Temperature dependence of In1−xGaxSb reflectivity in the far infrared

Materials Chemistry and Physics 125 (2011) 72–76

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Temperature dependence of In1−x Gax Sb reflectivity in the far infrared P.M. Nikolic´ a,∗ , K.M. Paraskevopoulos b , E. Pavlidou b , T.T. Zorba b , T. Ivetic´ a , S.S. Vujatovic´ a , O.S. Aleksic´ c , N. Nikolic´ c , O. Cvetkovic´ d , V. Blagojevic´ e , M.V. Nikolic´ c a

Institute of Technical Sciences of SASA, Knez Mihailova 35/IV, 11000 Belgrade, Serbia Physics Department, Solid State Section, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece c Institute for Multidisciplinary Research, Kneza Viˇseslava 1, 11000 Belgrade, Serbia d IChTM, Center of Chemistry, Studentski Trg 12, 11000 Belgrade, Serbia e Faculty of Electrical Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, 11000 Belgrade, Serbia b

a r t i c l e

i n f o

Article history: Received 25 February 2010 Received in revised form 14 July 2010 Accepted 23 August 2010 Keywords: Semiconductors Fourier transform infrared spectroscopy (FTIR) Optical properties Phonons

a b s t r a c t Far infrared reflectivity spectra of polycrystalline In1−x Gax Sb were measured and numerically analyzed using the classical dispersion formula and also a fitting procedure based on the modified plasmon-phonon interaction model in the temperature range from 10 K to 300 K. Optical parameters were calculated and discussed. A local mode belonging to the GaSb rich end and two-mode behavior were observed at low temperatures. © 2010 Elsevier B.V. All rights reserved.

1. Introduction Recently, increasing attention has been paid to developments in the field of semiconductor dots (QDs) based on InSb/GaSb [1–4], with lattice mismatch at 6.3%. Optical reflectivity properties of InSb at room and low temperatures [5,6] and magneto-optical transmission experiments at temperatures ranging from 300 K to 700 K [7] were measured a long time ago. Infrared reflectivity spectra of the mixed crystal system Ga1−x Inx Sb were measured at room temperature [8]. A detailed investigation of FIR and Raman spectra of thin film In1−x Gax Sb was conducted in [9]. Infrared reflectivity data enabled determination of the effective mass in n and p type films, while combined Raman and infrared data gave detailed information on TO and LO frequencies. In this work we have measured and analyzed far infrared reflectivity spectra for five samples with different compositions at room temperature and one in the temperature range between 10 K and 300 K. 2. Experimental InSb and GaSb compounds were synthesized from high purity elements (6N). Mixed crystal ingots were produced using a zone-leveling ingot of the desired composition with the zone travel rate of 1 mm/h. Samples between 1 mm and 2 mm thick were cut and highly polished with 1 ␮m grade diamond paste. The structural

∗ Corresponding author. ´ E-mail address: [email protected] (P.M. Nikolic). 0254-0584/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.matchemphys.2010.08.073

characteristics of all samples were determined by the XRD technique using a Philips PW1050 difractometer with a copper tube and a graphite monochromator. The composition of each sample was determined using EDS analysis on a JEOL JSM-84A SEM equipped with an EDS – Oxford ISIS 300 micro-analytical system. For each sample data was taken from several areas 1 × 1 ␮m in size and an average value was obtained enabling a measurement accuracy of ±0.2%. Highly polished samples were used for optical reflectivity measurements on a Bruker IFS 113 V Fourier transform spectrometer with an Oxford cryostat for low temperature measurements. The reflectivity measurements were made in the temperature range between 10 K and 300 K and the resolution was 1 cm−1 .

3. Results and discussion The measured far infrared reflectivity spectra of an In0.95 Ga0.05 Sb polycrystalline sample are shown in Fig. 1. A combined plasmon-LO phonon mode was observed [10] for each temperature and it was between 280 cm−1 and 300 cm−1 . In this case the pure LO modes of the lattice are strongly influenced by the plasmon mode (ωp ) of free carriers [10]. The room temperature mode is at the lowest wave number and it moves slightly towards higher wave numbers when the temperature decreases (Fig. 2). Two sharper minima are present in Fig. 1 for all temperatures at about 180 cm−1 and 200 cm−1 . When the temperature is decreased to 110 K or below, a third minimum, less exposed, is also observed at about 230 cm−1 . The origin of all three minima will be discussed later on. Fig. 3a shows the room temperature reflectivity spectrum versus wave number for In0.63 Ga0.37 Sb. The minimum is at about 130 cm−1

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Fig. 3. Room temperature far infrared reflectivity for (a) In0.63 Ga0.37 Sb (b) In0.6 Ga0.4 Sb (c) In0.26 Ga0.74 Sb and (d) In0.22 Ga0.78 Sb.

Fig. 1. Far infrared reflectivity spectra of an In0.95 Ga0.05 Sb polycrystalline sample in temperature range between 10 K and 300 K.

All experimental spectra were numerically analyzed using the following multi-oscillator model (Eq. (1)): ε(ω) = ε∞ +

and there are two sharp minima at about 187 cm−1 and 219 cm−1 . Fig. 3b shows a similar diagram obtained for In0.6 Ga0.4 Sb without a plasmon-LO phonon mode. When the content of indium is further decreased as for the case of In0.26 Ga0.74 Sb (Fig. 3c) and In0.22 Ga0.78 Sb (Fig. 3d) then the measured room temperature reflectivity spectra only have one sharp minimum at about 230 cm−1 and a slight minimum at about 185 cm−1 .



2 Sj ωTOj

j

2 − ω2 − iω ωTOj j

where ε∞ is the dielectric high frequency permittivity, Sj is the oscillator strength; ωTOj (ωLOj ) is the TO (LO) phonon frequency and  j is the damping factor of the j-th lattice oscillator. A similar model was also used by Macler et al. [9] to analyze infrared reflection spectra of In1−x Gax Sb films grown on GaAs substrate. A modified four-parameter model of coupled oscillators was also used (Eq. (2)) [10,11] where the dielectric function ε(ω) is:

2 

ε (ω) =ε∞

Fig. 2. Change of the plasmon-LO phonon mode with temperature.

(1)



j=1

ω2 + ilj ω − ωlj2

ω ω + ip





 r  2 2  ω + iln ω − ωln    2 2

ω2 + it ω − ωt

n=1

ω2 + ion ω − ωon

(2)

where ωlj and  lj represent the Eigen frequencies and damping factors of the plasmon-LO phonon waves, respectively. The parameters of the first denominator correspond to the transverse mode while  p is the damping factor of the plasma mode. The second term in Eq. (2) refers to the impurity mode where ωon and ωln are characteristic transverse and longitudinal frequencies, respectively while  on and  ln are their damping factors. The starting values of all parameters used during the fitting procedure were previously determined using Kramers–Kronig analysis [12,13]. All measured spectra were fitted using both Eqs. (1) and (2) and good agreement between obtained parameters was obtained. As an example, the fitting curve for FIR spectrum of the In0.95 Ga0.05 Sb sample measured at 10 K and 300 K are given in Fig. 4. The solid line is the calculated spectrum obtained by the fitting procedure using Eq. (2). The calculated values of all parameters for this sample in the range between 10 K and room temperature are given in Table 1. The values of their error bars are smaller than 2 cm−1 . One can note that the calculated plasma frequency decreases slightly (from 280.2 cm−1 to 262 cm−1 ) with increase in

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Fig. 5. Calculated values of transverse optical modes ωTOj versus temperature.

Fig. 4. Measured (dashed line) and calculated (solid line) FIR spectra of In0.95 Ga0.05 Sb at 10 K (a) and 300 K (b).

the temperature from 10 K to 300 K. The dependence of determined transverse optical modes ωTOj is shown in Fig. 5 in the temperature range between 10 K and room temperature, respectively. Two transverse optical modes of In0.95 Ga0.05 Sb are quite stable as a function of temperature, except the third mode that is not noticeable at temperatures above 200 K. However, for increased Ga content to 37 at.% or even 78 at.% at room temperature the two noted optical modes approached values belonging to pure GaSb and InSb compounds [8]. For five different compositions the calculated room

Fig. 6. Change of (a) optical mode, and (b) oscillator strength versus the In content.

temperature values (using Eq. (2)) were used to plot the two noted transverse optical modes (Fig. 6a). Longitudinal optical mode (ωLOj ) values were calculated using Eq. (2) e.g. a modified four parameter model of coupled oscillators, while transversal optical mode values were the same using both applied models. This once more

Table 1 Calculated values of optical parameters for In0.95 Ga0.05 Sb (all values are given in cm−1 ).

ωp p ωTO1  TO1 ωLO1  LO1 ωTO2  TO2 ωLO2  LO2 ωTO3  TO3 ωLO3 ε∞

10 K

30 K

50 K

90 K

110 K

280.7 39.5 182.3 3.8 202.3 5.1 203.7 5.8 228.6 7.8 229.6 6.3 232 15.6

278.6 41.6 182.4 4 202.7 3.8 203.7 3.8 229.9 13 231.6 9.8 232 15.6

277 50 183 3 202.3 5.8 204 5.7 229.6 11.2 230.3 9.5 231 15.5

277 38 180 4.5 201 4 202.2 4.2 228 13.2 228.9 11.2 230 14.7

279 32 183 4 202.6 4.2 204 4.2 225 11 226.8 11.4 227 13.1

130 K 279 34 184.8 3.9 201.6 3.9 203.2 4.2 224 8.7 224.3 8.9 225 13

200 K

300 K

270 30.5 181 4.2 199.6 4.9 201.2 5.2

261.8 28 180.9 4.2 198.6 7.3 201.2 7.1

15

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Fig. 7. Imaginary part of the dielectric permittivity versus wave number for In0.95 Ga0.05 Sb measured at: (a) 30 K and (b) 300 K and (c) In0.22 Ga0.78 Sb at 300 K.

confirmed the good quality of the fitting process. The oscillator strength was calculated for the two determined modes (S1 and S2 ) and is given in Fig. 6b as a function of composition (In content). One can get a clearer insight into changes of InGaSb properties with temperature and composition from diagrams of the imaginary part of the dielectric permittivity (ε2 ) and energy loss function (−Im (ε−1 )) versus the wave number. Fig. 7 and Fig. 8 show ε2 and −Im (ε−1 ) spectra versus the wave number, respectively for an In0.95 Ga0.05 Sb sample at 30 K and 300 K and an In0.22 Ga0.78 Sb sample at room temperature. It is obvious that at 30 K we can observe three transverse optical modes, while at room temperature there is

Fig. 8. Energy loss functions −Im(ε−1 ) versus wave number for In0.95 Ga0.05 Sb measured at: (a) 30 K and (b) 300 K and (c) In0.22 Ga0.78 Sb at 300 K.

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one less regardless of the sample composition. Similarly, the energy loss function −Im (ε−1 ) has three peaks in Fig. 8 at room temperature and four at 30 K. Since the strongest peak originates from the plasmon-LO phonon mode the three smaller peaks at 30 K belong to three longitudinal optical modes. At room temperature the weakest one disappears which belongs to the effect of Ga atoms. The positions of transversal and longitudinal optical modes given in Fig. 6a are thus confirmed. Our results obtained for the In0.95 Ga0.05 Sb sample can be compared to room temperature data determined by Brodsky et al. [8] who interpreted measured spectra in terms of a damped harmonic oscillator model. While at room temperature we both observed two modes, at low temperatures (Fig. 5) we registered one mode more that was closer to transversal and longitudinal modes of pure GaSb but at slightly lower frequencies. Ours were ωTO = 229.6 cm−1 and ωLO = 232 cm−1 while at room temperature according the literature [8] those modes are at 227 cm−1 and 238 cm−1 , respectively. Brodsky et al. [8] also concluded that variation of the TO-phonon frequencies (ωTOj ) and oscillator strengths (Sj ) with composition do not conform to the traditional types of behavior defining the long wavelength optical phonons in these pseudo-binary alloys. Our results given in Fig. 6 are in agreement with this observation. Brodsky et al. [8] considered carefully if the observed optical phonons in Ga1−x Inx Sb were representative of either one or twomode behavior. They proposed a classification scheme based on the behavior of impurities at either end of the alloy composition range, which helps to define better the general nature of two-mode behavior manifested in Ga1−x Inx Sb. They also discussed about dividing the observation of mixed crystal behavior into three categories. The simplest one is where both gap and local modes occur at the respective ends of the alloy system. The second category is one in which either the gap or local mode is allowed. They finally decided that the local mode is allowed and the gap mode is not. The model predicts that a local mode will be produced by the substitution of Ga for In in InSb and that is the reason why we chose to examine the In0.95 Ga0.05 Sb sample composition in a wide temperature range. Looking at the compositional dependence of the TO and LO phonon frequency obtained from the oscillator analysis (Fig. 6a) one can see that the high frequency band decreases for a small concentration of In in GaSb from about 230 cm−1 to about 200 cm−1 , when the In content is 0.95 closer to pure InSb. The set of frequencies (TO2 and LO2 ) decreases from GaSb towards InSb with increasing content of In. The second set of frequencies (TO1 and LO1 ) behaves differently. The LO1 frequency increases slowly, while the TO1 frequency decreases as the In concentration increases. This means that the low frequency band behavior of TO1 and LO1 is “two” mode-like but the high frequency band behavior (TO2 and LO2 ) is “one” modelike. Exactly the same behavior was registered by Macler et al. [9] for thin film In1−x Gax Sb on GaAs substrate for both room temperature and 80 K. If data, given in Fig. 6a, is compared with the data given in Fig. 5 it is obvious that three optical TO modes can be observed at low temperatures (Fig. 5) compared to the two observed at room temperature (Fig. 6). We can conclude that the third phonon mode, observed at slightly above 200 cm−1 belongs to the impurity mode of In in GaSb which should be below the TO-phonon frequency of GaSb. Ga1−x Inx As behaves similarly [14]. Brodsky et al. [8] reported that K1−x Rbx I behaves in the same way following MREI model results for TO and LO modes [15]. Both have features similar to both “one” and “two” mode systems. Analysis of optical reflectivity diagrams of these systems, together with analysis of GaP1−x Asx and PGa1−x Inx systems, at low temperatures would help to complete the classification of pseudo-binary mixed crystals. Besides optical reflectivity measurements at room temperature, only optical reflec-

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tivity measurements of thin film In1−x Gax Sb on GaAs substrate [14] and K0.95 Rb0.05 I have been done at 80 K [15]. The reflectivity spectrum of this system at 80 K also has three peaks, similar to our low temperature measurements of In0.95 Ga0.05 Sb (Figs. 3 and 4). Our room temperature dependence of the transversal optical mode behavior (Fig. 6) is also very similar to the wave number versus mole fraction of K1−x Rbx I with composition data given in [15]. 4. Conclusion In this work we have analyzed infrared reflectivity for the Inx Ga1−x Sb mixed crystal system. The experimental results were analyzed using the classical dispersion formula and a modified four-parameter model of coupled oscillators. At low temperatures we clearly observed a local mode belonging to the GaSb rich end. We also observed two other phonon modes. The low frequency band behavior of TO1 and LO1 is “two” mode-like, while the high frequency band behavior is “one” mode-like. These results were correlated with similar mode behavior noted in literature for In1-x Gax Sb thin films on GaAs substrate, Ga1−x Inx As and K0.95 Rb0.05 I.

Acknowledgments This work was performed as a part of project 142011G financed by the Ministry of Science and Technological Development of the Republic of Serbia. References [1] N. Deguffroy, V. Tasco, A.N. Baranov, E. Tournié, B. Satpati, A. Trampert, M.S. Dunaevskii, A. Titkov, M. Ramonda, J. Appl. Phys. 101 (207) 124309. [2] A. Koier, Mid-Infrared Semiconductor Optoelectronics, Springer, Berlin, 2006. [3] J.B. Rodriguez, P. Christol, F. Chevrier, A. Joullié, Physica E 28 (2005) 128. [4] K. Seeger, Semiconductor Physics, Springer, Berlin, 2006. [5] H. Yoshinaga, R.A. Oetjen, Phys. Rev. 101 (1956) 526. [6] G. Carelli, N. Ioli, A. Messina, A. Moretti, S. Schepis, F. Strumia, Int. J. Infrared Millimeter Waves 19 (1998) 1191. [7] P.Y. Liu, J.C. Maan, Phys. Rev. B 47 (1993) 16279. [8] M.H. Brodsky, G. Lucovsky, M.F. Chen, T.S. Plaskett, Phys. Rev. B 2 (1970) 3303. [9] M. Macler, Z.C. Feng, S. Perkowitz, R. Rousina, J. Webb, Phys. Rev. B 46 (1992) 6902. [10] A.A. Kukharskii, Solid State Commun. 13 (1973) 1761. [11] F. Gervais, B. Piriou, Phys. Rev. B 10 (1974) 1642. [12] D.M. Roessler, Br. J. Appl. Phys. 16 (1965) 1119. [13] D.M. Roessler, Br. J. Appl. Phys. 16 (1965) 1359. [14] M.H. Brodsky, G. Lucovsky, Phys. Rev. Lett. 21 (1968) 990. [15] J.H. Fertel, C.H. Perry, Phys. Rev. V184 (1969) 874.