GaAs structures grown by MOVPE and UHVE

Journal of Crystal Growth 395 (2014) 26–30

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Analysis of the VIS–NIR spectral reflectance of Bi/GaAs structures grown by MOVPE and UHVE M.M. Habchi a, I. Massoudi a, A. Rebey a,n, R. Ben Chaâbane b, B. El Jani a a b

Unité de Recherche sur les Hétéro-Epitaxies et Applications (URHEA), Faculty of Sciences, University of Monastir, Monastir, Tunisia Laboratoire de Physique et Chimie des Interfaces (LPCI), Faculty of Sciences, University of Monastir, Monastir, Tunisia

art ic l e i nf o

a b s t r a c t

Article history: Received 6 May 2013 Received in revised form 25 February 2014 Accepted 2 March 2014 Communicated by: C. Caneau Available online 12 March 2014

Bismuth films have been deposited onto (001) GaAs substrates by metal organic vapor phase epitaxy and ultra-high vacuum evaporation. The optical and morphological properties of the Bi/GaAs samples were investigated using spectral reflectance (SR) and atomic force microscopy. The real refractive index and the extinction coefficient of bismuth were determined in the wavelength range 400–1700 nm using theoretical analysis of in situ and ex situ SR measurements. Best simulations of SR data versus time and wavelength allow the decoupling of the effects on reflectivity of parameters such as bismuth film's thickness, roughness and temperature. In the near infrared domain, SR signals present a peak at around 0.9 eV which can be attributed to bismuth. & 2014 Elsevier B.V. All rights reserved.

Keywords: A1. Bismuth compounds A1. Crystal morphology A1. Refractive index A3. Metal organic vapor phase epitaxy B2. Semiconducting gallium arsenide

1. Introduction The growth of metals on semiconductors has received a lot of attention in the last few years. It allows the production of structures which combine the characteristics of both semiconductor and metal [1–4]. However, this heteroepitaxy is complicated by the strong chemical interactions between the materials. The semiconductor surface pre-treatment and metallic film's growth conditions have a deep impact on the quality of the metal– semiconductor interface. In addition, the surface segregation in such systems [5] and the substrate stoichiometry [6] perturb this epitaxial relationship. Recently, GaAs substrates with bismuth thin films have been of considerable interest in the fabrication of new materials suitable especially for microelectronic [7–9] and optoelectronic applications [10,11]. The Bi–GaAs interface is a Schottky barrier which prevents the current flow from the thin film of bismuth to the substrate and is very suitable for high-speed devices [12,13]. The Bi/GaAs structures have been grown by several techniques such as molecular beam epitaxy (MBE) [14], liquid phase epitaxy (LPE) [15], ultra-high vacuum evaporation (UHVE) [16,17] and metal organic vapor phase epitaxy (MOVPE) [18,19]. MOVPE was in situ monitored using many optical techniques such as laser reflectometry [20,21], reflectance difference

n

Corresponding author. Tel.: þ 216 73500274; fax: þ 216 73 500278. E-mail address: [email protected] (A. Rebey).

http://dx.doi.org/10.1016/j.jcrysgro.2014.03.001 0022-0248/& 2014 Elsevier B.V. All rights reserved.

spectroscopy [22,23], spectroscopic ellipsometry [24,25] and spectral reflectance, denoted by SR [26,27]. The aim of this work is the determination of the refractive indices of bismuth throughout the wavelength range 400–1700 nm. This study is mainly based on our previous work [28]. In order to confirm the optical properties of bismuth derived from in situ SR measurements, we have investigated ex situ recorded SR signals of Bi/GaAs structures grown by MOVPE and UHVE. Since the surface morphology is shown to affect the reflectivity, we have also explored the morphological properties of Bi/GaAs (001) by atomic force microscopy (AFM).

2. Experimental procedures The two different samples, denoted by A and B, consist of bismuth films grown on epi-ready (001) GaAs substrates by MOVPE and UHVE respectively. The substrate of sample A was exposed in an atmospheric pressure MOVPE reactor, during 43 min, to trimethylbismuth (TMBi) flow. Before starting the exposure, the substrate temperature was first ramped in a mixture flow of hydrogen (H2) and arsine (AsH3) till a temperature of 750 1C in order to remove the native surface oxide layer. H2 was purified through a palladium cell and used as a carrier gas at a total flow rate of 3 SLM (for “Standard Liter per Minute”) pressurized to 1 atm. When the substrate temperature was stabilized at 375 1C, we have introduced 3.9 mmol/min of TMBi in the

M.M. Habchi et al. / Journal of Crystal Growth 395 (2014) 26–30

reactor and we have stopped the arsine flow simultaneously. MOVPE was in situ monitored by a spectral reflectance apparatus. Continuous incident light was provided by a halogen lamp emitting from roughly 380 to 2400 nm. To carry the incident and the reflected beams, we use two optical fibers attached to the reactor windows with an angle of 301 with respect to the normal of the wafer surface. The reflected signal is detected by a spectrometer containing a charge coupled device (CCD1), pre-set to the 200– 1000 nm wavelength range. The spectrometer resolution is equal to 1.4 nm. On the other hand, sample B was grown by UHVE during 20 min, at a pressure of 2  10  6 mbar. The bismuth deposition was performed at room temperature. During the UHVE experiment, the bismuth was kept in a gas cylinder maintained at a temperature of 410 1C. Our apparatus is equipped with a quartz crystal microbalance (QCM) for layer thickness measurements. After the growth, the reflectivity of samples A and B was ex situ recorded at normal incidence in the visible–near infrared domain (VIS–NIR) using two different SR set-ups. The incident beams were provided by deuterium–halogen and halogen lamps to cover the spectral range 200–1700 nm. The SR signal was detected using the CCD1 mentioned above. The detection domain of the CCD2 associated with the second SR apparatus ranges from 1000 to 1700 nm. The surface morphology of the samples was analyzed by atomic force microscopy in contact and tapping modes.

3. Results and discussion Fig. 1a and b shows the variation of the experimental in situ reflectivity signal (R) as a function of the exposure time (t) for several selected wavelengths (λ) ranging from 400 to 1000 nm (full spheres). R is normalized with respect to the substrate's response: R¼ Rsample/Rsubstrate [29]. The curves were recorded during the deposition of bismuth thin film on a GaAs substrate by MOVPE (sample A). Note that R(t) exhibits different behaviors

27

for different incident wavelengths. For wavelengths lower than 500 nm, the reflectivity intensity remains constant for a few minutes, then decreases (see full spheres in Fig. 1a). On the contrary, for wavelengths longer than 500 nm, the introduction of TMBi flow into the reactor causes an immediate increase of the reflectivity, which reaches a maximum value Rmax and then decreases slowly. Durations of increasing and decreasing phases are dependent on wavelength. We have found that Rmax follows a linear dependence as a function of λ (see full spheres in Fig. 1c). The best linear fit is described by a slope α1 equal to 0.047%/nm (see Fig. 1c). The time at which the reflectivity of the Bi/GaAs structure presents the same intensity value as the GaAs substrate is called crossing time and denoted t100%. Fig. 1a shows that SR signals cross the 100% intensity-line (short-dotted line) at different times when λ varies. The variation of t100% versus wavelength is shown in Fig. 1d by full spheres. Similarly to the behavior of Rmax, we have found that t100% varies linearly with wavelength in the range 450–700 nm. The calculated slope is β1 ¼0.153 min/nm. The exposure time is not sufficient for the SR to cross the 100% intensity-line for λ 4700 nm. In our previous works [28,29], we have attributed the reflectivity change, in part, to the λ-dependence of the film's refractive indices [30–32]. The optical constants of sample A are not the only parameters affecting the SR signal. The change of the surface morphology during the epitaxy can also affect the reflectivity behavior. AFM measurements at different growth times (0, 9 and 43 min) lead to plot the Root Mean Square (RMS) roughness as a function of time (see Fig. 2). Note that the line joining the 3 points is just an aid to the eye. We have added in Fig. 2 AFM images in 3D representation showing the evolution of the surface morphology over time. The first image (5 μm  5 μm) is measured before starting the epitaxy. The second AFM image, over 10  10 μm², was taken at 9 min of growth. It shows the formation of Bi islands. They are assuming a rounded bumpy shape. Their average size is 976 nm in diameter and 206 nm in height. The bismuth island density is about 9  106 cm  2. The third AFM image (5 μm  5 μm)

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Fig. 1. (a) and (b) The temporal variation of the normalized reflectivity intensity (R) recorded during the growth of Bi films on GaAs substrate by MOVPE (full spheres). Continuous and dashed lines show the best simulation of the reflectivity response for incident wavelengths ranging from 400 to 1700 nm. (c) and (d) The dependence on incident wavelength of Rmax and t100% respectively. The experimental and calculated values of Rmax (and t100%) are represented by full spheres and open circles respectively.

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M.M. Habchi et al. / Journal of Crystal Growth 395 (2014) 26–30

where

40

"

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0

0 min

0

10

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t (min) Fig. 2. Root Mean Square (RMS) roughness measured by AFM as a function of exposure time. We have inserted in the same figure 3D AFM images showing the surface morphology of sample A grown by MOVPE for three exposure times: 0, 9 and 43 min. In the 3D AFM images, the lines parallel to one side of each scan are artifacts.

proves that islands change shape, size and density between 9 and 43 min of the epitaxy. They assume a rounded shape. Their dimensions are approximately halved (480 nm in diameter and 106 nm in height) compared to those measured after 9 min of deposition. The Bi island density increased to reach the value of 8  108 cm  2. The RMS roughness increases as a function of the exposure time. At 43 min, RMS roughness attains the value 37.7 nm, about twice the value measured at 9 min (18.2 nm). Many researchers remarked that the growth of bismuth films on the GaAs substrate follows the Stranski–Krastanov (S–K) mode [33–36]: the first monolayer (ML) is epitaxial while the second monolayer is two-dimensionally disordered. The three dimensional disorder begins with the third monolayer. The Bi atoms of the first monolayer form as chains on the GaAs substrate, and the chains have a characteristic length imposed probably by a lattice mismatch with the GaAs. This behavior introduces a weak periodicity in the surface potential. For Bi layers grown on a (110) GaAs substrates, Guo et al. [33] confirmed that the three dimensional islands appear at coverage beyond 3 ML. In spite of the crystallographic orientation difference of GaAs substrates our results agree with Guo et al. observations. In our previous work [28], we have shown that the simulation of the in situ reflectivity curves of Bi/GaAs cannot be done using the simple optical model (air/smooth film/substrate). In fact, several parameters such as the Bi island coverage rate, the RMS roughness and the growth temperature must be taken into account in the calculation. We have established a theoretical formulation for the computation of the theoretical reflectivity Rth as a function of time and wavelength [28]. The fitting of the experimental signal Rexp(t) was successfully performed for λ ¼550 nm. In the present work, we have used the same model to adjust Rexp(t) for each incident wavelength shown in Fig. 1. The challenge is greater because of the number of curves to simulate besides the not-well-known λ-dependence of the bismuth complex refractive indices ðn~ Bi ¼ nBi  ikBi Þ. First, we have determined an effective growth rate (0.57 nm/min) of the bismuth film. This value was determined from the simulation of the in situ SR signal for λ ¼550 nm, using measurements of the RMS at different growth time. In this calculation, we have included the roughness effect caused by Bi islands via the roughness factor F(sSR(λ)) which links the Fresnel complex reflection coefficient of a rough surface (Rrough) to the Fresnel coefficient of a mirror-like surface (Rsmooth) as follows [37–39]: Rrough ¼ FðsSR ðλÞÞRsmooth

ð1Þ

4π

λ

sSR ðλÞ sin θ

2 # ð2Þ

θ ¼ (π/2)  φ and φ is the incidence angle. sSR(λ) is a fitting parameter which represents the sensitivity of the incident wavelength to the surface undulations. In addition, we have used empirical laws in order to express the Bi coverage rate and the temperature effect [28]. The optical constants of bismuth are fitted parameters: nBi and kBi are obtained when the measured and calculated reflectivity curves are practically superposed (shown by open circles in Fig. 3a and b). The curves Rth,λi(t) are shown by continuous lines in Fig. 1a and b in the range 400–1000 nm. Obtained optical constants are in good agreement with the real and imaginary parts of bismuth given in the literature and determined using other characterization techniques [40–45]. We have added in Fig. 4a calculated values of the SR data taken at t¼43 min for each wavelength (open circles). The good agreement between the calculated data and the experimental ones (continuous line) are a proof of the complementarity between spectral and temporal reflectivity analysis. After the determination of nBi and kBi in the wavelength range 400–1000 nm, our aim is to find out the dispersion relation of the refractive indices of bismuth in the domain 1000–1700 nm. In Fig. 4b, the continuous line represents the reflectivity spectrum of sample A recorded ex situ using both CCD1 and CCD2 at normal incidence. Note that SR varies with λ: starting from λ ¼ 200 nm, and the reflectivity intensity decreases significantly until it reaches a minimum value at 248 nm. The rise in the reflectivity at high energies is due to the transitions from filled d bands to conduction band. The same phenomenon has been observed in a number of semi-metals and zinc-blende semiconductors [46–48]. According to experimental measurements done on a cleaved Bi sample by Cardona et al. [49], the transition corresponding to the critical point (CP) E4 occurs at 5 eV, equal to that found by our measurements. Another critical point observed at 400 nm corresponds precisely to E3 ¼ 3.1 eV. This transition was computed from the reflectivity data using the Kramers–Kronig (K–K) relation [50,51]. Beyond 400 nm, the reflectance increases momentously to reach a maximum value at approximately 1000 nm. This increase is due to @RT

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Wang et al. [41] Atkinson et al. [42] Hodgson [43] Dix et al. [44]

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Sande et al. [45]

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(nm) Fig. 3. Variation of bismuth optical constants at room temperature as a function of wavelength: (a) refractive index nBi and (b) extinction coefficient kBi. For comparison, we added nBi and kBi reported from the literature [40–45].

M.M. Habchi et al. / Journal of Crystal Growth 395 (2014) 26–30

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Fig. 4. (a) Reflected spectrum recorded in situ at 43 min of growth by MOVPE at 375 1C as a function of the wavelength (continuous line). Open circles show the best fitting of experimental data. (b) and (c) Continuous lines show the evolution of spectral reflectance recorded ex situ at 25 1C of samples A and B respectively. Open circles represent the best fitting of the reflectivity using calculated bismuth refractive indices. Insets show the variation of the sensitivity sSR as a function of wavelength.

the increase of bismuth's refractive indices in this range (see Fig. 3). According to Golin [52], an interband transition E2 occurs normally at about 1.38 eV (898 nm). This value was obtained from theoretical computing of bismuth's band structure. However, Cardona et al. [49] found that the bismuth E2 CP, given by the K–K analysis, takes place at 1.7 eV. The quantitative disagreement between these results is probably due to the inaccuracy of data obtained from the theoretical analysis because it was difficult to deduce the value of this CP directly from experimental measurements. For the rest of the studied spectral range (1000–1700 nm), the reflectivity intensity decreases slightly. This fact is probably due to a decrease of at least one of the bismuth refractive indices values in the NIR domain. A peak (multiplied by 10 in the figure) appears at around 0.9 eV. The location of the critical point responsible for this optical peak in bismuth has not yet been determined. The peak 0.9 eV has not been observed when we have measured R of bare GaAs substrates in the infrared domain. Since we have normalized the reflectivity response of the Bi/GaAs structure grown by MOVPE by that of the GaAs substrate, all changes of the recorded signals can be attributed to bismuth and this peak may be associated with bismuth. Using the Bi film thickness and refractive indices determined via simulation of in situ SR, we attempt in a first step to adjust the reflectivity spectrum of sample A measured ex situ at room temperature. Best simulations (Rfit) are shown by open circles in Fig. 4b in the range 400–1000 nm. The inset of Fig. 4b shows the variation of the sensitivity to roughness sSR(λ), as well as the

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roughness RMS measured by AFM for sample A. As a second step, we have used the same theoretical model, already used in the 400–1000 nm range, to simulate the reflectivity response in the wavelength range 1000–1700 nm. Good agreement between Rexp and Rfit was obtained for the values of nBi and kBi shown in Fig. 3a and b (see full spheres). The real refractive index of Bi increases in both domains (visible and near infrared) contrary to the bismuth extinction coefficient which presents a significant spectral change. kBi (λ) decreases in the NIR region after reaching a maximum value of 5.62 at around λ ¼1000 nm. This fact is consistent with the SR signal profile described in the first part of this work. To our knowledge, the only study on bismuth optical constants in the infrared domain was reported by Hodgson [43]. In spite of dispersion of our data compared to the literature, we remark that they present a similar trend. The discrepancy is mainly due to the dissimilarity in experimental conditions. Atkinson et al. [42] claim that it is difficult to ensure accuracy of the refractive index deduced from simulations performed on one film thickness. For that reason, we decided to perform measurements on a film of very different thickness. Ex situ SR measurement of sample B is shown by continuous line in Fig. 4c. It is important to note that Rexp of sample B presents the same bismuth CPs that have been observed on sample A. Furthermore, the measured spectrum shows the same peak at 0.9 eV attributed to bismuth, which confirms our measurements. By adopting smoothed curves between the data points of the Bi refractive indices (continuous line in Fig. 3a and b), we have simulated SR in the whole range 400–1700 nm. A good agreement was obtained between Rexp and Rfit of sample B (shown by open circles in Fig. 4c). This time, the fitting parameter was the bismuth film thickness (dBi). dBi of sample B was found to be equal to 1.2 μm. The growth rate of Bi in the UHVE reactor was determined as Vg E 1 nm/s by using a quartz crystal microbalance (QCM). This tool was calibrated basing on ex situ thickness measurements by scanning electronic microscopy. The uncertainty on growth rate is of about 0.1 nm/s. Since the duration of the epitaxy is equal to 20 min, the obtained fitting value (dBi ¼1.2 μm) agrees well with our predictions. The sensitivity sSR of incident wavelength to the surface roughness of sample B is also plotted as a function of wavelength in the inset of Fig. 4c. We clearly see that the two curves of sSR(λ) shown in the insets of Fig. 4b and c decrease considerably with the incident wavelength. This behavior is in good agreement with respect to the experimental results for sample A [28]. Indeed, the sensitivity of the SR signal to the roughness becomes more pronounced when the incident wavelength decreases and becomes almost the same size as the undulation describing the surface morphology (see AFM images in Fig. 2). After the corroboration of the Bi refractive indices, it will be possible to calculate the reflectivity as a function of growth time for any selected wavelength from 400 to 1700 nm. As examples, the theoretical reflectivity responses Rλi(t) (dashed lines) were added in Fig. 1b for λi ¼ 1100, 1300, 1500 and 1700 nm. For λ Z1100 nm, Fig. 1c shows that the reflectivity maximum values Rmax (shown by open circles) of the calculated signals present the same slope α2 as the experimental values of Rmax (shown by full spheres). Since the exposure time was stopped at 43 min, we can clearly see from Fig. 1a that t100% is only revealed for λ r700 nm. Because of the physical significance of t100%, we have reproduced theoretically the reflectivity signals for a larger exposure time in order to determine t100% for the rest of the treated wavelengths. The deduced crossing times shown by open circles in Fig. 1d are consistent with those determined experimentally. Indeed, t100% of calculated SR signals presents the same slope β1 as the experimental data up to about 1050 nm. Then, its evolution changes slope (β2 ¼  0.064 min/nm). This behavior observed for

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M.M. Habchi et al. / Journal of Crystal Growth 395 (2014) 26–30

Fig. 5. (a) Plane view AFM scans of sample B showing the surface morphology of bismuth film grown on GaAs substrate by UHVE. (b) AFM section analysis of one selected Bi island showing three reflections (003), (102) and (202) of the hexagonal phase.

both Rmax(λ) and t100%(λ) plots can be related to the change of the behavior of bismuth's refractive extinction coefficient around 1000 nm. In order to explore the morphological properties of the surface of sample B, we show in Fig. 5a an AFM image in tapping mode. The bismuth film grown by UHVE shows a rough surface (RMS roughnessE85 nm). The latter value is larger than double the RMS roughness measured for sample A. Qualitatively, the surface shows islands having hexagonal shape and different sizes. The cross-section profile of one typical island (shown by the solid line at the bottom of the 2D AFM image) is illustrated in Fig. 5b. Its size and height are equal to about 300 nm and 106 nm respectively. In addition, the hillock presents a pyramidal profile and three orientations (003), (102) and (202) of the hexagonal phase, which is consistent with results obtained by high resolution X-ray diffraction measurements (not shown here). Based on these findings, it appears that the spectral reflectance mainly results from (003) reflection planes. Scattered reflectivity of films is originated from (102) and (202) reflection planes justifying the use of the surface roughness as a fitting parameter in reflectivity response. 4. Conclusions In summary, two bismuth films were grown onto GaAs substrates by MOVPE and UHVE. In order to investigate the samples' optical properties, in situ and ex situ spectral reflectance measurements were performed. The surface morphology of the samples was studied using AFM. Theoretical simulations of SR signals as a function of time and wavelength were achieved through the decoupling of several parameters such as bismuth film's thickness, roughness and temperature. The Bi refractive indices were determined in the VIS–NIR domain ranging from 400 to 1700 nm. The bismuth critical points have been determined directly from spectral variation of the reflectivity. We have identified a peak around 0.9 eV which can be attributed to bismuth. Acknowledgment We thank Dr. Nawfel Sakly for its assistance and availability to do AFM measurements. We gratefully acknowledge financial support from the DGRST-Tunisia and the Third World Academy of Sciences (TWAS). References [1] I.P. Batra, J. Vac. Sci. Technol. B 3 (1985) 750. [2] Z. Zhang, Surf. Sci. 2 (2004) 1. [3] G. Oskam, J.G. Long, A. Natarajan, P.C. Searson, J. Phys. D 31 (1998) 1927.

[4] J. Yang, L. Levina, E.H. Sargent, S.O. Kelley, J. Mater. Chem. 16 (2006) 4025. [5] K.L. Moazed, Metall. Mater. Trans.A 23 (1992) 1999. [6] S.S. Cohen, G.S. Gildenblat, Metal–Semiconductor Contacts and Devices, 13, Academic Press, New York, 1986. [7] T. Lee, J. Liu, N.-P. Chen, R.P. Andres, D.B. Janes, R. Reifenberger, J. Nanopart. Res. 2 (2000) 345. [8] B.M. Trafas, Y.N. Yang, R.L. Siefert, J.H. Weaver, Phys. Rev. B 43 (1991) 14107. [9] D.A. Evans, M. Alonso, R. Cimino, K. Horn, Phys. Rev. Lett. 70 (1993) 3483. [10] R.R. Wixom, L.W. Rieth, G.B. Stringfellow, J. Cryst. Growth 265 (2004) 367. [11] C. McGinley, A.A. Cafolla, E. McLoughlin, B. Murphy, D. Teehan, P. Moriarty, D.A. Woolf, Appl. Surf. Sci. 158 (2000) 292. [12] P.M. Vereecken, P.C. Searson, Appl. Phys. Lett. 75 (1999) 3135. [13] A.B. McLean, R. Ludeke, M. Prietsch, D. Heskett, D. Tang, T. Maeda-Wong, Phys. Rev. B 43 (1991) 7243. [14] A. Duzik, J.C. Thomas, J.M. Millunchick, J. Lang, M.P.J. Punkkinen, P. Laukkanen, Surf. Sci. 606 (2012) 1203. [15] M. Milanova, P. Terziyska, Thin Solid Films 500 (2006) 15. [16] U. Resch, N. Esser, W. Richter, Surf. Sci. 251/252 (1991) 621. [17] N. Esser, M. Hunermann, U. Resch, D. Spaltmann, J. Geurts, Appl. Surf. Sci. 41/ 42 (1989) 169. [18] W.Y. Jiang, J.Q. Liu, M.G. So, K. Myrtle, K.L. Kavanagh, S.P. Watkins, J. Cryst. Growth 277 (2005) 85. [19] H. Fitouri, I. Moussa, A. Rebey, B. El Jani, J. Cryst. Growth 300 (2007) 347. [20] A. Rebey, M.M. Habchi, Z. Benzarti, B. El Jani, Microelectron. J. 35 (2004) 179. [21] A. Rebey, M.M. Habchi, A. Bchetnia, B. El Jani, J. Cryst. Growth 261 (2004) 450. [22] I. Kamiya, H. Tanaka, D.E. Aspnes, L.T. Florez, E. Colas, J.P. Harbison, R. Bhat, Appl. Phys. Lett. 60 (1992) 1238. [23] U. Seidel, T. Hannappel, J. Cryst. Growth 310 (2008) 2334. [24] A.M. Ramil, K. Schmidegg, A. Bonanni, H. Sitter, D. Stifter, L. Shunfeng, D.J. As, K. Lischka, Thin Solid Films 455/456 (2004) 684. [25] C. Simbrunner, T. Li, A. Bonanni, H. Sitter, A. Kharchenko, J. Bethke, K. Lischka, J. Cryst. Growth 308 (2007) 258. [26] I. Massoudi, M.M. Habchi, A. Rebey, B. El Jani, Physica E 44 (2012) 1282. [27] C.J. Vineis, C.A. Wang, K.F. Jensen, W.G. Breiland, J. Cryst. Growth 195 (1998) 181. [28] I. Massoudi, M.M. Habchi, A. Rebey, B. El Jani, J. Cryst. Growth 353 (2012) 77. [29] I. Massoudi, M.M. Habchi, A. Rebey, B. El Jani, J. Electron. Mater. 41 (2012) 498. [30] W.G. Breiland, K.P. Killeen, J. Appl. Phys. 78 (1995) 6726. [31] M.M. Habchi, A. Rebey, B. El Jani, Microelectron. J. 39 (2008) 1587. [32] M.M. Habchi, A. Rebey, A. Fouzri, B. El Jani, Appl. Surf. Sci. 253 (2006) 275. [33] T. Guo, R.E. Atkinson, W.K. Ford, Phys. Rev. B 41 (1990) 5138. [34] E. Puckrin, A.J. Slavin, Phys. Rev. B 41 (1990) 4970. [35] W.K. Ford, T. Guo, K.-J. Wan, Phys. Rev. B 45 (1992) 11896. [36] C. Li, Z.Q. Zeng, D.S. Fan, Y. Hirono, J. Wu, T.A. Morgan, X. Hu, S.Q. Yu, Zh. M. Wang, G.J. Salamo, Appl. Phys. Lett. 99 (2011) 243113. [37] H.E. Bennett, J.O. Porteus, J. Opt. Soc. Am. 512 (1961) 123. [38] D. Franta, I. Ohlıdal, Opt. Commun. 248 (2005) 459. [39] S.O. Rice, Commun. Pure Appl. Math. 4 (1951) 351. [40] A.P. Lenham, D.M. Treherne, R.J. Metcalfe, J. Opt. Soc. Am. 55 (1965) 1072. [41] P.Y. Wang, A.L. Jain, Phys. Rev. B 2 (1970) 2978. [42] R. Atkinson, P.H. Lissberger, Thin Solid Films 17 (1973) 207. [43] J.N. Hodgson, Proc. Phys. Soc. B 67 (1954) 269. [44] F.E. Dix, L.H. Rowse, J. Opt. Soc. Am. 14 (1927) 304. [45] J.C.G. de Sande, T. Missana, C.N. Afonso, J. Appl. Phys. 80 (1996) 7023. [46] H. Ehrenreich, H.R. Philipp, Proceedings of the International Conference on the Physics of Semiconductors, Exeter, England, 1962, p. 367. [47] M. Cardona, D.L. Greenaway, Phys. Rev. 131 (1963) 98. [48] P.J. Lin, J.C. Phillips, Phys. Rev. 147 (1966) 469. [49] M. Cardona, D.L. Greenaway, Phys. Rev. 133 (1964) A1685. [50] F. Abeles, Optical Properties of Solids, North-Holland, Amsterdam, 1976. [51] H. Yao, P.G. Snyder, J.A. Woollam, J. Appl. Phys. 70 (1991) 3261. [52] S. Golin, Phys. Rev. 166 (1968) 643.