Fine structure of indirect exciton in GaP

Solid State Communications, Vol. 24, pp. 801—803

,

1977. Pergamon Press. Printed in Great Britain

FINE STRUCTURE OF INDIRECT EXCITON IN GaP M. Caplzzi°, F. Evangelistit*+, P. Fiorini°, A. Frova~, and F. Patella~* °Istituto di Fisica, tJniversità di Roma, Rome, Italy tIBM Thomas J. Watson Research Center, Yorktown Heights, NY 10598 (USA) ~Istituto di Fisica, Università di Modena, Modena, Italy (Received 30

September 1977 by F. Bassani)

Wavelength modulation spectra of the is indirect exciton in GaP are reported. Four lines are found which can be easily explained taking into account the “Ca mel’s back’ structure of the conduction band. An exciton splitting of 0.9 meV ±0.2 has been measured.

Detailed theoretical calculations, extensive studies of electron—hole 11— quid and better quality of materials have raised increasing interest in the fine structure of indirect excitons in Si, Ge and GaP. In the former two materials a very good agreement between theory and experiments has been reached and the excitonic properties have been under stood in fine detail ~ GaP represents a notable exception. Early absolute mea surements showed two thresholds in ad dition to the lowest energy one, while theoretical calculations predict only a doublet of twofold degenerate levels. Very recently, it has been suggested that the conduction band minima are not at the X edge, but slightly inside the Brillouin zone, giving rise to the so— called “camel’s backflk~ . Support for this hypothesis comes from cyclotron resonan 6and ce ~, bound-etciton luminescence nonlinear optics ~. Although this conduction band shape is not expected to modify the two—level splitting of the exciton, a detailed optical measurement should be able to detect structures introduced by the different topological configuration in the density of states. To this purpose, we have performed wavelength—modulation absorption measu— rements on a series of GaP samples, urn— mersed in superfluid He. Wavelength mo— dulation was achieved by a thin quartz shOe, vibrating in front of the exit slit of a McPherson monochromator (1 in. focal length). The instrumental resolu— tion of 0.8 A was smaller than the natu— ral broadening of the lines. The trans— mitted intensity I and its derivative ~I/

6 p TO

.

I

2.375

I

2.380

LA

2.360

‘

PHOTON Fig. 1.

2.365 ENERGY (eVi

Wavelength derivative spectra of excit’onic transition assisted by the emission of one TO and one LA phonon respectively.

~ were separately recorded. To distinguish between intrinsic effects and possible extrinsic contributions from nearby bound exciton transitions, sam— pies of various growth and different ins purity content have been used. In Fig. 1 typical spectra of the phonon assisted excitorsic transitions

Permanent address: Istituto di Fisica dell’Universitã di Roma, Rome, Italy. +

K

Al$o at~Istituto ~i Fisica deii’UniversitA di Camerino, Camerino, Italy. 801

802

FINE STRUCTURE OF INDIRECT EXCITON IN GAP

are shown. One LA and one TO phonon emission are reported. The TA phonon gives essentially the same result. Its Lineshape is however more complicated ~nd sensitive to the impurity content of the sample because of a bound exciton

Vol. I

(a)

~

~ w -16

z w

transition which is very close in ener— gy. The intrinsic nature of the structu roe shown is supported by the following

Z -lB

observations. They start and lie just above the threshold of the free exciton transitions in the absolute absorption. Furthermore, they coincide in energy with the fine structure first observed by Dean and Thomas in the absorption measurements of exceptionally perfect”

0

energy side of each phonon replica and it does not vary from sample to sample, except for minor changes related to the perfection of the crystal. The strength of the observed extrinsic transitions is,

exciton transition is hineshape very to different. content. as expected, Finally, very the sensitive impurity of bound In fact, due to the Lorentzian shape of the absorption coefficient, these latter transitions exhibit a positive maximum followed by a negative minimun in derivative spectroscopy. Four lines are present in every ex citonic transition. As mentioned earlier, evidence of fine structure had been found previously 3. Only in two absolute subcomponents absorption have mea surements been detected in addition to the transi— tion threshold, very likely because the two intermediate structures are closely spaced and hard to resolve in a non-den vative experiment. The fourfold degenerate is indirect exciton state in GaP is split in two hevels by the conduction band anisotropy. Exchange interaction between the electron and the hole could in principle re move the twofold degeneracy of each le— vel giving rise to four states. However this effect is too small in covalent and Ill-V semiconductors be experimental8 and it to cannot explain the ly observable structure of Fig. 1, where separations of ‘~ 1 meV or more from one peak to the other exist, The existence of the camel’s back” structure in the conduction band can easily account for the experimental re— 2 sults.investigated have Very recently, the Altarehli influence of et al the camel’s back on the excitonic spectrum

i

0,03 k~(2i,-/a)

M iQ~~ 0.06

_____________

single crystals at 1.6 K. Moreover, their strength far exceeds that of the extrinsic structures present in the low

24, No. 12

(b)

(c) M

CI) Ui

1 Ui o

u~ 0

/ 7 -~

M~

/

M0 Ec

Fig. 2.

z 0

i~

I—

z

0

0 2 ENERGY (meV)

0 U) d 4

(a) Dispersion curves of the two excit onic levels in GaP as calculated in Ref. (9). The zero energy is the exciton ion— ization level. Kz is measured from the X point. (b) Schematic sity of states representation near M~j and N of the den 1 critical points. Er is the energy of the singular ity. (c) Qualitative behaviorfor of transition the absolute obsorption coefficient to the levels of section (a).

and found four critical points in its density of states. In Fig. 2(a) their calculated dispersion curves for the in direct exciton in the A direction of the Brillouin zone are presented. At the zo— ne edge the two excitonics bands have ne gative curvature in the longitudinal di— rection, while the curvature is always positive in perpendicular Therefore there are two M directions. 0 critical points at the minima of the exciton di— spersion and two M1 critical points at the zone edge. For clarity, we have sketched in Fig. 2 the qualitative con— tnibution of each critical point to the density ption coefficient of states which and the is absolute approximately absor proportional to the density of states. A wavelength derivative clearly will re—

Vol. 24, No. 12

FINE STRUCTURE OF INDIRECT EXCITON IN GAP

suits in a four lines structure in agre— ement with the experimental findings. The exact determination of the critical point energies is not easy. In fact, the derivative gives an asymmetri— cally shaped curve with an infinity at each critical point, which the intrinsic lifetime broadening tends to smooth off. Therefore a hineshape analysis is necessary to determine the excitonic splitting t~E and the width of the exci ton branches. We find AE=0.9±0.2mev which is in very good agreement with the estimated one. The distances~M 0to M1 are found to be~1= 2.5±0.3meV and = 3.9 ±0.3meV for the lower and the upper branch respectively, which are to 9 be = compared 3.0 meVwith and the L~ theoretical values 2 = 3.4 meV. In conclusion we report wavelength modulation spectra of the is indirect ex

citon in GaP. We observe a fine structure of four peaks, not three as previously inferred from absolute absorption measurements. The data can be interpre— ted in a straightforward manner by assu ming a “camel’s back” structure for the conduction band, thus giving strong su~ port to this hypothesis. We have also been able to determine experimentally for the first time the excitonic split— ting and the width of the exciton disper sion branches. ACKNOWLEDGEMENTS - The authors are grateful to M. Altarelli and N.0. Lipari for making available their results before publication. Stimulating discus— sion with hedged. WeN.0. also Lipari thank R.A. are also Logan, acknow— Bell Labs., for providing some of the samples used in the measurements.

REFERENCES

1.

2.

3. 4. 5.

6. 7. 8.

9.

ALTARELLI M. and LIPARI N.0. in “Proceedings of the XIII Conf. on the Physics of Semicon.” Ed. Fumi, Rome (1976), p.811. LIPARI N.0. and ALTAREL LI M. •Phys. Rev. P4 15, 4883 (‘1977). FROVA A., THOMAS G.A., MILLER R.E., and KANE E.O., Phys. Rev. Lett. 34 1572 (1975). CAPIZZI M., MERLE J.C., FIORINI P., and FROVA A. Solid State Commun., in course of publications. DEAN P.J., and THOMAS D.G., Phys. Rev. 150, 690 (1966) LAWAETZ P., Solid State Commun. 16, 65 (1975) LEOTIN J., OUSSET J.C., BARBASTE R., ASKENAZY S., SKOLNICK M.S., STRADLING R.A., and POIBLAUD C., Solid State Commun. 18, 363 (1975). SUZUKI K., and MIURA N., Solid State Commun. 18, 233 (1976). DEAN P.J. and HERBERT D.C., Journal of Luminescence 14, 55 (1976) GIBSON A.F., KIMMITT M.F., KOTHARI S., HATCH C.B., and SERAFETINIDES A., Appl. Phys. Lett. 30, 36 (1977) The effect of exchange interaction on the exciton spectra has been investigated by many authors ( e.g. K. Cho et al., Phys Rev. B 11, 1512 (1975)) and found to be small. More recently E.O. Kane and C. Morgan have found few hundredths of meV for the exchange interaction in Silicon. The binding energy and Bohr radius of excitons in GaP are very siesilar to those of Si and therefore one expects that the exchange interaction is equally unimportant here. ALTARELLI M.,

SABATINI R.A.,

803

and LIPARI N.0.,

to be published.