Energy band parameters of gallium antimonide

776

TECHNICAL

NOTES

3. WILD R. L. and ARCHER R. D., Bull. Am. Phys. Sot. Ser. II, 440 (1962). 4. McGUlRE T. R. and SHAFER M. W.,J. appl. Phys. 35,984 (1964). 5. B&TCHER C. J. F., Theory of Electric Polarisation, p. 417. Elsevier, Amsterdam (1952). 6. MULLIN J. H. and LAWSON A. W., Private communication.

J. Phys. Chem. Solids

GaSb
-

Vol. 30, pp. 776-778.

4

Energy band parameters antimonide

of gallium PHOTON

(Received 2 February 1968; in revisedform 19August 1968)

PRESENT paper concerns the determination of the energy band parameters of GaSb from the magneto-absorption data obtained by Zwerdling ef al.[l]. The calculation of energy levels in a magnetic field is carried out by using the method of Pidgeon and Brown [2], which includes the effect of the interaction between conduction and valence bands. The assumption of the spherical symmetry of the valence band has been made and exciton effect[3] has been neglected. We made a theoretical assignment in terms of only the principal allowed (An = O,-2) Landau transitions. In Figs. 1 and 2 are shown the experimental spectra obtained by Zwerdling et a1.[1]. The theoretical transition energies and relative strengths of the allowed transitions, calculated by us, are shown in Table 1 and beneath the spectra of Figs. 1 and 2. The following final set of parameters was obtained for a good fit of the experimental spectra: THE

P2 = 0.384 atomic units; K =

2.7;

y1 =

E, = 0.813 eV;

14.5;

7 = 4.5;

A = 0.81 eV

ENERGY

(sv)

Fig. 1. Plot of the ratio of transmitted intensity with the magnetic field to that without field, Z(H)/1(0), against photon energy for E _LH polarization. The theoretical positions and relative strengths of the allowed transitions are shown beneath the spectrum.

4

v

2 1

610

1

830 PHOTON

650 ENERGY

.670

690

(eV)

Fig. 2. Plot of the ratio of transmitted intensity with the magnetic field to that without field, Z(H)/Z(O), against photon energy for EllH polarization. The theoretical positions and relative strengths of the allowed transitions are shown beneath the spectrum.

parameters defined by Luttinger[6]; E, is the energy gap; A is the spin-orbit splitting. This determination was made without the use of the lowest transition line of Figs 1 and 2, which was indentified as exciton transition [1,41.

where P is the momentum matrix element defined by Kane[5]; yl, 7 and K are the band

Figure 3 shows computed magnetic energy levels as a function of magnetic field H. The

TECHNICAL

Table 1. Comparison between experimental and theoretical transition energies at 38.9 kG Polarization

Assignment?

Experiment (ev) 0.8177

EIH

EllH

0.8303 0.8405 0.8499 0.8604 0.8695 0.87% 0.8890

a+(3)ac( 1) 6+(2)by2) a+(4)ac(2) b+(3)@(3) u+(s)u”(3) b-(2)uC(O) u+(O)b=(O) fr(3)u”(l) u+(l)b’(l) b-(4)&(2) b-(5)aC(3) b-(6)uc(4) b-(7)uc(5) b-(8 u’(6) b-(9)u’(7)

0.8187 (0.830) 0.8327 og421 0.8533 0.8653 0.8754 0.8876 0.8975

NOTES

777

number of blackets are the Landau quantum number n for the levels and the arrows represent spin up and down. Figure 4 shows

Theory (eV) 0.8197 0.8212 0.8310 0.8396 0.8505 0.8591 0.8700 0.8784 0.8893 0.8185 0.8202 0.8307 0.8343 0.8425 0.8540 O-8653 0.8764 0.8873 0.8979

tThis notation is used by Pidgeon et a[.[21

K)

Fig. 4. Plots of the lowest Landau-level effective mass defined in equation (1) as a function of magnetic field for the conduction band of GaSb.

computed cyclotron mass for the conduction band as a function of magnetic field. which is defined as follows: mz(n, H) = eHlc(E;+l - E3

(1)

where e is the proton charge; c is the velocity of light; Eg is the electron energy in the n Landau level of the conduction band. Similarly Fig. 5 shows g-factor for the conduction band as a function of magnetic field, which is defined as ge*(n, H) = ~c(E;,~- ELc,.)/eH.

(2)

The g-factor of the n 2 4 Landau levels shows a change of sign with increasing magnetic field from zero to 200 kG. Extrapolating to low magnetic field and large n limit (classical limit) we obtain the following values for effective masses and g-factor:

me = O-045 m, m Ih = O-041 m0 g, =-6.5. H

(KG1

Fig. 3. Computed conduction-band energy levels for GaSb as a function of magnetic field. The numbers in brackets . . are the Landau quantum number n for the levels and the arrows represent spin up ( f ) and spin down ( J ).

Figure 6 shows that the g-factor for the conduction band depends upon the Landau quantum number n as well as the energy [7] in the conduction band.

TECHNICAL

778

NOTES Central Research Hitachi Ltd., Kokubunji, Tokyo, Japan

Laboratory,

E. ADACHI

REFERENCES 1. ZWERDLING 2. 3. 4. 5. 6. -(01 (n) -70.

0

1 loo

50 H

’ 150

’

200

IKG)

Fig. 5. Plots of the effective g-factor, defined in equation (2). as a function of magnetic field for the conduction band of GaSb. The landau quantum number are shown in brackets.

S., LAX B., BUTTON K. J. and ROTH L. M.,J. Phys. Chem. Solids 9,320 (1959). PIDGEON C. R. and BROWN R. N., Phys. Rev. 146,575 (1966). ELLIOTT R. J. and LOUDON R., J. Phys. Chem. Solids 15,196 (1960). JOHNSON E. J. and FAN H. Y.. Phvs. Reo. 139. A1991 (1965). KANE E. O.,J. Phys. Chem. Solids 1,249 (1957). LUTTINGER J. M. and KOHN W., Phys. Rev.

97,869 (1955). 7. ZAWADZKI W.. Phvs. Rev. Lett. 4.190 (1963). 8. CARDONA M. ad POLLAK c. H.,‘ Phyi. Rev.

142,530 (1966); POLLAK F. H., HIGGINBOTHAM C.W. and CARDONA M., Proc. Int. Conf. Semiconductor Physics. p. 20 Kyoto (1966).

J. Phys. Chem. Solids

Vol. 30, pp. 778-781.

E.S.R. studies of paramagnetic centres in irradiated Li,SO, . H,O (Received

01

03

a2 E-EC

04

LeV)

Fig. 6. Plots of the g-factor for the conduction band of GaSb vs. the electron energy in magnetic field ranged from 0 to 200 kG. Mean values of the electron energy of spin up and down are taken as the electron energy. The zero energy is taken at the bottom of the conduction band. The numbers in brackets are the Landau quantum number n for the levels in the conduction band. It must be pointed out the fact that light hole mass is smaller than conduction electron mass in GaSb. We computed the energy band structure and the band parameters of GaSb by the k-p method[8]; the computed results confirm the fact.

15 August

1968)

crystals of L&SO,. H,O grown from aqueous solution at room temperature and at 60°C were exposed to U.V. and X-radiation and e.s.r. spectra of these crystals were obtained at room temperature and liquid nitrogen temperature. There are two molecules in the monoclinic unit cell of this crystal with dimensions a = 5.43. b = 4.84, c = 8.14 A and p = 107”35’. The two crystal axes ‘u’ and ‘b’ and a third axis ‘c*’ are taken as the three orthogonal axes. The crystals were irradiated with X-rays from a 30 KV, 15 ma copper target for several hours. No visible coloration could be detected in the crystal even after heavy doses. A mercury discharge tube was used as the ultraviolet source. A Varian X-band spectrometer (type V4500) was used for taking the e.s.r. spectra in each SINGLE

0

6 June 1968; in revisedform