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The “trigonal chromium” in GaAs: A new no-phonon luminescence spectroscopy at 0.84 eV
0038-1098/82/390395-05503.00/0 Pergamon Press Ltd.
Solid State Communications, Vol. 44, No. 3, pp. 395-399, 1982. Printed in Great Britain.
THE "TRIGONAL CHROMIUM" IN GaAs: A NEW NO-PHONON LUMINESCENCE SPECTROSCOPY AT 0.84 eV J. Barrau, Do Xuan Thanh, M. Brousseau, J.C. Brabant, F. Voillot Laboratoire de Physique des Solides, Associ6 au CNRS, I.N.S.A., Avenue de Rangueil, 31077 Toulose-Cedex, France (Received 5 March 1982; in revised form 27 April 1982 by M. Balkanski)
New high resolution spectroscopy of the no-phonon luminescence at 0.84 eV in GaAs : Cr gives spectra of much higher quality than in previous works Lightowlers et al. [ 1]; Voillot et al. [2]. The associated energy level scheme shows some important differences with these preceding publications. These new experimental results lead us to the discovery of the adequate changes in the model.
1. INTRODUCTION THE WELL-KNOWN 0.84 eV luminescence in GaAs: Cr (Koschel et al. [3, 4]; Stocker et al. [5, 6] ; Lightowlers et al. [1] is now attributed to a trigonal centre. The first experimental evidence was presented by Killoran et al. [7] and Eaves et al. [8] independently. In a series of recent papers (Voillot et al. [2, 9, 10] ; Barrau et al. [ 11 ]) presented a new no-phonon luminescence spectrum with its splitting under uniaxial stress and proposed an interpretation of the different experimental results on the defect. This interpretation was based on a model in which transitions arise from a substitutional Cr2÷ ion on a Ga-site submitted to a perturbation of C3v symmetry. This perturbation is induced by an unknown defect present in the neighbourhood. The distinctive character of our model is that the trigonal interaction acts as a small perturbation, i.e. like the spin-orbit coupling on the vibronic SE and ST2 states which result from the effect of the cubic crystal environment on the lowest free-ion term 5D of Cr 2÷. Concerning the ground set of states ST2, this choice was discussed by Voillot et al. [10] and opposed to the other extreme hypothesis of a strong trigonal field, i.e. strong compared with the Jahn-Teller and spin-orbit couplings-adopted by Picoli et al. [ 11 ]. Two crude approximations were then adopted because they offered great advantages for hand calculations while preserving a rather coherent interpretation of most of the known experimental facts:
Fig. 1. Photoluminescence spectra in the phononless region recorded at different temperatures (lower resolution).
(i) The effective Hamiltonian describing the effect of the trigonal and spin-orbit perturbation within SE was reduced to the second order spin-orbit/trigonal mixed term; (ii) The effective Hamiltonian describing the effect of the trigonal and spin-orbit perturbation within ST2 was reduced to the spin-orbit first and second order terms and the trigonal effect was assumed so strongly
quenched by the T2@e Jahn-Teller coupling that it could be neglected. Some insufficiencies relative to the position of levels in SE, the oscillator strengths, the behaviour of the low-energy lines for stress parallel to [ 110], were noticed and ascribed to those simplifying assumptions. It was hoped that new experimental results would allow 395
D4 D~j~ A~ A~ B
I
B, B6B~]
l
e41
I
mPV
85
~
396
THE "TRIGONAL CHROMIUM" IN GaAs
Vol. 44, No. 3
L_L__L__I ~ _ . _ _ a _ _ _ ~ ~ A I A2
A3
A4
A5
A~
A7
/ C4
B I B2
B4
840
B5
B(3
B7
AI A2
A3
A4
859
A5
A6
A7
meV
Fig. 2. A photoluminescence spectrum at 4.2 K and at the middle resolution. Inset. A photoluminescence spectrum at 2 K and at the highest resolution. the introduction of the adequate improvements in the model. We have performed new high resolution luminescence spectroscopy on the no-phonon multiplet. The quality of the spectra is much higher than in previous works (Lightowlers et al. [ 1] and Voillot et al. [2]). We deduce the associated energy level scheme which shows some important differences with our preceding publication (Voillot et al. [2]). 2. THE EXPERIMENT The semi-insulating bulk materials come from three different Sumitomo's ingots. The position and the relative intensity of lines in the fine structure spectra are remarkably constant. The high resolution luminescence spectroscopy experiment is basically that described by Voillot et al. [2] but important improvements have been provided on the quality of optic, the choice of gratings and the signal treatment. A computer drives the experiment. The signal from the Northcoast Gedetector is digitalized and a suitable program achieves the rejection of noise and muon perturbations. The spectra displayed on Figs. I and 2 have been drawn by the graphic plotter connected to the computer output. The useful height of the slits of the Spex 1404 monochromator is 2 mm and the dimensions of the analysed sample surface is always smaller than
700 x 30/am. The intensity of the laser beam on the sample is typically 200 mW cm -2. Such experimental conditions ensure a good homogeneity of the observed region and a correct thermalization with the helium bath. The spectroscopic resolution is 0.01 meV and the measured G linewidth (FWHM) is 0.03 meV. Figure 1 shows spectra recorded at the lower resolution for different temperatures. Figure 2 shows the high resolution fine structure at 4K: this spectrum has been cut at 840.9 meV on the high energy side on which B' is missing and at 838.6 meV on the low energy side on which I is missing. Important new informations are gained. H and E are triplets. F and C are doublets. G also is a doublet (see the inset of Fig. 2). I is not resolved but is probably a multiplet. Comparatively, the J line is much more weak and broad and does not stand out clearly against the vibronic background: for this reason we now believe that it is most reasonable to maintain I in the no-phonon multiplet but throw back J into the vibronic wing. The present results lead us to a very sure energy level scheme. The hne naming adopted by Lightowlers et al. [ 1] appearing now very obscure we propose hereafter a most rational nomenclature in which a letter labels the initial level and a number the final level: correspondence with the preceding one is given in Table 1.
Vol. 44, No. 3
THE "TRIGONAL CHROMIUM" IN GaAs
397
Table 1. The observed lines in the no-phonon spectra. Their energy are given with respect to As: we determined for As the absolu te position: 839.18 -+ 0.06 meV. (As a consequence, the energy o f each line may be obtained by adding 839.18 meV to the energy given in the third column.) We mention in the first column the correspondence between the new nomenclature and that proposed previously by Lightowlers et al. [ 1] Relative position (meV)
Lightowlers' nomenclature
New nomenclature
F
A~ A2
0.215 -+ 0.005 0.163 -+ 0.005
0.054 0.057
G
As A4
0 -- 0.068 -+ 0.008
0.79 Small
H
As A6 A7
-- 0.345 -+ 0.008 -- 0.424 + 0.005 -- 0.513 -+ 0.005
0.016 0.046 0.035
I
A,n
-- 1.50 -+ 0.05
0.04
C
Bx B2
1.192 -+ 0.005 1.139 -+ 0.005
0.46 0.36
D
B4
0.909 + 0.005
0.10
Sum
Bs B6 B7
0.63 + 0.01 0.559 + 0.005 0.464 + 0.005
Small 0.48 0.60
--~ 2
E B'
C~
1.74 + 0.01
0.3
B
C4
1.46 + 0.01
0.7
A
Da
2.31
A"
Ds
2.04 -+ 0.05
Small
A'
E~
2.88 -+ 0.05
Undetermined
A"
E7
2.14 -+ 0.05
Undetermined
2.1. The ground set o f states A careful analysis of recordings at increasing temperatures unambiguously reveals that AxA2 (or F), AsA4 (or G), AsA6A7 (orH), A m (or I) are the cold lines. So, they have been recorded together - Am expcepted - at very high resolution and at 2 K shown in the inset of Fig. 2. As a consequence, the relative positions of these lines give exactly the energy level scheme of the ground set of states, Fig. 3. 2.2. The excited set o f levels The fine structure spectrum has been recorded at different temperatures between 4.2 and 14K: some of these recordings are reported on the Fig. 1. Very accurate thermal activation measurements of the intensity of the lines allow us to group the hot lines which have identical behaviour: this gives the following four groups: BI B2 B4 Bs B 6 BT. (It is a remarkable result that a shift by 0.980 meV of the cold part of the spectrum on Fig. 2 - A I to A7 gives exactly the position of this first set of hot lines
+ 0.02
Relative transition probability
Sum _~1
Sum ~'1
1 Sum --~1
with the exception that the replica of As which would be called Bs is not seen.) C1
C,
D4
Ds
E1
E7
So, the excited set comprises five levels. All the observed lines are then unambiguously positioned on a unique energy level scheme, Fig. 3. If the existence of additional levels at higher energy in the excited set cannot be completely excluded this seems to us unlikely: experiment at higher temperature reveals no new structure on the high energy side of the spectrum. On the other hand unmentioned hot transitions in the energy level scheme Fig. 3, may exist and probably do. But, on the contrary of cold lines which are now all seen, we are only able to detect the most intense among the hot lines the others being unavoidably lost in the broadened phononless emission. In Table 1, we give the position and the relative
398
THE "TRIGONAL CHROMIUM" IN GaAs
3
Vol. 44, No. 3
describes the fine splitting o f the ST2 ground set o f states to its pure spin-orbit terms, i.e. the terms in ~,/a, O hereunder, is a too drastic approximation. The trigonal field by itself adds a first and a second order term grouped into the c~-term hereunder - and a second order spin-orbit/trigonal mixed term - the/3 term hereunder. So, the complete effective Hamiltonian for the spinorder and trigonal interactions within the ST2 set of states takes the form [12]: 2 2 2 2 2 ~, Jfe~ = ~'IS +/a(lS) 2 + p(lxS~ + lySr + IzSz)
+ a [3 l~ -- l(l + 1)l + ~{ [3 l~ -- l(l + 1)l IS + lS[3l~ - l(l + 1)1}.
1 = (lx, ~, lz) - x, y , z denote the cubic axes - is an Hermitian effective orbital angular momentum operator defined in the basis o f the three vibronic states which belong to the T2 irreducible representation o f the Ta group; 1 lz = - ~ ( l x + l r + l z ) ;
Fig. 3. The new energy level scheme with the observed lines. The levels are now labelled by letters in the excited set and by numbers in the ground set (the level m is probably a multiplet). The relative positions are the following: 3 - 1 = 0.215 + 0.005 meV B - A = 0.980 + 0.005 meV 3 - 2 = 0.163 + 0.005 meV C - A = 1.53 -+0.01meV 4 - 3 = 0.068 + 0.008 meV D - A = 2.38 + 0 . 0 2 m e V 5 - 3 = 0.345 + 0.008 meV E - A = 2.66 -+ 0.05meV 6 - 3 = 0.424 -+ 0.005 meV 7 - 3 = 0.513 + 0.005 meV m - 3 = 1.50 -+0.01meV The cold lines are named AI A2 A3 A4 As An ATAm; the first hot lines Bx B2 . . . . Note that Ds and E 7 are not distinguished on the experimental spectrum. transition probability of each line. These probabilities are obtained directly from the product of the relative intensity by the Boltzmann factor.
herel= landS=2. The overall splitting gives ten levels. These ten levels may be found on the experimental energy level scheme for the ground set if we interpret the broader Am line as a triplet (As A9 Ato) due to the splitting of its final level. According to this interpretation, the trigonal field is accountable for the grouping of levels into (1, 2, 3, 4, 5, 6, 7) which belong to s/~ of Cav and (m = 8, 9, 10) which belong to SAt of C3v. The complete calculation shall be given in a separate paper. But we give here the f'mal result of the complete fit which takes the form o f the unique solution:* =-0.087meV; a = -- 0.384 meV;
0 = 0.193meV; the effect o f the/~ and fl terms is negligible.
If the interpretation o f Zeeman and uniaxial stress spectroscopy experiments given by Voillot et al. [2] and Barrau et al. [13] have now to be improved on the basis of this revised model we understand why the hypothesis of optical transitions between two sets o f slF (C3v) states could give to Eaves et al. [ 14] a valuable key for analysing their Zeeman spectroscopic data: indeed the final states of the optical transitions that the authors considered are all in the group o f ground states which belong to s/~ (C3v).
3. THE MODEL The novelty in those experimental results is mainly relative to the ground set o f levels, Fig. 3. It appears clearly now that the reduction of the Hamiltonian which
* According to the preceding simplified form o f the effective Hamiltonian - when ~eff was reduced to the ~',/s,p t e r m s - we found [10] p = 0.190meV, ~" = -- 0.050 meV and/a = -- 0.035 meV.
Vol. 44, No. 3
THE “TRIGONAL
CHROMIUM” IN GaAs
4. CONCLUSION
4.
We have obtained very good spectra of the nophonon luminescence at 0.84 eV from GaAs: Cr. The associated energy level scheme seems to us very sure. It allows the discovery of the convenient improvements in the model. Acknowledgements - The authors are very grateful to Dr C.A. Bates for interesting discussions on the problem of chromium in III-V compounds. This work was supported by Minis&e de la Defense, Direction des Recherches, Etudes et Techniques (D.R.E.T.).
9. 10.
REFERENCES 1.
2. 3.
E.C. Lightowlers, M.O. Henry & CM. Penchina, Proc. Int. Conf Phys. Semicond., Edinburgh, Inst. Phys. Conf. Ser. No. 43, p. 307 (1979). F. Voillot, J. Barrau, M. Brousseau & J.C. Brabant, J. Phys. Lett. 41,415 (1980). W.H. Koschel, S.G. Bishop & B.D. McCombe, Solid State Commun. 18.521 (1976).
11. 12. 13.
14.
399
W.H. Koschel, S.G. Bishop & B.D. McCombe, Proc. ht. Conf Phys. Semicond., Rome, p. 1065 (1976). H.J. Stocker & M. Schmidt, J. Appl. Phys. 47, 2450 (1976). H.J. Stocker&M. Schmidt,Prac. Znt. Conf Phys. Semicond.: Rome,p. 611 (1976). N. Killoran, B.C. Cavenett & W.E. Hagston,Proc. Semi-Insulating III- V Conf., Nottingham (1980). L. Eaves, T. Englert, T. Instone, C. Ulhlein, P. J. Williams & H.C. Wright, Proc. Semi-Znsulating III- V Conf , Nottingham (1980). F. Voillot, J. Barrau, M. Brousseau & J.C. Brabant, J. Phys. C: Solid State Phys. 14, 1855 (1981). F. Voillot, J. Barrau, M. Brousseau & J.C. Brabant, J. Phys. C: SolidState Phys. 14,572s (1981). G. Picoli, B. Deveaud & D. Galland, J. Phys. 42, 133 (1980). C.A. Bates, Phys. Rep. 35, 187 (1978). J. Barrau, F. Voillot, M. Brousseau, J.C. Brabant & G. Poiblaud, J. Phys. C: Solid State Phys. 14, 3447 (1981). L. Eaves, I. Englert & C. Ulhlein,Proc. O.Z.Z. Znt. Seminar. Hakone. Janan (1980).
Solid State Communications, Vol. 44, No. 3, pp. 395-399, 1982. Printed in Great Britain.
THE "TRIGONAL CHROMIUM" IN GaAs: A NEW NO-PHONON LUMINESCENCE SPECTROSCOPY AT 0.84 eV J. Barrau, Do Xuan Thanh, M. Brousseau, J.C. Brabant, F. Voillot Laboratoire de Physique des Solides, Associ6 au CNRS, I.N.S.A., Avenue de Rangueil, 31077 Toulose-Cedex, France (Received 5 March 1982; in revised form 27 April 1982 by M. Balkanski)
New high resolution spectroscopy of the no-phonon luminescence at 0.84 eV in GaAs : Cr gives spectra of much higher quality than in previous works Lightowlers et al. [ 1]; Voillot et al. [2]. The associated energy level scheme shows some important differences with these preceding publications. These new experimental results lead us to the discovery of the adequate changes in the model.
1. INTRODUCTION THE WELL-KNOWN 0.84 eV luminescence in GaAs: Cr (Koschel et al. [3, 4]; Stocker et al. [5, 6] ; Lightowlers et al. [1] is now attributed to a trigonal centre. The first experimental evidence was presented by Killoran et al. [7] and Eaves et al. [8] independently. In a series of recent papers (Voillot et al. [2, 9, 10] ; Barrau et al. [ 11 ]) presented a new no-phonon luminescence spectrum with its splitting under uniaxial stress and proposed an interpretation of the different experimental results on the defect. This interpretation was based on a model in which transitions arise from a substitutional Cr2÷ ion on a Ga-site submitted to a perturbation of C3v symmetry. This perturbation is induced by an unknown defect present in the neighbourhood. The distinctive character of our model is that the trigonal interaction acts as a small perturbation, i.e. like the spin-orbit coupling on the vibronic SE and ST2 states which result from the effect of the cubic crystal environment on the lowest free-ion term 5D of Cr 2÷. Concerning the ground set of states ST2, this choice was discussed by Voillot et al. [10] and opposed to the other extreme hypothesis of a strong trigonal field, i.e. strong compared with the Jahn-Teller and spin-orbit couplings-adopted by Picoli et al. [ 11 ]. Two crude approximations were then adopted because they offered great advantages for hand calculations while preserving a rather coherent interpretation of most of the known experimental facts:
Fig. 1. Photoluminescence spectra in the phononless region recorded at different temperatures (lower resolution).
(i) The effective Hamiltonian describing the effect of the trigonal and spin-orbit perturbation within SE was reduced to the second order spin-orbit/trigonal mixed term; (ii) The effective Hamiltonian describing the effect of the trigonal and spin-orbit perturbation within ST2 was reduced to the spin-orbit first and second order terms and the trigonal effect was assumed so strongly
quenched by the T2@e Jahn-Teller coupling that it could be neglected. Some insufficiencies relative to the position of levels in SE, the oscillator strengths, the behaviour of the low-energy lines for stress parallel to [ 110], were noticed and ascribed to those simplifying assumptions. It was hoped that new experimental results would allow 395
D4 D~j~ A~ A~ B
I
B, B6B~]
l
e41
I
mPV
85
~
396
THE "TRIGONAL CHROMIUM" IN GaAs
Vol. 44, No. 3
L_L__L__I ~ _ . _ _ a _ _ _ ~ ~ A I A2
A3
A4
A5
A~
A7
/ C4
B I B2
B4
840
B5
B(3
B7
AI A2
A3
A4
859
A5
A6
A7
meV
Fig. 2. A photoluminescence spectrum at 4.2 K and at the middle resolution. Inset. A photoluminescence spectrum at 2 K and at the highest resolution. the introduction of the adequate improvements in the model. We have performed new high resolution luminescence spectroscopy on the no-phonon multiplet. The quality of the spectra is much higher than in previous works (Lightowlers et al. [ 1] and Voillot et al. [2]). We deduce the associated energy level scheme which shows some important differences with our preceding publication (Voillot et al. [2]). 2. THE EXPERIMENT The semi-insulating bulk materials come from three different Sumitomo's ingots. The position and the relative intensity of lines in the fine structure spectra are remarkably constant. The high resolution luminescence spectroscopy experiment is basically that described by Voillot et al. [2] but important improvements have been provided on the quality of optic, the choice of gratings and the signal treatment. A computer drives the experiment. The signal from the Northcoast Gedetector is digitalized and a suitable program achieves the rejection of noise and muon perturbations. The spectra displayed on Figs. I and 2 have been drawn by the graphic plotter connected to the computer output. The useful height of the slits of the Spex 1404 monochromator is 2 mm and the dimensions of the analysed sample surface is always smaller than
700 x 30/am. The intensity of the laser beam on the sample is typically 200 mW cm -2. Such experimental conditions ensure a good homogeneity of the observed region and a correct thermalization with the helium bath. The spectroscopic resolution is 0.01 meV and the measured G linewidth (FWHM) is 0.03 meV. Figure 1 shows spectra recorded at the lower resolution for different temperatures. Figure 2 shows the high resolution fine structure at 4K: this spectrum has been cut at 840.9 meV on the high energy side on which B' is missing and at 838.6 meV on the low energy side on which I is missing. Important new informations are gained. H and E are triplets. F and C are doublets. G also is a doublet (see the inset of Fig. 2). I is not resolved but is probably a multiplet. Comparatively, the J line is much more weak and broad and does not stand out clearly against the vibronic background: for this reason we now believe that it is most reasonable to maintain I in the no-phonon multiplet but throw back J into the vibronic wing. The present results lead us to a very sure energy level scheme. The hne naming adopted by Lightowlers et al. [ 1] appearing now very obscure we propose hereafter a most rational nomenclature in which a letter labels the initial level and a number the final level: correspondence with the preceding one is given in Table 1.
Vol. 44, No. 3
THE "TRIGONAL CHROMIUM" IN GaAs
397
Table 1. The observed lines in the no-phonon spectra. Their energy are given with respect to As: we determined for As the absolu te position: 839.18 -+ 0.06 meV. (As a consequence, the energy o f each line may be obtained by adding 839.18 meV to the energy given in the third column.) We mention in the first column the correspondence between the new nomenclature and that proposed previously by Lightowlers et al. [ 1] Relative position (meV)
Lightowlers' nomenclature
New nomenclature
F
A~ A2
0.215 -+ 0.005 0.163 -+ 0.005
0.054 0.057
G
As A4
0 -- 0.068 -+ 0.008
0.79 Small
H
As A6 A7
-- 0.345 -+ 0.008 -- 0.424 + 0.005 -- 0.513 -+ 0.005
0.016 0.046 0.035
I
A,n
-- 1.50 -+ 0.05
0.04
C
Bx B2
1.192 -+ 0.005 1.139 -+ 0.005
0.46 0.36
D
B4
0.909 + 0.005
0.10
Sum
Bs B6 B7
0.63 + 0.01 0.559 + 0.005 0.464 + 0.005
Small 0.48 0.60
--~ 2
E B'
C~
1.74 + 0.01
0.3
B
C4
1.46 + 0.01
0.7
A
Da
2.31
A"
Ds
2.04 -+ 0.05
Small
A'
E~
2.88 -+ 0.05
Undetermined
A"
E7
2.14 -+ 0.05
Undetermined
2.1. The ground set o f states A careful analysis of recordings at increasing temperatures unambiguously reveals that AxA2 (or F), AsA4 (or G), AsA6A7 (orH), A m (or I) are the cold lines. So, they have been recorded together - Am expcepted - at very high resolution and at 2 K shown in the inset of Fig. 2. As a consequence, the relative positions of these lines give exactly the energy level scheme of the ground set of states, Fig. 3. 2.2. The excited set o f levels The fine structure spectrum has been recorded at different temperatures between 4.2 and 14K: some of these recordings are reported on the Fig. 1. Very accurate thermal activation measurements of the intensity of the lines allow us to group the hot lines which have identical behaviour: this gives the following four groups: BI B2 B4 Bs B 6 BT. (It is a remarkable result that a shift by 0.980 meV of the cold part of the spectrum on Fig. 2 - A I to A7 gives exactly the position of this first set of hot lines
+ 0.02
Relative transition probability
Sum _~1
Sum ~'1
1 Sum --~1
with the exception that the replica of As which would be called Bs is not seen.) C1
C,
D4
Ds
E1
E7
So, the excited set comprises five levels. All the observed lines are then unambiguously positioned on a unique energy level scheme, Fig. 3. If the existence of additional levels at higher energy in the excited set cannot be completely excluded this seems to us unlikely: experiment at higher temperature reveals no new structure on the high energy side of the spectrum. On the other hand unmentioned hot transitions in the energy level scheme Fig. 3, may exist and probably do. But, on the contrary of cold lines which are now all seen, we are only able to detect the most intense among the hot lines the others being unavoidably lost in the broadened phononless emission. In Table 1, we give the position and the relative
398
THE "TRIGONAL CHROMIUM" IN GaAs
3
Vol. 44, No. 3
describes the fine splitting o f the ST2 ground set o f states to its pure spin-orbit terms, i.e. the terms in ~,/a, O hereunder, is a too drastic approximation. The trigonal field by itself adds a first and a second order term grouped into the c~-term hereunder - and a second order spin-orbit/trigonal mixed term - the/3 term hereunder. So, the complete effective Hamiltonian for the spinorder and trigonal interactions within the ST2 set of states takes the form [12]: 2 2 2 2 2 ~, Jfe~ = ~'IS +/a(lS) 2 + p(lxS~ + lySr + IzSz)
+ a [3 l~ -- l(l + 1)l + ~{ [3 l~ -- l(l + 1)l IS + lS[3l~ - l(l + 1)1}.
1 = (lx, ~, lz) - x, y , z denote the cubic axes - is an Hermitian effective orbital angular momentum operator defined in the basis o f the three vibronic states which belong to the T2 irreducible representation o f the Ta group; 1 lz = - ~ ( l x + l r + l z ) ;
Fig. 3. The new energy level scheme with the observed lines. The levels are now labelled by letters in the excited set and by numbers in the ground set (the level m is probably a multiplet). The relative positions are the following: 3 - 1 = 0.215 + 0.005 meV B - A = 0.980 + 0.005 meV 3 - 2 = 0.163 + 0.005 meV C - A = 1.53 -+0.01meV 4 - 3 = 0.068 + 0.008 meV D - A = 2.38 + 0 . 0 2 m e V 5 - 3 = 0.345 + 0.008 meV E - A = 2.66 -+ 0.05meV 6 - 3 = 0.424 -+ 0.005 meV 7 - 3 = 0.513 + 0.005 meV m - 3 = 1.50 -+0.01meV The cold lines are named AI A2 A3 A4 As An ATAm; the first hot lines Bx B2 . . . . Note that Ds and E 7 are not distinguished on the experimental spectrum. transition probability of each line. These probabilities are obtained directly from the product of the relative intensity by the Boltzmann factor.
herel= landS=2. The overall splitting gives ten levels. These ten levels may be found on the experimental energy level scheme for the ground set if we interpret the broader Am line as a triplet (As A9 Ato) due to the splitting of its final level. According to this interpretation, the trigonal field is accountable for the grouping of levels into (1, 2, 3, 4, 5, 6, 7) which belong to s/~ of Cav and (m = 8, 9, 10) which belong to SAt of C3v. The complete calculation shall be given in a separate paper. But we give here the f'mal result of the complete fit which takes the form o f the unique solution:* =-0.087meV; a = -- 0.384 meV;
0 = 0.193meV; the effect o f the/~ and fl terms is negligible.
If the interpretation o f Zeeman and uniaxial stress spectroscopy experiments given by Voillot et al. [2] and Barrau et al. [13] have now to be improved on the basis of this revised model we understand why the hypothesis of optical transitions between two sets o f slF (C3v) states could give to Eaves et al. [ 14] a valuable key for analysing their Zeeman spectroscopic data: indeed the final states of the optical transitions that the authors considered are all in the group o f ground states which belong to s/~ (C3v).
3. THE MODEL The novelty in those experimental results is mainly relative to the ground set o f levels, Fig. 3. It appears clearly now that the reduction of the Hamiltonian which
* According to the preceding simplified form o f the effective Hamiltonian - when ~eff was reduced to the ~',/s,p t e r m s - we found [10] p = 0.190meV, ~" = -- 0.050 meV and/a = -- 0.035 meV.
Vol. 44, No. 3
THE “TRIGONAL
CHROMIUM” IN GaAs
4. CONCLUSION
4.
We have obtained very good spectra of the nophonon luminescence at 0.84 eV from GaAs: Cr. The associated energy level scheme seems to us very sure. It allows the discovery of the convenient improvements in the model. Acknowledgements - The authors are very grateful to Dr C.A. Bates for interesting discussions on the problem of chromium in III-V compounds. This work was supported by Minis&e de la Defense, Direction des Recherches, Etudes et Techniques (D.R.E.T.).
9. 10.
REFERENCES 1.
2. 3.
E.C. Lightowlers, M.O. Henry & CM. Penchina, Proc. Int. Conf Phys. Semicond., Edinburgh, Inst. Phys. Conf. Ser. No. 43, p. 307 (1979). F. Voillot, J. Barrau, M. Brousseau & J.C. Brabant, J. Phys. Lett. 41,415 (1980). W.H. Koschel, S.G. Bishop & B.D. McCombe, Solid State Commun. 18.521 (1976).
11. 12. 13.
14.
399
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