Resonance Raman scattering from amorphous As2S3

Solid State Communications,

Vol. 10, PP. 231—234, 1972. Pergamon Press.

Printed in Great Britain

RESONANCE RAMAN SCATTERING FROM AMORPHOUS As

2 S3*

R.J. Kabliska and S.A. Solin The James Franck Institute and Department of Physics, The University of Chicago, Chicago, Illinois, 60637

(Received 4 October 1971 by E. Burstein)

Resonance Raman Scattering from amorphous As2S3, obtaitied by temperature tuning the band edge through the He—Ne 6328 A laser line, is reported.

CURRENTLY, there is considerable interest in Resonance Raman Scattering (RRS) from crystalline solids.’ This interest is justified by the fact that RRS gives simultaneously information on the electronic and vibrational energy levels of a material. We wish to report here the first observation of RRS from an amorphous solid, As2S3, one of the chalcogenide glasses. This glass has been extensively studied by several workers and its

_______________________________________

IS

1 -~

T.44B~K

16.—

IS—

~

~ ~ ~

2 Moreover, it is extremely stable, thermal, electrical, and optical properties are well known. can be reproducibly prepared in bulk form, and is

I

3~

transparent in the visible region of the spectrum. Polished samples3 of vitreous As 2S3 were mounted in either an optical cryostat or an optical oven. In both cases, the sample was immersed in a bath of helium gas maintained at the temperature of observation. The Raman spectra were excited with a He—Ne laser (~80mW output power) and recorded using a Jarrel—Ash Model 25-100 double monochromator and a photon counting detection 4 Resosystem equipped for was computer processing. fiance enhancement obtained by temperature tuning5 the band gap of amorphous As 2 S3 through the He—Ne 6328 A emission line,

I

~ -500

\

/ T.

~

-4~

-300

-200

-100

~TI 0

RAMAN SHIFT IN

IOU

200

300

400

500

CENTIMETER5~

FIG. 1 (a) The computer smoothed right angle Raman Spectrum of amorphous As2 S3 recorded at 448°K. Incident light was polarized perpendicular to the scattering plane and no analyzer was used in the collection optics. (b) (1) Stokes and anti-Stokes approxiequations and (2) to the spectrum shown in mate density of states obtained byderived applying (a). The region A v~ 11 cm ~. The symbols a(0) and b(0) at the right of the figure indicate the baselines of curves (a) and (b), respectively.

In Fig. 1(a) shows the Stokes and anti-Stokes Raman spectrum of As2S3. The continuous

character of the spectrum along with the highly temperature dependent low energy (“ 30 cm 1) peak is characteristic of first6 order A more Raman complete scattering from solids. analysis of amorphous this spectrum as well as its polari-

* WorkGrant supported by U.S. Atomicand Energy Commission No. AT(11—1)—-2126 by Advanced Research Projects Agency.

zation properties and temperature dependence will be given elsewhere. 231

232

RESONANCE RAMAN SCATTERING FROM AMORPHOUS As

2 S3

In Fig. 1(b) we show the approximate density of vibrational states of amorphous As2S3, Stokes and anti-Stokes spectra, respectively [,os(z~)] and [pAs (i.’)I computed from the 7

‘2

IPAS(~)I

K =

2a~ +

Erf (a L3

a2 —~

)}

2a2j (3)

(1)

where the parameters L1, L2, L3, L4 and L5 correspond to the geometry shown in Fig. 2 and

(2)

R, !~(0),

~c.__~ ~ n

(a L4)

exp[— a2

3 —)]+Erf[a(L5+

exp[a~/4a2I xltErf[a(L2_ <

n(z~)+ 1

K

=

La]) —exp I [_(R+a1)L1jj a

Stokes and anti-Stokes spectra then =

(L1, L2, L3, L4, L5)

R/, (0)\r ((R + a11

according to the theory of Shuker and Gammon, i.e., if 15(V) and ‘AS (i’) are the observed

[Ps(~)]

Vol. 10, No. 2

‘2, a1, and a2 are defined in reference 8. In the limit a -~ equation (3) reduces to the expression in the first curly bracket which is Loudon’s result for an incident beam of zero diameter. Noting that R <
(~:~)

where i.- is the Raman shift in crn’, n(v) = [exp (hc z/k8T) —1]~’,k~is the Boltzmann constant, and K is a proportionality constant. To obtain a more accurate representation of

‘2

the density of states, three correction factors must be applied to equations (1) and (2): (1) The dispersion of the instrumental 4 Thus, transfer function, ~J,must be considered. equations[5(~o— (1) and7)]_t (2) should be multiplied byrespec the factors and [~J(~o + ~~~)]_l, tively. Here i-~ is the wave number of the mci dent radiation. (2) The i~’dependence of the scattering intensity on frequency (assumed negligible by Shuker and Gammon) should be included. For example, the relative magnitude of the 30 cm Stokes peak will be in error by 8 per cent if the i~’4dependenceis ignored. (3) A correction for the absorption of both incident and scattered radiation must be made when the photon energy of the exciting radiation closely matches the energy separation between any pair of electronic levels in the solid. Loudon8 derived such a correction for the case of an mci dent beam having zero beam diameter. It was not possible for us to focus the incident light into the sample without severly damaging it. Even with the sample immersed in superfluid helium, a modest input power density of ~2 kW/cm2 resulted in damage. Presumably, this was by the 2 of caused As very low thermal conductivity 2 S3. The damage problem was avoided by defocusing the incident laser beam. It is trivial to show that Loudon’s result, when modified to account for an axially symmetric Gaussian incident beamgives having a diameter 2/a at the 1/e2 power points,

(i~)

R(f-~,T)f(ILI,

=

~o,

~±

ii,

T, a) (4)

-

where T is the absolute temperature, I L —H IL 1, L2, L3, L4, L51, and the of a1 1’o dependence ± 1’ and T is on 1o and T and of a2 on implied. If the spectrum of Fig. 1(b) corresponds to a nonresonant spontaneous first order Raman effect, the densities of states deduced from the Stokes and anti-Stokes regions would be identical; the following equation [which includes the above described corrections to equations (1) and (2)] would be satisfied at all values of i~: F

~

1qs(i’) 1

~

2)1 F +

i

~o+ i~i4lf( LI, i~,l~o+ T, a)1 i~j[f(ILI, i’~i~o- T,a)J ~,

1.

~,

(5) The left hand side of equation (5) when evaluated for j2~= 15803 cm~, ~ = 342 cm , and T = 448°K gives 0.49. This breakdown of equality between Stokes and anti-Stokes derived densities of states can be interpreted as evidence of RRS9 The fact that we are indeed observing RRS from amorphous As 2S3is firmly established by the cuj~es shown in Fig. 3. In that figure we plot the relative Raman scattering efficiency [R of equation (3)1, evaluated at several phonon energies in both the Stokes and anti-Stokes spectrum, as a function of the energy difference the incident photon 1o = 1.96 eV) between and the band gap of vitreous

(hc As 2S3. The temperature dependence of the band

Vol. 10, No. 2

RESONANCE RAMAN SCATTERING FROM AMORPHOUS As

2 S3

233

edge was determined from the equation E9(T)

=

[2.32 + 6.70 x 10~ (300 — T) I eV,’°T being the approximation sample temperature when in applied °K. The to the assumption range 500°K of a linear dependence of E9 (T) on T while only an

L5~

T> 10°Kwill not appreciably affect the shape of the resonance curves shown in Fig. 3. The values of a1 and a2 used to calculate R from equation 11 (3) were obtained from the data of Tauc

>

et al.

I LI,

FIG. 2. Geometric representation of set,

of

scattering parameters used in equation (3).

1

worth mentioning. First, RRS occurs at all phonon

62 sto’es Sto~sI ASlI 58~ ~an~ 62 -

161

I

-

spectra. energies Second, in both the the Stokes anti-Stokes and anti-Stokes resonance at + ~ is always stronger than the corresponding Stokes resonance at 1~o— ~. Third, the degree of

-

resonance enhancement is weaker than that normally observed in RRS from crystalline solids.

-

~

342

(I, -

5u

-

>-

~46-

Fourth, and most interesting, is the pair of peaks which occur in each resonance curve between 0.4 and 0.5 eV below the band edge.

-

~42

-

z

-

-

-

~ 38~

Though theoretical treatments of RRS from

-

L.

-~

H

~ 34~— ~

The resonance enhancement of the Raman efficiency shown in Fig. 3 has several features

I—

crystalline solids have been carried out by several authors,8’2 there is to date no corresponding

-I

~ 30L-

treatment of RRS from amorphous semiconducting

—(0).

solids. Therefore, any attempt to explain the

~ 26L ~

—(10)’ (I0(u

Iw

features of the RRS from As2S3 is of necessity

-‘

I-

18— 22H

.0(0

(41—

lO~H 61

-6

speculative. Nevertheless, it is not surprising that RRS from an amorphous solid is weaker 3 than fromhave a crystal the energy bands in thethat former tails since of localized which will tend to broaden the range states’ over which RRS occurs while reducing the magnitude of the resonance. In this regard, notice from Fig. 3 that

— -

(10)0

--

((0)0

-

~5

-.4

(E,,,~-E

-3

-2

-(

0

9)in ELECTRON VOLTS FIG. 3. Resonance enhancement curves of the 62, 161, and 342 cm’ Stokes and anti-Stokes Raman scattering from amorphous As2S3. For only onethe typical setare of displaced error bars vertically is shown. and The clarity, curves symbols ‘(1.0)’ at the right of the figure indicate the baselines of the corresponding curves. Each curve has been normalized to unite relative Raman scattering efficiency at (E 1~~—E~) = —0.36eV the value corresponding to the room temperature band gap of amorphous As2 S3. Here, E1~0= 1.96e’~ the photon energy of the He—Ne 6328 A laser emission line.

there is evidence of resonance enhancement at AE ~ 10 hc ii whereas an analogous measurement for a crystal yields AE <2hc ~ If, as in the case of crystals, RX~Scan occur in an amorphous solid when either the incident or scattered 8 the anti-Stokes spectrum could by the photon is near in energy to be the enhanced gap energy, simultaneous occurrence of both types of resonance. Thus anti-Stokes resonance enhancement would be stronger than the Stokes enhancement in agreement with our observations. Again, making an analogy to the crystal, when the incident photon is in resonance with the band gap, RRS can occur from many of the phonons observable

234

RESONANCE RAMAN SCATTERING FROM AMORPHOUS As

2S3

Vol. 10, No. 2

in an allowed first order Raman process. This too is in agreement with our observations.

energies. Possibly, they owe their existence to electron—phonon correlation effects.

We do not believe that the peaks at 0.4—0.5 eV below the band edge arise from excitonic effects. They are not seen in the absorption spectra” of amorphous As2S3 and their positions correspond to excessively large excition binding

Acknowledgements — The authors gratefully acknowledge valuable discussions with Professor 0 en.

REFERENCES

mt.

1.

See e.g. Proc. 2nd

2.

KOLOMIETS B.T., MAZETS T.F. and EFENDIEV Sh.M., J.Non-Crystalline. Solids 4, 45 (1970) [electrical and optical properties]; WARD A.T., J. Phys. Chem. 72, 4133 (1968) [Raman spectrum]; Servo Corp. of Am. Publication No.2011, 1968 [thermal and optical properties].

3.

Samples were obtained from the Servo Corp. of Am., Hicksvill, N.Y. under the trade name Servofrax.

4.

SOLIN S.A. and RAMDAS AK. Phys. Rev. Bi, 1687 (1970).

5.

PINCZUK A. and BURSTEIN E., Phys. Rev. Leti. 21, 1073 (1968). RALSTON J.M., WADSWICK R.L. and CHANG R.K., Phys. Rev. Leit. 25, 814 (1970).

6.

FLUBACHER P., LEADBETTER A.J., MORRISON J.A. and STOICHEFF B.P., I. PhVS. Chen?. Solids 12, 53 (1969).

7.

SHUKER R. and GAMMON R.W., Phys. Ret-. Leti. 25, 222 (1970).

8.

LOUDON R., J. Phys. 26, 677 (1965).

9.

At the low power densities used in this experiment, simulated Raman scattering can safely be neglected.

Con, on Light Scattering in Solids, edited by MALKANSKE M. (to be published).

10.

We use the room temperature value of the gap energy, 2.32eV, given by KOSEK F. and TAUC J., Czech. J. Phys. B20, 94 (1970) and the change in ~au energy with temperature, 6.74 x 10-~V/°K, given by GETOV G., KANDILAROV B., SIMIDTCHIEVA P. and ANDREYTCHIN R., Phvs. Status Solidi. 13, K97 (1966).

11.

TAUC J., MENTH A. and WOOD D.L., Phys. Rev. Leit. 25, 749 (1970). The absorption data reported by these authors was also obtained from Servofrqx samples of As2 S3.

12.

BENDOW B. and BIRMAN J.L., Phys. Rev. 1, 1678 (1970); OVANDER L.N., Soviet Phvs. Solid State 3, 1737 (1969).

13.

FRITZCHE H., J. Non-Crystalline Solids

6,

49 (1971).

La diffusion résonante de Raman dans du As2S3 amorphe de la lumiére d’un laser ~ Hélium—Néon, obtenue grace ~ l’adjustement de Ia bande interdite par la temperature, est compte-rendue.