Al0.3Ga0.7As MQW's

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Applied Surface Science 63 (1993) 167-171 North-Holland

applied surface science

Photoreflectance versus ellipsometry investigation

of GaAs/A10.3Ga0.vAs MQW's V. Bellani, A. Borghesi, M. Geddo, G. Guizzetti, A. Stella Dipartimento di Fisica "A. Volta", Pavia University, 1-27100 Pavia, Italy

and Chen Chen-Jia Department of Physics, Peking University, Beiiing, China Received 2 June 1992; accepted for publication 31 July 1992

In this communication we report on experimental results obtained from the combined use of ellipsometry and photoreflectance to investigate the optical response of typical M Q W structures. The motivation for this approach is related to the need for a correct analysis of the lineshape of photoreflectance spectra. Ellipsometric data yield two important contributions about the nature and the degree of localization of the spectral structures in the excitonic region: (a) experimental curves instead of model profiles as starting reflectivity functions for derivations, (b) possible values of oscillator strengths of the transitions investigated. The energies of the main spectral features are compared with the quantized electronic levels obtained in the framework of the effective mass approximation in the envelope function scheme and a discussion of data previously reported in the literature ~s performed with the help of results obtained by the coupled techniques.

1. Introduction The optical investigation of microstructures in general and of superlattices (SL) and quantum wells (QW's) in particular has proved to be a powerful tool to get information from such systems and perform accurate analysis of the data obtained. It is well known that microstructures (i.e. structures characterized by dimensions which are small compared to the wavelength of the light) profoundly influence the optical properties of materials. By reversing the procedure one can use optical properties to study and determine the most significant parameters of the microstructure. When quantization occurs in thin layered structures, SL and QW's, the optical spectra present sharp and strong features, which are indicative of the quantized system [1,2].

A wealth of optical techniques is nowadays available to study the above mentioned quantum structures, such as reflectance (R), transmission (T), ellipsometry (EL), Raman spectroscopy, photoluminescence and modulation spectroscopy. However, in order to extract correct information from the analysis of the spectral features examined, it is essential to have a full comprehension of the various factors affecting the lineshapes, particularly when modulation spectroscopy techniques are adopted [3,4]. As a matter of fact, the systems containing SL a n d / o r QW's are rather complex since they are made by a repetition of alternating thin layers of two different materials with their interfaces and also, quite often, by the addition of cap layers, buffer layers, etc. Thus, the lineshape of the overall optical response is affected by several parameters and it is generally more difficult to interpret than in the case of the

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168

v. Bellani et al. / Photoreflectance versus ellipsometo, investigation of GaAs / AI o.~Ga o 7As MQW's

bulk particularly when derivatives of the R and T spectra are involved (like in the case of thermorcflectance, electroreflectance, photoreflectancc (PR), etc.). As a consequence, for instance in the case of photoreflectance, one has to deal not only with the problems concerning the separation between the first derivative nature of uncoupled transitions and the third derivative nature of higher-lying transitions in QW's, but also with the basic modifications of the lineshape due to optical interference from all interfaces in the multilayer sample [8-9]. In this work we intend to show some advantages due to the coupled use of two techniques like ellipsometry and photoreflectance to investigate the optical response of a specific MQW. The spectral features can thus be separated in two different categories: those which are present in both spectra and those which are detected only in PR. in section 2 we shall give the experimental details and in section 3 a short discussion will be presented.

2. Experimental details and results Multiple quantum wells GaAs-A10..~Ga0.7As have been grown by molecular beam epitaxy (MBE) on (100) oriented semi-insulating GaAs; the growth was characterized by temperatures between 600 and 610°C and rate of one monolayer/s. Sample A consists of three uncoupled QW's with well width L z = 74 _+ 3 .~ and barrier o width L b = 2 0 0 A , with no cap and a GaAs buffer layer ~ 0.5/~m thick separating the quantum structure from the substrate. Sample B presents 40 uncoupled QW's ( L z = 50 _+ 3 A, L b = 300 ~,), with a Al0.3Ga0.7As cap layer 0.1 /zm thick and two buffer layers (one 0.1 p.m thick of A10.3Ga0.7As and the other 0.5 p.m thick 017 GaAs). R o o m t e m p e r a t u r e (RT) ellipsometry spectra have been obtained by means of an automatic rotating-polarizer spectroellipsometer Sopra model ES4G, with an angle of incidence of 75 °. The ellipsometry measures the complex ratio p between the reflection coefficient of the light polarized parallel ( r p ) a n d perpendicular (r s) to

()l

OOO

~

O.ON 0.07 0.06 0 O5

(.;aAs-Al [

i

(;a As

MQW

74 )X

k

t

0.~

0.4 O.3

0.2 O. 1 . . . .

0

14

'

1.5

..........

,

~

1.6 energy

1.7

_ _ _ _ _

t

1.8

1.9

(eV)

Fig. 1. Tan tO and cos A spectra of sample A obtained by ellipsometric measurements.

the plane of incidence. By analyzing the state of the polarization of the reflected light, the functions tan g, and cos /I are determined, which are related to p by p = r p / r s = tan ~ exp(iA).

The photoreflectance spectra at near-normal incidence and at R T have been obtained by using a standard experimental configuration with an apparatus having as a probe source a 100 W halogen lamp and as an excitation source a H e N e laser (a = 6328 ,~ and power 5 mW). The laser beam was mechanically chopped at a frequency f = 220 Hz. The ellipsometric spectra of sample A show a rather monotonic behaviour, upon which some structures are superimposed either sharp or broadened (see fig. 1). The two relevant peaks at 1.485 and 1.508 eV in tan ~ can be attributed to H H I - C 1 and L H 1 - C 1 quantum well excitons. The H H , - C , , ( L H n - C n) standard notation indicates the transition between the nth heavy (light) hole valence subband and the nth conduction subband in the well. The small bumps at 1.65 and

IC Bellani et al. / Photoreflectance versus ellipsometry investigation of GaAs /Alo.3Gao. 7As MQW's 1.5

0.12 0.11

r

r

r

169 r

G a A s - A I G a As M Q W

1 GaAs-AI Ga As MQW

L = 74/~

0.1 0.5 9-

0.09

%

0.08 0.07

o -0.5

0.06 -1 0.05

08V'v i

i

-1.5

i

1.3

•

1.4

1.5 energy

1.6 (eV)

1.7

1.8

Fig. 3. RT photoreflectance lineshape of sample A.

0.6

0.4

0.2

0 1.4

i 1.5

i 1.6 energy

i 1.7 (eV)

1.8

1.9

Fig. 2. Tan 0 and cos A spectra of sample B obtained by ellipsometric measurements.

1.72 e V (which a r e m o r e e v i d e n t in t h e cos A s p e c t r u m ) c o r r e s p o n d to H H 2 - C 2 a n d L H 2 - C 2 q u a n t u m well excitons. T h e s p e c t r a of s a m p l e B exhibit oscillations d u e to i n t e r f e r e n c e in t h e m u l t i l a y e r s t r u c t u r e (see fig. 2). Two n a r r o w s t r u c t u r e s at 1.526 a n d 1.554 eV, a n d c o r r e s p o n d i n g to H H 1 - C 1 a n d L H 1 - C 1 q u a n t u m well excitons, can b e singled out from the large oscillations. M o r e o v e r , the d i r e c t o p t i c a l gaps o f G a A s a n d A I G a A s b u l k can b e o b s e r v e d at ~ 1.42 a n d ~ 1.85 eV; above that e n e r g y the i n t e r f e r e n c e fringes d i s a p p e a r . A s we shall specify b e l o w in m o r e detail, t h e d i f f e r e n c e

b e t w e e n t h e o p t i c a l r e s p o n s e o f t h e two s a m p l e s (which r e p r e s e n t s o m e w h a t two e x t r e m e cases) is mainly d u e to the total thickness of the m u l t i l a y e r system a n d to t h e p r e s e n c e of a c a p layer in s a m p l e B r a t h e r t h a n to the d i f f e r e n t values of L S a n d L b. A c t u a l l y , t h e a b s e n c e of a cap layer in s a m p l e A has e v i d e n c e d very clearly for the first time t h e excitonic s t r u c t u r e s c o r r e s p o n d i n g to n = 2 in e l l i p s o m e t r y . A s shown in fig. 3 ( s a m p l e A), d u e to the a b s e n c e o f a c a p layer a n d high p o w e r o f the excitation source used, values of A R / R even h i g h e r t h a n 10 -3 a r e o b t a i n e d in c o r r e s p o n d e n c e of the strong oscillations o b s e r v e d in t h e s p e c t r a l r e g i o n from 1.43 to 1.53 eV, whose n a t u r e will b e e x a m i n e d later. S u p e r i m p o s e d on the typical lines h a p e a r o u n d t h e g a p ( E 0) o f G a A s b u l k a n d the oscillations just m e n t i o n e d t h e r e a r e two structures at a b o u t 1.49 a n d 1.51 e V a n d a w e a k e r one at 1.65 eV. T h e e n e r g y p o s i t i o n s a n d s e p a r a t i o n of such structures, in g o o d a g r e e m e n t with ellips o m e t r i c data, a r e indicative of t h e i r q u a n t u m n a t u r e a n d justify t h e i r a t t r i b u t i o n to H H 1 - C I ,

Table 1 Comparison between experimental (ellipsometry) and calculated energies (meV) of heavy- and light-hole exciton transitions for samples A and B; the band parameters used for GaAs and Al0.3Gao.7As are reported, the masses are in free-electron mass unity L z (A) Sample A Sample B

HH1-CI

74 48

LH1-C1 Calc.

Exp.

Calc.

Exp.

Calc.

1485 1526

1475 1520

1508 1554

1498 1550

1650 -

1645 1770

GaAs: Eg = 1424 meV, m e 0.067, mlh = 0.094, mhh = 0.34. Alo.3Gao.7As: Eg = 1846 meV, m e 0.0916, rnlh = 0.1054, mhh = 0.493. Conduction band offset = AEc/AEg = 0.67. =

=

HH2-C2

Exp.

170

K Bellani et al. / Photoreflectance cersus ellipsometry im'estigation (~1"(;aAs / A I o ~Ga o 7As MQW's

LH~-C~ and H H 2 - C ~ quantum well excitons, respectively. In order to compare the experimental results with theory the energies of the light hole and heavy hole excitons have been calculated in the framework of the envelope function approximation. The band parameters which have been used are reported in table 1. It must be stressed that the effective masses for A10.3Ga~.TAS barriers have been obtained from a linear interpolation between those of GaAs and AlAs as a function of the stoichiometry index x. The binding energies of the excitons have been taken from recent theoretical calculations [10]. We note that the calculated transition energies, and in particular the differences between heavy- and light-hole excitonic levels, are in good agreement with the experimental values corresponding to the peaks in tan tO.

3. Discussion The critical dependence of the lineshape on the several parameters involved in complex systems like samples A and B deserves some comments. Actually, the problem of a correct analysis of the lineshape has been dealt with previously by other authors [5-9], mainly in connection with the role played by the cap layer. Here we focus the attention on the effect of the number of Q W ' s and total thickness of the overall sample in the absence of a cap layer. The coupled use of two techniques like EL and PR at high excitation power allows us to separate the spectral features in two categories, i.e. (a) those which are present in both spectra, (b) those which are present only in PR. It should be noted that a perturbative technique like PR (which is related to the application of relatively high electric fields) may produce effects like: (i) making allowed otherwise forbidden transitions, (ii) producing interference due to the variation of indexes of refraction in the layers caused by the creation of the free carriers, (iii) favouring Franz-Keldysh-like behaviour of the lineshape above the E 0 G a A s bulk structure [9].

The strong oscillations reported in fig. 3 (spectral region from 1.43 to 1.53 eV) are an interesting example of effects related to the technique of photoreflectance and are the object of analysis presently in progress. It is worth stressing that suitable simulation techniques have been tested in order to extract more information from the data. To this purpose, a computational program has been developed to calculate, with the help of the matrix method [11], tan to, cos A and R spectra in multilayered structures. Two Lorentz oscillators have been used to simulate the two excitons in order to take into account correctly the contributions of the quantum structures to the overall optical response. Calculations performed on three different systems (without cap layer and with pure G a A s as substrate) including one, two and three wells, respectively, evidenced a drastic dependence of the lineshapes on the number of wells included in the multilayered structure. In particular the lineshapes of R presented an evolution from dispersion-like (one well) to absorption-like (three wells) and the three-wells model fitted satisfactorily the experimental spectra of tan tO and cos A of sample A. In such a way the following values of the oscillator strength ( f ) and of the broadening p a r a m e t e r (7) have been determined: f = 0.01 (eV) 2 and 7 = 8 meV for HH~-C~ exciton; f = 0.006 (eV) 2 and 7 = 10 m e V for L H I - C 1 exciton. We note that the ratio between the two oscillator strengths is ~ 2, in agreement with theoretical results reported in ref. [10] where it was shown that the ratio must change from 3 to 2 when valence-band mixing is included in the calculations. As a conclusive remark, it can be noted that the clear dependence of the R lineshape on the number of QW's is expected to produce stronger effects on the derivative spectra.

Acknowledgements This work has been partially supported by G N S M of C N R and the C N R Progetto Finalizzato "Materiali Speciali per Tecnologie Avanzate".

V. Bellani et al. / Photoreflectance versus ellipsometry investigation of GaAs /Alo 3Gao 7As MQW's

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[6] X.L. Zheng, D. Heiman, B. Lax and F.A. Chambers, Appl. Phys. Lett. 52 (1988) 287. [7] H. Shen, S.H. Pan, F.H. Pollak and R.N. Sacks, Phys. Rev. B 37 (1988) 10919. [8] D. Huang, D. Mui and H. Morkoc, J. Appl. Phys. 66 (1989) 358. [9] F.H. Pollak, Superlatt. Microstruct. 10 (1991) 333. [10] L.C. Andreani and A. Pasquarello, Phys. Rev. B 42 (1990) 8928. [11] See, for example, R.F. Potter, in: Handbook of Optical Constants of Solids, Ed. E.D. Palik (Academic Press, New York, 1985) p. 11.