The far infrared optical constants of GaP

In/wed Phys. Printed

Vol. 29, No. 24. pp. 719-723. 1989 Britain. All rights reserved

in Great

THE FAR

Copyright

INFRARED

OPTICAL

CONSTANTS

c

0020-0891189 $3.00 + 0.00 1989 Pergamon Press plc

OF GaP

A. K. WAN ABDULLAH’*, G. A. GLEDHILL’, C. PATEL’ and T. J. PARKERIt ‘Department of Physics, Royal Holloway and Bedford New College, University of London, Egham Hill, Egham, Surrey TW20 OEX and ZDepartment

of Nuclear

Physics,

University

of Oxford,

Keble Road,

Oxford

OX1 3RH,

England

(Received 12 October 1988)

Abstract-The

FIR optical constants of GaP have been determined on either side of the Reststrahlen band by single pass transmission dispersive Fourier transform spectroscopy. These results extend the range of measured refractive index data for Gap, and reveal the dispersion in the refractive index in regions of weak absorption. Features in the spectrum are assigned as phonon combination bands with the aid of a critical point analysis based on phonon frequencies calculated using an 1l-parameter rigid ion model.

INTRODUCTION

The FIR optical properties of binary semiconductors have been of interest for many years. Apart from the need for accurate values of the optical constants, there has been considerable interest in the mechanisms responsible for the absorption in phonon combination bands in these materials.““) We have recently measured the FIR optical and dielectric properties of a selection of simple ionic solids and binary semiconductors by dispersive Fourier transform spectroscopy [DFTS4)] throughout the region where lattice absorption occurs by one- and two-phonon processes. In the region of the Reststrahlen band, measurements have been made by reflection DFTS, and either side of the Reststrahlen band complementary measurements have been made by single pass transmission DFTS. The aim has been to obtain more accurate information about the absorption mechanisms and to investigate trends in behaviour from simple ionic solids, through the II-VI compounds to the III-V compounds. In this paper we present measurements by single pass transmission DFTS of the FIR optical constants, n and k, of GaP on either side of the Reststrahlen band using an instrument which has been modified recently (u) for this work. Features in the measured spectrum are assigned as phonon combination bands with the aid of a critical point analysis based on an 1l-parameter rigid ion model for the dynamics of the crystal lattice. EXPERIMENTAL

The instrument used for these measurements was a modified (5,6)NPL/Grubb Parsons FIR cube interferometer. The specimen could be placed in the fixed arm of the interferometer so that the amplitude and phase transmission coefficients could be determined by single pass transmission DFTS.“’ Further modifications@) included the installation of a hydraulic moving mirror drive and a subsidiary He-Ne laser control channel to enable the interferograms to be sampled with high precision. RESULTS

AND

DISCUSSION

Measurements were made on an undoped single crystal of GaP of thickness 0.508 f 0.001 mm optically polished on both surfaces. With this thickness, the signatures associated with the transmitted partial waves, which arise from multiple reflections within the specimen, are well separated on the interferograms. Analytical difficulties associated with the interpretation of overlapping partial waves which can occur with thinner specimens are then avoided.(4*5) *Present address: School of Physics, Universiti Sains Malaysia, 11800 USM Penang, Malaysia. tTo whom correspondence should be addressed. 719

720

A. K.

WAN ABDULLAH et ul.

(6l)d

1

2000

1000 LASER

3000

4000

FRINGE

Fig. I. Illustration of the gross shift. (E - I)d. in optical path difference between the positions of the background interferogram, I,. and the sample interferogram. I,_

Interferograms were recorded in the usual way with and without the specimen in the fixed arm of the interferometer, using a sampling interval of eight laser fringes (2.531 pm).(6) The maximum point on each interferogram was then used as the origin of computation for that interferogram.‘4,5) In transmission DFTS’4,5’ it is necessary to determine the gross shift in optical path length between the two interferograms (Fig. 1). The magnitude of this shift is given to first order by the expression (fi - l)d, where ?i is the mean refractive index of the specimen in the measured spectral range and d is the specimen thickness. To measure this shift the specimen was partially inserted into the beam so that signals from the background and specimen interferograms could both be observed on the same scan, and the two interferograms were recorded on a single scan as shown in Fig. 1, using a sampling interval of one laser fringe (0.316~m). The shift in optical path difference between the maximum (or minimum) points on the two interferograms could then be determined very accurately by counting the laser fringes. With this method all parameters’4.5’ contributing to the determination of the refractive index, apart from the measurement of the specimen thickness, are determined with optical precision,‘h’ and potential phase errors arising from factors such as thermal expansion of the arms of the interferometer are eliminated, as the laser reference beam passes along the IR beam. The uncertainty in the determination of the refractive index is then limited almost entirely by the uncertainty in the specimen thickness. In the present work this is about 1 part in 500, because a thin specimen was used to permit measurements very close to the Reststrahlen band. However, in the case of low loss materials much thicker specimens could be used and this limitation would be considerably relaxed. It would then be possible to make much better use of the advantages of these sampling techniques and reduce the uncertainty in the refractive index measurement to the order of IO-” or 10m5 by eliminating all systematic errors other than those associated with the specimen geometry.“-” Details of the analytical techniques required to calculate the optical constants from the measured data, including the elimination of branching errors from the phase spectrum, have been given elsewhere.‘4.5’ The resulting spectra for n and k at a spectral resolution of 4 cm-’ are shown in Fig. 2, and a small part of the spectrum of Fig. 2 is reproduced in Fig. 3 to demonstrate the sensitivity of the technique to small changes in refractive index. It can be seen that the dispersion in the refractive index in the region of weak absorption bands is clearly revealed. Above the Reststrahlen band our values for the refractive index are about 1% lower than those from reflection measurements. Below the of Kleinman and Spitzer,“’ which were obtained Restrastrahlen band our values for n are about 0.3% higher than those of Parsons and Coleman,““’ which were obtained from measurements of the channel spectrum. Our values for the extinction

The FIR optical

constants

721

of GaP

-0.02

k -DO1

2.400

1.9001 30

270

spectra

for the refractive

510

390 WAVENUMBER

Fig. 2. The measured

Jo.00

I

150

630

CM-’

index, n, and extinction

coefficient,

k, of GaP at 300 K.

coefficient are generally consistent with published values for the absorption coefficient,“.“’ except that there is evidence of weak absorption due to free carriers at frequencies below lOOcm-‘. There are several reports in the literature ‘21”-‘3’of optical investigations of two-phonon processes in GaP, and the structure in Fig. 2 is most probably due to phonon combination bands as the sample was nominally undoped and of high purity. We give below a critical point analysis of this structure. The frequencies of phonons at the critical points in GaP at 300 K are listed in Table 1. These were obtained from calculations based on an 1l-parameter rigid ion model (RIM),‘14’ and the neutron scattering data of Borcherds et al.“” which are also listed in the table, were used to determine the model parameters. Earlier neutron data reported by Yarnell et a/.(‘@for the X and L points are also listed, and it can be seen that the two sets of data are in good agreement, apart from the reported values for LO(X). In Table 2 the observed features in Fig. 2 are assigned as phonon combination bands using the calculated critical point phonon frequencies listed in Table 1. The assignments as summation or

2.700

n - 0~0050

i.670,.

k

-0.0025

?.MO550

570

590 WAVENUMBER

610

630

0,000 650

CM-]

Fig. 3. A small part of Fig. 2 expanded to show the dispersion in the refractive the weak absorption bands.

index in the region

of

122

A.

K. WANABDULLAH et al

Table I. A comparison of critical point phonon frequencies in GaP calculated with the 1I-parameter RIM with values measured by neutron inelastic scattering Neutron Crltical point IX

L

W

K

I I-parameter RIM. Ref. (14)

TAX,

Table 2. Assignments

for observed

100 K

Neutron

130 152 I82 212 258

I30 152 I82 213 260

268

212

447 480 491 542 555 562 580 608

452 485 496 546 560 565 585 612

I I-parameter RIM, Ref. (14) 130.9 148.1 186.1 212.2 256.6 257. I 258.6 268.6 269.5 436. I 474.0 488.6

408.3 + I 7 366.7 it 250.0 2 3550* 104.3 + 405.3 +

353.3 _t 7 83.3 _t I 7

Ref

(16)

402.0 367.0 366.1 249.3 353.3 106.6 373.5 212.2 357.6 x5.4

k + k * i + + * + *

I3 II I2 4 x 3 x x 8 2

153.3 * 3.3 123.3 * 3.3 _ 350.0 * IO

105.0 k 6.7

spectrum

of GaP

data

Ref. (15)

Ref. (16)

146 191 209 251

127 143 161 212 247

245 270 437 471 489

273 443 472 458

_

IR data 20K, Ref. (12)

I80 213 258

274

__ 567.0 619.5 603.3

IO I3 I7 5 I7

features in the FIR transmission

This work 300 K

Ref.( 15)

402.X 36X.3 368.3 254.2 362.7 106.1 405.3 214.2 352.8 83.3 366.9 36.5.0 363.5 224.7 155.X 106.4 372.1 231 2 366.4 358 2 143 I 97.8

LO TO LO LA TO TA LO LA TO TA WI W? w3 w4 WS W6 IIOZ,

data

570 586

44x 483 503 544 554 564 5x4 609

Assignments LA(L) - TA(L) LA(X) - TA(X) LO(L) - LA(L) ZTA(X) TO(X) - TA(X) W3-W6 W2-W6 IOZ, ~ TAX:, TO(L) - TA(L) TO(L) + TA(L) LO(X) + TA(X) LO(L) + TA(L) 3.phonon’? 3.phonon’? TO(L) + LA(L) LO(L) + LA(L) IIOZ, + IlAX,

difference bands are supported by additional power transmission measurements in our laboratory density of states using at temperatures down to 4 K,“” and by calculated curves for the two-phonon the RIM, neither of which are shown here. In Table 2 the measured frequencies are compared with values reported by Koteles and Datars,“” and the calculated frequencies are compared with values It can be seen that the overall obtained from the neutron data”‘.‘@ using the same assignments. agreement between the measured frequencies and the results of the RIM is quite satisfactory. CONCLUSION The optical constants of a single crystal of GaP have been measured in the FIR either side of the Reststrahlen band by single pass transmission DFTS at 300 K. These measurements extend the reported range of refractive index data for GaP and demonstrate the capability of an instrument which has been designed to reduce systematic phase errors to a minimum. Features in-the spectrum have been assigned as phonon combination bands by carrying out a critical point analysis using phonon frequencies calculated with an 1 l-parameter rigid ion model. The overall agreement between the measured and calculated frequencies is quite reasonable.

The FIR optical

constants

723

of GaP

Acknowledgements-A. K. Wan Abdullah wishes to acknowledge the financial and Universiti Sains Malaysia which enabled him to carry out this work.

assistance

of the Government

of Malaysia

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

R. Geick, Phys. Rev. 138, 1495 (1965). D. A. Kleinman and W. G. Spitzer, Phys. Rev. 118, 110 (1960). H. Borik, Physica Status Solidi 39, 145 (1970). J. R. Birch and T. J. Parker, Infrared and MiNimeter Waves (Edited by K. J. Button), Vol. 2, Chap. 3. Academic Press, New York (1979). T. J. Parker, W. G. Chambers, J. E. Ford and C. L. Mok, Infrared Phys. 18, 571 (1978). A. K. Wan Abdullah and T. J. Parker, Infrared Phys. 29, 799 (1989). J. R. Birch, Mikrochim. Acta (Wien), 111, 105 (1987). J. R. Birch, J. D. Dromey and E. A. Nichol, Infrured Phys. 21, 225 (1981). M. N. Afsar and K. J. Button, Proc. IEEE 73, 131 (1985). D. F. Parsons and P. D. Coleman, Appl. Optics 10, 1683 (1971). R. M. Hoff and J. C. Irwin, Con. J. Phys. 51, 63 (1973). E. S. Koteles and W. R. Datars, Solid Stare Commun. 19, 221 (1976). B. Ulrici and E. Jahne, Physica Starus Solidi (b) 86, 517 (1978). C. Pate], W. F. Sherman and G. R. Wilkinson, Physicu Srafus Solidi (b) 111, 649 (1982). P. H. Borcherds, G. F. Alfrey, D. H. Saunderson and A. D. B. Woods, J. Phys. CS, 2022 (1975). J. L. Yarnell, J. L. Warren, R. G. Wenzel and P. J. Dean, Neutron Inelasfic Suffering, Vol. 1, p. 301. IAEA, Vienna (1968). G. A. Gledhill, S. S. Kudhail, R. C. Newman and G. Z. Zhang, Inr. J. Infrured millimefre Waves 2, 849 (1981).