Solid State Communications 126 (2003) 261–264 www.elsevier.com/locate/ssc
Resonance Raman spectroscopy of Ga12xAlxAs mediated via compositional variation D.J. Lockwood*, Z.R. Wasilewski Institute for Microstructural Sciences, National Research Council, 1200 Montreal Road, Ottawa, Ont., Canada K1A 0R6 Received 31 January 2003; accepted 4 February 2003 by M. Cardona
Abstract A specially prepared Ga12xAlxAs sample with a laterally graded alloy composition has allowed a novel investigation of resonance Raman scattering from the optical phonons. Instead of varying the exciting light energy, the resonance is probed by changing the alloy composition at fixed incident energy. Both incoming and outgoing resonances are observed at the direct gap of the alloy, free of the usual overwhelming photoluminescence background. q 2003 Elsevier Science Ltd. All rights reserved. PACS: 78.30.Fs; 71.20.Nr; 63.50. þ x Keywords: A. Semiconductors; A. Disordered systems; D. Phonons; D. Electronic band structure; E. Inelastic light scattering
Raman spectroscopy under resonant excitation conditions has been widely studied in a great variety of materials ranging from gases to solids [1,2]. Resonances occur when the exciting light (incoming resonance) or Raman scattered light (outgoing resonance) comes close to a natural electronic transition in the material, matching the corresponding poles in the energy denominators of expressions for the Raman scattering cross-section. In special cases, double resonances can be observed, i.e. simultaneously incoming and outgoing resonances, in systems with carefully chosen electronic energy level spacings. The material excitations involved in the scattering process may be molecular vibrations or rotations, lattice vibrations, spin waves, electronic transitions, plasmons, etc. By far the most widely studied materials are semiconductors [2]. In all of these studies, the resonance conditions are normally obtained by varying the excitation energy. In this paper, we provide a novel and a rare example of a system, namely the semiconductor alloy Ga12xAlxAs, whereby the resonance conditions are achieved by varying the sample composition and keeping the incident light energy fixed. * Corresponding author. Tel.: þ1-613-993-9614; fax: þ 1-613993-6486. E-mail address:
[email protected] (D.J. Lockwood).
Both the incoming and outgoing resonances are observed in this way for different alloy compositions. The multilayered sample used in this study was grown at 590 8C in a modified V80H VG-Semicon molecular beam epitaxy system [3]. The sample substrate was a 2 in. diameter (100) oriented vertical-gradient-freeze semiinsulating GaAs wafer and the layers were grown without substrate rotation in order to generate the desired range of alloy x values laterally across the water. With growth rates of 0.1 and 0.2 nm/s for GaAs and AlAs, respectively, x varied continuously from about 0.60 to 0.72 in the 2.5 mm thick undoped alloy layer, which was sandwiched between GaAs/AlAs calibration layers [3]. The sample was measured by high resolution X-ray diffraction to map the sample composition (see Ref. [3] for details). The Raman scattering experiments were carried out in an ambient atmosphere of helium at a temperature of 295 K in a quasi-backscattering geometry [4] with the incident light at an angle of 77.78 from the normal to the (100) surface. Spectra were excited with 300 mW of 530.9 nm krypton or 514.5 nm argon laser light, which had sufficient penetration depth to reach well into the alloy layer. The light scattered at 908 (external to the sample) was analyzed with a Spex 14018 double monochromator at a spectral resolution of 1.2 cm21, and detected with a cooled RCA 31034A photomultiplier.
0038-1098/03/$ - see front matter q 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0038-1098(03)00134-0
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The incident light was polarized in the scattering plane, while the scattered light was recorded without polarization analysis. The peak frequencies of the phonon Raman lines were obtained with high accuracy using a computer search algorithm [5] and each spectrum was frequency calibrated with respect to three reference points [the laser line position, the GaAs longitudinal optic (LO) phonon peak, and the AlAs LO phonon peak] that covered the complete scan. Representative Raman spectra from the graded concentration sample are shown in Fig. 1. Features at 290 (402) and 273 (360) cm21 are, respectively, the LO and transverse optic (TO) modes of the GaAs (AlAs) layers [3] in the sample. The peaks at lower frequency to the GaAs LO – TO pair and in between the AlAs LO– TO pair are LO and TO modes of the alloy due to GaAs-like (lower frequency) and AlAs-like (upper frequency) modes of vibration [6]. The Raman lineshapes were curve resolved using commercial peak fitting software (PeakFit by Systat Software, Inc.). Most bands could be represented by symmetric combined Gaussian – Lorentzian (GL) functions, but three bands required an asymmetric lineshape provided by the exponentially modified Gaussian (EMG) function of PeakFit. Besides the bands described above, an additional (weak) GL band was needed to represent the continuum between the LO and TO peaks of GaAs-like and AlAs-like bands. The frequencies of the alloy modes as a function of aluminum composition have been presented earlier [3,7]. Here we are interested in the intensities of the Raman lines. As is evident from Fig. 1, there is a big change in the alloy phonon intensities when changing the excitation light from 514.5 nm (2.410 eV) to 530.9 nm (2.335 eV). This shift in excitation energy is only a relatively small step at 0.075 eV, but it has an order of magnitude effect on the integrated intensity. Fig. 2 shows the variation in integrated intensity of the GaAs-like and AlAs-like LO phonons for 530.9 nm excitation as a function of alloy composition. Both phonons exhibit a pronounced enhancement in their intensities for 0:6 , x , 0:75; with a peak intensity at x ¼ 0:67 (with a doublet-like splitting of x ¼ ^0:01) and x ¼ 0:68 for the AlAs-like and GaAs-like modes, respectively. The observed composition profiles were each well-fitted with a pair of identical (except in x) GL bands, with the results shown in Fig. 2. The values obtained from the fits for the GL parameters are given in Table 1. An explanation for this interesting intensity behavior with x can come from a consideration of resonance effects. Earlier work on GaAs has shown that resonance Raman enhancements of the LO and TO phonon cross-sections can arise when the exciting or scattered light energy approaches that of the fundamental gap energy E0 (the sharpest resonance in energy) or higher lying states [2,8– 10]. In the Ga12xAlxAs alloy, the E0 gap (for 0:45 # x # 1:0) at room temperature varies as [11] E0 ðxÞ ¼ 1:656 þ 0:215x þ 1:147x2 ;
ð1Þ
Fig. 1. Room temperature Raman spectra from one spot on the graded composition Ga12xAlxAs sample recorded with 514.5 and 530.9 nm excitation in the regions of the GaAs-like and AlAs-like phonons. Note the difference in the Raman intensity scales for the two laser lines. The Raman lineshapes have been fitted with the various component bands shown underneath by the dotted lines.
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splitting between the two bands. The energies Ep of the LO phonons involved can be estimated from [3,7]
vðxÞ½GaAs-like ¼ 290:24 2 36:73x 2 0:15x2
ð2Þ
and
vðxÞ½AlAs-like ¼ 363:59 þ 50:35x 2 11:79x2
Fig. 2. Integrated Raman intensities at 295 K of the GaAs-like and AlAs-like LO phonons of Ga12xAlxAs as a function of aluminum composition. The peak in the response has been fitted with two identical GL bands, shown by the dotted lines underneath. The inset illustrates the resonances involving incoming ðEin Þ and outgoing ðEout Þ light with the separation D ¼ Ein 2 Eout corresponding to the GaAs-like or InAs-like LO phonon energy Ep :
which encompasses the laser excitation energies used here. The next higher energy gap, the spin– orbit split-off E0 þ D0 transition, is too high in energy to be considered here. The proposed mechanism is shown in the inset to Fig. 2. For incoming resonance Ein ¼ E0 and for outgoing resonance Eout ¼ E0 ; which is less than Ein by the GaAslike or AlAs-like phonon energy Ep : In the aluminum composition picture, Ep corresponds to D; which is the Table 1 Results (with standard errors) for GL band parameters from leastsquares fits to the Raman intensity versus alloy composition plots. For the GL lineshape, 1 represents a pure Gaussian and 0 a pure Lorentzian Bands 1 and 2
GaAs-like
AlAs-like
Agreement factor ðR2 Þ Amplitude (counts s21 cm21) Width ðxÞ Fraction Gaussian Position 1 ðxÞ Position 2 ðxÞ
0.971 15,550 (1610) 0.0438 (0.0058) 1.000 (0.551) 0.6670 (0.0016) 0.6962 (0.0015)
0.983 20,980 (790) 0.0467 (0.0021) 1.000 (0.406) 0.6496 (0.0010) 0.6939 (0.0010)
ð3Þ
giving respectively for the GaAs-like and AlAs-like modes at x ¼ 0:6670 and 0.6496 (position 1 from Table 1) frequencies (energies) of 265.7 (0.0329) and 391.3 (0.0485) cm21 (eV). The experimental values for the energies of the outgoing and incoming resonances have been calculated from Eq. (1) using positions 1 and 2 (in x) from Table 1. The predicted resonances are at the incident laser light energy of Ein ¼ 2:335 eV (incoming) and at Eout ¼ Ein 2 Ep (outgoing). The results are shown in Table 2, where it can be seen that within error the predicted and observed resonance energies are in agreement for both modes. Furthermore, the splittings D ; Ep are different in the two cases by 0.030 ^ 0.005 eV, which matches the difference in their phonon energies (0.016 eV). This confirms the assignments of the two Raman intensity peaks observed in Ga12xAlxAs versus x with fixed incident light energy as arising from outgoing and incoming resonances with the fundamental gap E0 of the alloy. In conclusion, this novel experiment has demonstrated another way of probing resonance Raman effects in semiconductor alloys. The measured Raman intensities need no correction for instrumental response, as the exciting light energy remains constant. In addition, the use of a sample structure essentially comprising an epilayer encompassed by multiple quantum wells has allowed observation of a direct gap Raman resonance without the usual overwhelming photoluminescence contribution. Use of such tailored structures, where carrier recombination occurs other than in the region of interest, would also benefit conventional resonance Raman studies. Table 2 Experimental and predicted energies (eV) for incoming and outgoing Raman resonances for LO phonons in Ga12xAlxAs at room temperature. The experimental resonance energies are calculated from Eq. (1) using the band positions and uncertainties given in Table 1 Resonance
GaAs-like
AlAs-like
Incoming Experiment Prediction
2.362 ^ 0.003 2.335
2.357 ^ 0.002 2.335
Outgoing Experiment Prediction
2.310 ^ 0.003 2.302
2.280 ^ 0.002 2.286
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Acknowledgements We thank Robin Radomski for performing the peak fitting analysis.
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[4] D.J. Lockwood, M.W.C. Dharma-wardana, J.-M. Baribeau, D.C. Houghton, Phys. Rev. B 35 (1987) 2243. [5] J.W. Arthur, J. Raman Spectrosc. 5 (1976) 2. [6] B. Jusserand, in: S. Adachi (Ed.), Properties of Aluminium Gallium Arsenide, IEEE, London, 1993, p. 30. [7] D.J. Lockwood, R. Radomski, Z. Wasilewski, J. Raman Spectrosc. 33 (2002) 202. [8] M. Cardona, in: E. Burstein (Ed.), Atomic Structure and Properties of Solids, Academic, New York, 1972, p. 514. [9] R. Trommer, M. Cardona, Phys. Rev. B 17 (1978) 1865. [10] M.H. Grimsditch, D. Olego, M. Cardona, in: J.L. Birman, H.Z. Cummins, K.K. Rebane (Eds.), Light Scattering in Solids, Plenum, New York, 1979, p. 249. [11] H.C. Casey, M.B. Panish, Heterostructure Lasers, Academic, New York, 1978, part A, p. 193.