+ Ex

(see figure 5 )

where E,, is the manganese ionisation energy in the SL, h v(X)andhv(Mn) the respective energies of excitonic and e-Mno transitions and Ex the binding energy of the exciton. This ionisation energy is modified with respect to the bulk value (110 meV) it is 132 meV in a 67 8, wide well and increases up to 192 meV in a 13 8, wide well. It is to be stressed that the e-Mno transition does not evidence the dependence of

Conduction band Exciton

A

h

II

e-Mn

a Valence band

I GaAlAs I

I

GaAs

GaAs GaAlAs

Superlattice

GaAlAs Bulk GaAs

GaAlAs Superlattice

Figure 5. ( a ) First hypothesis: Manganese is a deep level and is not influenced by the potential barriers of GaAIAs. The ionisation energy in the well is simply the sum of the bulk binding energy EL, and of the heavy hole confinement energy AEHHl.( b ) Second hypothesis: a is included in order to take into account the increase of the hydrogenic correction AEhydro binding energy of the hole around the manganese centre.

4286

B Plot, B Deveaud, B Lambert, A Chomette and A Regreny

the ionisation energy E M n on the acceptor position in the well, as it is observed for usual acceptors (C or Be) [21,27,28]: the linewidth of the luminescence keeps quite close to its bulk value. We have also observed that the energy separation between the zero-phonon line and the LO phonon replica changes with well width from 36 meV in bulk GaAs to 32 meV in wells narrower than 30 A. In superlattices of very large gaps (for example a 30-30 GaAsAlAs, not presented in table 1)the e-Ao transition of manganese is replaced by a broad unstructured band corresponding to Mn2+internal transition. 4. Discussion

In a first hypothesis we shall assume that in order to interpret our results the acceptor level of manganese is the same in GaAs and in superlattices or multiple quantum wells (see figure 5 ( a ) ) . Manganese is a deep level and, being highly localised in space, should not be sensitive to the GaAlAs barriers. Furthermore, as the position of the manganese level in GaAs and in GaAlAs is almost the same, the influence of the barrier if it occurs should be very small. Of course, the only Mn centres active in luminescence are localised in the GaAs wells due to the very short trapping times of photo-excited carriers in the in the SL is wells [29]. As a result of this hypothesis, the ionisation energy of Mn (EMn) simply the sum of the bulk binding energy EL, and of the heavy hole confinement energy AEHH, (see figure 5(a)) EMn = EL,

+ AEHH,.

The luminescence of manganese could then be used to characterise the SL and directly obtain the confinement energy of the holes. This is very interesting as this measure would help to determine the valence band offset, directly inside the real structure of the superlattice. The confinement energy of heavy holes obtained in such a model is reported in table 1 and compared with theoretical values for two different band offset partitions (80-20 and 60-40). The theoretical confinement energy of heavy holes is calculated within the framework of the effective mass approximation (EMA) as proposed by Bastard [30]. It is apparent at once that the values corresponding to the largest wells cannot be fitted using this simple model. The origin of this discrepancy might be due to the fact that manganese shows for some aspects a quasi-hydrogenic behaviour (see the discussion in the first paragraph). A second hypothesis might then be used to describe the manganese: that is as a usual acceptor, introducing a locally modified effective mass m&,in order to fit the observed binding energy (110 meV). Such a hypothesis is not very physical but helps to understand our system. In such a hydrogenic case, the binding energy of manganese would behave as a usual acceptor (see for example the description given by Masselink et a1 [2]), with some scaling factor. The Bohr radius of a 110 meV hydrogenic acceptor in GaAs would be 9 A and so the dependence of the binding energy on the position of manganese should be evidenced for wells below 40 A. For usual hydrogenic acceptors a second luminescence peak occurs, corresponding to acceptors close to the interface, for well widths below 100 A [21,27,28]. As we do not have evidence for such a splitting or even for a large broadening in wells around 30 A, of the luminescence transition, we can safely reject this second assumption.

Manganese luminescence in GaAslGaAlAs superlattices

4287

The usual description of deep acceptors, such as manganese, uses the hydrogenic wavefunctions and the potential is perturbed by a delta potential centred on the impurity. The perturbed Hamiltonian is written:

X

h 2 k 2 e' 2m* Er

= -- -

+ bc?(r)

where all symbols have their usual meaning and b is the strength of the &potential which describes the central cell correction. The value of b is usually adjusted in first-order perturbation to fit the binding energy of the centre. The same procedure can be applied to manganese with the difficulty that the binding energy in that case is four times the binding energy of a hydrogenic acceptor [ l l ] . In order to get more precise results, we have written our Hamiltonian XMnin a matrix form and computed the eigenvalues and eigenvectors (over the first five s states). When b is adjusted to get the ionisation energy of 110 meV, we find:

i 1

8-1

x

8-1 8-1

2

27-'* 64-'

2

'

'

(8 x 27)-'

(8 x 64)-'

(8 x 125)-'

(27 x 64)-'

(27 x 125)-'

64-'

(64 x 125)

125-'12 (8 x 125)-'

(27 X 64)-"'

*

125

-'

64-'

(8X27)-12 27-' (8 X 64)-'

'

27-112

(27 x 125)-'12 (64 x 125)-1'2 125-I

-'

1

*

E:, being the energy of the ns states for a hydrogenic acceptor. So the new ground-state wavefunction is: qis = 0.95q1,

+ O.27q2, + 0.14q3, + 0.099;4, + O.O6q:,,.

This wavefunction is not very different from the q l Shydrogenic wavefunction of a hole around a usual acceptor such as carbon or beryllium. As aconsequence, we propose that the effect of a superlattice might be described in the following way: The level of manganese is almost constant in a superlattice with a small correction due to the fact that the bound hole around the manganese atom is sensitive to the potential well into which its wavefunction is confined. The confinement of the hole increases the binding energy in a way that may be estimated, in first approximation, similar to the increase observed for a usual acceptor [28]. This assumption would lead to the following expression for the binding energy of manganese in a SL (figure 5(b)). EMn

=

+ AEHHl + AEhvdro

where AEhydrois the increase of the binding energy of a hole around a hydrogenic acceptor. In any case, this correction is rather small (-10 meV) and the error induced by the fact that manganese is not a true hydrogenic acceptor should not be too large.

4288

B Plot, B Deveaud, B Lambert, A Chomette and A Regreny Table 2. Second hypothesis: we include a hydrogenic correction in order to take into account the increase of binding energy due to the confinement of the bound hole. AE,,,,, is taken from Masselink eta1 [27].

Sample No

L, (A)

E,,.," (mev)

AEHydro

Exp.

328 294 330 297 278 361 362

67 50 40 30 26 20 13

132 139 145 154 164 177 192

8 10 11 13 14 15 10

14 19 24 31 40 52 72

AEHH] KP 70-30 11 17 22 31 37 45 63

EMA

60-40

12 18 24 35 43 53 77

Experimental values of A E H H , obtained on the basis of this new assumption are compared with theoretical values in table 2. Two models have been used: the Kronig-Penney model [31] (KP)and the effective mass approximation (EMA)[30]. It is generally admitted that the EMA model is more physical than the KP one. However, we have shown [32] on a series of samples including those studied here that, whatever the band offsets, the EMA cannot fit the observed confinement energies in small period superlattices. Only the KP model is able to fit the luminescence transition energies (for excitons) but this model is not quite satisfactory. So we compare our experiments with both models keeping in mind that none of them is considered to be safe. The model which seems to be the most consistent is the KP model where our results are close to calculations with an offset partition of 70%-30%. Note that a fit of the exciton energy (giving the sum of the confinement energies for electrons ( A E E I ) and for heavy holes ( A E H H , ) ) would lead to an offset partition closer to 80%20% and a fit of the heavy hole, light hole exciton splitting to a value of about 75%25%. The use of the EMA model, despite the impossibility to fit A E E 1 + A E H H , , would rather give an offset partition of 60%-40%. As a consequence, we need a better model, suited to small-period superlattices, in order to get an offset value from our experiments. Finally, it is to be noted that the observed behaviour in a superlattice is consistent with what we have observed in a GaAlAs layer. Manganese in both systems behaves partly as a deep level and partly as a hydrogenic acceptor. As a consequence the true description of the ground state of this ion in the III-V compounds might be a mixture of Mn3+(3d4 configuration) and Mn2+ a hole bound.

+

5. Conclusion

We have studied by luminescence the behaviour of manganese in GaAlAs and in GaAs/ GaAlAs superlattices. In GaAlAs, the binding energy of manganese increases more rapidly than what would be expected for a hydrogenic acceptor, but less rapidly than what would predict the pinning of transition metal levels to some 'internal vacuum level'. + 6A2internal luminescence is observed. Above 34% of aluminum in GaAlAs the In a superlattice, the electron to acceptor transition of manganese is observed at ver low power densities. The binding energy of manganese increases from 132 meV (67 wide wells) up to 192meV (13 A wide wells). This change is explained by the confinement

1

Manganese luminescence in GaAslGaAlAs superlattices

4289

of holes plus a small hydrogenic correction. We are not able to give an estimate of the band offsets due to the fact that available models fail for very small period superlattices. Acknowledgments

The authors wish to thank G Dupas for his technical assistance in the growth of samples, P Auvray and M Baudet for x-ray characterisation of samples, R Chaplain and M Gauneau for SIMS measurements, J Y Emery for having grown some of the samples, G Picoli and G Bastard for helpful discussions and B Rolland for his help in computation procedures.

References [ l ] Clerjaud B 1985 J . Phys. C: Solid State Phys. 18 3615 [2] Hemstreet L A 1980 Phys. Rev. B 22 4590 [3] Fazzio A, Caldas M J and Zunger A 1984 Phys. Reo. B 29 5999; 1984 Phys. Reu. B 30 3430 [4] Picoli G , Chomette A and Lannoo M 1984 Phys. Reu. B 30 7138 [5] Eaves L, Smith A W, Skolnick M S and Cockayne B 1982J. Appl. Phys. 53 4955 (61 Yu P W and Park Y S 1979J. Appl. Phys. 50 1097 [7] Lee T C and Anderson W W 1984 Solid State Commun. 2 265 [8] Lebedo L A and Ridley B K 1982J. Phys. C: Solid State Phys. 15 L961 [9] Lambert B, Clerjaud B, Naud C, Deveaud B, Picoli G and Toudic Y 1985 J . Electron. Mater. a 14 1147 101 Chapman R A and Hutchinson W G 1967 Phys. Rev. Lett. 18 443 111 Plot B, Deveaud B, Rupert A and Lambert B 1985J. Phys. C: Solid State Phys. 18 5651-7 121 Langer J M and Heinrich H 1985 Phys. Rev. Lett. 55 1414 131 Vink A T and van Gorkom G G P 1972J. Lumin. 5 379 141 Deveaud B, Picoli G , Lambert B and Martinez G 1984 Phys. Reu. B 29 5749 151 Caldas M J , Fazzio A and Zunger A 1984Appl. Phys. Lett. 45 671 [16] Rojo P, Leyral P, Nouailhat A, Guillot G , Lambert B, Deveaud B and Coquille R 1984 J. Appl. Phys. 55 395 [ 171 Clerjaud B, Naud C, Deveaud B, Lambert B, Plot B, Bremond G, Benjeddou C, Guillot G andNouailhat A 1985J . Appl. Phys. 56 4207 [18] Miller R C, Kleinman D A and Gossard A C 1984 Phys. Reu. B 29 7085 [19] Bastard G, Delalande C, Meynadier M M, Frijlink P M and Voos M 1984 Phys. Reu. B 29 1042 [20] Shantharama L G , Adams A R, Allen E M and Green P D 1984 Proc. 11th Int. Symp. on GaAs and related compounds (Biarritz) 1984 (Inst. Phys. Conf. Ser. 74) [21] Deveaud B, Emery J Y, Chomette A, Lambert B and Baudet M 1984Appl. Phys. Lett. 45 1078 [22] Deveaud B, Regreny A , Emery J Y and Chomette A 1986J. Appl. Phys. 59 1633 [23] Segmuller A, Krishna P and Esaki L 1977J. Appl. Cryst. 10 1 [24] Kervarec J , Baudet M, Caulet J, Auvray P, Emery J Y and Regreny A 1984J. Appl. Cryst. 17 196-205 (251 Greene R L and Bajaj K K 1983 Solid State Commun.45 831 [26] Lambert B, Deveaud B, Regreny A and Talalaeff G 1982 Solid State Commun. 43 4432 [27] Miller R C, Gossard A C, Tsang W T and Munteanu 0 1982 Phys. Reu. B 25 3871 [28] Masselink W J, Chung-Chang Y C and Morkoc H 1984J. Vac. Sci. Technol. B 2 376 [29] Erskine D J , Taylor A J and Tang C L 1984Appl. Phys. Lett. 45 54 (301 Bastard G 1981 Phys. Reu. B 24 5693 [31] Combescot A and Benoit & L aGuillaume C 1981Solidstate Commun. 39 651 [32] Chomette A, Deveaud B, Regreny A, Auvray P and Baudet M Preprint

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