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AlSb superlattices
Solid-State Electronics Vol. 37. Nos 4-6, pp. 625-628, 1994 Copyright © 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0038-1101/94 $6.00 + 0.00
Pergamon
INFRARED REFLECTIVITY OF STRAINED GaSb/AISb SUPERLATTICES G. SCAMARCIO1, C. GADALETAz, A. TAGLIENTE2, L. TAPFER2, K. PLOOG3, Y. OHMORI4 and H. OKAMOTO5 ~Dipartimento di Fisica-GNEQP, Universita' di Bari, via Orabona4, 1-70126 Bari, Italy, 2CNRSM, Mesagne, 1-72023 Brindisi, Italy, 3Paul-Drude-Institut fiir Festk6rperelektronik, O-1086, Berlin, Germany, 4Electronics Engineering Osaka University 2-1 Yamada-Oka sulfa, Osaka565, Japan and 5Chiba University, Faculty of Engineering 1-33 Yayoi-Cho, Chiba-Shi, Chiba 263, Japan Abstract--The careful analysis of far-infrared reflectivity spectra of GaSb/AISb superlattices allows us to obtain information on intermixed Al~Ga~_xSb layers at the heterointerfaces, namely, average chemical composition and thickness. Complementary information on structural properties and strain relaxation processes are obtained from X-ray diffraction.
1. INTRODUCTION
Far infrared spectroscopy is well known to be a primary tool for the investigation of vibrational properties of solids. Nevertheless, only very recently its usefulness for the study of semiconductor superlattices (SL) has been exploited[l-6]. The ability of far infrared reflectivity (FIR) to probe confined phonons in SLs has been documented even in the case of ultrathin layers[4]. The influence of the spatial configuration on the SL dielectric function is the origin of the high sensitivity of F I R to the structural properties of multiple heterostructures[7]. Particularly, the simultaneous analysis of far- and midinfrared reflectivity spectra, in the framework of the effective medium approximation, allows the assessment of the individual layer thicknesses with an accuracy comparable to that of double crystal X-ray diffraction[5]. To the best of our knowledge, no FIR investigation of strained layer SLs has been reported. GaSb/A1Sb superlattices have attracted attention for their possible application in laser diodes emitting in the 1.3-1.7 ~ m range[8]. Their structural properties are influenced by the moderate (0.65%) lattice mismatch between the constituent materials. Strain and confinement effects have been previously investigated by means of ion-channeling, X-ray diffraction[9] and Raman spectroscopy[10,11]. Strain relaxation takes place for total AISb thickness greater than the critical value he= II +6nm[9]. We report here far i.r.reflectivity and X-ray diffraction of GaSb/AISb superlattices. Our results show that a satisfactory description of FIR spectra can be obtained provided that not only strain and phonon confinement but also strain relaxation processes are considered. 2. EXPERIMENTAL
GaSb/AISb superlattices were grown by molecular beam epitaxy either on GaAs or n-doped GaSb 625
(001)-oriented substrates. Undoped buffer layers 0.4 p m thick were grown on n-doped GaSb wafers. The optimized growth procedure reported in Ref.[l 2] was used. Structural data on the samples were obtained from X-ray diffraction. Diffraction patterns were recorded with a high resolution double crystal diffractometer using CuK~ radiation close to the symmetric (400) and asymmetric (511) reflections in order to obtain the lattice mismatch and strain fields normal and parallel to the crystal surface. Structural parameters were obtained through comparison with the results of computer simulation based on the dynamical scattering theory[13]. The best fit values are listed in Table i. I.r. measurements were performed under nearnormal incidence at 10 K by using a Fourier-transform spectrophotometer operating under vacuum. 3. RESULTS AND DISCUSSION
Figure I shows the FIR reflectivity spectrum of sample 1, representative of the series grown on n-doped GaSb substrates. The high reflectivity band extending in the low energy part of the spectrum up to about 200cm -~ and the broad band around 400cm -~ originate from plasma oscillations in the doped substrate. The intense structure extending in the range 200-260 cm- ~is due to the combined effect of "Reststrahlen" (RS) from GaSb either in the SL or in the substrate. The edge at 229.5 cm- ~coincides in energy with the bulk GaSb TO and is ascribed to the substrate. The weak shoulder at 227 cm- ~appearing on the low energy side of the bulk GaSb RS band can be ascribed to GaSb-like TO phonons in the SL. The structure appearing in the range 300-330 cm-J is due to RS from AISb-like phonons in the SL. Figure 2 shows the FIR spectrum of sample 5 which is grown on GaAs. Due to the different substrate, several changes can be observed with respect to the spectrum of sample I. In particular, no
626
G, SCAMARCIO et al.
Table I. StructuralparametersofGaSb/AISbsuperlattices.Here N = numberof periods;d = superlatticeperiod; d, = individuallayer thicknessesmeasured by X-rays(samples 1-3) or FIR (samples4. 5); (Adld)~. (Ad/d)z lattice mismatchparalleland normalto the (001)-plane,respectively;valuesin bracketsindicatemeanvalues Sample Substrate N d(nm) Layer d,(nm) (Ad/d)z (Ad:d): 1
GaSb
50
16.04
2
GaSb
100
5.55
3
GaSb
200
2.78
4
GaAs
285
4.9
5
GaAs
196
5.6
GaSb AISb GaSb AISb GaSb AISb GaSb AISb GaSb AlSb
plasmon-like reflectivity features related to the substrate are present. The GaAs substrate manifests itself in the range 270-300 cm -t, where the bulk-like RS band is modulated by the interference of radiation in the epilayer. In this case, the GaSb-like and AISb-like RS bands around 230 and 320 cm- ,, respectively, are well separated from that of the substrate. A complete assignment of the spectral features of Figs 1 and 2 will be discussed later after detailed comparison with calculations. The theory of Refs[2,14] gives a very satisfactory description of FIR for an "ideal" SL grown onto a semi infinite substrate. The SL dielectric function is written in the effective medium approximation as the average of the dielectric function of the constituent layers weighted by the layer thicknesses[7]. For layers thinner than about 10 monolayers the confinement induced shift of phonon energies has to be considereal[15]. In the case of strained layers the influence of lattice distortion on phonon energies needs to be evaluated, too. The dashed lines in Figs 1 and 2 have been calculated according to the above model considering an ideal GaSb/AISb SL with abrupt interfaces. For sample 1 the substrate doping has been properly considered by introducing a plasmon oscillator in the
13.26 2,89 3,75 1,80 1,74 1.04 3.1 1,8 4.2 1.4
- 3 , 6 × 10 ~ 1,3 × 10 -' (4.1 x 10 -~)
(3.95 x 10 5)
0 1.29 x 10 -2 ( 8 . 1 3 x 1 0 2)
0 0 ( 6 . 5 × 1 0 -')
(8.14x 10-")
(6.68 × l0 :)
substrate dielectric function. In the calculations we have taken the layer thicknesses of Table 1. The following parameters have been adjusted for best reproduction of the experimental data: the plasmon frequency and damping tOp and jp; the phonon frequency and damping in the j t h layer, tOro.j and Fj. Although a good overall agreement was obtained, several important structures cannot be reproduced at all. In particular, there is no way to reproduce the dip at 316.7cm -t in Fig. 1. The same is true for the structured GaSb-like and AlSb-like RS bands in Fig. 2. This discrepancy will be corrected by taking into account strain induced structural deterioration, as explained in the following. Strain relaxation in a superlattice structure manifests itself by non-zero values of the in-plane lattice mismatch or by negative strain values in the GaSb layers. The values of Table I show a partial degree of relaxation for samples 1-3 grown on GaSb substrate, which increases at increasing the A1Sb layer and the total superlattice thicknesses. This expected behaviour is related to the individual layer and total AISb thicknesses by far exceeding the critical values in GaAs/AISb structures[9]. Lattice relaxation occurs through the formation of defects, misfit dislocations and intermixed layers at the heterointerfaces. This causes interface roughness and local fluctuations of
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Fig. 1. FIR spectrum of (GaSb)t32,m (AlSb):.~.= SL (sample 1) grown on n-doped GaSb substrate. Dotted line: experimental data. Dashed line: spectrum calculated as explained in the text for abrupt interfaces. Solid line: spectrum calculated considering 5% intermixing at the interfaces.
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Fig. 2. FIR spectrum of (GaSb)42,,, (AISb),4,m SL (sample 5) grown on GaAs substrate. Dotted line: experimentaldata. Dashed line: spectrum calculated for abrupt interfaces. Solid line: spectrum calculated for a AIo,Ga09Sb/Al07Ga0~Sb SL as explained in the text.
627
Infrared rettectivity of strained GaSb/AISb superlattices Table 2. Data on the intermixing in GaSb/AISb SL samples deduced by the fittingof FIR spectra. Here t and x indicate the average thicknessand A1 mole fraction of the Al~Gat_~Sblayer at the interface. The percentage of intermixingis evaluated as IO0[t/(dj+ d2)] Sample
t (nm)
x
%
I 2 3
0.87 0.80 0.10
0.15 0.40 0.32
5 14 3
strain fields in the layers. In fact, a satisfactory agreement between the calculated and experimental X-ray diffraction patterns of samples 1-3 was obtained only if 0.1-0.2 nm thickness fluctuations and ,,-10 -3 strain fluctuations were considered. Hence, the simplistic assumption of homogeneous and abrupt interfaces has to be abandoned. Considering moderate thickness fluctuations in the model of FIR, does not give substantial improvement to the reproduction of the experimental features in Fig. 1. On the other hand, the existence of an intermixed layer at the GaSb/AISb interface can have a strong influence on the SL "Reststrahlen" profile mainly because of the additional phonon resonances and the modification in the spatial configuration. Hence, we have included in the model of FIR the presence of an AlxGa~ _~Sb layer of thickness t at the interface. In this way we are considering one SL period as constituted by three layers of thicknesses d~ (GaSb), d~ (AISb) and t (AIxGal _xSb). The sum (d~ + d~ + t ) and the ratio (d; + t/2)/(d~ + t/2) are fixed at the X-ray values of the period d and the ratio dl/d: between the layer thicknesses, whereas the AI mole fraction x is left as a fitting parameter. The latter parameter fixes also the alloy phonon frequencies according to the known dependence from the chemical composition[16]. The dotted line in Fig. 1 was calculated considering a 0.87 nm thick Alo.~5Ga0.s5Sb layer at each heterointerface. All spectral features of Fig. 1 are now satisfactorily reproduced. A similar improvement is obtained also for samples 2 and 3. The best fit values of SL TO phonon frequencies are consistent with the moderate confinement and strain induced shifts calculated considering the measured structural parameters. Similar findings on the combined effects of strain and confinement on the LO phonon frequencies have been obtained from Raman scattering experiments[l 0,11 ]. A detailed description of the fitting procedure will be reported elsewhere in a more extensive form. For the sake of the present discussion it is worth to list in Table 2 the fitting parameters concerning the intermixing. The values of the AI mole fraction of Table 2 are close to the ratio d2/(dj +d2) between the X-ray thickness values. A simple explanation for this is that the chemical composition of the intermixing alloy layers is determined by the relative abundance of the AI and Ga atoms. Further, a correlation appears between the percentage of intermixing and growth
parameters such as the AISb overall thickness, and the relative thickness between GaSb and AISb layers. For drawing more quantitative conclusions on this point the investigation of a larger number of samples is needed. Our previous analysis shows that intermixed layers as thin as a few tenths of nanometers intercalated in the SL matrix reveal themselves as clearly detectable structures in the reflectivity spectra of Fig. 1. Indeed, the presence of a doped substrate, whose reflectivity behaviour resembles that of a metal, strongly enhances weak phonon resonances of the superlattice. Figure 3(a-c) show the AISb-like RS spectra calculated for different values of the substrate plasma frequency tOp and the AlxGa~_ ~Sb layer thickness, t. The remaining parameters in the calculations are the same used for fitting to the spectrum of sample I. In Fig. 3(a) we see that only very weak differences exist among the spectra corresponding to t = 0, 0.8 and 1.6 nm when tOp = 0, i.e. for an undoped substrate. In contrast, the "Reststrahlen" band lineshape changes dramatically in Fig. 3(b) when a metallic behaviour is switched on by setting tOp = 400 cm- ~, close to the actual value of tOp in sample I. A strong dip appears on the low energy side of the AISb-like band close to the TO frequency of the alloy. By further increasing the doping level, i.e. setting tOp = 800 cm-~ causes a stronger modification of the whole spectrum which becomes absorptive-like in Fig. 3(c). This behaviour closely resembles the reflectivity of a thin dielectric film deposited onto a metallic substrate[17]. In the case of samples 4 and 5, by considering the presence of only a thin intermixed layer at the
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320
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WAVE NUMBER ( c m - ) Fig. 3. AISb-like"Reststrahlen'" bands calculated for different values of plasmon frequencies: (a) tot=0; (b) t% = 400 cm-i; (c) top = 800 cm-i. Dotted lines: abrupt interfaces. Solid lines: 5% intermixing at the interfaces. Dashed lines: 10% intermixing at the interfaces.
628
G. SCAMARCIOet al.
interface gives no significant improvement in the reproduction of experimental data. The diffraction patterns of the superlattices deposited on GaAs substrate (samples 4 and 5) are characterized by much broader and weaker satellite peaks. This indicates a large amount of defect formation and, particularly, a strong intermixing. The structural deterioration in the above samples is mainly caused by the huge ( ~ 8 % ) lattice mismatch between GaAs and GaSb or AISb layers. The above structural data induced us to model the SL as a sequence of two alternating AI~Ga~_ ,.Sb and AI, Ga~ _,Sb layers, with the AI mole fractions x and y close to the nominally pure layer values 0 and 1. The dotted curve in Fig. 2 was calculated with x = 0.1 and y = 0.7. Since the spectral quality of the X-ray diffraction patterns is not good enough to allow the determination of the individual layer thicknesses in this case, they were fixed to the values of Table ! which give the best reproduction of F I R spectra. In spite of the roughness of the considered model a very satisfactory reproduction of all the spectral features is obtained. In particular, the dips at 226.7 and at 319.7 cm -~, which are peculiar of the GaSb-like and AlSb-like SL "Reststrahlen" bands, are now properly reproduced by the theory.
4. CONCLUSION Our results show that F I R is a powerful tool for the investigation of vibrational and structural properties of strained layer GaSb/AISb superlattices. In addition to strain and confinement effects on SL phonons, our analysis allows to obtain important information on the interface deterioration. Taking advantage from the enhancement of weak SL phonon resonances induced by the metallic behaviour of the doped substrate, the chemical composition and the average thickness of AI~Ga L_ ,Sb alloy layers formed at the interfaces are determined. X-ray diffraction is sensitive to thickness and strain fluctuations in the
structure. It clearly merges the close complementarity of the two techniques for the study of strain relaxation processes. Acknowledgernent--This work is partially supported by MURST and CNR. REFERENCES
I. K. A. Maslin, T. J. Parker, N. Ray, D. R. Tilley, P. J. Dobson, D. Hilton and C. T. B. Foxon, Solid St. Cornrnun. 60, 461 (1986). 2. Bo Lou, R. Sudharsanan and S. Perkowitz, Phys. Rer. 1138, 2212 (1988). 3. G. Scamarcio, L. Tapfer, W. K6nig and K, Ploog, Appl. Phys. A 51, 252 0990). 4. G. Scamarcio, L. Tapfer, W. K6nig, A. Fisher, K. Ploog, E. Molinari, S. Baroni, P. Giannozzi and S. de Gironcoli, Phys, Rev. B 43, 14754 (1991). 5. G. Scamarcio, C. Gadaleta, M. Sibilano and K. Ploog, Solid St. Cornrnun. 84, 757 (1992). 6. B. Samson, T. Dumelow, A. A. Hamilton, T. J. Parker, S. R. P. Smith, D. R. Tilley, C. T. Foxon, D. Hilton and K. J. Moore, Phys. Rec. B 46, 2375 (1992). 7. V. M. Agranovich and V. E. Kratsov, Solid St. Cornrnun. 55, 85 (1985). 8. Y. Ohmori, Y. Suzuki and H. Okamoto, Japan, J. appl. Phys. 24, L657 (1985); J. appl. Phys. 64, 6733 (1988). 9. H. J. Gossman, B. A. Davidson. G. J. Gualtieri, G. P. Schwartz, A. T. Macrander, S. E. Slusky, M. H. Grabow and W. A. Sunder, J. appl. Phys. 66, 1687 (1989). 10. P. V. Santos, A. K. Sood, M. Cardona. K. Ploog, Y. Ohomori and H. Okamoto, Phys. Rer. B 37, 6381 (1988). 11. G. P. Schwartz, G. J. Gualtieri, W. A, Sunder and L. A. Farrow, Phys. Rev. B 36, 4868 (1987) and references therein. 12. Y. Suzuki, Y. Ohmori and H. Okamoto, J. appl. Phys. 59, 3760 (1986). 13. L. Tapfer, Physica scripta T25, 45 (1989). 14. O. E. Piro, Phys. Rev. B 36, 3427 (1987). 15. See, e.g.B. Jusserand and M. Cardona, in Topics in Applied Physics, Vol. 66 (Edited by M. Cardona and G. Giintherodt), p. 49. Springer, Berlin (1988). 16. Landolt-B6rnstein, Numerical Data and Functional Relationships in Science and Technology (Edited by O. Madelung), Vol. 111 17-a. Springer, Berlin (1983). 17. D. V. Berreman, Phys. Rer. 130, 2193 (1963).
Pergamon
INFRARED REFLECTIVITY OF STRAINED GaSb/AISb SUPERLATTICES G. SCAMARCIO1, C. GADALETAz, A. TAGLIENTE2, L. TAPFER2, K. PLOOG3, Y. OHMORI4 and H. OKAMOTO5 ~Dipartimento di Fisica-GNEQP, Universita' di Bari, via Orabona4, 1-70126 Bari, Italy, 2CNRSM, Mesagne, 1-72023 Brindisi, Italy, 3Paul-Drude-Institut fiir Festk6rperelektronik, O-1086, Berlin, Germany, 4Electronics Engineering Osaka University 2-1 Yamada-Oka sulfa, Osaka565, Japan and 5Chiba University, Faculty of Engineering 1-33 Yayoi-Cho, Chiba-Shi, Chiba 263, Japan Abstract--The careful analysis of far-infrared reflectivity spectra of GaSb/AISb superlattices allows us to obtain information on intermixed Al~Ga~_xSb layers at the heterointerfaces, namely, average chemical composition and thickness. Complementary information on structural properties and strain relaxation processes are obtained from X-ray diffraction.
1. INTRODUCTION
Far infrared spectroscopy is well known to be a primary tool for the investigation of vibrational properties of solids. Nevertheless, only very recently its usefulness for the study of semiconductor superlattices (SL) has been exploited[l-6]. The ability of far infrared reflectivity (FIR) to probe confined phonons in SLs has been documented even in the case of ultrathin layers[4]. The influence of the spatial configuration on the SL dielectric function is the origin of the high sensitivity of F I R to the structural properties of multiple heterostructures[7]. Particularly, the simultaneous analysis of far- and midinfrared reflectivity spectra, in the framework of the effective medium approximation, allows the assessment of the individual layer thicknesses with an accuracy comparable to that of double crystal X-ray diffraction[5]. To the best of our knowledge, no FIR investigation of strained layer SLs has been reported. GaSb/A1Sb superlattices have attracted attention for their possible application in laser diodes emitting in the 1.3-1.7 ~ m range[8]. Their structural properties are influenced by the moderate (0.65%) lattice mismatch between the constituent materials. Strain and confinement effects have been previously investigated by means of ion-channeling, X-ray diffraction[9] and Raman spectroscopy[10,11]. Strain relaxation takes place for total AISb thickness greater than the critical value he= II +6nm[9]. We report here far i.r.reflectivity and X-ray diffraction of GaSb/AISb superlattices. Our results show that a satisfactory description of FIR spectra can be obtained provided that not only strain and phonon confinement but also strain relaxation processes are considered. 2. EXPERIMENTAL
GaSb/AISb superlattices were grown by molecular beam epitaxy either on GaAs or n-doped GaSb 625
(001)-oriented substrates. Undoped buffer layers 0.4 p m thick were grown on n-doped GaSb wafers. The optimized growth procedure reported in Ref.[l 2] was used. Structural data on the samples were obtained from X-ray diffraction. Diffraction patterns were recorded with a high resolution double crystal diffractometer using CuK~ radiation close to the symmetric (400) and asymmetric (511) reflections in order to obtain the lattice mismatch and strain fields normal and parallel to the crystal surface. Structural parameters were obtained through comparison with the results of computer simulation based on the dynamical scattering theory[13]. The best fit values are listed in Table i. I.r. measurements were performed under nearnormal incidence at 10 K by using a Fourier-transform spectrophotometer operating under vacuum. 3. RESULTS AND DISCUSSION
Figure I shows the FIR reflectivity spectrum of sample 1, representative of the series grown on n-doped GaSb substrates. The high reflectivity band extending in the low energy part of the spectrum up to about 200cm -~ and the broad band around 400cm -~ originate from plasma oscillations in the doped substrate. The intense structure extending in the range 200-260 cm- ~is due to the combined effect of "Reststrahlen" (RS) from GaSb either in the SL or in the substrate. The edge at 229.5 cm- ~coincides in energy with the bulk GaSb TO and is ascribed to the substrate. The weak shoulder at 227 cm- ~appearing on the low energy side of the bulk GaSb RS band can be ascribed to GaSb-like TO phonons in the SL. The structure appearing in the range 300-330 cm-J is due to RS from AISb-like phonons in the SL. Figure 2 shows the FIR spectrum of sample 5 which is grown on GaAs. Due to the different substrate, several changes can be observed with respect to the spectrum of sample I. In particular, no
626
G, SCAMARCIO et al.
Table I. StructuralparametersofGaSb/AISbsuperlattices.Here N = numberof periods;d = superlatticeperiod; d, = individuallayer thicknessesmeasured by X-rays(samples 1-3) or FIR (samples4. 5); (Adld)~. (Ad/d)z lattice mismatchparalleland normalto the (001)-plane,respectively;valuesin bracketsindicatemeanvalues Sample Substrate N d(nm) Layer d,(nm) (Ad/d)z (Ad:d): 1
GaSb
50
16.04
2
GaSb
100
5.55
3
GaSb
200
2.78
4
GaAs
285
4.9
5
GaAs
196
5.6
GaSb AISb GaSb AISb GaSb AISb GaSb AISb GaSb AlSb
plasmon-like reflectivity features related to the substrate are present. The GaAs substrate manifests itself in the range 270-300 cm -t, where the bulk-like RS band is modulated by the interference of radiation in the epilayer. In this case, the GaSb-like and AISb-like RS bands around 230 and 320 cm- ,, respectively, are well separated from that of the substrate. A complete assignment of the spectral features of Figs 1 and 2 will be discussed later after detailed comparison with calculations. The theory of Refs[2,14] gives a very satisfactory description of FIR for an "ideal" SL grown onto a semi infinite substrate. The SL dielectric function is written in the effective medium approximation as the average of the dielectric function of the constituent layers weighted by the layer thicknesses[7]. For layers thinner than about 10 monolayers the confinement induced shift of phonon energies has to be considereal[15]. In the case of strained layers the influence of lattice distortion on phonon energies needs to be evaluated, too. The dashed lines in Figs 1 and 2 have been calculated according to the above model considering an ideal GaSb/AISb SL with abrupt interfaces. For sample 1 the substrate doping has been properly considered by introducing a plasmon oscillator in the
13.26 2,89 3,75 1,80 1,74 1.04 3.1 1,8 4.2 1.4
- 3 , 6 × 10 ~ 1,3 × 10 -' (4.1 x 10 -~)
(3.95 x 10 5)
0 1.29 x 10 -2 ( 8 . 1 3 x 1 0 2)
0 0 ( 6 . 5 × 1 0 -')
(8.14x 10-")
(6.68 × l0 :)
substrate dielectric function. In the calculations we have taken the layer thicknesses of Table 1. The following parameters have been adjusted for best reproduction of the experimental data: the plasmon frequency and damping tOp and jp; the phonon frequency and damping in the j t h layer, tOro.j and Fj. Although a good overall agreement was obtained, several important structures cannot be reproduced at all. In particular, there is no way to reproduce the dip at 316.7cm -t in Fig. 1. The same is true for the structured GaSb-like and AlSb-like RS bands in Fig. 2. This discrepancy will be corrected by taking into account strain induced structural deterioration, as explained in the following. Strain relaxation in a superlattice structure manifests itself by non-zero values of the in-plane lattice mismatch or by negative strain values in the GaSb layers. The values of Table I show a partial degree of relaxation for samples 1-3 grown on GaSb substrate, which increases at increasing the A1Sb layer and the total superlattice thicknesses. This expected behaviour is related to the individual layer and total AISb thicknesses by far exceeding the critical values in GaAs/AISb structures[9]. Lattice relaxation occurs through the formation of defects, misfit dislocations and intermixed layers at the heterointerfaces. This causes interface roughness and local fluctuations of
100 100
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.
200
.
.
.
.
.
.
.
300
WAVE NUMBER
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400
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Fig. 1. FIR spectrum of (GaSb)t32,m (AlSb):.~.= SL (sample 1) grown on n-doped GaSb substrate. Dotted line: experimental data. Dashed line: spectrum calculated as explained in the text for abrupt interfaces. Solid line: spectrum calculated considering 5% intermixing at the interfaces.
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.
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L
250
300 WAVE NUMBER (em -'l)
Fig. 2. FIR spectrum of (GaSb)42,,, (AISb),4,m SL (sample 5) grown on GaAs substrate. Dotted line: experimentaldata. Dashed line: spectrum calculated for abrupt interfaces. Solid line: spectrum calculated for a AIo,Ga09Sb/Al07Ga0~Sb SL as explained in the text.
627
Infrared rettectivity of strained GaSb/AISb superlattices Table 2. Data on the intermixing in GaSb/AISb SL samples deduced by the fittingof FIR spectra. Here t and x indicate the average thicknessand A1 mole fraction of the Al~Gat_~Sblayer at the interface. The percentage of intermixingis evaluated as IO0[t/(dj+ d2)] Sample
t (nm)
x
%
I 2 3
0.87 0.80 0.10
0.15 0.40 0.32
5 14 3
strain fields in the layers. In fact, a satisfactory agreement between the calculated and experimental X-ray diffraction patterns of samples 1-3 was obtained only if 0.1-0.2 nm thickness fluctuations and ,,-10 -3 strain fluctuations were considered. Hence, the simplistic assumption of homogeneous and abrupt interfaces has to be abandoned. Considering moderate thickness fluctuations in the model of FIR, does not give substantial improvement to the reproduction of the experimental features in Fig. 1. On the other hand, the existence of an intermixed layer at the GaSb/AISb interface can have a strong influence on the SL "Reststrahlen" profile mainly because of the additional phonon resonances and the modification in the spatial configuration. Hence, we have included in the model of FIR the presence of an AlxGa~ _~Sb layer of thickness t at the interface. In this way we are considering one SL period as constituted by three layers of thicknesses d~ (GaSb), d~ (AISb) and t (AIxGal _xSb). The sum (d~ + d~ + t ) and the ratio (d; + t/2)/(d~ + t/2) are fixed at the X-ray values of the period d and the ratio dl/d: between the layer thicknesses, whereas the AI mole fraction x is left as a fitting parameter. The latter parameter fixes also the alloy phonon frequencies according to the known dependence from the chemical composition[16]. The dotted line in Fig. 1 was calculated considering a 0.87 nm thick Alo.~5Ga0.s5Sb layer at each heterointerface. All spectral features of Fig. 1 are now satisfactorily reproduced. A similar improvement is obtained also for samples 2 and 3. The best fit values of SL TO phonon frequencies are consistent with the moderate confinement and strain induced shifts calculated considering the measured structural parameters. Similar findings on the combined effects of strain and confinement on the LO phonon frequencies have been obtained from Raman scattering experiments[l 0,11 ]. A detailed description of the fitting procedure will be reported elsewhere in a more extensive form. For the sake of the present discussion it is worth to list in Table 2 the fitting parameters concerning the intermixing. The values of the AI mole fraction of Table 2 are close to the ratio d2/(dj +d2) between the X-ray thickness values. A simple explanation for this is that the chemical composition of the intermixing alloy layers is determined by the relative abundance of the AI and Ga atoms. Further, a correlation appears between the percentage of intermixing and growth
parameters such as the AISb overall thickness, and the relative thickness between GaSb and AISb layers. For drawing more quantitative conclusions on this point the investigation of a larger number of samples is needed. Our previous analysis shows that intermixed layers as thin as a few tenths of nanometers intercalated in the SL matrix reveal themselves as clearly detectable structures in the reflectivity spectra of Fig. 1. Indeed, the presence of a doped substrate, whose reflectivity behaviour resembles that of a metal, strongly enhances weak phonon resonances of the superlattice. Figure 3(a-c) show the AISb-like RS spectra calculated for different values of the substrate plasma frequency tOp and the AlxGa~_ ~Sb layer thickness, t. The remaining parameters in the calculations are the same used for fitting to the spectrum of sample I. In Fig. 3(a) we see that only very weak differences exist among the spectra corresponding to t = 0, 0.8 and 1.6 nm when tOp = 0, i.e. for an undoped substrate. In contrast, the "Reststrahlen" band lineshape changes dramatically in Fig. 3(b) when a metallic behaviour is switched on by setting tOp = 400 cm- ~, close to the actual value of tOp in sample I. A strong dip appears on the low energy side of the AISb-like band close to the TO frequency of the alloy. By further increasing the doping level, i.e. setting tOp = 800 cm-~ causes a stronger modification of the whole spectrum which becomes absorptive-like in Fig. 3(c). This behaviour closely resembles the reflectivity of a thin dielectric film deposited onto a metallic substrate[17]. In the case of samples 4 and 5, by considering the presence of only a thin intermixed layer at the
100
50
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L~ _J LL L~ IV'
i
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0
i
i
i
310
320
330
0 301
1 34-0
WAVE NUMBER ( c m - ) Fig. 3. AISb-like"Reststrahlen'" bands calculated for different values of plasmon frequencies: (a) tot=0; (b) t% = 400 cm-i; (c) top = 800 cm-i. Dotted lines: abrupt interfaces. Solid lines: 5% intermixing at the interfaces. Dashed lines: 10% intermixing at the interfaces.
628
G. SCAMARCIOet al.
interface gives no significant improvement in the reproduction of experimental data. The diffraction patterns of the superlattices deposited on GaAs substrate (samples 4 and 5) are characterized by much broader and weaker satellite peaks. This indicates a large amount of defect formation and, particularly, a strong intermixing. The structural deterioration in the above samples is mainly caused by the huge ( ~ 8 % ) lattice mismatch between GaAs and GaSb or AISb layers. The above structural data induced us to model the SL as a sequence of two alternating AI~Ga~_ ,.Sb and AI, Ga~ _,Sb layers, with the AI mole fractions x and y close to the nominally pure layer values 0 and 1. The dotted curve in Fig. 2 was calculated with x = 0.1 and y = 0.7. Since the spectral quality of the X-ray diffraction patterns is not good enough to allow the determination of the individual layer thicknesses in this case, they were fixed to the values of Table ! which give the best reproduction of F I R spectra. In spite of the roughness of the considered model a very satisfactory reproduction of all the spectral features is obtained. In particular, the dips at 226.7 and at 319.7 cm -~, which are peculiar of the GaSb-like and AlSb-like SL "Reststrahlen" bands, are now properly reproduced by the theory.
4. CONCLUSION Our results show that F I R is a powerful tool for the investigation of vibrational and structural properties of strained layer GaSb/AISb superlattices. In addition to strain and confinement effects on SL phonons, our analysis allows to obtain important information on the interface deterioration. Taking advantage from the enhancement of weak SL phonon resonances induced by the metallic behaviour of the doped substrate, the chemical composition and the average thickness of AI~Ga L_ ,Sb alloy layers formed at the interfaces are determined. X-ray diffraction is sensitive to thickness and strain fluctuations in the
structure. It clearly merges the close complementarity of the two techniques for the study of strain relaxation processes. Acknowledgernent--This work is partially supported by MURST and CNR. REFERENCES
I. K. A. Maslin, T. J. Parker, N. Ray, D. R. Tilley, P. J. Dobson, D. Hilton and C. T. B. Foxon, Solid St. Cornrnun. 60, 461 (1986). 2. Bo Lou, R. Sudharsanan and S. Perkowitz, Phys. Rer. 1138, 2212 (1988). 3. G. Scamarcio, L. Tapfer, W. K6nig and K, Ploog, Appl. Phys. A 51, 252 0990). 4. G. Scamarcio, L. Tapfer, W. K6nig, A. Fisher, K. Ploog, E. Molinari, S. Baroni, P. Giannozzi and S. de Gironcoli, Phys, Rev. B 43, 14754 (1991). 5. G. Scamarcio, C. Gadaleta, M. Sibilano and K. Ploog, Solid St. Cornrnun. 84, 757 (1992). 6. B. Samson, T. Dumelow, A. A. Hamilton, T. J. Parker, S. R. P. Smith, D. R. Tilley, C. T. Foxon, D. Hilton and K. J. Moore, Phys. Rec. B 46, 2375 (1992). 7. V. M. Agranovich and V. E. Kratsov, Solid St. Cornrnun. 55, 85 (1985). 8. Y. Ohmori, Y. Suzuki and H. Okamoto, Japan, J. appl. Phys. 24, L657 (1985); J. appl. Phys. 64, 6733 (1988). 9. H. J. Gossman, B. A. Davidson. G. J. Gualtieri, G. P. Schwartz, A. T. Macrander, S. E. Slusky, M. H. Grabow and W. A. Sunder, J. appl. Phys. 66, 1687 (1989). 10. P. V. Santos, A. K. Sood, M. Cardona. K. Ploog, Y. Ohomori and H. Okamoto, Phys. Rer. B 37, 6381 (1988). 11. G. P. Schwartz, G. J. Gualtieri, W. A, Sunder and L. A. Farrow, Phys. Rev. B 36, 4868 (1987) and references therein. 12. Y. Suzuki, Y. Ohmori and H. Okamoto, J. appl. Phys. 59, 3760 (1986). 13. L. Tapfer, Physica scripta T25, 45 (1989). 14. O. E. Piro, Phys. Rev. B 36, 3427 (1987). 15. See, e.g.B. Jusserand and M. Cardona, in Topics in Applied Physics, Vol. 66 (Edited by M. Cardona and G. Giintherodt), p. 49. Springer, Berlin (1988). 16. Landolt-B6rnstein, Numerical Data and Functional Relationships in Science and Technology (Edited by O. Madelung), Vol. 111 17-a. Springer, Berlin (1983). 17. D. V. Berreman, Phys. Rer. 130, 2193 (1963).