Magnetoluminescence in layer compound GaSe

Journal of Magnetism and Magnetic Materials 11 (1979) 143-145 © North-Holland Publishing Company

MAGNETOLUMINESCENCE IN LAYER COMPOUND GaSe Yoshiro SASAKI and Yuichiro NISHINA Research Institute for Iron, Steel and Other Metals, Tohoku University, Sendai 980, Japan

Received 4 August 1978

Magnetoluminescence of GaSe is investigated with a split-type superconducting solenoid at 4.2 K up to 10 T. The magnetic field dependence of the spectra between 2.05 and 2.10 eV indicates that most of the sharp lines originate from a complex of a triplet state of an indirect exciton and an ionized impurity.

The layer compound GaSe has a highly anisotropic crystal structure. The direct (Exa) and indirect (Eix) exciton edges lie very closely in energy (E d = 2.109 eV [ 1 ], Eix --~ 2.10 eV [2]). Furthermore, both the highest valence band and lowest conduction band are not degenerate even in the single group representation. No spin-orbit splitting exists at the fundamental edge. The behavior of the direct free exciton (DFE) in magnetic fields has been investigated in detail by Mooser and Schliiter [1] and by Brebner [3]. They suggest that the Zeeman splitting of the exciton can be explained in the L - S coupling scheme [1 ]. In the photoluminescence (PL) spectra at low temperature, many sharp lines are observed [4]. The lifetime and spectral analyses [2] show that the lines in the range from 2.05 to 2.10 eV are caused by the annihilation of the indirect bound exciton (IBE) with or without emission of a phonon. The origin of the exciton binding, however, has not been clarified in the experimental works published so far. It is the purpose of this paper to show with the application of high magnetic field that the observed IBE lines originate from indirect excitons bound to ionized impurity centers (I± xind), but not to neutral impurity centers (I o xind). The PL measurements in a magnetic field up to 10 T were performed in a split-type superconducting solenoid with horizontal bore. The sample was rota-

ted about the vertical axis through the gap so that the magneto-optical measurements were performed both in the Faraday and Voigt configurations. The sample was obtained by cleaving an ingot grown by the Bridgman method. It was immersed in liquid helium. The 488 nm beam of an Ar-ion laser irradiated the cleaved surface of the crystal. Fig. i shows a typical PL spectrum of GaSe at 4.2 K. The notations of the lines are as follows. DFEt: Triplet states of DFE, where the splitting

,

GaSe

i

i

i

|

4.2 K E~_c. H:O

~5 z~4

i ~

15

I211 zr

rll

i

i

i

^I 4

/~1

i

oFEt

I2-MCl I 13-MCI I I , I

~

15

(f :l,,

2.06

2.07

.......

2.08 2.09 PHOTON ENERGY (eV)

2.10

2.11

Fig. l. Photoluminescence spectrum of GaSe at 4.2 K. The notations are explained in the text. 143

144

Y. Sasaki and Y. Nishina / Magnetoluminscence in GaSe

of the lines is due to the stacking fault [5]. I i (i = 1 to 5): Zero-phonon lines of IBE. I i - M C I : Momentum conserving phonon replica of the I i line with the phonon energy of 14.1 meV. Fig. 2 shows the PL spectra o f the 15 line in the magnetic field of 8 T, where the background of the spectra has been subtracted. In the Faraday configuration for H II c, the I i lines are found nearly in circular polarization, and in the Voigt one for H l c they are nearly in linear polarization. The diamagnetic shift of the I i line has not been detected, and only a linear Zeeman splitting as shown fig. 2 has been observed. The experimental result of the Zeeman splittings on the DFE and the Ii lines are summarized in fig. 3, which also shows the Zeeman splitting pattern of DFE and IBE obtained from the following theory. The DFE state has been analysed theoretically by Mooser and SchliJter [ 1 ] according to SchliJter's band model [6]. The valence band maximum and the conduction band minimum at the P point have the symmetries of F 1 and P4, respectively [7]. The direct exciton consists o f the singlet, F,], and o f the triplet states, P t + F'~. The [',] exciton is dipole-allowed for E II c, and the F~ exciton is weakly (about l 0 - 2 of the F,] exciton) allowed for E I c by the s p i n - o r b i t interaction. The l' t is

I

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I

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4.2 K, H=8T.

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-

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DFE EXP. THEORY

oTr

(2-+ g~,r..= Ige,+(:Jt.d = 2.6-.I-0.1

g,rTr = Ige~ gl.ul = 2.05-1-0.15

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I I toi 5 lines

~ - - ~ " ~ ao-+-t- bo-_ EXP.

~

a / b = 5 to I0 CJo-o-=3.65+_0.1

arr+boao-+ bTr art+bo-

a/b=3_+0.5 g.,.~ 3.25+0.15

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THEORY

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g,ro-=lge+gh I , g.,r~lge--gh I IFE & THEORY

-

-

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~

o" o-

g(ro-=lge, +gh, I

IIC aTr+boao-+brr a l b = 3 ~ aTr+bcr

/

g~r~- = I ge.L+ghj_ I

Fig. 3. Zeeman splitting of the direct exciton and the indirect bound excitons. Notations like ga+o_ imply that the energy difference E(o+) - E ( o _ ) = ga+o_#BH. The formula aa + blr indicates that the state decays with the probability a for o polarization and with b for n polarization.

I

( b ) HJ..C

I

SPLITTING HJ..C

E.LC

FARADAY

I

ZEEMAN HIIC

I

2.100 2.098 2.100 PHOTON ENERGY ( e V )

Fig. 2. Zeeman spectra of the 15 line at 4.2 K in the magnetic field of 8 T for the following configurations: (a) the Faraday configuration with H II c, and (b) the Voigt configuration with / t 1 e. Arrows indicate the position of the I s line in zero field. Similar results have been obtained for the lines I l through 14 and their phonon replicas. The vertical scale is arbitrary, and not identical for both configurations.

dipole forbidden. In a magnetic field, the triplet exciton splits into three lines. In the PL spectrum of DFE, two lines observed in the Faraday configuration with H JJ c are circularly polarized, while in the Voigt configuration w i t h / / 1 c the two outer components are polarized in zr and the central one in o. The Zeeman splitting of DFE is shown in the top section of fig. 3 together with estimation o f respective g-values which are in good agreement with those reported in refs. [1] and [3]. The experimental result o f the I i lines are summarized in the second section of fig. 3. As one finds in figs. 2 and 3, the splitting pattern of the Ii lines is very similar to the DFE t line except for the purity of the linear and circular polarizations. For the case H It e, the degree o f circular polarization depends on the line. The value a / b is about 10 for the Is line

Y. Sasaki and Y. Nishina /Magnetoluminscence in GaSe

and about 3 for the lines 11 through I 3 corresponding to the degree of circular polarization Pc = (a - b)/(a + b) = 0.8 to 0.5 respectively in the high field limit. On the other hand, for H 1 c, a/b 3 + 0.5 independent of the lines. In the strong field limit, the linear polarization P2 ~- 0.5. The g-values of the I i lines are slightly larger and more isotropic compared to DFE as shown in fig. 3. As stated before, the I i lines have been assigned as IBE, but it is not clear whether they are due to (I O X ind) or to (I± xind). Since the conduction band minimum at the off zone-center exists at the M point (C2v) [6] and belongs to M s in double group representation (or to nondegenerate M 2 in single group representation) and the valence band maximum to P7, both valence and conduction bands can be denoted as (½, +-~). Then the Zeeman splitting of (Io X ind) is obtained easily as shown in the third section of fig. 3, where the line is shown to split into four in any field direction, and where the outer two components are polarized in o for the same sign ofge and gh. Multiplicity o f line splitting and the polarization for H 1 c contradict with the experimental result on the I i lines. In the case of (I± xind), the Zeeman splitting is expected to be very similar to that of the indirect free exciton (IFE) [8]. Since the conduction band minimum at M and the valence band maximum at P are non-degenerate, the L - S scheme offers a good approximation for IFE. In this scheme, the IFE consists of a singlet M~ and of a triplet Mt + Mt + Mt . We choose the bases for IFE as r'~ ~ M~, p t _~ Mt and (pt6+ + F t _ ) -~ M t and Mt , as expected from the k • p approximation, where 1-'~± indicates the two components in the r 't doublet. Then the Zeeman splitting is expected as shown in the last section of fig. 3. The calculated Zeeman splitting pattern agrees well with the experimental result. The theoretical result explains also the polarization of the split lines in t h e / / 1 c configuration but is inconsistent with the circular polarization observed

145

in H II c. From the discussion stated above, the I i lines are attributed to the triplet state of (I_+ xind). Quite recently, the I i lines have been assigned as triplet states from the measurements of the optically detected ESR [9].

Acknowledgements The authors would like to thank Prof. T. Goto and Dr. N. Kuroda for valuable discussions, and Prof. K. Morigaki for sending a preprint before publication. The authors also thank T. Nihei and K. Yamaguchi for their assistance in the experiments. This work was supported in part by the Grant-in-Aid for Scientific Research from the Ministry of Education (1977). One of the authors (Y.S.) wishes to acknowledge the Sakkokai Foundation for financial support.

References [1] E. Mooser and M. Schliiter, Nuovo Cimento 18B (1973) 164. [2] N. Kuroda and Y. Nishina, Phys. Stat. Sol. (b) 72 (1975) 81. [3] J.L. Brebner, Can. J. Phys. 51 (1973) 497. [4] J.P. Voitchovsky and A. Mercier, Nuovo Cimento 22B (1974) 273. [5] N. Kuroda and Y. Nishina, Nuovo Cimento 32B (1976) 109. [6] M. Schliiter, Nuovo Cimento 13B (1973) 313. Note that e-GaSe, usually grown by the Bridgman method, belongs to D3h, while Schliiter's calculation is performed for 3-GaSe which belongs to D6h. The notations, therefore, in the present paper (D3h) are different from Schliiter's. [7] We follow the notation used in G.F. Koster, J.O. Dimmock, R.G. Wheeler and H. Statz, Properties of the Thirty-Two Point Groups (MIT Press, Cambridge, MA, 1963). [8] D.G. Thomas and J.J. Hopfield, Phys. Rev. 128 (1962) 2135. [9] P. Dawson, K. Morigaki and B.C. Cavenett, to be published in Proc. 14th Int. Conf. on Physics of Semiconductors, Edinburgh, 1978.